holtz& kovacs - an introduction to geotechnical engineering.docx

7/23/2019 Holtz& Kovacs - An Introduction to Geotechnical Engineering.docx

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An·lntr oduction to

6eotechnical

Engineering

ROBERT 0. HOLTZ, PH.0., P.E.University of Washington

WILLIAM 0. KOVACS, PH.0., P.E.University of Rhode Island

PR ENTICE H A LL, Englewood Cliffs, New Jersey !"#$

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l. Jl,rory of Congras Ca1aloging in Puhlication Data

Ho%&, RoanT ', An introd%(tion to geote(hni(al engine)ring*

ln(l%des inde+*l* oil -ro-(rties* $* oil .((hani(s* l. /ova(s,

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C:antent§

PRE$ACE xi

I%TRC&CTIO% TO (EOTECH%ICAL E%(I%EERI%( 1

. eote(hni(al Engineering 11*$ Toe UniF%e Nat%re of oil and Ro(< Gaterials *

.! %ggested A--roa(h to the t%dy of eote(hni(alEngineering 4

1*2 (o-e of this 4oo< 5 .) oil or.ation and the Nat%re of oil Constit%ents 6 1*" Histori(al 'evelo-.ent of eote(hni(al Engineering !1*! Notes on y.:ols and Units +

* I%&E+ A%O CLASSI$ICATIO% PROPERTIES O$ SOILS 10

2.1 Introd%(tion 10

$*$ 4asi( 'efinitions and Phase Relations 11

2.3 ol%tion of Phase Pro:le.s 16

2.4 oil Te+t%re 25

*$* rain i&e and rain i&e 'istri:%tion 26

2.6 Parti(le ha-e 322.7 Atter:erg Li.its and Consisten(y Indi(es 34

2.8 A(tivity 41

Pro:le.s 41

# SOIL CLASSI$ICATIO% -

#*1 Introd%(tion -

#*$ Toe Unif ied oil Classifi(ation yste. UCB +

y

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12 C3n45n46

#*# Toe AAHT8 oil Classifi(ation yste.

#*2 Co.-arison of the UC and AAHT8Classif i(ation yste.s -Pro:le.s 72

2 CLA7 MI%ERALS A%O SOIL STRCTRE --

2*1 Introd%(tion !!2*$ Clay Ginerals -0

2*# Identifi(ation of Clay Ginerals 00

2*2 -e(ifi( %rfa(e 0+2 Iote(a(tion 4etweeo Wa ter a nd Clay Gioerals

+2*" Intera(tion of Clay Parti(les +2 =32*! oil tr%(t%re and a:ri( +

2*7 Cohesive oil a:ri(s +,

2*6 Cohes1onless oil a:n(s 1

Pro:le.s 1-

) COMPACTIO% 109

*1 Introd%(tion 1+

*# Theory of Co.-a(tion * 111

*2 Pro-erties and tr%(t%re of Co.-a(tedCohesive oils 11-

).) held Co.-a(tion EF.-.ent and Pro(ed%res 113*" ield Co.-a(tion Cotro3iand -e(ifi(at 11

*! Esti.ating Perfor.an(e of Co.-a(ted oils 12*

Pro:le.s 11

WATER I% SOILS, :

CAPILLARIT7, SHRI%KA(E, SWELLI%(,$ROST ACTIO% 166

"*1 Introd%(tion 1

"*$ Ca-ifla1ity 1-

"*# hrin<age Pheno.ena in oils 1-0

"*2 Eng.eenng 1gr%h(an(e of hrin<age andwelling 10

"* rost A(tion 1+

Pro:le.s 1+2



Contenta vll

WATER I% SOILS, :PERMEABILIT7, SEEPA(E, E$$ECTIVE STRESS 199

!*1 Introd%(tion 1++

!*$ 'yna.i(s of l%id low

.! 'ar(y3s Law for low Thro%gh Poro%s Gedia 203

!*2 Geas%re.ent of Per.ea:ility 1

!* Intergran%lar or Effe(tive tress 1*

!*" R elationshi- :etween Hori&ontal and Merti(altresses 2

!*! Heads and 8ne5'i.ensional low -

!*7 ee-age or(es, %i(<sand, and LiF%efa(tion *

!*6 ee-age and low Nets9 Two5'i.ensional low

!*1 Toe Gethod of rag.ents 20

!*11 Control of ee-age and ilters -

Pro:le.s -*

8 CO%SOLI&ATI O% A%O CO%SOLI&ATIO% SETTLEME%TS 0*

7*1 Introd%(tion 0*

7*$ Co.-onents of ettle.ent 0 7*# Co.-ressi:ility of oils 02

7 2 J:e Oedoroeter aod Coosolida tioo Testing 289

7* Pre(onsolidation Press%re@ Nor.al,

8*ereonsolidation, Under(onsolidation+

7*" Consolidation 4ehavior of Nat%ral oils ++7*! ! ettle.ent Cal(%lahons *+

7*7 a(tors Affe(ting the 'eter.ination of a4 *

7*6 Predi(tion of ield Consolidation C%rves *0

7*1 oil Profiles **2

7*11 A--ro+i.ate Gethods and Ty-i(al Mal%es of Co.-ression Indi(es 11

7*1$ tress 'istri:%tion *

9 IIME6*1

RA IE O$ CO%SOLI&AT IO% 376 Introd%(tion *-

6*$ Toe Consolidation Pro(ess 377

6 # Tenag:i3s 8ne 'i.easieaal Censolidation Theery 38()

6*2 'eter.ination of the Coeffi(ient of Consolidation cv

6* 'eter.ination of the Coeffi(ient of Per.ea:ility 6*" Ty-;(al V al%es of e v 2

,* 0



<

III Conlawla

6*! Eval%ation of e(ondary ettle.ent 52

ettle.ent Pro:le. 1

Pro:le.s 423

0 THE MOHR CIRCLE, $AILRE THEORIES, A%O STRESS PATHS 431

1*$ tress at a Point 432

1*21* Tests for t:e hear trength of oils

-

Pro:le.s 02

SHEAR STRE%(TH O$ SA%OS A%O CLA7S 490

11*1 Introd%(tion +

e o e-ose o an s11*# 4ehavior of at%rated ands '%ring 'rained hear +*

11*2 Effe(t of Moid Ratio and Confining Press%re on Mol%.e Change +

11* 4ehavior of at%rated and '%rin Undrained hear 2

11*" a(tors that Affe(t the hear trength of S6n=> 21

11*7

11*6

1 L6* I1 1*6*$

LiF%efa(tion and Cy(li( Go:ility 4ehavior ofat%rated ands 21

tress5'efor.ation and trength Chara(teristi(s ofat%rated 5Cosive oUs 2*

Consolidated5'rained C'B Test 4ehavior 2*0

Ty-i(al Mal%es of 'rained trength Para.eters 2*

1 1*6*# f ' tren th in En ineerin Pra(ti(e 22

1 1*6*21 1*6*

1 1*6*"1 1*6*!11*6*7

1 1*6*61 1*6*11 1*6*111 1*6*1$

Consolidated5Undrained CUB Test 4ehavior 22

Ty-i(al Mal%es of the U nd rained trength Para.eters

22* Use ofCU trength in Engine(rin Pra(ti(e 22

Un(onsolidated5U ndrained UUB TH 4ehavior 22+

Ty-i(al Mal%es of UU trengths 2

Un(onfined Co.-ression Test 566

8ther Ways to 'eter.ine the Undrained hear trength 2-

ensitivity 202

Use of Und rained UU hear tren th inEngine(ring Pra(ti(e 20

1 1*6*1# -e(ial Pro:le.s of the hear trength of Cohesive oils 2+2



Contenta l+

.0 Pore Press%re Para.eters 599. The Coeffi(ient of Earth Press%re at Rest for Clays 605

11*1$ tress Paths '%ring Undrained Loading5 Nor.allyConsolidated Clays 1

.! tress Paths '%ring Undrained Loading8ver(onsolidated Clays 630

." A--li(ations of tress Paths to Engineering Pra(ti(e 634Pro:le.s 640

APPE%&I+ A APPLICATIO% O$ THE ?SI? S7STEMO$ %ITS TO (EOTECH%ICALE%(I%EERI%( 665

A. Introd%(tion 665

A.* The I Getri( yste. 666

A.! 4asi( and 'erived I Getri( Units 667

A 2 I Units of lnterest te Ceeteehn;eal Engineer s and TheirConversion a(tors +

APPE%&I+ B- &ERIVATIO% O$ LAPLACE'S E@ATIO% 681

APPE%&I+ B-* &ERIVATIO% A%O SOLTIO% O$TERZA(HI 'S O%E-

&IME%SIO%AL CO%SOLI&ATIO%THEOR7 683

45$*1 Ass%.-tions 0*

45$*$ 'erivation 0*

45$*# Gathe.ati(al ol%tion 686

APPE%&I+ B-! PORE PRESSRE PARAMETERS 691

45#*1 'erivation of <e.-ton3s Pore Press%re EF%ation +1

45#*$ 'efinition of o1 and o# for Rotation ofPrin(i-al tresses +*

4 #*# er.%las for Por e Pr ess.e fara.eters for 'if f erent

tress Path Tests +45#*2 Proof that $ac $ 1e and $

., $te +

45#* 'erivation of the Hen<el Pore Press%re EF%ationand Coeffi(ients 696

RE$ERE%CES 701

I%&E+ -1+

*J



Preface

$n 6ntroduction to 7eotechnical Engineering is intended for %se in thefirst of a two5(o%rse seg%en(e in geote(hni(al engineering %s%ally ta%ght tothird5 and fo%rth5year %ndergrad%ate Civil Engineering st%dents* We ass%.e the st%deots :ave a wor<iog <oawledge of nndergrad%ate .e(hani(s,es-e(ially stati(s and .e(hani(s of .aterials in(l%ding fl%idsB* A <nowl edgeof :asi( geology, altho%gh hel-f %l, is not essential* We introd%(e the33lang%age= of geote(hni(al engineering in the first (o%rse, that is, the(lassif;(ation and engineering -ro-erties of soils* 8n(e the st%dent has awor<ing <nowledge of how soil :e:aves as an engineering .aterial, heQshe(an :egin to -redi(t soil :e:avior and, in the se(ond (o%rse, to (arry o%tthe design of si.-le fo%ndations and earthwor< syste.s*

We feel that there is a need for .ore detailed and .odero (overageof the engineering -ro-erties of soils than is fo%nd in roost %ndergrad%a tete+ts* This a--lies to :oth the st%dents =.a0oring= in geote(hni(al engineering and the general eiv il engineering %ndergrad%ate st%dent* M1Q3efind that o%r st%dents are involved in in(reasingly .ore (o.-le+ -ro0e(ts,es-e(ially in trans-ortation, str%(t%ral, and (onstr%(tion engineering* Environ.ental, e(ono.i(, and -oliti(al (onstraints de.and innovative sol%tioos to (ivil engineering -ro:le.s* Toe availa:ility of .odero analyti(alte(hniF%es and the digital (o.-%ter has had an al.ost revol%tionary effe(t

on engineering design -ra(ti(e* This develo-.ent de.ands a :etter <nowledge of site (onditions as well as :etter defined geote(hni(al engineeringdesign -ara.eters*

We have tried to .a<e the te+t easily reada:le :y the average%ndergrad%ate* To this end, $n 6ntroduction to 7eotechnical Engineering iswntten *at a si.-le rather than so-fOstt(ated level, altho%gh the .aterial(overed .ay :e rather so-:isti(ated at ti.es* Involved derivations, %nread

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the design and (onstr%(tion of fo%ndations and e.:an<.ents* Gost of the

g esigna--li(ations are %s%ally lef t to the se(ond (o%rs in o%ndation Enginer5ing* onseF%en y, . or er to .terest t e st% ent, we have tried toindi(ate wherever -ossi:le the en ineerin si nifi(an(e and s (ifi(a--li(ations of the soil -ro-erty :eing dis(%ssed* We have tried to e.5

and, to sorne e+tent, how it is a(t%ally %sed in -ra(ti(e* The only =design=5 %rse wee s is es%.at.g

the settle.ent of shailow fo%ndations on sat%rated (lays*1 The te+t iss% 1(1ent y e+1 e t at innovative instr%(tors (an add additional designe+a.-les sho%ld the so desire* I4 see.s that %nits ar wwith geote(hni(al engineers* In line with the trend towards the %se of *I*

(an o(iety for Testing and Gaterials, we have %sed this syste. in the te+t*y in e is(%ssion o * * . --en 1+ e -f%l* In

vol%.e in -ress%re (o.-%tations*

%se the latest definition of density .assQ%nit

nessential -art of the neo-hyte engineer3s e -erien(e with soils as a %niF%e

a er;a * ow e se 1s e yo%ng eng.eer to egin to develo- a=feel= for soils and soil :ehavior, so essential for the s%((essf %l ra(ti(e of geote(hni(al engineering Th%s, an e.-hasis on la:oratory and fieldtestin is fo%o%r f irst (o%rse has di(tated the organi&ation and develo-.ent of the

e assi i(a ion o soils, and si.-le (lassifi(ation tests* Th%s, the early (ha-ters introd%(e the

1s(1- .e o eote( r%(a ng.eenng, ase Relationshi-s and Inde+Pro-erties, oil Classifi(ation, and Cla Ginerals and oil

.aterial -rovides the :a(<gro%nd and ter.inology for the later 5,(ha-ters*

" and ! de.s(ri:e how. wa.ter infl.%en(es a nd af fe(ts soil :ehavior* To-i(s

as -er.ea:ility, see-age, and effe(tive stress* These two (ha-ters againserve as :a(<gro%nd for the ne+t fo%r (ha-ters whi(h deal with (onsolidation and shear strength*

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SIII

Toe treat.ent of these latter to-i(s is F%ite .ode. and %-5to5date*Toe (h.ert.ann -ro(ed%re for deter.ining field (o.-ressi:ility is in (l%dedas is a .odern treat.ent of se(onda (o. ression develo ed : Prof* Gesri and his (o5wor<ers* Prof* La.:e3s stress -ath .ethod isintrod%(ed in Cha-ter 1 and %sed to advantage in Cha-ter 11, es-e(iallywhen -ra(ti(a engineering a--li(ations of shear strength theory are dis5

%ndrained strength of sands is -resented in Cha-ter 1 1* Also in this( a-ter we 1s(%ss t e stress5defor.ation and strength (hara(teristi(s of (ohesive soils* Altho% the treat.ent is .odern :e(a%se this is ri.aril an %ndergrad%ate te+t:oo<, (onsiderations of strengtl anisotro-y, (riti(aV

-ara.eters have :een lef t to .ore advan(ed te+ts*

geote(hni(al engineering, advan(ed st%dents in other dis(i-lines and en5g.eers es.ng a re res er . eng.eenng -ro-erties .ay find the :oo< hel-f%l* 4e(a%se of the .an f%ll 5wor<ed e+a. le ro:le.s the :oo< is al.ost =self5tea(hing*= This as-e(t of the te+t also frees the instr%(tor in a

le(t%res* l4 allows the instr%(tor to (on(entrate on e+-laining :asi( -rin(i5. .

F%estion* The third gro%- we ho-e will find this :oo< %sef%l are -ra(ti(inggeote( .ea eng.eers* y-1(a va %es are g1ven or a ( ass1f1(ation atd

engineering -ro-erties for a wide variety of soils@ we have fo%nd s%(h a(o.-endi%. very %sef %l in o%r own engineering -ra(ti(e*

:le tas<* We have tried whenever -ossi:le to indi(ate :y ref eren(es or F%otations, (on(e-ts and ideas originating in the literat%re or with o%r for.er tea(hers, es-e(ially Profs* A* Casagrande and H* 4* eed* Wea-o ogi&e or any o.1ss1ns* e .%st a so .ention t e st% ents . o%r :eginning geote(hni(al engineering (o%rse at P%rd%e who have gra(io%slys%ffered thro%gh severa versions of $n lntroduction to 7eotechnical En5ineerin 2 n

have :een very val%a:le* Toe a%thors have greatly :enefited fro. dis(%s sionswith Prof* M: E* Harr of P%rd%e University regarding the se(tion on the

.ethod of frag.ents in Cha-ter !* We ho-e to :ring f%rther attention tothe -rofession of this -owerf%l design .ethod* 'r* E3* i.i% of the U** National 4%rea% of tandards (riti(ally read a re(ent version of the.an%s(ri-t and -rovided .any hel-f %l (o..ents* l4 sho%ld :e noted that

$n lntroduction to 7eotechnical Engineering was written while Willia. '*/ova(s was on the fa(%lty of P%rd%e University* Toe te+t has no (onne(tion with /ova(s3 -resent affiliation with the National 4%rea% of tan5

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55

xlvPretace

dards.* 8%.r f .aithf%l se(retaries Grs* Jani(e Wait 4ollinger, Giss Cathy

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. .., . 5(orre(ting the several draf ts* DToe first a%thor also wishes to gratef %lly

a(<nowledge the .terest ano en(o%rage.e. 1 nis wiie ,5 D D - 55

Her wor< with the oroofreading and (orre(tions is es-e(ially a--re(iated*We of (o%rse will a--re(iate any (o.rnents and (riti(is. of readers*

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ane

lntraductianta6eatechnicalEngineering

1.1 GEOTECHNICA ENGINEE!ING

7eotechnica/ engineering, as the na.e i.-lies, (on(erns the a--li(ation of (ivil engineering te(hnology to sorne as-e(t of the earth* Us%ally, thegeote(hni(al engineer is (on(e.ed only with the nat%ral .aterials fo%nd ator near the s%rfa(e of the earth* Civil engineers (all these earthen .aterials soil and roc! . oi/, in an engineering sense, is the relatively looseagglo.erate of .ineral and organi( .aterials and sedi.ents fo%nd a:ovethe :edro<* oils an :e relatively easily :ro<en down into their 8R

stit%ent .ineral or organi( -arti(les* )oc!s, on the other hand, have verystrong inte.al (ohesive and .ole(%lar for(es whi(h hold the (onstit%ent.ineral grains together* This is tr%e whether the ro(< is .assive :edro(< ora -ie(e of gravel fo%nd in a (lay soil* The dividing line :etween soil andro(< is ar:itrary, and .any nat%ral .aterials en(o%ntered in engineering *

-ra(ti(e (annot :e easily (lassified* They .ay :e either a **very sof t ro(<=or a **very hard soil*= 8ther s(ientifi( dis(i-lines have different .eaningsfor the ter.s soil and ro(<* In geology, for e+a.-le, roc!. .eans all the.aterials fo%nd in the earth3s (r%st, inde-endently of how .%(h the

.ineral -arti(les are :o%nd together* oils to a geologist are 0%st de(o.5 -osed and disintegrated ro(<s generally fo%nd in the very thin %--er -artof the (r%st and (a-a:le of s%--orting -lant life* i.ilarly, -edology soils(ien(eB and agrono.y are (on(e.ed with only the very %--er.ost layersof soil, that is, those .aterials relating to agri(%lt%re and forestry* eote(hni(al engineers (an lea. .%(h fro. :oth geology and -edology* 4oths(ien(es, es-e(ially engineering geology, are i.-ortant ad0%n(ts to geote(hni(al engineering and there is (onsidera:le overla- :etween these fields*4%t differen(es in ter.inology, a--roa(h, and o:0e(tives .ay (a%se sorne(onf %sion, es-e(ially for the :eginner*

.j



2 lntroductlan to r "eotec#olcal Englneel$lng

eote(hni(al engineering has severaV different as-e(ts or e.-hases*oil 8echanics is the :ran(h of geote(hni(al engineering (on(e.ed withthe engineering .e(hani(s and -ro-erties of soil, whereas roc! 8echanics is(on(erned with the engineering .e(hani(s and -ro-erries of ro(<, %s%ally

:%t not ne(essarily the :edro(<* oil .e(hani(s a--lies the :asi( -rin(i-iesaf roe(:a ni(s in(l%ding <ine.ati(s, dyna.i(s, fl%id .eehar%es, and the.e(hani(s of .aterials to soils* In other words, soil rather than water or steel 1 (on(1ete, fo1 e+a.-le, now :e(o.es the eng.eenng .atenalwhose -ro-erties and :ehavior we .%st %nderstand in order to :%ild withit or %-on it* A si.ilar (o..ent (o%ld also :e .ade for ro(< .e(hani(s* I4sho%ld :e noted, however, that there are signifi(ant differen(es :etweenthe :ehavior of soil .asses and ro(< .asses, and in -rin(i-ie there is not.%(h overla- :etwe(. the 4D3 disei-lines*

9oundation engineering a--lies geology, soil .e(hani(s, ro(< .e(ha5tries, and str%(t%ral engineering to the des1gn and (onstr%(hon of fo%nda tionsfor (ivil engineering and other str%(t%res* The fo%ndation engineer .%st :ea:le to -redi(t the -erfor.an(e or res-onse of the fo%ndation soil or ro(< tothe loads i.-osed :y the str%(t%re* orne e+arn-les of the <inds of -ro:le.s fa(ed :y the fo%ndation engineer in(l%de fo%ndations for ind%strial,(o.rner(ial, and residential :%ildings, and other ty-es of s%- -ort str%(t%resfor radar towers, as well as fo%ndations for o;l and other <inds 3 tan<sand off shore str%(t%res* Even sfO-s .%st have a dry do(< d%ring (onstr%(tion or re-airs, and the dry do(< .%st have a

fo%ndation* The s%--ort of ro(<ets and a--%rtenant str%(t%res d%ring(onstr%(tion andla %n(h have led to very ioterestiog a od (hallenging fo%ndation t.gineering

-ro:le.s* Related geote(hni(al engineering -ro:le.s fa(ing the fo%ndation engineer are the sta:ility of nat%ral and e+(avated slo-es, the sta:ilityof -er.anent and te.-orary earth5retaining str%(t%res, -ro:le.s of (on5str%(tion, (ontroll.g water .ove.ent and -ress%res, and even the .aintenan(e and reha:ilitation of old :%ildings* Not only .%st thefo%ndation safely s%--ort the stati( str%(t%ral and (onstr%(tion loads, :%tit .%st alsoadeF%a tely resist dyoa.i( loads d%e to :lasting, earthF%a<es, ete*

I yo% thin< a:o%t it, 24 is i.-ossi:le to design or5 (onstr%(t any (ivil

engineering str%et%ie wi tho% t %lti.a tely (onsidering the fo%ndahon s1lsand ro(<s to sorne e+tent, and this is tr%e whether the str%(t%re is :%ilt onthe earth or 1s e+traterrestrial* The -erfor.an(e, e(ono.y, and safety of an y (ivil engineering str%(t%re %lti.ately is affe(ted ar .ay eveo

:e (ontrolled :y its fo%ndation*Earth .aterials are of ten %sed as a eonstrnetion .a telial :e(a%se

they are the (hea-est -ossi:le :%ilding .aterial* However, its engineering -1-e1ties s%(h as strength and (o.-ress1fOhty are often nat%rally -oor,and .eas%res .%st :e ta<en to densif y, strengthen, or otherwisesta:ili&e and reinfor(e soils so that they will -erfor. satisfa(torily inservi(e*



.* T5 nlFG5 %64G5 3 S3ll 6nl R3 M6l5l6l> #

Highway and iailway e.:an<.ents, aitfields, ea1th a.i ro(< da.s, levees,and aF%ed%(ts are e+a.-les of earth str%(t%res, and the geote(hni(al

eng.eer 1s res-ons1:le for their des1gn and (onstr%(tion* 'a. safety andreha:ilitation of old da.s are i.-ortant as-e(ts of this -hase of geote(hni

(al engineering* Also related, es-e(ially for highway and airfield engineers,is the design of the final s%rfa(e layer on the earth str%(t%re, the -ave.ent*

Here the overla- :etween the trans-ortation and geote(hni(al dis(i-lines is

)oc! engineering , analogo%s to fo%ndation engineering for soils, is(on(e.ed with ro(< as a fo%ndation and (onstr%(tion .aterial* 4e(a%se.ost of the earth3s s%rfa(e is (overed with soil or water B, ro(< engineering%s%ally o((%rs %ndergro%nd t%nnels, %ndergro%nd -ower ho%ses, -etro

le%. storage roo.s, .ines, et( B 4%t so.eti.es ro(< engineeriog a((nrsat

the s%rfa(e, s%(h as in the (ase of :%ilding and da. fo%ndations (arried to :edro(<, dee- e+(avations to :edro(<, sta:ility of ro(< slo-es, et(*

In -resenting sorne of the ty-i(al -ro:le.s fa(ing the geote(hni(alengineer, we wanted yo% to see, first, how :road the field is and, se(ond,Dhow i.-ortant it is to the design and (onstr%(tion of (ivil engineeringstr%(t%res* In a very real sense, geote(hni(al engineering (o.:ines the :asi( -hysi(al s(ien(es, geology aod -edology, with hydra%li(, str%(t%ral,trans-ortation, (onstr%(tion, and .ining engineering*

* HE I%I@I IE %AIIIRE OE SOII A%O ROCK MATERIALS

eote(hni(al engineering is highly e.-iri(al and is -erha-s .%(h.ore of an =art= than the other dis(i-lines within (ivil engineering :e(a%seof the :asi( nat%re of soil and ro(< .aterials* They are of ten highlyvaria:le, even within a distan(e of a few .illi.etres* Another way of saying this is that soils are heterogeneous rather than ho8ogeneous .aterials*That is, their .aterial or engineering -ro-erties .ay vary widely fro. -oint to -oint within a soil rnass* %rther.ore, soils in general arenon/inear .aterials@ their stress5strain (%rves are not straight lines* To

f%rther (o.-h(ate th.gs as well as to .a<e the. .terest.gB s1Is arenonconservative .aterials@ that is, they have a fantasti( .e.ory5 theyre.e.:er al.ost everything that ever ha--ened to the., and this fa(tstrongly affe(ts their engineering :ehavior* Instead of :eing isotropic, soilsare ty-i(ally anisotropic, whi(h .eans that their .aterial or engineering -ro-erties are not the sa.e in all direetions* Gost of the theories we havefor the .e(hani(al :ehavior of engineering .aterials ass%.e that the.aterials are ho.ogeneo%s and isotro-i(, and that they o:ey linear stressstrain laws* Co..on engineering .aterials s%(h as steel and (on(rete do



< '

4 lntroductlon to Geotechnlcal Englneerlna

not deviate too signifi(antly fro. these ideals, and (onseF%ently we (an%se, with dis(retion, si.-le linear theories to -redi(t their res-onse %nder eng.eenng loads* With soils and ro(<, we are not so fort%nate* As yo%shall see in yo%r st%dy of geote(hni(al engineering, we .ay ass%.e a linear stress5strain res-onse, :%t then we .%st a--ly large e.-;ri(a (orre(tion or =safety= fa(tors to o%r designs to a((o%nt for the real .aterial :ehavior*%rther.ore, the :ehavior of soil and ro(< .aterials in sit% is of tengoverned or (ontrolled :y 0oints, fra(t%res, wea< layers and &ones, andother =defe(ts= in the .aterial@ yet o%r la:oratory tests and si.-lified.ethods of analysis of ten do not ta<e into a((o%nt s%(h real (hara(teristi(sof the soil and ro(<* That is why geote(hni(al engineering is really an =art=

rather than an eng.eenng s(1en(e* %((essf %l geote(hr%(al eng.eenngde-ends on the good 0%dg.ent and -ra(ti(a e+-erien(e of the designer,(onstr%(tor, or (ons%ltant* P%t another way, the s%((essf%l geote(hni(aleogioeer .%st deveXa- a =feeX= far saiX and ro(< :ehavior :efore a safe ande(ono.i( fo%ndation design (an :e .ade or an engineering str%(t%re (an :esafely :%ilt*

1.% &'GGE&TE( APP!OACH TO THE &T'() O*GEO I ECHNICA ENGINEE!ING

4e(a%se of the nat%re of soil and ro(< .aterials, :oth la:oratory and

field testing are very i.-ortant in geote(hni(al engineering* 8ne way thatst%dent engineers (an :egin to develo- a feel for soil and ro(< :ehavior isto gel s%.e e+-etien(e in the la:. at. y :y -et fo.ring Jhe standai d testsfor (lassifi(ation and engineering -ro-erties on .any different ty-es of soils and ro(<s* In tfOs way the nov1(e :eg.s :.ld.g %- a =.ental data :an<= of how (ertain soils and ro(<s a(t%ally loo<, how they .ight :ehave sho%ld, for e+arn-le, the arno%nt of water -resent (hange, how they .ight:e:ave %nder differeot <iods oY e%gioeeri%g laads, a%d wha t the ra nge of -ro:a:le n%.eri(al val%es is for the different tests* This is sort of a self5(ali:ration -ro(ess, so that w hen Bl8tt are faeed with a ne w soil de-osit or ro(< ty-e, yo% will in advan(e have sorne idea as to the engineering -ro:lernsyo% w11I en(o%nter at that s1te* o% (an also :eg. to J%dg e, at leastF%alitatively, the validity of la:oratory and field test res%lts for the .aterials atthat site* o la:oratory as well as field e+-erien(e is i.-ortantfor yo% to heX- deveXo- a =feeJ= for soil and ro(< :ehavior* 8f (o%rse,

0%st as with any other s%:0e(t, this e+-os%re in the la:oratory to soil 3andro(< -ro-erties and :ehaior .%st :e eo.-le.ented :y a diligent st%dyof the theoreti(al, e.-iri(al, and design (o.-onents of geote(hni(alengineering



1.+ &COPE O* THI& ,OO-

Rather than atte.-t an all5in(l%sive a--roa(h to geote(hni(al engineering, the -ri.ary e.-hasis in this te+t will :e on the engineering

behavior of soil 8aterials. oil .e(hani(s and the analysis and design of fo%ndations and earth str%(t%res is generally a faitly straightf1wa1d, :%t(reative, a--li(at;on of .e(hani(s, strength of .aterials, and ele.entarystr%(t%ral engineering* 8f ten the <ey in the s%((essf %l -ra(ti(e and a--li(atioa of geote(hni(al engineering lies in a so%nd <nowledge and %nderstand ingof the engineering Z99ro-erties [nd :ehavior of soils in sit%, when they are

s%:0e(ted to their engineering loads and environ.ental (onditions* Thereforewe feel that the :eginning st%dent .%st first develo- an a--re(i ation for theengineering -ro-erties of soils as distin(t fro. other (o..on (ivilengineering .aterials :efore -ro(eeding to 1nstr%(tion in the analysis anddesign -hases of fo%ndation and earthwor< engineering*

This is an elernentary te+t, and the a--roa(h we have tried to followis to e.-hasi&e the f%ndarnentals, with an eye toward the -ra(ti(aa--li(ations that yo% as a -ra(ti(ing (ivil engineer are li<ely to en(o%nter in yo%r engineering -ra(ti(e* inally, we ho-e yo% will <now eno%gh a:o%tsoils and soil de-osits to avoid serio%s tnista<es or :l%nders in thoseas-e(ts of yo%r -rofessional (areer that involve soil and soil .aterials*

In the first -art of the :oo<, we introd%(e sorne of the :asi(

definitions and inde+ -ro-erties of soil that are %sed thro%gho%t the :oo<*Toen sorne (o..on soil (lassifi(ation s(he.es are -resented* Classification

of soils is i.-ortant :e(a%se i t is the =Baog%age= eogineers %se to (o.5rn%ni(ate (ertain general <nowledge a:o%t the engineering :ehavior of thesoils at a -arti(%lar site* Toe rest of the :oo< is (on(erned with theengineering properties of soil, -ro-erties that are ne(essary for the design of fo%ndations and earth str%(t%res* To-i(s (overed in(l%de how water affe(tssoil :ehavior, their shrin<age and swelling (hara(teristi(s, and their -er .ea:ility how water flows thro%gh soilsB* Toen we get into the (o.-ressi :ility of soil, whi(h is the i.-ortant engineering -ro-erty one needs to -redi(t the settle.ent of engineering str%(t%res (onstr%(ted on soil .asses*inally, we des(ri:e sorne of the ele.entary strength (hara(teristi(s of :oth gran%lar and (ohesive soils* oil strength is i.-ortant, for e+a.-le,for the design of fo%ndations, retaining walls, and slo-es*

G%(h of the -ra(ti(e of geote(hni(al engineering de-ends on to-i(sthat in(l%de geology and the nat%re of landfor.s and soil de-osits* o%are strongly en(o%raged to ta<e a -hysi(al5 geology or an engineeringgeology (o%rse in (onne(tion with yo%r st%dies of geote(hni(al engineer ing*

5

.j



<,1

6 lntroductlon to Geotechnlcal Englneerlng

I4 is ho-ed that with the :a(<gro%nd of this te+t, yo% will :e -re-ared, , yo%

sho%ld <now how to o:tain the soil -ro-erti3es reF%ired for .ost designs,and yo% sho%ld have a -retty good idea as to the -ro:a:le iange of val%esfor a given -ro-erty if yo% <now the eneral (lassifi(ation of the soil* inally, yo% sho%ld have a fairly good idea of what to loo< for at a site,how to avoid (ostly and dangero%s .ista<es, and :e aware of yo%r ownli.itations and <nowledge of soils as an engineering .aterial*

O* &OI CON&TIT'ENT&

is the relatively loose agglo.eration of .ineral and organi( .aterials (o%rse, even s a ow

:edro(< is of interest to geote(hni(al engineers and sorne of these a--li(a5tions ave a rea y een .entioned*

o% .a re.e.:er fro. o%r :asi( s(ien(e (o%rses that the earth has a (r%st of graniti( and :asalti( ro(<s 1 to "0 <. thi(<* 8verlying this

what geologists (all unconsolidated .aterials* These .aterials (an vary in. .

and other geologi( -ro(esses a(t on the ro(<s at or near the earth3s s%rfa(eto or. t ese %n(onso 1 ate .atena s, or so1l* Weathering, whi(h %s%allyres%lts fro. at.os-heri( -ro(esses, alters the (o.-osition and str%(t%re of these ro(<s :y (he.i(al and -hysi(al .eans* Physica/ or 8echanica/

Physi(al weathering agents in(l%de free&ing and thawing, te.-erat%re(hanges, erosion, and the a(tivity of -lants and ani.als in(l%ding .an*Che8ical (eathering de(o.-oses the .inerals in the ro(<s :y o+idation,re %( ion, (ar ona 1n, an o er ( en%(a -ro(esses* enera y, ( en%(a weathering is .%(h .ore i.-ortant than -hysi(al weathering in soilfor.ation* In short then, soils are the -rod%(ts of the weathering of ro(<s*oils at a -arti(%lar site (an :e residual that is, weathered in -la(eB ortransported .oved :y water, wind, gla(iers, et(*B, and the geologi( historyof a -arti(%lar de-osit signifi(antly affe(ts its engineering :ehavior*

The nat%re of soil (onstit%ents is dis(%ssed in greater detailthro%gho%t this e+t* or now, we want to .a<e a few -oints 0%st to set thestage for what we are a:o%t to st%dy* o% already have a lay.an3s ideaa:o%t soil* At least yo% <now in general what sand and grave/ are, and

-erha-s yo% even have a general idea a:o%t fine5grained soils s%(h as silts

and c/ays. These terrns have F%ite -re(ise engineering definitions, as weshall later

55555555 555DDDD555D55 ** K , K K K ******* 55D55555D55 D55D55555555555555555555 D55555D



1.6 Hltorlcal (e/elo0ent ot Geotechnlcal Englneerlng 7

see, :%t for now the general (on(e-t that soils are -arti(les will s%ffi(e*Parti(les of what Well, %s%ally -arti(les of .ineral .atter or, .oresi.-ly, hro<en %- -ie(es of ro(< that res%lt fro. the weathering -ro(esseswe s-o<e of -revio%sly* l we 0%st tal< for now a:o%t the si&e of the -arti(les, gravels are s.all -ie(es of ro(< that ty-i(ally (ontain several.inerals, whereas sands are even s.aller and ea(h grain %s%ally (ontainsonly a single .ineral* l yo% (annot see ea(h grain of a soil, then the soil iseither a silt or a (lay or a .i+t%re of ea(h* In fa(t, nat%ral soils generallyare a .i+t%re of several d1fferent -arti(le si&es and .ay even (onta.organi( .atter* orne soils s%(h as peat .ay :e al.ost entirely organi(*%ther.ore, :e(a%se soils are a -arti(%late K.aterial, they have voids, andt:e voids a re 11s11a3lly filled w9i t : wa ter aod a ir Jt is the -:ysi(al aod

(he.i(al intera(tion of the water and air in the voids with the -arti(les of soil, as w ell as the interaetion of the -artieles the.selves, that .alees soil :ehavior so (o.-li(ated and leads to the nonlinear, non(onservative, andanisotro-i( .e(hani(al :ehavior we .entioned -revio%sly* Now, if yo%add the varia:ility and heterogeneity of nat%ral soil de-osits d%e to the(a-ri(io%sness of * nat%re, yo% -ro:a:ly (an :egin to see that so\s areindeed (o.-le+ engineering and (onstr%(tion .aterials* Hel-ing yo% -%tsorne order into 3this -otentially (haoti( sit%ation is o%r -ri.ary o:0e(tivein this :oo<*

1.6 HI&TO!ICA (E2EOP3ENT

O* GEOTECHNICAENGINEE!ING

As long as -eo-le have :een :%ilding things, they have %sed soils as afo%ndation or (onstr%(tion .aterial* Toe an(ient Egy-tians, 4a:ylonians,Chinese, and Indians <new a:o%t (onstr%(ting di<es and levees o%t of thesoils fo%nd in river flood -lains* An(ient te.-les and .on%.ents :%ilt allaro%nd the world involved soil and ro(< in sorne way* The A&te(s (onstr%(ted te.-les and (ities on the very -oor soils in the Malley of Ge+i(olong :efore the -aniards arrived in the New World* E%ro-ean ar(hite(tsand :%ilders d%ring the Giddle Ages lea.ed a:o%t the -ro:le.s of

settle.ents of (athed(a Bs aod Ba (ge :%ildiogs Ihe roost ootewort:y e+a ro5 -le is, of (o%rse, the Leaning Tower of Pisa* (andinavians %sed ti.:er -iles to s%--ort ho%ses and wharf str%(t%res on their soft (lays* Toe=design= of fo%ndations and other (onstr%(tions involving soil and ro(< was :y r%le of th%.:, and very little theory as s%(h was develo-ed %ntilthe .id5 l !3s*

Co%lo.: is the .ost fa.o%s na.e of that era* He was interested inthe -ro:le.s of earth -ress%res against retaining walls, and sorne of :is(al(%lation -ro(ed %res are still in %se today* Toe .ost (o.rnon theory for

,.



4 tntroc:luctlon to Geotechnlcal Englneertng

the shear streagth of soils is na.ed af ter hi.* '%ring the ne+t (ent%ry, theren(h engineers Collin and 'ar(y '3Ar(yB and the (ots.an Ran<ine.ade i.-ortant dis(overies* Collin was the fOst engineet to J5 (on(e.edwith fail%res in (lay slo-es as well as the .eas%re.ent of the shear strengthof (lays* 'ar(y esta:lished :is law for the flow of water thro%gh sands*Ran<ine develo-ed a .ethod for esti.ating the earth -ress%re againstretaining walls* In England, regory %tili&ed hori&ontal s%:drains, and(o.-a(ted earth5fill :%ttresses to sta:ili&e railroad (%t slo-es*

4y the t%rn of the (ent%ry, i.-ortant develo-.ents in the field too< -la(e in (andinavia, -ri.arily in weden* Atter:erg defined the (onsisten(y li.its for (lays that are still in %se today* '%ring the -eriod 1612516$$, . (onne(tion with investigations of sorne i.-ortant fail%res inhar:ors and railroads, the eote(hni(al Co..ission of the wedish tateRailways develo-ed .any i.-ortant (on(e-ts and a--arat%ses in geote(hni(al engineering* Gethods for (al(%lating the sta:ility of slo-es weredevelo-ed* They develo-ed s%:s%rfa(e investigation te(hniF%es s%(h asweight so%nding and -iston and other ty-es of sa.-lers They %nderstoodi.-ortant (on(e-ts s%(h as sensitivity of (lays and (onsolidation, whi(h isthe sF%ee&ing of water o%t of the -ores of the (lay* At that ti.e, (lays weretho%ght to :e a:sol%tely i.-ervio%s, :%t the wedes .ade field .eas%re.ents to show that they weren3t* The Co..ission was the first to %se theword geotechnica/ wedish9 geote! nis!a : in the sense that we <now ittoday9 the (o.:ination of geology and (ivil engineering te(hnology*

Even w ith these early develo-.ents in weden* the father of soil.e(hani(s is really an A%strian, Prof* /arl Ter&aghi* He -%:lished in 16$the f irst .odern te+t:oo< on soil .e(hani(s, and in fa(t the na.e =soil.e(hani(s= is a dire(t translation of the er.an word erdbau8echani! ,whi(h was -ai t %f the ti lle %f tha t :%%<* Tet &aghi was an % % tstanding andvery (rea tive engineer* He wrote severaV i.-ortant :oo<s and over $te(hni(al -a-ers and arti(les, and his na.e will a--ear .any ti.es in this :oo<* He was a -rofessor at Ro:ert College in Istan:%l, Te(hnis(heHo(hs(h%le in Mienna, G* l. T*, and at Harvard University fro. 16#7 %ntilhis retire.ent in 16"* He (ontin%ed to :e a(tive as a (ons%ltant %ntil hisdeath in 16"# at the age of 7*

Another i.-ortant eontri:%tor to the ad *anee.ent of .odern soil

.e(hani(s is Prof* Arth%r Casagrande, who was at Harvard Universityfro. 16#$ %ntil 16"6* o% will see his na.e of ten in this :oo< :e(a%se he.ade .any i.-ortant (ontri:%tions to the art and s(ien(e of soil .e(ha5ni(s and fo%ndation engineering* 8ther i.-ortant (ontri:%tors to the fieldin(l%de Taylor, Pe(<, Ts(he:otarioff , <e.-ton, and 40err%.* in(e the163s the field has grown s%:stantially and the na.es of those res-onsi:lefor its ra-id advan(e.ent are too n%.ero%s to .ention*



. %345> 3n SJ3l> 6n= nl4> 6

4oth Ter&aghi and Casagrande :egan the tea(hing of soil .e(hani(sand engineering geology in the United tates* 4efore the e(ond Worldw ar, the s%:Je(t was off ered only as a grad%ate (o%rse . very f ew%niversities* Af ter the war, it :e(a.e (o..on for at least one (o%rse in thes%:0e(t to :e reF%ired in .ost s(hools of (ivil engineering* In re(ent yearsgrad%ate -rogra.s in all -hases of geote(hni(al enginee[ng have :eenirn-le.ented at .any %niversities, and there has :een a real infor.atione+-losion in the n%.:er of (onferen(es, te(hni(al 0o%rnals, and te+t:oo<s

-%:lished d%ring the -ast two de(ades*I.-ortant re(ent develo-rnents yo% sho%ld <now a:o%t in(l%de de

velo-rnents in earthF%a<e engineering and soil dyna.i(s, the %se of digital(o.-%ters for the sol%tion of (orn-le+ engineering -ro:le.s, and theintrod%(tion of -ro:a:ility and statisti(s into geote(hni(al engineeringanalysis and design*

. %OTES O% S7MBOLS A%& %ITS

At the :eginning of ea(h (ha-ter, we list the -ertinent sy.:olsintrod%(ed in the (ha-ter* As with .ost dis(i-lines, a standard notation isnot %niversal in geote(hni(al engineering, so we have tried to ado-t thesy.:ols rnost (o..only %sed* or e+a.-leJ the A.eri(an o(iety for Testing and Gaterials ATG, 99 has a list of tandard 'efinitions of

Ter.s and y.:ols R elating to oil and R o(< Ge(hani(s, 'esignation '"#, vhi(h was -re-ared 0ointly sorne years ago with the A.eri(an o(ietyof Civil Engineers ACEB and the International o(iety of Ro(< Ge(hani(s IRGB* Re(ently the International o(iety for oil5 Ge(hani(s ado%ndatton Eng.eenng IG E, 16!!B -%:hshed an e+tens1ve :st of sy.:ols* Altho%gh there are sorne deviations fro. this list :e(a%se of o%r

-ersonal -referen(e, we have generally tried to follow these re(o..endations*

Units %sed in geote(hni(al engineering (an :e -olitely (alled a .essand, less -olitely, severa worse things* There has develo-ed in -ra(ti(e a

0%.:led .i+t%re of (gs5.etri(, I.-erial or 4ritish Engineering %nits andhy:tid E. o-ean .elt i( %nits* With the inh od%(tion %f the wrivet sal and

(onsistent syste. of %nits, =Le yste.e International d3Unit)s= IB in theUnited tates and Canada, we :elieve it is i.-ortant that yo% lea. to %sethose %nits in geote(hni(al engineering -ra(ti(e* However sin(e 4ritishEngineering %nits are still (o..only %sed, it is i.-ortant that yo% :e(o.efa.iliar with the ty-i(aB val%es of hoth sets of %nits To assist yo% with %ni t(onversion where ne(essary, we have in(l%ded a :rief e+-lanation of I%nits as a--lied to geote(hni(al engineering in A--endi+ A*

.j

5555555555 K K 55 K K 5 K D9 K a*,5** * **** KW*55555= 5 5 * ,=5555 ******** ,***** ,59 K9 KZZZ, ,55 555** K K , 5555555 55555 55 *** **5*5,555 5#4#45###5 59559 9K*a*K =5**J ,,*K,,K 5 , ******,



twa

lnde5 and Claiiificatian Pra0ertiei af7ail§

*. INT!O('CTION

In this (ha-ter we introd%(e the :asi( ter.s and definitions %sed :ygeote(hni(al engineers to inde+ and (lassify soils* Toe following notation is%sed in this (ha-ter*

y.:ol 'i.ension Unit 'efinition

A A(tivity EF* 5$#Bce Coeffi(ient of (%rvat%re EF* $5$B

(** Coeffi(ient of %nifonnity EF* $516B'io % .. 'ia.eter for 1] finer :y weight'# % .. 'ia.eter for #] finer :y weight

D % .. 'ia.eter for "] finer :y weighte de(i.alB Moid ratio EF* $51BLl or h LiF%idity inde+ EF* $5$#BLL or (% LiF%id li.itM, M <g Total .assM, " <g Gass of solidsM.., M <g Gass of water 11 (%) Porosity EF* $5$BPI or lp Plasti(ity inde+ EF* $5$$BPL or (p Plasti( li.it

s (%) 'egree of sat%ration EF* $52BL or ws hrin<age li.it

; v< .=,

L# .# Mol%.e of air L# .# ol%.e of solidsLJ .# Total vol%.e

v., L# .# Mol%.e of voids( (%) Water (ontent EF* $5B

p M/ L* <gQ.# Total, wet, or .oist density EF* $5"B p3 M/ L* <gQ.# 4%oyant density EF* $511B

Pd M/ L* <gQ.# & density EF* $56B

P, M/ L* <gQ.# 'ensity of solids EF* $5!B Poat M/ L* <gQ. # at%rated density EF* $51B P.. M/ L* <gQ.# 'ensity of water EF* $57B

18

55 555555555 5555555



*.* ,alc (eflnltlon and Phae Aela'on 11

In this list, L length and M .ass* When densities of soils andwater are e+-ressed in <gQ .#

, the n%.:ers are rather large* or instan(e,the density of water P( is 1 <gQ.#

in(e 1 <g l Gg, to .a<e then%. ers .ore .anagea e, we wt %s%a y %se Gg . for densities* l yo%are %nfa.iliar with I .etri( %nits and their (onversion fa(tors it wo%ld

:e a good idea to read A--endi+ A :efore -ro(eeding with the rest of this

!EATION&

with voids in :etween* The soil solids are s.all grains of different .inerals,i e ei er wi wa er, air, or i e -ar y w1

:oth water and air ig* $*1B* In other words, the total vol%.e =, of the soil.ass (onsists of the vol%.e of soil solids and the vol%.e of voids =v.

$2. *. S32l >5l543n 3n462n2n >3l2= N642l5> S 6n= 132=>D24 62 A 6n= D645 WB*

The vol%.e of voids is in general .ade %- of the vol%.e of water =( andthe vol%.e of air = > We (an s(he.ati(ally re-resent these three -hases 2n

a p ase 1a!a"

1g* . w 1( ea( o e t ree - ases 1s s ownse-arately* 8n the lef t si(,ie we %s%ally indiate the vol%.es of the three -hases@ on the right side we show the (orrt@s-onding .asses of the -hases*Even tho% h onl two di. Dvol%.e is any (onvenient %nit vol%.e s%(h as .# or (.#

In engineering -ra(ti(e, we %s%ally .eas%re the total vol%.e M,, the.ass of water "( , and the .ass of dry solids "s. Toen we (al(%late therest of the val%es and the .ass5vol%.e relationshi-s that we need* Gost of these relationshi-s are inde-endent of sa.-le si&e, and they are oftendi.ensionless* They are very si.-le and easy to re.e.:er, es-e(ially if

,* 0

1



J,t Air Pa

+ 1:1 _±1

1$ lnde5 and Claulflcatlon Pro0ertlea of &olla

V3lG5 Gass

$2. *.* V3lG542 6n= 6>>5l6423n>2N> 3 6>32l >3Dn

2n6 N6>5 =266.

\ V}_ :;Sf*jft=fi0!i __" # -"$

yo% draw the -hase diagra.* They -ro:a:ly sho%ld :e .e.ori&ed, :%t asyo% wor< -hase -ro:le.s .e.ori&ation will o((%r al.ost a%to.ati(ally*

There are three vol%.etri( ratios that are very %sef%l in geote(hni(alengineering, and these (an :e deter.ined dire(tly fro. the -hase diagra.,ig* $*$*

l. The void ratio, e?, is defined as

$51B

where =., /vol%.e of the voids, and#. vol%.e of the solids*

The void ratio $ is nor.ally e+-ressed as a deci8al. Toe .a+i.%. -ossi:le range of e is :etween 8 and oo* However ty-i(al val%es of voidratios for sands .ay range fro. *2 to a:o%t 1*@ ty-i(al val%es for (laysvary fro. *# to 1* and even higher for sorne organi( soils*

$* The porosity n is defined asv.,

n 5 S 00 ]B#,

$5$B

where =v /vol%.e of voids, and#, total vol%.e of soil sa.-le*

Porosity is traditionally e+-ressed as a percentage. Toe .a+i.%. rangeof n is :etween 8 and 1]* ro. $*$ and EFs* $51 and $5$, it (an :e shownthat

and

% & ' e

$5#aB1 e

n$ & '''

- nY$5#:B

Readers with 4ritish :a(<gro%nds will note the (orre(t ter.inology 2> voids ratio*

'



----- . 555D5 ---------******** - ***** -?



$*$ ,ealc (eflnltlona ancl Phaae !eletlona 13

#* Toe degree o@ saturation is defined as

= v

... , , + 1 ]B

$52B

Toe degree of sat%ration tells %s what percentage of the total vol%.e of voids (ontains water* I the soil is (o.-letely dry then Ao/a, and if the -ores are (o.-letely f%ll of water, then the soil is f%lly sat%rated and

1]* Now let %s loo< at the other side, the .ass side, of the -hase diagra.

in ig* $*$* irst, let %s define a .ass ratio that is -ro:a:ly the single .osti.-ortant thing we need to <now a:o%t a soil* We want to <now how

.%(h water is -resent in the voids relative to the a.o%nt of solids in thesoil, so we define a ratio (alled the (ater content ( as

( / ?' S 1 ]B s

$5B

where ".., .ass of water, and "s /.ass of soil solids*

The ratio of the a.o%nt of water -resent in a soil vol%.e to thea.o%nt of soil grains is :ased on the dry 8ass of the soil and not on the

total .ass* Toe water (ontent, whi(h is %s%ally e+-ressed as a percentage,(an range fro. &ero dry soilB to severaV h%ndred -er(ent* Toe nat%ral water (ontent for .ost soils is well %nder 1], altho%gh it (an range %- to ] or higher in sorne .arine and organi( soils*

Toe water (ontent is easily deter.ined in the la:oratory* ATG167B, 'esignation ' $$1", e+-lains the standard -ro(ed%re* A re-resentative sa.-le of soil is sele(ted and its total or wet .ass is detennined*Toen the soil sa.-le is dried to (onstant .ass in an oven at ll8>C* Nor.ally a (onstant .ass is o:tained af ter the sa.-le is lef t in the ovenove.ight* Toe .ass of t:e dryiog dis: .%st, of (o%rse, :e s%:tra(ted fro.

:oth the wet and dry .asses* Toen the water (ontent is (al(%lateda((ording to EF* $5* E+a.-le $*1 ill%strates how the (al(%lations for water

(ontent are a(t%ally done in -ra(ti(e*

E9A3PE .1

(215n:

A sa.-le of wet soil in a drying dish has a .ass of 2"$ g* Af ter drying inan oven at l l8>C overnight, the sa.-le and dish have a .ass of #"2 g* The.ass of the dish alone is #6 g*

.



1+ lnde5 and Claulflcatlon Pro0ertle ol oll

R5FG25=:

'eter.ine t:e wa ter (an ten t aY t:e soiX

S3lG423n:

et %- the following (al(%lation s(he.e@ fill in the =given= or .eas%redF%antities aB, :B, and ;d<= and .a<e the (al(%lations as indi(ated for eB,eB, and fB*

a* Gass of total wetB sa.-le dish /2"$ gb. Gass of dry sa.-le dish / #"2 g

(* Gass of water a 5 ) / 67 gd. Gass of dish 5 #6 ge* Gass of dry soil : 5 d ) / #$ gf. Water (ontent eQeB + 1] / #*$]

In the la:oratory, .asses are %s%ally deter.ined in gi a.s gB %n anordinary (he.i(al :alan(e*

Another very %sef %l (on(e-t in geote(hni(al engineering is density*o% <now fro. -hysi(s that density is .ass -er %nit vol%.e, so its %nitsare <gQ.#

ee A--endi+ A for the (orres-onding %nits in the (gs and

4ritish Engineering syste.s*B The density is the ratio that (onne(tsthe vol%.etri( side of the -hase diagra. with the .ass side* There areseveral (o..only %sed densities in geote(hni(al engineering -ra(ti(e*irst, we define the total, wet, or .oist density p, the density of the

-arti(les, solid density Ps , and the density of wate1 P(B 1, in tenns of the :asi( .asses and vol%.es of ig* $*$9

", "s "( p &' &

=, =,

"s Psv

s

$5"B

$5!B

P( / # (

$57B

In nat%ral soils, the .agnit%de of the total density p will de-end onhow .%(h water ha--ens to :e in the voids as well as the density of the.ineral grains the.selves, :%t p (o%ld range fro. slightly a:ove1 <gQ.# to as high as $2 <gQ .# 1* to $*2 GgQ .#

B* Ty-i(al val%esof Ps for .ost soils range fro. $ to $7 <gQ.# $* to $*7 GgQ.#

B*

Gost sands have Ps ranging :etween $*" and $*! GgQ .# or

e+a.-le, a

(



$*$ ,elc (eflnltlon end Phee !eletlon15

(o..on .ineral in sands is F%art&@ its Ps $*" MQ2. Gost (lay soilshave a val%e of Ps :etween $*" and $*7 GgQ.#, de-ending on the -1edo.inant .inernl in the soil, whereas orga.( sotls .ay have a Ps as lowas $* GgQ.

#ConseF%ently, it is %s%ally (lose eno%gh for geote(hni(al

wor< to assu8e a Ps of $*" or $*! GgQ.# for .ost -hase -ro:le.s, %nlessa s-e(ifi( val%e of P.. is given*

The density of water var;es slightly, de-ending on the te.-erat%re*At 2>C, when Nater is at its densest, P( e+a(tly eF%als 1 <gQ .#1 gQ(.

#B, and this density is sorrieti.es designated :y the sy.:ol p

or

ordinary engineering wor<, it is s%ffi(iently a((%rate to ta<e P( p1

/ 1<gQ.#

/ l GgQ.#

There are three other %sef%l densities in soils engineering* They areth e dry density p , the sat%rated density f3sal3 and the s%:.erged or

:%oyant density p.

".. pd & v, $56B

Psat 8, * 1]B $51B

p / Psat 5 P( $511B

tri(tly s-ea<ing, total p sho%ld :e %sed instead of Psat in EF* $511, :%t in.ost (ases (o.-letely s%:.erged soils are also (o.-letely sat%rated, or at

least it is reasona:le to ass%.e they are sat%rated* Toe dry density pd

is a(o..on :asis for 0%dging the degree of (o.-a(tion of eart: ero:ao<.ent*sCha-ter B* A ty-i(al range of val%es of pd, Psat , and p for severaV soil ty-esis shown in Ta:le $51*

ro. the :asi( definitions -rovided in this se(tion, other %sef%lrelationshi-s (an :e derived, as we show in the e+a.-les in the ne+tse(tion*

TA,E "1 S3n5 TN26l V6lG5> 3 &255n4 &5n>2425> 3 S3n5C33n S32l M64526l>

'ensity#

y-e Paat Pd p3

ands and gravels 1*65$*2 1*5$*# 1*51*#ilts and (lays 1*25$*1* *"51*7 *251*1la(ial tills $*15$*2 1*!5$*# 1*151*2Cr%shed ro(< 1*65$*$ 1*5$* *651*$Peats 1 8 ll CU @. 6*6 6*18rgani( silts and (lays 1*#51*7 *51* *#5*7

Godified af ter Hans:o 16!B*

Dl

>

1



555 5555 55 5 55555555555555

*.! SOLTIO% O$ PHASE PROBLEMS

Phase -ro:le.s are very i.-^@?rtant in soils engineering, and in thisse(tion, with the hel- of sorne n%.eri(al e+a.-les, we ill%strate how .ost -hase -ro:le.s (an :e solved* As is tr%e for .any dis(i-lines, -ra(ti(ehel-s@ the .ore -ro:le.s yo% solve, the si.-ler they :e(o.e and the .ore -rofi(ient yo% will :e(o.e* Also, with -ra(ti(e yo% soon rne.ori&e .ost of the i.-ortant definitions and relationshi-s, th%s saving the ti.e of l_o<ing%- for.%las later on*

Pro:a:ly the single .ost i.-ortant thing yo% (an do in solving -hase -ro:lerns is to dra( a phase diagra8. This is es-e(ially tr%e for the :eginner* 'on3t s-end ti.e sear(hing for the right for.%la to -l%g into*Instead, always draw a -hase diagrarn and show :oth the given val%es andthe %n<nowns of the -ro:le.* or sorne -ro:le.s, si.-ly doing thi leadsal.ost i..ediately to the sol%tion@ at least the (orre(t a--roa(h to the -ro:lern is %s%ally indi(ated* Also, yo% sho%ld note that there of ten arealternative a--roa(hes to the sol%tion of the sa.e -ro:le. as ill%strated inE+a.-le $*$*

E+AMPLE *.*

(215n: p / 1*!" GgQ .# total densityB

( / 0 water (ontentB

R5FG5=:

Co.-%te pd dry densityB, e void ratioB, n -orosityB, degree of sat%rationB, and Psat sat%rated densityB*

S3lG423n:

'raw the -hase diagra. ig* E+* $*$aB* Ass%.e that v4 1 .#

ro. the definition of water (ontent EF* $5B and total density EF*$5"B we (an solve for " and "(. Note that in the (o.-%tations water (ontent is e+-ressed as a de(i.al*

"(w *1 "

+

", "( " p / 1*!" GgQ. /- /---

=, 1* .#

1"

1

# 1



$*# &olutlon of Phae Pro#le 1!

V3lG5 #

B M6>> M

%'. A4t 4

Qvv

w "G.,

C...U. 4 -- :i

4%. s "&

2 2 1ig* E+* $*$a

%:stit%ting "( 8* lA"s we get K .lA"s "s

1*!" Gg #Q -

l *8 .#

"s / 1*" Gg and "( / *1" Gg

These val%es are now -la(ed on the .ass side of the -hase diagra. ig*E+* $*$:B, and the rest of the desired -ro-erties are (al(%laied*

ro. the definition of P( EF* $57B we (an solve for =,.,.

"(

P( Cv>

or

=( / "( / *1" Gg / *1" .#

P( 1 GgQ.#

Pla(e this n%.eri(al val%e on -hase diagra., ig* E+* $*$:*To eale%late J, we .%st ass%.e a val%e of the density of the solids

PsB Here ass%.e p., $*! GgQ.# ro. the definition of p., EF* $5!B we

V3lG5 # B M6>> M

3^3'? A

-- 2o3^3 o2 O . w *

..O.. .-

.... 2 r..-.-.

MO s 3

LO 2

ig* E+* $*$:

....

,.

4

N

?,n



18 lnde5 and Claulflcatlon Pro0ertlea ot &olla

(an solve for=.

dire(tly, or

# & "s

& s Ps

1*" Gg *6# .#

$*! GgQ .#

in(e =, / =< =( =., we (an solve for =< , sin(e we <now the otherter.s*

** = =.5 = 5 = 1* 5 *6# 5 *1" *$2! .#

8n(e the -hase diagra. has :een illed in, sol%tion of the rest of the -ro:le. involves 0%st -l%gging in the res-e(tive n%.:ers into the a- -ro-riate definition eF%ations* We re(o..end that when yo% .a<e the(o.-%tations, yo% write o%t the eF%ations in sy.:ol for. and then insert

the n%.:ers in the sa.e order as written in the eF%ation* Also, it is a goodidea to have the %nits a((o.-any the (al(%lations*

olving for the re.ainder of the reF%ired ite.s is easy*ro. EF* $56,

ro. EF* $51,

pd "s 1*" Gg

#, # l*" GgQ.#

e vv v a v ( *$2! *1" "7"=. #. *6# *

ro. EF* $5$,

n va 4, v( 1 *$2!1 *1" 1 / 2*!]

ro. EF* $52,

s v( / v( 188 / 1*1" * 188 / #6*#]vv va v( *$2! *1"

The sat%rated density Psat is the density when all the voids are filledwith water, that is, when 1] EF* $51B* Therefore, if the vol%.e of air =< were filled with water, it wo%ld weigh *$2! .#

S 1 GgQ.# or *$2!Gg* Then

/ "( "s / *$2! Gg *1" GgB 1*" Gg $ 1 G Q #

Q 1 2

Another, and -erha-s even easier way to solve this e+a.-le -ro:lern,is to ass%.e =. is a %nit vol%.e, 1 .# Then, :y definition, "s Ps / $*!when Ps is ass%.ed to :e eF%al to $*! GgQ .#

B* Toe (o.-leted -hasediagra. is shown in ig* E+* $*$(*

in(e ( "(/ "s *1, "( *$! Gg and "6 / "( "s / $*6!Gg* Also =( "( sin(e P( 1 GgQ .#

@ that is, *$! Gg of water o((%-ies

'

5

Psat # # g .

*



$*# &olutlon ot Phae Pro#lea 11

a vol%.e of *$! .# Two %n<nowns re.ain to :e solved :efore D5 (an -ro(eed9 they are # and =,. To o:tain these val%es, we .%st %se the given

infor.ation that p / 1*!" GgQ .#* ro. the definition of total density

EF* $5"B,

P 1*!" GgQ.# ", $*6! Ggv; v;

=.

ere ore

=. / M, / $*6! Gg3 P 1 .1

GgQ.#

1*"77 .#

va =, 5 v( 5 =#, l*"77 5 *$! 5 1* *217 .#

o% (an %se ig* E+* $*$( to verify that the re.ainder of the sol%tion isidenti(al to the one %sing the data of ig* E+* $*$:*

V3lG5 #B M6>> M

???2 A

5 -(o 2 2 9E 8? : **'U*

>,X;

s o,****

9E?2

$2. EY. *.*

?2

E9A3PE $*#

R5FG25=:

E+-ress the -orosity % in ter.s of the void ratio $ E*F* $5#aB and the voidratio in ter.s of the -orosity EF* $5#:B* 3

S3lG423n:

'raw a -hase diagra. ig* E+* $*#aB*or this -ro:le., ass%.e =#, 1 %nits ar:itraryB* ro. EF* $51,

(o %

w % s ,....



v., 5 e si% (e ., 1 Therefare 1 e .. EF $5$, the definition of

.j



-

..

$ lnde5 and Claalllcatlon Pro0ertle ot &oll

A

C C1? w,5

$26. EY. *.!6

,5 ? s

1

e LV,-

2w

e

$2. EY. *.!J

? s

n is # / =,, or n 5e

l e $5#aB

EF%ation $5#: (an :e derived alge:rai(ally or fro. the -hase dia5gra. ig* E+* $*#:B* or this (ase, ass%.e =, / l.

ro. EF* $5$, = n sin(e = 1* Therefore = 1 5 n. ro. EF*$51, the definition of e M

Q Jt9*

o

n4,.. .,...

1 5 n ,...55 ,

E9A3PE $*2

- , ==I 3^9111,

e *"$, ( 1], Ps $*" "g/ 8*>

R5FG25=:

7, J

b. p,*,, 5 55

1FGF:Al.

d. Psat for 1]

S3lG423n:

n5 ......-.'---- .. 5 ,5 )

..,

3C35 =B $,5DBr

a. in(e ' vol%.es are s-e(ified, ass%.e - 1 .#* J%st as .

5

5

?

A

1 5

+

1

-

.



5

. . ... 5 ------ ..... 5 .. D5 - 55 5 D555555555555,* 555555555555 5555D5555555 5555555 5 5 W J

. 5 5 55555555555 55D55555555555 555 555555



wCX)

enMo

C

-' l

-l')

>2]·..-,

A

sN!:)

M

. .#i$. %&. 2.

,....: > N (

$*# Solutlon of PhaM Problema 21

E+a.-le $*#, this .a<es the =., / e / *"$ .# and =, / 1 e 5 1*"$ .

ro. EF* $56,

and l.Js PsJ f ro. EF* $ !B* o K Ps=. K #

Pd - V: - e1

sin(e =. / . in ig* E+*$52

$*"1*"#" GgQ.#

1 *"$

Note9 Toe relationshi-

Pd 1 e

is of ten very %sef%l in -hase -ro:le.s*

$51$B

V3lG5 #B M6>> M

We <now that

"( / ("s fro. EF* $5B and "s 5 Psi,#.

Ps=. (psi,#. PsF 1 W B p

=, esin(e 2,:. 1

#

Pl%g in the n%.:ers*

p

1fOs relattonshl- is of ten %sef %l to <now*

Ps l wB p & l ` eB

$51#B

.¡

#

.



** lndex and Claulflcatlon Propertl ol Solla

Che(<9 pPd / (

1*77 Q #/ 1*l / 1*"#" Gg .

$512B

o% sho%ld verify that pd / p/ (1 ), whi(h is another very %sef%lrelationshi- to re.e.:er* 3

(* Water (ontent for / 1]* ro. EF* $52, we <now that =.., =., *"$ .#

* ro. EF* $57, ".., / =..,p.., / *"$ .# 1 GgQ.#B / *"$ Gg*

Therefore ( for 1] .%st :e ".., *"$

W>-00 "s $ *" *$ or $#*2

d. PsatD ro. EF* $51, we <now Psat F "s "..,:/ =,, or$*" *"$ #

Psa1 === 1*"$ $*16 or $*$ GgQ .

Che(<, :y EF* $51#9

psH l (: $*"1 *$#2B M QPsa, l $ 1*"$ D g .

E9A3PE $*

R5FG25=:

'erive a relationshi- :etween *, e, (, and PsB

S3lG423n:

Loo< at the -hase diagra. with / 1 ig* E+* $*B*ro. EF* $52 and ig* $*, we <now that =.., =., e. ror*1 the

definitions of water (ontent EF* $5B and Ps EF* $5!B, we (an -la(e the

V3lG5 Gass

(p, M,

ig* E+* $*

V v,

#2

$ $ #

t A

V 5 V S5

w G Iw `

4

2s

A G, P,

2



*.! S3lG4l3n 3 P6>5 P3Jl56 *!

eF%ivalents fot Ir 1 s and "( on tite -itase diagi a.* in(e f .. EF* $57, "( / P(=( , we now (an write the following eF%ation9

"( / P(v( / (" / Ps=..

or

in(e =,. I .#,

$51B

EF%ation $51 is one of the .ost %sef%l of ali eF%ations for -hase -ro:le.s* o% (an also verify its validity fro. the f%nda.ental definitionsof P( , , e, (, and p. . *

Note that %sing EF* $51 we (an write EF* $51# another way9

p2 P( e : s Ps Ps P( e

P / e e ^*- 1"B

When / 1], EF* $51" :e(o.es Ps P(e

sat l e

E+AMPLE *.

15n:

A silty (lay soil with Ps $! <gQ.#

* 1], and the water (ontent /

2"]*

R5FG25=:

Co.-%te the void ratio e, the sat%rated density, and the :%oyant or s%:rnerged deosity in <gQro#

S3lG423n:

Pla(e given infor.ation on a -hase diagra. ig* E+* $*"B*Ass%.e =,. 1 .#

@ therefore M #,p $! <* ro. EF* $51,we (an solve for e dire(tly9

e / p 1 *2" S $! 1 $2$ P( 1 S 1*

4%t e also eF%als =,., sin(e #, 1*@ li<ewise "( / 1$2$ <g sin(e "( is

,

11

K



24 lnde5 and Claaalflcetlon Pro0ertlea ol &olla

V3lG5 #B M6>>

P *$2. EY. *. 1]

n%.eri(ally eF%al to =( :e(a%se P( 1 <gQ .# Now that all the%n<nowns have :een fo%nd, we .ay readily (al(%late the sat%rated dens1tyE * $51B*

X M 1 X A ... Ms 1$2$ $!B <g #

Psat 5 J,3 5 l e

1!7 <gQ .I 1*$2B #

We* o%ld also %se EF* $51! dire(tlB*Ps P(e $! 1 1*$2$B #

Psat

1 e 1 1*$2$1!7 <gQ1119

W nen a soil is s%:.erged, the a(t%al %ni t weigh t is red %(ed :y the :%oyanteff e(t of the water* The :%oyan(y eff e(t is eF%al to the weight of the water dis-la(ed* Th%s, in ter.s of densities, EFs* $511 and $51!B9

p3 Psat P( 1!7 <g- 3.#

!7 <g 1.#

or P, P(e

P / - P(

Ps5 P(

e#

In this e+a.-le, p3 is less than the density of water* o :a(< and loo< atTa:le $51 for ty-i(al val%es of p3 . The s%:.erged or :%oyant density of soiB Dj :e f rn .d ta :e ve(y iro-arta n t la ter an in anr dis(%ssion of (onsolidation, settle.ent, and strength -ro-erties of soils*

In s%nnnaty, fot the easy sol%tion of -hase -ro:le.s, yo% don3t haeto .e.ori&e lots of (o.-li(ated for.%las* Gost of the. (an easily J5

1



. . .. -

5555555 5 D 5= D D5 5 5555555 55=55



2.4 S3ll T5Y4G5 2+

derived fro. the -hase diagra. as was ill%strated in the -re(eding e+a.5 -les* J%st re.e.:er the following si.-le r%les9

2.

3. l, if not given*

*." SOIL TE+TRE

, e (*

-art of the soil .ass* In Cha-ter we gave the %s%al definition of soil fro. an engineering -oin2

and organi( .aterials fo%nd a:ove the :edro(<* We :riefly des(ri:ed howweathering and other geologi( -ro(esses a(t on t e roe s at or near t e

earth3s s%rfa(e to for. soil* Th%s the solid art of the soil .ass (onsists -ri.arily of -arti(les of .ineral and organi( .a tter in vario%s si&es and

The teture of a soil is its a--earan(e or =feel,= and it de-ends on the

to their engineering :ehavior* In fa(t, soil te+t%r has :een the :asis for

agrono.y than in soils engineering* till, te+t%ra (lassif i(ation ter.sgrave s, san s, s1 ts, an e ays are %se % . a genera sense in geo e( ni(a

engineering -ra(ti(e* or fine5grained soils, the -resen(e of water greatlyaffe(ts their engineering res-onse5 .%(h .ore so than grain si&e or

w .iner 1 ains

and this .ay aff e(t their plasticity and their cohesiveness.

Te+t%rally, soils .ay :e divided into (oarse5grained vers%s finegrained soils* A (onvenient dividing line is the s.allest grain that is visi:leo e na e eye* oi s wi -ar i( es arger an is si&e a o%are (alled (oarse5grained, while soils finer than the si&e are o:vio%slyB(alled fine5grained* ands and gravels are (oarse grained while silts and(lays are fine grained* Another (onveoient way to se-arate or (lassify soilsis a((ording to their -lasti(ity and (ohesion -hysi(s9 (ohesion5 sti(<ing

.j



*rain sie: Coarse $raineCan s inii-

#ine $raineCannot se

#ine $raineCannot se

/.al $rains-J -J -

inii/al

- __ 0: _ _ inii/al

-......0 .,..Carateristis:

%t o3 water on en$inrin$ 4eaior:

CoesionlessNon5lasti *ran/lar6elatiel7 /ni85ortant e&5tion: loose sat- /rate $ran/lar 8ater-

CoesionlessNon5lasti *ran/lar 985ortant

CoesieP9asti-er7 i85ortant

ials an 7na8i. ..

-%t o3 $rain sie istri4/tion on en$ineerin$ 4e- aior:985ortant 6elatiel76elatiel7

/ni85ortant/ni85ortant

21 lnde+ end Cle%lfl(atlon Pro-ertle ol oll

TABLE *-* T5Y43, 6l 6n= O45 .(665452>42>> 3 S32l>

oil na.e9 ravels, ands ilts Clays

together of li<e rnaterialsB* or e+arn-le, sands are non-lasti( and non(ohesive (ohesionlessB whereas (lays are :oth -lasti( and (ohesive* ilts6ll :etween (lays and sands9 they 65 al the sa.e ti.e fine grained yet

non lasti( and (ohesionless* These relationshi-s as well as sorne generalengineering (hara(teristi(s are -resented . Ta e 5 * o% n oo:tain sorne -ra(ti(e, :est done in the la:oratory, in identifying soilsa((ording to te+t%re and sorne of these other general (hara(teristi(s s%(has -lasti(ity and (ohesiveness* Also yo% sho%ld note that the ter. e/ay

refers :oth to s-e(if i( .inerals (alled e/ay 8inerals dis(%ssed in Cha-ter 2B and to soils whi(h (onta. (lay ..erals* T5 :ehavior of >3n5 soiis issllongly af fe(ted :y the -resen(e of (lay .inerals* In geote(hni(alengineering, for si.-li(ity s%(h soils are %s%ally (alled clays, :%t we really.ean soils in (hich thepresence of certain e/ay 8inerals affects their

behavior.

*.) (RAI% SIZE A%O (RAI% SIZE&ISTRIBTIO%

A> s%ggested in the -re(eding se(t1on, the sI*e of the soil -art;(le,es-e(ially for gran%lar soils* has so.e effe(t on engineering :ehavior*Th%s, for (lassifi(ation -%r-oses, we are often interested 2n the -arti(le or grain si&es -resent in a -arti(%lar soil as well as the distri:%tion of thosesi&es*



Co44les *rae!

Coarse 1 Me1/8#ine

1

,a7 l.-;11;1 <A<=M9 22.? @B1

o/0ers ,,

1;;;

*.) (6ln Sl5 6n= (6ln Sl5 &l>4lJG4l3n $!

(6n >5

1 1 1 8 1 *1 1

# 2 ! $ 812B 11B

2$"0,

!1$1

* 1

T8

! $ 2$ *! 1

# ! 16 " ! * O 8 2$ 8 !

84> td* and G I T

$ " $ $ " $ " O $ O 00 O $

%3 " 1 2 1 $

$ " 12 $!

n%n si&e ..l

ASTM & A56n S3254 3 T5>4,n 6n= M64546l> 980AAHT8 & A.en(an Asso(1at1on for tate H,ghwav and

T6n>N34643n @¡64> 98UC =3 Untfied oil Classdi(at,on yste. U 4%rea% of

Re(la.ation, 16!2@ U** Ar.v Engineer WE, 16"1M.I.T & M6>>6G>544> ln>4,4G45 3 T5n3l3 T6l3. 9"8

$2. *.! (62n >25 6n5> 63=2n 43 >5156U 5n2n552n>32 l6>>226423n >>45> 3=225= 645 AI-HG>>62n2, 16!!B*

The range of -ossi:le -arti(le si&es in soils is tre.endo%s* oils n rangefro. :o%lders or (o::les of several (enti.etres in dia.eter down Dto%ltrafine5grained (olloidal .aterials* Toe .a+i.%. -ossi:le range is onthe order of 17

, so %s%ally we -lot grain si&e d*istri:%tions vers%s the /ogarith8 of average grain dia.eter* ig%re $*# indi(ates the divisions :etween the vario%s te+t%rasi&es a((ording to several (o..on engineer ing(lassifi(ation s(he.es* l4 sho%ld :e noted that traditionally 2n the

,, j

B3Gl=5> rave1

and

lit C46 C3ll3=>

Coarse $2n51

B3Gl=5> Co::les

rJvel and

Coarse 1 ine Coar I M5=2G1

$2n5

B3Gl=5> C3JJl5>

(615l and 11

Clay

Coarse M5=G $2n5 Coarse I Ged1%. 1 $2n5 C36>5 M5=GK 1 $2n5



r

28lnde5 and Claltlcatlon Pro0ertle ol &olla

United tates the %nits for the vano%s s1&es e-en on e grain si&e* or than a:o%t .. a:o%t l 2 in*B, in(hes are (o..only

%sed, altho%gh .illi.etres (o%ld :e %sed 0%st .as well* rain si&es :etw.een

n%.:er, whi(h of (o%rse (an :e related to a s-e(ifi( grain si&e as shown inig* 1 s .er t an e o* i.illi.etres or, for the very fine5grained (olloidal -arti(le , in .i(ro.etres*

How is the -ar ti(le si&e distri:%tion o:taine * e -ro(ess 1s (a e test . or (oarse5 rained soils, a sieve

analysis is -erfor.ed in whi(h a sa.-le of dry soil is sha<en .e(hani(ally

o-enings* in(e the total .ass of sa.-le is <nown, the -er(entage retainedor -assing ea(h si&e s1eve (an e eter..e y wei ing

il retained on ea(h sieve af ter sha<ing* 'etailed -ro(ed%res for this testare s-e(ified :y ATG 167B, 'esignations C 1#" and ' 2$$* e

re T $! and T 77* Toe U** tandard sieve n%.:ers (o..only e.-loyed for the -arti(le si&e analysiso so1 s are s owns-heres, when we s-ea< of -arti(le dia.eters, we really .ean an eLuivalent

TA,E "% .S. S46n=6= S2515 S25> 6n=

U ** tandard ieve 8-ening

1 $*

2 *2$*$

1 *112 *1"$ *!

l4 t%.s o%t that the sieve analysis is i.-ra(ti(al for sieve o-eningsless than a:o%t * to *! .. No* $ U** tandard sieveB* Th%s for the fine5grained soils, silts, and (lays, the hydro8eter analysis is (o..only%sed* The :asis for this test is to<e3s law for falling s-heres in a vis(o%sfl%id in whi(h the ter.inal velo(ity of fall de-ends on the grain dia.eter and the densities of the grains in s%s-ension and of the fl%id* Toe graindia.eter th%s (an :e (al(%lated fro. a <nowledge of the distan(e and ti.eof fall* Toe hydro.eter also deter.ines the s-e(ifi( gravity or densityB of the s%s-ension, and this ena:les the -er(entage of -arti(les of a (ertaineF%ivalent -arti(le diarneter to :e (al(%lated* As with the sieve analysis,



$* Graln &l>e and Graln &l>e (latrl#utlon 29

the -er(entage of total sa.-le still in s%s-ension or already o%t of s%s-ensionB (an therefore readily :e deter.ined* 'etailed -ro(ed%res for the hydro.eter test are given :y ATG 167B, 'esignation ' 2$$, andAAHT8 16!7B tandard Gethod T 77* Toe U**4*R* 16!2B and U**Ar.y Cor-s of Engineers 16!B also have si.ilar standardi&ed -ro(ed%resfor this test*

The distri:%tion of the -er(entage of the total sa.-le less than a(ertain sieve si&e or (o.-%ted grain dia.eter (an :e -lotted 2n either ahistogra. or, .ore (o..only, in a (%.%lative freF%en(y diagra.* ToeeF%ivalent grain si&es are -lotted to a logarith.i( s(ale on the a:s(issa,whereas the -er(entage :y weight or .assB of the total sa.-le either -assing finer thanB or retained (oarser thanB is -lotted arith.eti(ally on

the ordinate ig* $*2B* Note that this fig%re (o%ld 0%st as well :e -lottedwith the s.aller grain si&es going towards the right* orne ty-i(al grainsi&e distri:%tions are shown in ig* $*2* The (ell5graded soil has a goodre-resentation of -arti(le si&es over a wide range, and its gradation (%rve iss.ooth and gbnbrally (on(avb %-ward* 8n thb othbr hand, a p$$!/ !sd$d soil wo%ld :e one where there is either an e+(ess or defi(ien(y of (ertainsi&es or if rnost %f the -ar ti(les are a:o%t the sa.e si&e* The u8@or8

gradation shown in ig* $*2 is an e+a.-le of a -oorly graded soil* Toe gap5

graded or s!ip5graded soil in that fig%re is also -oorly graded@ in this (ase,the -ro-ortion of grain si&es :etween * and *1 .. is relatively low*

We (onXd, af (a.se, a:tain the nsna X sta tisti(a l -a ra roeters . ean,.edian, standard deviation, et(*B for the grain si&e distri:%tions, :%t this is.ore (o..only done in sedi.entary -etrology than in soil .e(hani(s* 8f (o%rse the range of -arti(le dia.eters fo%nd in the sa.-le is of interest*1#esides that, we %se (ertain grain dia.eters whi(h (orres-ond to aneF%ivalent =-er(ent -assing= on the grain si&e distri:%tion (%rve* or e+a.-le, 'I8 is the grain si&e that (orres-onds to 1] of the sa.-le -assing :y weight* In other words, 1] of the -arti(les are s.aller than thedia.eter 'I8* This -ara.eter lo(ates the grain si&e distri:%tion (%rve'B along the grain si&e a+is, and it is so.eti.es (alled the effective siMe.The coefficient of unifor8ity Cu is a (r%de sha-e -ara.eter, and it is defined

$516B

where (,+ grain dia.eter in ..B (orres-onding to "] -assing, and10 /grain dia.eter in ..B (orres-onding to 1] -assing, :y

weight or .assB*A(t%ally, the %nifor.ity (oeffi(ient is rnisna.ed sin(e the s.aller the

n%.:er, the .ore unifor8 the gradation* o it is really a (oeffi(ient of



==

e9**?**' .,,*** ??''

!."# 35

o, o(9 ***,Dl:5l *e

?' ?222o*

@ .5

Sl515 66l>2>.S.IS46n=6= >2,15

0 "

o

, Q

#

o**

'*o;

1 1 1U5<n9 0.

(2n =26lK545 l KK 1 l 1 .[LL1

1 1 1

X 00

1

*ig.? .+ 1 T@0i0al grin ie diBri#uti#n.

E

Ol

s95@

, "



3J



io D ;.;2 88, B; D ;.@ 88,

*.) (6ln Sl5 6n= (6ln Sl5 &l>4lJG3n #1

=dis%nifor.ity*= or e+a.-le, a Cu / 1 wo%ld :e a soil with only onegrain si&e* Mery -oorly graded soils, for e+a.-le, :ea(h sands, have CQs of $ or #, whereas very well5graded soils .ay have a Cu of 1 or greater*8((asionally, the Cu (an range %- to 000 or so* As an e+a.-le, the (lay(ore .aterial for 8roville 'a. in California has a Cu of :etween 2 and@ the si&es range fro. large :o%lders down to very fine5grained (lay -artl( es*

Another sha-e -ara.eter that is so.eti.es %sed for soil (lassifi(ation is the coefficient of curvature defined as

c / #

e 'ioV '"BV $5$V

where '# / grain dia.eter in ..B (orres-onding to #] -assing :ywe1ght or .assB* Ihe other ter.s were def .ed -rev1o%sly*

A soil with a (oeffi(ient of (%rvat%re :etween l and # is (onsideredto :e well graded as long as the Cu is also greater than 2 for gravels and "

E+AMPLE *.

(215n:

The grain si&e distri:%tion shown in ig* $*2*

'ete1 .ine 'io, Cu, and Ce for ea(h distri:%tion*

S3lG423n:

or EFs* $516 and $5$ we need 10 , '# and 00 for ea(h gradation (%rve

in ig* $*2*a Well5graded soil@ si.-ly -i(< off the dia.eters eorres-onding to1], #], and "] -assing*

92

*$

.j

c



% lnde5 and Clalflcatlon Pro0ertle ol &oll

ro. EF* $5$, *"B $*$B6B

in(e C*, 1 and Ce is :etween l and #, this soil is indeed well graded*b. a-5graded soil@ %se sa.e -ro(ed%re as in aB9

D 10 *$$, D30 *$, DLJ 1*$

ro. EF* $516,

.* G *$$

ro. EF* $5$,

C / '# B$ *

*$B / *1e F D( :F DLJ : *$$B 1 *$B

Even tho%gh :y the %nifor.ity (oeffi(ient (riterion, this soil is wellgraded, it fails the (oeffi(ient of (%rvat%re (riterion* Therefore it is indeed -oorly graded*

(* Unifor. soil@ %se sa.e -ro(ed%re as in aB9

D 6A / *#, D* *2#, D *

C / 60 / * / l 7, D

10 *# *

C / ' #o Q / *2#B / l*ll

e '1 B '" B *#B*B

This soil is still -oorly graded even tho%gh the Ce is slightly greater than %nity@ the C*, is very s.all*

$*" PA!TICE &HAPE

The sha-e of the individ%al -arti(les is at least as i.-ortant as thegrain si&e distri:%tion in affe(ting the engineering res-onse of gran%lar soils* l4 is -ossi:le to F%antify sha-e a((ording D to r%les develo-ed :ysedi.entary -etrologists, :%t for geote(hni(al engineering -%r-oses s%(h

$



.6 Partlcle &ha0e 33

refine.ents are rarely warranted* 8nly a F%alitative sha-e deter.ination is%s%ally .ade as -art of the vis%al (lassif i(ation of soils* Coarse5grainedsoils are (o..only (lassified a((ording to the sha-es shown in ig* $**

R3Gn=5= SGJ3Gn=5=

$2. *.) TN26l >6N5> 3 36>5-62n5= JGl N642l5>. P3436N J M. SG5n=6.

A distin(tion (an also :e .ade :etween -arti(les that are bul!y and n e+(ellent e+a. le

3 the latter, and 8ttawa sand is an e+a.-le of the for.er* Cylinders of ea( 2 er ra5555DDJgrains hardly (o.-ress at all, even when in a very loose state, :%t the .i(afla<es will (o.-ress, even %n er s.a -ress%res, %- o a o% one

* Dnal vol%.e* When we dis(%ss the shear strength of sands, yo%will learn that grain sha-e is very signifi(ant in deter.ining the fri(tional



@99*9*9999999*99***99**9K*9 *5 * 55 55555D5 55D5D*

*. ATTERBER( LIMITS A%&CO%SISTE%C7 I%&ICES

We .entioned Ta:le $5$B that the -resen(e of water in the voids of asoil (an es-e(ially affe(t the engineering :ehavior of fine5grained soils* Notonly is it i.-ortant to <now hov, .%(9h *vater is -resent in, f er e+a.-le, anat%ral soil de-osit the water (ontentB, :%t we need to (o.-are or s(alethis water (ontent against sorne standard of engineering :ehavior* This iswhat the Atter:erg li.its do5they are i.-ortant li.its of engineering :ehavior* l we <now where the water (ontent of o%r sa.-le is relative to

the Atter:erg li.its, then we already <now a great deal a:o%t the engineer ingres-onse of o%r sa.-le* The Atter:erg li.its, then, are water (ontents at(ertain li.iting or (riti(aV stages in soil :ehavior* They, along with the nat%ralwater (ontent, are the .ost i.-ortant ite.s in the des(ri-tion of fine5grainedsoils* They are %sed in (lassifi(ation of s%(h soils, and they are %sef %l :e(a%sethey (orrelate with the engineering -ro-erties and engineer ing :ehavior of fine5grained soils*

The Atter:erg li.its were develo-ed in the early I 63s :y a wed1shsoil s(ientist, A* Atter:erg 1611B* He was wor<ing in the (era.i(s in d%stry,and at that ti.e they had severaV si.-le tests to des(ri:e the -lasti(ity of a(lay, whi(h was i.-ortant :oth in .olding (lay into :ri(<s, for e+a.-le,and to avoid shrin<age and (ra(<ing when fired* Af ter .any e+-eri.ents,

Atter:erg (arne to the reali&ation that at least two -ara.eters were reF%iredto define -lasti(ity of (lays5 the %--er and lower li.its of -lasti(ity* In fa(t, he was a:le to define severa li.its of (onsisten(y or :ehavior and he develo-ed si.-le la:oratory tests to define these li.its*They are9

. U--er li.it of vis(o%s flow*$* LiF%id li.it5lower li.it of vis(o%s flow*#* ti(<y li.it5(lay loses its adhesion to a .etal :lade*2* Cohesion li.it5grains (ease to (ohere to ea(h other** Plasti( li.it5lower li.it of the -lasti( state*"* hrin<age li.it5lower li.it of vol%.e (hange*

He also defined the plasticity inde, whi(h is range of water (ontentwhere the soil is -lasti(, and he was the first to s%ggest that 24 (o%ld :e%sed for soil (lassifi(ation* Later on, in the late I 6$3s /* Ter&aghi and A*Casagrande 16#$:B, wor<ing for the U** 4%rea% of P%:li( Roads, standardi&ed the Atter:erg li.its so that they (o%ld :e readily %sed for soils(lassifi(ation -%r-oses* In -resent geote(hni(al engineering -ra(ti(e we%s%ally %se the liF%id li.it LL or L), the -lasti( li.it PL or p), andso.eti.es the shrin<age li.it L or s. Toe sti(<y and the (ohesionli.its are .ore %sef %l in (era.i(s and agri(%lt%re*

!"



'I

Zh3

tate9

,.

I Water e ntent9

4ri ttle e.i

sol id51 > 1 5Plasti( sol id l l X LiF% i

d

1

1

D ¡

o L PL L LLiF%idit

i nde+ LI ^ 8 LI 8 8 ^ LI ^ l L 1 LI 1

-

tress5strlai n9

& . & Z1 &

w ? ILL

.., '

$2. *. W645 3n45n4 3n42nGG >3D2n 45 1623G> >4645> 3 6 >32l 6> ¡D5ll > 45 5n56l25= >45>>->462n5>N3n>,

/

¡?'



D55 5555 5 5

3$ lnde5 and Clalflcatlon Pro0ertle ol &oll

in(e the Atter:erg li.its are (ater contents where the soil :ehavior (:a nges, we (an show these li.its on a water (ontent (ontin%%. as in ig*

$*"* Also shown are the ty-es of soil :ehavior for the given ranges of water (ontents* As the water (ontent in(reases, the state of the soil (hanges fro.a :rittle solid to a -lasti( solid and then to a vis(o%s liF%id* We (an alsoshow on the sa.e water (ontent (ontin%%. the generali&ed .aterialres-onse stress5strain (%rvesB (orres-onding to those states*

o% .ay re(all the (%rves shown in ig* $*! fro. fl%id .e(hani(s,where the shear velo(ity gradient is -lotted vers%s the shear stress* 'e-ending on the water (ontent, it is -ossi:le for soils to have a res-onsere-resented :y a J1 af thase (%rves e+(e-t -ossi:ly the ideal

Newtonian liF%idB* Note, too, how different this res-onse is fro. the stress5strain :eha v ior of other engineering .atcrials s%(h as steel, (on(rete o(waod

dv

/

S5615 346=25n4

o

$2. *. B56123 3 >5156l 64526l> 2nlG=2n >32l> 315 6 6n5 3 D645 3n45n4>.

Atter:erg3s original (onsisten(y li.it tests were rather ar:itrary andnot easily re-rod%(i:le, es-e(ially :y ine+-erien(ed o-erators* As .enDtioned, Casagrande 16#$:, 167B wor<ed to standardi&e the tests, and hedevelo-ed the liF%id li.it devi(e ig* $*7B so that the test :e(a.e .ore



X 0 .. 65 3 52n524 3 fall 3 GN

C6>66n=53312n 433l

6>> GN

0 ....

5 5-55555555

5--555 H6= GJJ5 3 -

--

a

H524 3 6ll 3 GN

5

e

dB

433l; =25n>23n> 2n 2ll2545>. J CG4 3315 N23 43 4Gn2n 45 6n. 5 A45 4Gn2n 45 6n 43 6NNl >G225n4 Jl3D> 3 45 GN 43 l3>5 45 3315 ! . =Pl6>42 l224 456=>. P64> 6 43G 5 645 H6n>J3 9). P3436N> J M.SG5n=6.

95 l



#7 ln=5Y 6n= Cl6>>l4l64l3n P3N54l5> ol S3ll6

o-erator5inde-endent* He defined the LL as that water (ontent at *whi(h astandard groove (%t in the re.olded soil sa.-le :y a grooving tool igs*$*7a, :B will (lose over a distan(e of 1# .. 4 in*B at $ :lows of the LL(%- falling 1 .. on a hard r%::er or .i(arta -lasti( :ase ig* $*7(B* In

-ra(ti(e, it is diffi(%lt to .i+ the soil so that the groove (los%re o((%rs ate+a(tly $ :lows, :%t Casagrande fo%nd that if yo% -lot the water (ontentsof tests where yo% get (los%re at other :low (o%nts vers%s the logarith. of the n%. :er of :lows, yo% gel a straight line (alled the flo. v c(ve. Mherethe flow (%rve (rosses $ :lows, that water (ontent is defined as the liF%idli.it*

The -lasti( li.it test is so.ewhat .ore ar:itrary, and it reF%ires

sorne -ra(ti(e to get (onsistent and re-rod%(i:le res%lts* Toe PL is definedas the wa te1 (ontent at whieh a thread of soil @u t (r%ro:l es w:en it is(aref%lly rolled o%t to a dia.eter of # .. ¡in*B* I4 sho%ld :rea< %- intoseg.ents a:o%t ! to 0 .. ¡ in* to V in*B long* I the threads (an :erolled to a s.aller dia.eter, then the soil is too wet a:ove the PLB@ if it(r%.:les :efore yo% rea(h # . . Z in*B in dia.eter, then yo% are -ast thePL* Pro-erly rolled o%t PL threads sho%ld loo< Bi<e those shown in ig*

$*7d*Even tho%gh Yhe liF%id li.it and -lasti( li.it tests a--ear si.-le,

:oth tests do ta<e sorne -ra(ti(e to get (onsistent res%l ts* In weden, the fall5(one test is %sed to deter.ine the liF%id li.it Hans:o, 16!B* l4 see.sto give .ore (onsisten t resnlts than the Casagrande deviCe, es-e(iallyfor @3edish (lays, and it is so.ewhat si.-ler and faster to %se*

/arlsson 161!B -1esents an e+(ellent dise%ssion of the relia:ility of :ot: -ro(ed%res

o.eti.es a one5point liLuid li8it test (an :e %sed :e(a%se, for soils

of si.ilar geologi( origin, the slo-es of the flow (%rves are si.ilar* Toen allyo% have to do is o:tain the water (ontent (n of the sa.-le with (los%re of the groove at any :low (o%nt n, and %se the following relat1onshl-

LL / (nF @ yan QJ $5$1B

where tan - is the slo-e of t:e flow (%rve* or :est res%lts the :low (o%nt %

sho%ld :e :etween a:o%t 1 and 2* La.:e 161B, U* 2r.y Cor-s of Engineers 16!B, and /arlsson 16!!B -rovide good dis(%ssions of t:e one5

-oint liF%id li.it test*o% .ay have noti(ed t:at we have not .entioned the ATG -ro(ed%res for the Atter:erg li.its tests* We do not re(o..end the ATG -ro(ed%res :e(a%se, for one thing, they reF%ire that the li.its :e (on d%(tedon air5dried s-e(i.ens* or sorne soils, s%(h a -ro(ed%re will give veryd1fferent res%lts than if the li.its are (ond%eted at the nat%ral water (ontent/arlsson, 16!!B* Toe other -ro:le. with ATG is the grooving tool for the liF%id li.it test* It does not allow for any (ontrol of the height



2.7 A445J5 L2246 6n= C3n5l545nIn=25 39

of the groove, and therefore it will give in(onsistent res%lts* or thisreason, we re(o..end the Casagrande grooving tool ig* $*7B :e %sed*

The range of liF%id li.its (an :e fro. &ero to 1, :%t .ost soilshave LL3s less than 1* Toe -lasti( li.it (an range fro. &ero to 1 or .ore, with .ost :eing less than 2* Even tho%gh the Atter:erg li.its arereally water (ontents, they are also :o%ndaries :etween different engineer ing :ehaviors, and Casagrande 1627B re(o..ends that the val%es :ere-orted (ithout the -er(ent sign* They are nu8bers to :e %sed to (lassify fine5grained soils, and they inde soil :ehavior* o% will, however, see the li.itsre-orted :oth ways and %sing :oth sy.:ols9 LL and PL, and L and p witha -er(ent sign*

The other Atter:erg li.it so.eti.es %sed in geote(hni(al engineering -ra(ti(e, the shrin<age li.it, is dis(%ssed in sorne detail in Cha-ter "*We .entioned earlier that Atter:erg also defined an inde+ (alled the

plasticity inde to des(ri:e the range of water (ontent over whi(h a soil was -lasti(* The -lasti(ity inde+, PI or 6P3 therefore is n%.eri(ally eF%al to thedifferen(e :etween the LL and the PL, or

PI LL 5 PL $5$$B

Toe PI is %sef%l in engineering (lassifi(ation of fine5grained soils, and.any engineering -ro-erties have :een fo%nd to e.-iri(ally (orrelate withthe PI*

When we first started the dis(%ssion on the Atter:erg li.its, we saidthat we wanted to :e a:le to (o.-are or s(ale o%r water (ontent with sornedef ined li.its or :o%ndaries or engineering res-onse* In this way, wewo%ld <now if o%r sa.-le was li<ely to :ehave as a -lasti(, a :rittle solid,or even -ossi:ly a liF%id* Toe inde+ for s(aling the nat%ral water (ontentof a soil sa.-le is the liF%idity inde+, LI or lv is defined as

( 5 PLLI / n PI $5$#B

where (n is the nat%ral water (ontent of the sa.-le in F%estion* l the LI isless than &ero then, fro. the water (ontent (ontin%%. of ig* $*", yo%wo%ld <now that the soil will have a :rittle fra(t%re if sheared* l the LI is

:etween &ero and one, then the soil will :ehave li<e, a -lasti(* I LI isgreater than one, the soil will :e essentially a very v;s(o%s liF%id whensheared* %(h soils (an :e e+tre.ely sensitive to :rea<down of the soilstr%(t%re* As long as they are not dist%r:ed in any way, they (an :erelatively strong, :%t if for sorne reason they are sheared and the str%(t%reof the soil :rea<s down, then they literally (an flow li<e a liF%id* There arede-osits of ultra sensitive F%i(<B clays in Eastern Canada and (andinavia*ig%re $*6 shows a sa.-le of Leda (lay fro. 8ttawa, 8ntario, in :oth the

95 l



<

40 lnde5 and Clalllcatlon Pro0ertle of &oll

L5=6 l6 3 O446D6, On4623. P3436N 3G45> 3 45&212>23n 3 BG2l=2n R5>56, %6423n6l R5>56 C3Gn2l 3 C6n6=6. H6n= J &. C. M6M2ll6n.

%ndist%r:ed and re.olded states at the sa.e water (onten * e %n is5n (ar a verti(al stress of .ore than 1 <Pa@ when

thoro%ghly re.olded, it :ehaves li<e a liF%id*

thoro%ghly re8olded soils, and when we dis(%ss the str%(t%re of (lays .C a-ter , we D see t a e na %ra s r%( %overns its en ineering :ehavior* o then how (o.e the Atter:erg li.its

wor< They wor< e.-iri(ally@ that is, they (orrelate with eng.eenng $tterber li8its Nnd the en ineer5

ing properties are affected by the sa8e things. orne of these =things= in(l%de

de-osit, et(* And these fa(tors are dis(%ssed in detail in the (ha-ter on soilstr%(t%re Cha-ter or now, JUt a((e- a ese D

engineering -%r-oses and that they (orrelate F%ite well with the engineer5



*.8 ACTIVIT7

In 16#, <e.-ton defined the activity A of a (lay as

$ PI(lay fra(tion

$5$2B

where the (lay fra(ti . is %s%ally ta<en as the -er(entage :y weight of thesoi J Jess t : a n $ 11 . Cl ay35 w:i(h have an a(tivity aronnd 1 8 ! 2 1*$B are (lassified as =nor.al=@ $ 8*! are ina(tive (lays and $ 1*$ar e aeti*De elay s* Aeti v ity has :een %sef %l for (ertain (lassifi(a tion andengineering -ro-erty (orrelations, es-e(ially for ina(tive and a(tive (lays*Also, there is fairQ good (orrelation of the a(tivity and the ty-e of (lay

.ineral Cha-ter 2B* However, the Atter:erg li.its alone are %s%allys%ffi(ient for these -%r-oses, and the a(tivity -rovides no really newi nf or.ation*

PROBLEMS

$5l* A water (ontent test was .ade on a sa.-le of silty (lay* The weightof the wet soil -l%s (ontainer was 1!*# g, and the weight of the drysoil -l%s (ontainer was 12*72 g* Weight of the e.-ty (ontainer was!*72 g* Cal(%late the water (onteat of the sa.-le*

$5$* '%ring a -lasti( li.it test, the following data were o:tained for oneof the sa.-les9

Wet weigh t ` (ontai ner $$*1$ g

'ry weigh t ` (on tai ner $*2$ gWeigh t of (on ta i ner 1* g

What is the PL of the soil

$5#* A sa.-le of f%lly sat%rated (lay weighs 1# g in its nat%ral stateand 6! g af ter dryiog Wha t is t:e na t%ral wa ter (onten t of thesoil

$52* or t:e soil sa.-le of Pro:le. $5#, (o.-%te aB void ratio and :B -orosfty*

$5* or the soil sa.-le of Pro:le. $5#, (o.-%te aB the total or wetdensity and :B the dry density* ive yo%r answers in GgQ.#

<gQ.# and l:fQf t# *

21

, -

,



Air

Eater

<oil

t1

1

11

t1

D -

ii,D -

t1

-·-- ----------·---··---- --

a

-- --D -

t

1

, D - w D -

t

!

Mw D -t

11

M Dt

-

1tM D

s - 1

1

t -- F1

1

.. ' ... : :? W

+ lnde5 and Clalflcatlon Pro0ertle of &olla

$5"* A I .! sa.-le of .o1st sotl we1ghs $ <g* Toe water (ontent >

1]* Ass%.e Ps is $*! GgQ .# With this infor.ation, fill in ali :lan<s in the -hase diagra. of ig* P$5"*

$2X P*-

$5!* or the infor.ation given in Pro:le. $5", (al(%late aB the voidratio, :B the -orosity, and eB the dry density*

$57* Toe dry density of a (o.-a(ted sand is 1*7$ GgQ .# and density of the solids is $*"! Gg Q .#

* What is the water (ontent of the.aterial when sat%rated

$56* A 1] sat%rated soil has a total density of $ <gQ.# and a wa ter

(ontent of $]* What is the density of the solids What is the dry density of the soil

$51* w hat 1s the water (ontent of a f %lly sat%rated so1l w1th a drydensity of 1*! GgQ .# Ass%.e P. / $*!1 GgQ .#

*

$511* A dry F%art& sand has a density of 1*"7 GgQ .#* 'eter.ine its

density when the degree of sat%ratton 1s !]* I he dens1ty of sohdsfor F%art& is $*" GgQ .#

$51$* Toe dry density of a soil is 1*" GgQ .# and the solids have a density %f $*"7 GgQ.#* ind (he aB water (ontent, oB void ratio, and eB totaldensity when the soil is sat%rated*

$51#* A nat%ral de-osit of soil was fo%nd to have a water (ontent of $]and to :e \0 sat . ated* Wha t is the void ratio %f this s%il

$ 12* The void ratio of (lay soil is * and the degree of sat%ration is !]*Ass%.ing the density of the solids is $! <gQ .#

, (o.-%te aB thewalet (onten t and :B d1y and wet densities in :%th I and 4ritishEngineering %nits*

$51* The vol%.e of water in a sa.-le of .oist soil is *" .# Toe

lol%.e of solids i5# is *$7 .# 8iven that the densi ty %f soil solids

Ps is $6 <gQ .#, find the water (ontent*



Problema 43

$*1" e(if y frn. first -rin(i-ies thatDl Ps P( e

aB p Ps 1e l e

:B p / P$ l w B eB ( Ps P(

/ *e

dB e 5 %I-

n

5 n 5$

I` e

$51!* 'erive an e+-ression for Ps in ter.s of the -orosity % and the water (ontent ( for aB a f%lly sat%rated soil and :B a -artially sat%rated

$517* 'erive an e+-ression for aB dry density, :B void ratio, and eBdegree of sat%ration in ter.s of p, p , P( , and (.

$516* 'evelo- a for.%la for aB the wet density and :B the :%oyantdensity in ter.s of the water (ontent, the density of the soil solids,and the density of water*

$5$* ro. Ar(hi.edes3 -rin(i-ie show that EF* $5ll, p / Psat 5 P( , isthe sa.e as F ps 5 P,**B Q1 eB*

$5$1* The =(h%n< density= .ethod is of ten %sed to deter.ine the %nitwe1ght and other ne(essary 1rifor.at1onB of a s-e(1.en of irreg%lar sha-e, es-e(ially of fria:le sa.-les* The s-e(i.en at its nat%ral

water (ontent is 1B weighed, $B -ainted with a thin (oat of wa+ or -araffin to -revent water fro. entering the -oresB, #B weighedagain A=, Wwa+ B, and 2B weighed in water to get the vol%.e of the sa.-le I wa+ eoating re.e.:er Arehi.idesB* inally, thenat%ral water (ontent of the s-e(i.en is deter.ined* A s-e(i.en of silty sand is treated in this way to o:tain the (h%n< density*= ro.the infor.ation given :elow, deter.ine the aB wet density, :B drydensity, eB void ratio, and dB degree of sat%ration of the sa.-le*iven9 W ^*9igh t 3 s-eei.rn 6l n64G6l wa ter 3n45A 4 I g J Kg g

Weigh t of s-e(i.en wa + (oat i ng 5 $1*6 W eigh t of s-e(i.en wa+ i n wa ter 7*i9B N a t % ral wa ter (onten t $*]

oil solid densi t y* p,W a+ solid densi ty* p

Hint9 Use a -hase diagra.*

$! <gQ .5 62 <g Q .1

$5$$* The total vol%.e of a soil s-e(i.en is 7 ..# and it weighs 12g* The dry weigh t of the s-e(i.en is 1$7 g, and the density of thesoil solids is $*"7 GgQ.#

ind the aB water (ontent, :B void ratio,eB -orosity, dB degree of sat%ration, eB wet dens1ty, and drydensity* ive the answers to -arts eB and O in :oth I and 4ritishEngineering %nits*

:l

2



55555555555555555555555555555555555555555555 55D555 *5555 ..5 5D5555555DD555

555

++ lnde5 and Clalflcatlon Pro0ertlea of &olla

$5$#* The val%es of .ini.%. e and .a+i.%. e for a -%re sili(a sandwere fo%nd to :e *2" and *"", res-e(tively* What is the (orres-onding range in the sat%rated density in <gQ .#

$5$2* A 77 (.# vol%.e of .oist sand weighs 11 g* Its dry weight is617 g and the density of solids is $"! <gQ .#

* Co.-%te the voidratio, the -orosity, water (ontent, degree of sat%ration, and the totaldens1ty . <gQ .#

*

$5$* A sa.-le of sat%rated gla(ial (lay has a water (ontent of ". 8n

the ass%.-tion that Ps / $*! GgQ .#

, (o.-%te the void ratio, -oros1ty, and sat%rated density*

$5$"* A sensitive vol(ani( (lay soil was tested in the la:oratory and fo%ndto have the following -ro-erties9

aB p 1*$7 GgQ .# :B e 6* (B 6]dB p 5 $*! Gg Q .# eB ( / #11]

In re(he(<ing the a:ove val%es one was fo%nd to :e in(onsistentwith the rest* ind the in(onsistent val%e and re-ort it (orre(tly*

$5$ Q* I he sat%rated dens1ty ,ai of a s1l 1s 1# l :f Q ft#* .d the :%oyant

density of this soil in :oth l:f Qf t # and <gQ.#

$5$7* A sand is (o.-osed of solid (onstit%ents having a density of $*"7 GgQ .#

The v1d ratio is *7* Co.-%te the dens1ty of thesand when dry and when sat%rated and (o.-are it with the densitywhen s%:.erged*

$5$6* A sa.-le of nat%ral gla(ial till was ta<en fro. :elow the gro%nd water ta:le* The water (ontent was fo%nd to :e ]* Est;.ate the wetdensity, dry density, :%oyant density, -orosity, and void ratio*Clearly state any ne(essary ass%.-tions*

$5#* Cal(%late the .a+i.%. -ossi:le -orosity and void ratio for a(olle(tion of aB -.g -ong :alls ass%.e they are # .. .

dia.eterB and :B tiny hall :earings *# .. in dia.eter*

$5#1* A (ylinder (ontains (.# of loose dry sand whi(h weighs ! g,and %nder a stat1( load of $ <Pa the vol%.e 1s red%(ed 1], andthen :y vi:ration it is red%(ed 1] of the original vol%.e* Ass%.ethe solid density of the sand grains is $*" GgQ .#

Co.-%te thevoid ratio, -orosity, dry density, and total densi ty (orres-onding to ea(h of the following (ases9

aB Loose sand* :B Under stati( load*(B Mi:rated and loaded sand*

2



Pro#lea 45

$5#$* The nat%ral water (ontent of a sa.-le ta<en fro. a soil de-osit wasfo%nd to :e 11*]* lt has :een (al(%lated that the .a+i.%. densityfor the soil will :e o:tained when the water (ontent rea(hes $1*]*Co.-%te how .any gra.s of water .%st :e added to ea(h 1 gof soil in its nat%ral stateB in order to in(rease the water (ontent to$1*]*

$5##* 8n five5(y(le se.ilogarith.i( -a-er, -lot the grain si&e distri:%tion(%rves fro. the following .e(hani(al analysis data on the si+ soils,A thro%gh * 'eter.ine the effe(tive si&e as well as the %nifor.ity(oeffi(ient and the (oeffi(ient of (%rvat%re for ea(h soil* 'eter.inealso the -er(entages of gravel, sand, silt, and (lay a((ording to aB

ATG, :B AAHT8, eB UC, and dB the 4ritish tandard*

U * tandard ieve No* Per(ent Passing :y Weight

Dor Parti(le i&e oil :A: oil 4 oiC oil ' oil E oil f3

$5#2* aB E+-lain :riefly why it3 is -refera:le, in -lotting ' (%rves, to -lot the grain dia.eter on a logarith.i( rather than an arith.eti(s ale*

:B Are the sha-es of ' (%rves (o.-ara:le for e+a.-le, do theyhave the sa.e Cu and CeB when -lotted arith.eti(ally E+5 -lain*

! .. # in*B 1 1#7 U !

16 26 1 61

6* #" 7!

No* 2 $! 77 71 1 No* 1 $ 7$ ! 1 76

No* 2 7 !7 26 61 "# No* " !2 #! No* 1 5 6 No* 12 " # 2 0 No* $ 2 55 #$ ! 12 . # #1 $! 21 99

$ . $ 16 $$ # 6$I8 . 1# 17 $ 7$5 " 1 1 12 7 !1$ . 11 $ " $ 1 #6

Note9 G1ss. data 1s .d;(ated : a dash . the (ol%.n*



48 lndex end Cle%lllcetlon Propertlea ot Solle

$5#* Toe soils in Pro:lern $5## have the following Atter:erg li.its andnat%ral water (ontents* 'eter.ine the PI and LI for ea(h soil andeo..ent on their general aetivity*

Pro-erty oil A oil 4 oil e oil & oil E oil

$5#"* C%nnnenl %n the validity %f the 1esnlts of Atter:erg li.its on soils and H*

oil ( oil H

22 38

$ 42L 2+

$5#!* Toe following data were o:tained fro. a liF%id li.it test on a siltye ay*

No* of 4lows Water Content, ]

29 41.8

$1 43.+1+ 22*6

Two -lasti( li.it deter.inations had water (ontents of $#*1 and$#*"]* 'eter..e the LL, PI, the flow .de+, and the to%ghnessinde+* Toe flow inde+ is the slo-e of the water (ontent vers%s log of n%.:er of :lows in the liF%id lirnit test, and the to%ghness inde+ isthe PI divided :y the flow inde+*

( ,O 27 14 14 11 7 *LL 13 3+ 3+ 28 "PL 8 29 18 NP NP 28



three

7oil Claiiification

%.1 INT!O('CTION

ro. the dis(%ssion in Cha-ter $ *n soil te+t%re and grain si&edistri:%tions, yo% sho%ld have at least a general idea a:o%t how soils are(lassified* or e+a.-le, in e(* $*2 we des(ri:ed sands and gravels as (oarse5grained soils, whereas silts and (lays were fine grained* In e(* $*, weshowed the s-e(ifi( si&e ranges on a grain si&e s(ale ig* $*#B for these soilsa((ording to the standards of ATG, AAHT8, et(* Us%ally, how ever,

general ter.s s%(h as saKld or (lay in(l%de s%(h a wide range of eng.eenng(hara(tensti(s that add1ttonal s%:divisions or .odifiers are reF%ired to .a<ethe ter.s .ore %sef%l in engineering -ra(ti(e* These ter.s are (olle(tedinto soil classification syste8s, %s%ally with sorne s-e(ifi( ngineering -%r-osein .ind*

A soil (lassifi(ation syste. re-resents, in effe(t, a lang%age of (o..%ni(ation :etween engineers* 1t -rovides a syste.ati( .ethod of (ategori&ing soils a((ording to their -ro:a:le engineering :ehavior, and allowsengineers a((ess to the a((%.%lated e+-erien(e of other engineers* A(lassifi(ation systern does not eli.inate the need for detailed soils investigations or for testing for engineering -ro-erties* However, the engineering -ro-erties have :een fo%nd to (orrelate F%ite well with the inde+ and

(lassifi(ation -ro-erties of a given soil de-osit* Th%s, :y <n,owing the soil(lassifi(ation, the engineer already has a fairly good general idea of theway the soil will :ehave in the engineering sit%ation, d%ring* (onstr%(tion,%nder str%(t%ral loads, et(* ig%re #*1 ill%strates the role of the (lassifi(ation syste. in geote(hni(al engineering -ra(ti(e*

Gany soil (lassifi(ation syste.s have :een -ro-osed d%ring the -ast years or so* As Casagrande 1627B -ointed o%t, .ost syste.s %sed 2n

47

,, 0



ClassiGation an 9ne& Pro5erties w, e, 5, <, *<, HH, P9, et.)

3o/nation.' a8s, et.)

%n$ineerin$ Pro5erties5er8ea4ilit7, o85ressi4ilit7, srinI -swell,

sear stren$t, et.)

-

%n$ineerin$ P/r5ose

+4 &oll Claaalllcatlon

. . n :?>45

?L6nG65? 1

1

$2. !. R3l5 3. l6>>226423n >>45 2n 5345n26l 5n2n552nN6426.

(ivil engineering had their roots in agri(%lt%ral soil s(ien(e* This is why

the first syste.s %sed :y (ivil engineers (lassified soil :y grain si&e or soilte+t%re* Atter:erg 16B a--arently was the first to s%ggest thatso.ething other than grain si&e (old :e %sed for soil (lassifi(ation* Tothis end, in 1611 he develo-ed his (onsisten(y li.its for the :ehavior of fine grained soils e(* $*!B, altho%gh at that ti.e for agri(%lt%ral -%r-oses* Later the U ** 4%rea% of P%:h( Roads :ased the (lassifi(ation3 fine5grained soils al.ost entirely on the Atter:erg li.its and other si.-le tests* Casagrande 1627B des(ri:es several other syste.s that have :een %sed highwayengineering, airfield (onst.(tioo, agri(%lt%re* geology, and soil s(ien(e*

Today, only the Unified oil Classifi(ation yste. UCB and theA.eri(an Assoeiation of tate Highway and Trans-ortation 8ffi(ials

AAHT8B syste. are (o..only %sed in (ivil engineering -ra(ti(e* ToeUr%f1ed oil Classifi(ation yste. is %sed .ostly J engineering agen(iesof the U** overn.ent U** Ar.y Cor-s of Engineers and U** 'e-art5.en t of t he I n terior, 4% rea% of Re(la.at1on B and .a ny geote(h n1(alengineeri ng (ons%lt ing fir.s and soil testi ng la:ora tories* W i t h sligh t.odi fi(ation t his syste. i s also i n fairly (o. .on %se i n rea t 4ri tai nand elsewht. o% tside t he J I ni ted tates Nea rly ali of t he st ate 'e-art.ents of Trans-ortation and Highways in the United tates %se theAAHT8 syste., whi(h is :ased %-on the o:senred :e:avior of soils

1 5D



-!.* T5 nlll5= S3ll Cl6>>ll64l3n S>45 SCS 49

%nder highway -ave.ents* The ederal Aviation Ad.inistration AAB of the U** 'e-art.ent of Trans-ortation had its own soil (lassifi(ationsyste. for the design of air-ort -ave.ents, :%t it now %ses the Unifiedoil Classifi(ation yste.*

8n(e yo% :e(o.e fa.iliar with the details, :oth the %ses andAAHT8 syste.s are easy to %se in engineering -ra(ti(e*

!.* THE %I$IE& SOIL CLASSI$ICATIO%S7STEM SCS

This syste. was originally develo-ed :y Professor A* Casagrande

l62B for %se in airfield (onstr%(tion d%ring World War 11* It was.odified in 16$ :y Prof essor Casagrande, the U** 4%rea% of Re(la.ation, and the U** Ar.y Cor-s of Engineers to .a<e the syste. alsoa--li(a:le to da.s, fo%ndatior*,@, and other (onstr%(tion U** Ar.y Engineer Waterways E+-eri.en t tation, 16"B* Toe :asis for the %ses isthat (oarse5grained soils (an :e (lassified a((ording to their grain si&edistri:%tions, whereas the engineering :ehavior of fine5grained soils is -rirnarily related to their -lasti(ity* In other words, soils in whi(h =fines=silts and (laysB do not affe(t the engineering -erfor.an(e are (lassifieda((ording to their grain si&e (hara(teristi(s, and soils in whi(h fines do(ontrol the engineering :ehavior are (lassif ied a((ording to their -lasti(ity(hara(teristi(s* Therefore, only a sieve analysis and the Atter:erg li.its arene(essary to (o.-letely (lassify a soil in this syste.*

The fo%r .a0or divisions in the UC are indi(ated in Ta:le #51*They are 1B coarse5grained , $B fine5grained , #B organic soils, and 2B peat.Classifi(ation is -erfor.ed on the .aterial -assing the ! .. sieve, andthe a.o%nt of =oversi&e= .aterial is noted on the drill logs or data sheets*Parti(les greater than # .. eF%ivalent dia.eter are ter.ed boulders,while .aterials :etween ! .. and # .. are (alled cobbles. eoarse g1ainedsoils, sands, and gravels are those having ] or .ore .atenal retained on the No* $ sieve* These fra(tions have :een ar:itrarily :%t (onvenientlys%:divided as shown in Ta:le #51* ine5grained soils are those having.ore than ] -assing the No* $ sieve* The highly organi( soils and -eat

(an generally :e identified vis%ally*The sy.:ols in Ta:le #51 are (o.:ined to for. soil gro%- sy.:olswh;(h (orres-ond to the na.es of ty-i(al soils as shown in Ta:le #5$*

The (oarse5grained soils are s%:divided into gravels and gravelly soilsB and sands and sandy soils B* The gravels are those having the greater

-er(entage of the (oarse fra(tion -arti(les larger than 2*! .. dia.eterBretained on the No* 2 sieve, and the sands are those havin,g the greater -ortion -assing the No* 2 sieve* 4oth the gravel B and the sand B

.j



--??'?/ ....,.,.../ -:,-;--:--,----------///////--/::?:?.?:?........

***559555559995



-

<

&o Soll Claultlcatlon

'()*+ !- G>5> &52n2423n> 3 P6 42l5 S25, S25 A695>, 6= SJ3l>

oil ra(tionor Co.-onent y.:ol i&e Range

oulder s

Cobb/es1B Coarse5grained

soils9

None None

reater 46n # ! to #

7rave/

Coarseine

and

Coarse

Gedi%.

ine

$B ine5grainedsoils9Fines

ilt

Clay

( 12 to No* 2 sieve

! .. to 16 ..16 .. to No* 2 sieve

2*! s No* 2 F.12 ..B to

No* $ *! No* 2 2*! ..B to

No* 1 $* ..B No* 1 $* ..B to

No* 2 *2$ ..B No* 2 *2$ ..B to

No* $ *!

Less than No* $ si(*e*! ..B

M No s-e(ifi( 62nsi&e %se Atter:ergli.itsB

e No s-((ifi( grain si9%9%se Atter:(rg li.itsB

#B 8rgani( oils9 o No s-((ifi( 62n si&eB 2B Peat9

7radation y8bo/sWell5graded, WPoorly5graded, P

Pt No s-e(ifi( 62n si&eB

%iLuid %i8it y8bols

High LL, HLow LL, L

gro%-s are divided into fo%r se(ondary gro%-s, W and W, P and P,G and G, C and C, de-ending on the grain si&e distri:%tion andnat%re of fines in the soils* Well5graded W soils have a good re-resentation of ali -arti(le si&es whereas the -oorly graded PB soils are either %nifor. or s<i-5 or ga-5graded ig* $*2B* Whether a gravel or sandy soil iswell graded (an :e dete11nined :y -lotting the g+ ain sae dist+ i:%tion (w veand (o.-%ting the (oeffi(ient of %nifor.ity C*, and the (oeffi(ient of (%rvat%re Ce. These (oeffi(ients are defined in Cha-ter $ as

5 // D

$516B

*, Dio

and the (oeffi(ient of (%rvat%re is

e // D

e Dio +

D $5$B#



5#*$ The 'nltled &oll Clalflca'on &@te ;'&C&< 51

w:e(e 32*a 5 grain dia.eter at 0 -assing,*/ grain dia.eter at !0 -assing, and

1/ grain dia.eterD at 0 -assing :y weight or .assB*

radation (riteria for gravelly and sandy soils are shown in Ta:le #5$(ol%.n "B* The W and W gro%-s are well5graded gravelly and sandysoils with less than ) -assing the No* *00 sieve* Toe P and P gro%-s are -oorly graded gravels and sands w1th httle or no non-lastl( f .es*

Toe fine5grained soils, those having 8ore than )0 -)ssing the No*$ sieve, are s%:divided into silts G for the wedish ter.s 8o / veryfine sandB and 8@iila siltBX and (lays CB :ased on their liF%id li.it and -lasti(ity inde+* 8rgani( soils 8B and -eat PtB are also in(l%ded in this fra(tionaltho%gh, as shown in Ta:le # l, no grain si&e range is s-eeified* ine5grained

soils are silts GB if their liF%id li.its and -lasti(ity indi(es -lot belo( theA5line on Casagrande3s 1627B -lasti(ity (hart ig* #*$B* The fines are (lays CBif the LL and PI -lot above the A5line* Toe A5line generally se-arates the .ore(layli<e .aterials fro. those that are silty and also the organi(s fro. theinorgani(s* TheD e+(e-tion is organi( (lays 8L and 8HB whi(h -lot :elowthe A5line* However, these soils do :ehavesi.ilarly to soils of Jowe( -la sti(ity T:e silt, (la y, aod o(ga oi( f(a(tions a(ef%rther s%:divided on the :asis of relatively low LB or high HB liF%idli.its* The dividing line :etween the low and high liF%id li.its has :eenar:itrarily set at * Re-resentative soil ty-es for fine5grained soils are alsoshown in ig* #*$* This fig%re, (ol%.ns 2 and of Ta:le #5$, and Ta:le !-!, will :e hel-f %l in the vis%al identifi(ation and (lassif i(ation of finegrained soils* o% (an see fro. ig* #*$ that severaV diff erent soil ty-estend to -lot in a--ro+i.ately the sa.e area on the LL5PI (hart, whi(h.eans that these soils tend to have a:o%t the sa8e engineering behavior.

This is why the Casagrande (hart is so %sef%l in the engineering (lassifi(ation of soils* or e+a.-le, Casagrande 1627B o:served the :ehavior of soils at the sa.e liF%id li.it w ith -lastieitB inde+ as eo.-ared V1 ith their

:ehavior at the sa.e -lasti(ity inde+ :%t with an in(reasing liF%id li.it,and he o:tained the following res%lts9

C:ara(teristi(

'ry strerithTo%ghness near PLPer.eal?ilf tyCo.-ressi:ilityRate of vol%.e (hange

oils at EF%al LLwith In(reasing PI

In(reasesIn(reases$5A:o%t the sa.e$5

oils at EF%al PIwith In(reasing

LL

$5$5In(reas(sIn(reases

To%ghness near the PL and dry strength are very %sef%l vis%al(lassifi(ation -ro-erties, and they are defined in Ta:le #5#* Toe other (:ara(te(isri(s are eogioeering -ro-erties, and they are dis(%ssed in great



JJa,or /11s1ons

*ro/5

ir:011 Na8es

*E

*P

Eetl-$rae $raels, $rae! san 81&t/res. ttle or no Gnes

Poorl7 $rae $raels, $rael san 8/et/res, l 1ttle or no Gnes

*M

*C

<t7 $rael-0, $rae! san·stlt 81&:/res

Cla7e7 $ra,eis. $ra... el san laK8i& t/res

<P

t'oorl7 $r,rneo sanos. '::l' o!11tie ?3 11; 3 !li'i

-· n.r ::o r::onne o3 saes w1t sorne 1nter8e1ate s1es r-niss1nL

<M

1------se

tKJon5last/.0 Gnes or Gnes0 w1t low 5last11t

t------------------------------ 3or 1ent131ation 5roe/res see MH 4etow)

Plast1 3nes 1or 1ent1Gat1on 5,oe/ressee C H 4elowi

lent13 3at1on Proe/re'ion #rat1on <8aer tan No ; <,ee <1e

r7 <tren$tr/'i1n$ aratenst1si

?atan7 reat1on to saI.1nL) =o/$ness onssten7 near P

None to sli$t

?/1I to slow None

None to er7slow

#1el lenti3O.ation Proe/rese&.l/1n$ 5art1les lar$er tan 88an 4as1 n$ 1rat1ons on esti8a .......

Eie ran$e 8 $ra8 s1es an s/4stan1.1ala8o/nts o3 all inter8e1ate 5art1le st.es

Preo8,nantl7 one sie or a r_ ·-:i- ---w,t so8e inter8e1ate s1es 81ss,1 n$

Non5lasti Gnes or Gnes w1t low 5last11t7

3or ,enti31at,on 5roe/res see MH 4elow)

J> /. o. % - _! ro o ·-· ''- 1 ·--

see CH 4elow)

.,0- C: e

eQi <ilt,,- sans san s1i! 111111: t/res

+-------------------C!a7e sJr1s. .rn· ia7 1,..l',.. t/ res

0

-0.

o

oe .,

00,

a100,

>R

MH

'?

.i' S:F, --o

':, -:::. CH

e o

lnor$a8 s1lts an Pr7 Gne sans. roITo/r, st or .la,7e7 Gne sans or lae s1lts. wt Kli$t 5last11t7!nor$an1,: las ol low to rne1/8 5last11t7, $raell7 !as. san·.,i la7s, sllt7 la7s, lean la7s

e,0F0,i

., .00 :U

.e>- ?H

?rLan1 sllts an or$an1 st7 tas o3 low 5last1it7

<$t to8e,/8 <low <l1$t

- o 000

V

e

iti

.>

. MW

lnor$an1 silts, 81aeo/s or1atornaeo/s ne san7 or s1lt7 soils. elasC silts <lt$t to

8eJ1/8 <low to none

- 'o

<l,$t to8e-1/ri1

e

'

R-o

%Y .C'C - CW

lnor$an, la.7s o3 t$ 51ast11t7. 3atla7s

Wt$ to er 7t$ None W1$

B :i,

i

Z 0F..J

?W ?r$an, a7s o3 8ei/8 to 1$

5las11it7, or$a8 silts. Me1/8 to i$ None to er7slow

<$t to8e,/8

Pt Peat an oter i$l7 or$an1 soils 6ea,l7 1entiGe 47 olor. oor. s5on$7 3 eel.

an 3reZ/entl7 47 314ro/-'0 te,i0t/re,

0

$ oll Claaaltl(atlon

TABLE !-* n225= S32l Cl6>>226423n S>45

t B3Gn.=6 6>>4,6 3n> 342> N3>>5>>n 665 >4> 34 D3 3GN> 65 =5>n645= J 32Jn6 4,3n> 34 3GN >43l> $3 5Y6N5 WDCD5ll-6=5= 615U >6n] C.4G5 D 46 J2n=5

AII >515 >5> 3n n> Ln64 65 G S6n36=

Af ter U** Ann Engineer Waterways E+-eri.ent tation 16"B and Howard 16!!B*



-'2

!.* T5 nll5= S3ll Cl666ll63n S645 SCS #

TA,E !-* C3n42nG6=

La:oratory Class1f1(at1onC2456

n

',o

"

greater tnan F*

ee e( $ 1

Not .eeting ali 6=6423n reF%,re.ents 6 W

A445J5 li.1ts J5l3D A n5, 3

r5555,**K PI l5>> t5' "

AJ315 A- ln5 D24Pl :etween" 6n= 65 J3=5l2n5

with PI !$a$! than ! =G6l >J3l>.

.0 5645 46n %C*

, ' 11

/ n- ... n-- J54D55n 6n= !

ee e(* $D1

- -N_1 __1&_'__5_11_&_5__51_&_(' $;_<_& $_3_&-,-f (-$ _) -&--I

Atter:era l1.1ts :elow A n5, or PI l5>> 46n "

Aner:erg l1.1ts a:ove A-lUn5w1th PU oreater than !

eo

2Plasti(ity Chart

$6 U6J3643 (lassif1(at1on 3 2n5-62n5=>32l>

L24> Nl344n 2n

645=&one w1tn netw2 and ! are :ordert ne6>5> 5FG2n G>5 3 ,...,,l ?'IS.

Co.-anng soils at eF%a1 11F%,a 11.1t WQto%ghness and dry strength in(reasewith in(reasing -lasti(1ty inde+*

...^**Jo** $

1 5

'?>?$"?

CL-ML! *,*

oo 1

, $ #

V

2 "

LIOI& LIMIT

3! 7 6 1

,.

C 0

#

=



i

60 11 1 1 1 1 1 1 l #

55

555553

=*51555555

,J,,

333R, 3B,B

f555 5 5 5

Q* ,353 3 5155555

MU**5Q = / ,:, W:I'U 5555 A----

+L?O

9 1140

5 Q , 55`555555Q ftnorgani( I lays of 5555

55H11 1 , K l **1 high -last i Dity .# /

Q CH Q I

j 2

U¡,

E Q Q

5#

1 9 i,G d3 , 5 Q

Q Gi(a(eo%s or e iato.a(eo%s5155555

1= f i ne sandy an( si l ty soi ls@¡ ow - * * 5 Q e ,% n, Q Q 1 tD D1

Xe or * * 555515555

42U5 e ays@ sand y a nd Q N1 as 3,* L*L5 **K K 55r55 K K K (lays, and si l t (lavs

%;L 1

ast1( .orga1 1( A as 1( s, ts@ gani( stlts,

55 ,norga, ,e 5

201 Q P 5 5 5 55 555 58H 5 55555555155555 555 55555? 5

- 1 U Q Q 5

55 5 -----W

Kil ty e as@ Q 5 K 55 or 5555 555555----C------l

5(layey stlts QU Q 55 5555 355555 55555 555 50 5and sa ,ds 3 = 2,,L Q X OL::X MH -------- ---------W

' Q 1 ,organi( and orga ,i( sil ts 5555555555555555(%QL ;.On G L 555 and silty (lays of 1^ w 55555555 5 555555555

!.., X, --'---------

-

ast1.

(1.ty@ ro(< f lo%r@

" G L ,*, s l ty or (layey f i ne sands 50

o n 3 20 3( 40 60 70 >J 90 1

Lid% id l i.it

ig* #*$ j6>66n=5'> Nl6,4224l 64, >3D2n l>5156l 5N5>5U464215 >32l 4N5> =515l3N5= 3 UC6>6.

6n=5, 162* 6n= H3D6=, 116!!B*

1

LQ3

a55s l ty (la ys K, :3 (la Q 5 555555`5555 5

o



l.



#*$ The 'nlfled &oll Claaalflcallon &@le ;'&C&< 55

TA,E %"% E25l= l=534226423n P65=G5> 3 E235-(6235= S62l> 6 $6423n>These -ro(ed%res are to :e -erfor.ed on the .in%s No* 2 sievesi&e -arti(les, a--ro+i.ately *2 ..* or field (lassifi(ation -%r -oses, s(reening is not intended@ si.-ly re.ove :y hand the (oarse -arti(les that interfere with the tests*

'ilatan(yrea(tion to sha<ingB9 'ry trength

(r%shing (hara(teristi(sB9

After re.ov.g -arti(les larger than No* 2 sieve si&e, -re-are a -at of .oist soil

After re.oving -arti(les larger than No* 2 sieve si&e, .old a -at of soil to the

with a vol%.e of a:o%t 2 (.# Add eno%gh (onsisten(y of -%tty, adding water if ne(es

water if ne(essary to .a<e the soil soft :%tnot sti(<9y* Pla(e the -al in the o-en -al. of one hand and sha<e vigoro%sly against theother hand severa ti.es* A -ositive rea(tion(onsists of the a--earan(e of water on thes%rfa(e of the -at, whi(h (hanges to a Iivery(onsisten(y and :e(o.es glossy* When thesa.-le is sF%ee&ed :etween the fingers, thewater and gloss disa--ear fro. the s%a(e,the -at stiffens, and finally it (ra(<s or (r%.5 :les* The ra-idity of a--earan(e of water d%ring sha<ing and of itsdisa--earan(e d%r ing sF%ee&ing assist inidentifying the (har a(ter of the fines in a

soil* 1 ery fine (lean sands g;ve theF%id9

5est and .ost distin(t rea(tion, whereas a -lasti( (lay has no rea(tion* Inorgani( siltss%(h as a ty-i(al ro(< flo%r show a .od eratelyF%i(< rea(tion*

sary* Allow the -al to dry (o.-letely :yoven, san, ot ah, and then test its strength J :rea<ing and (r%.:ling :etween the fingers*This strength is a .eas%re of the (hara(ter and F%antity of the (olloidal fra(tion (ontained in the soil* The dry strength in(reaseswith in(reasing -lasti(ity*

High dry strength is (hara(teristi( for (lays of the CH gro%-* A ty-i(al inorgani(silt -ossesses only very slight dry strength*ilty fine sands and silts have a:o%t the sa.eslight dry strength :%t (an :e disting%ished

:y the feel when -owdering the dried s-e(i.en* ine sand feels gritty, whereas a ty-i(al

s;lt has the s.ooth feel of flo%r*

To%ghness(onsisten(y near -lasti(li.itB9

Af ter re.oving -arti(les larger 46n the No* 2 sieve si&e, a s-e(i.en of soil a:o%t

2in* (%:e in si&e is .olded to the (onsisten(y of -%tty* I too dry, water .%st :e added and*

if sti(<y, the s-e(i.en sho%ld :e s-read o%t in a thinayer and allowed to lose so.e .oist%re :y eva-oration * Toen the s-e(i.en is rolled o%t :y hand on a s.ooth s%a(e or :etween the

-al.s into a thread a:o%t # .. in dia.eter* Toe thread is then folded and refoldedre-eatedly* '%ring this .ani-%lation the .oist%re (ontent is grad%ally red%(ed and the

s-e(i.en stiffens, finally loses its -lasti(ity, and (r%.:les when the -lasti( li.it is rea(hed*After the thread (r%.:les, the -iej sho%ld :e I%.-ed together and a slight <neading

a(tion (ontin%ed %ntil the l%.- (r%.:les* DToe to%gher the thread near the -lasti( li.it and the stiffer the l%.- when it finally

(r%.:les, the .ore -otent the (olloidal (lay fra(tion in the soil* Wea<ness of the thread at the -lasti( li.it and F%i(< loss of (oheren(e of the l%.- :elow the -lasti( li.it indi(ate either inerganie elaB ef le5w -lastieitB er .ateriaJs s%eh as <aalin ty-e lays aad ^?TgRPi lays whiho((%r :elow the A5line*

Highly organi( (lays have a very wea< and s-ongy feel at the -lasti( li.it*

After U** Ar.y Engineer Waterways E+-eri.ent tation 16"B and Howard 16!!B*

*



&oll Clalflcatlon5$

detail later in this :oo<* or now, 0%st rely on yo%r general <nowledge andingen%ity to fig%re o%t what those words .ean

The %--er li.it line U5lineB shown in ig* #*$ indi(ates the %--er range of -lasti(ity inde+ and liF%id li.it (oordinates fo%nd th%s far for soils A* Casagrande, -ersonal (o..%ni(ationB* Where the li.its of anysoil -lot to the lef t of the U5hne, they sho%ld :e 1e(he(<ed* o.e highlya(tive (lays s%(h as :entonite .ay -lot high a:ove the A5line and (lose tothe U5line* lt is shown in Cha-ter 2 that Casagrande3s -lasti(ity (hart (aneven :e %sed to identif y F%alitatively the -redo.inant (lay .inerals in asoil*

Coarse5grained soils with 8ore than 1O fines are (lassified as G

and G if the fines are silty li.its -lot :elow the A5line on the -lasti(ity(hartB and C and C if the fines a1e (lay ey li.its -lot a:ove the A5lineB4oth well5graded and -oorly graded .aterials are in(l%ded in these twogro%-s*

oils having bet(een 2O and 1O -assing the No* $ sieve are(lassed as =:orderline= and have a d%al sy.:ol* Toe hrst -art %f the d%alsy.:ol indi(ates whether the (oarse fra(tion is well graded or -oorlygraded* The se(ond -art des(ri:es the nat%re of the fines* or e+a.-le, asoil (lassified as a P5G .eans that it is a -oorly graded sand with :etween ] and 1$] silty fines* i.ilarly a W5C is a well5gradedgravel with *sorne (layey fines that -lot a:ove the A5line*

ine5grained soils (an also have d%al sy.:ols* 8:vio%sly, if the li.its

-lot within the shaded &one on 1g* #*$ PI :etween 2 and ! and LL :etween a:o%t 1$ and $B, then the soil (lassifies as a CL5GL* Howard16!!B .a<es the -ra(ti(al s%ggestion that if the LL and PI val%es fall near the A5Xioe ar oear the LL line, then d%al sy.:ols sho%ld :e %sed*Possi:le d%al sy.:ols then are9

CL5CH8L58H

CL5GLCL58L

CH5GH

4orderline sy.:ols (an also :e %sed for soils with a:o%t ] finesand (oarse5grained fra(tions* In this (ase -ossi:le d%al sy.:ols are9

G5GH

8C5CH

G5GLG5GH

C5CLC5CH

55 ,.. X

555 5 .. 5 -- 5 ,, 57

'

- 55 -



tion*

t31g%re J*J is a -ra(Lil9a1 %i ,@@ v1 . . . - ==D..:=.F= 2I. ..,....,......

%I$ IE& SOIL CLASSI$ICATIO% S7STEM B3=5l2n5 Cl6>>226423n>

C36>5-(62n5= S32l> --- - - - $n5-(6n5= -S3>

,* 1r ML

(615U i@A J

?' (615U 8IVI )l 1

S2l4 MH(P ?' (C ?' 1

.G. 1 OH?'

.U:: 1 '/

S6n=

;::.,M;o 1 r

S6n=2

.IV 1

;::J 1

-33a9B

CLCl6 CH

al se 1 OL

11

? e 1*, 2 00

P5 :N>>2n 45******** X....,..., ******** *****

%345: Onl 4D3 3GN >J3l> 6 J5 G>5= 43 =5>2J5 6 >32l. B3=5l2n5l6>>226423n> 6n 5Y>4 D,4n 56n OT lllt9 =GG1? , v% f3=D

$2. !.! (G2=5 3 J3=5l2n5 6>5> 3 >32l l6>>226423n 645 H3D6=,16!!B*

A ste535:v5sten nro(ed%re for UC (lassifi(ation of soils, (onveni5ently -resented . ig* #*2, shows a -ro(ess of eli.ination of all the

. . . . . , - - --'- - -- - -4'P . P4.-

. >.J **** . ... Bfollowing ste-s, ada-ted fro. the Cor-s of Engineers, .ay hel- in this

-ro(ess U*5* A*r.y5

5 .11 aL(1 >;<R;3 5* ' .. KK ,,* 55*5#5$ and ig* #*295

sif i(ation sho%ld :e done in (on0%n(tion with Ta:le

l. 'eter.in e if the soil is (oarse grained, fine grained,.or highly orgar%(*.s is aone oy vis%a1 5* a%%Z v u#, -the a.o%nt of soil -assing the No* $ sieve*

2.I coarse graSned #(,3=3M=3 analysis and nlot the ITT=ain si&e distri:%tion

(%rve* 'eter.ine the -er(entage -assing the No* ", sieve and. . , J****** 11*ln *d*

.......X 8''-'A.# -V ,- 555 5or sand greater -er(entage -assing No* 2B* .. - 5 :* *%eter..e .e a.o%. %i C4,

- 1.llC ../ v. ==3=== o.3.a0 ... 01 .1..1

. less than ] -asses the No* $ sieve, e+a.ine the sha-e of the

grain si&e (%rve@ if well graded, (lassify as UW or w @ -oorly graded, (lassify as P or P*(* I :etween ] and 1$] of the .aterial -asses the No* $ sieve,

it is a :orderline (ase, and the (lassifi(ation sho%ld have d%al

j^ .j

K,

5 5? . 555 55 5 55 ,K* **

K, ***** , , *K*

D5K D K K** D..5

-

1

2

G

,. 4 1

11

1

.555 .

5 ? '-? ''- r"$1

. . , .

** 5 ..

&_ . ,*** . . .

.



Wl*WH[ ?6*AN1C <?JH<Pt)

14ro/s te&t/re. olor, oor. er7 i$ 8o1-st/re ontent, 5artiles o3 e$e/14le8atter stiIs, leaes. et.)

*6A%H 9*9

*reater 5ere-nta$e o3 oarse 3rat1on F

retaine on No s1e J

J etwee,.. \ a-n 12' 5an No 2;; s1eeMore tan 12\ 5assNo. 2;; siee

orerne, to ae o/4le s784ol a55ro5r1ate to $ra,n$ iin 5last11t7arterist,s.

e $., *E *M

<

7 oll Cleaalll(etlon

M65 12>G6l 5Y6n643n 3 >32l 43 =5452n5 D545 242> HIHL 8RANIC, C8ARE RAINE'* 3 INE RAINE8* In

:orderline (ase1 deter.ine a.o%nt -assing No $ sieve

COARSE (RA4%E&] 3 len -ass No* $ %eve

A%n >515 anatysis

r55 SA%O IS

U reater 9-er(tontage of (oarse fra(tion -ass No 2 >515

less ttiar -ass%3 *00 sieve

NoteD ieve s1&es are U* tandard 11 2nn intfere w1th free5dra1ning -ro-ert1es %se do%:le>J3l s%(h G (W(M, et(

85D55n ) 6,n= *N6>> %3. *00 >5

4orderline, to have do%:le>J3l a--ro-riate tograaing and olas1i(1ty

(hara(ter1st,(s1 e g * W 3G

$2. !." AGY2l26 l6J3643 2=5n4226423n N35=G5 645 SAEWES. 90.



- ---------?-? ..5 .

!.* T5 nll5= S3n Cl6 .ll=3n ysle. SCS +9

INE RAINE8Gore th5, PNI, No* $ sieve

RGn LL n= PL 3n 2nG> No* "025D ??':52I

l

l2,lid li.it lea then

HLtl*lid li.it ****5tf%n

B5l3D A-Hn5 lf3tdhat(hed &one5 on

Li.its -lot .2245= &one on

A:(we A5line andhlt(hN &one on

A%n ll 1nd PL on.in%s No* 2sieve fr11etion

Color, oda,, -oooi:lyLL PL on oven

dry toil

Colar, oda,,5D

ll ond Pl on 3Dn =4ooil

CL C?

ig* #*2 Contin%ad*

,._



60

W5G, W5G, et(*B*

&oll Clalflcatlon

(hara(teristi(s

d* I .ore than 1$] -asses the No* $ sieve, -erfonn the Atter :erg li.its on the .in%s No* "0 sieve f ra(tion* Use the -lasti( ity(hart to deter.ine the (orre(t (lassifi(ation G, G, e,se, G5C, or G5CB* *

#* I fine grained #a* Perf or. Atter:erg li.its tests on .in%s No* "0 sieve .aterial*

l the liF%id li.it is less than , (lassify as L, and if the liF%idli.it is greater than , (lassif y as H*

:* or L9 l the li.its -lot :elow the A5line and the hat(hed &one

on the -lasti(ity (hart, deter.ine :y (olor, odor, or the (hangeD D Dt (a%sed : oven5drying the soil,whether it is organi( 8LB or inorgani( GLB* l the li.its -lotin the hat(hed &one, (lassif y as CL5GL* I the li.its -lot a:ovethe A5line and the hat(hed &one on the -lasti(ity (hart ig*#*$B, (lassify as CL*

the li.its lot :elow the A5line on the -lasti(ity(hatt, deter.ine whether organi( 8HB or inorgani( the li.its -lot a:ove the A5line, (lassif y as CH*

d* or li.its whi(h -lot in the hat(hed &one on the -lasti(ity(hart, (lose to the A5line or aro%nd LL / , %se d%al :order ine s .:ols as shown in ig* #*#*

Altho%gh the letter syrn:ols in the %ses are (onvenient, they do not(o.-letely des(ri:e a soil or soil de-os1t* or t 1s reason,sho%ld also :e %sed along with the letter sy.:ols for a (o.-lete soil(lassif i(ation* Ta:le #52 fro. U** Ar.y Engineer Waterways E+-eri.enttation 16"B -rovides sorne %sef %l infor.ation for des(ri:ing soils*

In the (ase of all soils, s%(h (hara(teristi(s as (olor, odor, and

ho.ogeneity of the de-os1t s o%des(ri-tion*

or (oarse5grained soils s%(h ite.s as grain sha-e, rnineralogi(al(ontent, degree of weathering, in sit% density and degree of (o.-a(tion,and -resen(e or a:sen(e of f ines sho%ld :e noted and in(l%ded* Ad0e(tives

s%(h as ro%n e , ang% ar, angrain sha-e see ig* $*B* The in sit% density and degree of (o.-a(tion isnor.ally o:tained indire(tly :y o:serving how diffi(%lt the .aterial is toe+(avate or to -enetrate with devi(es (alled penetro8eters. Ter.s s%(h asvery loose , /oose , 8ediu8, dense , and very dense are %sed to des(ri:e in sit%



#*$ The 'nlfled &oll Clalflcatlon &@te ;'&C&< 11

TA,E %"+ ln36423n R5FG25= 3 &5>2J2n S32l>Coarse5gra.ed so1ls9

or %ndist%r:ed soils add infor.ation on stratifi(ation, degree of (o.-a(tness, (e.enation, .oist%re (onditions anddrainage (hara(teristi(s*

ive ty-i(al na.e* Indi(ate a- -ro+i.a te -er(entages of sand and gravel,.a+i.%. si&e, ang%larity, s%rfa(e (ondition, and hardness of the (oarse grains,lo(al or geologi( na.e and other -ertinen tdes(ri-tive inf or.ation, and sy.:ol in

-arentheses*

E+a.-le9ilty sand , gravelly* A:o%t $] hard,

ang%lar gravel -arti(les 1$ .. .a+i.%. si&e, ro%nded and s%:ang%lar sandgrains (oarse to fine, a:o%t 1] non-lasti(fines with low dry strength, well (orn -a(tedand .oist in -la(e, all%vial sand, GB*

ine5gi9ained soils*ive ty-i(al na.e* lndi(ate degree

and (hara(ter of -lasti(ity, a.o%nt and.a+i.%. si&e of (oarse grains, (olor inwet (ondition, odor ;f any, lo(al or geologi( na.e, and other -ertinentdes(ri-tive infor.ation, and sy.:ol in -arentheses*

or %ndist%r:ed soils add infor.ation on str%(t%re, stratifi(ation, (onsisten(y in %ndist%r:ed and re.oldedstates, .oist%re and drainage (onditions*

E+a.-le9C/ayey silt , :rown, slightly -lasti(,

s.all -er(entage of fine sand, n%.ero%sverti(al root holes, finn and dry in -la(e,loess, GLB*

Note9 4e -re-ared for wide variations in soil des(ri-tion a.ong organi&ations and testingla:oratories* They ali have their own ways of doing things*

After U** Ar.y Engineer Waterways E+-eri.ent tation 16"B*

:y hand wo%ld :e (onsidered very loose, whereas a de-osit of the sa.e.aterial whi(h reF%ires -ower tools for e+(avation wo%ld :e des(ri:ed asvery dense or -erha-s (e.ented*

or the fine5grained fra(tion, nat%ral water (ontent, (onsisten(y, andre.olded (onsisten(y sho%ld :e noted in the sa.-le des(ri-tion* Con

sistency in the nat%ral state (orres-onds in sorne res-e(ts to degree of (o.-a(tion in (oarse5grained soils and is %s%ally eval%ated :y noting theease :y whi(h the de-osit (an :e e+(avated or -enetrated* %(h ter.s asvery soft , soft , 8ediu8, stiff , very stiff , and hard are e.-loyed to des(ri:e(onsisten(y* o.eti.es the word fir8 is %sed synony.o%sly with the ter. stiff .: ine5grained soils .ay :e additionally des(ri:ed :y %sing the testse+-lained in Ta:le #5# for dilatan(y, to%ghness, and dry strength* 8ther

te(hniF%es for vis%al (lassifi(ation of soils sho%ld :e learned and -ra(ti(edin the la:oratory* E+(ellent des(ri-tions of vis%al (lassifi(ation and identi9fi(ation -ro(ed%res are fo%nd in the U**4*R* 16!2B Earth "anual, A- -endi+E5#, and ATG 167B 'esignation ' $277*

.j



5555555555555DDD555 55555555555D -- -

O ' ?

5DDa a 5D *5 A* *,*

- K99@@ =D1

(215n:.

ieve analysis and -lasti(ity data for the following three soils*

*** ... oil l, oil $, oil #,

555 5 55 ?,*'*,*5 5

C 66 - -D

a,Q **,,

No* 2 66 6! 1 No* 1 6$ 6 1

No* 2 86 2 1 No* 1 &J6

No* $ 0 2 91

LL $ - 1$2'I (@ A.-

PI 2 NPk 77

kNon-lasti(*,,

R5FG25=:

Classify the three soils a((ording to the Unified oil Classifi(ation yste.*

,** K* K K ***: K K K

Use Ta:le #5$ and ig* #*2*

15D&

- .. L.. ---U- ..: X.. .. ---- .... -- L .. L-.... .... .. Q .. .. X ; X

353 'ig* E+* B*#*1

$* or soil 1, we see fro. the (%rve that .ore than ] -asses the No* $ sieve "]B@ th%s the soil is a fine5grained soil and theAtter:erg Ii.its are reF%ired to f%rther (lassify the soil* WithLL // $ and PI // , the soil -lots inD the hat(hed &one on the -lasti(ity (hart* Therefore the soil is a CL5GL*

#* oil $ is i..ediately seen to :e a (oarse5grained soil sin(e only2O -asses the No* $ sieve* in(e 6!] -asses the No* 2 sieve, thesoil is a sand rather than a gravel* Ne+t, note the a.o%nt of .aterial -assing the No* $ sieve ]B* ro. Ta:le #5$ and ig* #*2, thesoil is =:orderline= and therefore has a d%al sy.:ol s%(h as P5G or W5G de-ending on the val%es of CG and C* ro. thegrain si&e distri:%tion (%rve, ig* E+* #*1, we find that DFJl: //*!1 .ni, '# // *#2 , and '1 // *17 ..* The (oeffi(ient of

1$

**

-

5



55 ,



;I

UI* tanrard ?2o-en,rg 0in*B U** tandardl sieve .B.:ers H@d=oeter

' loo

6

7155

2;E

,¡ .!.1 "

.Ul'

6

4

r

3 2 )} 1 11 - 1 3 6 510 14116 20 J: 40 + 10

11402D

Z5, TI

19o

S32l .,# 3 E

o--140

41 9

1Z9

Z

91

Z

USO

..#.l.T 1 2

?*G*

i 1#

*0

4t--t- 11--*--*- \------1 .jj-.&..j. -- -!+0 b

?" 7

E4,8(;;:..,i, t-----t--\*---&_&::-*-**-----!-3&&-- E!(&.&. & 4

*

7

I: 1 F--F---F-i--t--*--t-*--1 1--&-..(.::8,,*- G-.F.F.._ -*--!-- (o

)00

11Co::ls

1 1

1001 +0.)rairl, si&e ll

(,l15l anorse I ,G Coarsel I Gd,%. 1 1 *ine

*1

&11t or cla@

1100

S632nNl5 %F. El51. or deth Class,f l(at1on %6 D I LL

$PL P3¡5 t E ! 1+

*# $2 474 49 $2

radat1n C%rve'ate

21 *ig. EYj !.

5

l l

.



12 oll Claaalll(atlon

%nifor.ity C*, is Do *!1C*, D1 *17 / #*6 ^ "

and the (oeffi(ient of (%rvat%re Ce is

*#2B$

*17 S *!1 *6l 3*999999 l

or a soil to :e (onsidered well graded, it .%st .eet the (riteriashown in (ol%.n " of Ta:le #5$@ it does not, so the soil is

(onsidered -oorly graded and its (lassifi(ation is P5G* The soilis G :e(a%se the fines are silty non-lasti(B*2* A F%i(< glan(e at the (hara(teristi(s for soil # indi(ates the soil is

fine grained 6!] -asses the No* $ sieveB* in(e the LL is greater than 1 we (annot dire(tly %se the -lasti(ity (hart ig* #*$B* Useinstead the eF%ation for the A5line on ig* #*$ to deter.ine if thesoil is a CH or GH*

PI *!#LL 5 $B / *!#1$2 5 $B !*6=

in(e the PI is !7 for soil #, it lies above the A5line and th%s thesoil is (lassified as a CH*

!.! THE AASHTO SOIL CLASSI$ICATIO%S7STEM

In the late 16$3s the U** 4%rea% of P%:li( Roads now the ederalHighway Ad.inistrationB (ond%(ted e+tensive resear(h on the %se of soilses-e(ially in lo(al or se(ondary road (onstr%(tion, the so5(alled **far.5to.ar<et= roads* ro. that resear(h the P%:li( Roads Classifi(ation yste.was develo-ed :y Hogentogler and Ter&aghi 16$6B* The original syste.was :ased on the sta:ility (hara(teristi(s of soils when %sed as a roads%rfa(e or with a thin as-halt -ave.ent* There were severaV revisions sin(e

16$6, and the latest in 162 is essentially the -resent AAHT8 16!7Bsyste.* The a--li(a:ility of the syste. has :een e+tended (onsidera:ly@AAHT8 states that the syste. sho%ld :e %sef%l for deter.ining therelative F%ality of soils for %se in e.:an<.ents, s%:grades, s%::ases, and :ases* 4%t yo% .ight <ee- in .ind its original -%r-ose when %sing thesyste. in yo%r engineering -ra(ti(e* ee Casagrande, 1627, for sorne(o..ents on this -oint*B



!.! T5 AASHTO S3ll Cl6>>ll64l3n S>45 7

TABLE !.) AASHTO &52nl423n> 3 (615l, S6n=, 6n= S2l4-Cl6oil ra(tion S25 Range

o ersraveCoarse sandine sand

ve ..12 .. to No* 1 sieve $* ..B

No* 1 $* ..B to No* 2 *2$ ..B No* 2 *2$ ..B to No* $ *! ..B

silt and (layB sieve

oil fra(tions re(o D ed in the AAHT8 s ste. are listed in Ta:le #5* 4o%lders sho%ld :e e+(l%ded fro. the sa.-le to :e (lassified, :%t as

silty if they have a PI less than 1 and (layey if the PI is greater than 1*e sys e. ( assi ies soi s in o ei r r

A57, and it in(l%des severa s%:gro%-s* oils within ea(h gro%- areeval%ated a((ording to the group inde, whi(h is (al(%lated :y an e.-iri(alfor.%la* Toe onl tests re %ired are the sieve anal sis and the Atter:er li.its* Ta:le #5" ill%strates the (%rrent AAHT8 16!7B soil (lassif i(ation*

. .

graded, whereas A5# soils are (lean, -oorly graded .sands* A5$ .aterials.are

signifi(ant a.o%nt of silts and (lays* A52 to A5! are fine5grained soils, the silt5(lay .atena s* ey are erentlate on t e as1s o t e1r tter erg li.its* i%re #* (an :e %sed to o:tain the ranges of LL and PI for gro%-s A52 to A5!and for the s%:gro%-s in A5$* Highly organi( soils in(l%ding -eats and.%(<s .ay :e -la(ed in gro%- A57* As with the UC, (lassifi(ation of A57soils is .ade vis%ally*

:ased on the servi(e -erfor.an(e of .any soils, es-e(ially when %sed as -ave.ent s%:grades* l4 .ay :e deter.ined fro. the e.-iri(al for.%lagiven at the to- of ig* #*", or yo% .ay %se the no.ogra-h dire(tly*

Using the AAHT8 syste. to (lassify soils is not diffi(%lt* 8n(e yo%

have the reF%ired test data, -ro(eed fro. lef t to right in the (hart of Ta:le #5", and find the (orre(t gro%- :y the -ro(ess of eli.ination* Toe first gro%-fro. the lef t to fit the test data is the (orre(t AAHT8 (lassifi(a tion* A(o.-lete (lassifi(ation in(l%des the gro%- inde+ to the nearest wholen%.:er, in -arentheses, af ter the AAHT8 sy.:ol* E+a.-les are A5$5"#B, A52B, A5"1$B, A5!51!B, et(*

ig%re #*! will :e hel-f%l in (lassifyingD soils a((ording to the AAHT8syste.*

,. j

.



TABLE !- Cl66226423n 3 S3ll6 6n= `32l-A5645 M2Y4G5>

eneral Cl%sifi(ation

ran%lar Gaterials ilt5Clay Gaterials#] or less -assing *! ..B Gore than #] -assing *! ..B

ro%- (lassifi(ation

ieve analysis, -er(ent -assiog9$* .. No* 1B*2$ .. No* 2B*! .. No* $B

Chara(teristi(s of fra(tion -assing *2$ .. B3lo* 2B9LiF%id li.itPlasti(ity inde+

Us%al ty-es of signifi(an (oostit%ent .aterial

eneral rating as s%:grade

A51 A5$ A5!

ADlDa A515: A5# A5$52 A5$5 A5$5" A5$5! A52 A'* A.., $515

A5!5"

.a+*# .a+* 8 .a+* 1 rnin*1 .a+* $ .a+* I8 .a+* * .a+* # .a+* # .a+* * .a+* #" .io* #" .io* #" .io* #" .io*

2 .a+* 21 .in* 2 .a+* 21 .io* 2 .a+* 21.io* 2 .a+* 21 .io*" .a+* NP I8 .a+* I8 .a+* 11 .in* 11 rnin* I8 .a+* I8 .a+* 11 .in* 11 .io*

tone frag.ents, ine sand ilty or (layey grave and sand ilty soils Clayey soilsgrave, and sand

E+(eJlen t to good air to Poor >CA.eri(an Asso(iation o f tate Highay and Trans-ortation 8ffi(ials, 16!7* Used :y -er.ission*4 Plasti(ity inde+ of A5!5 s%:gro%- is ZeF%al to or less han LL .in%s #* Plasti(ity inde+ o; A5!5" s%:gro%- is greater than LL .in%s # see f ig* #*B*

L



3.3 T5 AASHTO S3ll Cl6>>lll63n yste. 87

t,eQ*QQ Q0

Q, Q QQ

)0 l3?

,,Q'SQ*l.) .Q 'I:

?.U: "0***

Q h,,,,

5DZ9Z

!0118

, XQA-- LQ' Q6?::' A- ...X Q

*0 Q

67 ) ,

QQ A--)

11QQ KQ #

Q l.'

Q Q3 A-" A-)<Q

3 0 *0 !0 "0 0 0 80 90 ' 00

L2FG2= l224

$2. !.) A445J5 l224> 6n5> 3 >GJ6=5 >GJ3GN> A-", A-), A-,6n= A-. %345 464 C6>66n=5'> A-l2n5 6n= -l2n5 J615 J556 >N52-N3>5= 3n 45 64 645 L2G, 90, 6n= AI-HG>>62n2, 9.

E+AMPLE ! *

,ven@

Toe following data for soils 2 and 2. ee ig* E+* #*1 for the grain si&edistri:%tion (%rves*

ieve i&e

No* 2

] iner

99

] iner

$# No* 1 6" 17

No* 1 !6 s

LL 26 -PL $2PI $ NP

R5FG25=:

Classify the soils a((ording to the AAHT8 oil Classifi(ation yste.*

Z,*

0

.,

,,



'

<

(3GN 2n=5Y (2l / $ - !)<0.* 0.00) LL - "0 _ 0.0 $ - )PI - 0,D55 $ / ] N6>>2n 0.0) >2515, LL / l2FG2= l224, 6n= PI/ Nl6>4224 2n=5Y.

W5n D32n D24 A-*- 6n= A-*- >GJ3GN> 45 P6426l (3GN ln=5Y P(I2> =5452n5= 3 45 PI 3nl.

W5n 45 3J2n5= N6426l 3GN 2n=25> 65 n564215, 45 3GN 2n=5Y >3Gl= J5

5N345= 6> 53.

)0--

*0 %54?O

?8

'%!0 54

"0!)-

"0

!0 )0

·99

S o

0 oeo*

::

*0 - O

O

D,U ^

\

5 K*_** 0 ?'o*-'

C?l*' .:: e

G

Cl*B 5

3 ,.T3 80

1 4*#; ,o

%.0-:

90

1

Y6N 5:8* N6>>2n @.0) >2515 LL !8PI / *

5n:P(I / 8.9 3 LLP(I / ." 3 PI(I =

$2. !. (3GN 2n=5Y 64 645 AASHTO, 16!7B* a A526n A>>326

G3n 3 S4645 H2D6 6= Tt 6>N3 46423 O226l>, 16!7* >5= JN52> >23n.

"7

&e e

5

3



a<e 5Y6 n643n oftso,I 43 detr.tne wDether isran%lar o s1ltD(lay .ater,als

'eter tne a.o nt -ass.g No* $ ,eve

1

5 5 5 llt5(lay atenals

6nGl6 6456l>

#] less -ass No* $ s ve ! 3 35 N6 > %3. *00 2 515

R%n LL and PL n .on%s t> D21s,eve atenai

1

PI les

s,l

tthan 9 18

Cl6

P1 greater th n 11

R%n s,eve anal s,s, 6l>3 LL 6n= P 3n

.in%s N * 2 s1eve .aterial

1ilty

R%n LL - - d PL on .%s No* 2 teve .ate 1al

CU151

L greater than " LL less han 2l

A5!LL greater than 21

less t an 1] -ss%3 $ >515

% nNl6>42

PI lless than i8

PI greatr than 11

LL ess than L great*er2 than 21 , *,

lPI g eater than

46n LL 1n%s !0 LL .in%s #or

PL eF%a or PL less 446n

greater t an # #

lG A5@52 7 > A5$5! A52 A-) 2 .

$2j !. C64 3 GY2l22l4 l642364F l6>22R23n 35G5> l43 4E AASHTOI S32l Cl6>>2,6423n S> O45 L2G, 16t8B*

lr

I

l

I I

l 3X >3

o,



; 51

'()*+ !- C3N66Jl5 S32l (3GN> 2n 45 AASHTO 6n= G>5> S>45>

oil ro%- Co.-ara:le oil ro%-sin 2n AAHT8 yste. Unified

Gost Possi:l( :%t yste. Pro:a:le Possi:le I.-ro:a:le

W A515a A5$52, A5$5,A5$5", A5$5!

P A515a A515: A5#, A5$52,

A5$5!

A515:, A5$2, A5$5" A52, $5 ,

!

A5$5, A5$5 ! A5", $515 ,A5!5", A515a

C A5$5", A5$5! A5$52, A5" A52, A ! ",A5!5

>D A515: A515a A5#, A5$52,A5$5, A5$5",A5 5

S A #, A 1 : 1 a H-2-4 A5$5,A5$5", A5$5!

G A515:, A5$52, A5$5", A52, A5", A5!5,

A5$5, A5$5! A5 A5!5", A515a

se A5$5", A5$5! A5$52, A5",A52 A5!5"

A5!5

GL A52, $5 A5", $515

CL A5", A5!5" A52

8L A52, $5 A5", A5!5,

A5!5"

GH $515 , A5 A5!5"

CH A5!5" $515

11 A- , $ ;355155



'()* !- CGl42nG5=

oil ro%- Co.-ara:le oil ro%-s2n 2n Unified yste.

AAHT8 Gost Possi:le :%tyste. Pro:a:le Possi:le I.-ro:a:le

A515a W, P W, P G, G

G, G

A5# P W, P

A5$52 G, G o( se W, P

W, PA*$* G, G

W, P,W, P

A*$*" C, C G, G W, PW, P

A*$*! G, C, W, P,

A52 GL, 8L CL, G, G, C

se25 8H, GH, G, G

GL, 8L A- C GL, 8L, C, G,

se G

A*!* 8H, GH GL, 8L, G, G,CH C, C

A*!*" CH, CL GL, 8L, 8H, GH,

G

1. 4e(a%se .ore than #] of soil 2 -asses the No* $ sieve, fro.Ta:le #5" we see that the soil is an A52 or higher* in(e the LL is26, the soil is either A5 or A5!* with a PI of $, the soil is an A5!*A (he(< of ig* #* shows the soil is (lassified as an A5!5"*

l* 4e(a%se soil has less than #] -assing the No* $ siee, it isgran%lar* A glan(e at ig* E+* #*1 -rovides the sa.e infor.ationBPro(eeding fro. lef t to right in Ta:le #5", we see that the 2>4gro%- fro. the lef t that .eets the (riterion is A515a*

!1

*D* = ,5555955



!." COMPARISO% O$ THE G>5> A%O AASHTO CLASSI$ICATIO% S7STEMS

There are several signifi(ant differen(es :etween the UC andAAHT8 soil (lassifi(a tion syste.s, whi(h is not s%r-rising (onsideringthe dif feren(es in their history and -%r-ose* o% (an see the =2 eren(es inthe treat.ent of (oarse5grained soils :y (o.-aring Ta:le #1 with #5* Toe.a0or diff eren(es in the fine5grained soils are shown in ig* #*, where wehave s%-eri.-osed :oth the A5line and the U5line on the LL5PI (hart*AAHT8 16!7B a(t%ally -lots LL vers%s PI, :%t we have t%.ed the (hart

6> for easy (o.-arison with the Casagrande -lasti(ity (hart ig* #*$B*The differen(es are signifi(ant* Also, %se of PI / 1 as the dividing line :etween silty and (layey soils see.s rather ar:itrary and -ro:a:ly does notrealisti(ally relate to the engineering -ro-erties of fine5grained soils* Al5H%ssaini 16!!B dis(%sses several other signifi(ant differen(es :etween thetwo syste.s*

Ta:le #5! shows a (o.-arison of the two syste.s in ter.s of the -ro:a:le (orr*es-onding soil gro%-s*

PROBLEMS

#5 l* Classif y soils 2 and in E+a.-le #*$ a((ording to the Unified oilClassifi(ation yste.* E+-lain yo%r ste-s* Co.-are with Ta:le #5!and E+a.-le #*1*

#5$* Classify soils 1, $, and # in E+a.-le #*1 a((ording to the AAHT8oil Classifi(ation yste.* Co.-are with Ta:le #5! and E+a.-le #*$*

#5#* iven the grain si&e distri:%tion (%rves of Pro:le. $5## and theAtter:erg li.1ts data of Pro:le. $5#, (lass1f y s1ls A thro%gh %singthe %ses and AAHT8 soil (lassifi(ation syste.s*

#52* or the data :elow, (lassif y the soils a((ording to the UC*

aB 00 .aterial -assed No* 2sieve, $] retained on No*$ sieve*ines e+hi:ited 9Gedi%. to low -lasti(ity*'ilatan(y5 none to very slow*& strength5 .edi%. to high*

:B "] .aterial retained on No* 2 sieve, #$] .aterialretained on No* $ sieve*G / #, ce l *

!$



Pro#lea

eB l ] -assed No* 2 sieve,] -assed No* $ sieve*'ry strength5low to.edi%.* 'ilatan(y5.oderately F%i(<* LL / $#,PL / 1!*

eB 1] .aterial -assed No* 2

73

dB ] retained on No* 2 sieve,!] -assed No* 2 and reDtained on No* $ sieve*

ines e+hi:ited low -lasti(ityand high dilatan(y

fB 6].aterial -assed No* 2

sieve, $] retained on No*$ sieve*ines e+hi:it high -lasti(ity*'ilatan(y5 none*'ry strength5 high*

gB ] .aterial retained on No* 2 sieve, !] -assed No* 2 sieve and retained on No* $ sieve*ines e+hi:ited .edi%. dry

strength, .edi%.to%ghness* 'ilatan(y5none*LL $, PL 1*

sieve, and retained on No*$ sieve*C*, #, Ce l *1] -assed No* $sieve* ines e+hi:ited highdilatan(y*

hB !] .aterial retained on No* 2 sieve, $!] retainedon No* $ sieve*5,, - , ce 5 1**

#D* or the soils of Pro:le. # 2, esti.ate the (o.-ressi:ility, -er.ea:ilD ity,and to%ghness*

#5"* rain si&e distri:%tions and Atter:erg li.its are given for 1" soils inthe si+ gra-hs (o.-rising ig* P#*"* Classif y the soils a((ording to aBUC and :B AAHT8 syste.s* Ali data fro. UAEWE, 16"*B



;1< .S. S46n=6= >2515 >25# D2n. %3. " %3. 0 %3. "0 %3. $

! 2n.'-..&&-B,,,B--& VB-&--$&.&-&--&--$--i-$BB,,,B,!!, ........&.....--&.&..&&&.B,B,,..--&---&--..&&.&.-$$&-$-..--$---&

90 ,11'1 ******* 55

1

1 *******K ,11

.U

en 9r5# 9r $.

.3

..1 1 * 9

?e9';*;*:*?'

I

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55`55U5

1

D5 555 555555555555555

1 3 1 U

55555`5 5515555501 55555 3 55I ........... ...... --.. X

00 0 .0 0. 0.0 0.00

(62n >25

COBBLES

G! A2E S(%

*ine Coare 3ed1u *=ne&I T O! CA )

CG15 19 n23 2n5 >6n=; n3nNl6>42.

CG15 $9

CG15 #9

P33l 6=5= 615ll >6n= 2Y4G5; n3nNl6>42. ANN3Y2645l !]2n5> 65> 42> 6 J3=5l2n5 >32l, >J3l SP-SM.C36>5 43 5=2G >6n=; n3nNl6>42. ANN362n Gn23 6=6423n.

* .S. S46n=6= >2515 >25# *2 ,n* %3. " %3. 0 %3. "0

'2

%3. *00

?E'

555555r551

4 "0;.;.:. !0 2---..----------P----2---------P-------L------ ---- --------

e9

?**'* *0o=**3

U 1 1 1 9 U

13

000 .0

(62n >5

6 ( + * &ANO&T O A CA )

Coare *ine Coar&e 3ed1u *ine

CG15 19 O6n2 l6 42=6l l64>; LL/9), PI/!9.CG15 *: Al6l2 l6 D24 36n2 6445; LL-, PI *.CG15 !: O6n2 >2l4; LL/0, PI/!! n64G6l D645 3n45n4; LL/)!, PI/9 315n =25=.

*ig. P%" 6

74

200

1

13

-5

5t5D5e9

1

1 1



#B U** t*ndard sieve si&e No * 2 No* 2 No* $

****

11

?E' 7 1

**** 1 1 U !

1**e " ---------

Xj 51555555555==D55

!: ?5*e,*K

2?e9'5

1 $ **

*** #1

?' $

'a ?*' 1 =5

1 ----1

3 1 1 1* *1 *1 *1

rain si&e .rn B

A AME L SHN> COBBLES I LT 8R CLA

Coa ne f i ne Coarse M5=2G $2n5

C% rve 1 9 Clayey sand@ LL$#, PI 1* Poorly graded .i+t%re of sand5(lay and f .e slity sand*C% rve $9 Li.ero(< and sand .i+t%re@ L L$#, P17* Poorly graded*

2B ** tandard sieve s;&e

%3 0 %3 "0

62?E' 7

$... !

**e "!: *e,*K

2e=93

1

1

1 1 ¡

.*;**:

# 5DD5D5555t55555 -P--- :-5555t55

?'D$

a?*' 1

1 1 1 1

1 9 1 1

3 -,I---------- .1..!!.G...1...500I... ...--..._G.G.G.I...I..G-------- ....I<......-.........-.J.....K=-.--_.L...-

1 1 1* *1 *1 *1ra;n si&e ..B

@MHV SA%OCORB4 ES I LT 8R CLA

Coarse A 2n5 C36>5 M5=2G $2n5

C% rve 1 9 1l ty gravelry sano@ non -lastt(* G,(a(eo%s slit sta:li1&ed w1th sandy (hert gravel*C% rve $D Gi +t%re of gravel 5sand and fine sil ty sand@ non-lasti(* Poorly graded .i+t%re@ note

a:sen(e of (oa rse and .edi%. sand*C%rve #9 ilty f i ne sand@ L L$$, Pl*

$2. P!- C3n42nG6=.

7+

:1 1

1

?

e9



SANOSILT OR CLA Y

)

" 1n*

U ** tandard sieve si&e

l',@, " l' 6. 0

?E' E

(9n 5D*@

*et 2e;*;*:* #I $a=*3

1o

1 1 1*8 *1rai n si&e .. B

*1 *1

CO,,E&

C%rve 19 Pit r%n gravel@ non-lasti(@ wel l graded@ s.all -er(entage of f i nes*C% rve $9 andy gravel@ non-lasti(@ no f i nes*

;6< U** tandard sieve si&e

1 # i n* Ui n* No* 2 No* 1 N o* 2 No* $

6??'' 7E

E ! E

" '-D*@

*e

... 2=e3 1

;;: K L 3e B; ?5***3 D=3 $a?*' $ Q D

***

1 1* *1 *1 *1rai n si&e .. B

(A A VEL SA%O

CO,,E&SILT OA CLA 7

Coere *ine Coare 3ed=u *ine

C tJ r*e 1 9 Clayey silt@ :: +6= PI 1"C% rve $9 Unifor. sandy silt@ LL 5 #, PI #*C%rve #9 andy si lt@ L L #2, PI #eneral9 Note (%rves $ and # have a:o%t the sa.e -lasti(ity :%t vary i n grain si&e dist ri :%tion*

*ig. P%" 6 Continuad.

71

# D

e

=3

e,,

,

o



ur

la@ 3ineral§and 7oil7tructure

+.1 INT!O('CTION

At this stage it is %sef %l to again define the terrn e/ay. Clay (an refer to s-e(ifi( rninerals s%(h as <aolinite or illite, as are dis(%ssed in detail in

v ineerin * el of ten rneans a e/a soil5asoil whi(h (ontains sorne (lay .inerals as well a

.

s other

.

.iner

.

al (on5

indi(ated in Cha-ter $ Ta:le $5$B, :%t not. ali fin. e5grained . soils are

silt grains, li<e (lays, are invisi:le to the na<ed eye, :%t silts are non(ohe siveand non-lasti(* Ro(< flo%r is another e+a.-le of a very fine5grained(ohesionless soil*

Also re.e.:er that (ertain (hara(teristi(s of gran%lar soils s%(h asthe grain si&e distri:%tion and the grain sha-e affe(t the engineering

:ehavior of these soils* 8n the other hand, the -resen(e of water, with a

(ontrast, for (lay soils the grain si&e distri:%tion has relatively little

infl%en(e on the engineering :ehavior, :%t water .ar<edly affe(ts their :ehavior* ilts are an =in :etween= .aterial* Water affe(ts their :ehavior 5they are dilatant5yet they have little or no -lasti(ity PI 3*99999 8B, and their strengths, li<e sands, are essentially inde-endent of water (ontent*

As we indi(ate in this (ha-ter, (lay rninerals are very srnall -arti(leswhi(h are very a(tive ele(tro(he.i(ally* Toe -resen(e of even a s.alla.o%nt of (lay .inerals in a soil .ass (an .ar<edly affe(t the engineering

D-ro-erties of that .ass* As the arno%nt of (lay in(reases, the :ehavior of the soil is in(reasingly governed :y the -ro-erties of the (lay* When the(lay (ontent is a:o%t ], the sand and silt grains are essentially floatingD h v little effe(t on the en ineerin :ehavior*

!!

,. j



!7 Cl6 M2n56l 6n= S3ll S4G4G5

In this (ha-ter, we :riefly des(ri:e the i.-ortant (lay rninerals, howthey are identified, and how they intera(t with water and with ea(h other*We also*des(ri:e sorne of the latest thin<ing a:o%t soil fa:ri( and str%(5t%t e, (on(e-ts whi(h are f%nda.entally i.-ortant for a good %nderstanding of (ohesive soil :ehavior* inally, (ohesionless soil str%(t%res and the(on(e-t of relative density are dis(%ssed*

8nly one new sy.:ol is introd%(ed in this (ha-ter*

y.hoJ 'i.ension J Init 'efinitinn

]B Relative density or density inde+

".* CLA7 MI%ERALS

Clay 8inerals are very tiny (rystalline s%:stan(es evolved -ri.arilyfro. (he.i(al weathering of (ertain ro(<5for.ing .inerals* Che.i(ally,they are hydrous alu8inosilicates -l%s other .etalli( ions* Ali (lay .ineralsare very s.all, (olloidal5si&ed (rystals dia.eter less than l *.B@ Dand they(an only :e seen w1th an ele(tron .1(ros(o-e* he .d1v1d%al (rystals Ioo< li<e tiny -lates or fla<es, and fro. S5ray diffra(tion st%dies s(ientists havedeter.ined that these fla<es (onsist of .any (rystal sheets whi(h have a

re-eating ato.i( str%(t%re* In fa(t, there are only two f%nda.ental((ysta*l sheets, the tetrahedral or silica , and the octahedral or alu8ina ,

sheets* Toe -arti(%lar way in whi(h these sheets are stae<ed, together ll'24ll different :onding and dif ferent .etalli( ions in the (rystal latti(e,(onstit%te the diffe1enl (lay .ineials*

The tetrahedral sheet is :asi(ally a (o.:ination of sili(a tetrahedral%.ts wfO(h (onsist of fo%r o+ygen ato.s at the (orners, s%rro%nding asin gle sili(on ato.* ig%re 2*1a shows a single sili(a tetrahedron@ ig* 2*1:shows how the o+ygen ato.s at the :ase of ea(h tetrahedron are (o.:inedto forro a sheet strn(t%re The o+ygens at the :ases of ea(h tetrahedron arein one -lane, and the %n0oined o+ygen (orners all -oint in the sa.edireetion* A eo..on se*he.ati( re-1esentation 3 the tetrahedral sheetwhi(h is %sed later is shown in ig* 2* l(* A to- view of the sili(a sheetshowing how the o+ygen ato.s at the :ase of ea(h tetrahedron :elong totwo tetrahedrons and how ad0a(ent sili(on ato.s are :onded is shown in1g* 2* ld* Note the he+agonal =holes= in the sheet*

The o(tahedral sheet is :asi(ally a (o.:ination of o(tahedral %nits(onsisting of si+ o+ygen or hydro+yls en(losing an al%.in%., .agnesi%.,irno, or other ato.* 2 single o(tahedron is shown in ig* 2*$a, while ig*2*$: shows how the o(tahedrons (o.:ine to for. a sheet str%(t%re* Toerows of o+ygens 0 hyd1+yls in the sheet ate in two -lanes* ig%1e 2*$( is



DDD 55555D55D5555555

6 J

@ 6n= 8 6n= e S2l23n>

()

8 OY5n> 2n Nl6n5 6J315 >23n>

S2l23n>

OY5n> l2n5= 43 3 n54D3

OG4l2n5 3 J6>5> 3 >2l26

45465=6

OG4l2n5 3 5Y63n6l >2l26 n54D3

4D3 =25n>23n6l; 6l>3 2n=2645>J3n=> 3 2 . 2 J3n= 3 56 >2l23n 2> N5N5n=2Gl6 43Nl6n5 3 N6N5

()

$2. 2*1 6 S2nl5 >2l26 45465=3n 645 (2, 166B* J l>3542 125D 3 45 45465=6l 3 >2l26 >554 645 (2, 166B* 5S5642 5N5>5n46423n 3 45 >2l26 >554 645 L6J5, 16#B* =T3N 125D 3 45 >2l26 >554 645 W6>6D 6n= R3, 16"1B*

a s(he.ati( re-resentation of the o(tahedral sheet whi(h we %se later* or a to- view of the o(tahedral sheet showing how the different ato.s are

shared and :onded see ig* 2*$d*%:stit%tion of diff erent (ations in th( o(tahedral sheet is rather

(o..on and leads to different (lay .inerals* in(e the ions s%:stit%ted are a--ro+iro a tely the sa.e -:ysi(al si&e, sn(h s%hstitntioo is (alled

!%".!' phous. o.eti.es not ali theB o(tahedrons (ontain a (ation, whi(h res%lts ina so. eD hat different erystalline str%et%re with slightly different -hysieal -ro-erties and a diff erent (lay .ineral* I all the anions of the o(tahedralsheet are hydro+yls and two5thirds of the (ation -ositions are filled withal%.in%., then the .ineral is (alled gibbsite. I .agnesi%. is s%:stit%ted

79



Al Al

48 ClB Nlneral and &oll &tructure

8 6n= 1 ) / H=3Yl> 3 AlG2nGn:>, 6n5>2G>,

54. 3Y5n>

;.<. H=3Yl> 2n GNN5 Nl6n5

AlG2nG>

0 V66n4 3465=6l N3>2423n> D3Gl= J5 2ll5= 2n JG245 65

m H=3Yl> 2n l3D5 Nl6n5

OG4l2n5 3 43>5 65> 3 -6lG2n6 3465=6 66ll5l

43 l3D5 Nl6n5 3 =3Y l>

OG4l 2n5 3 43>5 65> 3 ---166n4 3465=6 N66ll5l

43 l3D5 Nl6n5 3 =3Yl>

B3n=> 3 6lG2nG> 43J=3Yl> 3 566lG2nG

$2. ".* 6 S2nl5 6lG2nG 3 6n5>2G 3465=3n 645 (2,9)9. J l>3542 125D 3 45 3465=6l >554 645 (2, 9)9.

5 S5642 5N5>5n46423n 3 45 3465=6l 3 6lG2n6 3 6n5>26 >554 645 L6J5, 9)!. = T3N 125D 3 45 3465=6l>554 645 W6>6D 6n= R3, 9.

for t:e a B% .in %. in the sheet and it fills all the (ation -ositions, thenthe .ineral is (alled brucite. The variations in the :asi( sheet str%(t%resrna<e %- the do&ens of (lay .inerals whi(h have :een identified* All(lay rninerals (onsist of the two :asi( sheets whi(h are sta(<ed together in(ertain %niF%e ways and w1th (ertain (ations -i esent in the o(tahedral andtetrahedral sheets* or engineering -%r-oses it is %s%ally s%ffi(ient todes(ri:e only a few of the .ore (o.rnon (lay .inerals wht(h are fo%nd in

(lay soils*



+. Cla@ 3lnerala 41

AlS2

?55 5 55 55555 1 5 ZO. * o.

$2. ".! S5642 =2663 45 >4G4G5 3 63l2n245645 L6J5, 9)!.

C9*** J l11

1

Kaolinite (onsists :asi(ally of re-eating layers of one tetrahedralsili(aB sheet and one o(tahedral al%.ina or gi::siteB sheet* 4e(a%se of thesta(<ing of one layer of ea(h of the two :asi( sheets, <aolinite is (alled a19 l (lay ro.eral 1g* 2*#B* The two sheets at e held t%getltet in s%(h a waythat the ti-s of the sili(a sheet and one of the layers of the o(tahedral sheetfor. a single layer, as shown in ig* 2*2* This layer is a:o%t *!$ n. thi(<

OY5n>

AlG2nG>

e 0S2l23n>

$. 4.4 A432:: >4G::4G5 3 63l2n245 ;afte (3 9)9



82 Cla@ 3lneral and &oll &1ructure

$2. ".) S6nn2n 5l543n236N 3 6 D5ll->46ll25=63l2n245 3 (5326. T5l5n4 3 45 l24 J6 2> ) [N3436N J R. &. H3l4.

and e+tends indefinitely in the other two dire(tions* A <aolinite (rystal,then, (onsists of a sta(< of several layers of the :asi( *!$ n. layer*%((essive layers of the :asi( layer are held together :y hydrogen :onds

:etween the hydw+yls %f the %(tahedial sheet and the o+ygens of thetetrahedral sheet* in(e the hydrogen :ond is very strong, it -reventshydration and allows the layers to sta(< %- to .a<e a rather large (rystal*A ty-i(al <aolin (rystal (an :e ! to 00 layers th(<* ig%re 2* is as(anning ele(tron .i(rogra-h EGB of <aolinite*

/aolinite is the -ri.ary (onstit%ent in (hina (lay@ it is also %sed inthe -a-er, -aint, and -har.a(e%ti(al ind%stries* or e+a.-le, as a -har.a(e%ti(al it is %sed in /ao-e(tate and Rolaids*

Another 191 .ineral *related to <aolinite is halloysite. l4 differs fro.<aolinite in that when it was for.ed it so.ehow :e(a.e hydrated :etweent:e layers, (a%sing a distortion or rando. sta(<ing in the (rystal latti(e sothat it is t%:%lar in sha-e ig* 2*"B* The water (an easily J5 driven o%tfro. :etween the layers :y heating or even air drying, and the -ro(ess isirreversi:le* That is, the halloysite will not rehydrate when water is added*Halloys1te, aitho%gh not very (o..on, o((asionally -lays an i.-ortant

T5 l5n4 3 45 U24 J6 2> ) [N3436N J R* &. H3l4.



4.2 Cla 3inarai 83

engineering role* Classifi(ation and (o.-a(tion tests .ade on air5driedsa.-les (an give .ar<edly differen t res%lts tha n tests ao sarn- les at their nat%ral water (ontent* I the soil will not :e air dried in the field, it (an :ee+tre.ely i.-ortant that la:oratory tests :e (arried o%t at the field water (ontents so that the res%lts will have sorne validity*

" ont8orillonite , also so.eti.es (alled s8ectite , is an i.-ortant.ineral (o.-osed of two sili(a sheets and one al%.ina gi::siteB sheetig* 2*!B* Th%s .ont.onllo.te 1s (alled a $9 ro.eral* fhe o(tahedralsheet is :etweeo the two sili(a sheets with the ti-s of the tetrahedrons(o.:ining with the hydro+yls of the o(tahedral sheet to for. a singleBa yer, as s:owo in Eig 2 7 Ihe t:i(<oess af ea(: $D Bayer is a:o%t 8 6"

n., and Ji<e <aolinite the layers e+tend indefinitely in the other twodireetions* 4eea%se the :onding :y *an der Waals3 forees :et ween the to-sof the sili(a sheets is wea< and there is a net negative (harge defi(ien(y inthe o(tahedral sheet, water and e+(hangea:le ions (an enter and se-arate

e+(hangea:le (at ions U 55W:://///////:::: tS2 1

Al 0.9 n

S2

U****9555*55!1

1

1

$2. ". S5642 =266 3 45 >4G4G5 3 3n432ll3n245645 L6J5. 9)!.

n H $ la yers a



---- -- 55DD5D5555555555D. . 5D5555D55555

84

Cla@ 3inarai and &oll &trueture

nH$

O l65> 6n= 5Y6n56Jl5 6423n>

@ OY5n> b H=3Yl> AlG2nG, 23n, 6n5>2G

8 6n= e S2l23n, 36>23n6ll 6lG2nG

$2. ".8 A432 >4G4G5 3 3n432ll3n245 645 (2, 9)9.

the layers* Th%s .ont.orillonite (rystals (an :e very s.all ig* 2*6B, :%tat the sarne ti.e they have a very strong attra(tion for water* oils(ontaining rnont.orillonite are very s%s(e-ti:le to swelling as they (hangein(reaseB water (ontent, and the swelling -ress%res develo-ed (an easilyda.age light str%(t%res and highway -ave.ents* Gont.orillonite is alsothe -ri.ary (onstit%ent in drilling .%d and <itty litter, and it has .any



4.2 Cla@ 3lneral85

$2. ".9 S6nn2n 5l543n236N 3 %6-3n432ll3n2453 W32n. T5 45n4 3 45

l24 J6 2> [ N3436NJ R. &. 3 .

other i.-ortant ind%strial and -har.a(e%ti(al a--li(ations* It is even %sed

6llite , dis(overed :y Prof* R* E* ri. of the University of Illinois, isanother i.-ortant (onstit%ent o e ay soi s* a sosi.ilar to .ont.orillonite, :%t the interlayers are :onded together with a -otassi%. ato.* Re.e.:er the he+agonal hole in the sili(a sheet ig*

D D ter so that a otassi%. ato. 0%st fills that he+agonal hole and rather strongly :onds the layers together

. . .

al%.ini%. for sili(on in the sili(a sheet*Illites have a (rysta str%(t%re s1I'1 ar o e .i(a

less otassi%rn and less iso.or-ho%s s%:stit%tion@ th%s they are (he.i(ally .%(h .ore a(tive than the other .i(as* ig%re 2*11 is a EG of illite*

D rnade of re eatin la ers of a sili(a sheet, an al%.ina sheet, another sili(a, and then either a

gi::site or r% 2Chlorite (an also have (onsidera:le iso.or-ho%s s%:stit%tion and :e.issing an o((asional :r%(1te or g1 s1te ayer@ %s i .ay s%sto swellin :e(a%se water (an enter :etween the sheets* enerally, how5 ever, it is signifi(antly less a(tive than .ontrnorillonite*

As .entioned -revio%sly, there are literally do&ens of (lay .inerals,with virt%ally every (on(eiva:le (o.:ination of s%:stit%ted ions, interlayer water, and e+(hangea:le (ations* orne of the .ore i.-ortant fro. anengineering view-oint in(l%de ver8iculite, whi(h is si.ilar to .ontrnorillonite, a $9 1 .ineral, :%t it has only two interlayers of water* Af ter it isdried at high te.-erat%re, whi(h re.oves the interlayer water, 33e+-anded=ver.i(%lite .a<es an e+(ellent ins%lation .aterial* Another (lay .ineral,attapulgite, ig* 2*1#, does not have a sheet str%(t%re :%t is a (hain sili(ate@it (onseF%ently has a needle or rodli<e a--earan(e* "ied5layer .inerals

.¡

. .



<

K ,

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3C##.## ,, J

$2. ".O S5642 =266 3 2ll245 645 L6J5, 9)!.

$2. ". S6nn2n 5l543n236N 3 2ll245 3 $2426n.lll2n32>. T5 l5n4 3 45l2 4 .

:y R. '* H3l4.

88



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r/ite

te 4ars o3 li$t is ;. ^85oto$ra5 47 6. ?. Wolt).

E " * S5642H:: c266 3 5l3245 625, M245ll, 9.



77 Cl6 Mln56l> 6n= S3ll S4G4G5

are relatively (o..on@ they wo%ld in(l%de, for e+a.-le, .ont.orillonite.i+ed with (hlorite or illite* 4e(a%se al/ophane is an al%.ino5sili(ate, it isof ten (lassified as a (lay .ineral* However, it is a8orphous, whi(h .eansit has no reg%lar (rystalline str%(t%re* Under s-e(iali&ed (onditions of weathering, it .ay :e a lo(ally i.-ortant (onstit%ent of (lay soils*

".! I&E%TI$ICATIO% O$CLA7 MI%ERALS

in(e the (lay .inerals are so very s.all, their 1dentih(ation :y the

%s%al o-ti(a l roioeralagi(aB te(hniF%es %sed in geology is not -ossi:le soother .eans .%st :e e.-loyed to identify the.* ro. yo%r engineering.aterials (o%rses, yo% .ay re.e.:er that .aterials with reg%lar or re-eating -atterns of (rystal str%(t%re will diffra(t S5rays* 'iff erent .iner5als w1th d1fferent (rystalhne str%(t%res will have different V 5,ay di@f,action

-atterns, and in fa(t these different -atterns were how the .inerals wereidentified in the first -la(e* The -atterns for the (o..on ..erals are -%:lished, and it is relatively si.-le to (o.-are the diffra(tion -atte. of yo%r %n<nown with the -atterns of <nown .inerals* There is a -ro:le.,however, with soils whi(h are .i+t%res of (lay .inerals, soils whi(h(ontain organi(s and other non5(lay .ineral (onstit%ents, and soils with .i+ed5

layer .inerals* Us%ally a detailed F%antitative analysis is i.-ossi:le5a:o%t all that one (an tell is whi(h .inerals are -resent and ro%ghlyhow .%(h of ea(h*

Another te(hniF%e that is so.eti.es %sed to identify (lay .inerals isdifferential ther8al analysis 'TAB* A s-e(i.en of the %n<nown soil alongw1th an .ert (ontrol s%:stan(e is (ontin %o%sl9y heated to several h%ndreddegrees in an ele(tri( f%rna(e, and (ertain (hanges in te.-erat%re o((%r

:e(a%se of the -arti(%lar str%(t%re of the (lay .inerals* The (hanges o((%r at s-e(ifi( te.-erat%res for s-e(ifi( .inerals, and the re(ord of these(hanges .ay :e (o.-ared with those of <nown .inerals* E,3ect,on 8icroscopy , :oth trans.ission aod s(a ooing, (an :e %sed toidentif y (lay .inerals in a soil sa.-le, :%t the -ro(ess is not easy andQor

F%antitative* DA si.-le a--roa(h s%ggested :y Prof* Casagrande is to %se theAtter:erg li.its* l4 was .entioned e(* $*7B that the a(tivity has :eenrelated to s-e(ifi( a(tive or ina(tive (lays* Gont.orillonites will :ehighly a(tive sin(e they are very s.all and have large -lasti(ity indi(es*Use of Casagrande3s -lasti(ity (hart ig* #*$B (an also tell yo% 0%sta:o%t as .%(h, at least fro. an engineering -oint of view, as the .oreso-histi(ated diffra(tion and 'TA analyses* Toe -ro(ed%re is shown inig* 2*12* o%si.-ly lo(ate yo%r sa.-le on the LL5PI (hart, and (o.-are its lo(ation



4.4 SN5ll SG465 89

"

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5o*e

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#,

M3n432ll3n245>

6?:' $

1

3 . . ------*----- ,--.& ---...G&_ P

8 1 $ # 2 " ! 7 6 1Cl3245>

L2FG2= l224

$2. "." L36423n 3 33n l6 2n56l> 3n C6>66n=5'>!l6>42>24 >64 54515l5!554 5 C6>66n545, 9"8, 6n54 5l646 2n

M245ll, 9.

with those of <nown .inerals* l yo%r sa.-le has Atter:erg li.its that -lothigh a:ove the A5line near the U5line, then (han(es are that it (ontains alot of a(tive (lay .inerals s%(h as .ont.orillonite* Even 2 the soil is(lassified as a CL, for e+a.-le a sandy (lay CLB, and still -lots near the U5line, the (lay -ortion of the soil is -redo.inantly .ont.orillonite* Toegla(ial la<e (lays fro. aro%nd the reat La<es region 2n the United tatesand Canada are -redo.inantly illiti( and they -lot right a:ove the A5line*(andinavian .arine (lays whi(h are illiti( also -lot in this region*/aolinites, whi(h are relatively ina(tive .inerals, -lot right :elow the A5line* Even tho%gh they are te(hni(ally (lays, they :ehave li<e GL5GH.aterials*

"." SPECI$IC SR$ACE

pecific sur@ace is the ratio of the s%rfa(e area of a .aterial to eitherits .ass or vol%.e* In ter.s of vol%.e

s-e(ifi( s%rfa(e / s%rfa(e areaQvol%.e 251B

2



8 Cla@ 3lnerala and &oll &tructure

The -hysi(99*1 signifi(an(e of s-e(ifi( s%rfa(e (an :e de.onstrated%sing a 1 + 1 + 1 (. (%:e*

"1 (. Bs-e(ifi( s%rfa(e / / "Q(. / *"Q..

1 (.#

l the (%:e is 1 .. on a side, the s-e(ifi( s%rfa(e wo%ld :e

"1 ..$ B / "Q..l#

l the (%:e is 1 ." on a side, the s-e(ifi( s%rfa(e wo%ld :e

"1 ,,.$ B

*.# / "Q ." - "Q This ill%strates that large -arti(les, whether (%:es or s1I -arh(les, haves.aller s%rfa(e areas -er %nit of vol%.e and th%s s.aller s-e(ifi( s%rfa(esthan s.all -arti(les* To o:tain the s-e(ifi( s%rfa(e 2n ter.s of .ass, yo% 0%st divide the val%e in ter.s of vol%.e :y the .ass density ps4 %nits wo%ldthen :e .$

Q g or .$Q<g* Now, if s%ffi(ient water was -resent to 0%st ^la.-en the s%rfa(e area

of the (%:es in the aoove e+a.-le, it wo%ld ta<e ten ti.es as .%(h water to wet the s%rfa(e of all the grains when the (%:es were 1 .. on a sidethan when the sa.e vol%.e o((%-ied a single (%:e of l (.# Note alsothat if one were trying to re.ove water fro. the s%rfa(e wet soil, there

wo%ld :e ten ti.es as .%(h water to re.ove fro. the s.aller grains* -e(ifi( s%rfa(e is inversely -ro-ortional to the grain si&e of a soil*We generally do not (o.-%te the s-e(ifi( s%rfa(e for -ra(ti(a(ases sin(etheD soil grains are too irreg%lar in sha-e to do so* 4%t it sho%ld :e (lear that a soil .ass .ade %- of .any s.all -arti(les will have on the average alarger s-e(ifi( s%rf a(e than the sa.e .ass .ade %- of large -artides*

ro. the (on(e-t of s-e(ifi( s%rfa(e, we wo%ld e+-e(t larger .ois t%re(ontents for fine5grained soils than for (oarse5grained soils, all other thingss%(h as void ratio and soil str%(t%re :eing eF%al*

o% .ay re(all fro. yo%r .aterials (o%rses that s-e(ifi( s%rfa(e is a -ri.ary fa(tor in (on(rete and as-halt .i+ design* In :oth (ases it isne(essary to -rovide s%ffi(ient (e.ent -aste or as-halt D to (oat the aggre

gate s%rfa(es*

+.7 INTE!ACTION ,ETJEEN JATE!

ANO CA) 3INE!AK

As .entioned -revio%sly, water %s%ally doesn3t have .%(h effe(t onthe :ehavior of gran%lar soils* or e+a.-le, the shear strength of a sand isa--ro+i.ately the sa.e whether it is dry or sat%rated* An i.-ortant



2* lnteractlon ,etLeen Jater ancl Cla@ 3lneral 11

e+(e-tion to this fa(t is the (ase of water -resent in loose de-osits of sand

s%:0e(ted to dyna.i( loadings s%(h as earthF%a<es or :lasts*8n the other hand, fine5grained soils, es-e(ially (lay soils, are strongly

infl%en(ed :y the -resen(e of water* Toe variation of water (ontent givesrise to -lasti(ity, and the Atter:erg li.its are an indi(ation of this in fl%en(e*rain si&e distri:%tion only rarely is a governing fa(tor in the :ehavior of fine grained soils*

Why is water i.-ortant in fine5grained soils Re(all the dis(%ssion of s-e(ifi( s%rfa(e, in the -revio%s se(tion, where the s.aller 1he -arti(le, thelarger the s-e(ifi( s%rfa(e* Clay .inerals, :eing relatively s.all -arti(les,h1ve large s-e(ifi( s%rfa(es, and everything else :eing eF%al, yo% .ighte+-e(t tha t they wo%ld have very a(tive s%rfa(es*

The relative si&es of fo%r (o..on (lay rninerals and their s-e(ifi(s%rf a(es are shown in ig* 2*1* /aolinite, the largest (lay .ineral* has a

TN26lT2n5>>

TN26l&26545

SN522SG 65

E=5 V5D n n $ Q

M3n432l l3n245 # 100-1000 0.8

ll245 30 10000 0.08

Cl3245 30 10000 0.08

K63l2n245 +0-2000 300-4000 0.01 +

$2. ".) A1565 16lG5> 3 5l64216 >25>, 42n5>>5>, 6n= >N522>G65> 3 45 33n l6 2n56l>645 73n 6n= W65n42n,9).

,. j



55555555555555555555555555555555555555

92 Cla@ 3ineral and &oll &tructure

thi(<ness or edge di.ension of a:o%t 1 ., while .ont.orillonite, thes.allest (lay .ineral, has a thi(<ness of only a few nanornetres* in(e the(rystals have ro%ghly the sa.e average =dia.eter,= at least within an order of .agnit%de, it is not s%r-rising that the s-e(ifi( s%rfa(es are se different*8f (o%rse, there are rather wide variations in the si&es of the (rystalsde-end.g on weathering and other fa(to+s, :%t the val%es given at eaverage val%es* in(e s%rfa(e a(tivity is related to the -arti(le si&e, yo% (ansee why rnont.orillonite, for e+arn-le, is .ore =a(tive= than <aolinite*i.ilarly, the s%rfa(e a(tivity of a sand or silt grain is -ra(ti(ally &ero*

In e(* $*7, we defined the activity of a (lay asPI

A (lay fra(tion $ $2B

where the (lay fra(tion is %s%ally ta<en as the -er(entage of the sa.-le lessthan $ rn <e.-ton, 16#B* W e rnentioned that there was a -retty good(orrelation :etween a(tivity and the ty-e of (lay .ineral* This (orrelationis shown in Ta:le 251*

Now, it see.s that (lay -arti(les are al.ost always liydrated innat%re@ that is, there are layers of water s%rro%nding ea(h (rystal of (lay*This water is (alled ads1bed ((e,. As dise%ssed in the ne+t se(tion, thestr%(t%re of (lay soils and th%s their engineering -ro-erties %lti.ately

de-end on the nat%re of tfOs adsor:ed water ayer*How is water adsor:ed on the s%rfa(e of a (lay -arti(le irst, yo%

rnay re(all frorn (hernistry or .aterials (o%rses that water is a dipolar

.ole(%le ig* 2*1"B* Even tho%gh water is ele(tri(ally ne%tral, it has twose-arate (enters of (harge, one -ositive and one negative* Th%s the water .ole(%le is ele(trostati(ally attra(ted to the s%rfa(e of the (lay (rystal*e(ondly, water is held to the (lay (rystal :y hydrogen bonding hydrogen

TA,E +"1 A42124,5> 3 V6n3G> M2n662>

A(tivit

Na5.ont.orillonite 4-7Ca5.ont.orillonite 1*Illite *51*#/aoliniteHalloysite dehydratedB *Halloys1te hydrat(dB *1Atta-%lgite *51*$

o- an(Gi(a .%s(ovit(B *$

%art& o

After <(.-ton 16#B and Git(hell 16!"B*



+.7 lnteractlon ,etLeen Jater and Cla@ 3lneral 93

$2. ". S5642 =2663 6 D645 3l5Gl5 645 L6J5,9)!.

of the water is attra(ted to the o+ygens or hydro+yls on the s%rfa(e of the(layB* The third fa(tor is that the negatively (harged (lay s%rfa(e alsoattra(ts (ations -resent in the water* in(e all (ations are hydrated to sornee+tent, de-ending on the ion, (ations also (ontri:%te to the attra(tion of water to the (lay s%rfa(e* 8f these three fa(tors, hydrogen :onding is -ro:a:ly the .ost i.-ortant fa(tor*

The attra(tion of water to the (lay s%rfa(e is very strong near thes%rfa(e and di.inishes with distan(e fro. that s%rfa(e* l4 see.s that thewater .ole(%les right at the s%rfa(e are very tightly held and stronglyoriented* Geas%re.ents show that sorne ther.odyna.i( and ele(tri(al

-ro-erties of the water ne+t to the (lay s%rfa(e are diff erent than that of =free water= Git(hell, 16!"B*

The so%r(e of the negative (harge at the s%rfa(e of the (lay (rystalres%lts fro. :oth iso.or-ho%s s%:stit%tion, .entioned earlier, and i.-er f e(tions in the (rystal latti(e, es-e(ially at the s%rfa(e* =4ro<en= edges

(ontri:%te grnatly to %nsatisf ied valen(e (harges at the edges of the (rystal*in(e the (rystal wants to :e ele(tri(ally ne%tral, (ations in the water .ay :e strongly attra(ted to the (lay, de-ending on the a.o%nt of neative(harge -resent* 'ifferent (lays have diff erent (harge defi(ien(ies and th%shave diff erent tenden(ies to attra(t the e+(hangea:le (ations* They are(alled echangeable sin(e one (ation (an easily :e e+(hanged with one of the sa.e valen(e or :y two of one5half the valen(e of the original (ation*As .ight :e e+-e(ted fro. their relative si&es and s-e(ifi( s%rfa(es,.ont.orillonite has a .%(h greater (harge def i(ien(y and th%s a .%(hgreater attra(tion for e+(hangea:le (ations than <aolinite* Illite and (hio riteare inter.ediate in this res-e(t*

Cal(i%. and .agnesi%. are the -redorninant e+(hangea:le (ations

in soils, whereas -otassi%. and so*di%. are less (o..on* Al%.ini%. andhydrogen are (o..on in a(idi( soils* The de-ositional environrnent aswell as s%:seF%ent weathering an- lea(hing will govern what ions are

-resent in a -arti(%lar soil de-osit* As .ight :e e+-e(ted, .arine (lays are-redaroioa tely sadi%ro aod .agnesin. sin(e these are the .ost (o..on(ations in sea water* Cation e+(hange or re-la(e.ent is f%rther (o. -li(ated :y the -resen(e of organi( .atter*

,* X



+ Cle 3lnerI -nd Soll &tructure

The ease of re-la(e.ent or e+(hange of (ations de-ends on severalfa(tors, -ri.arily the valen(e of the (ation* Higher valen(e (ations easilyre-la(e (ations of Iower valen(e* or 1ons of the sa.e valen(e, the si&e of the hydrated ion :e(o.es i.-ortant@ the larger the ion, the greater there-la(e.ent -ower* A f%rther (o.-li(ation is the fa(t that -otassi%., eventho%gh it is .onovalent, fits into the he+agonal holes in the sili(a sheet*Th%s it will :e very strongly held on the (lay s%rfa(e, and it will have agreater re-la(e.ent -owe1 than sodi%., for e+a.-le, whi(h is also .ono5valent* The (ations (an :e listed in approi8ate order of their re-la(e.enta:ility* The s-e(ifi( order de-ends on the ty-e of (lay, whi(h ion is :eingre-la(ed, and the (on(entration of the vario%s ions in the water* In order of in(reasing re-la(e.ent -ower the ions are

There are several -ra(ti(a (onseF%en(es of ion e+(hange* The %se of (he.i(als to sta:il;&e or strengthen soils is -ossi:le :e(a%se of ion e+(hange* or e+a.-le, li.e Ca8HB sta:ili&es a sodi%. (lay soil :y re5

-la(ing the sodi%. ions in the (lay sin(e (al(i%. has a greater re-la(ing -ower than sodi%.* The swelling of sodi%. .ont.orilloniti( (lays (an :esignif i(antly red%(ed :y the addition of li.e*

What ^loes a (lay -arti(le loo< li<e with adsor:ed water on it ig%re2*1! shows a sodi%. .ont.orillonite and <aolinite (rystal with layers of adsor:ed water* Note that the tht(<ness of the adso1:ed water is a-

-ro+irnately the sa.e, :%t :e(a%se of the si&e differen(es the .ont.orillonite will have .%(h greater a(tivity, higher -lasti(ity, and greater swelling, shrin<age, and vol%.e (hange d%e to loading*

In this se(tion only a :rief overview of the very (o.-le+ s%:0e(t of the intera(tion :etween wate1 and da9, .inerals has :een -resented or additional ;nfor.ation, yo% sho%ld (ons%lt ong and War<entin 16!Bari*d Gif(hell 16!"B and ref eren(es .(l%ded there.*

A=>3J5= D645

M3n432ll3n245>46l

$2. ". R5l64215 >25> 3 6=>3J5= D645 l65> 3n >3=2G3n432ll3n245 6n= >3=2G 63l2n245 645 L6J5, 9)86.



". I%TERACTIO% O$ CLA7 PARTICLES

The asso(tatlon of (lay rn.erals and their adsor:ed wa te9 layet -rovides the -hysi(al :asis for soil str%(t%re* The individ%al (lay -arti(lesintera(t thro%gh their adsor:ed water layers, and th%s the -resen(e of d1ff etent ions, organi( .aterials, diff erent (on(entrations, et(*, affe(t or (ontri:%te to the .%lti t%de of soil str%(t%res fo%nd in nat%ral soil de-osits*Clay -arti(les (an t e-%lse ea(h other eleetrostatieally, :%t the -ro(essde-ends on the ion (on(entration, inter-arti(le s-a(ing, an^l other fa(tors*i.ilarly, there (an :e attra(tion of the individ%al -arti(les d%e to thetenden(y for hydrogen :onding, van der Waals3 for(es, and other ty-s of (he.i(al and organi( :onds* Toe inter-arti(le for(e or -otential fieldsde(r ease w ith in(reasing distan(e fro. the .ineral s.fa(e, as shown inig* 2*17* The a(t%al sha-e of the -otential (%rve will de-end on thevalen(e and (on(entration of the dissolved ion and on the nat%re of the :onding for(s*

$2. ".8 C526l, 5l543>4642,54., N345n426l 15>G> =2>46n53 45 l6 2n56l >G65. &2>46n5

Parti(les (an flo((%late or :e re-elled dis-erse , se-arateB* lhey(an flo((%Xa te io several -ossi:le (onfig%rations@ edge5to5fa(e is the .ost(o..on, :%t edge5to5edge and fa(e5to5fa(e flo((%lation are also -ossi:le*Toe tenden(y towards flo((%lation will de-end on increasing one or .oreof the following La.:e, 167aB9

Con(entra tion of the ele(trolyte

Te.-erat%re

or decreasing one or .ore of the following9

'iele(tri( (onstant of the -ore fl%idS2.5 3 the hydrated ion

-HAnion a(lsor-tion



96 Cl6 Mln56l6 6n= S3ll S4G4G5

J%st a:o% t all na t . al (la9y soils are flo((%lated to so.e e+tent O3in very dil%te sol%tions at very high water (ontentB is dis-ersion of (lay

-arti(les -ossi:le, [nd this .ight o((%r in a sedi.entary de-osit d%ring

de-osition*

". SOIL STRCTRE A%O $ABRIC

In geote(hni(al engineering -ra(ti(e, the structure of a soil is ta<en to.ean :oth the geo.etri( arrange.ent of the -arti(les or .ineral grains aswell as the inter-arti(le for(es whi(h .ay a(t :etween the.* oil fabric

ref ers o%ly ta the geo.etri( arrange.ent of the -arti(les* In gran%lar or (ohesionless soils, the inter-arti(le for(es are very s.all, so :oth the fa:ri(and str%(t%re of gravels, sands, and to sorne e+tent silts are the sa.e* 8nthe (ontrary, however* in ter-arti(le for(es are relatively large in fine5grained(ohesive soils* and th %s :oth these for(es and the fa:ri( of s%(h soils .%st

:e (onsidered as the str%(t%re of t he soil* The str%(t%re strongly aff e(ts or,sorne wo%ld say, governs the engin(ering :ehav1r of a -arti(%lar soil* Allthe (lay str%(t%res fo%nd in nat%re and des(ri:ed in the ne+t se(tion res%ltfro. sorne (o.:ination of these fa(tors* the geologi( environ.ent atde-osi tion, the s%:seF%ent geologi( and engineering stress :ista(y, a nd thenat%re of the (lay . ineral* We st%dy these very (o.-li(ated fa(tors

:e(a%se they f %nda.entall y aff e(t soil :ehavi. and the engineering -ro-erties of soil* eote(hni(al engineers .%st (onsider the soil str%(t%re andfa:ri( at least F%alitatively when (ohesive soils are en(o%ntered in en5

gineering -ra(ti(e*A (o.-lete des(ri-tion of the str%(t%re of a fine5grained (ohesive soil

reF.res a <nowledge %f :oth the inter-arti(le for(es as well as thegeo.etri(al arrange.en t fa:ri(B of the -arti(les* in(e it is e+tre.elydif f i(%lt, if not i.-ossi:le, to dire(tly .eas%re the inter-arti(le for(e f ieldss%rro%nding (lay -arti(les, .ost st%dies of (ohesive soil str%(t%re involveonly the fa:ri( of these soils, and fro. the fa:ri( (ertain inf eren(es are.ade a:o%t the inter-arti(lb for(es*

".8 COHESIVE SOIL $ABRICS

Classifi(ation of (ohes1ve s.l f a:n(s into si.-le syste.s involv ing3n a few (lay -arti(les is not really -ossi:le* ingle grain or single

-arti(le %nits o((%r only rarely in nat%re and then in only very dtl%te (lay5water syste.s %nder s-e(ial environ.ental (onditions* ro. re(ent st%dies of real (lay soils with the s(anning ele(tron .i(ros(o-e EGB, the



--------------- -- D55D5D55555555555555

+.4 Cohel/e &oll *a#rica 97

individ%al (lay -arti(les see. to always :e aggregated or flo((%latedtogether in s%:.i(ros(o-i( fa:ri( %nits (alled do8ains. 'o.ains then int%rn gro%- together to for. clusters, whi(h are large eno%gh to :e seenwith a visi:le ig t .1(ros(o-e* %sters gro%- toget er to or. pe aneven gro%-s of -eds* Peds (an :e seen witho%t a .i(ros(o-e, and they andother .a(rostr%(t%ral f eat%res s%(h as 0oints and fiss%res (onstit%te the

and heeran 16!#B is shown in ig* 2*16@ a .i(ros(o-i( view of a .arine

so.ewhat .ore ela:orate syste. for des(ri:ing .i(rofa:ri( f eat%res in

ing defina:le -hysi(al :o%ndaries and a s-e(ifi( .e(hani(al f %n(5

tary -arti(le arrange.ents or s.aller -arti(le asse.:lages, andt ey are s own . 1g* *

#* Pore s aces within and :etween ele.en tary -arti(le arrange.ents

and -arti(le asse.:lages*

Collins and G(own 16!2B s ow rr%(ro- otogra- s o severa nat%rasoils whi(h ill%strate their ro osed s ste.*

A EG -hotogra-h of a silty (lay -ed fro. Norway is shown in ig*2*$$* Note how (o.-le+ the str%(t%re a--ears, whi(h s%ggests that theengineering :ehavior is also -ro:a:ly F%ite (o.-le+*

-osits, has an i.-ortant infl%en(e on soil :ehavior in engineering -ra(ti(e*Joints, f iss%res, silt and sand sea.s, root :oles, varves, and other **defe(ts=of ten (ontrol the en ineerin :ehavior of the entire soil .ass* Us%ally, thestrength of a soil .ass is signifi(antly less along a (ra(< or fiss%re than

thro%gh the inta(t .aterial, and th%s if the defe(t ha--ens to :e %nfavora :ly oriented with res-e(t to the a--lied engineering stresses, insta:ility or fail%re .ay o((%r* As another e+a.-le, the drainage of a (lay ayer (an :e.ar<edly aff e(ted :y the -resen(e of a silt or sand layer or sea.*ConseF%ently, in any engineering -ro:le. involving sta:ility, settle.ents,or drainage, the geote(hni(al engineer*.%st investigate (aref%lly the (lay.a(rostr%(t%re*

Gi(rostr%(t%re is .ore i.-ortant fro. a f%nda.ental than an engineering view-oint, altho%gh an %nderstanding of the .i(rostr%(t%re aids

*J



55****,,**,**,,,5555,55,,****,,**55*,,**55555555555555555555 5 5 * ** 5 ********



B

o8ai ns ane /sters w1t 8iro5ores

E n l arge.ent

$2. ".9 S5642 =266 3 45 >32l 236J2 6n= 636J2 >>45 N3N3>5= J 73n 6n= S556n 9! 6n= PG>9!: , =362n; *, lG>45; !, -ed@ ", >2l4 62n; ), 23N35; 6n=, 63N35.

..



+.4 Cohel/e &oll *a#rica 99

6

5

= 5

$2. ".*0 S5642 5N5>5n46423n> 3 5l55n46 N642l566n55n4>: 6 2n=212=G6l l6 Nl645l54 2n456423n; J 2n=212=G6l>2l4 3 >6n= N642l5 2n456423n; 5 l6 Nl645l54 3GN 2n456423n;= l345= >2l4 3 >6n= N642l5 2n456423n; 5 N64l =2>5n2Jl5N642l5 245 6423 645, C3ll2> 6= M(3D, 1 6!2B*

in a general t.derstanding of soil :eha v ior* The .i(1ostw(twe of a (layrefle(ts the entire geologi( and stress Khistory of that de-osit* Mirt%allyeverything that ever ha--ened to that soil wht(h w1ll aff e(t the eng.eenngres-onse of the (lay is i.-rinted in sorne .anner on the .i(rostr%(t%re*The .i(rostr%(t%re refle(ts the de-ositional history and environ.ent of thede-osit, its weathering histoty, :oth (he.i(al and -hysi(al D in effe(tits stress history, that is, ali (hages (a%sed :oth geologi(ally and :y .an*

R e(ent resear(h on (lay .i(rostr%(t%re s%ggests that the greatestsingle fa(tor infl%en(ing the final str%(t%re of a (lay is the ele(tro(he.i(alenv O on.en t e+isting al the ti.e of sedi.en tation* lo((%lated str%(t%resor aggregations (an res%lt d%ring sedi.entation in virt%ally all de-ositionalenv1ron.ents, whether .anne, :ra(<ish, or . fresh water* Toe degree of

.j



5D 55555555

,2 ---

S2l4 3 >6n=

54:B.,.Q uQ

6 J 5

g% * r65=4 1 ons

S2l4 3>6n=

= 656423n> 5 f B 9

1 n4:U QP=1 I n

:% ne l24':,

J*@5959, ,9, 5, /;W4F

$2. ".* S5642 5N5>53464233> ot N642l5 6>>5Jl65>: 6

J, 6n= 5 3nn543>; = 25Gl6 656423n> l2n5= J 3nn543 6>>5Jl65>; 5 25Gl6 656423n> 32n 6 3n53J66n55n4; .5Gl6 656423n> 2n45642n D24 >2l4 3 >6n=62n>; 5Gl6 656423n 2n45642n D24 N642l5 642Y; 2n45D5612n JGn5> 3 l6; 2 2n45D5612n JGn5> 3 l6 D24>2l4 2nlG>23n>; j l6 N642l5 642Y; 6nGl6 N642l5 642Y645 C3ll2n> 6n= M(3Dn 9".

1



4.8 C35>l15 S3ll $6Jl> 181

$2. ".** &65n >2l4 l6: l65 N5= 3 >2l4 6n= l6 D24 D56l2n> 43 345 N5=> 3 B6=5n 6n= M(3Dn, 9!;N3436N 3G45> 3 A. M(3Dn.

o-enness of the str%(t%re is a--arently infl%en(ed to a large degree :y the(lay .ineralogy as well as the a.o%nt and ang%larity of silt grains -resent* ilt -arti(les have :een o:served to have a thin s<in of a--arently stronglyorit.ted (lay -arti(les or even a.or-ho%s .aterials -arallel to their

s%rfa(es* orne grain5to5grain (ont^@15(ts of silt -arti(les have :een o:servedsee ig* 2*$#B, :%t at -resent it is diffi(%lt to as(ertain whether a(t%al.ineral (onta(t o((%rs in (lays*

In s%..ary, the str%(t%re of .ost nat%rally o((%rring (lay de-osits ishighly (o.-le+* The engineering :ehavior of these de-osits is stronglyinfl%en(ed :y :oth the .a(ro5 and the .i(rostr%(t%re* At -resent, noF%antitative (onne(tion e+ists :etween .i(rostr%(t%re and the engineering



-<

18Cla@ 3lneral and &oll &tructure

W 1 1

$2. ".*! SEM 3 >2l4 62n-436n 3n464 2n SD5=2> 42ll 3M(3Dn, 9!.

-ro-erties, :%t it is i.-ortant for the engineer to have an a--re(1ahon othe (o.-le+ity of the str%(t%re of (ohesive soils and their relation toengineering :ehavior*

+. COHE&ION

rains of soil whi(h (an settle o%t of a soil5fl%id s%s-ension inde-endently of other grains generally larger than 8*8 l to *$ ..B will for.what is (alled a single grained str%(t%re* This is the str%(t%re of, for e+a.-le, a sand or gravel -ile, and sorne sand5silt .i+t%res* The weight of t e gra.s (a%ses Dthe fl%id as soon as the velo(ity (an no longer s%--ort the -arti(les ins%s-ension*

'e-osition .edia in(l%de :oth air loess de-osits, sand d%nes@ grainsi&e generally * ..B and water rivers, :ea(hes, et(*B*

void ratio or low densityB or 3=dense= low void ratio or high densityB*'e-ending on the grain si&e distri:%tion as well as the -a(<ing or arrange.ent of the grains, a wide range of void ratios is -ossi:le* Ta:le 25$ listssorne ty-i(al val%es for a variety of gran%lar soils* lt is -ossi:le, %nder

r .aterial to a(hieve a honey5(o.:ed str%(t%re ig* 2*$B whi)h (an have a very high void ratio* %(h astr%(t%re is .eta5sta:le* Toe grain ar(hes (an s%--ort stati( loads, :%t the



555555DDD 5D5=5555DD5DDD555555555D555DD

+. Cohealonlea &oll *a#rica 18%

6 L33>5 J &5n>5

$2. ".*" S2nl5 62n5= >32l >4G4G5>.

str%(t%re is very sensitive to (olla-se when vi:rated or loaded dyna.i(ally*Toe -resen(e of water in very loose grain str%(t%res also (an alter their engineering :ehavior* Pheno.ena t y-i(al of loose grain str%(t%res, s%(h asbul!ing, a (a-illary -heno.enon, and Luic!sand are dis(%ssed in Cha-ters" and !*

The greatest -ossi:le void ratio or loosest -ossi:le (ondition of a soilis (alled the 8ai8u8 eoid ratio e6Y . l4 is deter.ined in the la:oratory

:y -o%ring dry sand very (aref %lly with no vi:ration into a (ali:rated.%id %f <n%wn v%l%.e* ro. the weight of sand in the .old, 56Y (an :e(al(%lated* i.ilarly, the 8ini8u8 void ratio 52n is the densest -ossi:le(ondition that a given soil (an attain* Toe val%e of 52n is deter.ined :y

vi:rating a <nown weight of dry sand into a <nown vol%.e and (al(%latingthe void ratio* Toe range of -ossi:le void ratios for sorne ty-i(al gran%larsoils are shown in Ta:le 25$*

The relative density ,, also (alled the density inde+ 6D, is %sed toeo.-are the *o;d ratio e of a gi*en soil w ith the .a+i.%. and .;ni.%.void ratios* Relative density is defined as

56Y 5e / 6D / + 1]B

r e 5 e25$B

and is %s%ally e+-ressed as a -er(entage* Relative density (an also :estated . ter.s of .a+i.%. and .;ni.%. dry densities as

1 + p * 1 % p D, / 6v / 'a , -., S 1]B 25#B

1Q Pd 8in 5 1QPd .a9s *

where pd dry density of the soil with void ratio e,

a .;ni.%. dry density of the soil with the 3 void ratio $"ax , andPd 6Y .a+i.%. dry density of the soil with the void ratio 5n

The relative density of a nat%ral soil de-osit very strongly affe(ts itsengineering :ehavior* ConseF%ently, it is i.-ortant to eond%et la:oratory



TA,E "-* Ty-i(al lnde+ Pro-erties for ran%lar oifs

Parti(le i&e and radation Moids

A--ro+* i&e A--ro+* *5--ro+* Range Moid Ratio 1orosity ]B

Range Dio e.a+ ein n ,,... n2n

'.a+ '.in HG looseB denseB l3oseB denseB55

l* Unifor. .aterials9aB EF%al s-heres

:B tandard 8ttawa sandeB Clean, %nifor. sand

fine or .edi%.BdB Unifor., inorgani( silt

$* Well5graded .aterials9aB ilty sand:B Clean, fine to (oarse sandeB Gi(a(eo%s sanddB ilty sand and graveB

Godified af ter 4* /* Ho%gh 16"6B, asl oils Engineering , m 16"6 :y the Ronald Press* Co* Re-rir ted

J -er.ission of John Wiley # ?ns, In(*

2 ' l 1 ''

- 55 55 1* *6$ *# 7 26

*72 *6 *"! 1*1 *7 * 44 ##

5 - - -- 1*$ to $* 1* *2 35

$6

* * *1$ 1*$ to $* 1*1 *2 $ $6

$* * *$ 43 1 *6 *# , ! $#

$* o*os *6 2 to " *6 *$ #9 1!

5 55D5 - - 1*$ *2 2 29

1 * *$ 1 to # *7 *12 9 1$

1

1



1

':)*+ "-* C3 42nG5= 'ensity GgQ.# Bt

'ry 'ensity, Pd Wet 'ensity, p %:.erged 'ensi , p

Gi * 1] Ga+* Gin* Ga+* Gin* G I+.

God*

looseB Pro(tor denseB looseB denseB looseB de9%eB

l* Unifor. .ated ls9aB EF%al s-heres

theorti(al lval%esB - 5 5 5 5 - - -

:B tandard 8tt1%wa sandeB Clean, %nifon : sand

fine or .ee i%.BdB Unifor., ino1 gani( silt

9* Well5graded .aterials9aB ilty sand:B Clean, fine to 5(o%rse sand

eB Gi(a(eo%s sa9ddB ilty sand an( gravel

f e a:%lation is :ase l4 on p, / $*" Gg Q. # G%lti-ly :y "$*2 t P o:tain l:f Qf t #

l *^ 6 5 l*!7 1*1 $*1$ *6# 1*1$

l*3 2 l*7" l*6$ 1*#! $*$ *7 %s1*9 6 5 l*6$ 1*#1 $*$ *7# l*17

l* l l*67 $*" 1*2# $*# *77 l*1$7

l. 7 $*12 $*$# l*2 $*#6 *7" l*11B

L # 5 1*6 1*$2 $*$# *!! 1*1$#

l*12 5 $*#" l*2" $*1 *61 l*116



< '

$2. ".*) H3n53J >4G4G5.

$2. ".* P345n426l 6n5> 2n N62n 3 2=5n426l N642l5> 64 45>65 5l64215 =5n>24 (. A. L53n6=>, 9, N5>3n6l 3Gn26423n.



555555D555 55D5555

Pro:le.s 1!

tests on sa.-les of the sand at the sa.e relative density as 2n the field*a.-ling of loose graZ,%Var .aterials, es-e(ially at de-ths greater than afew roet(es, is veJ3 diffi(%lt* ineb thb .aterials are **ery sensitive to eventhe slighte9@t vi:ration, one is never s%re the sa.-le has the sa.e density as the93i*dt%ral soil de-osit* Therefore different <inds of -enetro.eters are %sed inengineering -ra(ti(e, and the -enetration resistan(e val%es are ro%ghly(orrelated with relative density* or de-osits at shallow de-thswhere dire(t a((ess is -ossi:le, other te(hoiF%es have :een develo-ed to.eas%re the in5-la(e density of (o.-a(ted soils* These te(hniF%es aredis(%ssed in detail in Cha-ter *

inally, it sho%ld :e noted in this dKis(%ssion of the str%(t%re of gran%lar soils that relative density alone is not s%ffi(ient to (hara(teri&e

their engineering -ro-erties* It is -ossi:le for two sands* for e+a.-le, tohave identi(al void ratios and relative densities :%t signifi(antly differentfa:ri(s and th%s signifi(antly different engineering :ehaviors* ig%re 2*$"is a two5di.ensional e+a.-le of s%(h a fa:ri(* 4oth =sands= are identi(al5they have the sa.e grain si&e distri:%tions and the sa.e void ratios* 4%ttheir fa:ri(s are o:vio%sly very different* tress history is another fa(tor that .%st :e (ons1dered when deal.g with sands and gravels in engineer ing -ra(ti(e* 'e-osits of gran%lar .aterials whi(h have :een -reloaded :ynat%re or .an will have very different stress5strain -ro-erties and thereforevery different settle.ent res-onses La.:re(hts and Leonards, 16!7B*

PROBLEMS

25 l. Cal(%late the s-e(1fi( s%rfa(e of a (%:e aB 1 .., :B 1 ..,5 1 ", and dB 1 n. on a side* Cal(%late the s-e(ifi( s%rfa(e 2n

ter.s of :oth areas and .$Q<g* Ass%.e for the latter (ase that Ps /$*" GgQ.#

25$* Cal(%la re the s-e(ifi( s%rfa(e of aB ten.s :alls, :B -ing -ong :alls,eB hall :earings 1 .. in dia.eter, and dB fly ash with a--ro+i.*atelys-heri(al -arti(les of " in dia.eter*

25#* The val%es of 52n and 56Y for a -%re sili(a sand F P.i# / $*" GgQ.#B

D54 5 fo%nd to :e *2" and *"", res-e(:vely* aB What 1s the (orres-onding range in dry density :B l the in sit% void ratio is *"#,what is the density inde+



184 Cla@ 3lnerala and &oll &tructure

252* 'es(ri:e :riefly the (rystalline or ato.i( st.(t%re oY t:e YoBBowingten .inerals* Also list any i.-ortant disting%ishing (hara(teristi(s*

aB .e(titedB Atta-%lgite

:B 4r%(iteeB 4entonite

eB i::sitefB Allo-hane

gB Halloysite hB Illite iB Gi(aj Chlorite

25* 'es(ri:e the following ty-es of :onding agents fo%nd with (lay

.inerals*

aB Hydrogen :ond :B Covalent :ondeB van der Waals3

(es

dB Ja.es :ond

25"* The wet density of a sand in an e.:an<.ent was fo%nd to :e1*6 GgQ.# and the f1eld water (ontent was 1]* In the la:1ato1y,the density of the solids was fo%nd to :e $*"" GgQ.

#and the

.a+i.%. and .;ni.%. void ratios were *"$ and *22, res-e(tively*Cal(%late the relative density of the sand in the field*

25!* Whi(h sheet, sili(a or al%.ina, wo%ld yo% wear to a toga -arty Why

257* iven the -arti(les in ig* 2*$", is it realisti( f show that all the -arti(les are in (onta(t with ea(h other for this given -lane Anygiven -lane Why

,



fi/e

Co0action

). INT!O('CTION

In geote(hni(al engineering -ra(ti(e the soils at a given site are of tenless than ideal for the intended -%r-ose* They .ay :e wea<, highly(o.-ressi:le, or have a higher -er.ea:ility than desira:le fro. an engineering or e(ono.i( -oint of view* l4 wo%ld see. reasona:le in s%(hinstan(es to si.-ly relo(ate the str%(t%re or fa(ility* However, (onsidera tionsother than geote(hni(al of ten govern the lo(ation of a str%(t%re, and the

engineer is for(ed to design for the site at hand* 8ne -ossi:ility is toDada-t the fo%ndation to the geote(hni(al (onditions at the site* Another -ossi:ility is to try to stabiliMe or i.-rove the engineering -ro-erties of thesoils at the site* 'e-ending on the (ir(%.stan(es, this se(ond a--roa(h.ay :e the .ost e(ono.i(al sol%tion to the -ro:le.* ta:ili&ation is%s%ally 8echanical or che8ica/ , :%t even ther.al and ele(tri(al sta:ili&a5tion have o((asionally :een %sed or (ons1dered*

In this (ha-ter we are -ri.arily (on(erned with .e(hani(al sta:ili&ation or densifi(ation, also (alled co8paction. Che.i(al sta:ili&ation inel%des the .i+ing or in0e(ting of (he.i(al s%:stan(es into the soil* Portland (e.ent, li.e, as-halt, (al(i%. (hloride, sodi%. (hloride, and -a-er

.ill wastes are (o..on (he.i(al sta:ili&ation agents*8ther .ethods for sta:ili&ing %ns%ita:le fo%ndation soils in(l%dede(atering, whi(h is the re.oval or red%(tion of %nwanted e+(ess gro%ndwater -ress%res, and preloading , in whi(h the fo%ndation soils are surcharged

with a te.-orary overload so as to in(rease the strength and de(reaseanti(i-ated settle.ent* The details of these and other* .ethods are de s(ri:edin te+t:oo<s on fo%ndation and highway engineering* A good state

18

. j



118 Compectlon

of the art dis(%ssion and ref eren(e to .ethods for i.-roving the engineer5ing (hara(teristi(s of soils is -rovided in the ACE 16!7B (o.r.tteere-ort =oil l.-rove.ent5History, Ca-a:ilities, and 8%tloo<*=

Co.-a(tion and sta:ili&ation are very i.-ortant when soil is %sed asan engineering .aterial@ that is, the str%(t%re itself is .ade of soil* Earthda.s and highway* e.:an<.ents are e+a.-les of earth structures. I soilsare d%.-ed or othetwise -la(ed at rando. in a fill, the res%lt will :e ane.:an<.ent with low sta:ility and high settle.ent* In fa(t, -rior to the16#3s, fOghway and railroad hlls were %s%ally (onstr%(ted :y end5d%.-ingsoils fro. wagons or tr%(<s* There was very little atte.-t to (o.-a(t or densif y the soils, and fail%res of even .oderately high e.:an<.ents were(o.rnon 8f (o%rse earthwor<s s%(h as levees are al.ost as old as .an,

:%t these str%(t%res, for e+a.-le in an(ient China or India, were (onstr%(ted :y -eo-le (arrying s.all :as<ets of earth and d%.-ing the. inthe e.:an< .ent* Peo-le wal<ing over the d%.-ed .aterials (o.-a(tedand th%s strengthened the soils* Even ele-hants have :een %sed in sorne(o%ntries to (o.-a(t soils, :%t resear(h has shown that they are not verygood at it Geehan, 16"!B*

The following sy.:ols are introd%(ed in this (ha-ter*

%* " / % * GgQ.# Ga+i.%. dry densityld " / % * GgQ. # ield = density

).* CO3PACTION

Co8paction is the densifi(ation of soils :y the a--li(ation of .e(ha5

ni(al energy* l4 .ay also involve a .odifi(ation of the water (ontent aswell as the gradation of the soil* Cohesionless soils are effi(iently (o. -a(ted :y vi:ration* In the field, hand5o-erated vi:rating -lates and.otori&ed vi:ratory rollers of vario%s si&es are very effi(ient for (o.-a(ting sand and graveV soils* R%::er5tired eF%i-.ent (an also :e %sedeffi(iently to (o.-a(t sands* Even large free5falling weig:ts have :een%sed to dyna.i(ally (o.-a(t loose gran%lar fills* orne of these te(hniF%esare dis(%ssed later in this (ha-ter*


1 ro 'e-t: oY io8%eo(e EF 5$B g %/ & .Qs$ A((eleration of gravity, 6*7"".Qs $

R*C* ]B Relative (o.-a(tion EF* 5#B( " + Gass of falling weight EF* 5$Bwo- or 8GC ]B 8-ti.%. water (ontent@ so.eti.es (alled the

o-ti.%. .oist%re (ontent 8GCB



).! T53 3l C3N64l3n 111

ine5grained and (oh =ive soils .ay :e (o.-a(ted in the la:oratory :y falling weights an( ha..ers, :y s-e(ial **<neading= (o.-a(tors, andeven stati(allv tl a (o..on loading .a(hine or -ress* In the field,(o..on (o.-a(tion eF%i-.ent in(l%des hand 5o-erated ta.-ers,sht-sfoot rollers, r%::er5tired rollers, and other ty-es of heavy (o.-a( tioneF%i-.ent e(* *B* Considera:le (o.-a(tion (an also :e o:tained :y

-ro-er ro%ting 3 the ha%ling eF%i-.ent over the e.:an<.ent d%ring(onstr%(tion*

The o:0e(tive of (o.-a(tion is the i.-rove.ent of the engineering -ro-erties of the soil .ass* There are several advantages whi(h o((%r thro%gh (o.-a(tion9

'etri.ental settle.ents (an :e red%(ed or -revented*

oil strength in(reases and slo-e sta:ility (an :e i.-roved*

4earing (a-a(ity of -ave.ent s%:grades (an :e i.-roved*

Undesira:le vol%.e (hanges, for e+a.-le, (a%sed :y frosta(tion, swelhng, and shrin<age .ay :e (ontrolled*

) ! THEOR7 O$ COMPACTIO%

The f%nda.en tals of (o.-aetion of eohesi v e soils are relati **ely ne *R* R* Pro(tor in the early 16#3s was :%ilding da.s for the old 4%rea% of

* Waterwor<s and %--ly in Los Angeles, and he develo-ed the -rin(i-ies of (o.-a(tion in a series ,of arti(les in Engineering 'e(s5)ecord Pro(tor,16##B* In his honor, the standard la:oratory (o.-a(tion test whi(h hedevelo-ed is (o..only (alled the Proctor test.

Pro(tor esta:lished that (o.-a(tion is a f %n(tion of fo%r varia:les9 l B dry density a , $B water (ontent w, #B (o.-a(tive effort, and 2B soilty-e gradation, -resen(e of (lay .inerals, et(*B* Co8pactive ef@ort is arneas. e %f the .e(hani(al ener gy a--lied to a soil .ass* In (o%nh ieswhere 4ritish Engineering %nits are %sed, (o.-a(tive effort is %s%ally

re-orted . f t DlJQ #, whereas the I %r%ts are J Q .# J / Jo%lesB* .(e1 J l N D., and %sing the (onversion fa(tors in A--endi+ A, we (an

deter.ine that l f tDl:f Qf t

#

/ 2!*77 JQ .

#

* In the field, (o.-a(tive effortisthe % % ro:er af -asses o( =(averages= of the roHer of a (ertain ty-e andweight on a given vol%.e of soil* In the la:oratory, i8pact or dyna8ic,

!neadi11g , and static ee8paetion are %s%ally e.-loyed* '%ring i8pact

co8paction , whi(h is the .ost (o..on ty-e, a ha..er is dro--ed severalti.es on a soil sa.-le in a .old* The .ass of the ha..er, height of dro-,n%.:er of dro-s, n%.:er of layers of soil, and the vol%.e of the .old ares-e(ified* or e+a.-le, in the standard Proctor test also standard AAHT8

.j



11$ C3N54l3n

16!7B, 'es1gnation T 66, and ATG 17B, 'esignation ' "67X, the .assof the ha..er is $*26 <g * l:B and the height of fall is #2*77 .. 1 f tB*Toe soil is -la(ed in three layers in an a--ro+i.ately litre *622 + 15# .# or 1Q# f t # B .old, and ea(h layer is ta.-ed $ ti.es* Co.-a(tive ef fort (an then :e (al(%lated as shown in E+a.-le *1*

E+AMPLE ).

(215n:

tandard Pro(tor test ha..er and .old*

R5FG25=:

Cal(%late the (o.-a(tive ef fort in :oth I and 4ritish Engineering %nits*

S3lG423n:

a* 6 units#

(o.-a(lve K $*2 <g *71 . Qs* B*#27 .B# layersB$

:lowsQlayerBeffort 5 *622 + 15# .#

/ 6$*! <JQ .#

I e+a(t val%es of g and the vol%.e are %sed, the standard Pro(tor(o.-a(9ive effort is 6$*!" <JQ .#

:* ritish Engineering units#

* ff * l:f l f tB#B$B (o.-a(lve e ort / X.:...X:.....:.....:.... .:....--'-- ***L f t#

#

1$,#! f tDl:f ft3

ThO, (al(%lation is, stri(tly s-ea<ing, in(orre(t sin(e the * l: ha..er isreally a .ass not a weight* However, the differen(es are negligi:le*

or other ty-es of (o.-a(tion, the (al(%lation of (o.-a(tive effort isnot so si.-le* In <neading (o.-a(tion, for e+a.-le, the ta.-er <neadsthe soil :y a--lying a given -ress%re for a fra(tion of a se(ond* Toe



5.3 Theor@ ol Co0actlon 113

<neading a(tion is s%--osed to si.%late the (o.-a(tion -rod%(ed :y ashee-sfoot roller and other ty-es of field (o.-a(tion eF%i-.ent* In static

co8paction , the soil is si.-ly -ressed into a .old %nder a (onstant stati(stress in a la:oratory testing .a(hine*

The -ro(ess of (o.-a(tion for (ohesive soils (an :est :e ill%strated :y (onsidering the (o..on la:oratory (o.-a(tion or Pro(tor test* everalsa.-les of the sa.e soil, :%t at different water (ontents, are (o.-a(teda((ording to the standard Pro(tor (o.-a(tion test s-e(ifi(ations given

-revio%sly* Ty-i(ally, the total or wet density and the a(t%al water (on tentof ea(h (o.-a(ted sa.-le are .eas%red* Toen the dry density for ea(hsa.-le (an :e (al(%lated fro. -hase relationshi-s we develo-ed in Cha-ter $*

$5"B

p

Pd / ( $512B

When the dry densities of ea(h sa.-le are deter.ined and -lottedvers%s the water (ontents for ea(h sa.-le, then a (%rve (alled aco8paction curve for standard Pro(tor (o.-a(tion is o:tained ig**1, (%rve AB*

'egree of "] 7] 1] for X, & $*! GgQ. #

sat% ra t i on9

M

Xb83l

5o

DZZ@

11B

=8

o

.9 5

.8 5

1*!

Li neof

=ero air QK,, voids=

1 20

5 1 1+

10+

5o

DZZ@e=8

3

AB tandardPro(tor

1.6 _-.G.G G&--!.-!.-1..-0_.!....._0.G_G...-8&......G.._...G.._ _._..-G!-.--Q.......-= 100> + 10 1 + 20 2+

Water (ontent D

$2. ). S46n=6= 6n= 3=225= P343 3N6423n G15> 3C3>J B 42ll.

...***



114Co0actlon

Ea(h data -oint on the (%rve re-resents a single (o.-a(tion test, and%s%ally fo%r or five individ%al (o.-a(tion tests are reF%ired to (o.-letelydetennine the (o.-aetion e%rve* This (%rve is %niF%e for a given sail ty-e,.ethod of (o.-a(tion and (onstantB (o.-a(tive effort* Toe -ea< -oint of the (%rve is an i.-ortant -oin t* Corres-onding to the 8ai8u8 d1density

fId .a+ is a water (ontent < nown as the opti8u8 (ater content wo-t

also <nown as the o-ti.%. .oist%re (ontent, 8GCB* Note that the.a+1.%. dry density is only a .a+i .%. for a s-e(ifi( (o.-a(tive 3,

ef fort and .ethod of (o.-a(tion* This does not ne(essarily refle(t the.a+i.%. drydensity that (an :e o:tained in the field*

#

Ty-i(al val%es of .a+i.%. dry density are aro%nd 1*" to $* GgQ .1 to 1$ l:f Q f t # B with the .a+i.%. range fro. a:o%t 1*# to $*2 GgQ .7 to 1 J:f Qf t # B* 'ensities are also given in 4ritish Engineering %nit=

:e(a%se yo% are li<ely to en(o%nter the. in -ra(ti(e*B Ty-i(al o-ti.*water (ontents are :etween 1] and $], with an o%tside .a+i.%. rangeof a:o%t ] to 2]* Also shown on ig* *1 are (%rves re-resentingdiff erent degrees of sat%ration of the soiL ro. EFs* $51$ and $51, we (anderive the eF%ation for these theoreti(al (%rves*

Pd / ( P( P#s

51B

The e+a(t -os1hon of the degree %f sat . ation (%nes de-ends only on theval%e of the density of the soil solids PsB Note that at o-ti.%. water (ontent for this -arti(%lar soil, is a:o%t !]* N ote too that the (o.-a( tion(%rve, even at high water (ontents, never a(t%ally rea(hes the (%rve for =1] sat%ration= traditionally (alled the Mero air voids (%rveB* And this istr%e even for higher (o.-a(tive ef forts, for e+a.-le, (%rve = of ig**1* C%rve is the (o.-a(tion (%rve o:tained :y the 8odified Proctor

co8paction test .od1fied AAH l 8 16!7B, 'esigna tion T 17, and ATG167B, 'esignation ' 1!X* This test %tili&es a heavier ha..er 2*#" <gor 1 l:B, a greater height of fall 2! .. or l* f tB, and layers ta.-ed $ti.es into a standard Pro(tor rooJd o% sho%ld verify that the (o.-a(tive

effort is $"6# <JQ .# or ",$ f t Dl:f Q f t #* The .odified test was develo-edd%ring W orld War II :y the U** Ar.y Cor-s of Engineers to :etter re-resent the (o.-a(tion reF%ired for airfields to s%--ort heavy air(raf t*Toe -oint is that in(reasing the (o.-a(tive effort tends to in(rease the.a+i.%. dry density, as e+-e(ted, :%t also de(reases the o-ti.%. water (ontent* A line drawn thro%gh the -ea< -oints of several (o.-a(tione%rves at diff erent (o.-a(tive efforts for the sa.e soil will :e al.ost

-arallel to a 00 S (%rve* lt is (alled the fine o@ opti8u8s.

#



*# Theor@ of Co0actlon 117

Ty-i(al (o.-a(tion (%,,es for diff erent ty-es of s1ls are 1Il%strated

in ig* *$* Noti(e ho= *9@ands that are well graded W soils, to- (%rveBhave a higher dr= **9t9nsity than .ore %nifor. soils P soils, :otto. (%rveB*or (lay s4 r 9*s, the .a+i.%. dry density tends to de(rease as -lasti(ity in(r=*es*

Why do we get (o.-a(tion (%rves s%(h as those shown in ig* *1and *$ tarting at low water (ontents, as the water (ontent in(reases, the

-arti(les develo- larger and larger water fil.s aro%nd the., whi(h tend to=l%:ri(ate3= the -arti(les and .a<e the. easier to :e .oved a:o%t andreoriented into a denser (onfig%ration* However we event%ally rea(h awa ter (ontent where the density does not in(rease any f%rther* At this

-o.t, wa ter starts to re-la(e soil -arti(les in the .old, and sin(e p.., Y Ps

the dry density (%rve starts to fall off , as is shown in ig* *#* Note that no.atter how .%(h water is added, the soil never :e(o.es (o.-letelysat%rated :y (o.-a(tion*

Co.-a(tion :ehavior of (ohesive so;ls as des(ri:ed a:ove is ty-i(alfor :oth field and la :oratory (o.-a(tion* Toe (%rves o:tained will vary

*.*

2.1 -

No*

*

oi l te+t%re and -lasti(ity data

'es(ri -tion and i l t Clay . PI

Wel l 5graded l oa . y sand 88 0 $ 1" N*P*Wel l 5graded sandy loa. !$ 1+ 13 1" N *P*

M

Cl

?4l@.

¡:-

*.0

.9 5

7 Poorl y graded sand 94 5 " 5 N *P*

555ero air voids, 1]

DZ@@ .8 @

5o

o.!

1*"

)1 1 *0 2+

Water (ontent D

$2. ).* W645 3n45n4-= =5n>24 5l6423n>2N> 3 524 >32l>3N645= 63=2n 43 45 >46n=6= P343 543= 645 3n>3n 6n= S6llJ5, 90.

# Ged5graded sandy loa. 73 6 18 22 4

2 Lean sa nd y si l ty (lay 32 33 3+ 28 6 Lean s; l ty (lay .. + 64 31 #" 1+" Loess;a l si l t 7 1 26 2! Heavy (lay " 22 !$ 67 2



.9 'ensi ty Pwet , as 555555555`

(o. -a(ted

M

**

.8 5 'ensi ty when(o. -a(ted dry

5 -l %s .ass of o, . 55

water aFded

·9e9a,

o

-

.)

."

.!

3

=55'ensi ty when (o.-a(ted dry

0 ) *0 *) !0 !)

Water (ontent w oQoB

$2. ).! T5 D645 3n45n4-=5n>4 526G3n>2N 2n=26Gn 45 2n56>5= =5n>24 5>Gl42n 3 45 6==2423n 3 D645 6n= 464 =G5 4345 6NNl25= 3N6423n 534. S32l 2> 6 >2l4 l6, LL !, PI 5 ",>46n=6= P343 3N6423n 645 3n>3n 6n= S6llJ5, 16"B*

*0.9

M

:4Ee

D.Z.Z..@e

.8 M

**C'l

DZZ@e9a,

a, 5e5e *** 00 . 2o

.)

90 1 ) *0 *)

Water (ontent oQoB

$2 S " C3N62>6n 3 25l= 6n= 6J3643 3N6423n. 1V L6J3643 >4642 3N6423n, *000 N>2; * 3=225= P343; !>46n=6= P343; " l6J3643 >4642 3N6423n, *00 N>2; )25l= 3N6423n, GJJ5-425= l36=, 31565>; 25l=3N6423n, >55N>334 3ll5, N6>>5>. %345: S4642 3N6423n3 43N 6n= J3443 3 >32l >6Nl5. A45 TGnJGll, 16, 6n= 6>245= J L6J5 6n= W246n, 16"6*B

114

0



7.+ Pro0ertle and &tructure ot Co0acted Cohel/e &olla 117

so.ewhat, that is, have different sha-es and -ositions on the pd

vers%s(

-lot, :%t in general the res-onse will :e si.ilar to that shown in ig* *2,where the sa.e soil is (o.-a(ted %nder different (onditions* Toe standardand .odified Pro(tor la:oratory tests were develo-ed as a standard of (o.-arison for field (o.-a(tion, that is, to see if the rolling or (o.-a(tionwas s%ffi(ient* The a--ro+i.ation to field (o.-a(tion is not e+a(t, as.entioned, sin(e the standard la:oratory (o.-a(tion is a dyna.i(5i.-a(tty-e, whereas field (o.-a(tion is essentially a <neading5ty-e (o.-a(tion*This diff eren(e led to the develo-.ent of the Harvard .iniat%re (o.-a(tor Wilson, 16!B as well as larger <neading (o.-a(tors* ield (o.-a(tion (ontrol -ro(ed %res are des(ri:ed in e(* *"*

7.+ P!OPE!TIE& AN( &T!'CT'!EO* CO3PACTE( COHE&I2E &OI&

Ihe str%(t%re and th%s the engineering -ro-erties of (o.-a(ted(ohesive soils will de-end greatly on the .ethod or ty-e of (o.-a(tion,the (o.-a(tive effort a--lied, the soil ty-e, and on the .olding water (ontent* Us%ally the water (ontent of (o.-a(ted soils is referen(ed to theo-ti.%rn water (ontent for a given ty-e of (orn-a(tion* 'e-ending ontheir -osition, soils are (alled dry >J? opti8u8 , near or at opti8118 , or (et of

opti8u8. Resear(h on (o.-a(ted (lays has shown that when they are

(o.-a(ted dry %f o-ti. %., the st+ %(t%,e of the soils is essentiall9y inde-en5dent of the ty-e of (o.-a(tion eed and Chan, 166B* Wet of o-tirn%.,however, the ty-e of (o.-a(tion has a signifi(ant effe(t on the soilstr%(t%re and th%s on the strength, (o.-ressi:ility, et(*, of the soil*

The (o..ents in this se(tion are very general, and yo% sho%ld <ee-in roi%d tha t the real fa:ri( of (o.-a(ted (lays is a:o%t as (o.-le+ as thefa:ri( of nat%ral (lays des(ri:ed in Cha-ter 2* At the sa.e (o.-a(tiveef fort, w ith inereasing 1 ater eontent, the soil fa:rie :eeo.es in(reasinglyoriented* 'ry of o-ti.%. the soils are always flo((%lated, whereas wet of o-h.%. the fa:ri( :e(ornes .ore oriented or dis-ersed* In ig* *, fo,e+a.-le, the fa:ri( at -oint @ is .ore oriented than at -oint A. Now, if the(o.-a(tive effort is in(reased, the soil tends to :e(o.e .ore onented,

even dry of D o-ti.%.* Again, referring to ig* *, a sa.-le at -oint E is

signifi(ant than dry of o-ti.%.*Pe1111ea:ility Cha-te1 !B at (onstant eo.-aetive effort deereases

with in(reasing water (ontent and rea(hes a .ini.%. at a:o%tthe



114 Co0ectlon

o-ti.%. l t:e (o.-a(tive effart is io(reased, the (oeffi(ient of -er.ea5 :ility de(reases :e(a%se the void ratio de(reases in(reasing dry %nitweightB* This ehange in -er.ea:ilitB with .olding water eontent is shownin ig* *"a, where it (an :e seen that the -er.ea:ility is a:o%t an order of .agnit%de higher when this soil is (o.-a(ted dry of o-ti.%. than when itis (o.-a(ted wet of o-ti.%.*

Co.-ressi:ility Cha-ter 7B of (o.-a(ted (lays is a f%n(tion of thestress level i.-osed on the soil .ass* At relatively low stress levels, (lays(o.-a(ted wet of o-ti.%. are .ore (o.-ressi:le* At high stress levels,the o--osite is tr%e* In ig* *": it (an :e seen that a larger (hange in voidratio a de(reaseB ta<es -la(e in the soil (o.-a(ted wet of o-ti.%. for agiven (hange i11(1easeB in a--lied -t ess%t e*

welling of (o.-a(ted (lays is greater for those (o.-a(ted dry of o-h.%.* I hey have a relatively greater deh(1en(y of water and thereforehave a greater tenden(y to adsor: water and th%s swell .ore* oils dry of o-ti.%. are in general .ore sensitive to environ.ental (hanges s%(h as(hanges in water (ontent* This is 0%st the o--osite for shrin<age as shownin ig* *!a, where sa.-les (o.-a(ted wet of o-ti.%. have the highestshrin<age* Also ill%strated in the %--er -art of this fig%re is the effe(t of different .ethods of (o.-a(Dting the sa.-les*

The strength of (o.-a(ted (lays is rather (o.-le+* However, for now, 0%st re.e.:er that sa.-les (o.-a(ted dry of o-ti.%. have higher strengths than those (o.-a(ted wet of o-ti.%.* Toe strength wet of o-ti.%. also de-ends so.ewhat on the ty-e of (o.-a(tion :e(a%se of differen(es in soil str%(t%re* I the sa.-les are soa<ed, the -i(t%re(hanges

H2 3N64215Q 5 34

E 1

G

1

1

L3D: 3N64215 534

W645 3n45n4

$2. ).) E54 3 3N6423n 3n >32l >4G4G5 645 L6J5, 9)86.

o



,--- - - -- .- - 5 . 55DD DD55 -- - .,. . . - -- -

\1 s '

=,

-/- :

1C 1 2*o

==J

Ea4a**

1

0 ! 35

1

55 555 5 5e ?'

d 1'l 111 ,e59 ?5?*, 5

,%5 -1

1 5 ******* K**** C/h:...: ....; 535*5*555 @=3--- Q *.R ?- ·e,- *.0

5 **

+

1

E'=and density fro. -er .eation K

*** . .

3*o

¡¡;e

2Q8 ***** ....

Q ------ ??P 5

E

,**-,,

s . ·999

Q --------$--------_*N2

?'

' a0..##

$

*,--------

55r5****

5,.,P....:::: o

¡--....X

0

2-----5

5L . .8

- D5' ? 1 **9,

,... 1 Hl lQ 8 9

Water (ontent

,- 5,*, , l l(@IUI I L7 1:.C.<l..< u: sanay (1ay*

, K

$6. I***, Ch*,*,9*,**,* 2n . . ....,

***La.:e, 167:B*

55 -A--

E

1

'

1 J 15

?' 5

5=3 55

-

?C

*****

, - .



111

55

55 55 55



'r y (o.-a(ted or % nd ist% r:ed sa.-le

3 P ress% re, nat% ral s(a le

b--- J+ Wet (o. -a(ted orre.olded sa.-le

="M"" ""55Re:o% nd for :oth sa.-les 5,55o Press% re, l og s(ale

H igh 5 -ress% re (onsol idat ion*

J

*ig. 7.6;#< Change in co0rei#ilit@ Lith olding Later content ;after

a#e= 174#<.

18

---



?5ti8/8-water ontent

Eet o3 o5ti8/8

1

@

r7 o3 o5ti8/8-+--+- ---1

_ neain$

lC1)

'i-------1--11

11

111

1

.:,t'.

?'>

.!:i1

1

..e

'X

i

2

112<tati o85ation

@ neain$ o85ation

M

..

1.

:% .

!!::: 1;` M

-;-'->

%

e-eC1) 1.;

1;2

* " 1 17 $22 $2 1*7

* " 8 $ 22 $2

1*" 6

$,. ). 6 S65 6> 6 4Gn4,3n 34 D645 3n45n4 6n= 4N5 34 3N6423n 645 eed 6n= C6n, 9)9.



Í '

*% trength stress reF% i red to (a%se

E...X e,,

0e

5o**%..

?' 3

.L8 N

@

^8 ,

$] strainB vs* water (ontent

?:::',

9 2

-3 2 D55 ---

.:::,

8e3

?'$ 5 5 -

.?e.'. Un(onsol idated5 % nd rained testsConf i ning -ress%re 1 <gQ(. $

V

0 * 12 1" 17 $ $$ $2 $"

trength stress reF% ired to (a%se

..E ] strain B vs* water (ontente,, 1

e5D

7 X X . Layers Ta. -s -er ootL8 ayer -ress%re

=:::3,^8 ! 1 $!" -siG

9 ! 1 1#" -si

-32

o ! 1 " -si999,83 1

@ U

?' $ 5555 1 -4----$(i;

M....*.*..* X * ,I

o1 1$ 12 1" 17 $ $$ $2 $"

11"

11$

17

Golding water (ontent

(T)

$2. ).J S45n4 6> 6 Gn423n 3 3N64215 534 6n= 3l=2n D6453n45n4 645 S55= 6n= C6n, 9)9.

-.

..G

- '-

MB A

%

.

@

"

5--,

u

****



TA,E )4 C3N62>3n 3 S32l P3N5425> J,4D55n & 3 @N42G 6n= W4 3 ON42G C3N423nPro-erty

Co.-i2risonl* tr%(t%re9

A* Parti(le arrange.ent4* Water defi(ien(y

C* Per.anen(e

$* Per.ea:ility9A* Gagnit%de

'ry ide .ore rando@

'ry side .ore defi(ie t@ th%s i.:i:es. re water, swells ore, has lowerre -ress%re

'ry side str%(t%re sefiitive to (:ange

4*Per.anen(e

'ry ide .ore -ennea-le'ry ide -er.ea:ility red%(ed .%(h .ore

: -er.eation#* Co.-ressi:ility9

A* Gagnit%de

4* Rate

Wett3de .ore (o.-rei:le 2n low -r s%re range, dry id( in high -r s%re rang(

'ry ide (onsolidates ihore ra-idly

2* trength9

A* As .olded9aB Undrained:B 'rained

4* Af ter sat%ration9

aB Undrained

:B 'rained

C* Pore water -ress%reat fail%re

ti '* tress5strain .od%l%sE* ensitivity

'ry id( .%(h higher 'ry ide so.ewhat hier

'ry 3de so.ewhat hier 2 swelling -re ented@ wet side Flil :e high(r 2sw lling -er.itt(d

& s de a:o%t the sa. or slightlygr ter

Wet s de higher

& sde .%(h greater & s31e .ore a-t to :el sensitive

kAfter l*2.:e 167:B*

..



1$2 C3N54l3n

d%e to swelling, es-eeially dry of o-ti.%.* Toe strength (%rves far a silty(lay (o.-a(ted :y <neading (o.-a(tion for three dif ferent (o.-a(tiveefforts are shown in ig* *!:* They show the stress reF%ired to (a%se $]strain %--erB and ] strain .iddleB for the three (o.-a(tive ef forts* Toestrengths are a:o%t the sa.e wet of o-ti.%. and in(rease signifi(antly onthe dry side of o-ti.%.*

Note too that at a given water (ontent wet of o-tiin%., the stress at] strain is aet%all*B less for the higher (o.-a(tion e*ergies T%is fa(t isalso shown in ig* *7, where strength is .eas%red :y the C4R California :eanng ralloB test* In tfOs test, the resistan(e to -enetI ation %f a # in*

$

-istan develo-ed in a (o.-a(ted s-e(i.en is (o.-ared to that develo-ed :y a standard sa.-le of densely (o.-a(ted (r%shed ro(<* Toe C4R is a

(o..on -ave.ent design test* In ig* *7 a greater (o.-a(tive effort -rod%(es a greater C4R dry of o-ti.%., as yo% wo%ld e+-e(t* 4%t noti(e

how the C4R is a(t%ally less wet of o-ti.%. for the higher (o.-a(tionenergies* This fa(t is i.-ortant in the -ro-er design and .anage.ent of a

(o.-a(ted earth hll@ we shall dts(%ss ns i.-li(ation later in this (ha-let *Ta:le 51 fro. La.:e 167:B is a s%..ary of the effe(ts of wet

vers%s dry of o-ti.%. (o.-a(tion on several engineering -ro-erties*

).) $IEL& COMPACTIO% E@IPME%T A%O PRO(E&RES

oil to be %sed in a (o.-a(ted fill is e+(avated fro. a borro( area.

Pu(e, shovels , d,ag 'nes and self5-ro-elled scrapers or ;pans; an99 %sed toe+(avate the :orrow .aterial* A self5loading s(ra-er is shown in ig* *6a andan elevating s(ra-er in ig* *6:* o.eti.es =do&ers= are ne(essary tohel- load the s(ra-er* (ra-ers .ay (%t thro%gh layers of differentrnateri5 als, allowing several grain si&es to be .i+ed, for e+a.-le* Toe -ower shovel.i+es the soil :y digging along a verti(al s%rfa(e, whereas the s(ra-er .i+es the soil :y (tting a(ross a slo-ing s%rfa(e where different layers.ay :e e+-osed*

The :orrow area .ay :e on site or several <ilo.etres away* (ra-ers,off the road vehi(les, are of ten %sed to trans-ort and s-read the soil in lMJtson the fill area* Tr%(<s .ay :e %sed as well, on or off the highway, andthey .ay end du8p, side du8p, or botto8 du8p the fill .aterial ig* *1aB*or e(ono.i( reasons, the ha%ling (ontra(tor %s%a11y tries to s-read the fill.aterial when d%.-ing in order to red%(e s-reading ti.e* However, %nlessthe :orrow .aterials are already wi thin the desir ed water eontent range,the soil rnay need to :e wetted, dried, or otherwise rewor<ed* Where

-ossi:le, the (ontra(tor dire(ts his earth5.ov.g eF.-.ent over -rev1o%sly



100

,883D

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Q#,

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::, 2+

o

9010 1 + 20 *)

W645 3n45n4

**, 55n

V )) Jl3D> N5 l65

o 3 * Jl3D> N5 U65

( Jl3D> N5 l65

%345: 0 lJ 65, 8? =3N3=225= P343

$2. ).8 S45n4 6> 56>G5= J 45 CBR 6n= 45 = =5n>24 15>G>D645 3n45n4 3 l6J3643 2N64 3N6423n 645 TGnJGll 6n= $3> ler,16"B*

.j

+



<

6

:B

$2. ).9 TD3 4N5> 3 >6N5>: 6 C3n15n423n6l 3 >5l-l36=2n >6N5.S35425> 6 ?=35? 3 4D3 5lN> NG> 45 ?N6n? 43 l36= GN. H55 454D3 >6N5> 65 6>>2>42n 56 345 l36= GN 2n NG>-NGll. J El51642n>6N5 D55 45 5l51642n 62n5 l36=> J 24>5l 6n= 5l22n645> 45n55= 43 6 NG>n5. P3436N> 3G45> 3 C645N2ll6 T643 C3.



. _0: -0.,.F... '--.. - ·..,: ' .

6

J

$2. ).0 EY6Nl5> 3 5FG2N5n4 G>5= 3 6Gl2n 6n= >N56=2n 2lln6526l>: 6^ 2ll 64526l 552R 6Gl5= :y 5,,= =GN 4G; J 343

6=5 >N56=2n 6n= N5N62n 2ll >GJ6=5 N3436N> 3G45> 3 C645N2ll6 T643 C3..

%n(o.-a(ted soil, t here:y red%(ing the a.o%nt of (o.-a(tive effortreF%ired later*

8n(e :orrow .a tena has :een t rans-orted to the fill area, bu/15

doMers# front Ioaders, and 8otor graders, (alled blades ig* * I8:B, s-readthe .aterial to the desired ayer or lift t hi(< ness* Lif t thi(<ness .ay rangefro. 1 to .. " to 17 in*B or so, de-ending on the si&e and ty-e of (o.-a(tion eF%i-.ent and on the .a+i.%. grain si&e of the 2ll.

The <ind of (o.-a( ting eF%i-.en t or ro/Jers %sed on a Jo: w1llde-end on the ty-e of soil to :e (o.-a(ted* EF%i-.ent is availa:le to

a--ly -ress%re, i.-a(t, vi :ration, and <neading* ig%re *11 shows twoty-es of rollers*

A s8ooth (heel, or dru8, roller ig* *1 laB s%--lies 1] (overage%oder t:e w:eel, with gro%nd (onta(t -ress%res %- to #7 <Pa -siB and.ay :e %sed on ali soil ty-es e+(e-t ro(<y soils* The .ost (o.rnon %se for

en%s :ovinas .as(%lin%s sona.:%lor%.*

127

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aB

:B

$2. *11 TN5> 3 3ll5>: 6 >334-D55l 3ll5; :B GJJ5-42 5= 3ll5>5l-N3N5ll5= N3436N> 3G45> 3 H>45 C3N6n, C3n>4G423n

EFG,N5n4 O212>23.

121



* *leld Co0actlon Eul0ent and Procedurea 1

large s.ooth wheel rollers is for proofrolling s%:grades and (o.-a(ting as-halt -ave.ents* The pneu8atic, or rubber5tired , roller ig* *11:B has a:o%t 7](overage 7] of the total area is (overed :y tiresB and tire

fills, as well as for earth da. (onstr%(tion*

ty-e of (o.-a(tor %sed today is the sheepsfoot roller. This roller, as itsna.e 1.- 1es, as .any ro%n or re(tang% ar s a-e -ro r%sions or eeig* *1$aB atta(hed to a steel dr%.* The ar(a of these -rotr%sions ranges

fro. # to 7 (.* to 1$ in** . 4e(a%se of the 7] to 1$] (overage, very. 7

1 -siB de-ending on the dr%. si&e and whether the dr%. is f illed with

2= whi(h .eans 2 f t long and 2 f t in dia.eterB roller -rovides a higher s rengt (o.-a(te 1 . ( ay so1 s an a eavier, i er -ress%re y= roller :e(a%se there is less <neading or shearing a(tion with the =2 :y 2=than the = :y = roller, whi(h -rod %(es a different soil str%(t%re see ig*

w d in tande. : (rawler tra(tors orare self5-ro-elled, as shown in ig* *1$:*

the foot -ro0e(ting a:o%t 1 to $ .. fro. the dr%.B and wor<s itsway %- e i as e n%. er o -asses in(rea=wal<s o%t= of the fill as the %--er -art of the lif t is (o.-a(ted* Theshee-sfoot roller is :est s%ited for (ohesive soils*

8ther rollers with -rotr%sions have also :een develo-ed to o:tainhigh (onta(t -ress%res for :etter (r%shing, <neading, and (o.-a(ting of a

. . .

-ro-elled* &a8ping foot ro/lers ig* *1#B have a--ro+i.ately "0 (over age and generate high (onta(t -ress%res fro. 12 to 72 <Pa $ to1$ -siB, de-ending on the si&e of the roller and whether the dr%. is filledor a ed weight* The s-e(1a .ge eet 1g* * a o t e ta.-.g ootroller a--ly a <neading a(tion to the soil* These rollers (o.-a(t si.ilarly

to the shee-sfoot in that the roller event%ally =wal<s o%t= of a well(o.-a(ted lif t* Ta.-ing foot rollers are :est for (o.-a(ting fine5grainedsoils*

till another <ind of roller is the 8esh, or grid pattern , rol/er witha:o%t ] (overage and -ress%res fro. 12 to "$ <Pa $ to 6 -siBig* *12B* The .esh roller is ideally s%ited for (o.-a(ting ro(<y soils,gravels, and sands* With high towing s-eed, the .aterial is vi:rated,(r%shed, and i.-a(ted*

.



* #=K*y l $ =BG56G 3 R5l6643n B

C3N> 3 En2n55

NN5 N3426n3 >6n

L3D5 N3426n3 >6n

**

,, BG56G 3 ;¡ R5l66423n

1 ,, C3N> 3 En2n55>

6

J

$2. ).* S55N>334 3ll5>: 6 =5462l 3 6 n:446nGl6 >55N>334 =6D23 N312=5= J H>45 C3N6n, C5n>4n.(425n EF.2N5n4 &272>25n;J >5l-N3N5ll5= >55N>334 3ll5 2n 353Gn= ?N6n? 2n J63Gn=N3436N 3G45> 3 C645N2ll6 T643 C3..

1#

Z55 *,** K

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9#

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46N2n 334 3N646. %345 3D 45 Jl6=5 2> G>5= 43 >N56= 4564526l J535 3N6423n J 45 3ll5> =6D2n 6n= N3436N3G45> 3 C645N2ll6 T643 C3..

131

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<1

Co0actlon132

$2. U2." (2= 3ll5 NJ3436NJ 3G45> 3 H>45 C3N6n,

C3n>4G- 423n EFG2N5n4 &212>23n.

evera (o.-a(tion eF%i-.ent .an%fa(t%rers have atta(hed verti(alvi:rators to the s.ooth wheel and ta.-ing foot rollers so as to .oreeff i(iently densif y gran%lar soils* ig%re *1 shows a vi:rating dr%. on as.ooth wheel roller (o.-a(t.g a gravelly .aterial* Also av aila:le are

$vibrating plates and ra88ers that range in si&e fro. $# to 1$$ .rn 6 to

2 in*$ B and weigh fro. to # <g 1 to " l:B* Co.-a(tion de-thfor even the larger -lates is less than 1 .etre* These devi(es are %sed in

$2. ).) V2J642n =G 3n >334-D55l 3ll5 N3436N 3G45> 345 H>45 C3N6n, C3n>4G423n EFG2N5n4 &212>23n.



7.7 *leld Co0actlon Eul0ent and Procedurea1%%

areas whe1e the la1ge1 1olle1s (annot o-erate* 4ro.s and orss:lad 16"6Bhave listed the different ty-es of vi:ratory soil (o.-a(tors see Ta:le 5$Band also ind1(ate the (o..on freF%en(y of o-eration* In Ta:le 5#, theyill%strate the -ra(ti(a a--li(ation of these .a(hines*

Pro:a:ly the :est e+-lanation of why roller vi:ration (a%ses densifi(ation of gran%lar soils is that -arti(le rea rra ogeroeo t o((%rs d%e to (y(li(defor.ation of the soil -rod %(ed :y the os(illations of the roller* Inadd1t1on, v1:ratory (o.-a( tio n (an w. < in .aterials with so.e (ohesionelig and oo, 16!!B* When os(illation is added to a stati( (o.-onent,(o.-a(tion is signif i(antly in(reased, as shown in ig* *1"* or soils(o.-a(ted on the dry side of o-tif31t., adding the dyna.i( (o.-onent

res%lts in in(reased density*There are .any varia:les whi(h (ontrol the vi :(a tory (o.-a(tion or densif i(ation of soils* orne are (o.-a(tor de-endent and sorne de-end onthe soil :eing (o.-a(ted* The list of varia:les wo%ld in(l%de9

Chara(teristi(s of the (o.-a(tor9Gass si&e 8-erating freF%en(y and freF%en(y range

Chara(teristi(s of the soil9Initial densityrain si&e and sha-eWater (ontent

Constr%(tion -ro(ed%res9 N%.:er of -asses of the rollerLif t thi(<nessreF%en(y of o-eration of vi:rator Towing s-eed

The (o.-a(tor (hara(teristi(s infl%en(e the stress level and de-th of infl%en(e of the dyna.i( for(e, and the initial density strongly infl%en(esthe f inal density* or e+a.-le, the %--er # (. of .edi%. dense sand.ay never :e(o.e (o.-a(ted highe1 than the initial density, whereasdense sands will :e vi:rated loose in the to- # (.* 8n(e the (o.-a(tor is(hosen, the a(t%al (onstr%(tion -ro(ed%res essent1ally govern the res%lts*The infl%en(e of o-erating freF%en(y for vario%s soil ty-es is shown in ig**1!* Note how a -ea< in the density5freF%en(y (%rve develo-s for .ost of the soils, even (lays* The freF%en(y at whi(h a .a+i.%. density isa(hieved is (alled the opti8u8 freLuency. lt is a f%n(tion of the (o.-a(tor solisyste., and it (hanges as the density in(r eases d%ring the -roeess of (o.-a(tion* Clearly, it is desira:le for a (o.-a(tor to have the (a-a:ilityto vary its o-erating freF%en(y and have the range reF%ired to o:tain

1

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TA,E 51 &255n4 TN5> 3 V2J643 l32l C3N 43n;

%rfa(e Mi:ra ors lnter911al Mi l?rators

Ty-e of G lChine Gass reF%en(y Ty-e of Ga(hine 'ia.eter i9@=reF% n(y1

=ibre ting tol 18perJ ra.1tnersB9 ncrete vibra1 ors#Ha.l5g%idedd C 51 ICg A:o% 1 H & Gan%allw o-eiated ( r 2 1 Cll ll I5$ H& I

15#B l:B ra(to 5.o%ted $e5" 2n.

,

5e9555

1

1

1

A4, r 4ronis anti or s:lad 16"6 * 9

t %s( d on li.i1ed sede* *

*9

.

3 * 1 1 1

<

=ibri ting p33ate co8pactors#elf5-ro-el ed, hand5gtided # <g

1B 5"B l:B1$58 H&

=ir,ro@lo,3FJtion BCip.:

Crane5.o%nte91 $#5#7 (. Aho%t #iB H&6 1 2n

G%lt3-le5tB-e, . l%nte^ on $B5# <g #5! H&tra(tors, et(* "0&-0C l:B

Cralle5.o ntedt U- to $ ons 115 1 H &

=ibrc ting r3rJl/ers#elf5 l?ro-el ed, hi nd5gt ided $ 51 <g 2157 H &

11e or tlwo d..sB 15#' l :Belf5,ro-el ed, tande. ty-e 8* 51 t lns #57 H &elf5,ro-el ed, n ::er 1 ires 2 $ tons $52 H &

Tra( or5dnwn l*3 51 tBns $58 H &



55D55555555 55D5555D DDD5D D55DDD DD5DDD D 555DD 5Wr W ****** DDDD DDD5DDDDDD DD55DDDD5DW555D5DD5D55D 55D DDDD55D55555555555555

TA,E )-! ANNl26423n> n V2J643 S32l C3N6423n

Ty-e of Ga(h;n A--li(ations

=ibrating ta8pers ra..ersB9 treet re-air* ills :ehind :ridge a:%t.ents, retainingand :ase.ent walls, et(* Tren(: fills*

=ibrating plate co8pactors #elf5-ro-elled, hand5g%ided 4ase and s%::ase (o.-a(tion for streets, sidewal<s, et(*

treet re-air* ills :ehind :ridge a:%t.ents, retainingand :ase.ent walls, et(* ills :elow floors* Tren(h fills*

% 1- e5 y-e

df5-ro-elled, hand5g%ided 4ase, s%::ase, and as-halt (o.-a(tion for streets, side

wal<s, -ar<ing ar(as, garage driveways, et(* ills :ehind :ridge a:%t.ents and retaining walls * ills :elow;loors* Tren(h fills*

elf5-ro-elled, tande. ty-e 4ase, s%::ase, and as-halt (o.-a(tion for hig:ways,streets, sidewal<s, -ar<ing ar(as, garagedriveways, et(* s ow oors*

elf5-ro-elled, r%::er tires 4ase, s%::ase, and e.:an<.ent (o.-a(tion for hig:ways,

ills soil or ro(<B %sed as fo%ndations for residential and

Tra(tor5drawn 4ase, s%::ase, and e.:an<.ent (o.-a(tion on hig:ways,

fill da.s* ills soil or ro(<B %sed as fo%ndations for

nat%ral de-osits of sand*

Af ter 4ro.s and orss:lad 16"6B*

-...X .......

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Water (ontent

$2. ). C3N6423n 5>Gl4> 3n !0 * 2n. l65> 3 >2l4 >6n=, D246n= D243G4 12J6423n, G>2n 6 00 ,000 lJ 43D5= 12J6433ll6 645 P6>3n>, 54 6l., 9*, 6> 245= J S5l2 6n= 733. 9.

1#

.j

1$

1$ 5ero air voids

$*

1*6$

11 1*72

11 1*!"

1 1*"7

1 1$ 12 1" 17 $ $$

...



1%6

SJ3l R 3ll5 wt* SJ3l R 3ll5 wt*

Co0actlon

tJ*55ti* ,)00 lJ

o555.o ,)00

o55oo ,000

----W ),800

+---+ !.00

*.*""0

!0(615l->6n=-l6 *.08

M E.f and 1?5 --S6n= l6 --

.9*

`;5;3;

ea*,=8

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=38

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Cl65 >32l

00 .

90

H561 l6

000 *000 !000

V2J6423n 5FG5n N

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$2. *1! V626423n D24 5FG5n 3 3N6423n J >334-=G 12J6-43 3ll5> 645 >5156l >3G5> 6> 245= :y S5l2 6n= 733, 16!!B*

.a+i.%. density* However, the -ea<s are gentle and, -er(entagewise, a

wide freF%en(y range is not ali that i.-ortant*The infl%en(e of the n %.:er of -asses of a roller and the towing

s-eed are shown in ig* *17 3 a !! <g roller (o.-a(ting a >heavy=high LLB e ay an a we 5gra e san * Dthe n%.:er of -asses or (overages in(reases, %- to a -oint* Not so o:vio%sis that, for a given n%.:er of -asses, a higher density is o:tained if the

vi:rator is towed .ore slowlyThe eff e(t of lif t thi(<ness .ay :e ill%strated :y the wor< of

--o o.a, e a * , so-erating at a freF%en(y of $!* H& is %sed to (o.-a(t a $2 (. thi(<layer of northern Indiana d%ne sand* The initial relative density was a:o%t

M

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* *leld Co0actlon Eul0ent and

Procedure

137

en:E

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o 2 7 *R 3ll5 31565>

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$2. *17 E54 3 3ll5 4615l >N55= 3n 63Gn4 3 3N6423n D4 00 ,000 lJ 43D5= 12J643 3ll5 645 P6>3n>, 54 6l., 9*, 6> 245=

:y S5l2 a11d , 33, 16!!B*

] to "]* ield density tests were .ade in test -its :efore and af ter (o.-a(ttion* Note how the density var;es with de-th* In lhe %--et 1 (. "in*B, the soil is vi:rated loose, whereas the soil rea(hes its .a+irn%. densityfor a given n%.:er of (overages at a:o%t 2 (.@ thereafter the .(rease .density ta-ers off* When (o.-a(ting -ast five or so (overages, there is not

a great in(rease in density*

E9A3PE *$

(215n:

It is de(ided, :ased on e(oooroi(s, that five (overages of a (ertain roller and o-erating freF%en(y shall :e %sed*

,.

***



1%4

R5FG25=:

Co0actlon

What wo%ld :e the .a+i.%. lif t thi(<ness to o:tain a .;ni.%. relativedensity Use the data shown in ig* *16*

S3lG423n:

Tra(e the relative density vers%s de-th (%rve for five -asses on onions<in -a-er* %-eri.-ose that drawing over the original one, and slide it %- anddown %ntil the desired relative density is o:tained shown in ig* E+* *$B*A:o%t 2 (. 17 in*B is indi(ated as the .a+i.%. thi(< ness* A(t%ally*

however* the lif t (o%ld :e thi(<er as (o.-a(tion of the to- ayer densifiesthe lower ayer the se(ond ti.e aro%nd*

& =5n>24 lJ Q 4 # B & =5n>24 lJU4 #B

1 0) 0

* 2 5*e # #f.l; ao

2 555

o 4 a l * 3ll5 N6>>5>

lJ ) 3ll5 N6>>5>

"5555`5555555`55555 DKJ*

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"0 )0 " 0 80 90 00

R5l64215 =5n>24

& =5n>24 lJQ4 #B

"0 )0 " 0 80 90 00

R5l64215 =5n>24

& =5n>24 lJQ4# B

6 1o

0) 0 1 0) 0

* *5-) o*o, l;

o -¡ X 2) r35l5l55 N56>5>555>

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$2. ).9 &5n>24-=5N4 5l6423n>2N3 6 )0 3ll5 3N5642n 64 *.)H 3 6 *"0 l24 524 645 &'ANN3l3n26, 54 6l., 99.

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D5555555555555 D55555D5DD55555555 55 55 555 555D5D5 5555 --- ---------

).) $l5l= C3N64l3n EFGlN5n4 6n= P35=Gn48 !9

R5l6U215 =53>24 l B5l6U215 =53>24 " 70 80 90

E*a

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-...*a

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o2

&5n>24-=5N4) 5l6423n>2N 3

l65 l24 524G>2n ) 3ll5N6>>5>

$2. EY. ).* ANN3Y2645 543= 3 =5452n2n l24 524 5FG25= 43654'42515 6 2A2G 55N6545= 5l642',..5 =5A>24 5 ) D244'4 215 5ll5 N6>>5>, G>23 =646 3 6 l65 l24 524 645 &'ANN3l3n26, 54 6l., 99.

ig%re *$ s%..ari&es the a--li(a:ility of vario%s ty-es of (o.-a(tion eg%i-.ent as a f%n(tion of soil ty-e, e+-ressed as a -er(entage of sand to (lay* These =&ones= are not a:sol%te, and it is -ossi:le for a given -ie(e of eF%i-.ent to (o.-a(t satisfa(torily o%tside the given &one*

When str%(t%res are to :e fo%nded on relatively dee- de-osits of loose gran%lar .aterials, densifieation :y even heavy s%rfaee vi:ratoryrollers is %s%ally ins%ffi(ient, and other te(hniF%es .%st :e e.-loyed* EcavatMon and replace8ent of the soil in (o.-a(ted layers .ay J5 e(ono.i(al %nder (ertain (onditions* 4lasting has also :een %sed at sorne sitesGit(hell, 16!B* =ibro5flotation Git(hell, 16!B is often %sed to in(reasethe density of :%ilding fo%ndations on loose sand* Another te(hniF%ewhi(h is gaining in -o-%larity is dyna8ic co8paction. 4asi(ally, the .ethod(onsists of re-eatedly dro--ing a very :eavy weig:t J8 to 2 tons roassBsorne height 1 to 2 .B over the site* The i.-a(t -rod%(es sho(< wavesthat (a%se densifi(ation of %nsat%rated gran%lar soils* In sat%rated gran%lar soils, the sho(< waves (an -rod%(e -artial liF%efa(tion of the sand, a(ond1tton s1.tlar to F%1(<sand d1s(%ssed . Cha-ter !B, followed :y(onsolidation dis(%ssed in Cha-ter 7B and ra-id densifi(ation* The varia5 :les in(l%de energy dro- height and weight of -o%nderB, the n%.:er of dro-s at a single -oint # to 1B, and the -atte. of the dro-s at the s%rfa(e to 1 . (enter5to5(enterB* ig%re *$1 shows a -%nder 0%st i.-a(tingthe s%rfa(e of a loose sand layer Event%ally this site will loo< li<e a set of

-

o @



1+8 Co0actlon

COMPACTIVECOMPAC IOR ZO%ES O$ APPLICA I IO% E $ $OR I

00Cl6

S55N>334

00S6n= R3

-(-2=

S4642 D4, n56=2n

S4642 D4, n56=2n

V2J643 S4642 D4, 12J6423n

464 D4.

MGl42425= Nn5G642 S4642 D4, n56=2n

T3D5= 46N2n 334 S4642 D4, n56=2n

H2->N55= 46N2n 3345 S4642 wt, n56=2n, 2N64, 12J6423n

$2. ).*0 ANNl26J2l24 3 1623G> 4N5> 3 3N6423n 5FG2N5n4 3 6215n >32l 4N5 3=225= 645 C645N2ll6 T643 C3., 9.

organi&ed .oon (raters* The (raters (an :e f illed with sand and additionally ta.-ed or the area :etween the. s.oothed o%t :y the -o%nder itdf*

'yna.i( (o.-a(tion was a--arently first %sed in er.any in the .id5

16#3s d%ring (onstr%(tion of (he A%to:ahns Loos, 16#"B* lt has also :een%sed in the UR to (o.-a(t loessial soils %- to . dee- A:elev, 16!B* Thete(hniF%e was f %rther refined and -ro.oted in ran(e and elsewhere :y Lo%isG)nard G)nard and 4roise, 16!B, who -ioneered in the develo-.ent of very heavy -o%nders %- to $ .etri( tons .assB and .assive (ranes andtri-ods for lif ting the. to dro- heigl5ps %- to 2 .* l.-rove.ent is (lai.edto de-ths down to 2 .* In the United tates, dy na.ie eo.-aetion has :een %sed on a .ore .odest seale by eontraeto1s %sing ordinary eF%i-.entLeonards, C%tter, and Holt&, 167@ L%<as, 167B*

The de-th of infl%en(e , in .etres, of the soil %ndergoing (o.-a(5tion is (onservatively given :y Leonards, et al* 167B as

lYWhB 11$ 5$Bwhere W .ass of falling weight in .etri( tons, and

h dro- height in .etres*The heavier the weight andQor the higher the dro- height, the greater

the de-th of (o.-a(tion* Leonards, et al* 167B also fo%nd that thea.o%nt of i.-rove.ent d%e to (o.-a(tion in the &one of .a+i.%.i.-rove.ent (orrelates :est with the -rod%(t of the energy -er dro- ti.esthe total energy a--lied -er %nit of s%rfa(e area*

5 55

5D555555



7.6 *leld Co0actlon Control and &0eclflcatlon 1+1

$2. ).* &n62 3N6423n 64 6 >245 2n B6nl6=5>. T5 00 43n 6n52> =3NN2n 6 542 43n D524 !0 3G45> 3 S. V66>2n,T5n2FG5> L3G2> Mgn6=, L3njG56G, $6n5.

7.6 *IE( CO3PACTION CONT!OANO &PECI*ICATION&

in(e the o:0e(tive of (orn-a(tion is to sta:ili&e soils and i.-rovethe% eng.)er.g :ehavior, it is i.-ortant to <ee- in .ind the desiredengineering properties of the fill, not 0%st its dry density and water (ontent*This -oint is of ten lost in earthwor< (onstr%(tion (ontrol* Ga0or e.-hasis

DJ



1+ Co0ectlon

is %s%ally -la(ed on a(hieving the s-e(ified dry density, and little (onsider5ation is given to the engineering -ro-erties desired of the (o.-a(ted fill*'ry density and water (ontent (orrelate well with the engineering -ro-er5ties e(* *2B, and th%s they are (onvenient (onstr%(tion (ontrol -ara.e59ters*

The %s%al design5(onstr%(t -ro(ed%re is as follows* La:oratory testsare (ond%(ted on sa.-les of the -ro-osed :orrow .aterials to define the

-ro-erties reF%ired for design* Af ter the earth str%(t%re is designed, the(o.-a(tion s-e(ifi(ations are written* ield (o.-a(tion control tests ares-e(ified, and the res%lts of these :e(o.e the standard for (ontrolling the

-ro0e(t* Constr%(tion (ontrol ins-e(tors then (ond%(t these tests to see thatthe s-eeifieations are .et :y the eontraetor*

There are :asi(ally two (ategories of earthwor< s-e(ifi(ations9 1Bend5product spec1J1cat(ns and $B 8ethod specificat(ns. With the first ty-e, a(ertain relative co8paction, or percen, co8paction , is s-e(ified* Relative(o.-a(tion is defined as the ratio of the field dry density pd rield to thela:oratory .a+i.%. dry density Pd"ax D a((ording to sorne s-e(ified standard test, for e+arn-le, the standard Pro(tor or the .odified Pro(tor test@or

relative (o.-a(tion R*C*B / Pd i$d + 1]B 5#B <

o% sho%ld note the differen(e :etween relative (o.-a(tion and re/ative

density D, or density inde lv, defined in Cha-ter 2* Relative density, of

(o%rse, a--lies only to gran%lar soils* I sorne fines are -resent, it isdiffi(%lt to de(ide whi(h ty-e of test is a--li(a:le as a standard test*ATG 167B, 'esignation ' $26, s%ggests that the relative density isa--li(a:le if the soil (ontains less than 1$] fines -assing the No* $sieveB@ otherwise the (orn-a(tion test sho%ld :e %sed* A relationshi-

:etween relative density and relative (o.-a(tion is shown in ig* *$$* Astatisti(al st%dy of -%:lished data on 2! different gran%lar soils indi(ated

'ry density

e == void ratioea5

o 1'ensity i nde+ I 8 or relative density ',

oRelative (o.-a(tion A*C*

R.C. / 80 1

$2. ).** R5l64215 =5n>246n= 5l64215 3N6423n 3n5N4> 645L55 6n= S2n, 9.



7.1 *leld Co0actlon Control and &0eclflca'ona 143

that the relative (o.-a(tion (orres-onding to &ero relative density is a:o%t

With end5product specifications, whi(h are %sed for .ost highwaysan %i ing o%n a 1ons, as ong as t e (ontra(tor 1s a e 43 o ta. es-e(ified relative (o.-a(tion, how he o:tains it doesn3t .atter, nor doesthe eF%i-.ent he %ses* The e(ono.i(s of the -ro0e(t s%--osedly ens%rethat the (ontr r wThe rnost e(ono.i(al (orn-a(tion (onditions are ill%strated 2n ig* *$#,

diff erent (o.-a(tive efforts* Ass%.e that (%rve re-resents a (o.-a(tivey e+ts .g (o.-a(tton eF%1-.ent* en

L2n5 3

--,

00 >64G6423nl2n5

¡¡;

90 R .C.

e9@l

?(i

''3

a : e

W645 3n45n4

$2. ).*! & =5n>24 15>G> D645 3n45n4, 2llG>4642n 45 3>45225n4 3n=2423n> 3 25l= 3N6423n 645 S55=, 9".

, . _

...9



Í'

144 Compactlon

to a(hieve, say, 6] relative (o.-a(tion, the -la(e.ent water (ontent of the (o.-a(ted fill .%st :e greater than water (ontent a and less thanwater (ontent (* These -oints are fo%nd where the 6] R*C* line interse(ts(o.-a(tion (%rve l. I the -la(e.ent water (ontent is o%tside of the rangea to $, then it will :e diffi(%lt, if not i.-ossi:le, to a(hieve the reF%ired

, -er(entage of relative (o.-a(tion (alled for, no .atter how .%(h the (ontra(tor (o.-a(ts that lif t* This is why it .ay :e ne(essary at ti.es to wet or dryrewor<B the soil -rior to rolling in the field*

Now that we ha v e esta:lished the range of -laee.ent water eontents,the (ontra(tor .ight as<9 =What is the :est -la(e.ent water (ontent to%se= ro. a -%rely e(ono.i(al view-oint, the .ost effi(ient water

(ontent wo%ld :e at , where the (ontra(tor -rovides the 8Sni8u8 (o. -a(tiveef fort to attain the reF%ired 6] relative (o.-a(tion* To (on sistentlya(hieve the .ini.%. relative (o.-a(tion for the -ro0e(t, the (ontra(tor will%s%ally %se a slightly higher (o.-a(tive effort, as shown :y (%rve $ of ig**$#* Th%s the .ost effi(ien t -la(e.ent water (ontents e+ist :etween theo-ti.%. water (ontent and .

However what .ay :e :est fro. t he (ontra(tor3s view-oint .ay not -rovide a f ill wi th the desired engineering -ro-ert;es* Co.-a(ting a soil onthe wet side generally res%lts in a lower shear strength than (o.-a(ting thesoil on the dry side of the o-ti. %. water (ontent igs* *! and *7B* 8ther -ro-erties s%(h as -er.ea:ility and shrin<5swell -otential will also :ediff erent* Th%s a range of -la(e.en t water (ontents sho%ld also :e s-e(i fied

:y the designer in addition to the -er(en tage of relative (o.-a(tion* This -oin t ill%strates why the desired engineering -erfor.an(e of the fill rather than 0%st the -er(entage of (o.-a(tion . %st :e <e-t in .ind when wri ting(o.-a(tion s-e(ifi(ations and designing field (ontrol -ro(ed%res*

ig%res *$# and *1 also ill%strate that s-e(ified densities (an :ea(hieved at higher water (ontents if .ore (o.-a(tive ef fort is a--lied,either :y %sing heavier rollers or .ore -asses of the sa.e roller* 4%t, asshown in ig* *7, at higher water (ontents the strength .eas%red :y theC4R test (%rves (ross, and a lower strength will :e o:tained with higher (o.-a(tion energies wet of o-ti.%.* This effe(t is <nown as overco8pac

tion. 8ver(o.-a(tion (an o((%r in the field when wet of o-ti.%. soils are proofrolled with very heavy, s.ooth wheeled rollers ig* *11aB or an

e+(essive n%.:er of -asses are a--lied to the lif t Gills and 'ealvo,16!7B* 8therwise even good .aterial (an :e(o.e wea<er* o% (an alsodete(t over(o.-a(tion in the field :y (aref%l o:servation of the :ehavior of the soil i.rnediately %nder the (o.-a(tor or the wheel of a heavilyloaded s(ra-er* I the soil is too wet and the energy a--lied is too great, pu8ping or (eaving of the fill will res%lt as the wheel shoves the wetwea<er fill ahead of itself* Also, shee-sfoot rollers won3t :e a:le to =wal< o%t*=



7.6 *leld Co0actlon Control and &0eclflcatlon 145

In 8ethod specifications, the se(ond general (ategory, the ty-e andweight of roller, the n%.:er of -asses of that roller, as well as the lif tthi(<nesses are s-e(ified :y the engineer* A .a+i.%. allowa:le si&e of

.aterial .ay also :e s-e(ified* In (ontrast to the end5-rod%(t s-e(ifi(a tions,where the (ontra(tor is res-onsi:le for -ro-er (o.-a(tion, with .ethod

s-e(ifi(ations the res-onsi:ility rests with the owner or owner3s engineer asto the F%ality of the earthwor<* I (o.-a(tion (ontrol tests -erfor.ed :y the

engineer fail to .eet a (ertain standard, then the (ontra(tor will :e -aide+tra for additional rolling* This s-e(if i(ation reF%ires -rior <nowledge of the :orrow soils so as to :e a:le to -redi(t in advan(e how .any -asses of,

for PSa.-le, a (ertain ty-e of roller will -rod%(e adeF%ate (o.-a(tion -erfor.an(e* This .eans that d%ring de sign, test fills .%st :e

(onstr%(ted with differen t eF%i-.ent, (o.-a(tive ef forts, et(*, in order todeter.ine whi(h eF%i-.ent and -ro(ed%res will :e the .ost effi(ient* in(etest fill -rogra.s are e+-ensive, .ethod s-e(ifi(a tions (an only :e 0%stified

for very large (o.-a(tion -ro0e(ts s%(h as earth daros* However,(onsidera:le savings in earthwor< (onstr%(tion %nit (osts are -ossi:le

:e(a%se a .a0or -art of the %n(ertainty asso(iated with (o.-a(tion will :eeli.inated for the (ontra(tor* He (an est;.ate F%ite well in advan(e 0%st

how .%(h (onstr%(tion will (ost* The (ontra(tor also <nows that if e+trarolling is reF%ired he will :e adeF%ately (o.-ensated* How is relative

(o.-a(tion deter.ined irst, the test site is sele(ted*l4 sho%ld :e re-resenta tive or ty-i(al of the (o.-a(ted lif t and :orrow.aterial* Ty-i(al s-e(ifi(ations (al for a new field test for every 1 to# .# or so, or when the :orrow .aterial (hanges signifi(antly* I4 is alsoadvisa:le to .a<e the field test at least one or .ay:e two (o.-a(ted lif ts :elow the already (o.-a(ted gro%nd s%rfa(e, es-e(ially when shee-sfootrollers are %sed or in gran%lar soils*

9ield control tests (an either :e destructive or nondestructive. 'estr%(tive tests involve e+(avation and re.oval of sorne of the fill .aterial,whereas nondestr%(tive tests deter.ine the density and water (ontent of the fill indire(tly The ste-s reF%ired far the (ornrnon destr%(tive field testsare9

t. E+(avate a hole in the (o.-a(ted fill at the desired sa.-ling

elevation the si&e will de-end on the .a+i.%. si&e of .aterial inthe fillB* 'eter.ine the .ass of the e+(avated .aterial* ,$* Ta<e a water (ontent sa.-le and deter.ine the water (ontent*#* Geas%re the vol%.e of the e+(avated .aterial* Te(hniF%es (o.

.only e.-loyed for this in(l%de the sand (one, the :alloon

.ethod, or -o%ring water or oil of <nown density into the holeig* *$2B* In the sand (one .ethod, dry sand of <nown dry

.j



<,1

(l6>> j6 D24 *0-!0 O446D6Q 3 >22l6 >6n=

6 S6n= 3n5

- A2 N5>>G5C5 16l

B6ll33n N6426ll NG>5= 2n435Y61645= 3l5

J B6ll33n

5 O2l 3 D645 543=

*ig. 7.+ &oe ethod for deterining denit@ in the field.

141



55 555 5D55555555D5555555 5 . 555D5 . 55555555555555555 555

5.$ *leld Co0actlon Control and &0eclftcatlon 147

density is allowed to flow thro%gh a (one5-o%ring devi(e into thehole* The vo:.e of the hole (an then easily :e deter.ined fro.the weight of sand in the hole and its dry density* lt is ne(essarythat the (ontra(tor sto- earth5.oving eF%i-.ent fro. vi:ratingand densifving9 the sand in the hole d%ring9 the sand (one testDotherwise the .eas%red -er(ent relative (o.-a(tion will J5 lower th*,**, 55W ***, J . T5 L- 1***511555 L - ;

. dire(tly :y the e+-ansion of a :alloon dire(tly in the hole*

*** *.,.., .. . . .

UH99 lU li911 p. :E''' Do ,*,*,,, llC9 vli911 %ta*9*9* Ul 1Ile.aterial e+(avated fro. the hole, and the vol%.e of the hole, we(an (o.-%te p. .(e we also <now the water (ontent, we (ano:tain the dry densitv of the fill, n ,*

* C*eZ K o,., -are Pd f ietd with Pd .a+ and (al(%late relative (o.-a(tion EF*,

E9A3PE ).!

(215n:

A ;..1A 53 **K ****** @IC3*=. - ' L- '- - .. **J F@ e =3 * 3 J ,* oD 53D5 B r

55 The following data were o:tained fro. the test9. .Gass of soil re.oved -an / 16 g

Gass of 53an - l3J

4alloon readings9 -,**5

!::&' 1 ,5

**5

*,*5

n5

n 5DDD

#

Initial / #7 (.#

Water (ontent infor.ation 9

Gass of wet soil -an / 22*6 Gass of dry soil -an / #"*6 gGass of -an / 1$$*g

5

R5FG25=:

a* Co.-%te the dry density and water (ontent of the soil*b. Using (%rve = of ig* *1 as the la:oratory standard, (o.-%te5the

relative (o.-a(tion*-

D5

5 5

Z,

).. . . .

'$

+ . - 5

?



, 5 5 555 5 555 555



1+4 Co0actlon

S3lG423n:

M,6. Co.-%te the wet density, p / -

16 5 1$ g p &

1$77 5 #7 (.#12" g

! (.#l*6 gQ(.# / l*6 GgQ.#

Water (ontent detern%nahon9

l. Gass of wet soil -an 3 22*6 g$* Gass of dry soil -an / #"*6 g#* Gass of water "( l 5 $B #6* g4. Gass of -an 1$$* g

* Gass of dry soil "s $ 5 2B / $2#*6 g"* Water (ontent ( M../ M,) + 1 # P B / 1"]

or (al(%lation of dry density, %se EF* $5129

p l*6 GgQ .##

P.1l ( l *1"

l *"7 GgQ .

b. or (al(%lation of relative (o.-a(tion, %se EF* 5#9

R *C* Pd ;iel( t 1 *"7 S l 88 6 K #Pd .a+ l *7"

T :ere a re severa -ro:le.s a sso(ia red wi t: t:e (o..on destrn(tivefield density test* irst, the la:oratory .a+i.%. density .ay not :e<nown e+a(tly* l4 is not %n(o..on, es-e(ially in highway (onstr%(tion, for a series of la:oratory (o.-a(tion tests to :e (ond%(ted on =re-resentative=sa.-les of the :orrow .atenals for the fOghway* Then, when the held testis (ond%(ted, its res%lt is (o.-ared with the res%lts of one or .ore of these 0o: =standard= soils* I the soils at the site are highly varia:le, this is a -oor -ro(ed%re* Another alternative is to deter.ine the (o.-lete (o.-a(tion(%rve for ea(h field test5a ti.e5(ons%.ing and e+-ensive -ro-osition*

A se(ond alternative is to -erfor. a field chec! point , or l -ointPro(tor test* When the field engineer <nows in advan(e that the soil in

whi(h he is -et fo.ring a field density test does not e+a(tly vis%ally .at(hone of the :orrow soils, an e+tra a.o%nt of soil is re.oved fro. the(o.-a(ted fill d%ring the test* The total a.o%nt of soil re.oved sho%ld :es%ffi(ient to -erfor. a single la:oratory (o.-a(tion test* The only restri(5tions ne(essary for the -erfor.an(e of the field (he(< -oint are that9

l. '%ring (o.-a(tion, the .old .%st :e -la(ed on a s.ooth solid.ass of at least 1 <g, a reF%ire.ent whi(h .ay J5 diffi(%lt toa(hieve in the field* As-halt -ave.ent or (o.-a(ted soil sho%ldnot :e %sed*



7.4 *leld Co0actlon Control end &0eclflcetlon 141

$* The soil to :e (o.-a(ted .%st :e dry of o-ti.%. for the nd to <now when the soil is d of

o-ti.%. ta<es sorne field e+-erien(e*

The reason for this se(ond reF%ire.ent .ay :e a--arent fro. ig*

given (onstr%(tion 0o: :orrow area* Toe soil 0%st tested for density, asidentified :y the field engineer, does not .at(h any soils for whi(h (%rvese+ist* Toe field (he(< -oint is -lotted as -oint V on the gra-h* 4y drawinga line -aral el to t e ry s1 e o o-ti.%. o (%rves , an anrea(hin a .a+i.%. at the 33line of o-ti.%.s,= a reasona:le a--ro+i.a5 tion of the .a+i.%. dry density .ay :e o:tained* I the soil was not

:e o:tained* Toen it wo%ld :e diffi(%lt to disting%ish whi(h la:oratory

density wo%ld :e i.-ossi:le* orne e+-erien(e is reF%ired to =feel= when

Li ne of

o-ti .% .s55

1] sat%rat ion

¡;;e

3?

A

Pd 8a>

e

Water (ontent

$2. ).*) P2n2N25 3 45 5 N32n4 45>4.

555555555555 55=555=53 55 555 K@K9@K 5 K5 5 55 5555555555559(*999****9*** 595*@5 K,59*59*@599555599***999@55 K 59 K K 55 5555 5 5 5 55 55555 5555 DD

...



1 Co0ectton

r ro:le. with the (o..on destr%(tive densitytest -ro(ed%re is that the deter.ination of the water (ontent ta<es ti.e

severa ho%rs or overnight a((ording to ATG, 167B* Ti.e is of ten of the%t.ost

Dval%e on a (o.-a(tion 0o:, and if it ta<es a day or even several ho%rs :efore the res%lts are availa:le, severaV lif ts of fill .ay have :een -la(edand (o. a(ted over the 33:ad= or =failing= test area* Toen the engineer hasa diffi(%lt de(ision to .a<e9 sho%ld the (ontra(tor :e reF.re to tear o% alot of -ossi:ly good fill 0%st to i.-rove the relative (o.-a(tion of that one=:ad= lif t Contra(tors %nderstanda:ly are very hesitant to do that, andyet how .any &ones of =:ad= (o.-a(tion are allowa:le in an e.:an< .ent 8f (o%rse, the -ro:le. is statisti(al and again, on a ty-i(al 0o:, it isdiffi(%lt and e+-ensive to (ond%(t s%ffi(ient tests for a statisti(al analysisof the (o.-a(tion res%lts*

in(e deter.ining the water (ontent ta<es the .ost ti.e, several.ethods have :een -ro-osed to o:tain a .ore ra-id water (ontent* Pandrying or =f rying= the sa.-le over an o-en fla.e is (o..only %sed, :%tsin(e 24 is diffi(%lt to (ontrol the te.-erat%re, it gives -oor res%lts,es e(ially for fat (lay CHB soils* The =s-eedy= .oist%re .eter, in whi(hthe water 2n the soil rea(ts with (ar 1 e to -ro %(e a(e y e Danother alternative* Toe gas -ress%re shown on a D (ali:rated gage is

-ro-ortional to the water (ontent* 4%rning with .ethanol and the s-e(ialal(ohol5hydro.eter .ethod are also so.eti.es %sed Toe (orrelation withstandard oven drying for these .ethods is a--ro+i.ate5 generally satisfa(tory for s1lts and lean (lays :%t -oor f. . gani( soils and fat (lays*

Another .ethod for F%i(<ly and eff i(iently deter.ining the relative

(o.-a(tion of (ohesive soils was develo-ed in the 163s :y the U**4%rea% of Re(la.ation 16!2, and Hilf, 16"1B* Toe -ro(ed%re .a<es 24

-ossi:le to deter.ine a((%rately the relative (o.-a(tion of a fill as well asa very (lose a--.+i.ation of the differenee :et*veen the o-ti.%. wa ter (ontent and the fill water (ontent witho%t oven drying the sa.-le* a.-lesof the fill .aterials are (o.-a(ted a((ording to the desired la:oratory

standard at the fill water (ontent and, de-ending on an esti.ate of how(lose the 2ll is to o-ti.%., water is either added or s%:tra(ted fro. thesa.-le ig* *$"B* With a little e+-erieo(e i t is relatively easy to est;.atewhether the 2 .aterial is a:o%t o-ti.%., slightly wet, or slightly dry of o-ti.%.* ro. the wet density (%rve, the e+a(t -er(ent relative (o.-a( tion :ased on dry density .ay :e o:tained* 8nly one water (ontent, the fill water

(ontent, need :e deter.ined and that only for re(ord -%r-oses* Toeroain advantage of the =ra-id= .ethod is that the (ontra(tor has the res%ltsin a very short ti.e* E+-erien(e has shown that it is -ossi:le to o:tain thenl%es reF%ired for eontrol of (onstr%(tion in a:o% 4 J : fro. the ti.ethe lield density test is -erforrned*



1

7.6 *leld Co0actlon Control and &0eclflcatlon 171

3f i 11

'i vide i nto th ree -a rts

Add, say, 2 g water* Add, say , 7 g water* Add, say, 1$ g water*G i + and (o. -a(t as 1 n Gi + and (o. -a(t as i n G i + and (o.-a(t as i nstandard test* Geas% re 3 standard test* Geas% re , standa rd test* Geas%redensity of (o. -a(ted sa.-l e*9 dens1ty of (o. -a(ted sa. -le* 3 dens1ty of (o.-a(ted sa.-l e*

Pl ot res% l ts

wet density

1 & +

& G water addedG .oist soil

density of .oist soi l i n f i l ldegree of (o.-a(tion of f il l 5555555555555D555

.a+i .% . density s(aled fro. a:ove gra-h , S

$2. ).* P35=G5 3 6N2= 543= 3 =5452n2n =555 33N6423n 3 2ll 645 S55=. 9)9.

8ther -ro:le.s with destr%(tive field tests are asso(iated with thedeter.ination of the vol%.e of the e+(avated .aterial* The sand (oe,of ten ta<en as the =standard,= is s%:0e(t to errors* or e+a.-le, vi:raionfro. near:y wor<ing eF%i-.ent will in(rease the density of the sand in thehole, whi(h gives a larger hole vol%.e than it sho%ld have@ this res%lts in alower field density* All of the (o..on vol%.etri( .ethods are s%:0e(t toerror if the (o.-a(ted fill is gravel or (ontains large gravel -arti(les* Any

,.



5 55D555D555DD55555555D 5 5DD55555D55555D5555 ---.- 55 5555D5555D555 5 5 ------ ?-' ...5K5

(652

K*,,,,55'ete(tors

o% r(e

6

(65

'ete(tors

o% r(e

J

(65

'ete(torso% r(e5

()

$2. ).* %Gl56 =5n>24 6n= D645 3n45n4 =5452n6423n: 6=254 46n>2>>23n; J J6>6445; 5 62 6N 645 T3Yl5 El543n2 L6J364325>, ln., R5>56 T26nl5 P6, %34 C63l2n6.



55 55 555 55555555555555

). E>4l64ln P536n5 34 C3N645= S3ll> 1#

<ind of %nevenness in the walls of the hole (a%ses a signifi(ant error in the :alloon .ethod* I the soil is (oarse sand or gravel, none of the liF%id.ethods wor<s well, %nless the hole is very large and a -olyethylene sheetis %sed to (ontain the water or o;l*

4e(a%se of sorne of the -ro:le.s with destr%(tive field tests, nondestr%(tive density and water (ontent testing %sing radioa(tive isoto-es hasin(reased in -o-%larity d%ring the -ast few years* N%(lear .ethods haveseveral advantages over the traditional te(hniF%es* Toe tests (an :e (on d%(tedra-idly and res%lts o:tained within .in%tes* Therefore the (ontra( tor andengineer <now the res%lts F%i(<ly, and (orre(tive a(tion (an :e ta<en :efore too .%(h additional fill has :een -la(ed* in(e .ore tests (an :e(ond%(ted, a :etter statisti(al (ontrol of the fill is -rovided* An average val%e

of the density and water (ontent is o:tained over a signifi(ant vol%.e of f ill, and therefore the nat%ral varia:ility of (o.-a(ted soils (an :e(onsidered* 'isadvantages of n%(lear .ethods in(l%de their relatively highinitial (ost and the -otential danger of radioa(tive e+-os%re to field -ersonnel*tri(t radiation saf ety standards .%st :e enfor(ed when n%(lear devi(es are%sed*

4asi(ally, two ty-es of so%r(es or e.itters are ne(essary to deter.ine :oth the density and the water (ontent* a..a radiation, as -rovided :yradi%. or a radioa(tive isoto-e of (esi%., is s(attered :y the soil -arti(les@the a.o%nt of s(atter is -ro-ortional to the total density of the .aterial*The s-a(ing :etween the so%r(e and -i(<%-, %s%ally a s(intillation or eiger (o%nter, is (onstant* Hydrogen ato.s in water s(atter ne%trons, and

this -rovides a .eans where:y water (ontent (an :e deter.ined* Ty-i(alne%tron so%r(es are a.eri(i%.5:erylli%. isoto-es* Cali:ratiori Dagainst(o.-a(ted .aterials of <nown density is ne(essary, and for instr%.entso-erating on the s%rfa(e the -resen(e of an %n(ontrolled air ga- (ansignifi(antly affe(t the .eas%re.ents*

Three n%(lear te(hniF%es are in (o..on %se* Toe direct trans8ission.ethod is ill%strated s(he.atl(ally . hg* *$ Qa, and the bac!scatter te(hniF%e is shown in ig* *$!:* The less (o..on air5gap .ethod ig**$!(B is so.eti.es %sed when the (o.-osition of the near5s%rfa(e .aterialsadversely aff e(ts the density .eas%re.ent*

). ESTIMATI%(PER$ORMA%CE O$COMPACTE& SOILS

How will a given soil :ehave in a fill, s%--orting a fo%ndation,holding :a(< water, or %nder a -ave.ent Will frost a(tion :e a (riti(alfa(tor or f%t%re referen(e, we -resent the e+-erien(e of the U** Ar.y



17+ Co0ectlon

Cor-s of Engineers on (o.-a(tion (hara(teristi(s a--li(a:le to roads andairf ields Ta:le 52B and the e+-erien(e of the U** 'e-art.ent of theI nterior* 4% rea % of Re(la.a t ion for severa t y-es of eart h str%(t % res Tahle

In Ta:le 52, the ter.s base, subbase, and subgrade (ol%.ns !, 7,and 6B refer to (o.-onents of a -ave.ent syste., and t ey are e .e ini * *$7* In (ol%.n the ter. C4R re resents the California :earinratio* The 5R is %sed :y the Cor-s of Engineers for the design of fleible

for rigid -ave.ent design* Tho%gh the differen(e is rather ar:itrary, the%--er ayers o e+i e -av(on(rete, whereas rigid -ave.ents are .ade of Portland (e.ent (on(rete*

A good referen(e for the design of -ave.ents 1s t e oo yWit(&a< 16! *

The %se of these ta:les in engineering -ra(ti(e is :est shown :y an

the .ost s%ita:le (o.-a(tion eF%i-.ent, and for ra-id (he(<ing of field

8 Weari ng s%rfa(e9 *0-*) (. Portland (e.ent or *-8 (. as-halti( (on(rete*

4ase9 )-8 (. as-hal ti( (on(rete, )-!0 (. sand5gravel :ase, *0-!0 (.soi l 5(e.ent, or )-*0 (. as-91al t sta:1 1&e san *

0 % ::ase .aterial this layer .ay :e o.itted B9 )-!0 (. sand5gravel*

(o.-a(ted -rior to the -la(e.ent of the other la yers of the -ave.ent*

$2. ).*8 &52n2423n> 3 45> 5l642n 43 N6155n4 >>45>, D244N26l =25n>23n> 6n= 64526l> 3 56 3N3n5n4.



U

TABLE l)-" C6645=>42> IP542l25n4 to R3=> 62= A2l25l=>

y n1:ol Mtl%l3 as :radl3 11 M l %=I3 %:: D se Mal%e4'4asl3

ot1*9nt1al Co. -r(Dssi:ility

GaJor 'ivisin1n, L(tte llatlrhinZ, Color

N9J .W ,Dn not %:J(rt hen not % e,Dt43 ID 3'24 rtion 0 1 3,4 A43n

Wh(n not %:J((t43 $3l2 A423n

l r.,t AL'4lOn

andJ*3+ -a .i%n

$B ! " ) 8 t 0

I J B

P .r#. W(llD rD d(d r (h or D a(lD@*tnd ((l<nt $,nI (nt Cood %3L'. to ver

yn%+ %r(s* lll4 or 111 qI8L33 ,l%9ht

Red raded D3==3Is 0 *ra vel5,and @, od 0 . ((llent Cood

Al.ost non(

PoorlI air 1

*, od Nohe to verD Al.os non(lAMEL 1111, %r,Ds* httle or 3= l rn(s g ,Jrht 1 1

\;R AV N llLL I J. . .. . . ,. 3,l od t o e l=l3II nt 3 d I? . t o ( od ir ht to ni M(ry ,Jiht

4' ,oo Dair llll3di% I L G 15 5 tlty r v(ls* rllv(l5san^ D^tlt .l l% res *K 5 K 355 K 555555 K K K K K **** K K K ***K

K K K K

% (llow e@, od htr Poor to n ,1 ,%rta:le S2 ht 1 lighl

(-ARrK **1 O;O'

-/- Cla (y rav(l,* rav(l5sa ndDday .i+t%re ( od 1D*atr Poor lo n ,t ,%11a:< S2 hl Ido Ihght

1,AI Nf1 111nll%111

llll' Illl

8I L W W(llgr@ drd san, or Xr. v(lly sand,* ( od I atr ood Poor Noh,D to v(ry Al.ost n3l4.', R,Dd httl Dor no rnes slr(ht

AN Nl'l 99999999 Poorly radLDd ?2 nd, or J ;J3l3lly ,*ind3i, * * No to VL' jP lilll, or no neD, 1 , 4 to o d Lnr Poor to n:t s%lla:< ,hht D Al.ost none

li ht toJ * * I ir to o, d 15air 1 ood Poor hiBh M(ry slihl

AN'G l551

51hy sands* san1l5silt .1 t%r(s

*K

1555555 55 (** K K K K 555555555555555555555555555555555555555555555555155 5555

11*

h' -- --K2-

(llow 1 , ir Poor 1n fair Not1

*s%rta le

h 111 11 1:d,I:, 1

liBhl to .(di%.

1 1 1 1C la y( y Da nd s* , * nd 5d ay *n i, t % r( s P, or lo fa r Poor Not ==3d I ir 3

lnora n e silts and v(ry in( sands* ro(<

lihl to .(di% rn111 1 1

G L

L NTllC AL I CL

( @r((n

llo% * silly or =6L'7 finLD ,and3lo or day D ,ilt, llh sliBh l -lastidly

lnora nl1l3 da y *** ,f low 11, .(di%. -la,w,lly* rav(lly l(i*oys, ,ndy day*s, 31lt y

l3For to falr

Pdor lo fJlr

Not sr0ita:<

Nn1 ,11a:<

Nnt s%ila< IIII IO

l'A ht=h

%34 ,%i1*1Z1hD Gl3 111111 to

hght to .(dt% .

GlDdi%.

5rnr LTII % )

I/daB3 * le*in ,lan

IHU

AINU 8L8IL

OlU6OÍL ,ilh* n tH,CJnl1 ,1l h9lay, 3 P N 4l2G 43low ,t*a,tinl , or ot ,t lla:< Nol ,t%l*il < l%h G(d1%111 to htBh

I LT GIi lnorK 1n l ,111* 111/anD%1 1K, or d1 1 11 anDt %**@ Pl or Not ,, Ha:h9 lol ,.1*i <D GlD i%11*, t11 lh h N' lrn,D sandy o stlt y = 11, d*1,lll3 stlt, er l%h

Cl A lnorZ5*,n ,D davs ,f ht(h I lastil5lly* fal ,

L Is@++ 4l%( ,1ay D D Po to fJ r Not >2 ila:l( N,11 s111la G(oi11111 HtBh

---P-



***R I ATI R , 8rt,ani, daB s ol 111l3dt%1 1 1 ht(hTII N )0 11 .:U -las 1%1,* o ,Da.e sil , DJH^@IILI 8R NI3

P3l3 43 3JtDty N33 Not ,Ha:le Nnt s.talll( G(^11i% . Hth

8ILPt

M: :ran(d lP(at an2 ,,thl3f ilo(hly 8lCJnt( ??I' Ndt s%ita:1,D Nol sZ0i1*1:l( Not ,%1t*1llle hlht M(ry hih

Att(r U* wa,(rway E+-ri.(k tat0on 1"B*



***'()*+ Continuad

'I

y.:ol'r.ag(

Ty-i(al '(sign Mah0esUnit 'ry 'ensities

%:grade Go%l%s

Ga0 o1 ' visi ons L(tt(r Hat(hing Color *1 1 CharaFt(ris%(s Con0-a(%on LF.-.(ntl:fQft # GgQ.#

C4R l :fQi *3B

1B $B #B 2B esZ WP 1 #B

W 5cellE$)iitCrawl(r5ty e t ra(tor* r%::er5tired

=3=3 roll(r **t(d5wh(eled roll(r

P +(ell( ICrawler5ty e tra(tor* r%::(r5tired K 1*!"5$*$2 #5" #5

roll(r* Dt((l5wh((led roller R AA N'MU I d

R%::(r5tir d roll(r* slwe-sfoot 1$512 $ 5$ #$ 1 25",RAMELL G 15 K Dair to -oor

roll(r@ Dlos( (ont rol of .o,st% e 5558IL

I%

C8ARE5 1 1 CRAINE'

ellowPoorto -ra(ti)iily :i@,1 (d i!J1(r* ili(@@0@sf%oti.- rvio%s rol l(r Poor to -ra(t1(ally R%::er5t1 (d roller* sh(e-foot

i.- TM1U rollp

8IL 1 SW E+(ell(nt Crawler5tK -e tra(tor* r%::er5tir(roller

PAN'

2

######4#4##i*,,99 9999

Red *E+((ll nt

Cra wl(r51B -e t ra(tor* r% ::(r5rne( roll(r 151 # 1*"75$*1" l 152 152

AN'dAN' SM.X -

8IL %***L

air toZ -oor

ellow It-@;f -,@@tT9i\,1=1er/1ou

R%::* ,r 5t i (d rol le r* sh(e-s foot l $51 # l.6$5$*1" 152roll(r9 Dlose (ontrol %f .o1st% eR%::5@5 ti (d,@iZe@959,@@95(-sf@@@9@t

roller

152

---- ---

Poor t -ra(t;(al ly R%::er5t1 (d roll(r, sh(e-sfooti. ervio%s 3ll

ILT GLAN' i-

air tF -oor R%::(rDt r ed roller* ^h((-sfoot K 1*225$*7 1

*>3rolln< clo&e control of mo!t re le&&

15$

CLA CLLLILEQ?. Pradi a lly R% ::er5 ti 3d ro ll er , sh(e- ,.oot 651# 1 225$*7

l1essor reen i. ( rv1o%s roller 51B

INE5 1 THAN 1 8LRAINE'

Poor R%::(rDt red roll(r* she(-, oot 651 t*2251*"7

l

(sosr roll(r D

51

8IL ILT 1 GHAN'f air t -oor he(-sfo-t roller, r%::(r5tlr(d Q 1 5 , 1*$751 "7 , l or 51

rol<rl less

CLA CHLLI 4l%e Pra(tially1Pcr/1ou hee-sfo-t r oll(r* r%::(r5t ned Q 1 6511 1 1*2251*72 1 i3(sor 3lll

REATER ITHAN 8H

/ QQ

B// Pia(tiYally

1.-ervio%s h(e-sfFot roll(r, r%::(r5tir(d Q 1 7511 1$751*!" 1e93 rnllerl

$5I8

HIHL 8RANICIL 1 Pt Mb 8rang(I air t -oor Co.-a( 01on not -ra(ti(a

:¡Z1

IU'I

i Q

Q'

5 11 12

" 1B 1"B 1!B

1$512 $*5$ $2 257 1 #5

K

I#

555

1*725$*1" K K 555#5

5 51#512 $*75$*#$ $52 $5

II8Dl # J*!"5$*7 $52 $52

5

¡se

5 @@ @@5 15$

K l8 15#

151# 1*"5$*1" 5$ 15#

6 1#

1

51

U



<

l



5 *,K .55 555

5555 K@55

5

TA,E 7"+ C3n42nG6=

Notes9

1* In (ol%.n #, division of G and G gro%-s into s%:div11ons of ^1 an^l % are ror roaas anoairfields only* %:division is on :asis of Atter:erg li.its@ s%ffi+ d e*g*, GdB D2ll :e G>5=when the liF%id li.it is $ or less and the -lash(1ty .de+ 1s 9, or 1ess@ tne s%.+ % wi%*,*,

%sed otherwise*

$* In (ol%.n 1#, the eF%i-.ent listed will %s%ally -rod%(e the reF%ired densities with areasona:le n%.:er of oasses when rnoist%re (onditions and thi(<ness of lift are -ro-(rly(ontrolled* In sorne instan(es, severa ty-es of eF%i-.ent are listed :e(a%se varia:le soll

(hara(teristi(s within a given soil gro%- .ay reF%ire different eF%i-.ent* In sorneinstan(es, a (o.:ination of two ty-es rnay :e ne(essary*

5 1.on ...nterials and other anvu/ar 8ateria/s. teel5wheeled and r%::er5tired?

rollers are re(o.rnended for hard, ang%lar rnaterials with li.ited fines or s(reenings*R%h:er5tired eo%io.ent is re(o..ended for sof ter rnaterials s%:0e(t to degradation*

:* 9inishing. R .%::er5tired eF%.i. -.ent is re(o.r n.e.nded for rolling d%ring final sha-ing

. 5 --?- K K .(* ELuip8ent siMe. The following si&es of eF%i-.ent are ne(essary to ass%re the high

.

55 . . .. . Crawler5ty-( tra(tor5total weight in e+(ess of #, l: 12 <gB*

R%::er5tired eF%i-rnent5wheel load in e+(ess of 1, l: ! <gB, wheel loadsas :i11h as 2, l: 17 <gB .ay :e ne(essary to o:tain the reF%ired densitiesfor sorne .aterials :ased on (onta(t -ress%re of a--ro+i.ately o9, to 19,% -st or

2 <Pa to 1 <PaB*hee-sfo.ot roller5%nit --ress%re on " to 1$ in* * or 2 to 7 (rn

* footB to :e in

- -- *** ***,*,**?' . . ao L:-L. aW ,r@,@n 5W@ A,6#< +! 'aB OIV

K*,*K,*** ***,*,** MI K***,M ! 'D = ( ***,M 5W ***,*, . 5 . :.e ne(.essary to o:tain the reF%ired densities for sorne .aterials* Toe ar(a of the

' ' '-- 5 --. 71G r L- 551 . a-aa nf the dr%.* %sino the . .dia.eter rneas%red to the fa(es of the feet*. . . 5 ** 5 K K K ,* K 5 5

53D 1n C8lUUll*l9? l3t **** ,9@, *** - . .rnodified AAHT8 (orn-a(tion effort*

2* In (ol%.n 1", the rna+irn%. val%e that (an o( %seo 2n aesign %ili.ited :y gradation and -lasti(ity reF%ire.ents*

1

. 5D

..

l#S: lil ..,X....... X,

17M

,. _

. :

,



TBLEI )-) T6JI6423> 3 n2nl552n4 P3N542> 3 F3N45=S32>>5= 2n E64 S4G4G5>

Irt0-ortantl Enginring Pi0o-ertie

RelatZve 'esira:ilitylfor M72o%s Uses(t,lo* 1 is (onaidFred thel:estB

P ea5

h ar t gth

en

Co.-Zss5i:iliWhe

oUedEartlill &66 Canal e(tiona o%n2ationa Road===ya

ills

,Wor<a:ltity f*o.o5

4rost

lBy-i(al a.es

3 oil 8ro%-s

^,ro%-y.:ols

:i ityen

Co. (ted

Co.0a(ted ICo.-al@9ted a d and

at ated at%raled

a& a neou&

Fonstr%( Don E :an<5Gateri .ent

ErosionCore heU I Resistan(e

C-.-a(tedE64Lining

ee-age eave rostge Not Not Heav,

1a*nt I I.-ortan P ssi:le Possi:le %a(ing

Zow Peryio%s I E+(ellent I Negli111:le

1 8P I Mery Z0ervio%s 1 09?? 1 Negli111:le

E+(elle-t

88^i * * # #

siltlayey

I8G I e.iPfrvio%s 09?? Negli1:leto i.ikrvio%s

o( l.fio%s I ood 3> fair I Mery

1Z,w

^ $ 2

88 i

2 " 2 2 +

# $ "

SW Pertio%s

P Pertio%s

G e.ikrvio%sto 1r/18u

E+(ellent

'R?'Fod Lo air

gravell gravelly7

" s if gravelly

serosion # 1(riti(a

0 "

Negli111:le E+(elle-t#2 " $ $ $ "

graveUB" 1

Mery 1Q@?w air 2 2 " "



I'



T3

1

3

3

5 5 5

U

Clayey sands, -oorly

grad(d sand5(lay se l.J Crvq8U oo 11 to fair LFw oi,d # $ - s $i+t%res

lnorgani( silts and very1

fine sands, ro(< no%r, GL e.i -(rvio%s air Ge, G a & " " - t5 erosi,n

silty or (layey fine sands to in9 -(rvio%s (riti,alwith slight -lasti(ity

lnorgani( (lays of low to

.(di%. -lasti(ity, CL l.Zlervio%s air Ge, G ood t - fair s # - fJ #gravelly (lays, sandy (lays,silty (lays, lean (lays

8rgani( silts and organi( !silt5(lays of low 8L e.i-(rvio%s 1 oor Ge^ %. a ir 7 7 - t5 erosin -l%ti(ity to 2 -(rvio%s (riti(lnorgani( silta, .i(a((o%s or

diato.a(eo%s fine GH e.it?(rvio%s air o -oor HilJh Po(r 6 6 - - -Glldy or silty soil1, to 2 :(rvio%sel%ti( lilta

7voh. e

Inorgani( (lays of high CH I.-, r/iou P ?r HiZih Poo ! ! - 1 (:anZe -lalti(ity, fal (lays (riti(iJ

8rgani( (lays of .(di%.

to high -lasti(ity 8H l.-etvio%s P(-r Hig Poor 1 J8 - 5 - 1 " " " -

Peal and other highlyorgani( soils P4 5 5 - - - - - - - - 5 - - -

>Alter U4R 16!2B*

1

1

1

5

" 7 ! $

" 6 1 11 5

s 1 6 !

! 11 11 1 55

7 1$ * 11# -

6 1# 1# 7 5

1



E9A3PE *2(215n:

A soil, (lassified as a CL a((ording to the UC, is -ro-osed for a(o.-a(ted f 2ll.

R5FG25=:

Consider the soil to :e %sed as9

a* %:grade"* Earth da.

(* o%ndation s%--ort for a str%(t%re Use

Ta:les 52 and 5 and (o.rnent on9

1. The overall s%ita:ility of the s1I$* Potential -ro:le.s of frost #* ignifi(ant engineering -ro-erties4 A --ro-ria te (oro-a(tiao eF%i-.ent to %se

23n:

Pre-are a ta:le for soil ty-e CL*

Itero Use9 %:grade Earth 'a. tr%(t%ral o%ndation

1* A--li(a:ility

Poor tofair

Usef%l as(entral (ore

A((e-ta:le if (o.-a(teddry of o-ti.%. and 2 notsat%rated d%ring servi(e life

$* rost -otential Gedi%. to Low 2 (overed. :y nonf

rostheaving soil

Gedi%. to high 2 not (on5trolled :y te.-erat%re andwater availa:ility

#* Enginee1 ingGetii%.

de-th :ew -er.(a:il

Pot(ntial fer -eer strength -ro-erties (o.-ressi:ilityfair streogt:

ity, (o.-a(t6 low -er.ea5

aod therefore -oor -erfor.an(e

CBR :;; ) :ility aod highstreo th :%t also for fle+i:ility

2* A--ro-riate (o.-a(tion :ee-sfoot andQeF%i-.ent or r%::er5tired

:ee-sfoot andQor r%::er5tired

:ee-sfoot andQor r%::er5tired

roller roller roller

Note9 8n(e yo% have finished with this :oo< and a (o%rse in fo%ndationengineering, yo% (o%ld readily e+-and the infor.atlon . thls ta:le*



P!O,E3&

51* o1 the data in ig* *19

aB Esti.ate the .a+i.%. dry density and o-ti.%. water (ontentfor :oth the standard (%rve and the .odified Pro(tor (%rve*

:B What is the -lae.t.t water (ontent range far 6] reBa tive(o.-a(tion for the .odified Pro(tor (%rve and 6] relative(o.-a(tion for the standard Pro(tor (%rve

(B or :oth (%rves, esti.ate the .a+i.%. -la(e.ent water (ontentfor the .ini.%. (o.-a(tive effort to a(hieve the -er(ent relative (o.-a(tion in -art :B*

5$* The nat%ral water (ontent of a :orrow .aterial is <nown to :e 1]*Ass%..g 000 g 3 (et sotl > %sed for la:oratory (o.-a(tion test -oints, (o.-%te how .%(h water is to :e added to other 000 gsa.-les to :ring their water (ontents %- to 1#, 1!, $, $2, and $7]*

5#* or the s1I shown in ig* *1, a field densi ty test -rnvided thefollowing infor.ation9

Water (ontent / 12]Wet density / 1*76 GgQ.# 117 l:f Qf t

#B

Co.-%te the -er(ent relative (o.-a(tion :ased on the .odifiedPro(tor and the standard Pro(tor (%rves*

52* or the data given :elow F Ps $*"2 GgQ .#B9

aB Plot the (o.-a(tion (%rves*:B Esta:lish the .a+i.%. dry density and o-ti.%. water (ontent

eB Co.-%te the degree of sat%ration at the o-ti.%. -oint for data. (o %.n

dB Plot the 1] sat%ration &ero air voidsB (%rve* Also -lot the !,7, and 6] sat%ration (%rves* Plot the line of o-ti.%.s*

e .odifiedB standardB

low energyB

Pd GgQ.#B ( ]B Pd GgQ.#

B ]B , Pd GgQ.JB ]B

1*7!# 6*# 1*"61 6*# 1*"$! 1*61*61 1$*7 1*!1 11*7 1*"#6 1$*#

1*7# 1* 1*! 12*# 1*!2 1"*#

1*"66 17*! 1*!2! 1! " 1 !! $ 1

1*"21 $1*1 1*"7 $*7 1*"2! $$*2

1*"16 $#*

,j



- 5 5 -

55

555 5 5*

5* A field (o.-a(tion (ontrol test was (ond%(ted on a (o.-a(ted lif t*The .ass of the .aterial re.oved fro. the hole was 1712 g and thevol%.e of the hole was fo%nd to :e 622 (.# A s.all sa.-le of the

. soil lost 1 g in the drying test and the .ass re.aining af ter dryingwas 1 g* Toe la:oratory (ontrol test res%lts are shown 2n ig* P5*Q, X ' ' T. , 5 .. W ,rvv,, .

and ( / o-ti.%. 5 #]B to o-ti.%. 1]B, deter.ine thea((e-ta:ility of the field (o.-a(tion and state why this is so* 1

:B I it is not a((e-ta:le, what sho%ld :e done to i.-rove the(o.-a(tion so that it will .eet the s-e(ifi(ation

1*7 35

M

E

3e,,*

5 X?O 1*! 35

QQ

.*%

=1 1 1

1 1 $ $D

$2.P)-)

5"* Cal(%late the (o.-a(tive effort of the .odified Pro(tor test in J34, 3 55 - . - * * ** -<H64 J. " 'lll9U 5 UUH*?*

5!* Why does the relative (o.-a(tion de(rease if there is vi:rationd%ring the sand (one test

57* In a field density test, %sing the oil .ethod, the wet .ass of soilre.oved fro. a s.all hole in the fill was 1*6 <g* The .ass of oil s-* gr* *6B reF%ired to fill the hole was *71 <g, and thefield water (ontent was fo%nd to :e $]* I the Ps of the soilsolids is $! <gQ .#

, what is the dry density and degree of sat%ration of the fill

56* Let3s -retend yo% are an earthwor< (onstr%(tion (ontrol ins-e(tor and yo% are (he(<ing the field (o.-a(tion of a layer of soil* Toe

G . . W *K *K 3M 5 -

-

-

-

55



5 5



Pro#lea113

la:oratory (o.-a(tion (%rve for the soil is shown in ig* P56*-e(ifi(ations (all for the (o.-a(ted density to :e at least +2O of the.a+i.%. la:oratory val%e and within k $] of the o-ti.%. water

es , e vo %.e o s1 e+(avated was 11# (.#

* lt weighed $$6 g wet and 17!6 g dry*aB What is the (o.-a(ted dry density:B What is the field water (ontenteB What is the relative (o.-a(tion

*

eB What is the degree of sat%ration of the f ield sa.-le

the water (ontent

M

1 *!

.

.) ...

* 12 8 $

$2. P)-9

(ontrol (%rve has the following val%es9

0" "1* 1"0 81 $1#* **11 $2



X ******** , K , . * 5 --- ...5* 5 5 5 5 5 5 55 .- 5 5, 5

K

- 55 555555 555555 5555

1"2Co0ec'on

The s-e(ifi(ation for (o.-a(tioo states that the (o.-a(ted fieldsoil .%st :e at least 6] of the .a+i.%. (ontrol density andwithin$] of the o-ti.%. rnoist.e for the (ontrol e%rve* o% dig ahole of 30o f t# in the (o.-a(ted layer and e+tra(t a sa.-le that

weighs 2 l:wet and #*2 l: dry*aB W:a t is the (o.-a(ted pdI The (o.-a(tion I The -er(ent

(o.-a(tion 'oes the sa.-le .eet the s-e(ifi(ations:B l the density of solids is $*! GgQ.#

, what is the (o.-a(teddegree of sat%ration l the sa.-le were sat%rated at(onstantdensity, what wo%ld :e the water (ontent After C* W* Lovell*B

511* A .i+t%re (ontains #] :y dry (eight fines and !] (oarse* Whenthe (oarse .aterial has a ( / $], its affinity for water is(o.-letely satisfied* The f ines have a PL / $ and an LL 2*

This .i+t%re is co8pacted :y rolling to Pd / 1# -(f and D2Y /1]* What is the water (ontent of the fines in the (o.-a(ted.ass What is the liF%idity inde+ of the fines in the (o.-a(ted.ass Af ter C* W*Lovell*B

51$* A soil -ro-osed for a (o.-a(ted fill (ontains 2] fines and o/o(oarse .aterial :y dry (eight. When the (oarse fra(tion has ( 1*],its affinity for water is (o.-letely satisfied that is, it is sat%rated :%ts%rfa(e dryB* The Atter:erg li.its of the fines are LL $!andPL / 1$* The soil is (o.-a(ted :y rolling to a Pd $* GgQ .

#at

( 1#]* Note9 This is the water (ontent of the entire soil .i+t. e*

aB What is the water (ontent of the fines in the (o.-a(ted .ass:B What is the li<ely (lassifi(ation of the soil ive :oth theUnified and the AAHT8 (lassifi(ationsB*

eB What is the liF%idity inde+ of the finesdB What (an yo% say a:o%t the s%s(e-ti:ility of the fill to

1B shrin<age5swelling -otential$B -otential for frost a(tion

eV Is there a (ertain ty-e of (o.-a(tion eF%i-.ent yo% wo%ldes-e(ially re(o..end for this 0o: Why

51#* A fine sand with -oor gradation is to :e %sed as a s%:grade for afle+i:le -ave.ent* ive as .%(h infor.ation as yo% (an a:o%t the

s%ita:ility of this soil as a -ave.ent s%:grade*512* What soils, if -ro-erly (o.-a(ted, wo%ld .a<e the :est fo%ndation

.aterial for a str%(t%re ive yo%r answers in ter.s of the Unifiedoil Classifi(ation yste. sy.:ols*

51* The sa.e as -ro:le. 512, for an earth da.*



55555555555D555DDDD 5D55* D5 ************ 5DD---- -** ****** ************* K - 5 D55DD5D5D5555555555555555555555

Pro#le 147

51"* iven9 The data shown in ig* *$* oil ty-es # and 2 are .i+ed inthe :orrow area to sorne %nl.own e+tent* Af ter air drying a re-resentative sa.-le of the (o.:ined .aterial to a %nifor. water (ontent ho-ef%lly on the dry side of o-ti.%.B, a (o.-a(tion test is -erfor.ed and a val%e of 1*7 GgQ.# dry density at water (ontent is o:tained* aB Esti.ate the .a+i.%. dry density of theeo.:ined soils* :B I a field dry density of 1*7 GgQ .# wereo:tained af ter (o.-a(tion :y a shee-sfoot roller, (o.-%te the relative (o.-a(tion*

51!* The (ore of an earth da. is to :e (o.-a(ted on the wet side of o-ti.%. so as to ens%i9e low -er.ea:ility and fle+i:ility a non:rittle stress5strain relationshi-B* o% have the (hoi(e of %sing ashee-sfoot roller or a s.ooth wheel roller to (o.-a(t the soil* Tored%(e -otential shr.<age of the da. (ore, wfO(h 1s the :est -1e(eof eF%i-.ent to %se I the soil were to :e (o.-a(ted dry of o-ti.%., wo%ld it .atter

,J



555555555555555555555555555555555555D55555 5



!!>

Jater in 7oili=I:Ca0illarit@=7hrinage=7Lelling.*roit Action

6. 1 INT!O('CTION

ro. -revio%s dis(%ssions on the Atter:erg li.its, (lassifi(ation of soils, and soil str%(t%re, yo% sho%ld now reali&e t-at the -resen(e of water in soils is very i.-ortant* Water very strongly affe(ts the engineering :ehavior of .ost soils, es-e(ially fine5grained soils, and water is ani.-ortant fa(tor in .ost geote(hni(al engineering -ro:le.s* A few e+a.5

-les in(l%de (a-illarity, swelling, and frost a(tion in soils, dis(%ssed in this(ha-ter, and see-age of water thro%gh da.s, levees, et(*, dis(%ssed inCha-ter !* Pro:le.s of settle.ent of str%(t%res (onstr%(ted on (lay soilsand the sta:ility of fo%ndations and slo-es also involve water to sornee+tent* As an indi(ation of the -ra(ti(aV i.-ortan(e of water in soils, it has :een esh.ated that .ore -eo-le have lost their hves as a res%lt of fail%resof da.s and levees d%e to see-age and =-i-ing= Cha-ter !B than to all theother fail%res of (ivil engineering wor<s (o.:ined* In the United tates,da.age fro. swelling soils an n%a lly (anses a grea ter e(oooroi( Joss than floods, h%rri(anes, tornadoes, and earthF%a<es (o.:ined*

In general, water in soils ean :e tho%ght of as either statie or

dyna.i(* The gro%nd water ta:le, even tho%gh it a(t%ally fl%(t%atesthro%gho%t the year, is (onsidered to :e stati( for .ost engineering -%r-oses* Adsor:ed water Cha-ter 2B is generally stati(* i.ilarly, (a-illarywater is %s%ally ta<en to :e stati(, altho%gh it too (an fl%(t%ate, de-endingon (li.ati( (onditions and other fa(tors* In this (ha-ter we shall (on5(entrate on stati( soil5water -ro:le.s*

114



$.2 Ca0lllarlt@ 1$7

The following notation is introd%(ed in this (ha-ter*


Pat. ML' 1 G'2 <Pa At.os-heri( -ress%re

L ., .. Radi%s of .enis(%s

6. CAPIA!IT)

Capillarity arises fro. a fl%id -ro-erty <nown as surface tension ,

whi(h is a -heno.enon that o((%rs at the interfa(e :etween dif ferent.a teria Bs or soils, it o((%rs hetween s%rfa(es of water, .ineral grains*and air* %nda.entally, s%rfa(e tension res%lts fro. differen(es in for(esof attra(tion :etween the .ole(%les of the .aterials at the interfa(e*

The -heno.enon of (a-illarity .ay :e de.onstrated in .any ways*Pla(ing the end of a dry towel in a t %: %f watet will event %ally 1esalt in asat%rated towel* To iU %strate the eff e(ts of (a-illarity in soils, we (an %sethe analogy of s.all dia.eter glass t%:es to re-resent the vo1ds *l@?etweenthe soil grains* Ca-illary t%:es de.onstrate that the adhesion for(es :etween the glass walls and water (a%ses the water to rise in the t%:es andfor. a .enis(%sk :etween the glass and the t%:e walls* Toe height of rise isinversely -ro-ortional to the dia.eter of the t%:ing@ the s.aller the insidedia.ete1 of the t%:e, the greater the height of ea-illary rise* The .enis(%sfor.ed is (on(ave %-ward with the water =hanging,= so to s-ea<, on thewalls of the glass t%:e ig* "* laB* With sorne .aterials the internaV (ohesionfor(es are greater than the adhesion for(es, and the s%:stan(e will not =wet=the gBass t%:e* Ger(%ry, for e+a.-le, has a de-ressed .enis(%s@its sha-e is (onve+ ig* "*1 :B*

I we loo< .ore (losely at the .enis(%s geo.etry for water in a fine(a-illary t%:e ig* "*B, we (an write eF%ations for the for(es a(ting in the

Af ter ia(o.o Genis(%s 1226511$B, a Menetian -hysi(ian and friend of Leonardo daMin(i* We are inde:ted to Prof* G* E* Harr, P%rd%e University, for this little <nown fa(t*B

d L ., .. 'ia.eter F MLG' 2 N or(ehe L . Height of (a-illary rise

G u

MG ' 2

ML' +G' N<Pa

%rfa(e TensionPore water -ress%re

uca

ML' 1 G'2 <Padegree

Ca-illary -ress%reConta(t angle



.

r-...

'Mer/r7

.

Eater

8

1

wF K--+-

Ko

_Ci =

- ..

-- K=ension)

/ Co85ression)

1-1ll D - n a

ePat8

lll .......-D-

-1K

K w D bPw L

K W7rostati)

'8 2 os & +) K

K'

$2. . M5n2>2 2n l6>> 4GJ5> 2n 6 D645 6n= J 5G.

Pat . U 1

$2 . "*$ M5n2>G> 5354 3 6N2ll6 2>5 3 D645 2n 6 l6>>4GJ5.



"*$ Ca0lllarlt@ 16

water (ol%.n* The for(e a(ting downward, (onsidered -ositive, is theweight of the (ol%.n of water, or

"51B

Toe %-ward for(e is the verti(al (o.-onent of the rea(tion of the .enis(%sagainst the t%:e (ir(%.f eren(e, or

L $G / GdG C8 a "5$B

where & isD the surface tension of the water5air interfa(e whi(h a(ts aro%ndthe (ir(%.f eren(e of the t%:e* The s%rfa(e tension has di.ensions of for(eQ %nit length* The other ter.s are f%n(tions of the geo.etry of the

syste. and are defined in ig* "*$*or eF%ili:ri%. % 9v / 8, and

"5#B

olving for the height of (a-illary rise, for (lean glass t%:es and -%rewater, a 'K 8 and (os a 5` l* Th%s

h / --e P( gd "52B

Toe (a-illary rise is %-ward, a:ove the free (ater sur@ace, :%t is has anegative val%e :e(a%se of the sign (onvention shown in Pig* "*$* %rfa(etension G is a -hysi(al -ro-erty of water and, fro. the Zandboo! of

Che8istry and Physics 16!!B, at $>C, & is a:o%t !# dynesQ(. or !# .NQ.*in(e P( / 1 <gQ.! and g / 6*71 .Qs*

, for -%re water in (lean glasst%:es EF* -" red%(es to

h 5#15

B. 5*# .

e din .B din ..B

"5B

This for.%la is easy to re.e.:er* or the height of (a-illary rise in.etres, divide *# :y the dia.eter in .illi.etres*

Ali the -re(eding dis(%ssion is for (lean glass t%:es and -%re water %nder la:oratory (onditions* In reality, the a(%al height of (a-illary rise is

li<ely to :e so.ewhat less d%e to the -resen(e of i.-%rities and i.-er fe(tly (lean s%rfa(es*

E9A3PE "*1

(215n:

Toe* dia.eter of a (lean glass (a-illary t%:e is *1 ..*

.j



<1

1! W645 In S3ll6, : C6Nlll6l4, Sln65, SD5llln, $364 A4l3n

R5FG25=:

E+-e(ted height of (a-illary rise of water*

S3lG423n:

Use EF* "5*he 3 *#

.B

/8

.! .

Also shown in ig* "*$ is the -ress%re or stress distri:%tion in thewater* 4elow the s%rfa(e of the water reservoir, the -ress%re in(reaseslinearly with de-th hydrostati( -ress%reB* A:ove the reservoir s%rfa(e, thewater -ress%re in the (a-illary t%:e is negative or less than &ero gage

-ress% re referen(ed to at.os-heri( -ress% reB* ro. EF* "52, i ts .agni t %de

I

& 5$T - - /--

d r8D "5"B

Toe sha-e of the .enis(%s is a(3t%ally s-heri(al a r.r%.%. energy(onditionB with radi%s r8 ig* "*$B* The radi%s is greater than or eF%al tothe radi%s of the t%:e, de-ending on the (onta(t angle o9* When o9 isa--ro+i.ately &ero, then r8 / dQ$*

What is the .a+i.%. negative -ress%re that (an :e attained Inlarge t%:es, the li.itation is the va-or -ress%re of water* When the

-ress%re goes negative, that is, less than at.os-heri(, water will (avitate, or =:oil,= when the a.:ient -ress%re rea(hes the va-or -ress%re* In a:sol%teter.s, the va-or -ress%re of water is 1!*2 .. Hg or $*#2 <Pa a:sol%te at$>C fro. the Zandboo! of Che8istry and Physics 16!!BX* Toe relationshi-s :etween a:sol%te, gage, and va-or -ress%re of water is shown in ig*

"*#* Toe eF%ivalent (a-illary t%:e dia.eter at the va-or -ress%re is a:o%t #.* Now, if the t%:e is s.aller than this dia.eter, then the water (annot (avitate :e(a%se the s%rfa(e tension is too high and a :%::le (annot for.* In this

(ase, the height of (a-illary rise in s.aller t%:es de-ends only on the t%:edia.eter, and the rise .ay :e .%(h greater than 1 .* irnilarly, the(a-illary -ress%re -ore water tensionB in this (ase .ay :e .%(h greaterthan 5 1 at. or 5 l <Pa* l4 sho%ld :e noted that for /arge tubes the.a+i.%. allowa:le tension or s%(tion in water de-ends only on theat.os-heri( -ress%re and has nothing to do with the dia.eter of the t%:e*Ca-illary rise in s8a/1 tubes, on the other hand, has no relation toat.os-heri( -ress%re and is a f%n(tion of the t%:e dia.eter only Ter&a*ghiand Pe(<, 16"!B*

*



V6N N5>>G5 3 D645 64 * 5

$*#2 P6 6J>8*8 1!2 K H-6J>*#2 N>26

8 64K-6J> 1 64-6J>8 P6-6J> 11 #$ P6-6J8 H-6J> 8 !" H-6J`8 N>26 ABSOLTE PR ESSR E 12 "6" N>26 1

64K-65 (A(E PR ESSR E 64 65 P5>>G551o-$) P6-65 O P6 M6M50. ) H-65

V6N N5>>G5 3 D645 64 $ >C H-65

512*"6 ) N>2 1 N>2

567*66 P6-6558* !2$ H-65512*#" N>2

$2. .! T5 5l6423n>2N N54D55n 643>N52 6n= 16N3 l5>>G5> D645 2n 45> 3 6J> lG45 6n= ) 5 N5>>G5>.

******

5

...



1;.1 8

E9A3PE .*

(215n:

Toe -ress%re relationshi-s shown in ig* "*#*

R5FG25=:

a* how that the .a+i.%. height of a water (ol%.n in a large t%:e

is a:o%t 1 .*b. how that the eF%ivalent -ore dia.eter at the va-or -ress%re is

S3lG423n:

a* In large t%:es, the .a+i.%. height of a water (ol%.n is governed :y the v a-or -ressare or the .a+lro% ro negative -ress%re in thewater* ro. ig* "*#, at the va-or -ress%re, the -ress%re is 567*66<Pa* Using EF* "5" we have,

h 567*66 <Pae P( g 1 <gQ .# B6*71 rnQs

$B

*5 99K 18 *1 . riseB

sin(e <Pa / 1! <g DrnQs* Q.* A--endi+ AB*b. Use EF* "5*

Even tho%gh soils are rando. asse.:lages of -arti(les and theres% lt.g v1ds are si.ilarly rando. and highly irrng%lar, the (a-illary t%:eanalogy, altho%gh i.-erfe(t, hel-s e+-lain (a-illary -heno.ena o:servedin real soils* In -rin(i-ie, (a-illary or negative -ress%res and (a-illary rise

will :e si.ilar in soils and in glass t%:es* Let3s loo< at a series of (a-illaryt%:es in ig* "*2* T%:e has a diarneter de, and th%s the (orres-ondinghe1ght of (a-11lary rise is he. The f%ll9y d%elo-ed .enis(ns :as a radi%s re.

In t%:e $, h ^ he 4 the water will try to rise to he :%t (annot* ConseF%ently,the radi%s of the .enis(%s in t%:e $ will :e !$a$! than re sin(e it is -hysi(ally i.-ossi:le for the (orres-onding (a-illary -ress%re and therefore the re : to develo-* In t%:e #, a large :%::le ot void e+ists, and there isno way for the water to :e -%lled a:ove a void with diaroeter greater than

172



I

JateQ

re re

'

he



1M+ Jater In &oll= 1: Ca0lllarlt@= &hrlnage= &Lelllng= *rot Actlon

d e. However, i+ as is shown in t%:e 2 water inf iltrates down fro. the to-,then it is -ossi:le for the .enis(%s at the to- of the t%:e to s%--ort theentire (ol%.n of water* The walls of the void s%--ort the water in the voido%tside of a (ol%.n of water of dia.eter de . T%:e is filled with soil, andthe water wo%ld rise to the s%rfa(e of the soil sin(e the average or e@fective

-ore dia.eter is .%(h less than de. Toe (a-illary .enis(i hang on the -arti(les, whi(h in(reases the (onta(t for(es :etween the -arti(les* A.agnified -i(t%re of two sand -arti(les (onne(ted :y .enis(i of radi%s r8

is shown in ig* "*a* Toe intergran%lar (onta(t stress is o3 .In soils, it is (o..on to ass%.e the effe(tive -ore dia.eter is a:o%t

$] of the effe(tive grain si&e ' 1B* Using this ass%.-tion, we (anest;.ate a theoreti(al height of (a-illary rise and the (orres-onding

(a-illary -ress%re for a fine5grained soil* This ass%.-tion -oints %- thei.-ortan(e of pore siMe, not grain si&e, as the (ontrolling fa(tor iri (a-illar5

(5)

$2. .) 6 TD3 >32l 62n> 5l= 43545 :y 6 6N2ll6 2l.

J

$2. .) J BGl2n >4G4G5 2n >6n=.



9

8.2 Ca-lllarlty 17+

ity* Resear(h at P%rd%e University ar(ia54engo(hea, et al*, 16!6B has(ontent, yo% (an get very different -ore si&e distri:%tions in the sa.e soil*

ri( o na %ra soi s a so vanestre.endo%sly, and it is -ossi:le to have very different -ore si&e distri:%5tlons . s1 s wit the sa.e

1>

Cal(%late aB the theoreti(al height of (a-illary rise and :B the (a-illaryress%re in a (la soil with D of l .*

. S3lG423n:

Effe(tive -ore dia.eter *$ '0 / *$ ." *$ + 15! ..

a* Ca-illary rise EF* "5B9

h /------

e *$ S 15# ..

:* Ca-illary*-ress%re EF* "5"B9

1 . a:o%t ftB

intergran%lar stresses :etween the soil grains are of the sa.e order of .agnit%de* Toe intergranular or ef@ective stress a3 ig* "*aB, whi(h isdis(%ssed in .ore detail in the ne+t (ha ter, is defined as the total stress a

.in%s the -ore water -ress%re u,

a3 a 5 u "5!B

at.os-heri( -ress%re, or the total stress a 8 &ero gage -ress%reB* Toen a3

/ -O-uJ / uc or, for E+a.-le "*#, a3 1 <Pa* Rarely in nat%re dothe (a-illary -ress%res a(t%ally rea(h s%(h a .agnit%de* orne of the voidsin nat%ral soils are large eno%gh that the water (an va-ori&e and :%::les (anfor.* Th%s, .enis(i are destroyed and the a(t%al height of (a-illary rise isred%(ed* 4%t still heights of (a-illary rise (an :e signifi(ant



1M4 Jater n &oll= 1:Ca0lllarlt@= Shrln?a@e: Swellln@: *rot Actlon

TA,E 6"1 ANN3Y2645 H524 3 C6N2ll6 R2>5 2n O255n4 S32l>L33>5 'ense

Coarse sandGedi%. sand

*#5*1$ .*1$5* .

*25*1 .*#51*I8 .

ine sand *#5$* . *25#* ilt 1*5l8 . $*51$ Clay 1 .

After Hans:o 16!B*

in es-e(ially fine5grained soils, and (a-illary -ress%res (an :e i.-ortant*Ta:le "51 lists sorne ty-i(al heights of (a-illary rise for several soil ty-es*

At the to- of the soil5water (ol%.n, the tension in the water -%lls thegrains of soil together, as was shown in ig* "*a* Toe greater the (a-illarytension, the greater the intergran%lar (onta(t stress, and therefore a higher fri(tional resista(e develo-s :etween the grains* Toe effe(t is si.ilar towhat ha--ens when sorne sand is -la(ed in a r%::er .e.:rane, sealed,and a va(%%. drawn on the sa.-le* Toe e+terna air -ress%re holds thegrains tightly together and there:y in(reases their strength (onsidera:ly*

The .oist%re fil. s%rro%nding the individ%al grains res%lts in =a- -arent(ohesion*= I4 is not tr%e (ohesion in a -hysi(al sense* In sorne (ases, for e+a.-le, end d%.-ing of .oist sands, a very loose honey(o.:ed str%(t%resi.ilar to ig* 2*$B res%lts, as is shown in ig* "*:* The grains are ali heldtogether :y (a-illary f il.s, and the res%lting str%(t%re, al tho%gh it has a

very =loose= relative density, is fairly sta:le as long as the (a-illary .enis(i are -resent* This (ondition is (alled bul!ing , and it o((%rs only in .oist sands* l4 is -ossi:le to destroy the (a-illary .enis(i :y flooding and there:y de(reasethe vol%.e signifi(antly* till, flooding is not a very good way to in(reasethe overall density of a sand fill@ the relative density of flooded fills willstill :e very low and th%s not a very good fo%ndation .aterial* ig%re "*:also shows why it is not a good ideato -%r(hase .oist sand :y the vol%.e5 one .ay end %- :%ying a lot of air

Another i.-ortant (onseF%en(e of the in(rease in eff e(tive stress thato((%rs d%e to (a-illarity is ill%strated :y the ra(etra(< at 'aytona 4ea(h,

lorida ig* "*"B* Toe sands are very fine and have :een densifiedso.ewhat :y wave a(tion* Toe (a-illary &one, whi(h is relatively wide d%eto the flat slo-e of the :ea(h, -rovides e+(ellent driving (onditions d%e tohigh (a-illary -ress%res* As in t%:e of ig* "*2, the (onfining -ress%reres%lts fro. the (ol%.ns of water hanging on the .enis(i at the s%rfa(e of the :ea(h* Where the o(ean water destroys the .enis(i, the :earing(a-a(ity is very -oor, as anyone who has ever tried to es(a-e a rising tideat a :ea(h in an a%to.o:ile <nows



5 55555555555555555555555555D55DD5D55D,555D5D5DD55555 *5DD5DD5 5555DD55555D55555

.* C6Nlll6l4 1!!

Poor :earing Poor :eari ng(a-a(ity = oo K d K :Kea K rK in K g K ( K a K - K aK (K itv

K K K ra K ( K eK t K ra K ( K < K *i5`555 (a - K a K ( K it K v

1

Q ro% nd water ta:le

has relatively -oor :earing (a-a(ity, es-e(ially for .oving vehi(les* Thee sarne, ye e

:earing (a-a(ity is signifi(antly different si.-ly d%e to (a-illarity*a-1 anty a so a ows e+(avations to :e (onstr%(ted in silts and very

fine sands5rnaterials that, if d , wo%ld readil fall to their nat%ral an o@ repose ig* "*! and Cha-ter 11B* 4elow the gro%nd water ta:le, e+(ava5

$2. . lllG>46423n 3 45 6nl5 3 5N3>5 N3436N J M. SG5n=6.



< '

178 Jater In &olla= 1: Ca0lllarlt@= &hrlnage= &Lelllng= *rot Actlon

there A:ove the gro%nd water ta:le and within the &one of (a-illarity,

the (%t* However s%(h e+(avations are e+tre.ely %nsta:le* They have :een<nown to (olla-se d%e to even very slight i:rations, s%(h as fro. tr%(<son near:y streets or near:y (onstr%(tion o-erations li<e -ile driving*o.eti.es well -oints and other .ethods for lowering the gro%nd water ta:le are %sed to (a%se a tension in the ore water Ter&aghi and Pe(<,16"!B* I -%.-ing is sto--ed :e(a%se of a -ower fail%re, for e+a.-le, the

. . .

sons3 :a(<s have :een :la.ed for the (olla-se of %ns%--orted e+(avationsin the organi( silts (alled bu/l 3s /iver : along the H%dson River in Newor<*

6.% &H!IN-AGE PHENO3ENA IN &OI&

We (an get an idea of how (a-illary stresses (a%se shrin<age in (laysoils :y st%dying the analogy of a hori&ontal t%:e with (o.-ressi:le elasti(

filled with water and the radii of the .enis(i, whi(h haven3t rea(hed their final sha-e yet, are very large* As eva-oration o((%rs, -ress%re in the water de(reases and the .enis(i start to for. ig* "*7:B* As eva-oration (ontin%es, the radii :e(o.e s.aller and s.aller, the (o.-ression in the

(o. ressi:le walls of the t%:e in(reases and the t%:e shrin<s 2n len th anddia.eter* The li.iting (ase, shown in ig* "*7(, is when the radii of thernenis(i are at the .;ni.%. eF%al to one5half the dia.eter of the t%:eBand are f%lly develo-ed* Toe negative -ress%re in the (a-illary t%:e is theneF%al to the val%e (o.-%ted fro. EF* "5", and the walls of the t%:e haveshr%n< to an eF%ili:ri%rn (ondition :etween the rigidity of the walls andthe (a-illary for(es* I the t%:e is i..erse . water, t e .erns(1 aredestroyed and the t%:e (an e+-and :e(a%se the (a-illary for(es a(ting onthe t%:e walls are destroyed*

Unless the walls of the t%:e are -erfe(tly elasti(, the t%:e will notret%. (o.-letely to its original length and dia.eter*

shown in ig* "*6* As with the -revio%s (ase, the t%:e initially is (orn-letelyfilled with water* As eva-oratton t es - a(e, t e .er%s(1 eg. to or.and, at the :eginning, the largest -ossi:le radi%s is the radi%s of the larger end, r 1D At the s.aller end, the radi%s is also eF%al to r 1D lt (annot :e anys.aller :e(a%se then the -ress%re wo%ld have to :e lower .ore negativeBand that (annot ha--en* 4y hydrostati(s, the -ress%re in the water .%st :e



.! Sln55 Phenoene In &olla 1M

1 ' ' 1, 5555551

6

5555555Q$5555 1

J

516N36423n 6n= >G65 45n>23n 645 T562, 9*.

$r 1 r,

$2. .9 C6N2ll624 2n 6 4GJ5 3 Gn5FG6l 6=22 645 A. C6>66n=5.

the Iower .ore negativeB -ress%re* A> eva-oration (ontin%es, the .enis(iretreat %ntil the (ondition indi(ated :y the (ro..ss5hat(hed se(tion o.f

the[

the s.aller se(tion of the (a-illary t%:e@ the (a-illary -ress%re .ay go nof%rther no .ore negativeB and (orres-onds to the -ress%re whi(h (an :es%--orted :y the s.aller dia.eter radii* This -ress%re is given :y EF* "5"*Event%ally, the t%:e will :e(o.e e.-ty if eva-oration (ontin%es*

Another si.-le analogy was %sed :y Ter&aghi to ill%strate the effe(tsof (a-illary -ress%res 2n a -oro%s .aterial Casagrande, 16#7B* A loose hallof a:sor:ent (otton is s%:.erged in a :ea<er and allowed to :e(o.e(o.-letely sat%rated* I the hall is (o.-ressed then released, the fi:ers D2llF%i(<ly swell again* However, if the (o.-ressed hall is re.oved fro. the

._

1



148 Jater In &oll= 1: Ca0lllarlt@= &hrlnage= &Lelllng= *rot Actlon

of the (a-illary .enis(i that forrn aro%nd the fi:ers* In fa(t, the hall will :erather ir. as ong as 1t oesn ry o% oo D Di..ersed in water, the .enis(i are destroyed and the fi:ers again :e(o.e e+tre.ely loose and soft* i.ilar :ehavior res%lts when (otton 1s

loose on(e the (o. ression is

released*

analogy with shrin<ing soils is very %sef%l* A soil sa.-le slowly dryingt at 1s, %n ergo.g es1((a 1n w1 or. (a-i aryindivid%al soil rains* As a res%lt, the stresses :etween the grains in5

tergran%lar or effe(tive stressesB will in(rease and the soil will e(rease nis(i :e(o.e s.aller and the

(a-illary stresses in(rease, whi(h f%rther red%(es the vol%.e* A -oint is

sat%ration still essentially 1]* The water (ontent at whi(h this o((%rs isdefined as t e s !i% a$ 1"1 or (5 , an I I oli.its .entioned in Cha ter $* At this -oint, the (a-illary .enis(i 0%st

:egin to retreat :elow the soil s%rfa(e, and the (olor of the s%rfa(e (hanges effe(t is o:served when

a dilatant soil Cha-ter #X I stressed5 the .enis(i retreat :elow thes%r s%rfa(e (hanges*B

How is the shrin<age li.it deter.ine *w r< was with s.all (la :ars whi(h he allowed to dry slowly* Heo:served the -oint at whi(h the (olor (hanged and at the sa.e ti.e he

r&a 2

fig%red o%t that one (o%ld 0%st as well .eas%re the dry vol%.e and dry.ass an a( (vol%.e* ig%re "*1 ill%strates this -ro(ed%re* A s.all a.o%nt of soil of total .ass "4 is -la(ed in a s.all dish o own vo %.e @ an a owe o

Af ter the oven d .ass " is o:tained, the vol%.e of the drysoil Mdry is .eas%ed :y eghin the a.o%nt of rner(%ry the soil sa.-le

a

or

:B L W5

d ry P(

"s+ 1 ]B "56B

The two eF%ations (orres-ond to the two -arts of ig* "*1 and rnareadily :e derived fro. the fig%re and the f%nda.ental -hase relationshi-9**of Cha-ter $*



,1

ol/8e 8 )0 >---

olor

Can.,0n

--i- 6esi/al

Note: <lo5e D 1:1 i3 Pw is /nit7

,, ,

,'srinIa$e

,,, ,

,

--

r

t 1 1 1

Can$e in

_ ...--+,

-------

8.3 Shrln?a@e Phenomen- n Solla 111

"& GbL G,

M6>>

V3lG5 # B

S W¡

W645 3n45n4

$2. .O &5452n6423n 3 45 >2n65 l224, J6>5= 3n 6 4346l6>>, 6n= J D645 3n45n4.

Altho%gh the shrin<age li.it was a -o-%lar (lassifi(ation test d%ringthe 16$3s, it is s%:0eet to (onsidera:le %n(ertainty a.i th%s is no longe1(o..only (ond%(ted* The test has sorne %ndesira:le feat%res* They in5el%de errors res%lt.g fro. entra--ed air :%::les . the dry sod s-e(1.en,(ra(<ing d%ring drying, weighing and other .eas%re.ent errors, and thedanger of .er(%ry -oisoning to the o-erator* Casagrande s%ggested dryinglarge sa.-les and -hysi(aHy rneas%ring their di.ensians to avoid the

._



17$ Jater In &oll= 1:Cepll&rfl: ........:.: Swelltn@: *roet Actlon

.er(%ry -oisoning -ro:le.* 8ne of the :iggest -ro:le.s with the shrin <ageli.it test is that the a.o%nt of shrin<age de-ends not only on the grain si&e :%t also on the initial fa:ri( of the soil* Toe standard for e+a.-le, ATG'esignation ' 2$!B -ro(ed%re is to start with the water (ontent near the liF%idli.it* However, es-e(ially with sandy and silty (lays, this often res%lts in ashrin<*age li.it greater than the -lasti( li.it, whi(h is .eaningless ig* $*"B*Casagrande s%ggests that the initial water (ontent :e slightly greater than thePL, if -ossi:le, :%t ad.ittedly it is diffi(%lt to avoid entra--ing air :%::les*

I the soil is in a nat%ral %ndist%r:ed stte, then the shrin<age li.itof ten is greater than the -lasti( li.it d%e to the str%(t%re of the soil* This ises-e(ially tr%e for highly sensitive (lays a((ording to /arlsson 16!!B*ig%re "*11 shows the res%lts of tests on several wedish (lays, :oth

%ndist%r:ed and re.olded, in whi(h the shrin<age li.its are -lotted vers%sthe -lasti( l;.its* or highly sensitive (lays, the shrin<age li.it of %ndist%r:ed sa.-les is (onsidera:ly greater than the -lasti( li.it, while for .edi%. sensitive (lays the L is (lose to the PL* or organi( soils, the Lis signifi(antly :elow the PL for :oth ty-es of sa.-les* Altho%gh sensitivity has a -re(ise engineering definition Cha-ter 11B, yo% already havesorne notion of it fro. o%r -revio%s dis(%ssions of Atter:erg li.its e(*$*!B and (lay .i(rostr%(t%re e(* 2*7B*

I one follows Casagrande3s advi(e and :egins the test slightly a:ovethe -lasti( li.it, then the following res%lts are generally o:tained* Whenthe Atter:erg li.its for the soil -lot near the A5line on the -lasti(ity (hartig* #*$B, the shrin<age li.it is very (lose to $* I the li.its -lot a:ove theA5line, then the L is less than $ :y an a.o%nt a--ro+i.ately eF%al tohow far the li.its are a:ove the A5line* i.ilarly, for GL and GH and8L and 8HB soils, the shrin<age li.it is greater than $ :y an a.o%nta--ro+i.ately eF%al to how far :elow the A5line the li.its -lot* Therefore,if the verti(al distan(e a:ove or :elow the A5line is IJ..p4, then the

L / $ k Ilp4 "51B

This -ro(ed%re and eF%ation have :een fo%nd to :e as a((%rate as theshrin<age li.it test itself*

An even si.-ler -ro(ed%re has :een s%ggested :y Prof* A*Casagrande in :is le(t%res at Harvard University* I the U5line and A5line

of the -lasti(ity (hart ig* #*$B are e+tended, they (onverge at a -oint with(oordinates 52#*, 52"*2B, as shown in ig* "*1$* A line is e+tended fro.that -oint to the (oordinates of the liF%id li.it and -lasti(ity inde+ on the

-lasti(ity (hart@ the shrin<age li.it is where that line (rosses the liF%idli.it a+is* Altho%gh not an e+a(t -ro(ed%re, it is (lose eno%gh for geote(hni(al wor<* However, the shrin<age li.it test, as (ond%(ted a((ording toATG, for e+a.-le, is not -arti(%larly e+a(t either* l yo% (an o:tain a



8.3 &hrlnage Phenoena In &olla 183

n=2>4GJ5= R5n23l=5= S32l TN5 S5n>242124

l &5424G> 36n2 L3D

5B U65 =424G> 36n2 L3D5 n **K, / =3=351*1 1 1*UJ IIJl U IJ** L8W

B O6n2

l6

L3D5 5

" V615= l6 M5=2Go B P3>4-l626l l6 M5=2Go M62n5 l6 H2;- l V615= l6 H2

1 55

M

7

1 1 1 1 1 1 Q

Q10 -

" 5 Q 6 2 Q#

*

$

QQ

&0 8----- G--- --

-- --1......G.--- 8. .1 ..1 . 1.

--

0 $ # 2 " ! 7 61 $Pl6>42 l224, PL

5;;,3l=5= >6Nl5> 6n= 45 Nl6>42 l224 3 >51;6l SD5=2> l6;645 K6l>>3n, 9.

reasona:le est;.ate of the shrin<age li.it fro. the -lasti(ity (hart ig*"*1$B then the shrin<age li.it test need not :e -erfor.ed sin(e it -rovidesn*n , * * 3 *

Note that the (a-illary -ress%res .%st :e very large for very finegrained (lay soils with highly a(tive (lay .inerals near the U5lineB* Thesesoils will have shrin<age li.its aro%nd 7, a((ording to the Casagrande

-rol,@t@U%re* In ra(t, rror* Ulagrande nas o:served shrin<age li.its as lowas " for .ont.orilloniti( (lays* oils at the shrin<age li.0t will have a verylow void ratio :e(a%se the (a-illary -ress%res are so large, .%(h greater than (an :e a(hieved :y (o.-a(tion* for e+a.-le*

.j

.5 r@nn I

Q



P9

<oil 2) : <H D 2`

184 Jater In &olla= 1: Ca0lllarlt@= &hrln"=e= &Lelllng= *rot Actlon

$2 . .* C6>66n=5'> N35=G5 3 5>42642n 45 >2n65l224.

E9A3PE 6.+

Cal(%late the void ratio and dr y density of a soil with a slnin9<9age linrit %f 7* Ass%.e Ps / $*! GgQ .#

*

u 18n:

Use EFs* $51$ and $51* Ass%.e / 1]*

(p., *7$*! GgZ.#B *

e 5/ / 8*$$ P.,.. 1 G #

P., $*! GgQ.#

Pa1 e 1*$$ $*$1 GgQ .# 1#!*6 l:f Qf t#



t

"*# &hrlnage Phenoena In &olla 185

in(e the density of (on(rete is a:o%t $*2 GgQ rn#, yo% (an see that the

(a-illary -ress%res .%st :e very large to (a%se soil to :e(o.e so dense* I4sho%ld not :e s%r-rising then that sorne (lay soils have very high drystrengths*

8ne way to show that high (a-illary -ress%res (an e+1st . sods 1s toallow a fat (lay CHB soil at a high water (ontent to dry slowly on the s<in*Toe high shrin<age -ress%res will a(t%ally (a%se -ain@ in fa(t, this -ro(esswas %sed d%ring an(ient ti.es as a tort%re syste.* A h%.an :ody (overed with(lay drying slowly in the s%n has %lti.ately very little resistan(e to -ress%reswhi(h (an rea(h severa at.os-heres ee E+a.-le "*#B*

Another -heno.enon that de-ends on (a-illarity is sla!ing , whi(h

o((%rs when a (lod of dry soil is i..ersed in a :ea<er of water* The (lodi..ediately starts to disintegrate, and with sorne soils the disintegration isso ra-id that the (lod a--ears to al.ost e+-lode* la<ing is a very si.-leway to disting%ish :etween soil and a ro(< @ ro(<s don3t sla<e, whereas soilsdo* The soil (l%.- has to :e dry sin(e, if i t is a:ove the shrin<age li.it, itwill grad%ally swell* 4elow the shrin<age li.it, the (a-illary stresses drawwater in and the air :%::les tra--ed in the voids are (o.-ressed :y the.enis(i* Event%ally, the internal air -ress%re gets high eno%gh to e+(eedthe tensile strength of the soil* In a ro(< frag.en t the inte.al (ohesion iss%ffi(iently strong to resist the (a-illary for(es*

Ter&aghi 162#B %sed the t%:e analogy si.ilar to that hown in ig*"*7 to ill%strate sla<ing* Toe differen(e is that the (a-illary t%:es are

s%:.erged and the ea-illary .enisei are tryin* te95 -%ll water into the voids,as shown in ig* "*1#* 4y drawing a free5:ody diagra. of the t%:e walls,one (an se( hat the walls are in tersion, and if Jhe tensile strength is lessthan the tension a--lied :y the .enis(i, the walls will fra(t%re, whi(h ise+a(tly what o((%rs when a soil sla<es*

A ' j A2 2n 132=> Gn=5 N5>>G5

$2. .! C6N2ll6 4GJ5 6n6l3 3 >l62n 645 T562, 9"!.

5 ------ D5D5555 55D5555

D55555555555555



." E%(I%EERI%( SI(%I$ICA%CEO$ SHRI%KA(E A%& SWELLI%(

The eff e(ts of shr;n<age of fine5grained soils (an :e of

??'''?(ons;dera:le

signifi(an(e fro. 3 .,.. ,**5,*engineering -oint of view* or e+a.-le, shrin<ag.e.

,,**,,,,**,* (ra(<s ean Do((%r lo(ally when the (a-illary -ress%res e+(eed the (nor the teiisile strength of the soil* These (ra(<s, -art of the (lay .a(rostr%( t%re Cha-ter 2B, are &ones of wea<ness whi(h (an signif i(antly red%(e theoverall strength of a soil .ass and aff e(t the sta:ility of (lay slo-es and the

:baring (a-a(ity of f ..dations* The desi((ated and (ra(<ed dry (rnst%s%ally fo%nd over de-osits of sof t (lay aff e(ts the sta:ility of, for e+a.-le,highway e.:an<.ens* *(onstr%(ted on these de-osits* hrin<age andshrin<age (ra(<s Dare (a%sed :y eva-oration fro. the s%rfa(e in dry (h.ates,low @.g of the gro%nd water ta :le, and even des1((at1on of soil :y treesd%ring te.-orary dry s-ells in otherwise h%.id (li.ates* When the(li.ate (hanges and the soils have a((ess to water again, they tend toin(rease in vol%.e or swell* The vol%.e (hanges res%lting fro. :othshrin<age and swelling of fine5grained soils are of ten large eno%gh toserio%sly da.age s.all :%ildings and highway -ave.ents* Jones and Holt&16!#B have esti.ated that shrin<ing and swelling soils (a%se a:o%t $*#bSl/ions of da.age ann%ally in the United tates alone whi(h, to -%t thingsin -ers-e(tive, is IJ1r( than twi(e the ann%al (ost of da.age fro. floods,h%rri(anes, to.adoes, and earthF%a<es (o.:.ed

A (o..on o((%rren(e is that a -ave.ent or :%ilding is (onstr%(tedwhen the to- soil layer is relatively dry* The str%(t%re (overing the soil -revents f %rther eva-oration fro. o((%rring and the soils in(rease in water (ontent d%e to (a-illarity@ then the soils .ay swell* l the -ress%re e+erted :ythe -ave.ent or :%ilding is 2;ss than the swelling -n99ss%re, then heave willres%lt* It is %s%ally %neven and (a%ses str%(t%ral da.age*

The -rn(ess %f sln in<ing and sweIJing is not %.-letely reversi:le5the soil always has a .e.ory of its stress history and will show the effe(tsof -rev1o%s shr.<age and dry.g (y(les* I h%s sof t (lays :e(o.e what is

(alled overconso/idated and less (o.-ressi:le :e(a%se of the in(rease ineffe(tive stress (a%sed :y (a-illary a(tion* 8ver(onsolidation is dis(%ssed

welling is a so.ewhat .ore (o.-le+ -ro(ess thal shrin<age ongand War<entin, 16!B* The a...t of swelling and tLe .agnit%de of swelling -ress%re de-end on the (lay .inerals -resent in foe soil, the soilslI %(t %re and fa:ri(, and seve1al -hysi(o5(he.i(al as-e(ts %f the soil s%(h asthe (ation valen(e, salt (on(entration, (e.entation, and Z,resen(e of organi(.atter* Everything else :e.g eF%al, .ont.orillonites well .orethan illites, whi(h swell .ore than <aolinites* oils with rando9n fa:ri(s

an



." Enln55ln Slnll6n5 3 Sln65 6n= SD5llln 17!

tend to swell .ore than soils with oriented fa:ri(s* 'ist%r:an(e of or re.oldingof old ,**,,at%ral (lays .ay in(rease the a.o%nt of swelling* Gonovalent (@99*l*ions in a (lay for e+a.-le, sodi%. .ont.orilloniteB will swell .ore thandivalent (lays for e+a.-le, (al(i%. .ont.orilloniteB* 3^*9.entation andorgani( s%:stan(es tend to red%(e swelling*

welling, li<e shrin<age, is generally (onfined to the %--er -ortionsof a soil de-osit* Th%s swelling da.ages lighter str%(t%res s%(h as s.all

:%ildings, highway -ave.ents, and (anal linings* welling -ress%res ashigh as 1 <Pa have :een .eas%red, whi(h is eF%ivalent to an e.:an< .ent thi(<ness of 2 to .* 8rdinarily, s%(h high -ress%res do not o((%r,

:%t even wi th .ore .odest swelling -ress%res of 1 or $ <Pa ane.:an<.en t of or " . wo%ld :e reF%ired to -revent all swelling of

s%:grade, for e+a.-le* or (o.-arison, an ordinary :%ilding weighsso.ething on the order of 1 <Pa -er story*B Pra(ti(ally s-ea<ing, the threeingredients generally ne(essary for -otentially da.aging swelling to o((%r are IB -resen(e of .ont.orillonite in the soil, $B the nat%ral water (onten t .%st :e aro%nd the PL, and #B there .%st :e a so%r(e of water for the -otentially swelling (lay ro.<o, 16!2B*

How is swelling -redi(ted Gany .ethods and soil tests have :een -ro-osed* These i n(l %de swelling tests and other si.-le la:oratory tests,(he.i(al and .ineralogi(al analyses, and (orrelation with the (lassifi(ation and inde+ -ro-erties of the soil* Ta:le "5$ is a s%.rnary of thee+-erien(e of the U** 4%rea% of Re(la.ation :ased on (onsidera:leresear(h on swelling (lays and e+-ansive soils* ro.<o 16!2B -rovidessorne additional (orrelations with soil tests that Dhave :een s%((essf%llya--lied to -redi(t swelling* ig%re "*12 relates swelling and (olla-se to theliF%id li.it and the in sit% dry density of soils5again, :ased on thee+-erien(e of the U** 4%rea% of Reda.a tion

TABLE -* P3J6Jl5 EYN6n>23n 6> E>42645= 3 Cl6>>226423n T5>4 &646

Pro:a:le E+-ansionas a ] of the Total

'egree Mol%.e Change 'ry Colloidal Plasti(1ty hrin<ageof to at%rated Content lnde+, Li.it,

E+-ansion ConditionBt ] 5l 11.B PI L

Mef high # $7 # ^ 11High $5# $5#1 $521 !51$Gi%. 15$ 1#5$# 15$7 151"Low ^ 1 ^ 1 ^ 17 1

After Holt& 166B and U**4*R*16!2B* tUnder a s%r(harge of "*6 <Pa l -siB*



< 1


*.0

U

1 1 1

1.8 L3D 1 M5=. H2 1V5 2

..-- 1 5 1

1M 1 11

Xb . 1 1

:::,¡:

¡¡:;eClB

=8

=8;:¡¡:;

.E .* C3ll6N>5 YN6n>23n

.0

0.83 1 20 30 40 +0 60 70 80 90 100

LL

$2. ." (G2=5 43 3ll6N>2J2l24, 3N5>>2J2l24, 6n= 5YN6n>23nJ6>6= 3n 2n >24G = =5n>2425> 6n= 45 l2FG2= l224 6=6N45= 3M245ll 6n= (6=n5, 9), 6n= (2JJ>, 99.

or (o.-a(ted (lays, eed, et al* 26"$B develo-ed the relationshi-ssho wn in ig* "*1 for artifi(ial .i+t%res of sands and (lays (oro-a(ted ta.a+i.%. %nit weight :y standard Pro(tor (o.-a(tion and allowed toswell against a "*6 <Pa 1 -siB s%r(harge* These relationshi-s :etween a(tivityand -er(ent (lay si&es have also :een shown to :e a--li(a:le to nat%ral soils if differen(es in the liF%id li.it devi(es %sed in the United tates and reat4ritain are (onsidered* Toe ter. activity was originally defined :y <e.-tone(* $*7B as the ratio of -lasti(ity inde+ to (lay fra(tion -er(en iner than*$ .. or $ ."). ConseF%ently, for nat%ral so;ls, the following defin;tionof a(tivity has :een -ro-osed9

. . A -lasti(ity inde+

a(t1v1ty, / 555555535555] 5$ *.B 5 "511B

Toe -%r-ose of ig* "*1 is to identify a -otentially swelling soil, whi(h.ay reF%ire f%rther st%dy and tests s%(h as an e+-ansion or swell test*ig%re "*1 sho%ld not :e %sed for design -%r-oses*

8ne of the si.-le swelling identifi(ation tests develo-ed :y the U**4%rea% of Re(la.ation is (alled the free5s(ell test Holt& and i::s, 16"B*The test is -erfor.ed :y slowly -o%ring 1 (.# of dry soil, whi(h has -assed

."



4.+ Engln..rtng &lgnlflcance of &hrlnage end &Lelllng

2

#

114

*SD. 5ll2n N345n426l & *)

,SD5ll2n N345n426l & )Q Q

,SD5ll2n N345n426l & .)

M5=2G

o 1 $ # 2 60 ! 80 6 1

P5 54 l6 >25> 25, 4l,6 0.00* n.n.

$2. .) Cl6>>226423n 64 3 >D5ll2n N345n4264 6 45 S55=, 54 6l.,

16"$B*

the No* 2 sieve, into a 1 (.# grad%ated (ylinder filled with water, ando:serving the eF%ili:ri%. swelled vol%rne* ree swell is defined as

ree swel K final vol%.eB .1t1al vol%.eB + 001

B

"51$B

l 5 * * * vo%.e

-

or (orn-arison, highly swelling :entonites .ostly Na5.ont.orilloniteBwill have free5swell val%es of greater than 1$]* Even soils with freeswe lls of 1] .ay (a%se da.age to light st1(t111es w hen they :eeo.ewet@ soils with free swells less than ] have :een fo%nd to e+hi:it onlys.all vol%.e (hanges*

8ther la:oratory tests for swelling and swell -ress%res rese.:le theone5di.ensional oedo.eter test des(ri:ed later* A s-e(i.en of soil is(onfined in a rigid :rass ring, %s%ally a:o%t $ to $ .. :igh aod to00 .. in dia.eter* o.eti.es the s-e(i.en is s%r(harged, flooded, andthe -er(entage of swell is o:served* Another variation is to <ee- loading

1.t1a



16 Water In olla, 19 Ce-lllerlty, hrln<age, welllng, roat A4l3n

the s-e(i.en af ter it is in%ndated so thar the height of the s-e(i.enre.ains (onstant* Toe verti(al stress ne(essa to .ain tain &ero vol%.e(hange is the swelling -ress%re*

What (an engineers do to -revent da.age to str%(t%res fro. shrin< ingand swelling soils or (o.-a(ted fill .atrial, it has :een fo%nd that soils(o.-a(ted wet of o-ti.%. and at a lower density show less tenden(y to

swell, -ro:a:ly :e(a%se of a .ore oriented soil str%(t%re* Prewettings%s-e(te soi s will a low -otentta y a.ag.g swe .g or (o a-se o a e

la(e rior to (onstr%(tion* Goist%re :arriers and water-roof .e.:raneshave :een %sed to -reven t water fro. rea(hing the swelling so;l* l the

water (ontent of the fo%ndation soil is -revented fro. (hanging, novol%.e (hange will ta<e -la(e* K Che.i(al sta:ili&ation has also :een

s%((essf%lly e.-loyed to red%(e the swelling of es-e(ially sodi%..ont.orilloniti( (lays* Toe reason why it wor<s is dis(%ssed 2n Cha-ter 2*in(e the -otential da.age to light str%(t%res and -ave.ents d%e to

shrin<age and swelling of soils is so great, the engineer .%st -ay s-e(ialattention to this -ro:le. if it is s%s-e(ted that s%(h soils e+ist at a site*

Anyti.e the air te.-erat%re falls :elow free&ing, es-e(ially for .orethan a few days, it is -ossi:le for the -ore water in soils to free&e* rost

a(tion in soils (an have several i.-ortant engineering (onseF%en(es* irst,vol%.etri( e+-ansion of water %-on free&ing* A se(ond :%t signifi(antly.ore i.-ortant fa(tor is the for.ation, of i(e (rystals and lenses in the soil*These lenst9s (an even grow to severa (enti.etres in thi(<ness and (a%seheaving and da.age to light s%rfa(e str%(t%res s%(h as s.all :%ildings andhi w v I oils si. I fro&e and e+ anded %nifor.l str%(5t%res wo%ld :e evenly dis-la(ed sin(e i(e is signifi(antly stronger thanthese light str%(t%res* However, 0%st as with swelling and shrin<ing soils,the vol%.e (hange is %s%ally %neven, differential .ove.ent o((%rs, andthat is what (a%ses str%(t%ral da.age*

Toe -ro:le.s do not end here* '%ring the s-ring, the i(e lenses .elt

and greatly in(rease the water (ontent and de(rease the streng o t e so1 *Highway -ave.ents es-e(ially (an s%ffer serio%s str%(t%ral da.aged%ring the s-ring thaw (alled, Ior o:vio%s reasons, the =s-ring :rea<%-=B*

An %nderstanding of the real .e(hanis. of i(e lens for.ation as wellas the (onditi:ns ne(essary for detri.ental frost a(tion only (arne a:o%t

a%to.o:ile traffi(, roads were ief t snow (overed for sleds d%ring the



"* Aroat (ctlon 11

winter* in(e snow is a good ins%lator, de-ths of frost -enetration wereh.1ted a9-*d rarely was f rost heave a -ro:le.* 4e(a%se the traffi( loadswere light, there were also few -ro:le.s d%ring the s-ring thaw*

The -ro:le.s :egan when it :e(a.e ne(essary to re.ove snow for (ar traffi( A t first, frost heave D6> -o-%Jarly attrih%ted soJeJy to the J8]vol%.etri( e+-ansion of water %-on free&ing* 4%t sorne enter-rising yo%ngengineers .ade sorne .eas%re.ents, :oth 3 the .agnit%de of heave andof the water (ontent of highway s%:grades* Prof* Casagrande relates t:at,on one stret(h of :adly frost heaving road 2n New Ha.-shite, .eas%re.ents d%ring the winter of 16$75$6 showed that the de-th of frost -enetration was a:o%t 2 (., and the total s%rfa(e heave was a:o%t 1# (.*The water (ontent, nor.alJy :etween 7] and 1$], had in(reased and

ranged :etween 0 and 11]* When a test -it was e+(avated, thes%:grade was f %ll of i(e lenses with a total thi(<ness of yo% g%essed itB 1#(. The water ta:le had :een lo(ated at sorne $ . de-th in the a%t%.n,yet d%ring the s-ring it was right :elow the -ave.ent* When the soil :eganto thaw in the s-ring, the %--er layers :e(a.e water sat%rated and very sof t5the water was tra--ed the s%:grade :etween the thawed s%rfa(e layer and the to- of the still fro&en soil :elow*

Now the F%estion was9 how did the water get %- there l4 wasn3tthere :efore the winter season* Ca-illarity see.ed to he i8Jved in the(a%se* Also, the o:servation was .ade that there was very little i(e 2n(lean sands and gravels, :%t with silty soils, iee lenses were -lentif%l*%rt*her investigations showed that t:e for.ation of i(e lenses also

de-ended on the rate of free&ing of (he soil* I the soil fro&e ra-idly, as.ight o((%r d%ring a (old sna- early in the winter :efore there wassignifi(ant snow, then less i(e lenses tended to for.* With a slower rateof free&ing, it see.ed thatthere were .ore i(e lenses, and the thi(<er lenses tended to 3 nearer the

:otto. of the fro&en layer* o one of the (onditions for i(e lens for.ationro%st :e that there is a so%r(e 3 water near:y

Resear(h d%ring the -ast 2 years has e+-lained .%(h of the o:sened -heno.ena assoeiated with soi9I free&ing and frost a(tion* A> nght :e e+-e(ted, the -ro(ess, es-e(ialJy with fine5grained soils, is a rather (o.-h(ated heat5d1ff %s1on ther.odynar.(B and -ore water5(her.stry -ro:le. and is related to the soil5water -otential and water .ove.ent 2nfro&en soils ong and War<entin, 16!B*

4asi(ally* three (onditions .%st e+ist for frost a(tion and 4J5 36- tion of i(e lenses in soils to o((%r9

l. Te.-erat%res :elow free&ing*$* o%r(e of water (lose eno%gh to s%--ly (a-illary water to the frost

line*# rost s%s(e-ti:le soil ty-e ar%l 62n -oreB si&e distri:%tion*

1

#J

5555555D5D5DDDD D5D55555DD55D55DD5 55



1 Jater In &olla= 1: Ca0lllarlt@= &hrlnage= &Lelllng= *roat Actlon

ree&ing te.-erat%res de-eiid on the (li.ati( (onditions at the site*ro%nd (over, to-ogra-hy, -resen(e of snow, and other fa(tors lo(allyaff eet the rate and de-th of frost -enetration* A gro%nd w ater ta:le w ithinthe height of (a-illary rise -rov;des the water to feed growing i(e lenses*Toe soil .%st :e fine eno%gh for relatively high (a-illary -ress%res todevelo- and yet not so fine that the flow of water -er.ea:ilityB isrestri(ted* As is dis(%ssed in the ne+t (ha-ter, the -er.ea:;lity of (lay soils isvery low* Even tho%gh the (a-illary -ress%res are very high, %nless the (layis relatively sandy or silty, the a.o%nt of water that (an flow d%ring a free&ings-ell is so s.all that i(e lenses have little (han(e to for.* However, -ra(ti(ally s-ea<ing, (lay soils near the s%rfa(e are of ten (ra(<ed and fiss%red,as des(1i:ed -t evio%sly, whi(h .ay allow s%.e wa tet .ove5 .ent to thefrost line*

ig%re "*1" shows a sa.-le of fiss%red (lay whi(h fro&e down fro.the to-* Note how the water (ontent in(reased within the fro&en &one andhow this (o.-ared with the val%e :efore free&ing* Note too how the i(elenses develo-ed in the fro&en &one* They were (ontin%ally s%--lied fro.the water ta:le thro%gh the fiss%res and (ra(<s in the (lay*

What are frost s%s(e-ti:le soils ,A*s s%ggested a:ove, i(e lenses willsi.-ly not forrn in (oarse5grained soils* Casagri9tnde 16#$aB and other 1esear(l1e1s li<e 4es<ow 16#B in weden in the early thir ties fo%nd thati(e lens forrnation in fine5grained soils de-ended on :oth a (riti(a grains1&e and the gra. s1&e d1stn:%tion of the soil* 4es<ow fo%nd *1 .. to :e

the .a+i.%rn si&e that wo%ld -er.it i(e lens forrnation %nder any (ondi5 tions* Casagrande fo%nd *$ .. to :e a (riti(aV grain si&e@ evengravelswi t: only ] to 1] of 8 @* siJt we(e f(ost s%s(e-ti:le Casagrande also fo%nd that with well5graded soils, only #] of the .aterial finer than*$ .. D6> reF%ired to -rod%ee frost hea v ing, whereas fairly %nifonnsoils rn%st have at least 1] of that si&e to :e dangero%s* I4 seerns thatsoils with less than s.aller than 0.0* .. also rarely frost heaved*4es<ow3s 16#B li.iting grain si&e (%rves are shown in ig* "*1! for wedish gla(ial tills and si.ilar soils* oils a:ove the to- (%rve werefo%nd to :e frost

heaving@ those :elow the :otto. (%rve never heaved* C%rrent wedis: -ra(ti(e is given in Ta:le "5#*

A > with other (a-illary -heno.ena, it is the -ore si&es and not thegrain si&es that really (ontrol frost a(tion* Re(ent resear(h at P%rd%eReed, et al*, 16!6B has shown that an intrinsi(ally frost s%s(e-ti:le soil, as

-redi(ted :y te+t%re andQ or gradation, (an a(t%ally have .any levels of s%s(e-tifOhty, de-ending on the details of its (o.-a(tion* The e+-lanationfor these different res-onses l;es in the distri:%tion of -orosity into vario%s -ore si&es, whi(h was .eas%red :y .er(%ry intr%sion*

J%st as wit: swelling a nd s:rin<ing soils, frost a(tion serio%sly affe(tsstr%(t%res s%(h as s.all :%ildings and highway -ave.ents whi(h are fo%nd



$' 1

- 1

9 e lenses l)

.%

Cl

e

].:::o:,

%.ol) ...l)

a eo.,

-.

ol)

·-- -- -- ·- - --- ,.._ 1 #rost l i ne c

Water (ontent

A 4I

$2. "*1" &266 >3D2n 45 5l6423n J54D55n =255n4 25l65> 2R >5R >>2l A*B 6R= 45 G645 (SR45R4 =2>42JG42>R (G158. T5 >32l 2> 6>>G5= 43 J5 6 5=2G l6 D24 N56n5n4

6>:a 35n N64, b =25= 3G4 3n5 J5l3D 45 3>4 l2n5. S2n5 45 l6 3n462n> N56n5n4 6>, 45 3Gn= D645 >G65 2> 56l,464 2>, 45 l515l D55 45 6> 3n462n 55 D645, #l= 2>45535 n3425= 6> 6 2n 2n 45 D645 =2>42JG423n G15 645 B5>3D, 9!).

dire(tly on the gro%nd s%rfa(e* 'a.age to highways in the United tatesand Canada :eea%se of frost aetion is esti.ated to a.o%nt to .illions of dollars ann%ally* 4%t :e(a%se of the rather good f%nda.ental %nderstand5ing of the fa(tors .volved in frost a(tion and heave, eng.eers havedevelo-ed relatively s%((essf %l .ethods for dealing with these -ro:le.s*Load restri(tions on se(ondary roads d%ring the s-ring =:rea<%-= are

(o..on in the northe. United tates and in Canada* Gore -ositive.eas%res for dealing with the -otential da.age to str%(t%res and highwaysin(l%de lowering of the gro%nd water ta:le and, de-ending on the de-th of frost -enetration, re.oval of frost s%s(e-ti:le soils in the s%:grade or fo%ndation* Use %f i.-et vio%s .e.:tanes, (henri(al additives, and evenfoa.ed ins%lation tyrofoa.B %nder highways, :%ildings, and railroadshave :een s%((essf %lly e.-loyed* 4%1Id.g fo%ndat1ons as well as water and sewer lines sho%ld :e -la(ed well :elow the .a+i.%. de-th of frost -enetration*

193

DJ 1



..1

$ 1 7

.S. IS46n=6=>2515

2

Z#Z=

r 1, ** 1t r

e9,,5:

l****

ee

9,,

*# * *1 *1 *$ *# *2 *! 1*

&2545

# ! 18 l4 $1 # 2 "

$2. "*11! L224> J54D55n 3>4 >G>5N42Jl,/4 6n= n3n-3>4->G>5N42Jl5lY4G> 3 l626l 42ll> 3 >22l6 2Y4G5 645 B5>3D, 16#B*

¡:IfZD91

'



4,



TA,E 6"% $3>4 SG>5N42J2l24 S32l (3GN>

rost %s(e-ti:ilityro%- or 'anger oils

None ravel, sand,gravelly tills

Goderate ine (lay "0(layt (ontentB@sandy tills,(layey tills with1"] finesk

trong ilt, (oarse (lay (layt (ontent15$]B@ silty

tills

Alter Hans:o 16!B*4 8efined as 5$ .*i 'efined as 5*" ..*

P!O,E3&

"51* The end of a (lean glass t%:e is inserted in -%re water* What is theheight of (a-illary rise if the t%:e is aB *1 .., :B *1 .., and eB*1 .. in dia.eter

"5$* Cal(%late the .a+i.%. (a-illary -ress%re for the t%:es in Pro:le.

"51*

"5#* Cal(%late the theoreti(al height of (a-illary rise and the (a-illarytension of the three soils whose grain si&e distri:%tion is shown inig* $*2*

"52 A t%:e, si.ilar to ig* "*7, has a *$ .. inside dia.eter and iso-en at :oth ends* The t%:e is held verti(ally and water is added tothe to- end* What is the .a+i.%. height h of the (ol%.n of water that will :e s%--orted Hint9 A .enis(%s will for. at the to- and atthe :otto. of the (ol%.n of water, as shown in ig* P"52* After Casagrande, 16#7*B

Water

T ¡ Gon,e%,

$2. P-" A45 C6>66n=5,16#7*B

Genis(%s

115




"5* The t%:e shown in ig* "*6 is filled with water* When eva-oration(%s i

e+-lained in the te+t* Ass%.ing this .enis(%s to :e f%lly for.ed,derive an e+-ression for the (onta(t angle at the other end of thet%:e in ter.s of the two radii, r 1 and rs.

"5"* 8n a ost(ard fro. 'a tona 4ea(h, lorida, fo%r answers weregiven to the F%estion =Why (an I drive on the :eai(h here * * * :%t not

U,

aB A gently slo-ing o(ean :otto.* Toe water 1 .iles o%t is a:o%t2 f t dee-@ at .iles, only " f t* This long grad%al slo-e

(a%ses s%rf to have a downward -o%nding .otion, th%s -a(<ingthe sand*

:B A sili(a (o.-o%nd in F%antity in sand hel-s .a<e a fir., hard :ase when .i+ed with salt water*

(B The -resen(e of titani%. a very hard .etalB (ontri:%tes tof irrnness*

dB '%ring the long t%.:ling 0o%rney fro. the eorgia and Carolina(oasts, ea(h grain :e(o.es s.ooth and ro%nd, with shar- edgesworn down, allowing it to -a(< (losely*

Are these reasons valid E+-lain*"5!* aB Wo%ld the shrin<age li.it of a (lay :e different if the water in

the voids were re-la(ed :y sorne other liF%id with a s"a/$! s%rf a(e tension Why

:B Wo%ld there :e .ore or less shrin<age Why

"57* Ass%.e that eF%ations develo-ed for height of (a-illary nse .(onstant5dia.eter t%:es (an :e a--lied* Cal(%late the net (o.-ressive stress on a soil -at at the shrin<age li.it where the averagedia.eter of the s%rfa(e -ores is *1 ..*

soil -at was fo%nd to :e 1*!" (.# and its dry .ass was $$*"7 g* I the shrin<age li.it was 11*1, what is the density of the soil solids

"511* Est;.ate the vol%.e (hange of an organi( silty (lay with LL "$and PL / 2$, when its water (ontent red%(ed fro. ] to $]*



Pro#le 1M

"51$* Co..ent on the validity of Casagrande3s -ro(ed%re ig* "*1$B for esti.ating the shrin<age li.it for %ndist%r:ed soils* 'oes it .atter whether the soils are sensitive or not Why

"51#* A sat%rated sa.-le of (lay with an L of $$ has a nat%ral water (ontent of #]* What wo%ld its dry vol%.e :e as a -er(entage of itsoriginal vol%.e if Ps is $*!

"512* A sa.-le of (layey silt is .i+ed at a:o%t its LL of 2* I4 is -la(ed(aref%lly in a s.all -or(elain dish wi th a vol%.e of 16*# (.# andweighs #2*"! g* Af ter oven drying, the soil -at dis-la(ed $1"*7 g of .er(%ry* aB 'eter.ine the L of the soil sa.-le* :B Est;.ate the Ps

"51* The LL of a :entoniti( (lay is 2 and the PL is !* The L wasdeter.ined to :e a:o%t 1* Cal(%late the e+-e(ted vol%.etri( de(rease when a sa.-le of this :entonite is dried, if its nat%ral water (ontent was 7]*

"51"* The shrin<age li.it of a *1 .# sa.-le of a (lay is 1, and its nat%ralwater (ontent is #2] 2 ss%.e the density of the soil solids is $ "7GgQ.#

, and est;.ate the vol%.e of the sa.-le when the water (ontent is 1$*!]*

"51! '% ring the deter.ioa tioo o t:e s:rio<age liroit 3 a saody (Jay, t:efollowing la:oratory data was o:tained9

Wet wt* of soil dish 7!*7

g 'ry wt* of soil dish / !"*61g Wt* of dish / $*! g

Mol%.etri( deter.ination of soil -at9

Wt* of dish .er(%ry / 2#*7 g

Wt* of dish / $22*"$ g

Cal(%late the shnn*<age Inr%t of the sod, ass%..g Ps / $*" GgQ.#

"517* Toe LL of a .edi%. sensitive wedish -ost5gla(ial (lay is " and thePI is $7* At its nat%ral water (ontent, the void ratio is 1*# while after shrin<age the .;ni.%. void ratio is *!$* Ass%.ing the density of the soil solids is $*!$, (al(%late the shrin<age li.it of the (lay*

"516 'erive EFs "57 aod '9 far t:e s:rin<age Iiroit, nsing -:ase relation5shi-s* how that they are identi(al*

'j



5 5 55

14 Jater In &oll= 1: Ce0lllerlt@= &hrlnege= &Lelllng= *ro.t Acllon

"5$* Esti.ate the swelling -otential of soils A5, Pro:le.s $5## and$5#* Use :oth Ta:le "5$ and ig* "*1*

"5$1* Est;.ate the frost s%s(e-ti:ility of soils A5, Pro:le.s $5## and$5#, a((ording to 4es<ow ig* "*1!B and (%rrent wedish -ra(ti(e*



5555555555555 555555555

ie/en

Jatin 7oili= 11:Pern"i"ea#ilit@=7ee0age=E"P ecti/e §treii

. I%TRO&CTIO%

33he i.-ortan(e in (ivil engineering of water in soils is .entioned atthe :eg.n.g of Cha-ter "* Gost geote(hni(al engineering -ro:le.sso.ehow have water asso(iated with the. in vario%s ways, either :e(a%seof the water flowing thro%gh the voids and -ores in the soil .ass or :e(a%se of the state of stress or -ress.e io the water in the -ores* o.e of these effe(ts are des(ri:ed in this (ha-ter*

The following notation is introd%eed 2n this (ha-te1*


$

a ,a3 L 'istan(e fro. i.-ervio%s :o%ndaryto hnttn. oYs:eet -ile Ta:le ! $B

h L Energy or head, head loss, alsoD24 s%:s(ri-ts 6 L. .B layer thi(<ness

i,,

L

%Q#

Press%re head EF* !5 2BHydra%li( gradient EF* !51BCriti(al hydra%li( gradient EF* !5$1BE+;t grad;ent

ee-age for(e -er %nit vol%.e

! .Qs 'ar(y (oeffi(ient of -er.ea:ility

K Ratio of hori&ontal to verti(al

Coeffi(ient of lateral earth -ressnre ar r9est EF !516B

199

,. _



2,,Jater In &oll= 11: Perea#lllt@= Seepa@e: Effecff/e &tre

y.:ol 'i.ens1on lJni 4efinitionPara.eters related to for. fa(tor

fa:le !5#B

% % Length of sa.-le

+ L Unit or (hara(teristi( length %n(tion of s and T EF* !5#1B" N%.:er of eF%i-otential =dro-s=

d in a flow net EF* !5$"B

N%.:er of flow (hannels . a flow9

net EF* !5$"B

p " %& 52 % or(e or load EF* !51"B p ML' 1 !' 2 <PA Press%re EF* !5 2BL L3 G' 1 .#Qs low rate so.eti.es -er %nit

widthB EFs* !5#, !5B

\ LJ .J Mol%.e of flow EF* !57B ilter ratios fa:le !5B

s , s', s" % . Length of sheet -ile f a:le !5$B

& L . Thi(<ness of layer

u ML- r5* <Pa Pore water -ress%re EFs* !51#, !51B

LG 1 .Qs Melo(ity EF* !5$B

=s LG .Qs ee-age velo(1ty EF* !5tiB

M L Potential :ead@ de-th

&,* L 'e-th to the water ta:le EF* !51B

F1ML' 1!' 2 <Pa Total nor.al stress EF* !51#B

a3 ML-,* <Pa Effe(tive nor.al stress EF* !51#B

N ML' D!' <Pa Total hori&ontal stress EF* !517B

aS. ML 1r $ <Pa Effe(tive hon&ont al stress EF*1516B

o,, ML' 1 r52 <Pa Total verti(al stress EF* !512B

a ML5r5$ <Pa Eff((tiv( verti(al stress EF* !516B

? or. fa(tor

!*$ O)NA3IC& O* *'I( *OJ

o% .ay re(all fro. yo%r :asi( fl%id .e(hani(s (o%rses that thereare sveral d1ff erent ways to des(ri:e or elassif y fl%id flow 1ow (an :e steady or unsteady , whi(h (orres-onds, res-e(tively, to (onditions that are(onstant or vary with ti.e* low (an also :e (lassified as one5, t(o5, or three5

di8ensional. 8ne5di.ensional flow is flow in whi(h all the fl%id -ara.eterss%(h as -ress%re, velo(ity, te.-erat%re, et(*, are (onstant in any (ross se(tion -er-endi(%lar to the direetion of flow @ (o%rse, these -ara.eters (an varyfro. se(tion to se(tion along the dire(tion of flow* In two5di.ensional flow,the fl%id -ara.eters are the sa.e in -arallel -lanes, whereas in three5di.ensional flow, the fl%id -ara.eters vary in the three (oordinate dire(tions*or -%r-oses of analysis, flow -ro:le.s in geote(h r%(al eng.eering are%s%ally ass%.ed to :e either one5 or two5di.ensional,whi(h is adeF%ate for .ost -ra(ti(aT(ases*

) i s , )



l. Ha8inar 99. =ransition

!*$ (@nalc of *luld *loL 2,1

4e(a%se density (hanges (an :e negle(ted at ordinary stress levels for .ost geote(hni(al engineering a--li(ations, flow of water in soils (an :e(onsidered inco8pressible.

low (an also :e des(ri:ed as la8inar , where the fl%id flows in -arallel layers witho%t .i+ing, or turbulent , where rando. velo(ityfl%(t%a tions res%lt in .i+ing of the fl%id and internaV energy dissi-ation*There (an also :e inter.ediate or transition states :etween la.inar andt%r:%lent flow* These states are ill%strated in ig* !*1, whi(h shows howthe hydraulic gradient (hanges with in(reasing velo(ity of flow* Hydra%li(gradient i, a very i.-ortant (on(e-t, is defiiled as the energy or head loss h

-er %nit length Q, or

5 !51B

The energy or head loss in(reases linearly with in(reasing velo(ity as longas the flow is la.inar* 8n(e the transition &one is -assed, :e(a%se of interna eddy (%rrents and .i+ing, energy is lost at a .%(h greater rate&one 111, ig* !*1B and the relationshi- is nonlinear* 8n(e in the t%r:%lent&one, if the velo(ity is de(reased, the flow re.ains t%r:%lent well intotransition &one II %ntil the flow again :e(o.es la.inar*

or flow in .ost soils, the velo(ity is so s.all that the flow (an :e(onsidered la.inar* Th%s, fro. ig* !*1, we (o%ld write that v is -ro-or5

Melo(ity, v

$2. . Z3n5> 3 l62n6 6n= 4GJGl5n4 l3D 645 T6l3, 9"8.

.j

.



Jater In &olla= 11: Perea#lllt@= Seepa@e: Etfectl/e &......2,2

tional to i , or V !i

EF%ation !5$ is an e+-ress1on for Darcy 3s ia(, whieh is dis(%ssd later inthis (ha-ter*

Another i.-ortant (on(e-t fro. fl%id .e(hani(s is the la( of con5

serv ation of 8ass . or ineo.-ressi:le steady flow, this law red%(es to the

eLuation of continuity , or L v A v A

1 1 $ $(onstant !5#B

#

where L rate of dis(harge %nits9 vol%.eQti.e, . QsB,v i, v / velo(ities at se(tions l and $, and

A1, $

the (ross5se(tional areas at se(tions and $*

The othet well5<no n eF%ation fro. ;l%id .e(hani(s that we shall%se is the ernoulli energy eLuation for in(o.-ressi:le steady flow of a

fl%id92 2

= i P i gMW/

=i Pi gMi / (onstantenergy

!52aB

$ P $ P(

where vi , =i / velo(ities at se(tions 1 and $, g / a((eleration of gravity,

P( / density of the fl%id waterB, p ,- / -ress%res at se(tions 1 and $, and&

1, &

$distan(e a:ove s%.e ar:itrary dat%. -lane at se(tians

1 $ and $*This eF%ation is the steady5flow energy eF%ation in ternis of energy

-er %nit of .ass of fl%id %nits9 JQ <gB* However in hydra%li(s it is .ore(o..on to e+-ress the 4erno%lli eF%ation in ter.s of energy -er %nitweig:t :y dividing ea(h ter. in the eF%ation :y , the a((eleration of

gravity, or $ $

= i P i M , =M P$ Mi / (onstant total head !52:B

$ g P( g $ g p...,g

EF%ation !52: states that the total energy or head . the syste. is the s%.of the velocity head vi/ g, the pressure head p/ p...,g F -Qy***, B, and the potential position : head M. Whether the flow is in -i-es, o-en (hannels, or thro%gh -oro%s .edia, there are energy or head losses asso(iated with thefl%id flow* Us%ally an energy or head loss ter. h 6 is added to the se(ond

-art of EF* !52:@ th%s

!52(B



1

=A

K

.! &6' L6D for $l3D T3G P33G M5=26 *0!

Why do we say head for ea(h ter. 2n the 4erno%lli eF%ation 4e(a%seea(h ter. has %nits of length, and ea(h is (alled the velo(ity head, -ress%rehead, or -otential head, as the (ase .ay :e* or .ost soil flow -ro:le.s,the velo(ity head is %s%ally negle(ted sin(e 24 is s.all in (o.-arison to theother two heads*

.! &ARC7'S LAW $OR $LOW THRO(HPOROS ME&IA

We have already .entioned that the flow of water thro%gh the -ores

or voids in a soil .ass (an in .ost (ases J5 (onsidered la.inar* We alsostated that for la.inar flow the velo(ity is -ro-ortional to the hydra%li(gradient, or v !i EF* !5$B* 8ver one5h%ndred years ago, a ren(hwaterwor<s engineer na.ed 'ar(y '3Ar(y, 17"B showed e+-eri.entallythat the rate of flow in c/ean sands was -ro-ortional to the hydra%li(gradient EF* !5$B* EF%ation !5$ is %s%ally (o.:ined with the (ontin%ityeF%ation EF* !5#B and the definition of hydra%li( gradient EF* !51B* Usingthe notation as defined in ig* !*$, Darcy 3sla( is %s%ally written as

L v$ !i$ / ! O

%* !5B

-L T$2. .* SGN5226l 6n= >55N65 15l32425> 2n Gn23 n3D 645 T6l3, 9"8.

5



Í '

2,4 Jater In &oll= 11: Perea#lllt@= &ee0age= Eflectl/e &treaa

where B is th*e total rate of flow thrn%gh the (ross5se(tiooa B area A , a ndthe -ro-ortionality (onstant ! is (alled the Darcy coefficient of per8eability.

Co..only, in (ivil engineering, it is (alled si.-ly the coefficient o@per8ea

bility or, even .ore siZn-ly, the per8eability. Toe -er.ea:ility is a soil property whi(h e+-resses or des(ri:es how water flows thro%gh soils*

/nowledge of -er.ea:ility is reF%ired for the design of engineering wor<swhere see-age of water is involved* Note that -er.ea:ility has %nits of

velocity :eea%se i is di.ensionless* Units (o..onJy %sed are .Qs, (. Qsfor la:oratory wor<, or f tQ day in the 4ritish Engineering syste. of %nits*

W hy do we %se the total (ross5se(tional area in EF* !5 8:vio%sl9y ,the water (annot :e flowing thro%gh the solid -arti(les :%t only thro%ghthe voids or -ores :etween the grains* o why don3t we %se that area and

(o.-%te the velo(ity :ased on the area of the voids lt wo%ld :e relativelyeasy to (o.-%te the area of the voids fro. the void ratio EF* $51B, eventho%gh the void ratio is aD*ol%.etrie ratio* or a %nit vidth of sa.-le inig* !*$, we (an write e =vf =s $v / $s. Now the a--roa(h velo(ity v< and the d1s(harge velo(ity vd . ig* !*$ :oth eF%al v L/ $ , the dis(ha1geB divided :y the total (ross5se(tional area $ . Th%s the v in this relationshi-is really a superficial velo(ity, a fi(titio%s :%t statisti(ally (onver%ent=engineering= velo(ity* The a(t%al seepage velo(ity vs , the a(t%al velo(ityof the water flowing in the voids, is greater than the s%-erfi(ial veBo(ity* We(an show this :y

ro. ig* !*# and EF* $5$, $v / $ =v/ = / % then,

!5"B

!5!B

in(e ] n 1], it follows that the see-age velo(ity 1s alwaysgreater than the s%-erfi(ial or dis(harge velo(ity*

ro. the -re(eding dis(%ssion yo% (an see that the void ratio or -orosity of a soil affeets how water flows thro%gh it and th%s the val%e of the -er.ea:ility of a -arti(%lar soil* ro. theoreti(al relationshi-s for flowthro%gh (a-1llary t%:es develo-ed :y Hagen and Poise%ille a:o%t 8"0 andfro. the .ore re(ent hydra%li( radi%s .odels of /o&eny and Car.an, we

A

P6>5 =6 6 3>55N65 6n= >GN5226l 15l32

F F 425> 3 l3D l3D 2> N5N5n=2G-

A l6 43 N65.



.! &5'> L6D 3 $l3D T3G P33G> M5=25 $

<now tha t severa other fa(tors also affeet -er.ea:ility* Leonards, 16@$,Cha-ter $, -rovides an e+(ellent s%..ary of these develo-.ents*B Toeeffe(tive grain si&e or, :etter, the effe(tive -ore si&eB has an i.-ortantinfl%en(e, .%(h as it does on the height of (a-illary rise e(* "*$B* Toesha-es of the voids and flow -aths thro%gh the soil -ores, (alled tortuosityalso aff e(t . All of the -revio%s dis(%ssion of -er.ea:ility was for sat%rated soils only, so the degree of sat%ration .%st infl%en(e the a(t%al -er.ea:ility* inally the -ro-er ties of tite fl%id haie sorne effeet@ viseosity,whi(h de-ends on the te.-erat%re, and the density i..ediately (o.e to.ind*

in(e 'ar(y originally develo-ed his relationshi- for (lean filter sands, how valid is his law for other soils Caref%l e+-eri.ents have shown

that EF* !5 is valid for a wide range of soil ty-es at engineering hydra%li(gradients* In very (lean gravels and o-en5graded ro(< fills, flow .ay :et%r:%lent and 'ar(y3s law wo%ld :e invalid* At the other end of thes-e(tr%., (aref %l investigations :y Hans:o 16"B fo%nd that in (lays atvery low hydra%li( gradients the relationsfO- :etween v and 1 1s nonlinear ig ! 2B* ield .eas%re.ents Holt& and 4ro.s, 16!$B showed that thee+-onent n has an average val%e of a:o%t 1* in ty-i(al wedish (lays*However, there is :y no .eans (o.-lete agree.ent with the (on(e-tshown in ig* !*2* Git(hell 16!", --* #265#1B s%..ari&es severalinvesti gations a:o%t this -oint, and he (on(l%des that =***all other fa(tors held (onstant, 'ar(y3s law is valid*=

V / Zn

$2. ." &5126423n 3 &6'> l6D 3J>515= 2n SD5=l> l6> 645H6n>J3, 90.



M.+ 3EA&'!E3ENT O* PE!3EA,IIT)

How is the (oeffi(ient of -errnea:ility deter.ined A devi(e (alled a per8ea8eter is %sed in the la:oratory, and either a constant5head test or a fal/ing5head test is (ond%(ted igs* !*a and :B* In the field, -%.-ing tests are%s%ally (ond%(ted, altho%gh it wo%ld :e -ossi:le in -rin(i-le to %tili&e either (onstant5 or falling5head tests*

or the (onstant5head test, the vol%.e of water (olle(ted in ti.e t

ig* !*aB is

/ $vt

= i / QL

so

h$t !57B

w:ere - tota l dis(:a rge val% roe, .#, io ti.e ,, s, a od

A (ross5se(tional area of soil sa.-le, .*

X4=

tQ1 U

t

K

X HP

X o

5W5at t/ t$

$

-4

a

6 6 b)

A A

Ae@. !*

(

(eterining the coeff!c!ent of permeab!l!t b Ba con&tant0headtet= Bb falling"head tet.

!



X 1 8.) 1 3 t )r8 ) 3/rlon$s )

+>(MP*+ !*1

(215n:

A (ylindri(al soil sa.-le, !*# (. 2n dia.eter and 1"*7 (. long, is tested 2na (onstant5head -er.ea:ility a--arat%s* A (onstant head of ! (. is.aintained d%ring the test* Af ter l .in of testing, a total of 62*! g of water was (olle(ted* Toe te.-erat%re was $>C* Toe void ratio of the soilwas *2#*

R5FG25=:

Co.-%te the (oeffi(ient of -er.ea:ility in eenti.etres -er se(ond and 2nf%rlongs -er fortnight*

S3lG423n:

irst, (al(%late the (ross5se(tional area of the sa.-le**,,vi *,,

A /2

/ 2!*# (.B / 21*6 (.*

ro. Eg* !57* solve for :

! \%

62 ! # + 1" 7

! (. + 21*6 (.* S 1 2n + " sQ.in

/ *7 (.Qs

To eon**ert to f%rlongs -e1 fo1tnight see A--endi+ AB*

o*os H B" . n BAoo !B$2 9B12 fort ght B

or the falling5head test ig* !*:B the velo(ity of fall in the

dh dt

2,7

,j

*



2,8 Jater In &olla= 11: Perea#lllt@= Seepa@e: Effectl/e &tre

and the flow into the sa.-le is

ro. 'ar(y3s law EF* !5B, the flow o%t is

Lout / !i$ ! 1 $

4y EF* !5# (ontin%ityB, Lin / Lout] or dh h

- a' & ! 5$dt %

e-arating varia:les and integrating over the li.its,

we o:tain a% 1! 55 ln 5 !56aB

$IJ.t h 2

where IJ.t 5 7 2 - 7 1 D In ter.s of logZg,Y!56:B

w here a area of stand-i-e, $ , % / soil sa.-le area and length,

at ti.e for stand-i-e head to de(1ease D O 1 43 O 2 D

E9A3PE !*$

A la:oratory falling5head -er.ea:ility test is -erfor.ed on a light5graygravelly sand WB, and the following data is o:tained9

a & "*$ (.*

(.

L / 1"*$7 (. O 1 / 1"*$ (.

i 2 7*1 (., and

J. - 6 s for the head to fall fro. O I to O $

Water te.-erat%re / $>C*



M.+ 3eaureent ol Perea#lllt@ 2,9

R5FG25=:

Co.-%te the (oeffi(ient of -er.ea:ility in (.Qs*

S3lG423n:

/ *! (. s at $>C*

Note9 I the water te.-erat%re is different than $>C, a (orre(tion for

1 eren(es . e vis(osi y is .a e*

everaV fa(tors .ay infl%en(e the relia:ility of the -er.ea:ility test

.[y (o.e o%t of sol%tion fro. the water* The degree of sat%ration (o%ldth%s :e less than 1], whi(h wo% a e(t t e test res% ts s1g. 1(ant y*Gi ration of fines in testin sands and silts also aff e(ts the .eas%redval%es* Te.-erat%re variation, es-e(ially in tests of long d%ration, .ay

than the la:oratory test te.-erat%re, a vis(osity (orre(tion sho%ld :e

:e re-resentative of field (onditions, it is diffi(%lt to d%-li(ate the in sit%so1 str%(t%re, 5es-e(ia y o gran% ar e-os1 s an o s ra 1 1e an o er nonho.o eneo%s .aterials* To -ro-erly a((o%nt for the nat%ral varia:ilityand inho.ogeneity of soil de-osits and diffi(%lties in la:oratory tests, the

w loverall average (oeffi(ient of -er.ea:ility*

la:oratory one5di.ensional (o.-ression (onsolidationB test or :y testinga soil sa.-le in the tria+ial (ell* The %se of these devi(es is dis(%ssed inCha-ters 7 and 1*

4esides the dire(t deter.ination of -er.ea:ility in the la:oratory,%sef%l e.-iri(al for.%las and ta:%lated val%es of e+ist for vario%s soil

ty-es* or e+a.-le, ig* !*", ada-ted fro. Casagrande 16#7B, is %sef%l* In

range of -er.ea:ilities in soils is so large* Note that (ertain val%es of ,1*, 152* and 156 (.Qs are e.-hasi&ed* These are Casagrande3s bench

8ar! values of -er.ea:ility, and they are %sef%l referen(e val%es for engineering e av1or* or e+a.- e, * (. s 1s t e a--ro+i.ate %n ry :etween la.inar and t%r:%lent flow and se-arates (lean gravels fro. (lean



1$ 1 1*

C8EIICIENT 8 PERGEA1 LIT(.Qs log s(aleB

1D 1n5$ 1D3 ,15 1D 1 " 1D3 1 B 1 6

'r1in363 -r ty 2 ood drinage P0or drain0ige n¡ 1

Pra(ti(allM ;.-erv,o%s

1 1A--li(,ltion in arth1N.1 a di<es Y

l.-ervi % s se(tions of earth da.s and di<

Ty-es ofsoll

Clean grave1

Merv fi e sands organi( and inorgani(

1 .i+t%res silts9 . *t%res o *sand, >?l4. andK(lav*gla(ial 111, strat11ed (lav de-os1ts, et(*

I 1

=l.-ervio%s= soiwhi(h fe .odifZed :ythe effe(t of veget tion an weathe ing*

fiss%r* weather (lays@ f a(t,%red 8C (lays

=l .irvio%s=l soils e*g*,ho. geneo%s (laysJ5l3 3n5 3weat ering

1

'ire(t Eer.inlitionof (oef i(ient o

-er.ea ility

'ire*Zt testingl of soil in its origBnal -osilion e*g*l* well -ointsl* 9lf -r ly (nd%(ted, relia:l @ (onsid*a:le e+t,erien(e reF%ired* ¡

Constan Head Pr.ee.er@little e+-erien(e reF%ired

NFte9 eon,idera:le e+-erien(e 1alsF reF% ire . this range* 1 1

Constant head test in trla+ial (elll@ 1

5l26Jl5 D24 5YN525n 6n= n3 56> Z9

eha:le@ittle e+J?lerien(eeF%ired

alling Hea Per.e09eter@Range of %nst :le -er ea:il ityJG 5YN525 5 n55> 3 (orre(t inter-r tation

1

airly relia:le@(onsidera:le e+-elien(e ne09essaryIdo in tria+,al (ellB

lnDre(deter.inationof (oef i(ient o -er 3litv

Co.-%tation9ro. the grainf3&e dist :X%tione*g*, Ha&en3s fo .%laB* nlya--li(a:le to el an, (oh ionlesssands and grave

Hori&rntal Ca-illarity Test9Mery ittle e+-erien(e ne(essarytiD es*-e(ially%seD f%l fo ra-id testing of a large n .:er os,.-les in the field witho%t la:or1tory fa(ilities

1

¡I

Cfrool%(otnasotilioation 11

test *@ e+-**=s ve la:or 643 5FGN 5n4 6n= 11(on 1dera:le e+-er ien( reF%1r 1 1

U

1$ 1 .0 1 1 0 $ 1 3 1^1D 1 1 D 1 ! 1 t 1 6

i, T'U '

'%e to rnigrlli8I3 >3 fine,* (hann,0ls, and alr in voids*

0g* !* P556ll24, 6ln65, >n 4C. 6nHU 543=> 43 =54ln 45 l 35l25n4 3 5J2ll4O45 - 666=5, 9!8, Dl4 l'?ln3l 6==l l3n5.



M.+ 3eaureent ol Perea#lllt@ 11

sands and sandy giavels* A of 1 2 (.Qs is the a--ro+9i.ate :o%ndary :etween -ervio%s and -oorly drained soils %nder low gradients* oilsaro%nd this val%e are also highly s%s(e-ti:le to .igration of fines or piping. Toe ne+t :o%ndary, 156 (.Qs, is a--ro+i.ately the lower li.it of the -er.ea:;lity of so;ls and (on(rete, altho%gh sorne re(ent.eas%re.ents have fo%nd -er.ea:il;t;es as low as 15 for highly -lasti( (lays at the shrin<age li.it* Prof* Casagrande re(o..ends that :e related to the nearest :eneh.ar< val%e, fer e+a.-le, *1 + 1 52 e.Qsrather than 15" (.Qs* or vario%s so;l ty-es, ;g* !*" also indi(ates their general drainage -ro-erties, a--li(ations to earth da.s and di<es, andthe .eans for dire(t and indire(t deter.ination of the (oeffi(ient of

-er.ea:;lity*An e.-iri(al eF%ation relating the (oeffi(ient of -er.ea:ility to Dio,

the effective grain siMe, was -ro-osed :y A* Ha&en 1611B* or clean sandswith less than ] -assing the No* $ sieveB with Dio si&es :etween *1and #* .., the (oeffi(ient of -er.ea:ility is

! / CD !51B

whe1e the %nits %f ! at e in (.Qs and those %f tite effe(tive giain si&e ate in..* Toe (onstant C var;es fro. *2 to 1*$, with an average val%e of 1, andta<es into a((o%nt the (onversion of %nits* Toe eF%at;on 2> valid for ! 15# (.Qs ;g* !*"B*

To est;.ate at vo;d ratios other than the test void ratio, Taylor 1627B offers the relationshi-

!511B

where the (oeffi(ients C and C,, whi(h de-end on the soil str%(t%re, .%st :e deter.ined e.-iri(ally* =ery approi8ately for sands, C1 C$ Another relationsh;- whi(h has :een fo%nd to :e %sef%l for sands 2>

* * * !51$B

ratio e and the logarith. of -er. a:ility ! is far fro. linear ig* !*!B*They showed that -ore si&e distri:%tion -ara.eters -rovide a :etter relationshi- with the ratio for sorne (o.-a(ted soils*

.j



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.) INTE!G!AN'A! O! E**ECTI2E&T!E&&

Toe (on(e-t of intergran%lar or effective stress was introd%(ed in e(*"*$* 4y def inition,

where a total nor.al stress,

a a3 u (7-13)

o3 intergran%lar or effe(tive nor.al stress, andu -ore water or ne%tral -ress%re*

4oth the total stress and -ore water -ress%re .ay readily :e esti.ated or (al(%lated with <nowledge of the densities and thi(<nesses of the

soil layers and lo(ation of the gro%nd water ta:le* The effe(tive stress(annot :e .eas%red@ it (an only :e (al(%latedThe total verti(al stress is (alled the body stress :e(a%se it is gener

ated :y the .ass a(ted %-on :y gravityB in the :ody* To (al(%late thetotal* verti(al stress o., at a -oint in a soil .ass, yo% si.-ly s%. %- thedensities of all the .aterial soil solids waterB a:ove that -oint .%lti -lied :y the gravitational (onstant , or

a., _oh pgdM !512aB

l p is a (onstant thro%gho%t the de-th, then

Rv pgh !512:B

Ty-i(ally, we divide the soil .ass into n layers and eval%ate the total stressin(re.entally for ea(h layer or

n

a., / L P40`4@51

(7-14)

As an e+a.-le, if a soil (o%ld have &ero voids, then the total stress e+ertedon a -arti(%lar -lane wo%ld :e the de-th to the given -oint ti.es thedensity of the .aterial or, in this (ase, Ps ti.es the gravitational (onstant .l the soil were dry, then yo% wo%ld %se pd instead of PsB

Toe ne%tral stress or -ore water -ress%re is si.ilarly (al(%lated for

stati( water (onditions*l4

is si.-ly the de-th :elow the gro%nd water ta:leto the -oint in F%estion, M..,, ti.es the -rod%(t of the density of water p..,and , or

(7-1+)

It is (alled the neutral stress :e(a%se it hh no shear (o.-onent*Re(all fro. fl%id .e(hani(s that :y definition a liF%id (annot s%--ortstati( shear stress* It has only nor.al stresses whi(h a(t eF%ally in all

211



214 Jater In &olla= 11: Perea#lllt@= &ee0age= Effectl/e &tre4a

dire(tions* 8n the other hand, total and eff e(tive stresses (an have* :oth the

differen(e :etween the total and ne%tral stresses*

is %sef%l even tho%gh in reality, on the .i(ro s(ale, it has no .eaning

-arti(%lar diff erential area yo% (hose ended %- in a void 8f (o%rse thes ress wo% ave o e &ero* e n t ne+t oor, w ere two grave -arti(les .ight :e in -oint5to5-oint (onta(t, the (onta(t stress .ight :e

e+tre.ely high@ it (o%ld even e+(eed the (r%shing strength of the .ineralains* tress then reall II r D

the s(ale, real .aterials are not really (ontin%o%s* oils, es-e(ially, are not

(olle(tions of dis(rete .ineral -arti(les held together :y gravitational,

stress. However it is not really the sa.e as the grain5to5grain (onta(t stress

with ro%nded or s-heri(al grains the (onta(t area (an a--roa(h a -oint* s ress (an e very arge* a er, e .tergran %lar stress is the s%. of the (onta(t for(es divided :y the total or grosseng.eeringB area, as shown in ig* !*7* I we loo< at for(es, the totalverti(al for(e or load P (an :e (onsidered to :e the s%.lar (onta(t for(es P -l%s the hydrostati( for(e F $ 5 $c :u in the -ore

. .

area, to get force the ne%tral stress u .%st :e .%lti-lied :y the area ofthe voids $ 5 $c , or

P / P A - A u

where $ total or gross engineeringB area, and

$c/

(onta(t area :etween grains*'ividing :y the gross area A to o:tain stresses, we have

!51":B

or

!51"(B



!* lnter@renular or +ffectlve .tre.... 215

-1

55D55555

$ 2. .8 P64255> 2n >6l2= nn464 6445 S5N43n, 90^.

or

o o3 l 5 a:u !51"dB

where a (onta(t area :etween -arti(les -er %nit gross area of the soil

<e.-ton, 16"B*In gran%lar .aterials, sin(e the (onta(t areas a--roa(h -oint areas, a

a--roa(hes &ero* Th%s E(9Z* !51"d red%(es to EF !51#, or a a3 u This eF%ation, whi(h defines effe(tive stress, was first -ro-osed in the16$3s :y Ter&aghi, who is (onsidered to :e the father of soil .e(hani(s*EF%ation !51# is an e+tre.ely %sef %l and i.-ortant eF%ation* We :elieve that the effe(tive stresses in a soil .ass a(t%ally (ontrol or gove. the eng.eering :ehavior of that .ass* The res-onse of a soil.ass to (hanges in a--lied stresses (o.-ressi:ility and shearingresistan(eB de-end al.ost e+(l%sively on the effe(tive stresses in that sailroass Toe -rin(i-ie of eUe(tive stress is -ro:a:ly the single .ost

i.-ortant (on(e-t in geote(hni(al engineering*We have dise%ssed ef feeti=e stresses for gran%lar -ar ti(%late .ateri5als* What does the (on(e-t .ean for fine5grained (ohesive soils ro. thedis(%ssion in Cha-ter 2, 1t 1s do%:tf %l that the ..eral (rystals are ina(t%al

-hysi(al (onta(t sin(e the y are s%rro%nded :y a tightly :o%nd water fil.* 8n the .i(ro s(ale, the inter-arti(le for(e fields whi(h wo%ld(ontri:%te toeffe(tive stress are e+trernely diUi(%lt to inter-ret and -hiloso-hi(allyi.-ossi:le to .eas%re* Any inferenr*e a:o%t these for(e fields (o.es fro.a st%dy of the fa:rie of the soil* o, in view %f this (o.-le+ity, what -la(e

,. _



5555 ---555 555

14 Jater In &on:: 11: Pennee#lllt@= S%pe@e: Elfec'/e &treu

does s%(h a si.-le eF%ation as !51# have in engineering -ra(ti(e E+-eri5 * as well as a (aref %l analysis :y <e .-ton 16"B hasshown that for sat%rated sands and (lays the -rin(i-ie of eff e(t1ve stress >an e+(ellent a--ro+i.ation to reality* However it is not so good for -artially sat%rated soils or sat%rated ro(<s and (on(rete* WhateverD it is -hysi(ally, effe(tive stress is defined as the differen(e :etween an engineer ing total stress and a .eas%ra:le ne%tral stress -ore water -ress%reB* Toe(on(e-t of effe(tive stress is e+tre.ely %sef %l, as we shall see in later (ha-ters, for %nderstanding soil :ehavior, inter-reting la:oratory test re s%lts,and .a<ing engineering design (al(%lations* Toe (on(e-t wor<s, andthat is why we %se it*

%ow we shall wor< thro%gh sorne e+a.-les to show yo% how to

(al(%late the total, ne%tral, and eff e(tive stresses in soil .asses*

E9A3PE !*#

(215n:

The (ontainer of soil shown in ig* E+* !*#* The sat%rated density is *

GgQ .!

!euired:

Cal(%late the total, ne%tral, and effe(tive stresses at elevation $ when aBthe water ta:le is at elevation $ an Delevation =.

El51. B

El51. A -



!* lntergrenuler or Effectl/e &trea..H 217

S3lG423n:a. Ass%rne the soil in the (ontainer to :e initially saturated :%t not

s%:rnergedB* Toe water ta:le is lo(ated at elevation A. Use EFs* !512:, !51, and !51# to (al(%late the stresses at elevation A.

Total stress EF* !512:B9

o Psat gh $* GgQ rn#+ 6*71 r nQs$

+ .

67 1 NQrn$ / 67*l <Pa

Ne%tral stress EF* !51B9

u / p..,gM.., 1 GgQ .#S 6*71 .Qs$

S O // O

rorn EF* !51#9o3 5 o 5 67* l <Pa

Re(all that 1 N 1 <gD.Qs $ and that 1 NQ.$ 1 Pa A--endi+ AB*b. I we raise the water ta:le to elevation =, a (hange in ef fe(tive

stresses a t eleva tion A o((%rs sin(e the sat%rated soil :e(o.ess%:.erged or :%oyant* Toe stresses at elevation A d%e to t:e soiland water a:ove are as follows9

Total stress9

$* + 6*71 + B I + 6*71 + $B

a Ne%tral stress9

u p..,gF M .., h :

1 S 6*71 S $ B

"7*! <Pa

Effe(tive stress at elevation A :

o3 o 5 u F Psat gh p..,gM.., : 5 p..,gF M.., h:

11!*! 5 "7*! 26* <Pa

Th%s :y raising the elevation of the gro%nd water ta:le the intergran5%lar -ress%re or effe(t1ve stress . E+a.-le !*# dro-s fro. 67 <Pa to 26<Pa, or a red%(tion of ] When the gro%nd water ta:le is lo(ered, thereverse o((%rs and the soil is s%:0e(ted to an increase in effe(tive stress*This overall in(rease in verti(al stress .ay lead to s%:stantial areals%:siden(e as is o((%rring, for e+a.-le, in Ge+i(o City and Las Megas*



5 5 555 5555 555555 55 55

------------

$17 Weter In olle, 119 Per.ea:lllty, ee-ege, Etfe(tlw treae

ro%nd water is :eing -%.-ed for .%ni(i-al water s%--ly, and theres%lting settle.ents have (a%sed s%:stantial da.age to streets, :%ildings,and %ndergroood %tilities*

Another way to (al(%late the effe(tive stress in -art :B of E+a.-le!*# is to %se the s%:.erged or :%oyant density EF* $511B* Note that

p3gh !51!B

E+AMPLE ."

(215n:

Toe data of E+a.-le !*#*

R5FG25=:

Use EF* !51! to (o.-%te the effe(tive stress at elevation A when the water

ta:le is at elevation =.

S3lG423n: p Psat 5 P( $* 5 1* 1* GgQ.#

o3 p3gh 1* S 6*71 S 2 26* <Pa

E+AMPLE .)

Toe soil -rofile as shown in ig* E+* !.2

R5FG25=:

What are the total and effe(tive stresses at -oint $U



555555555555555 555555D5D55D5

7.+ lntergrenuler or Eflectl/e >45.... 219

y,'r/,F5y/!,..Q

* *.0 MQ#

;;; /.V.R /.)R /- .

andn / .

4*

Psat / *.0 MQ#

" Clay

A

$2. EY. .)

S3lG423n:

irst find PJ and Psat of the sand* This will :e a review of -hase relations*Let =, // 1.#

@ therefore n // # and,

// 1 5 # // 1 5 n . ro. EF* $5!, "s // PsF l 5 n:

M . // $*! GgQ.# I - *B .# / 1*# Gg or 1#<gB

# pd // s // I.

?, g // 1*# GgQ .# or 1# <gQ .#B

Psat // "s "( $H * P(=v

//=, =,

1*# Gg ` 1 GgQ.#*.#B K Q

Psat // l .# 5 1*7 Gg .Toe total stress at $ is P4gh4#

1*# GgQ .!S 6*71 .Qs* + $ . // $"*26 <NQ.*

1*7 GgQ.! + 6*71 .Qs* + $ . / #"*# <NQ.*

` $* GgQ .# + 6*71 .Qs$ + 2 . // !7*27 <NQ.$

121*$! <N Q.*, or 121*# <Pa*

Toe eff e(tive stress at A is

(

/ 121*# 5 1 GgQ.# + 6*71 .Qs$S " .B // 7$*2 <Pa

,. j

4 p /

2

l J

1

#



5555555 55 5555555 5555555555555

220Jater In &olla= 11: Perea#lllt@= Seepa@e: Effectl/e &tre

The effe(tive stress .ay also :e (o.-%ted :y the V9 pgh a:ove thewater a '

1*# GgQ .# + 6*71 .Qs$ + $ . / $"*26 <Pa

Y1*7 5 1*B +D6*71 + $ 1"*"7 <Pa

$* 5 1*B + 6*71 + 2 / #6*$2 <Pa7$*21 <Pa (he(<sB

Note9 In -ra(ti(e, (o.-%tations wo%ld -ro:a:ly only : (arried

o%t to the nearest whole <Pa*

E9A3PE !*"

(215n:

The soil -rofile of E+a.-le !**

Plot the total, ne%tral, and effe(tive stresses with de-th for the entire soil

-rof ile*

o %t,on9

ig%re E+* !*"* o% sho%ld verify that 4 e n%.en(a va %esfig%re are (orre(t* As in the -revio%s e+a.-le, (o.-%tations to the nearestwhole <Pa are generally a((%rate eno%gh*

Note how the slo-es of the stress -rofiles (hange as the density(hanges* Profiles s%(h as those shown in ig* E+* !*" are %sef %l info%ndation engineering, so yo% sho%ld :e(o.e -rofi(ient in (o.-%tingthe.* In engineering -ra(ti(e, the :asi( soils infor.

.ation (o.es fro.

.investiga 1ons ansite

(ant soil layers, the de-th to the water ta:le, and the water (ontents anddensities of the vario%s .aterials* tress -rofiles are also %sef %l for ill%strating and %nderstanding what ha--ens to the stresses in the gro%nd when(onditions (hange, for e+a.-le, when the gro%nd water ta:le is raised or o D D in or floodin

orne of these eff e(ts are ill%strated in the following e+a.-les*



/ r Pa );1`r+----.--+---r+----r+--r+-

12--,-t--...F-...

a)

/' I Pa l;`;1

`

3

*

2

"

7

*id. E5. !*"



E 9A3PE M M

(215n:

Toe soil -rofile of E+a.-le !**

R5FG25=:

Plot the total, ne%tral, and effe(tive stresses with de-th if the gro%nd waterta:le rises to the gro%nd s%rf a(e*

S3lG423n:

ig%re E+* !*!* Note that the effe(tive stress at -oint $ at M / 7 .B is reduced U Had

the gro%nd water ta:le dro--ed :elow its original elevation, the effe(tivestress at -oint A wo%ld have in(reased*

E9A3PE !*7

(215n:

Toe soil -rofile of E+a.-le !**

R5FG25=:

Plot the total, ne%tral, and effeetiDf3e stresses with de-th for the (ase wherethe gro%nd water ta:le is $ . above the gro%nd s%rfa(e*

ig%re E+* !*7* ee -age $$2*B

Consider (aref %lly how the stress -rofiles (hange as the water ta:leelevation (hanges* Note es-e(ially how the effe(tive stresses de(rease asthe water ta:le rises E+a.-le !*" vers%s !*!B and then how the ef fe(tivestress is not (hanged even when the gro%nd water ta:le > above the gro%nd



a P6

40 80 *0

G P6

40

a P6

80 40 80

:M..,:...@

lg* E+* !*!

4

.

o



a <PaB

% < Pal

IP a3 < Pa B

Q5 * "0 80 *0 >*

"0 80 "0 7

Q Q @3v o

*

E**e**a,

o 2

"

7

2. EY..8

a*



M.1 Aelatlonahl0 ,etLeen Horl>ontal end 2ertlcel tre...a 225

s%rfaee E+a.-le !*7B* 8f eo%rse, for that (ase :oth the total and ne%tralstresses in(rease as the water ta:le rises a:ove the gro%nd s%rfa(e, :%t theeffe(ttve stresses re.a. unchanged . The reasoning :ehind why the effe(tive stresses re.ain %n(hanged is a very i.-ortant (on(e-t, and yo%sho%ld :e s%re yo% %nderstand why it ha--ens*

i.ilar :%t o--osite (hanges in effe(tive stresses o((%r when thegro%nd water ta:le is lowered* or e+a.-le, this .ight :e (a%sed :y -%.-ing fro. a dee-er -en 1io%s layer* I this ha--ens, as yo% .ights%s-e(t :y analogy, the effe(tive stresses in the (lay layer a(t%ally increase,

(a%sing (o.-ression of the (lay and (onseF%ent s%rfa(e settle.ents, as weshall see later* In a (lay this -ro(ess doesn3t o((%r overnight@ on the(ontrary 1t .ay ta<e several de(ades for the (o.-ress1on to o((%r* Ihese

-ro(esses are dis(%ssed in detail in Cha-ters 7 and 6*

. !EATION&HIP ,ETJEEN HO!IRONTA ANO2E!TICA &T!E&&E&

o% .ay re(all fro. hydrostati(s that the -ress%re in a liF%id is thesa.e in any dire(tion5 %-, down, sideways, or at any in(lination, itdoesn3t .atter* However this is not tr%e in soils* Rarely in nat%ral soilde-osits is the hori&ontal stress in the gro%nd eF%al e+a(tly to the verti(alstress* In other words, the stresses in sit% are not ne(essarily hydrostati(*

We (an e+-ress the ratio of the hori&ontal to verti(al stress in the gro%ndas

(7-18)

where K is an earth pressure coefficient. in(e the gro%nd water ta:le (anfl%(t%ate and the total stresses (an (hange, the (oeffi(ient K is not a(onstant for a -arti(%lar soil de-osit* However, if we e+-ress this ratio inter.s of effe(tive stresses, we ta<e (are of the -ro:le. of a varia:le water ta:le, or

(7-19)

S 1s a very 1.-ortant (oefh(1ent . geote(hr%(al engineenng* l4 1s (alled

the coef@icient of lateral earth pressure at rest. I4 e+-resses the stress(onditions in the gro%nd in ter.s of effective stresses, and it is inde-endentof the lo(ation of the gro%nd water ta:le* Even if the de-th (hanges, S will :e a (onstant as long as we are in the sa.e soil layer and the densityre.ains the sa.e* However this (oeffi(ient is very sensitive to the geologi(and engineering stress history, as well as to the densities of the overlyingsoil layers see for e+a.-le, Gassars(h, et al*, 197+). Toe val%e of S isi.-ortant in stress and analyses, in assessing the shearing resistan(e of

,j



*9****9 K K 9*955*9999@55

226 W645 In S3ll>, : P5nn55Jlll4, S55N55, E515 S45>>

-arti(%lar soil layers, and in s%(h geote(hni(al -ro:le.s as the design of earth5retaining str%(t%res, earth da.s and slo-es, and .any fo%ndationengineering -ro:le.s*

The S in nat%ral soil de-osits (an J5 as low as *2 or * 3forsedi.entary soils that have never :een -reloaded or %- to #* or greater for sorne very heavily -reloaded de-osits* Ty-i(al val%es of S ent geologi( (onditions are given in Cha-ter t t *

E+AMPLE .9

(215n:

for differ5

Toe stress (onditions of E+a.-le !** Ass%.e S for this soil de-osit is *"*

R5FG25=:

Cal(%late :oth the hori&ontal total and eff e(tive stresses at de-ths of " .and 7 . in the de-osit* Also, deter.ine the val%e of K at these de-ths*

S3lG423n:

ro. ig* E+* !*", at 2 ., o is 2# <Pa* ro. EF* !516, o4. *" S 2#

<Pa $" <Pa* At 7 , . *" Y 7$ 26 <Pa* or the total hori&ontal

stresses, we (annot %se EF* -8 dire(tly :e(a%se we do not <now S. o we%se EF* !51# to get oh , or oh o4. u. At 2 ., oh $" $ 2" <Pa* At7 ., oh / 26 6 / 17* Using EF* !517, we (an deter.ine the val%e of the total stress (oeffi(ient K.

At 2 .,

At 7 .,

aO 2"S & ' & ' & 0.13

"#

a,. 17S & ' & ' & 0.11o., 121

Note that S is not ne(essarily eF%al to S > To get S, we have to gothro%gh S and add the -ore water -ress%re to the effe(tive stress for thede-th in F%estion*

1

1



. HEA(& ANO ONE"(I3EN&IONA *OJ

Mery early in this (ha-ter we .entioned the three ty-es of headsasso(iated with the 4erno%lli energy eF%ation EF* !52B* They were thevelo(ity head v

/ g, the -ress%re head hP / p/ p( g , and the -osition or

elevation head M. We dis(%ssed why the energy er %nit .ass or wei twas (a e ead and had %nits of length* And we also stated that, for .ostsee-age -ro:le.s in soils, the velo(ity head was s.all eno%gh to :enegle(ted* Th%s total head h :e(o.es the s%. of the pressure head and theeleva/ion head , or h / hP M.

The elevation head at any -oint is the verti(al distan(e a:ove or

:elow sorne reerence elevation or datu8 plane. I4 is .ost often (onvenientto esta:lish the dat%. -lane for see-age -ro:le.s at the tailwater elevation, :%t yo% (o%ld 0%st as well %se the :edro(< or sorne other (onvenient -lane as the dat%.* Press%re head is si.-ly the water -ress%re divided :y P( K EF* !52B* The F%antity hP &B is also (alled the pieMo8etric head

sin(e this is the head that wo%ld :e .eas%red :y an o-en stand-i-e or pieMo8eter ref eren(ed t sorne dat%rn -lane* The elevation of the water level in the stand-i-e is the total head whereas the a(t%al height of rise of the wa ter (ol%.n in the stand-i-e is the -ress%re head hP. These (on(e-ts areill%strated in ig* !*6* Here we have an o-en5ended (ylinder of soil si.ilar tothe -er.ea.ete1 %f ig* !*a* The flow .to the (yhnder is s%ffi(ient to.aintain the wa ter elevation at A, and the tail water is (onstant at eleva

tion T. All energy or head is lost in the soil* Note that for -ie&o.eter e in the fig%re the -ress%re head hP is the

distan(e A@ and the elevation head M is the distan(e @T. Th%s the totalhead at -oin t e is t:e s%. of these two distanees, or AT. 'ete.rinationsof the -ie&o.etri( heads at the other -oints in ig* !*6 are .ade in asi.ilar .anne1, and these 65 shown in the ta:le :elow the ftg%re* 4e s%reyo% %nderstand how ea(h of the heads, in(l%ding the head loss thro%gh thesoil, is o:tained in ig* !*6* Note that it is -ossi:le for the elevation headas well as the -ress%re headB to he oegative, de-ending on the geo.etry of the -ro:le.* The i.-ortant thing is that the total head .%st eF%al the s%.of the -ress%re and elevation head at ali ti.es*

As .entioned, we ass%rne that ali the energy or head lost in thesyste. is lost in flowing thro%gh the soil sa.-le of ig* !*6* Th%s at

elevation C no head loss has yet o((%rred@ at , the .id-oint of thesa.-le, half the head is lost i AT ) and at , ali of the head has :een lost $E .

The following e+a.-les ill%strate how yo% deter.ine *the vario%sty-es of heads and head loss in sorne si.-le %ne5di.ensional flow syste.s*

227

,,¡



228Jater In &olla= 11: Perea#lllt@= Seepa@e: Effectl/e &tre

$3 N253545 5:

...--?--- A

`4th-

C $2l45 >55n 4346l 3

N25354256=

&64G

+ E

P5>>G5 El516423n T346l H56= L3>>

P32n4 H56= H56= H56= 43G S32l

B

( AB

AC

BE AE oCE AE o

& C& &E CE AE

$ E$ -E$ o AE

$2. .9 lllG>46423n 3 4N5> 3 56= 645 T6l3, 9"8.

E9A3PE M .1O

(215n:

The test set%- of ig* !*6 has the di.ensions shown in ig* E+* !*18a*

= e J

----- A )

6

$2. EY. .06

B



!,! Heeda and On(lenalonal *loL 229

R5FG25=:

aB Cal(%late the a(t%al .agnit%de of -ress%re head, elevation head, total head,and head loss at -oints =, C, , and F, in (enti.etres of water* :B Plot theheads vers%s the elevation*

S3lG423n:

a* List di.ensions and heads in a ta:lb as in ig ! 6, as shown :elow@ the heads are in %nits of (enti.etres of water*

20 20 2 o!* 20 20

F + 5 o 2

b. ee ig* E+* !*1:*

2A

B ''' 56= # ' Q

'E P5>>G5 ' Qe $ e;:;lI

D

1

>

51 o 1 20 #

H56= 3 D645

J

$2. EY. .0J

PointPress%re

HeadElevation

HeadTotalHead

HeadL3>>

= 3+ 2 o

'

/ = '



E9A3PE M *11

(215n:

Toe (ylinder of soil and stand-i-e arrange.ent shown in ig* E+* !*11*

J

--- A

B

e

=

,..X24'- ----- '

$2. EY. . A45 T6l3, 9"8.

R5FG25=:

'eter.ine the -ress%re head, elevation head, total head, and head loss at -oints =, C, and .

S3lG423n:

et %- a ta:le si.ilar to that of ig* !*6 and E+a.-le !*1*

PointPress%r(

H(adEl(vation

H(adT346lH(ad

H(adL3G

$. BE $.E 3

' T T o $.E

$#



··'·· .:,':: 55 555555DD55555555 55D55 55555 -

E9A3PE M *1$

(215n:

J ne non&ontaJ (y1.oer 1soil as shown . *t31g* !*$* Ass%.e L / 1 (., $ 1 (.

*, and $h (.* Tailwater elevation is (. a:ove the (enterline

of the (ylinder* Toe soil is a .edi%. sand D24 e *"7*

R5FG25=:

'eter.ine the -ress%re, elevation, and total head at s%ffi(ient -oints to J5a:le to -lot the. vers%s hori&ontal distan(e*

S3lG423n:

l.- . . .. nl..- 1**5 .-

5*, . X . X :X. X n -'- --...... 555 5 .*K

55

Redraw ig* !*$ in ig* E+* !*1$a with the <ey di.ensions* Est;.ate theT

DD

dat.%.. is the elevation of the tailwater* et %- a ta:le as in ig* !*6, and fill111 GG;; * 11%, U111L*ll )911 C 111 MI W)9lLCf*

. .<6

T T

(. h / (.

1 l9

(. A56 / 0 (.$1

jX A. W *t U *U %

U ? ^9 ^999 ?b?

l52 (. 5Z55s I I #506

.$2. EY. .*6

231

Z, .j

D555*555

5

- .

-

T5



5 5 5 5



232 Jater In &oll= 11: Perea#lllt@= Seepa@e: Ettectl/e tre..

*995

1$ Press%re head----.U...

8 --- --- ******** *******K*

?#9' 4

o Total headE o. 1 vation head

?O-4

K K K KlK K 99i99

-8

e ' E

o 2 6 12 1!

J

$2. EY. .*J

Press%re Elevation Total llead

Point Head Head Head Loss

A 1 - + 5 o+ 5 o

e 7$ - + 2$ $

5 - + o 5

T + - + o 5

The -lot of heads vers%s hori&ontal distan(e is in ig* !*1$: for the(enterline of the (ylinder*

M.4 &EEPAGE *O!CE&= D'IC-&AN(=

(% ID'E*ACTION

When water flows thro%gh soils s%(h as the flow of water in the -er.ea:ility tests already dis(%ssedB it e+erts for(es (alled seepage forces

on the individ%al soil grains* And yo% .ight i.agine, see-age for(es affe(tthe intergran%lar or effe(tive stresses in the soil .ass*

Let %s re(onsider the . (ol%.n of soil of E+a.-le !*#* 4y(onne(ting a riser t%:e to the :otto. of the sa.-le, we (an flow water intothe (ol%.n of soil, as shown in ig* !.18* When the water leveV in the riser Dt%:e is at elevation =, we again have the stati( (ase and all the stand-i-es

---- K K K

?

2



a 4 e

%le.

%le. C -F-2 8%le. A -

#ilter sreen

-------- ----.------------------

1 1 &ee0ega Aorcea: OulcHnd and luefactlon 233

$2. .0 S6Nl5 3 >32l 3 EY6Nl5 .!, JG4 D24 6 2>5 4GJ5 3n n545=43 45 J3443 3 45 >6Nl5. S46n=N2N5> 65 >3Dn 3 45 6>5 Dn55 4n5

D645 l515l 2n 45 2>5 N2N5 2> 64 6 =2>46n55 + 6J6¡¡5 5l5'l6425$I .

wo%ld :e at elevation =. I the water in t:e (iser t%he is :elow elevation =.water will flow do(n(ard thro%gh the soil@ the reverse is tr%e when thewater elevation in the tiset t%:e is a:oe elev ation =. This is the sa.e(ase as the falling5head -er.ea.eter test set%- of ig* !*: in whi(hwater flows up(ard thro%gh the s1I9 when th1s ha--ens, the water losesso.e of its energy thro%gh f ri(tion* The greater the head h a:oveelevation 2n ig* !*1, the larger the energy or head loss and thelarger the see-age

for(es traosroitted to the soil As the see-age for(es in(rease, they grad%5ally over(o.e the gravitational for(es a(ting on the soil (ol%.n, andevent%ally a Luie! eondition F%i(< aliveB or boiling wiU o((%r Another na.(@9 for this -heno.enon is Luic!sand . To have a sand .ass in a F%i(< (ondition, the effe(tive stresses tln o%gho%t the sa.-le .%st :e &ero*

D What is the height h a:ove elevation that (a%ses the soil to :e(o.e F%i(<irst fro. ig* !*1 we (an (al(%late the total, ne%tral, and effe(tive stressat elevation A when the water level in the riser t%:e is at elevation =. Wewill negle(t any fri(tion losses in the riser t%:e* Total stress at the:otto. of the sa.-le eBeva tioo $ : is

a Psat g% ` p,.,gh,., / p3g% p,.,gF % ` h ,*,B aB



$#2 Jater In oll, 119 Pennea#lllt@= &ee0age= +llectlve

Stre8a

The -ore -ress%re at that -oint is

e(ttve stress 1s

Let the water level rise a distan(e O a>#$ elevation = Now the -ore water -ress%re at the :otto. of the sa.-le is

J

e

EFs* aB 5 dBX9

&& p3g% P( gF % h( : 5 p( gF % h.., h:

Th%s the effe(tive stress de(reased :y e+a(tly the in(rease in -ore water -ress%re u at the :ase of the sa.-le EFs* fB 5 eB eBB*

What ha ens when the effe(tiv(ol%.n is &ero Note that o3 (annot :e less than &ero*B et EF* fB eF%al to

Luic! (ondition, or %p3 O &&'

Rearranging, 5h

,* 5 p3

,* !5$B

% P( e

gradient i. The val%e i when a F%i(< (ondition o((%rs is (alled the critica/

hydraulic gradient ic.

In E+a.-le $*" we o:tained the following relationshi- for the s%:5ens1 y - 9

, Ps 5 P..,

P 1 e $517B

Co.:ining EFs* !5$ and $517 we o:tain an e+-ression for the (riti(alhydra%li( gradient ne(essary for a F%i(< (ondition to develo-,

* Ps 5 P(

33= 1 e :p..,!5$1B



5555555

D555555555555555555555

!*a ee-age or(ea, %l(<%nd, end LlF%elllCllon 23+

or

i 1 p., 5

e l ` e P(

!5$$B

The a roa(h D%st %sed to o:tain i is :ased on(onditions o((%r when the effe(tive stress at the :otto. of the soil (ol%.nis &ero*

Another way to o:tain the for.%la for the (riti(al gradient is to

water ress%re a(tinthe soil (ol%.n, or

The total weight of soil and water a(ting downward at the :otto. of . .

F. . /

EF%ating these two for(es, we o:tain

give the sa.e res%lts*We (an (o.-%te ty-i(al val%es of the (riti(al hydra%li( gradient,

ass%.ing a val%e of p., $*"7 GgQ.# and void ratios re-resentative of .

e

Ta:le !51* Th%s, for esti.ation -%r-oses, ic is often ta<en to :e a:o%t%nity, whi(h is a relatively easy n%.:er to re.e.:er*

TABLE - TN26l V6lG5> 3 i1 ! N

7 *.8 MQ#

Moid Ratio

.sA--ro+i.ate Relative 'ensity

'enseWe

.*.12 Gedi%. *6"1* Loose *72

E+AMPLE .!

(215n:

1B

. .



<,1

236 W645 In S3ll6, : P556Jlll4, S55N65, E515 tren

R5FG25=:

a* ind the head reF%ired to (a%se F%i(< (onditions* :* ind the (riti(al hydra%li( gradient*

S3lG423n:

a* ro. EF* !5$,

h p3 % Psat5 P( % P( P(

:* The (riti(al hydra%li( gradient EF* !5$B is

We (o%ld also %se EF* !5$1 if we <new the val%e of Ps and e.

Ass%.e Ps $* g F* 5 , so ve or e / .

Therefore

$*" 5 1*B

1 *"

.0

ee-age for(es, whi( .ay %t not ne(essan y (a%se F%i( sanvelo are alwa s resent in soils where there is a gradient (a%sing the

flow of water* ee-age for(es affe(t sands .ore than (lays :e(a%se sandsD D D i n whi(h

holds the -arti(les together* To eval%ate the see-age for(es, let3s loo< againat 1g* * or F%i( (on 1 1d%e to the head h on the lef t side of the fig%re .%st 0%st eF%al the effective

downward for(e e+erted :y the s%:.erged soi (o %.n on t

%-ward for(e downward for(e

P( gh$ / p3 g%$ 5 a

1s eF%a ion we ge p - P,.,

/1 e

Af ter a ge ra1( .a.-% atton, t 1s eg%a ion 1s 1 en i%nifor. flow the % ward for(e P(0h$, the lef t5hand side of EF* !5$#a, isdistri:%ted and dissi-atedB %nifor.ly thro%gho%t the vol%.e %$ o t e



7.5 ee-ege $35>, @Gl>6n=, 6n= FG5l64l3n 237

soil (ol%.n* Th%s !5$#(B

The ter. ip( g is the seepage force per unit volu8e, and it 2> (o..onlyre-resented :y the sy.:ol ?. The val%e of this for(e at F%i(< (onditionse %als i p , and it a(ts in the dire(tion of fl%id flow 2n an isotro-i( soil* l the right5hand side of EF* !5$#a is divided :y LA, the %nit vol%.e, then we

? & p 3g !5$#dV

These e+-ressions, EFs* !5$#( and !5$#d, (an :e shown to :e identi(alwhen F%i(< (onditions o((%r see EF* !5$1B*

E+AMPLE ."

(215n:

e so1 sa.- e an

R5FG25=:

a* ind the head reF%ired to (a%se a F%i(< (ondition*

.(* how, %sing see-age for(es, that F%i(< (onditions really develo-

%nder the head of -art aB*=. Co.-%te the total see-age for(e at elevation A.

a* ro. E+a.-le !*1#, h a:ove elevation to (a%se a F%i(< (ondi tionis * .*

:* The see-age for(e -er %nit vol%.e is (o.-%ted fro. EF* !5$#(*

Gg + 1 / 6*71 <Ns

J

Ass%.e, as in E+a.-le !*1#, p., $*" GgQ .# Then e *"*

Therefore* $*" 5 1*

6l <N

1 &1*" g *

.#

Note that the %nits (he(< ( F/ L / ML' r B*

.



$#7 Water In olla, 119 Per.ea:lllty, H-age, Effe(tlve tress

(* %i(< (onditions develo- when the %-ward see-age for(e JUteF%als the downward :%oyant for(e of the soil* 8r, fro. EF* !5$#(and d9

K0Kl volB j / p(v )J,vo

6 71 S 2 S 1 $ $* 1*B Gg S 6*71 . V 5 . S I .$

.J

26* <N0 26* <NJ,

.# $

d* The total see-age for(e at elevation A is

<N ? volV 6*715 V 5 V 1 .$ 26* <N

!

This for(e is distri:%ted %nifor.ly thro%gh the vol%.e of the soil(ol%.n*

The see-age for(e 1s a real for(e and it is added ve(torially to the :ody or gravitational for(es to give the net for(e a(ting on the soil -arti(les* We (an re-resent these for(es in two different ways :%t ea(hway gives identi(a J res%Jts In E+a.-le !*12 we treat the -ro:le.eonsidering see-age for(es and s%:.erged densities* A F%i(< (onditionres%lted J5- ea%se the effe(tile 0 :%oyan t density of the soil vol%.ea(t.g down wardB 0%st eF%alled the see-age for(e a(ting %-wardB*

An alte.ative a--roa(h is to (onsider the total sat%rated weight of soil and the :o%ndary water for(es a(ting on the soil, to- and :otto., as shown in E+a.-le !*1*

E+AMPLE .)

(215n:

The soil sa.-le and (onditions of ig* !*1 and E+a.-les !*# and !*12*

R5FG25=:

ow, %sing total sat%ratedB weight of the soil a:ove elevation $ andthe :o%ndary water for(es, that F%i(< (onditions develo- when the headhis 5 .*

1 *



--------------- - ..---- ------ - --------- -------------

55DDDDDD5DD555D 5

!*7 S55N65 $35>, @Gl>6n=, 6n= LlFG564l3n $#6

or a F%i(< (ondition, 9v / 8*

oil/ Psat g%$

5 $*8 G g S 6*71 S 2 S I *- 67 1 <

N.# s$

waler to- / P( Kh ( $

5 1 Gg + 6*71 + $ + l *- 16*"

<N.# s$

water :otto. Í / P( gF % h( h BA

/ I Gg Y 6*71 Y $ B

.! s*

11!*! <N

Therefore down %- for a F%i(< (ondition 11!*! <N 11!*! <NB*

E+AMPLE .

(215n:

Toe soil and flow (ondit;on of ;g* !*1, e+(e-t that the lef t5hand riser t%:eis at elevat;on C, or $ . a:ove elevation $.BAss%.e the water leveis.aintained (onstant at elevation C.

R5FG25=:

Co.-%te aB the hydra%li( gradient, :B effe(tive stress, and eB see-ageforee at elev ation A.

ol%tion9

In ,this (ase the flow of water is downward thro%gh the soil* Ass%.e theda%. -lane is at the tailwater elevation, or at elevation =.

a* Use EF* ! l @ sinee the head loss is 2 . :elow elevation 4B,

' U '5

% 2

:* The ef feetive stress at elention A .a9y J5 (o.-%ted in t:e twoways 0%st des(ri:ed*



Z1

24,Jater In &olla= 11: Pennea#lllt@= See0age= Etfec'/e Stre--

t* Using boundary water for(es and sat%rated densities we get%nits are the sa.e as E+a.-le !*1B

soil q / Psat g%$

$*6*71BB1B 67*1 <NiD

16*71B$B1B 16 " <N

water :otlo. t / P(0h$

16*71B$B1B 16*" <Nt

L 9 v.., 16*" 67*1 5 16*"

/ 67*1 <Ntnet or effe(tive for(eB

the effe(tive stress A 67*1 <NQ.

Th%s the filter s(reen at elevation A .%st s%--ort a for(e of 67* l <N -er %nit area or a stress of 67*1 <N Q .

$in this (ase*

$* Toe other way to (o.-%te the effe(tive stress at elevation $ isto %se see-age for(es, :%oyant densities, and EF* !5$#* Notethat O / 5 . ref eren(ed to elevation =.

4 / PwgivolB / 16*71B BB1B

/ 26 * <N a(ting down in the dire(t;on of flowTo this we add the effe(tive or :%oyant weight9

downq / p3 g%$ Psal 5 P( :g%$

$* 5 1B6*71BB1B 26* <Ni

Therefore adding ve(torially these two for(es, we get the see-agefor(e -l%s the effe(tive soil for(e a(ting on area A, or 26* 26* / 67*1 <N -er %nit area as :efore* 8r the effe(tive stressat A / 67* l <NQ.* Note that this se(ond a--roa(h also a%to.ati(ally gives the sol%tion to -art (B, the see-age for(e at A. - Note that the see-age for(e at the to- of the soil is &ero and

in(reases linearly to 26 < N a t elevation A.

An a--arat%s that is (o..only %sed in soil .e(hani(s tea(hingla:oratones to de.onstrate the -heno.enon of F%i(<sand is shown in ig!*11* lnstead of a stand-i-e as in ig* !*1, a -%.- is %sed to (reate the%-ward flow in the F%i(<sand tan<* Toe water flows thro%gh a -oro%s

? 55 555 5555555555

*



55 555555555555555555555555555

Pie&o.eters

5

_ _599

_9599_

9599_

95599_

9559_

9955_

9 5_5_

999

K5599

K 9559

K 9955

K 9 99

K95599

K9 Water 5

#99

-9559

-9955

-9

99-95599-95599-9559 K--59-995-559 9-9959-995-559 -5-5959995599955

low.eter * 6lQ2n 6N624

Malve AB5

22,

Malve )6)

l

iiiiiiiJiiiiiiiiiili i li5

- 9?---2I$2. . &266 3 6 FG2>6n= 46n 3G45> J* O. O>45J5, %34D5>45n n215>24.

241

,.

-------------------- 555

- 9e3e3e399e33,W645, 46n



242 Jater In &olla= 11: Peree#lllt@= &ee0ege= Eflectl/e &tre

stone to distri:%te the -ress%re evenly on the :otto. of the sand .ass*Pie&o.eters at vario%s levels on the tan< ena:le heads to :e o:served and.eas%Hd* As valve l is grad%ally o-ened, the head a--lied to the :otto.of the sand .ass in(reases, and event%ally it :e(o.es s%ffi(ient t8= (a%sethe entire sand .ass to :oil or liLuefy. As in E+a.-les !*12 and !*1, thesee-age for(es are a(ting %-ward and 0%st :alan(e the downward5a(tinggrav1tatlonal for(es* The eff e(tive stresses :etween the sand gra.s are &ero,and the soil has no shear resistan(e* As long as the -%.- is r%nning, thesoil .ass (an easily :e stirred with a rod or .etre sti(<, and it a(ts li<e adense liF%id ig* !*1$aB*

Ne+t we sh%t off the -%.-, (lose valve 1, and o-en valve $* Now thedireetion of the 1 ater flow is re* ersed, and the see-age forees aet doDn-

ward along with gravity and in(rease the eff e(tive stresses* A rod or .etre sti(< lef t :%ried in t he sand has resistan(e to .ove.ent, and the sand .ass (an 11

longer :e stirred easily* Even tho%gh the sand is very loose, it (an s%--ortsorne stati( loads at the s%rfa(e, as shown in ig* !* l $:* This (ase is si.ilar to E+a.-le !*1"* Therefore, de-end ing on their dire(tion, see-age for(es(an signifi(antly in(rease the eff e(tive stresses and the strength of the soil.ass*

orne -ra(ti(aV e+a.-les of F%i(< (onditions in(l%de e+(avations ingran%lar .aterials :ehind (offerda.s alongside rivers* To e+(avate and

-ro(eed with (onstr%(tion, the water ta:le at the site is lowered :y asyste. of wells and -%.-s* 8f (o%rse water fro. the river invaria:ly see-s

into the e+(avation and .%st :e -%.-ed o%t to <ee- the e+(avation dry* I %-ward gradients a--roa(h %nity, the sand (an :e(o.e F%i(< and fail%reof the (offerda. (an o((%r* As is e+-lained in the ne+t se(tion, s%(hfail%res are %s%ally (atastro-hi( so high safety fa(tors .%st :e %sed indesign* l3**nother -la(e F%ie< eonditions often oee%r is :ehind levees d%ringfloods* The water see-s %nder the levee and, as in the (ase of the(off erda., if the gradient is high eno%gh lo(ali&ed F%i(< (onditions (ano((%r* This -heno.enon is <nown as a sand boi/ and .%st :e haltedF%i(<ly %s%ally :y sta(<ing sand :ags in a ring aro%nd the :oilB, otherwisethe erosion (an s-read and %nder.ine the levee* %i(< (onditions are also

-ossi:le al.ost any -la(e where artesian -ress%res e+ist, that is, where the :ead is grea ter ha n r:e %s%a l srari( wa ter -ress%re %(h -ress% res o((%r

where a -ervio%s %ndergro%nd strat%. is (ontin%o%s and (onne(ted to a -la(e where the head is higher*

Contrary to -o-%lar :elief, it is not -ossi:le to drown 2n F%i(<sand,%nless yo% really wor< at lt, :e(a%se the dens1ty of F%1(<sand 1s .%(hgreater than that of water* in(e yo% (an al.ost float in water, yo% sho%ldeasily :e a:le to float in F%i(<sand*



4)

...... ,-

eB

$2. .* @G2>6n= 46n: 6 Gn=5 6n GND6= 6=25n4, 45 >6n=6>> 2> 56>2l >425= D24 6 545 >42; J 6=25n4 2> =3DnD6=;>6n= 2> 6Jl5 43 >GNN34 6 >4642 l36=; 5 645 6 >3 l36= 2> 6NNl25=43 45 >2=6 3 45 46n, 45 >6n= 6>> l2FG525> 6n= 35n462l l3>5>6ll J562n 6N624. %3425 D645 l515U 2n N253545> N3436N JM. SG5n=6; 6n= J R.&. H3l4.

$2#



E9A3PE M .1M

(215n:

The (onditions as shown in ig* E+* !*1!* The silty elay a(ts as ani.-ervio%s layer and -revents flow of water %- fro. the fine sand layer :elow it* 4e(a%se of a river near:y, the fine sand layer is %nder a head of water greater than the e+isting gro%nd s%rfa(e artesian (onditionsB* l astand-i-e or -ie&o.eter were installed thro%gh the silty (lay layer, it wo%ldrise a distan(e h a:ove the to- of the sand layer* I Zs is not s%ffi(iently

large, the %-lif t -ress%re in the .iddle of the e+(avation (o%ld (a%se the :otto. of the e+(avation to =:low %-*=

!euired:

Cal(%late how dee- an e+(avation (an :e .ade, :ased on the ass%.-tionthat yo% negle(t the shear for(e on the sides of the soil -l%g*

S3lG423n:

At eF%ili:ri%., h 9

or

/

8*

Pwgh''

s

ilty

E +(avation

Pie&o.eter 5555555555

elay *9 55,5555@5 551H, H H ` 9 -gH ,

k Negle(t shear along sides*

$2. EY. .

244

1

U

R:



5555555555 DD5555555555555 5 5555555555555555 555555555555555555555555555555555555555555

7.8 &ee0age *orce= Dulcand= and luefactlon 245

ail%re will o((%r 2 Zs ^ P( Kh/ pg. I Zs ? P( Kh/ pg, then fail%re (annotha--en* In -ra(ti(e, the fa(tor of safety against :low %- sho%ld :e rather high sin(e, if it o((%rs, it is (atastro-hi(* o% .%st :e very (onservative indesigning s%(h sit%ations :e(a%se of the -ossi:le (onseF%en(es*

Another -heno.enon related to F%i(<sand is liLuefaction, whi(h (an :e de.onstrated in a F%i(<sand tan<* Af ter the sand has :een .ade F%i(< and in a very loose state, the flow is reversed and the water level is allowedto dro- 0%st slightly :elow the sand s%rfa(e* A shar- :low is a--lied to theside of the tan<, and instantly the enti;e soil .ass liF%efies and the sand

loses ali :earing (a-a(ity ig* !*1$(B* This rea(tion is e+a(tly whatha--ens when a loose sat%rated de-osit of sand is s%:0e(ted to loads of very short d%ration, s%(h as o((%r d%ring earthF%a<es, -ile driving, and :lasting* Toe loose sand trieds to densify d%ring shear and this tends tosF%ee&e the water o%t of the -ores* Nor.ally, %nder stati( loading, thesand has s%ffi(ient -er.ea:ility so the water (an es(a-e and any ind%(ed -ore water -ress%res (an dissi-ate* 4%t in this sit%ation :e(a%se the loadingo((%rs in s%(h a short ti.e, the water doesn3t have ti.e to es(a-e and the -ore water -ress%re in(reases* in(e the total stresses have not in(reasedd%ring loading, the effe(tive stresses then tend toward &ero :y EF* !51#B,and the soil loses ali strength* Note the -osition of the water level in thestand-i-es of ig* !* l $(* The -hotogra-h was ta<en 0%st af ter a shar- :lowagainst the side of the tan<*

Casagrande 16#"aB was the first to e+-lain liF%efa(tion in ter.s of soil .e(hani(s, and he also des(ri:es 16, 16!B sorne sit%ations in -ra(ti(e where liF%efa(tion has o((%rred* A.ong these are the fail%re of t* Pe(< 'a. in Gontana in 16#7 and flo( s/ides along the lower Gississi--i River* Here sands are de-osited d%ring floods in a very loosestate* o.ehow strains are ind%(ed in these de-osits, and it see.s thatthey al.ost s-ontaneo%sly liF%efy and flow o%t into the river* Toe -ro:le.is that they of ten ta<e levees and other flood -rote(tion wor<s along withthe., and re-airs of these feat%res are e+-ensive* 4an< erosion leading to -rogressive liF%efa(tion, see-age -ress%res fro. high water ta:les, and

even traffi( vi:rations have :een :la.ed for flow slides* low slides alsoo((%r in .ine tailings Kda.s* These str%(t%res are of ten very large and(onstr%(ted hydra%li(ally of very loose sands and silts* in(e they are awaste d%.-, very little engineering and (onstr%(tion ins-e(tion goes intothe.* ail%res are relatively (o..on*

in(e the Niigata, Ja-an, and the An(horage, Alas<a, earthF%a<es of 16"2, where severe da.age o((%rred d%e to liF%efa(tion, there has :eenin(reasing interest in liF%efa(tion* l4 has :een fo%nd that liF%efa(tion (ano((%r in the la:oratory in even .oderately dense sands d%e to a re-eated

,j



246 Water In olla, 119 Par.ea:lllty, ee-age, Efle(Uve tre%

or (y(li( a--li(ation of shear stress, whi(h .eans that if an earthF%a<elasted long eno%gh, then even .oderately dense sat%rated sands (o%ld -ossi:ly liF%efy This i.-orta %t, t:o%gh (ontroversiaX -oin t, isdis(nssed :y Casagrande 16!B and eed 16!6B* ee e(* 11*7*B

.9 SEEPA(E A%& $L0'." %ETS:TWO-&IME%SIO%AL $LOW

The (on(e-t of head and energy Joss as water flows thro%gh soils has :een .entioned severaV ti.es in this (ha-ter* When water flows thro%gh a -oro%s .edi%. s%(h as soil, energy or head is lost thro%gh ri(tion si.ilar to what ha--ens in flow thro%gh -i-es and in o-en (hannels* As in thela:oratory -er.ea:ility test des(ri:ed earlier, for e+a.-le, si.ilar energyor head losses o((%r when water see-s thro%gh an earth da. or %nder asheet -ile (off erda. ig* !*1#B*

'ifferent <inds of heads and head losses were des(ri:ed in e(* !*!,and it .ight :e a good idea to review that .aterial :efore -ro(eedingf%rther in this se(tion* ig%re !*12 shows how the -ie&o.etri( heads( Op ` & B .ight :e deter.ined fro. the -ositions and elevations of the

6

... . . B.#.. ,.

5 5 5 y 5 9K D,9* *5*K99 K9K5*K9 3D*9D99D D 9. Q - .. . .

$2. .! En2n552n 5Y6Nl5> 3 56= l3>> J56G>5 3 >55N6543G >32l>.



1 c l#h a 11

C'

/j * 1

1lA 9 17 t )

;;

LC / 9

135 W "r"

L& I / "

-4-,.: L E:) 1 1 11 1at%.

5a0le of lN253542 head and head lo l=G5 to ee0age unde a da. All l=25n>23n> 2n .

¡

i ...

1 1 *



248 W645 In S3ll6, : P556Jlll4, S55N65, E54l15 S45G

water levels in the stand-i-es* Also shown in this fig%re is how energy or head is lost in flowing %nder a da.* Note how the water levels in ea(hsa((essive -ie&o.eter deerease as vi*ater flows fro. the heel to the toe of the da.* E+a.-le !*17 e+-lains in detail how head (orn-%tations are.ade*

E+AMPLE .8

(215n:

Toe da. with -ie&o.eters shown in ig* !*12*

R5FG25=:

6. Cal(%late the -ress%re heads OP and the total -ie&o.etri(B heads Ofor -ie&o.eters A thro%gh T.

J. 'eter.ine the %-lif t -ress%re [(ting on the :ase of the da. at -oint C.

S3lG423n:

a* Press%re and total -ie&o.etri(B heads*Pie&o.eter A 9 The -ress%re head is the length of the (ol%.n of

water in the stand-i-e, or hP h$ M$ h 16 ! $" .

Note that this di.ension is also n%.eri(ally eF%al to

OL h $ / 16 ! $" I'

The total or -ie&o.etri( head is

h 5 F hp & B 5 h$ `$ 5 `$ 5 16 .

whi(h is the height of rise a:ove the dat%.*Pie&o.eter 49

h p h ` / 1 ^ 6 #2 I'*

Note that h is also n%.eri(ally the sa.e as

OL OL= or h 16 2 ro

Pi(&o.eter C:

D55555D555D5 55555D5D55 .... .



!*6 &ee0age and *loL Net: TLo"(lenlonal *loL 249

C he(<D h 5 h % h %c 5 16 6 5 O ro BPie&o.eter '9

h p / h D ` D / ) 9 / *" 2

h / hn Mn 5 MD .

Che(<9 h / h 5 h % D / 9 - " / .*BPie&o.eter E9

p 2

O / hp 5 ` E / ! 5 ! / m

h% / 9 2

Note that at the tailwater all of the head has :een lost* Th%s thetotal head at this -oint is &ero*b. U-lif t -ress%re at -oint C9

Pe hp p( g h e ` Mc:p( g F h % 5 h %c ` Mc:p( g

$ . 1 <gQ .# B6*71 .Qs$B 16"*$ <Pa

We (o%ld re-resent the flow of water thro%gh the fo%ndation %nder the da . in ig* !*12 :y flo( linev, whi(h wo%ld he the average flow -ath of a -arti(le of water flowing fro. the %-strea. reservoir down to the

tailwater* i.ilarly, we (o%ld re-resent the energy of flow :y lines of eF%al -otential, (alled, nat%rally, eLuipotential fines. Along any eF%i-otential line,the energy availa:le to (a%se flow is the sa.e@ (onversely, the energy lost :y the water getting to that line is the sa.e ali along that line* Toe networ< of flow lines and eF%i-otential lines is (alled a @lo( net , a (on(e-t thatill%strates gra-hi(ally how the head or energy is lost as water flows thro%gha -oro%s .edi%., as shown in ig* !*1*

o% -ro:a:ly (an see that we (o%ld, if we wanted to, draw aninf inite n%.:er of flow lines and eF%i-otential lines to re-resent theseeZ,age shoyi, n in ig* !*1, :%t it is .ore eon*enient to seleet onlB a 5Dre-resentative lines of ea(h ty-e* The hydra%li( gradient :etween any twoad0a(ent eF%i-otential lines is the dro- in -otential headB :etween thoselines divided :y the distan(e traversed* 8r, in ig* !*1 along flow line $,the gradient :etween eF%i-otential lines a and : is the head dro- :etweenthose lines divided :y l. 4e(a%se in an isotropic soil the flow .%st follow -aths of the largest gradient, the flow lines have to (ross the eF%i-otentiallines at right angles, as shown in ig ! 1* Note that, as the eF%i-otentiallines :e(o.e (loser togethe, de(reases and the gradient in(reases*

ig%re !*1 re-resents a ty-i(al (ross se(tion of the da. and fo%ndation* Th%s the flow (ondition is t(o di8ensional, li<e all see-age -ro:le.s

,.



a.e elevation@ 9*lsa.e -otential t-tal headB

Pl

!

h- h-

&

K low lines =,

1 EFG2N345n4l26l l2n5>

a :

$2. ) EFG2N345n426l 6n= l3D l2n5>l3nl 6 5D >3¡Vn.



M. &ee0age anc:I *loL Neta: TLo"(lenlonal *loL 251

eonsidered in this te+t* Three di.ensional flow is the .ore general sit%ation in .any geote(hni(al -ro:le.s, :%t see-age analyses of these -ro:5le.s are 0%st too (o.-li(ated to :e -ra(ti(aV, so we %s%ally s1.-:fy the -ro:le. to two di.ensions* Also in this te+t we will only (onsider thesi.-le (ase of confined flow, that is, where the see-age is (onfined :etweentwo i.-ervio%s s%rfa(es* or a dis(%ssion of %n(onfined flow -ro:le.ss%(h as for earth da.s and see-age toward wellsB, see Casagrande 16#!B,Taylor 1627B, Leonards 16"$B, and Cedergren 16!!B*

low nets are very %sef l in solving see-age -ro:le.s in engineering -ra(ti(e, for e+a.-le to esti.ate see-age losses fro. reservoirs, %-lif t -ress%res %nder da.s, and (he(< *-oints of -otential detri.ental erosionwhere 1 5 3(rD We shall e+-la. the te(hr%F%es . tfOs se(tlon*

A flow net is a(t%ally a gra-hi(al sol%tion of %aplace 3s eLuation intwo di.ensions,

ah ah-

ax P

ay / O

!5$2B

where and are the two (oordinate dire(tions* La-la(e3s eF%ation,derived in A--endi+ 4, is a very i.-ortant eF%ation in .athe.ati(al -hysi(s@ it re-resents the energy loss thro%gh any resistive .edi%.* or e+a.-le, :esides the flow of water thro%gh soils, it des(ri:es ele(tron flow,the flow of -eo-le to hos-itals, et(* I the boundary conditions geo.etry,

flow (onditions, and head (onditions at the :o%ndariesB are si.-le, then itis even -ossi:le to solve the eF9%ation in (losed for., that is, e*+a(tly* 4%tfor .ost -ra(ti(al engineering -ro:le.s, 24 is si.-ler to solve s%(h -ro:le.s gra-hi(ally al:eit so.ewhat ine+a(tly* low nets are s%(h gra-hi(alsol%tions to La-la(e3s eF%ation for a given set of :o%ndary (onditions*

How do yo% .a<e a flow net 4y s<et(hing* or two5di.ensionalsteady5state -ro:le.s, yo% si.-ly draw the .edi%. with its :o%ndaries tosorne (onvenient s(ale* 4y trial and error .ostly error, %ntil yo% get sorne -ra(ti(eB s<et(h a networ< of flow lines and eF%i-otential lines s-a(ed sothat the en(losed fig%res rese.:le 33sF%ares*= Their sides interse(t at rightangles* Loo< again at ig* !*1 and the sF%are= en(losed :y flow lines and $ and eF%i-otential lines a and . Not all the =sF%ares= in a flow net

have to :e the sa.e s;&e either* in(e the sF%ares are .ade of (%rved lines,they are only sF%ares in the stri(test sense when they (an :e s%:divideddown the tr%ly eF%ilateral fig%res* Note that a flow line (annot interse(t ani.-ervio%s :o%ndary@ in fa(t, an i.-ervio%s :o%ndary is a flow line* Notetoo that all eF%i-otential lines .%st .eet i.-ervio%s :o%ndaries at rightangles* Neither the n%.:er of flo( channels (hannels :etween flow linesB

.j



252 Jater In &olla= 11: Perea#lllt@= 0aga= Eflectl/e &tre

nor the n%.:er of eLuipotential drops a drop is the de(rease in head t#].hfro. one eg%i-otential line to the ne+tB need to :e a whole n%.:er@fra(tional sF%ares are allowed* ig%re !51" defines sorne of the ter.sasso(iated with flow nets* Loo< at the =sF%are= with di.ensions a S . Note that the gradient is

. 7:8. O 7:8. O Odd / -/-/

---"*Q b b

!5$B

where the length of the flow -ath in one sF%are is b / "*Q* Toe eF%i-oten5tial dro- :etween two flow lines is 7:8.O - Od d, where d 1s the totaln %.her of -otential dro-s, and O1. is the total head lost in the syste.*

ro. 'ar(y3s law we <now that the flow in ea(h flow (hannel is

B ! y7:8. O $ ! ( Od

bd ) a

and the total dis(harge B -er %nit de-th -er-endi(%lar to the -a-erB is

!5$"V

where , is the total n%.:er of flow (hannels in the flow net* I we

$l3D 6nn5l ----

/

5FG2N345n426l?=3N?

345n426l l2n5 ,,/

$2. . $l3D n54 2llG>4642n >3n5 =52n2423n>.



D5555555DDD5 5

M. &ee0ege end *loL Neta: TLo"(lenlonal *loL 253

With (onfined flow -ro:le.s, where there is no -hreati( freeBs%rfa(e, s<et(hing a flow net is not so diffi(%lt* tart with a s<et(h, to s(ale,of the soil .ass, :o%ndaries, et(* /ee- the s<et(h s.all so yo% (an o:servethe entire -i(t%re as it develo-s* Use good F%ality -a-er, a soft -en(il, andhave a good eraser ha ndy yo%3U need 2l' ra w the honndaries 0n 0n< onthe reverse side of the sheet* tart with, at .ost, only three or fo%r lines atfirst@ :y trial and error, s<et(h the net lightlyB %ntil yo% get =sF%ares=thro%gho%t the region of flow* It3s easier if yo% (an .anage to <ee- then%.:er of flow (hannels *to a whole n%.:er* Toe flow lines and eF%i-otentiallines sho%ld :e s.ooth, grad%al (%rves, all interse(ting at right angles* As.entioned, yo% sho%l( :e a:le to s%:divide ea(h sF%are to .a<e additional

s.all sF%ares* Toe flow net shown in ig* !*1! is an e+a.-le of a fairlywell5drawn flow net for (onf ined flow*We .entioned earlier that flow nets were valid for isotro-i( soils

only, a (ondition that is %nli<ely in nat%ral soil de-osits or even in earthda.s* However it is easy to ta<e the dire(tional differen(e in -er.ea:ilityinto a((o%nt :y transfor.;ng the s(ale to whi(h yo% draw the flow net* or e+a.-le, if the hori&ontal -er.ea:ility is .%(h greater than the verti(al -er.ea:ility, then yo% shorten the h.i&ontal di.ensions of the -ro:le.

:y the ratio ! h/ ! v * The -roof of this transfor.ation as well ase+a.-les for its %se are shown in Taylor 1627B* EF%ation !5$7 for theF%antity of see-age then :e(o.es

or %n(onfined flow, where there is a free s%rfa(e at at.os-heri( -ress%re for e+a.-le, see-age thro%gh earth da.s, levees, and towardwellsB, the .aJor -ro:le. is to esta:lish the sha-e of the to- line of see-age* This is not so easy, and if yo% have s%(h a -ro:le. it is :est to (ons%ltone of the referen(es (ited earlier in this se(tion* 8ne of the serio%s -ro:le.s, -ra(ti(ally s-ea<ing, is when the to- line of see-age interse(ts the to-downstrea. s%rfa(e of an earth da. or levee* This (ondition leads tos%rfa(e erosion, -i-ing, and event%ally -ossi:le fail%re of the str%(t%re*Therefore, in design, <ee- the to- line of see-age well :elow the down strea.s%rfa(e* In the da. of ig* !*1#a, the toe drain tends to <ee- the to-

see-age line fro. interse(ting the downstrea. s%rfa(e*8ther .ethods :esides s<et(hing for o:taining flow nets in(l%de

.athe.ati(al sol%tions for e+a.-le, Harr, 16"$B, ele(tri(al analogs,vis(o%s flow Hele5hawB .odels, s.all5s(ale la:oratory flow .odels, andthe .ethod of frag.ents Harr, 16"$B* This 1#t .ethod is so si.-le and -ra(ti(a that we e+-lain it in the ne+t se(tion*

E+a.-le !*17 indi(ates how the %-lift -ress%re %nder a da. (an :e(al(%lated* ro. the flow net, it is not diffi(%lt to deter.ine what the hP is

.j



1----t---t--*- 40--1- -

... = -

.,sheet l -ile 5

N% .i0er 3eF%i-:tentialdro-s

50

2

d

* r 3. . . ..

ye t I E

.

!0

eD 0."

l .l-erviB%s A S6l5: O 1 .

$l. . EY.jNl5 3 6 5,>3n6Jl D5ll-= Dn lD n54 3 3n2n5= l

!



----.. - 555D *** 555555555555

7.9 &ee0age and *loL Net: TLo"(lenalonal *loL 255

at the :otto. of the da.* Then the distri:%tion of %-lif t -ress%res (an :erawn* I Istn %tion I I.-ortant or t e ana ysis o t e sta 1 1ty

o (on(rete gravity da.s*Another i.-ortant %se of flow nets is to deter.ine gradients, es-e

(ially at (ertain (riti(a -oints, for e+a.-le, at the toe of a da. or any -la(e where see-age water e+its* ro. e(* !*7 yo% <now that when the

piping and erosion and .ay lead to (o.-lete fail%re of the str%(t%re* Pi-ingI a - eno.enon w ere see-.g water -rogressive y ero es or was es awaysoil -arti(les, leaving large voids -i-esB in the soil* These voids si.-ly(ontin%e to erode and wor< their way :a(<wards %nder the str%(t%re, or they .ay (olla-se* Either way, if -i-ing is not sto--ed -ro.-tly, fail%re isi..inent* The (riti(a -la(e for -i-ing is %s%ally right at the (o.er of the

net at the toe ig* !*17B*

6 &6 3n>4G45= =254l 3n 3Gn= >G65.

J &6 Nl65= >35D64 J5l3D 3Gn= >G65

$2. .8 EY24 6=25n4> 64 435 3 =6>.

.j



258 Jater In &olla= 11: Perea#lllt@= ee0age= Effectl/e &tre..

or the (ase of the darn -la(ed foolishlyB right on the gro%nd s%rfa(eig* !*17aB, if we <ee- s%:dividing the sF%ares, ra-idly a--roa(hes &eroand, sin(e M, is still finite, the gradient ra-idly in(reases* I this a(t%a llyha--ened in a real str%(t%re, -i-ing and -ro:a:ly fail%re of the str%(t%re:y %nder.iningB wo%ld o((%r*

or the e+arn-le shown in ig* !*l 7:, the da. is so.ewhat saf er thanin ig* !*17a sin(e, for ty-i(al (ases, the e+it gradient is .%(h less thaneriti(al* ro. EF* !5$, the e+it gra dieot iE eF%als AOL/ ., where AO1. :eF%als the head loss O L divided :y the n%.:er of eF%i-otential dro-s 'd .

Th%s if ali other things are the sa.e, an ern:edded fo%ndation will have.ore eF%i-otential dro-s and a lower e+it gradient* Re.e.:er that theflow net in its enlarged (ondition in ig* !*17 .erely shows the concentra

tion of flow* As the sF%ares get s.aller and s.aller, the tenden(y is tothin< that the e+it gradien t is steadily in(reasing This is not so* As then%.:er of eF%i-oten tial dro-s in(reases, OL also de(reases -er dro-, andthe ratio of tl h % 6 tl.l re.ains a:o%t the sa.e* or this e+a.-le, too, yo%(an see why the (riti(al -la(e is right ne+t to the downstrea. toe* There,the " is the least for a given tl h LE The ne+t flow (hannel over, for e+a.-le, is safer sin(e the sa.e head ( OL) 1s lost over a greater lengthgreater distan(e :etween eF%i-otential linesB*

or -ra(ti(aV -ro:le.s, where there is a danger that i (o%ld a--roa(hic, :e very (onservative in yo%r design* Use a fa(tor of safety of at least or " for s%(h (ases* or one thing, fail%re is %s%ally (atastro-hi( ando((%rs ra-1dly and wtth httle warning* or anothet , it is e+he.ely diffie%ltto <now e+a(tly what is going on %ndergro%nd, es-e(ially lo(ally* Lo(aldefe(ts, gravel -o(<ets, et(*, (an signifi(antly alter the flow regi.e and(on(entrate flow, for e+a.-le, where yo% .ight not want it and not :e -re-ared for it* Con(entration of flow o((%rs, too, at (orners of te.-orarystr%(t%res li<e (offe1darns* As Tay lor 1627B -oints o%t, the entire flowregi.e .ay :e widely diff erent fro. that ass%.ed in o%r ideali&edB flownet* reat variation in hon&ontal and verti(al -errnea:ility .ay e+ist ft o. -oint to -oint %nder a fo%ndation@ the flow .ay not :e entirely twodi.ensional@ geologi( defe(ts in the %nderlying s%:soils .ay -rovidee+-ress ro%tes for the water to (on(entrate and see- %nder and o%t of afo%ndation* I sheet -iling is %sed, (%toff is of ten %n(ertain for e+a.-le,

-1hng %n<now.gly driven into :o%lder sB, and yo% wo%ld :e wise toass%.e that the worst -ossi:le (onditions (o%ld ha--en5 then -re-are for s%(h event%alities* in(e fail%re of (off erda.s is of ten (atastro-hi(, it ise+tre.ely i.-ortant that large fa(tors of safety :e %sed, es-e(ially where -eo-le3s lives are at sta<e* ail%res of earth str%(t%res res%lting fro. -i-inghave (a%sed .ore deaths than ali other fail%res of (ivil eogioeeriogstr%(t%res (o.:ined* Therefore yo%r res-onsi:ility is (leai5:e (aref %land (onservative, and :e s%re of yo%r gro%nd (onditions and design*



E9A3PE M *16

(215n:

The darn and flow net shown in ig* !*1!* The da. is 1$ . long and has4D3 18 sheet -iles driven -artially into the gran%lar soil layer* 'at%. is at

R5FG25=:

a* The F%antity of see-age loss %nder the da. when / $ S 152

(.Qs* D

:* The e+it gradient at -oint S B*(* The -ress%re distri:%tion on the :ase of the da.*

S3lG423n:

a* ro. EF* !5$", the F%antity of see-age is

L !h %F : V /ength

/ $ + 152 (. BY . B1$ .#51$ .

(. 1*2

/ 7*#1 + 1 5#

.#

s

b. At -oint V , the e+it gradient is

1T / % / TI3 / . ,w 1( 1s not (ntl(a

' ote# t].h % / h %/ 'd / 1$ .Q1*2 / 1*1 .* L / 7* ., s(aledfro. ig* !*1!, is the length of sF%are R.

(* Press%re heads are eval%ated for -oint $ thro%gh 9 along the :aseof the da. in ig* E+* !*16*

A B e ' E

.,, -6*#7

7*$# !*!! "*"$"*2

H56=

$2. EY. .9 P5>>G5 56= 3 l36423n> .A 43G F.

257

.j

Q

78.O L 1*l 8 12 h3 h * * * I



258 Jater In &oll= 11: Perea#lllt@= &ee0age= Effectl/e &tre

The -ress%re head at -oint A. at the :ase of the da. and 0%st tothe right of the lef t sheet -ile is fo%nd this way9 the -er(entage of thehead loss is -ro-ortional to the n%.:er of eF%i-otential dro-s* 8f thetotal of I*2 dro-s for the entire flow net, only #* have o((%rred :y

-oint $ . Th%s the -ress%re head at -oint $ is#*

h $ / 1$ . 5 1$ . S 1

K 2

$ .

1$ 5 2*2 $ / 6*6" .

The e+tra * . :rings the head fro. the water5soil interfa(e down tothe :ase of the da.*

In a si.ilar .anner* we (an (al(%late the head at -oint &:

*2hv 1$ 5 1$ S K 1 2

` $ !*!! .

The heads at all the -oints %nder the da. are as follows9

Lo(ation Head .B Press%re <PaB

A 6*6" 6!*! 6*#7 6$*e 7*$# 7*!

D !*!! !"*$ E "*"$ "2*6 9 "*2 6*$

These val %es of head are -lotted i n ig* E+* !* 16* To (o.-% tet he upli/1 pressurlIs on t he :ase of t he da.* we . %lt i -l y t he head t i .est he -rod %(t p., g . The -ress% res are gi 3en a:ove* l t he densit y of (on(rete is $*2 GgQ . * t hen t he -ress% n@ e+erted :y $ . of (on(rete is

$*2 GgQ .#S 6*71 .Qs $

S $ . 2! < Pa

Th%s at any -oi n t along t he :ase of t he da. f ro. -oi n t @ t h ro%gh F t he % -li f t for(e e+(eeds t he wei gh t of t he da. so t he da. i s unstahlewi t h t h is design*

M.18 THE 3ETHO( O* *!AG3ENT&

The 8ethod of frag8ents -resents a %sef %l, ra-id, altho%gh a--ro+i.ate, analyti(al design .ethod for the sol%tion of (onfined flow -ro:le.s*Af ter yo% learn the -ro(ed%re, .any (ases .ay :e investigated in little.ore than the ti.e it %s%ally ta<es to asse.:le -a-er, -en(ils and erasersfor drawing flow nets* The .ethod originated with Pavlovs<y 16"B andwas :ro%ght to the attention of the western world :y Harr 16"$B* The



555555555 555 555 55 555555

TA,E M" &uar@ of *ragent T@0e and *or *actora

Ty-eIll%stration or. a(tor, 2?

X (O is head loss thro%gh frag.entB

-- --' :· ' 4 &

. S !! s

.., - S ' ?? & 11

II

jI? *,,5

8 5 (os

-- + -

5 J tannD5 `

tan5&5

& & &

5H 5G 9 .od%l%s @UQ3 b

IM $pproi8ate solutionQ

s b

^I? / In 1 t Bb E-s:

jI? In

1 a s :

b'''5

:9 s'

After 7round(ater and eepage J M. +. Darr. Co0@right:U 19$2 Mcraw0D!ll )oo?

Co.-any* Used D24 -er.ission*

74

.j

rag.ent

S



55 5 e555,, 55,5 5 DJJ,55555 WK 5 555 5 55555 55555 5, 55555555555 555555555553 555555555



r9*ig*.entTy -e

'()*+ -* C3n42nG5=or . a(tor* ^t?

L $s9L

^t? / $ In 1 i L

% *: s#

^t? * In

a B Q& ##Q B

s P s

^t? 1n g I ;L O 1 :: ll % 5 F s3 K sE

G

L & s K sE :

M I^t? I n < L

% ^s3 s;

^I? I n I -;- L l -a a;

whi9r(

. / 5^i 5 K B31

.. L ' ( s ' sE )D5D555 55D5

*

:asi( ass%.-tion in this a--roa(h is that the eF%i-otential lines at sele(ted(riti(aV -oints in a flow net are vertical and that they divide the flow netinto frag8ents. Ta:le !5$ s%..ari&es frag.ent ty-es and for. fa(tors*

Perha-s the :est way to ill%strate the -ro(ed%re is :y an e+a.-le* I yo% are interested in the theory :ehind the .ethod, (ons%lt Harr 16"$

and 16!!B*

s % 5

b 5



5D555555D5 ***9K99



E9A3PE !*$

(215n:

Toe da. with the sa.e data as in E+a.-le !*16 shown in ig* E+* !*$aB*

1$ .

E A . o D

"> .$. W W D== W * D* *8 * ":;,,. D*,2D* >.B#.#

o*** ?'

1

!0 T

T / *8 T / !0

L "0 *1

R5FG25=:

4y .eans of the .ethod of frag.ents, (o.-%te9

a* Toe Fpantity of see-age loss %nder the da. when ! / $ + 15(roQs, -er .etre nf daro

b. The e+it gradient at -oint E.e* The -ress%re distri:%tion on the :ase of the da.*d. Co.-are these val%es with those o:tained fro. the flow net 2n

E+a.-le !*16*

S3lG423n:

a* 'ivide the flow syste. into frag.ents* Toe (riti(al -oints (hosen are the :otto.s of the sheet -iles* Refer *to Ta:le ! $ and review the frag.ents*Toe heavy lines re-resent i.-ervio%s :o%ndaries whi(h (an :e

281

.j

.

0 0 j



Z N1 N1 NF

-2L)

262 Jater In &oll= 11: Perea#lllt@= &ee0age= Effectl/e &tren

in verti(al or hori&ontal dire(tions* o% (hoose the frag.ents to .at(h the -arti(%lar :o%ndary (ond1t1ons of yo%r -ro:le.* Noti(e how the deh.tions of s and T are %sed* Their val%es are shown in ig* E+* !*$a* Toeverti(al, dashed eF%i-otentialB lines se-arate the flow regi.e into threefrag.ents, as shown (ir(led in t:e f ig%re Cleady, the flaw L thro%gh ea(:frag.ent .%st :e the sa.e and is stated :y EF* !5$"* However in the.ethod of frag.ents this eF%ation is (hanged slightly to

B !h ' 1 !h85

!5$!B

L 'd >8"

where h8 is the head loss in the . th frag.ent where 8 / 1, $, #, * ** , n, and>68" is the di.ensionless for8 factor for the . th frag.ent* The for. fa(tor is eF%al to 'd / ' 1.

In this e+a.-le OL * . T h8 , that is, the s%. of the head lossin ea(h frag.ent* Also, sin(e the flow is eF%al in ea(h frag.ent and iseF%al to the total flow, we have

or

and, finally, the flow is

L % !5#B

"& +

The ne+t ste- is to define the ty-es of frag.ents for o%r -ro:le. andto deter.ine the val%e of the for. fa(tors ^I? for ea(h frag.ent* i+ generalty-es of frag.ents are shown in Ta:le !5$, where the heavy lines re-resenti.-en io%s :o%ndat ies* 8the1 f iag.en ts at e also availa:le in the liLeiat%1e*

* Also given are the val%es of ^I? in ter.s of the geo.etry of ea(h -ro:le.* I yo% st%dy 1g* E+* !*$a, yo% (an see that frag.ents 1 and # are ty-e 11 :%t Dfrag.ent $ is a ty-e V frag.ent* Had the sheet -iles :een of different lengths,then frag.ent $ wo%ld :e a ty-e MI instead of ty-e M frag.ent*

Ne+t, we :ave ta deter.ine the forro fa(tors for o%r two ty-es of frag.ents* or ty-e IIfrag.ents, we see fro. Ta:le !5$ that l / S/ S.4oth S and S are f %netions of 8, hieh is def ined as

8 5 s.. +G*

21 !5#1B

where s 5de-th of the sheet -ile, andG thi(<ness of the soil Bayer*

5



DDD55D D5D 555D 5555555555



M.18 'he 3ethod ol *ragenta 2$3

%:stit%ting the val%es for s and G of o%r e+a.-le into EF* !5#1, wefind that

* W 3&& 3&& 1$

8 / s.

& s.$ #

/ *77

The val%e of S/ S (an :e fo%nd fro. Ta:le !5#* or 8 *77, 8 /*#2, so S/ S is eF%al to a:o%t *" J inter-olationB, whi(h eF%als " 4y ins-e(tion, is also eF%al to ! These val%es are ta:%lated in Ta:leE+* !*$a*

TA,E E9. M.8a

rag.ent Ty-e

11 S/ S ..*7"

# 11 S/ S / *7"

or frag.ent $, whi(h is a ty-e M, weDneed to (o.-are % and s too:tain 5 or o%r e+a.-le, L / 2 . and s / $ .* in(e L s, " is *

WV* $ In Y 1 L s

/ * ln 1

U 2 5

#0 + 1

/ *772 *!12 / 1*67

Note that the distan(e a 17 . is the distan(e fro. the :otto. i.-ervio%s :o%ndary to the :otto. end of the sheet -ile*

The F%antity of flow is fo%nd fro. EF* !5#,

L% *7" 1*67 *7"

8

!*$1 Y 15 .$ Qs -er .etre of da.

.:/ 7*" Y 15# .#Qs for a 1$ . long da.

This (o.-res satisfa(torily with the val%e of 7*#1 S 15# .#Qs o:tainedin E+*a.-le !*16*

An alternative way to deter.ine the for. fa(tor is to %se ig* !*16*in(e s/ & 1Q$7 *#", find lQ$ffJB eFaal to *" for b/ & 8* olvingfor *we o:tain *7#, whi(h is (lose to o%r -revio%sly deter.ined val%e of *7"*

b. Co.-%tation of the e+it gradient i E at -oint T is easy* ro.



1

W

·W

:_ K:)_: . .

, K.K'.-0KK·- -

K 1

K-·- --

>-----r-........;. .2

K......... 'r---

--·- ---1 -;.

.F,,...._

d..1.2

1

-:::---

r--:::::::s

---

<'

2$4 Jater in oiis, li9 Perea#lllt@= &ee0age= Effecil/e &tre

1*

1 *2

1*# U

1*$

1*1

1*

*6

1U :QT 8

$^1?*7

*!

*" ' 5*** JK 535*

*2

*#

*$

*1

1*

1*

5

r5

5

5

-- ***

5******

5*****

38 *1 *$ 8*J *2 * 8 " *! 8 7 6 l 8

T

$2. .9 R5l6423n>2N J54D55n 3 643 " 6n= s/ & 6423 3 4N5 II 6n= 4N5 III 65n4>. A45 H6, 9, 4, 3N24M(6D-H2ll B33 C3N6n. >5= D24 N52>>23n.

Ta:le !5$, frag.ent ty-e 11, we find the for.%la for the e+it gradient is

WE $@ . !5#$B

where the val%e of " is fro. EF* !5#1 and eF%als *77@ the val%e of O isthe head loss in the third e+itB frag.ent* Toe val%e of S is fo%nd in Ta:le!5# for " *#2@ inter-olating, K 1*!21* Toe val%e of h to %se in EF*!5#$ is the head loss in the third @rag8ent , where the water e+its, and it is

1



1

1

1 --.....-

1

1

TA,E M"% V6lG5> 3 66545 s >5= 3 TN52 6n 111 65n4> J5>2J5= n T6l 5 - I 1

"2 K K'K K'

"2 8$ *

K K'K K'

"2 K'

* 1*!1 C+ * 1* '*$1 1*"" $*$# C *!2 1*#2 *!6

*1 l*!1 2*721 *#$ #*7 *666 '*$$ 1*"! $*$12 *!2 1*## *!7

.*$ 1*!$ 2*26 *#26 $*7" *667 '*$# 1*"! $*162 C *!"# 1*#1 *!!*# 1*!$ 2*$6# *#"" $*!# t?*66! '*$2 1 "7 $*1! *!!# 1*$6 *!"

.. *2 1*!$ 2*1 *#!6 $*"2 t?*66" '*$ l "7" $*1! *!7$ 1*$7 *!* 1*!# 2*#6 *#76 $*! *66 '*$" l "61 $*1#6 *!61 1*$" *!2*" 1*!# #*626 *#67 $*1 t?*662 '*$! l "6! $*1$$ C *7 1*$ *!#*! 1*!2 #*7!$ *2" $*2" t?*66# '*$7 l !$ $*1" Do*sos 1*$2 *!$*7 1*!2 #*7" *21# $*2$ '*66$ '*$6 1 !7 $*6 *71! 1*$$ *!1*6 1*!2 #*!27 *2$ $*#7 *661 '*#o 1 !12 $*! *7$" 1*$1 *!*1 1*! #*"6" *2$" $*# *66 ,o*#1 1 !$ $*"1 *7#2 1*$ *"6*$ 1*!6 #*#2 *2!1 $*1$ *67 '*#$ 1 !$" $*2! *72# 1*16 *"7

v. *# 1*7# #*1" *$ l*66 t?*6! 1 *## 1 !#$ $ ## *7$ 1*1! *"!*2 1*7! #*1" *$" 1*6 '*6" '*#2 1 !#7 $ $B *7" 1*1" *""

* 1*61 $*67 *2! 1*7# *6 ,oJ 1 !22 $*J *7"6 1*1 *",3 *" 1*6 $*7$1 *" 1*!! t?*62 1 '*#" l!1 l66 *7!! 1*12 *"2

*! 1*66 $*!2! *7$ l*!$ B*6# '*#! l!! l67# *77" 1*1# *"#*7 1*"2 $*"72 *67 1*"! *6$ t?*#7 1 !"2 l6!$ *76 1*1$ *"$

.. *6 1*"7 $*"$7 *"1$ 1*"# B*61 '*#6 l !!1 1 6"1 *6# 1*11 *"1*1 1*"1$ $*!7 *"$ 1*" B*6 '*2 l !!7 1 6 *611 1*1 *"

' *11 1*"1! $*## *"#7 1*! *76 '*21 l!7 1 6#6 *6$ 1*6 *6

*1$ 1*"$1 $*26# *" 1*2 B*77 , tB*2$ l!6$ 1 6$6 6$6 1*7 *7*1# 1*"$" $*2 *""$ 1*1 B*7! , tB*2# l !66 l 617 6#7 1*! *!*12 1*"#1 $*2$1 *"!2 1*27 B*7" ,'*22 l 7" l 66 62" 1*" *"*1 1*"# $*#76 *"72 1*2" *7 ,o*2 l 712 1 766 6 1* *

l *1" 1*"2 $*#6 *"6 1*22 *72 I',2" l 7$$ 1 76 6"2 1*2 *2

· - 5 *1! 1*"2 $*##1 *!" 1*2$ l*7# 1 *2! l 7$6 1 77 6!# 1*# *#

*17 1*" $*# *!1" 1*2 U$ *27 l7#! 1 7!1 67$ 1*$ *$IX

' *16 1*" $*$71 *!$" 1*#7 l*71 *26 l 72" 1 7"# 8 661 1*1 *1*$ l*"" $*$! *!# 1*#" I'*7 * l72 1 72 l 1* *

Nen .3$ K' K K' K "2 3=3$ S K' K

K K'355 . $K K'

2

2

K' K

<



1---- -+--

1--- -+--- +-- +----

+----+----

,3-- -- --l--- -- +--- --

;.` +----+---l

;. -+----+--- +---+--- '

;.2 +--+--+-----'------'-----11

268 Jater In &oll= 11: Perea#lllt@= Seepe@e: Eflecll/e Stre&&

fro. EF* !5$6 h3* h *7" S 1$ . /

# 1$# WÍV #*#$7 D . !5##B

85 1

%:stit%ting these val%es and . # *77 into EF* !5#$, we o:tain* #*1$ . 31T B1

T / $ + 1*!21 + # + *77 / 8*l "

This res%lt (o.-ares well with the val%e of *12 fo%nd in E+arn-le !*16*An alte.ative -ro(ed%re to find the e+it gradient at -oint EBis to %se

ig* !*$* or this e+a.-le, s/ & 1$Q# *2@ enter the gra-h and find

F iEs :/ h8 *"* olving for iE> we find thati / .h8 / *" + #*1$ . / 8*l " E 1$ I&

(* To (o.-%te the -ress%re distri:%tion %nder the da., the ass%.- tion is.ade that the head loss varies linear/y fro. frag.ent l to frag.ent #*

1* ,5555,,5555,5 5 555555555555

o *$ 0." *" 3.6 2*8UT

$2. .*0 (6N 43 516lG645 45 5Y24 6=25n4 i E 64 N32n4 T 43 6 4N5 65n4 3 6 215n s/ & 6423. A45 H6, 9, CC] 3N24 M(6D-H2ll B33 C3N6n. >5= D24 N52>>23n.



.1; The Methoc:I of Fragmenta

3) D9 +2 + 3,B

. . < .!! . " . " . A ." # ·. -. !-.! ,# -

A.L2 8 .;` 8

#

8

12 8 ..- ..-. -'-'----3

=2 8

' A' #'

f!7

/ *7" 1*67 *7" / #*#$7The head loss -er frag.ent is given :y EF* !5##,

O, 9 5 *7"@ @$ - #*1$

O / * O / 1*67 + 1$ /5 !"#*#$7 D .

h! / h d%e to sy..etry

Redraw the da. to s(ale and -la(e the val%es of head at sele(ted -oints ig* E+* !*$:B* At eF%i-otential f ine A, the head loss is O

1 #*1$.@ the head loss is therefore h 5 h 1 / 1$ . 5 #*1$ . / 7*77 .* i.ilarly,at eF%i-otential line F, O / *!" .* Therefore the head at 9 is

h h 1 h5 1$ 5 #*1$ *!" 5 #*1$ .

Ass%.ing that the head loss varies linearly fro. -oints A'A'F'F,

whi(h is eF%al to the total distan(e of 1 . 2 . 1 . / " ., thenthe head loss -er .etre is hiJ ., or *!" .Q" . *6" .Q.* Th%sthe head at -oint $ 5 the head at $3 1 . + *6" . -er .etre, or

7*77 5 1 S *6" 5 !*6$ .* Li<ewise, the head at F is 2*7 .*

1

7*77 -------21

8 : 0

$2. EY. .*0J

1

#*1$ . Z

1

@5 X

$

0



. oo .

A 1---'. A

---- - ---l #.o ·.

Z

1

268 W645 In S3ll>, : P555Jlll4, S55N55, El54l15 S45>>

.9* * / 9.9*

$2. EY. .*0

To this head we add the tailwater head of $ .* Toe verti(al %-lif t -ress%res .ay now :e (o.-%ted, as shown in ig* E+* !*$(* These val%es(o.-are al.ost e+a(tly with those shown in ig* E+* !*16*

d* Corn-arison of val%es of flow, e+it gradient, and %-lif t -ress%res asdeter.ined :y the two different -ro(ed%res are s%rn.ari&ed in Ta:le E+*!*$:*

TABLE E+. .*0J

Para.(ter ro. low Net ro. Gethod of rag.ents

¡

E

U-lif t -ress%res atAD U-lift -ress%res at*

*126*6" ."*2 .

*1"6*6$ ."*7 .

D1n .etres of water*

E+AMPLE .*

(215n:

everal (ases of (onfined flow*

R5FG25=:

Witho%t (o.-%ting the F%antities as we did in E+a.-le !*$, 0%st identifythe frag.ent ty-es shown in ig* E+* !*$1*



. --- ---- ------ ----'/?--



55555D5D55D 5DD 5 --- 55555555555 ... 5D55555 55 5 5 5 DDDD555555555 555555 555

Ty-e II Ty-e II

III MI II

l .-ervio%sQ

H-------n=-0l

:la n<et

III

5

16*



$! W645 In S3ll6, : P556Jlll4, ee-age, E515 tress

S3lG423n:

ig* E+* !*$1*

It sho%ld :e o:vio%s now that the .ethod of frag.ents is a -owerf %lanalyti(al and design te(hniF%e* ol%tions to .any (o.-le+ -ro:le.s (an

:e fo%nd F%i(<ly, whereas to solve a series of (o.-le+ -ro:le.s :y .eansof flow nets wo%ld reF%ire a large a.o%nt of ti.e* Ta<e, for e+a.-le, the

-ro:le. ill%strated :y E+a.-le !*$1(* A -ra(ti(al design F%estion is9 Howlong sho%ld the drainage :lan<et :e (onstr%(ted to red%(e the F%antity of flow :y one5third or to red%(e the %-lif t -ress%res :y one5half Gany trial

and error flow net sol%tions wo%ld :e reF%ired to solve the -ro:le.,whereas with the .ethod of frag.ents the sol%tion (o%ld :e o:taineddire(tly

. CO%TROL O$ SEEPA(E A%O $ILTERS

In the dis(%ssion of see-age for(es and flow nets, -i-ing and erosionwere .entioned as a -ossi:ility if, so.ewhere in the -oro%s .edi%., thegradient e+(eeded the (riti(al gradient* Pi-ing (an o((%r any -la(e in thesyste., :%t %s%ally it o((%rs where the flow is (on(entrated, as shown in

ig* !*17* 8n(e the see-age for(es are large eno%gh to .ove -arti(les, -i-ing and erosion (an start, and it %s%ally (ontin%es %ntil either ali thesoils in the vi(inity are (arried away or the str%(t%re (olla-ses* Cohe sionlesssoils, es-e(ially silty soils, are highly s%s(e-ti:le to -i-ing, and if yo% ro%st%se s%(: soils io ao e.ha n<.en t da., for e+a.-le* then yo% .%st :e very(aref %l to see that the see-age is (ontrolled and that the (han(e for -i-ingto o((%r is very s.all*

How is see-age (ontrolled Gethods %sed de-end on the sit%ation, :%t so.eti.es a (%toff wall or tren(h is (onstr%(ted to (o.-letely :lo(< the see-ing water* o.eti.es the drainage -ath is lengthened :y ani.-ervio%s :lan<et, so that .ore of the head is lost and th%s the gradientin the (riti(a region is red%(ed* I -ro-erly designed Dand (onstr%(ted,

relief wells and other <inds of drains (an :e %sed to -ositively relieve high%-lift -ress%res at the :ase of hydra%li( str%(t%res Cedergren, 16!!B*

Another way to -revent erosion and -i-ing and to red%(e -otentiallyda.aging %-lif t -ress%res is to %se a protective Ji/ter. A 2lter (onsists of one or .ore layers of free5draining gran%lar .aterials -la(ed in less

-ervio%s fo%ndation or :ase .aterials to -revent the .ove.ent of soil -arti(les that are s%s(e-ti:le to -i-ing while at the sa.e ti.e allowing thesee-age water

----- -



7.11

$2. .*

to es(a-e with relatively little head loss* Th%s the see-age for(es within the

large as 1 ti.es the grain si&e of a %nifonn fo%ndation soil and still -revent -artt( e .ove.en * is e ear aof the filter .aterial also affe(t this li.iting si&e*

Ha&en 9 was wor<ing with water treat.ent filters aro%n t ective siMe of a filter was the

D for e+a.-le, EF* !51B@ that is, this si&e affe(ted the -erfor.an(e of a10

lahora tory tests :y 4% rea %

t i v( f i ller are9

l. The filter .aterial sho%ld :e .ore -ervio%s than the :ase .aterialt the

f ilter and ad0a(ent str%(t%res*e voi s o e 2

-revent :ase .aterial -arti(les fro. -enetrating the filter and

(a%sing (logging and fail%re of t e -rote(t1ve 1 ter syste.*the rote(tive filter .%st :e s%ffi(iently thi(< to

-rovide a good distri:%tion of all -arti(le si&es thro%gho%t the

where frost a(tion is involved*4. i ter .atena -art1( es .%s e -reven e r

the drainage -i-es :y -roviding s%ffi(iently s.all slot o-enings or -erforat;ons, or additional (oarser filter &ones if ne(essary*



$!$ Water In olla, 119 Per.ea:lllty, ea-age, Efle(Uve S45G

The last reF%ire.ent (o%ld :e f%lfilled :y sorne of the .ode.nonwovere(ent years*

radation reF%ire.ents for -rote(tive 1 ters are g1ven .The f irst ratio ) ens%res that the s.all arti(les of the .aterial to :e -rote(ted are -revented fro. -assing thro%gh the -ores of the filter@ the. . .

, , :ly s.all* l the (riteria in this ta:le (annot :e .et :y one layer of filter

. . ..a en ,

orne additional -ra(ti(a reF%ire.ents for the design of filters arealso shown in Ta:le !52*

A s e(ial (o..ent (on(ernin the %se of .odero woven and non5 woven fa:ri( rnaterials for filters9 these .aterials have re(ently :een

However, :e(a%se of the rather li.ited resear(h and e+-erien(e with the.,

and gravel :e(o.e de-leted, fa:ri( filters will :e(o.e in(reasingly i.5 -ortant in rainage an see-age (ontro * An a 1tlona a vantage 1s t atthe are eas to %se in the f ield, and th%s (onstr%(tion (osts are of ten lessthan with (onventional gran%lar filters* or additional inforrnation a:o%t

16!"B, and teward, et al* 16!!B*

ilter GaterialC:ara(terisiti(s

)so

Unifor. 62n si&e filters, C*, 5 # to 2 2 to 0

raded filters, ang%lar -arti(les " to 17 6 to O

W ..- 1 s of filter .aterial-----/-/'-------

1s 1s of .aterial to :e -rote(ted2 of filter .aterial

) so 5 o5f .35a3terial to :e rote(ted

Notes9 Ga+i.%. si&e of the filter .aterial s:o%ld :e less than !" .. # in*B*Use the .in%s No* 2 fra(tion of the :ase .aterial for setting filter= li.itsw:en the graveB (ontent -l%s No* 2B is .ore than 1], and the fines .in%s

$ -arti(les to -revent e+(essive .ove.ent of f;nes in t:e filter and intodrainage -i-es* T:e grain si&e distri:%tion (%rves of the filter and t:e :ase.aterial sho%ld a--ro+i.ately -arallel in the range of finer si&es*

kAlter U**4*R* 16!2B*

.

. .



D55 D5 55 555 .- 55555555555555555555D55D5555555 555 5555555555DDDDDD5 DD D5DDDDD DD

P!O,E3&

!51* A (lean sand having a -er.ea:ility of S 1 5$ (.Qs and a voidratio of * is -la(ed in a hori&ontal -er.ea:ility a--arat%s, asshown in ig* !*$* Co.-%te the dis(harge velo(ity and the see-agevelo(ity as the head ::..O goes fro. 8 to 1 (.* The (ross5se(tionalarea of the hori&ontal -i-e is 1 (.$

, and the soil sa.-le is * .long*

!5$* A sa.-le of .edi%. F%art& sand is tested in a (onstant head -er.ea.eter* The sa.-le dia.eter is .. and its length is 1$ ..*Under an a--lied head of (., 11# (.# flows thro%gh the sa.-le in

.in* The "s of the sa.-le is #7 g* Cal(%late aB the 'ar(y(oeffi(ient of -er.ea:ility, :B the dis(harge velo(ity, and (B thesee-age velo(ity* Af ter A. Casagrande*B

!5#* A -er.ea:ility test was r%n on a (o.-a(ted sa.-le of dirty sandygravel* The sa.-le was 1 .. long and the dia.eter of the .old1 ..* In 7# s the dis(harge %nder a (onstant head of 2 (. was#6$ (.#

* The sa.-le had a dry .ass of # g and its Ps was $"7<gQ .#

* Cal(%late aB the (oef fi(ient of -er.ea:ility, :B the see-agevelo(ity, and (B the dis(harge velo(ity d%ring the test*

!52* '%ring a falling5head -er.ea:ility test, the head fell fro. to #(. in 2* .in* Toe s-e(i.en was (. in dia.eter and had alength of 6 ..* Toe area of the stand-i-e was * * .$

Co.-%tethe (oeffi(ient of -er.ea:ility of the soil in (.Qs, .Qs, and f tQd*What was the -ro:a:le (lassifi(ation of the soil tested Af ter A.Casagrande*B

!5* A falling5head -er.ea:ility test is to :e -erfor.ed on a soil whose -er.ea:ility is esti.ated to :e # + 1 5! .Qs* What dia.eter stand-i- e sho%ld yo% %se if yo% want the head to dro- fro. $!* (.to $* (. in a:o%t .in Toe sa.-le3s (ross se(tion is 1 (. $ andits length is 7* (.* Af ter Taylor, 1627*B

!5"* how that the %nits of EF* !52a are in fa(t energyQ.ass* how that

EF* !52: has %nits of energyQweight, and that this (o.es o%t as alength headB*

!5!* F have 0%st :een -la(ed in (harge of a s.all soils la:oratory andthere is a tight :%dget for -er.ea:ility eF%i-.ent* Ga<e a de(isionas to what type of eF%i-.ent yo% wo%ld order so as to -erfor.la:oratory tests on the widest range of soils*

M%



274 Jater In &olla= 11: Perea#lllt@= &ee0age= Effectl/e &treu

!57* 4riefly des(ri:e e+a(tly how yo% .a<e a (orre(tion for te.-erat%rein a -er.ea:ility test if the water is not e+a(tly $>C* tate yo%r

!56* In E+a.-le !*1, the void ratio is s-e(ified as *2#* I the void ratio of the sa.e soil were *#7, eval%ate its (oeff i(ient of -er.ea:ility* irstest;.ate in w hieh direetion will go, higher or loD*ver@ then -roeeed*

!51* Est;.ate the (oeffi(ient of -er.ea:ility for soil $ of ig* E+* #*1* Willthe sa.e a--roa(h wor< for soil l of the sa.e fig%re

!511* A falling5head -er.ea:ility test on a s-e(i.en of fine sand 1" (.* inarea and 9 (. long gave a ! of ! + 152 (.Qs* The dry .ass of the

sand s-e(i.en was $1 g and its Ps was $*"7 GgQ .#* The testte.-brat%re was $">C* Co.-%te the (oef fi(ient of -er.ea:ility of the sand for a void ratio of *! and the standard te.-erat%re of $>C* Af ter A. Casagrande*B

!51$ The (oeffi(ient of -er.ea:ility of a (lean sand wa s 2 + 152

(.Qs at a void ratio of *2$* Est;.ate the -er.ea:ility of this soilwhen the void ratio is *7*

!51#* Per.ea:ility tests on a soil s%--lied the following data9

$ .0 2 1*7 + 1 2

Est;.ate the (oeffi(ient of -er.ea:ility at $>C and a void ratio of *7* Af ter Taylor, 1627*B

!512* or the soil -rofile of E+a.-le !5 -lot the total, ne%tral, andef fe(tive stresses with de-th if the gro%nd water ta:le is lo(ered 2 . :elow the gro%nd s%rfa(e*

!51* oil :orings .ade at a site near Chi(ago indi(ate that the to- " . isa loose sand and rnis(ellaneo%s fill, with the gro%nd water ta:le at #. :elow the gro%nd s%rfa(e* 4elow this is a fairly sof t :l%e5gray silty

(lay with an average water (ontent of #]* The :oring was terrninatedat 1" . :elow the gro%nd s%rfa(e when a fairly stiff silty (lay wasen(o%ntered* Ga<e reasona:le ass%.-tions as to soil -ro-erties andeale%late the total, ne%tral, and effeeti* e stresses at #, ", 11, and 1" . :elow the gro%nd s%rfa(e*

!51"* Plot the soil -rofile of Pro:le. !51 and the total, ne%tral, andeffe(tive stresses with de-th*

!51!* A soil -rofile (onsists of rn of (o.-a(ted sandy (lay followed :y . of .edi%. dense sand* 4elow the sand is a ayer of (o.-ressi:le

R%n No* e T(.-* >CB F c8/ s :

*! 2+*#$ S 1



55 55555555D555555D5555555555

Pro#lea M7

silty (lay $ . thi(<* The initial gro%nd water ta:le is lo(ated at the :otto. of the first layer at . :elow the gro%nd s%rfa(eB* The

densities are $** GgQ.#

-B, 1*62 GgZ.# Psat B, and 1*$$ GgQ .#

-3B for the three layers, res-e(tively* Co.-%te the effe(tive stress ata -oint at .idde-th in the (o.-ressi:le (lay layer* Toen, ass%.ingthat the .edi%. dense sand re.ains saturated . (o.-%te the effe(tive stress in the (lay layer at .id-oint again, when thegro%nd water ta:le dro-s . to the to- of the silty (lay layer*Co..ent on the differen(e in effe(tive stress*

!517* or the initial (ase in Pro:le. !51!, (o.-%te the head of waterreF%ired at the to- of the silty (lay layer to (a%se a F%i(< (ondition*

!516* and is s%--orted on a -oro%s dis( and s(reen in verti(al (ylinder, asshown in ig* P!516* These are eF%ili:ri%. (onditions*

o &

L L

.BB B#

.******* . .

0

...

. . ...9*95K***: ,9K9*5* #B#...

X 4 :,.·:i; 7 f9RQB999935 L

. . ' ........ ·9·

D9^$D*590QQ (::

Case III Case IM* Ass%.e that the sand is fineeno%gh to re.ain 1] sat%rated % - toits to- s%rfa(e J (a-illarity*

ig* P!516

,. j

4

.



·:: :··:·.- :.0..0.·........::...::-..:.:.. -

27$ Jater In &olla= 11: Peree#lllt@= Seepe@e: Effectl/e &tre

Case M* Ass% .e an ideal i&ed (ase i nwhi(h the height of (a-illary rise ishe* Ali soi l :elow that height is1] sat%rated, and ali soil a:ove

that height is ] sat% rated*

$2. P-9 C3n42nG5=

aB or ea(h of the five (ases, -lot the total, ne%tral, and ef fe(tivestresses vers%s height* These -lots sho%ld :e a--ro+*i.ately tos(ale*

J 'erive for.%las for those three stresses in ter.s of the di.ensions shown and e, Ps , and p..., for ea(h (ase at :oth the to- and :otto. of the sand layer* or (ase IM, ass%.e the sand is 1]sat%rated to the %--er s%rfa(e :y (a-illarity* or (ase M, ass%.e

t he sand a:o3e leveB O , is (o.-letely dry and :elow O , is(o.-letely sat% ra ted* Af ter A. Casagrande*B

!5$* -e(ify the (onditions %nder whi(h it is -ossi:le for / to eF%al S.

!5$1* or the soil -rofile of Pro:le. !51, (al(%late :oth the hori&ontal,total, and ef fe(tive stresses at #, ", 11 and 1" . de-ths, ass%.ing aB

is * and :B K is 1**

!5$$* The val%e of K for the (o.-ressi:le silty (lay layer of Pro:le. !51!is *!* What are the total and effe(tive hori&ontal stresses at.idde-th of the layer

!5$#* iven, the soil (ylinder and test set%- of E+a.-le !*11, with a(t%aldi.ensions as follows9 A= (., =@ 1 (., @ 1 (., and DE / (.* Cal(%late the -ress%re, elevation, and total heads at -oints $ thro%gh E in (enti.etres of water, and -lot these val%esvers%s elevation*

!5$2* or ea(h of the (ases I, 11, and 111 of ig* P!5$2, deter.ine the -ress%re, elevation, and total head at the entering end, e+*it end, and -oint $ of the sa.-le* Af ter Taylor, 1627*B

K 1

1



Pro#le 277

2 .

1 . 5

D999K9*3DQ99999DD9D9D@=*9KU2 .

1i::1 1 1 .

TCase I

Case 11

2 .

)

0552 . 550

5 51 .Case III

ig* P!5$2

!5$* or ea(h of the (ases shown in ig* P5$2, deter.ine the dis(harge53*elo(ity, the see-age velo(ity, and the see-age for(e -er %nit vol%.e aB a -er.ea:ility of *1 (.Qs and a -orosity of ] and :B a -er.ea:ility of *1 (.Qs and a void ratio of *"!* After Taylor,1627*B

!5$"* An in(lined -er.ea.eter t%:e is filled with three layers of soil of

T

6

T



278 Jater In &olla= 11: Perea#lllt@= Seepa@e: Effectl/e &tre

tH

t?&

'

$2. P-*

different -er.ea:ilities as in ig* P!5$"* E+-ress the head at -oints A, =, C, and with res-e(t to the dat%. indi(atedB in ter.s of thedifferent di.ensions and -er.ea:ilities* aB Wor< the -ro:le. firstass%.ing < / < * / ! * . :B Then wor< it ass%rning #< / < * / ! * >

Plot the vario%s heads vers%s hori&ontal distan(e for :oth -arts aBand :B* Af ter A. Casagrande*B

!5$!* Ass%.e the soil of ig* !*1* has a sat%rated density of 1*62 GgQ .#

I the head of water h a:ove elevation is $*#2 ., (o.-%te theeffe(tive stress at elevation A at the :otto. of the soil sa.-le d%ringflow * What is the effe(tive stress %nder these (onditions at .idheig h t in the soil (ol%.n d%ring steady5state flow

!5$7* aB how that EF* !5$ is identi(al to EF* !5$1* :B how that EF* gBin e(* !*7 also red%(es to EF* !5$1* eB how that EF* !5$#( isidenti(al to EF* !5$#d at a (riti(al (ondition*

!5$6* The fo%ndation soil at the toe of a .asonry da. has a -orosity of 21] and a p. of $*"7 GgQ To ass%re safety against -i-ing, the

*

s-e(ifi(ations state that the %-ward gradient .%st not e+(eed $] of the gradient at whi(h a F%i(< (ondition o((%rs* What is the .a+i.%. -er.issi:le %-ward gradient Af ter Taylor, 1627*B

!5#* how that it is i.-ossi:le to drown in F%i(<sand* Hint9 Cal(%late thedensity of the F%i(<sand*

!5#1* A (ontra(tor -lans to dig an e+(avation as shown in ig* P!5# l. l the river is at level A, what is the fa(tor of safety against F%i(<

5 5D 5DDD55555 5D5 555555555DDDDD555 -. 5555 55

T



-----DD55555555

Problem- 279

!0

E *0 5

EY616423n

L515l A El51. / 8

D@@4l

R215 ?

o

51

Cl6, p / *000 Q#

V5 N5123G> >6n= .

$2. P-!

(onditions Negle(t any verti(al shear* To what elevation (an thewater rise :efore a F%i(< (ondition will develo- Af ter '* N*H%.-hrey*B

!5#$* iven, the e+(avation as shown in E+a.-le !*1!, with h / $ . and p 17 <gQ .# Cal(%late the .;ni.%. allowa:le Z.,.

!5##* A sheet -ile wall has :een installed -artially thro%gh a silty sand

layer, si.ilar to the one shown in ig* !*1#:* Ass%.e a 12 . longsheet -ile -enetrates ! . half wayB into the silty sand layer of thi(<ness 12 .* or this (ondition9

aB 'raw a flow net %sing three or fo%r at .ostB flow (hannels* Note that the flow net is (o.-letely sy..etri(al a:o%t the :otto. %f the sheet -ile* This -art is needed fer the sol%tion of Pro:le. !5#*B

:B I the water height on the %-strea. side is . and l . on thedownstrea. side, (o.-%te the a.o%nt of water flowing %nder the sheet -ile -er .etre of wall if the (oeffi(ient of -er.ea:ilityis $ S 152 (.Qs*

(B Co.-%te the .a+i.%. hydra%li( gradient at the downstrea. sideof the sheet -ile*

!5#2* Using the data of ig* !*1!, (o.-%te the total head, -ie&o.etri(head, -ress%re head, and elevation head for -oints @ and C3* Ass%.eany (onvenient dat%.*

!5#* Ass%.ing that yo% have (o.-leted the flow net of Pro:le. !5##,(o.-%te the total head, -ie&o.etri( head, -ress%re head, and elevation head for a -oint half way %- the sheet -ile fro. its :ase, oneither side of the sheet -ile* Ass%.e the dat%. is at the :otto. of the silty sand layer* Plot gradient vers%s de-th of -iling and e+tra-olate to find the e+it gradient*

2:* J

1"

*D* 5K9D?*



48 Jater In &oll= 11: Perea#lllt@= Seepa@e: Effectl/e &trea

!5#"* 'raw a flow net for the (ase shown in ig* P!5#"* Ass%.e three orfo%r flow (hannels* Use any (onvenient s(ale, li<e 1 (. / .*

2

555555

1 A e,*!

WlA

9 --HG43AA D6ll

!0

CV 4

t l55 1* 2

$2. P-! A=6N45= 3 T6l3, 9"8.

!5#!* 'raw a flow net for the (ase shown in ig* P!5#!* Use any (onveni

ent s(ale*

$2. P-! A=6N45= 3 T6l3, 9"8.

-

-



Pro#lea 41

! #$* or the (o.-leted flow net of ig P5#7, (o.-%te the fiow %nder the da. -er .etre of da. if the (oeffi(ient of -er.ea:ility is#* + 152 (.Qs*

-- - &

!5#6* or the (o.-leted flow net of ig* P!5#7, (o.-%te the %-lif t -res5s%re all along the :ase of the da.*

!52* 8iven, the data of P1:le. !5##* Using the .ethod of f1ag.entsdeter.ine9

aB Toe a.o%nt of water flowing %nder the sheet -ile -er .etre ofwall*

:B The e+it gradient*

!521* or the da. of ig* !*12 set %- the -ro:le. and solve as far as yo%(an :y the .ethod of frag.ents*

!52$* Using the .ethod of frag.ents* show that one (ase of ig* !*17 is.ore (riti(aV than the other*

!52#* I one of the rows of sheet -des fiad to :e re.oved for the -ro:le.

given in ig* E+* !*$a, whi(h one when re.oved wo%ld (a%se theleast red%(tion in flow

!522* a.e as Pro:le. !52#, :%t do for the least a.o%nt of %-lif t -ress%re*ive yo%r answer in ter.s of head*

!52* Ass%.e a row of sheet -iles as shown in ig* E+* !*$1a* Toe totalthi(<ness of the soil layer is $ ., while the =2 eren(e :etween thehead and tailwater is 1 .* Plot a gra-h showing how the flow %nder the sheet -ile var;es when the de-th of the sheet -ile goes for 7 .

,j



282 Jater In &olla= 11: Perea#lllt@= Seepa@e: Eflectl/e &1reu

and a--roa(hes $ .* Ignore -ro:le.s asso(iated with the e+itgradient*

!52"* %--ose there is a -ro:le. with the e+it gradients, as in Pro:le. !52* 8ne sol%tion wo%ld :e to -la(e a hori&ontal filter over the soil wherethe water e+its* How does this hel- Is it :etter for the filter to have asi.ilar (oeffi(ient of -er.ea:ility 8ne that is .%(h s.aller 8r onethat is .%(h larger E+-lain whi(h one is .ost desira:le*

!52!* oil 2 of ig* E+* #*1 is %sed as the (ore .aterial of a (o.-a(tedearth da.* 'esign a filter to -rote(t this soil* Presen t yo%r res%lts ona grain si&e distri:%tion (%rve or se.ilog -lotB as in ig* E+* #*1*

!527* A -rote(tive three5layer filter is -ro-osed :etween the fo%ndationand ro(< drain lo(ated near the toe of a (o.-a(ted earth5fill da.*a.-les were ta<en and the grain si&es of the .aterials were de ter.inedto :e as follows9

Di s ..B Dss ..B

o%ndation, finest sa.-les *$2 *1o%ndation, (oarsest sa.-les *1$ *6ilter Bayer No* 1 *# 1*ilter ayer No* $ $* #*iller layer No* # * 1*Ro(< drain

1* 2*

Analy&e this filter with the U**4*R * 16!2B (riteria* 'oes it .eetthe (riteria I not, (o..ent :riefly on any -ra(ti(al (onseF%en(es*Af ter Taylor, 1627*B

- 5 5. 55555 555555 .



eight

Con§olidation andCon§olidation 7ettleenti

4.1 INT!O('CTION

o% are %ndo%:tedly aware that when .aterials are loaded or stressed they defor. or strain* o.eti.es, s%(h as with etas*ti( .aterials,the res-onse %nder load is instantaneo%s* 8ther .aterials sorne soils arevery good e+a.-lesB reF%ire a relatively long ti.e for defor.ations too((%r@ this is es-e(ially tr%e for (lay soils* Gost of this (ha-ter is devotedto the (o.-ressi:ility of these <inds of soils*

The si.-lest ty-e of stress5strain5ti.e relationshi- a--lies to elastic.aterials5 where, as .entioned, the stresses and strains o((%r si.%ltaneo%sly* In fa(t, elasti( stress5strain relationshi-s (an either :e linear or

D D nonlinear. Gaterials whi(h have ti.e as a fa(tor in their stress5strainres-onse are (alled visco5e/astic. oils, then, are vis(o5elasti( .aterialsfro. the view-oint of their .e(hani(al :ehavior* The -ro:le. with %singthe theory of vis(o5elasti(ity is that, in its -resent state of develo-.ent, thetheory is only a--li(a:le to .aterials that are linear and, as we shall soonsee, soils are highly nonlinear .aterials* In other words, the interrelationshi- :etween stress, strain, and ti.e for soils is not si.-le and (annot :etreated .athe.ati(ally with -resent theory* oils have another -ro-ertythat (o.-li(ates .atters9 they have a =.e.ory*= Th%s the .aterial is

nonconservative. When soils are stressed, they defor., and even when thestress is released sorne -er.anent defor.ation re.ains* 'efor.ations ingeneral (an :e either a (hange of sha-e distortion B, or a (hange of vol%.eco8pression B, or :oth*

Toe following notation is introd%(ed in this (ha-ter*


a., M' 1LG 2 <PaB51

B L

ce

Coeffi(ient of (o.-ressi:ility EF* 75BWidth of footing EF* 75$$BCo.-ression inde+ EF* 75

283

.j



55 555555555555555555555555 *****K********=====3 ====3535,@**5*



284 Conolldatlon and Conolldatlon &ettleenta


e, Re(o.-ression inde+ EF* 751B@ CE and C, are so.eti.es %sed

, Eoed

eU H

L

LIR

8CR p

r

ML- D ! ' <Pa Constrained or oedo.etri( .od%l%s EF* 75"B

de(i.alB Change in void ratioL . D D al thi(<ness of a soil la er * 75#BL . Change in thi(<ness of a soil layer EF* 75#B

lnfl%en(e fa(tor E . 75#BL . Length of fo%ndation EF* 75$#B

Load in(re.ent ratio EF* 75$BRatios of fo%ndation width to de-th EFs* 75$7 and 75$ B

M- %& <PaB5 Coeffi(ient of vol%.e (hange EF* 75"BInfl%en(e fa(tor EF* 75$BInfl%en(e fa(tor EF* 75#2B8ver(onsolidation ratio EF* 5

MG' Line load EF* 75$"Bor(e or oa

ML- > r52 <Pa %rfa(e or (onta(t stress EF* 75$!B.

s L

W L I..ediate or distortion settle.ent EF* 75lB

L Total settle.ent EF. 751B

Initial or hydrostati( -ore water -ress%re

]B Hori&ontal strain EF* 75##B

I Poisson 3s ratio EF. 75##Ba E .75$$

ML' D !' <PaML' 1 G'2 <Pa

Merti(al effe(tive (onsolidation stressnsolidation stress or .a+i.%. ast

verti(al effe(tive stress EF* 75$B@ p and a@,,*are so.eti.es %sedMerti(al effe(tiveB over:%rden stress EF* 75$BMerti(al stress at de-th & EF* 75$$B

4. CO3PONENT& O* &ETTE3ENT

When a soil de-osit is loaded, for e+a.-le :y a str%(t%re or a .an5.ade fill, defor.ations will o((%r* Toe total verti(al defor.ation at thes%rfa(e res%lting f rorn the load is (alled settle8ent. Toe .ove.ent .ay :edownward with an in(rease in load or %-ward (alled s(elling : with a

C



8.! C3N5>>lJlll4 3 S3ll> 28+

de(rease in load* Te.-orary (onstr%(tion e+(avations and -er.anente+(avations s%(h as highway (%ts will (a%se a red%(tion in the stress, andswelling .ay res%lt* As shown *in Cha-ter !, a lowering of the water ta:lewill also (a%se an in(rease in the effe(tive stresses within the soil, whi(hwill lead to settle.ents* Another i.-ortant as-e(t a:o%t settle.ents of es-e(ially fine5grained soils is that they are of ten ti.e5de-enden 4.

In the design of fo%ndations for engineering str%(t%res, we areinterested in how .%(h settle.ent will o((%r and how fast it will o((%r*E+(essive settle.ent .ay (a%se str%(t%ral as well as other da.age, es-e(ially if s%(h settle.ent o((%rs ra-idly* Toe total settle.ent, s,, of a loadedsoil has three (o.-onents, or

where s4 / the i88ediate, or distortion , settle.ent, se / the consolidation ti.e5de-endentB settle.ent,and ss / the secondary (o.-ression also ti.e5de-endentB*

751B

The i..ediate, or distortion, settle.ent altho%gh not a(t%ally elasti(is %s%ally esti.ated :y %sing elasti( theory* Toe eF%ations for this (o.-onent of settle.ent are in -rin(i-ie si.ilar to the defor.ation of a (ol%.n%nder an a+ial load P, where the defor.ation is eF%al to P%/ $E. In .ostfo%ndations, however, the loading is %s%ally three di.ensional, whi(h(a%ses sorne distortion of the fo%ndation soils* Pro:le.s arise (on(erningthe -ro-er eval%ation of a (o.-ression .od%l%s and the vol%.e of soil

that is stressed* I..ediate settle.ents .%st :e (onsidered in the design of shallow fo%ndations, and -ro(ed%res for dealing with this -ro:le. (an J5fo%nd in te+t:oo<s on fo%ndation engineering* D D

The (onsolidation settle.ent is a tirne5de-endent -ro(ess that o((%rsin sat%rated fine5grained soils whi(h have a low (oeffi(ient of -er.ea:ility* The rate of settle.ent de-ends on the rate of -ore water dra.age* e(ondary (o.-ression, whi(h is also ti.e5de-endent, o((%rs at(onstant effe(tive stress and with no s%:seF%ent (hanges in -ore water -ress%re* ettle.ent (orn-%tations are dis(%ssed in this (ha-ter@ the ti.erate of (onsolidation and se(ondary (o.-ression are dis(%ssed in Cha-ter 6*

8.! COM:RESSI BILIT7 O$ SOILS

Ass%.e fo the ti.e :eing that the defor.ations of o%r (o.-ressi:lesoil layer will o((%r in only one di.ension* An e+a.-le of one5di.ensional (o.-ression wo%ld :e the defor.ation (a%sed :y a fill(overing a very large area* Later on we shall dis(%ss what ha--ens when astr%(t%re of finite si&e loads the soil and -rod%(es defor.ation*



When a soil is loaded, it will (o.-ress :e(a%se of 9

e onna ion o soi grains,$* (o.-ression of air and water in the voids, andQor #* sF%ee&ing o%t of water and air fro. the voids*

y 2

.ineral grains the.selves is s.all and %s%ally (an :e negle(ted* 8f ten,(o.-ressi:le soils are fo%nd :elow the water ta:le, and they (an :e(onsidered f%ll sat%rated* At least we %s%all ass%.e 00 sat%ration for .ost settle.ent -ro:le.s* Th%s the (o.-ression of the -ore fl%id (an :e

(hange of loaded soil de-osits* A> the -ore fl%id is sF%ee&ed o%t, the soil

grains rearrange e.se ves in o a .or s eand a de(rease in vol%.e and s%rfa(e settle.ent res%lts* How fast this -ro(ess o((%rs de-ends on the -ennea:ility of the soil* How .%(h rearran e.ent and (o. ression ta<es la(e de ends on the ri idit of thesoil s<eleton, whi(h is a f%n(tion of the str%(t%re of the soil* oil str%(t%re,

of the de-osit*

(o.-ressed* The (%rve shown in ig* 7*1a is ty-i(al for sands in (o.-res5sion in ter.s of stress5strain@ ig* 7*1 s ows t e sa.e ata as a vo1 ratiovers%s ress%re (%rve* Note that it is (o..on to rotate the (oordinate a+es6> when -lotting e vers%s data* ig* 7*1( shows the (o.-ression vers%s

. .

. .in a very short ti.e d%e to the relatively high -er.ea:ility of gran%lar

Gany ti.es, for all -ra(ti(aV -%r-oses, the (o.-ression of sands o((%rsd%ring (onstr%(tton an , as a res% t, .ost o t e sett e.ents ave ta en

la(e : the ti.e the str%(t%re is (o. leted* However, :e(a%se they o((%r so fast, even the relatively s.all total settle.ents of gran%lar layers .ay :edetri.ental to a str%(t%re whi(h is -arti(%larly sensitive to ra-id settle.ents* Toe settle.ent of gran%lar soils is esti.ated :y %sing EF* 751 with

e s

fo%ndation engineering*

When (lays %ndergo loading, :e(a%se of their relatively low -ennea:ilit their (o.-ression is (ontrolled :y the rate at whi(h water issF%ee&ed o%t of the -ores* This -ro(ess is (alled consolidation, whi(h is astress5strain5ti.e -heno.enon* 'efor.ation .ay (ontin%e for .onths,years, or even de(ades* This is the f%nda.ental and only differen(e :etween the (o.-ression of gran%lar .aterials and the (onsolidation of (ohesive soil9 (o.-ression of sands o((%rs al.ost instantly, whereas(onsolidation is a very ti.e5de-endent -ro(ess* Toe differen(e in settle.ent rates de-ends on the differen(e in -ennea:ilities*



t

e

5555555555555555555555D

a

oal

J

< -

EoG 804?

103555 :::::::t::==V===:V::==:::T==8

0..-=:$::

T25 2n

5

$2. 7*1 S45>>->462 6= >4,5>>-425 G15> 3 6 4N26l >6n=. aB>45>> 15>G> >462n; Y:B 132= 6423 15>G> N5>>G5; 5 3N5>>23n15>G> 425 645 T6l3 1627B *

287



288 Conolldatlon and Conolldatlon &ettleent

315JG=5nl36= V6l15 >25 2>

6n6l33G> 43N556J2l24

SN2n>32l>5l543n

.:a K315JG=5n

6 A4 5FG2l2J2G. J n=5 l36=, .: a.%345 2n56>5= N35 D645 N5>>G5 6n= D645 l3D.

V

.:a K < v

5 A4 5FG2l2J2G Gn=5 av .:a.%345 >544l55n4 >.

$2. 8.* SN2n 6n6l3 6> 6NNl25= 43 3n>3l2=6423n.

The (onsolidation of (lay is readily e+-lained :y the spring analogyshown . 1g* 7*$* A -1ston P 1s loaded vertl(ally and (o.-resses a s-nnginside the (ha.:er, whi(h is filled with water* Toe s-ring is analogo%s tothe soil .ineral s<eleton, while the water in the (ylinder re-resents thewa ter io the sail vaids T:e valve # at t:e to- af the -istan re-resents the -ore si&es in the soil, and at eF%ili:ri%. when the valve is o-en no water flow s o%t* This sit%ation is analogo%s to one where a soil layer is ateF%ili:ri%. with the weight of all soil layers (alled overburden : a:ove it* A

<



8 " T5 O5=3545 6n= C3n>3ll=64l3n 75.,ln *A

-ress%re gage is (onne(ted to the (ylinder and it shows the hydrostati( -ress%re u at this -arti(%lar lo(ation in the soil* Now the soil layer isloaded :y an additional load in(re.ent Ilo, ig* 7*$:* At the start of the(onsolidation -ro(ess, let %s ass%.e that the valve # is initially (losed*U-on a--li(ation of the load, the -ress%re is i..ediately transferred tothe water inside the (ylinder* in(e the water is relatively in(o.-ressi:leand the valve is sh%t so that no water (an get o%t, there is no defor.ationof the -iston, and the -ress%re gage reads $u Ao ig* 7*$:B* The -orewater -ress%re .u is (alled the ecess hydrostatic pressure sin(e it is ine+(ess of the original hydrostati( -ress%re C >

To si.%late a fine5grained (ohesive soil with its low -er.ea:ility, we(an o-en the valve and allow water to slowly leave the (ylinder %nder theinitial e+(ess -ress%re .u. With ti.e, as the water flows o%t, the water -ress%re de(reases and grad%ally the load .o is transferred to the s-ring,

*vhi(h (o.-resses %nder the load* inally, at eF%ili:ri%. ig* 7*$(B nof%rther water is sF%ee&ed o%t of the (ylinder, the -ore water -ress%re is

again hydrostati(, and the s-ring is in eF%ili:1i%111 with the load, o*, 5` o*Altho%gh the .odel is rather (r%de, the -ro(ess is analogo%s to what

ha--ens when (ohesive soils . the field and Ia:orator y are Ioaded*Initially, all the e+ternal load is transferred into e+(ess -ore water or e+(esshydrostati( -ress%re* Th%s at first there is no (hange in the effe(tive stressin the soil rad%ally, as t:e wa ter is sFnee&ed o%t nnder a -ress%regradient, the soil s<eleton (o.-resses, ta<es %- the load, and the effe(tive

stresses inerease* The eo.-ressi:ility of the s-ring is analogo%s to the(o.-ressi:ility of the soil s<eleton* Event%ally the e+(ess Dhydrostati( -ress%re :e(o.es &ero and the -ore water -ress%re is the sa.e as thehydrostati( -ress%re -rior to loading*

8." HE OE&OME IEH A%O CO%SOLI&ATIO%ES I%(

When soil layers (overing a large area are loaded verti(ally, the(o.-ression (an :e ass%.ed to :e one di.ensional* To si.%late one5di.ensional (o.-ression in the la:oratory, we (o.-ress the soil in as-e(ial devi(e (a1led an oedo8eter or consolido8eter Prin(i-al (o.-onents

1

of two ty-es of oedo.eters are shown in ig* 7*#*An %ndist. :ed soil s-e(i.en, whi(h 1e-1esents an ele.ent %f the

(o.-ressi:le soil layer %nder investigation, is (aref%lly tri..ed and -la(ed.to the (onf ..g nng* Ihe nng 1s relat1vely ngid so that no lateraldefor.ation ta<es -la(e* 8n the to- and :otto. of the sa.-le are -oro%s=stones= whi(h allow drainage d%ring the (onsolidation -ro(ess* Poro%ss ta%es are roa de af si%tered (arn%d %ro ar -aro%s :rass rdi%a(ily, the to-



L36=2n Nl645

;,, . : . ....... . D*@ .

.... . P33G> >43n5 :) :.

. . .

DW* ># .B.B .B # 5,.B. D*D * **** * 5 * . ...B6>5

6

L36=2n Nl645

. . . 5* 59..... ... . .B # . 5 9 . . ># *5, .

V6l15

S32l >N525n

.., ... . . ** . .... .. . : X. *@ :.. P33G> >43n5

5 K D.. 5#B # . :..,. .

:

$2. 8.! S5642 3 6n 35=3545 3 3n>3l2=6423n 45>4 6NN664G>: 6l3642n-2n 35=3545; J 2Y5=-2n 35=3545 645 .S. A 3N>3 En2n55>, 90.

-oro%s stone has a dia.eter a--ro+i.ately * .. s.aller than the ring,so that it does not drag along the side of the ring when the s-e(i.en ise.g oa e * s%a 4 e ratio o e 1a.eter to e1 t o e s-e(i.en is :etween $* and , and the dia.eter de-ends on the dia.eter of the%ndist%r:ed soil sa.-les tested* There is .ore tri..ing dist%r:an(e with

D r nsD on the other hand, taller s-e(i.ens have greater side fri(tion* ide fri(tion (an :ered %(ed to sorne e+ten t :y t he %se of (era.i( or Teflon5lined rings or :ya--li(ation of a l % :ri(ant li<e .oly:den %. dis%l-hide*

In the floating5ring test ig* 7*#aB the (o.-ression ta<es -la(e fro.

:oth fa(es of the soil sa.-le* I4 (an :e shown La.:e, 161B th[t the ring

.. ....: .. ...



8.4 The Oedoeter and Conolldatlon Tetlng 291

f ri(tion is so.ewhat less in this test than in a fied5ring test ig* 7*#:B, inwhi(h all .ove.Pn t is downward relative to the ring* Toe -ri.ary advantage of the fi+ed5ring test is that drainage fro. the :otto. -oro%sstone .ay e .eas%re or ot erwtse (ontro e * n 1s .anner, or e+a.-le, -er.ea:ility tests .ay :e (ond%(ted in the oedo.eter*

To esta:lish the relationshi- :etween load and defonnation in the

as the defor.ation of the sa.-le are (aref%lly .eas%red* tress is of (o%rse. .

(o..on -ra(ti(e to load the s-e(i.en in(re.entally, either thro%gh a.ee ar%(a ever5ar. syste. or y an air or a1r5 y ra% i( -ress%re (y in der*Ea(h stress in(re.ent is a--lied, and the sa.-le is allowed to (onsolidateand (o.e to eF%ili:ri%. with little or no f%rther defor.ation

teleF%al to &ero* Th%s the final or eF%ili:ri%. stress is an ef@ective stress. Toe

.

the stress5defor.ation (%rve*

we (an -redi(t the settle.ent of the soil layer in the field*

Two .ethods are shown in ig* 7*2* In one, percent conso/idation or vertical straMn 1s - otte vers%s e eF. 1 n%. or e ec 8e conso + a (n s ress oveB

The s%:s(ri-ts ve refer to verti(al (onsolidation, and the -ri.e .ar< indi(ates effe(tive stress*B A se(ond way is to relate the void ratio to the

effective consolidation stress. 4oth of these gra-hs show that soil is a strainhardening .aterial@ that is, the instantaneo%sB rnod%l%s in(reases as the

in(e the stress5strain relationshi-s shown in ig* 7*2 are highlynonlinear, .ore (o..on ways to -resent the res%lts of a (onsolidation testare shown in ig* 7** Toe data shown in ig* 7*2 are now -resented as -er(ent (onsolidation or verti(al strainB an vo1 ratio vers%s e oga

rith8 of effe(tive (onsolidation stress* lt (an :e seen that :oth -lots have

two a--ro+i.ately straight line -ortions (onne(ted :y a srnooth transi tional(%rve* The stress at whi(h the transition or =:rea<= o((%rs in the (%rvesshown in ig* 7* is an indi(ation of the 8ai8u8 verti(al over :%rden stress that this -arti(%lar sa.-le has s%stained in the -ast@ thisstress, whi(h is very i.-ortant in geote(hni(al engineering, is <nown as the preconso/idation pressure , o4. o.eti.es the sy.:ol p4 or o48 is %sed,wherethe s%:s(ri-t 8 indi(ates .a+irn%. -ast -ress%re*

,,

.



1

?

e?'D54;

f2G

4l.

30

40o 2+ +0 7+ 100

Effe(tive (onsol idation stress, a c < Pa B

a B

2.6

2.4

2.2

l*B 2.0

,:;

?O3

1.8

? 1.6

1.4

1.2

1.0

1 1

20 40

o 2+ +0 7+ 1

Effe(tive (onsol idation stress, a#c <Pa B

(T)

$2. 8." TD3 D6> 43 N5>5n4 3n>3l2=6423n 45>4 =646: 6 N55n4 3n>3l2=6423n 3 >462n 15>G> 554215 >45>>; J 132= 6423 15>G>554215 >45>>. T5>4 3n 6 >6Nl5 3 S6n $6n2>3 B6 MG= 3 -

.! .

$6$

2



1

6 ?

e??D** $

??¡2? j

9@a,

#

2 0---1.....0.....1-..G......1--8- ......G---8-----..._..................

1

E54215 3n>3l2=6423n >45>>, a9(P6

(5)

00

$*"

$*2

$*$

a, $*oDD*9@

L6J3643122n

?..'.¡;

1*7

1*"

1 *2

1*$

1*1

0 00

E54215 3n>3l2=6423n >45>>, a c P6

J

$2. 8.) C3n>3l2=6423n 45>4 =646 N5>5n46= 6>: 6 N55n4 3n>3l2=6423n3 >462n 15>G> l3 554215 >45>> 6n= J 132= 6423 15>G> l3 554215>45>> >65 =646 6> 2n $2. 8.".

*9!

D*.



4.7 P!ECON&OI(ATION P!E&&'!EFNO!3A CON&OI(ATION=O2E!CON&OI(ATION='N(E!CON&OI(ATION

oils have a =.e.ory,= so to s-ea<, of the stress and other (hangesthat have o((%rred d%ring their history, and these (hanges are -reserved inthe soil str%(t%re Casagrande, 16#$(B* When the s-e(i.en or soil de-ositin the field is loaded to a stress level greater than it ever =e+-erien(ed= inthe -ast, the soil str%(t%re is no longer a:le to s%stain the in(reased loadand the str%(t%re starts to :rea< down* 'e-ending on the ty-e of soil andits geologi( history, this :rea<down .ay res%lt in a F%ite drasti( differen(e

in the slo-es of the two -ortions of the (onsolidation (%rve* In other words, the transition region .ay :e s.all, and s%(h soils are of ten verysensitive to even s.all (hanges in the a--lied stresses* With other lesssensitive soils, for e+a.-le silty soils, there never really is a =:rea<= in the(%rve :e(a%se the fa:ri( grad%ally alters and ad0%sts as the a--lied stressin(reases* The initial flatter -ortion of the void ratio5log -ress%re (onsolidation (%rve is ter.ed the reconsolidation (%rve, and th -art af ter the=:rea<= in the (%rve is (alled the virgin co8pression curve ig* 7*:B* Asthe latter na.e i.-lies, the soil has never :efore =e+-erien(ed= a stressgreater than the -re(onsolidation stress*

We say that the soil is nor8al/y consolidated when the -re(onsolidation -ress%re o4 0%st eF%als the e+isting ef fe(tive verti(al over:%rden

-ress%re 0 that is, o4 /

B* I we have a soil whose -re(onsolidation

-ress%re is greater than the e+isting over:%rden -ress%re that is, o4 0 :,

then we say the soil is overconsolidated or preconsolidated :. We (andefine the overconsolidation ratio, 8CR, as the ratio of the

-re(onsolidation stress to the e+isting verti(al eff e(tive over:%rden stress,or

8CR / Q:Q>Jv

75$B

oils that are nor.ally (onsolidated have an 8CR 1, and soilswith an 8CR ? 1 are over(onsolidated* Also, it is not i.-ossi:le to find asoil that has an 8CR 1, in whi(h (ase the soil wo%ld :e underconsolidated. Under(onsolidation (an o((%r, for e+a.-le, in soils that have onlyre(ently :een de-osited, either geologi(ally or :y .an* Under these (onditions, the (lay Vayer has not yet (o.e to eF%ili:ri%. %nder the weight of the over:%rden load* I the -ore water -ress%re were .eas%red %nder (onditions of %nder(onsolidation, the -ress%re wo%ld :e 2n e+(ess of hydrostati(*

There are .any reasons why a soil .ay :e over(onsolidated* lt (o%ld :e d%e to either a (hange in the total stress or a (hange in -ore water

+

0

1

+



5 5 5 5D555 55 D555555555D555555555



4.7 Precon&olldatlon PrD&ure *9)

-ress%re, :oth (hanges wo%ld altet the effe(tive st1ess* 8eologi( de-ositionfollowed :y s%:seF%e9@nt erosion is an e+a.-le of a (hange in the totalstress that will -re(onsolidate the %nderlying soils* 'esi((ation of the

%--er layers d%e to s%rfa(e drying will also -rod%(e over(onsolidation*o.eti.es an in(rease in o4 o((%rs d%e to (hanges in the soil str%(t%reandalterations of the (he.i(al environ.ent of the soil de-osit* Ta:le 751 listssorne of the .e(hanis.s leading to -re(onsolidation of soils*

How is the -re(onsolidation -ress%re deter.ined everal -ro(ed%reshave :een -ro-osed to deter.ine the val%e of o4. The .ost -o-%lar .ethod is the Casagrande Y16#":B (onstr%(tion, whi(h is ill%strated in ig*7*", where a ty-i(al void ratio vers%s log -ress%re (%rve is -lotted for a (laysoil* The -ro(ed%re is also a--li(a:le to :v vers%s log o#c (%rves* Toe

TA,E 4"1 M56n2>> C6G>2n P53n>3l2=6423n

Ge(hanis. Re.ar<s and Referen(es

Re.oval ofover:%rden Paststr%(t%res la(iation

ange . -ore water -ress%re %e to9Change in water ta:le elevation

esian -ress%r

'ee- -%.-ing@ flow into t%nnels'esi((ation d%e to s%rfa(e drying'esi((ation d%e to -lant life

Change 2n soil str%(t%re d%e to9e(ondary (o.-ressionagingBt

eologi( erosion or e+(avation :y .an

/enney 16"2B gives sea leveB (hanges

Co..on in .any (itiesGay have o((%rred d%ring de-ositionGay have o((%rred d%ring de-osition

Ra0% 16"B

Che.i(al alterations d%e to =weathering,=

-re(i-itation, (e.enting agents, ion e+(hange

Change of strain rate on Joading9t9

40err%. 16"!B

Lowe 16!2B

After 4r%.%nd Jonas and Ladd 16!"B*t Toe .agnit%de of o4/ related5to se(ondary (o.-ression for .at%re nat%ral de-osits

of highly -lasti( (lays .ay rea(h val%es of 1*6 or higher*:¡: %rther resear(h is needed to deter.ine whether this .e(hanis. sho%ld ta<e the -la(e

of se(ondary (o.-ression*

0



Conolldatlon and Coneolldatlon &ettleenta29$

M2n2G N3>>2Jl5

M3>4 N3J6Jl5 C6>66n=5

T M6Y2G N3>>2Jl5

P32n4: E B &

t t t

M2n2G N3>>2Jl5 a ...a 5M3>4 N3J6Jl5

--------- M6Y2G N3>>2Jl5 a

e

3?

E54215 3n>3l2=6423n >45>>, a (

$9. 8. T5 C6>66n=5 9!J 3n>4G423n 3 =5452n2n 45 N53n>3l2=6423n >45>>. Al>3 >3Dn 65 45 n2G N3>>2Jl5, 45 3>4

N3J6Jl5, 6n= 45 6Y2G N3>>2Jl5 N53n>3l2=6423n >45>>5>.

Casagrande -ro(ed%re is as follows9

t. Choose :y eye the -oint of .;ni.%. radi%s or .a+i.%. (%rva

t%reB on the (onsolidation (%rve -oint $ in igK 7*"B**. 'raw a hori&ontal line fro. -oint A.!. 'ra w a line tangent to the (%rve at -oint A.4. 4ise(t the angle .ade :y ste-s $ and #** E+tend the straight line -ortion of the vi!i% (o.-ression (%rve %-

to where it rneets the :ise(tor lir**e o:tained in ste- 2* The -oint of interse(tion of these two lines is the -re(onsolidation stress -oint



4.7 Preconolldatlon Preure 297

An even si.-ler .ethod for esti.ating the -re(onsolidation stress is%se y sorne eng.eers* e two stra1 t .e -ort1ons o t e (onso 1 at1on(%rve are e+tended@ their interse(tion defines another =.ost -ro:a:le=

-re(onsolidation -ress%re -oint C of ig* 7*"B* I yo% thin< a:o%t it,the.a+i.%. -ossi:le a4 is at -oint , the .ini.%. -ossi:le a4 is at -oint T,the interse(tion of the virgin (o.-ression (%rve with a hori&ontal line

oD

How is 24 -ossi:le that these gra-hi(al -ro(ed%res -redi(t the -re(on5 - e e

stress5strain history of a sedi.entary (lay soil d%ring de-osition, sa.-ling,and finally reloading in the la:oratory :y the (onsolidation test* Thish;story is shown in ig* 7*!* Toe line A$ re-resents the relationshi-

:etween the void ratio and the logarith. of effe(tive stress of a -arti(%lar

de-osited a:ove o%r ele.ent, and the -ro(ess (onsolidates the ele.ent to -oint A. This -oint re-resents the in sit% e vers%s log a4c (oordinates of the

nor.ally (onsolidated (lay ele.ent* When a :oring is .ade and the soil issa.-led, the over:%rden stresses are re.oved :y the sa.-ling o-eration

and the sa. le re:o%nds or swells alon the dashed (%rve A=. When thesa.-le is transferred fro. the sa.-ling t%:e into a (onsolido.eter ring

and then reloaded in the (onsolidation test, the salidB reloading (%rve C

is o:tained* A:o%t -oint C, the soil str%(t%re starts to :rea< down, and if

loading (ontin%es the la:oratory virgin (o.-ression (%rve CD is o:tained*Event%ally the field and la:oratory (%rves A$D and CD will (onvergeeyon -o.t yo% -er or. t e asagran e (onstr%(t1on on t e (%rvein ig* 7*!, yo% will find that the .ost -ro:a:le -re(onsolidation -ress%re

is very (lase to -oint A on the gra-h, whi(h is the a(t%al .a+*i.%. -ast -ress%re* 8:servations of this sort ena:led Casagrande to develo- his

gra-hi(al -ro(ed%re to find the -re(onsolidation stress* I the sa.-ling

str%(t%re o((%rred, a different (%rve C3 D long dashesB wo%ld res%lt %-onreloading of the sa.-le in the (onsolido.eter* Note that with the =dist%r:ed= (%rve the -re(onsolidation stress has ali :%t disa--eared within(reasing .e(hani(al dist%r:an(e@ the reloading (%rve will .ove away

fro. in Dis .%(h .ore diffi(%lt to define when sa.-le dist%r:an(e has o((%rred*

s-e(i.en is re:o%nded in(re.entally to essentially &ero stress -oints D toT of ig* 7*!B* This -ro(ess allows yo% to deter.ine the final void ratio,whi(h yo% need in order to -lot the entire e vers%s log ac (%rve* orne ti.esanotl;er reload (y(le is a--lied, li<e (%rve E to 9 of ig* *!* J%st as withthe initial re(onsolidati Dre0oins the virgin (o.-ression (%rve*



ll

.@-

*7

*7

*!

R5J3Gn==G5 43>6Nl2n

$25l= 122n3N5>>23nG15 2n >24G

9$

L6J3643*! 3n>3l2=6423n

45>4 G15

*"

E R53n>3l2=6423n

1

E54215 3n>3l2=6423n >45>>, ac P6

$2. 8. V32= 6423 15>G> l3 N5>>G5 G15 2llG>4642n =5N3>2423n,>6Nl2n Gnl36=2n 6n= 53n>3l2=6423n 2n 45 3n>3l2=6423n 45>4 6NN664G>.

4



E+AMPLE 8.

(215n:

Toe res%lts of the la:oratory (onsolidation test of ig* 7*!*

R5FG25=:

or the la:oratory D(o.-ression (%rve ( =@), deter.ine aB the -re(onsolidation stress %sing the Casagrande -ro(ed%re@ :B find :oth the 2n2.%. and .a+i.%. -ossi:le val%es of this stress@ and eB deter.ine

the 8CR if the in sit% effe(tive over:%rden stress is 7 <Pa*

a* o thro%gh the ste-s of the Casagrande (onstr%(tion as shown onig* 7*"* The o4 is a:o%t 1# <Pa*h Ass% .e e 5 @ 72 G;ni.%. -ossihle o3 is aho%t 6 <Pa, and the

0

.a+i.%. -ossi:le o4 is

a:o%t

$ <Pa*P

>CMo p3 1#

1*"

74e(a%se of the %n(ertainties in deter.ining :oth a4 and 0 1 ,

8CR3s are %s%ally given to only one de(i.al -la(e*

8. CO%SOLI&ATI O% BEHAVIORO$ %ATRAL SOILS

Iy-1(al (onsohdatton (%rves for a w1de vanety of sotls are -resented

in igs* 7*7a thro%gh 7*70* o% sho%ld :e(o.e fa.iliar with the generalsha-es of these (%rves, es-e(ially aro%nd the -re(onsolidation stress, for the differen t soil ty-es Also st%dy the a.o%nt of (o.-ression e as well asthe slo-es of the vario%s (%rves*

The test res%lts in ig* 7*7a are ty-i(al of soils fro. the l^Mner Gississi--i River Malley near 4aton Ro%ge, Lo%isiana* These soils, -ri.arily silts and sand silts with (lay sti9ata, are slightly over(onsolidated d%eto wetting and drying (y(les d%ring de-osition /a%f.an and her.an,16"2B* igs* 7*7: and 7*7( show test res%lts fro. heavily over(onsolidated

. j



1.B;

1.2;

'' '

1.1; ' '''K.

'a, 1 ;;

' ' ''''

·0:0

%

o' ''?

·o> ;.L;

;.`;

;.;

?.@?---1.----l.....J-H...H9.../.J.._...J.._..J......i.-'--'...H9..l..l._---1.. H....H.1..HH.,H.J.J.....D.....

Atter4er$ Hi8its =estNo.

%le.8)

ClassiGation wn\)

a:,.,IPa)

aIPa)

e

`L1;11121B

-`.`--L.`-1.1-2;[email protected]

CH-la7, so3t

CH-la7, G'r8 MH-san7 silt CW-la7, so3t <P-sanCW-la7 wsilt strata

HH1

;B1`1

1

PH2

2B22

Non5lasti2`

P91

2@@

eS

B.;[email protected].`;.@2.`BB.B

;.L1.;;;.`B1.B;.`B1.1

1@;1;2B;2`;B2;B;

2;;2;B;B;- 2L;

;.B

;.;.1@;.`

-;.2

11 1

E 54215 3n>3l2=6423n >45>>, a c P6

6

$2. 8.8 6 %56l n36ll 3n>3l2=645= l6> 6n= >2l4> 645 K6G6n6n= S56n, 9".

#



C3n>3l2=64l3n CG15:Gn3Y2=25= $I

*#"

*2$

C3n>Nl2=6423n CG15:NY2=25= 422l B644l53= 36423n

6Nl5 3

454 325 %3. *

*#$ e>

- X ''3P3 6

*#7 e> S6n=l l6:

@

*g3 *$7

5Deo

5 ,* 3, 3 / --

I '' wn 11]

@

g3

-o

5

*#2

*$2

*$

*#

*$"

*1" 1 11 ,Z , 1 1 1 1 l ii il ' 'l??1

El54215 3n3l2=6423n >45>>, o ( P

*$$ 3 ' ?' I' H 'I ¡

1E5421- 3n>3l2=6423n >45>>, 3'.L P6

J

$2. 8.8J O153n>Nl 2=645= U2 42ll> 645 M6O3nl= 6n= saZ%er, 90.

1-

'



3. 1 1 I I I 11 1 1 11

a : !. P6

1 1 1 1 I 1 1 1 1

Cl6 42ll

1 1 1 1 1 1 1

I R ange of a

,5 5D5 55 *5 L L /Z2P L / 8w

n / !

CIV

oDD*9@

3

*" 5 tandar test9) .. 26..8 . = N4

*

3."3 10

1 1 'I 1 1 D 1 l 1 1 1 'I , 1 1 5 1 5l I I' , , , , ,1

3n>3l2=6423n >4>>, a le P`

5

$2. 8.8N O53>3l2=645= l6 4Ull>, >3D2nUI, 54454> 3 =25n4 4N5>3 >6Nlln 65 S3=56n 6n= K2,, 90.

5555D555D555555 ,* K DDD5555555555**99@9*@55

s

e=C



4.4 Con4811datlon ,eha/lor of Natural &oll 3,3

*.*

*.0

.8

o3 .¡:;

?..'.

?O

>*2

.*

.O

0.8

PL *9

8

0.

E54215 3n>3l2=6423n >45>>, a c P6

=

$2. 8.B= L5=6 l6 645 @G2l5 6n= T3N>3n, 9.

(lays* Note the very low void ratios for the -re(o.-ressed gla(ial till soils fro. anada in ig* 7*7: Ga('onald and a%er,16!B* e e e(ts o

tills are shown in i * 7*7(* Note how the(onsolidation (%rves .ove downward and to the lef t see ig* 7*!B as

. . .

Co.-ression (%rves for another Ca'nadian. (lay, a sensitiv.e .arine

dra.ati(ally*1g%re * e s ows e (onso i

(la R%tledge, 1622B* This sedi.ent is not really a (lay :%t is (o.-osed -ri.arily of .i(rofossils and diato.s* Toe -oro%s str%(t%re o e oss s

nat%ral water (ontent and (o. ressi5

:ility* Ge+.i(o City (

.lay was -revio%sly tho%ght to :e (o.-osed

. -ri.arily a.or-ho%s to S5rays* Note the e+tre.ely high

void ratios of Ge9+i(o City



14.+.--,,B,B14.> i,*555****@*****@****99***@@* 5

13.+1------&-_

1*

1*

6* %345: T25 2n4516l

9.0 J54D55n l36= 2n55n4>/ 2 =6>

7*

8.0

.)

6.+

6.0

+.+

+.0

4.+

4.0

3.+

3.0

2.+

2.0

1.+

1.0

0.+

3 2 10 100 1 +000

E54215 3n>3l2=6423n >45>>, a#c P6

5

$2. 8.85 M5Y23 C24 l6 645 RG4l5=5, 9"".

!0"



a*,

o=D@@

?'

*"

0.)P65$5#

I%&IA%A (LACIA L CLA7

****** K **** X CP# Re.oldedQ W5 ***KK K ,

. CP$ 5WW / $$*#]

*$

$2. 8.8 C263 6n= In=26n6 l626l l6 645 RG4l5=5, 9"".

#

.j

0



0.8*

0.8

0."

5555a.-le 1 3n15n43n6l test

0.055a.-le $D (y(li( re:o% nd5reload

test loadingB

test I re:o%ndB

wn / !., :oth sa.-les

0.62---!-----0---1._G_ .G....G...G...G.._G_..!-..G..-G......j....G....! - ..G..---810 100 1000 #

E54215 3n>3l2=6423n >45>>, a9( P6

$2. 8.8 SD5ll2n l6> 3 T5Y6> 645 &6D>3n, 9"".

(lay* Also, see how the (o.-ression in(reases .ar<edly on(e the -re(onsolidation stress is rea(hed* As e+-e(ted, re.olding al.ost (o.-letely

destroys the -re(onsolidation effe(t see the dashed (%rveB*ig* 7*7f shows the (onsolidation (%rves for two ty-i(al gla(ial la<e

(lays R%tledge, 1622B* 4oth of these (lays are rather silty and have .%(hlower in sit% void ratios and nat%ral water (ontents than either the Leda or Ge+i(o City (lays*

Highly e+-ansive or swelling (lays fro. the so%thwest United tateshave (o.-ression (%rves li<e those shown in ig* 7*7g* 4oth tests startedo%t at a:o%t the sa.e void ratio and water (ontent* 4oth were initiallyloaded so that the void ratios re.ained (onstant* Toen one sa.-le 1B wasloaded in(reinentally and (ontin%o%sly in the (onventional .anner@ theother was re-eate*dly re:o%nded and reloaded* Noti(e how .%(h re:o%ndswellB o((%rred and also that the (y(li( test $B had essentially the sa.e(o.-ression (hara(teristi(s as the (onventional test* These variations -ro:a:ly o((%rred :e(a%se the sa.-les had a long history of alternate wettingand drying desi((ationB, whi(h (a%sed the soils to :e heavily over(onsoli5 dated Cha-ter " and Ta:le 751B*CaosaBidatiao (%rves far wind:Bawn silts laessB are s:awn in Eig 7*7h*The first fig%re fro. Clevenger 167B shows dry density vers%s



D5 -- 5DD5*,D5DDD55555DD55 D555555555DDD5555D5D 5 --,,----- 55 555DD 5 - DD55 5D5 ,....... '? ------ '?---- - --- 55555555DD

72.

1 1 1 1 1 1 1

7" 35

1*277 f55

L3D-=5n>24 l35>>

l3D n64G6l 32>4G5 5

- 6 5 L3D-=5n>24 l35>>, 5e

3r

5 :3 =8 H2-=5n>24 l35>>,

... 1*5 .... V l3D n64G6l 32>4G5

·99e

-3-3

',6" 5 '

H2-=5n>24 l35>>,Q N5D5445= 5

I: 15 G .... 55 X -a

675 ***** .....C **** *****

-544

5=-

*************** ****** *****

1*" 15 nn f55 -- **-**-5.... 5

D5-5- 35

5555

1 1

" !_& 3 *n *,

' - 15

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1* **** L3D 2n2426l =5n>24 5

*6 5 -- ***** **** --W-5-44-5=-------.-...

.1i G;-2.. ,n,`, I rlan @`% 3'.3 - ', -

' -- -- ..... 555

.... 55555Do

*! 5

*" 5

5555L3D D

-- ? :;::.' 5

5

P5D5445=

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ,D

1 1 1 I8

E54215 3n>3l2=6423n >45>>, o#,., P6

.

$2. 8.8 L35>>26l >32l> 3 45 M2>>3G2 R215 B6>2n, >3D2n 5545 3 N5D5442n 3n 3n>3l2=6423n. %345 45 =6>42 5=G423n 2n 45 132=

6423 D5n 45 l3D n64G6l D645 3n45n4 >32l 2> D5445= 645Cl515n5, 9)8.

5

GK .5e55n 555 6$ f55 -

> 62 5

----1 1 1 1

1 $ # 2

5D

5&

5

-3

5



!0

j: ,J1

55

5

5 5



1.;

;.`

CI?

o3Z9Z

e_

?

E54215 3n>3l2=6423n >45>>, o9( P6

$2. 8.8 2 %5D3Gn=l6n= >2l4 645 T6l3, 9"8.

$$

17

CI?

";:;

=tJ

3 0

"

1E54215 3n>3l2=6423n >45>>, a9( P6

j

$2. 8 8 j %5D3Gn=l6n= N564 6445 T6l3, 9"8.

#7

D

e



8.7 Setttement Calculetton 3,9

a--lied load arith.eti(B for an initially low and an initially high densitysarn-le* The se(ond fig%re is the sa.e data (onventionally -lotted as an e

, .ve

In its nat%ral state, loess is ty-i(ally -artially sat%rated, and when it is.

l G

tion is shown :y the -rewetted dashedB (%rves of ig* 7*7h* Toe arno%nt of(olla-se %-on wetting de-ends, as yo% .ight e+-e(t, on the 1nitia density*Had the water not :een a*dded the (onsolidation wo%ld have followed the %--er (%rve* o.eti.es -rewetting loessial soils .ay :e desira:le to

Consolidation (hara(teristi(s of another %ndist%r:ed silt are shown in

soils, and it .a<es deter.ination of the -re(onsolidation stress diffi(%lt in -ra(ti(e*

4esides Ge+i(o City (lay, -eats and other highly organi( soils alsohave high void ratios and high nat%ral water (ontents* The very high voidf the (o. ression (%rve is t i(al for -eat, as shown in ig* 7*70*J%st as with silts, deter.ination of the

4.M &ETTE3ENT CAC'ATION&

ow are* se e.en s (aheight Z that is (o.-osed of :oth solids and voids, as shown in the .iddleof the fig%re* ro. the -hase relationshi-s des(ri:ed in Cha-ter , we (anass%.e that the vol%.e of solids = is e %al to %nit , and therefore thevol%.e of voids is eF%al toe

. .

, the initial or original void ratio* inally,1. . .

shown at the right side of ig* 7*6* The vol%.e of solids re.ains the sa.e,

<now, linear strain is defined as a (hange in length divided :y the originallength* Li<ewise, we .ay define the verti(al strain in a soil layer as the

ratio of the (han e in hei t to the ori inal hei t of o%r soil (ol%.n*train .ay :e related to void ratio :y %sing ig* 7*6, or $% $ Z s $e K B

E*, %o or Zo Zo 1 e

olving for the settle.ent s in ter.s of the void ratio, we o:tain9

* l $X

Zo Ev Zo

752B

.

7

$



Í '1

#1 Coneolldatlon and Consolldallon S5l4l55n4>

H / s

1

H

$2. 8.9 C6lGl6423n 3 >544l55n4 3 45 N6>5 =266.

Note that EF* 752 is :ased only on -hase relationshi-s and a--lies for :oth

sands and (lays*

E+AMPLE 8.*

(215n:

Dor o - a(e.en o a (ovenng a arge area at a s1te, t e 1( ess o a(o.-ressi:le soil layer was 1 .* lts original in sit% void ratio was 1**orne ti.e after the fill was (onstr%(ted, .eas%re.ents indi(ated that theaverage void ratio was31?*7*

R5FG25=:

Esti.ate the settle.ent of the soil layer*

S3lG423n:

Use EF* 752* / lle Z / 1* 5 *7 1 / 1 8

1 $ o 1 1*

y ow.g e re ations 1- etween v1 ratio an e e(tive stress 1tis -ossi:le to (o.-%te the settle.ent of a (o.-ressi:le layer d%e to thea--lied load* This relationshi- is, of (o%rse, deter.ined fro. a onedi.ensional (o.-ression or (onsolidation test, and we have already shownseveral ways to dis-lay the test res%lts* Toe slo-e of the (o.-ression (%rve,

. .

1

.



5555=5555D555555 5 55 5 555D5DD555555555 55555 55 555 5 555 5D . . .

8.7 &effleent Calculatlon 311

co8pressibility, a.,,or 5de

a., ,1Q ,

75aB

in(e the (%rve is not linear see i$s* 7*l: and 7*2:B* a is annro+i.atelv(onstant over only a s.all -ress%re range, a i t @ or

a 55***** ** =3$

75:B= Ila oS 5 oiwhere the void ratios e1 and e (orres-ond to the res-e(tive -ress%res o4

ano o >

E9A3PE 4.%

15n:

The (o.-ression (%rve shown in ig* 7*2:*

R5FG25=:

Co.n5ntP* thP* N,,*,ffi(ient of n.o

5 ressihilitv5$ to 2 <Pa*

n*** for the strP*9** 2n Dfrn.

. .

S3lG423n:

2:;3-- 2:;-:- .,n5**, **-* i595***91 l.- .. 9***91 --:A4 .. -5 l..-4- 555

5 5e,W # -e1 / 1*!" and e / 1*2!* Using EF* 75h we have,

a.,

1*2! 5 1*!"*12 -er <Pa

=TM _*v

Note that the %nits of a., are the reciproca/ of stress, or 1Q<Pa or .$Q<N@a., (o%ld :e re-orted as 1 .$QN*

'1

When the test res%lts are -lotted in ter.s of the -er(ent (onsolida5tion or strain as in iJt* 7*2a, then the slooe of the (o.oression (%rve is thecoefficient of volu8e change, 8.,, or

df.., *, a. ,8., / --/ -//

175"B

da4 lla3 1 e D

19

-1

A



D55



#1$ C3n>3ll=64l3n 6n= C3n>3ll=63n S544l55n45

where Iv is the verti(al (o.-ression or strain EF* 75#B, and is theconstrained or oedo8etric 8odulus. o.eti.es the sy.:ol Eoed is %sed for . In one5di.ensional (o.-ression, Iv is eF%al to eQ1 e B*

E+AMPLE 8 "

(215n:

Toe (o.-ression (%rve shown in ig* 7*2a*

R5FG25=:

a* Co.-%te the (oeffi(ient of vol%.e (hange 8. , for the stressin(re.ent fro. $ to 2 <Pa*

J. 'eter.ine the (onstrained .od%l%s .

a* ro. ig* 7*2a, the F v (orres-onding to o of $ <Pa is $#*!]and the Iv (orres-onding to 2 <Pa is #1*2]* Use EF* 75"*

/ *#12 5 *$#! / 8 <Pv 2 5 $ * -er a

As with < v> the %nits of 8v are the re(i-ro(aV of stress*

:* The (onstl ained .od %las is the 1e(i-1(al %f 8v, 1 / Eoed / $" <Pa

E+AMPLE 8.)

(215n:

The res%lts of E+a.-les 7*# and 7*2*

R5FG25=:

how that 8v / av/ F 1 ` e : for the in(re.ent $ to 2 <Pa*

S3lG423n:

ro. E+a.-les 7*# and 7*2, av / *12 -er <Pa and 8v / *#6 -er

55555555555555555 5555 555555 5

8 #7



e D- - e-

4.M &ettleent CaleatatlonL %1%

<Pa* w. ig* 7*2:, e

$*"*

1`

$ K

"/ *2, D 1( 1s ( ose to *#6*

When test res%lts are -lotted in ter.s of the void ratio vers%s thelogarith8 of effe(tive stress ig* 7*:B, then the slo-e of the virgin(o.-ression (%rve 1s (alled the co8pression inde Ce, or

e d log olog o 5 log o4 o3

log5

75!B

E9A3PE 7*"

15n:

The (onsolidation test data of ig* 7*:*

R5FG25=:

'eter.ine the (o.-ression inde+ of this soil :y aB EF* 75! and :Bgra-hi(ally*

a. The virgin (o.-ression (%rve of ig* 7*: is a--ro+i.ately linearfro. 1 to 7 <Pa* At least we (an ta<e the average slo-e :etweenthe se two -oints* Therefore fro. EF* 75!, we have

$ 1 $1

1* 3.98logl8

Note that Ce is di.ensionless*b. To detennine the Ce gi a-hi(ally, we note that

o3 1log log

R 1log 1

T5herefore if we find the differen(e in void ratio of the virgin (o.-ression (%rve over one /og cycle , we a%to.ati(ally have t he @, :e(a%se t he

,, J

*12 h= h * l

D 55



!" C3n63ll=4l3n 6n= COn44Ol=64l3n S544l55n46

deno.inator of EF* 75! is oneB* I yo% do t his for t he log (y(le 1 to 1 < Pafor e+a.-le, yo% find t hat e is sligh t ly less than l* for a l i ne -arallel tothe average slo-e :et weelB 1 and 7 < Pa* Therefore @, is slightly less t ha nl*, whi(h (he(<s the (al(%la tion of -a rt 6.

E+AMPLE 8.

(215n:

Toe (onsolidation test data of ig* 7*7a*

R5FG25=:

'eter.ine the Ce of tests 6 and 1#*

S3lG423n:

';

We (an either %se EF* 75! or do this gra-hi(ally* or test 6, %sing EF* 75!,

ce *77 "2 o 2$

log55"00

This is (lose to what /a%f .an and her.an 16"2B o:tained *22B, as

sHown in ig* 7*7a* in(e the vtrg. (o.-ress1n (%rve 1s not e+a(tly astraight line -ast o@, the val%e of Ce de-ends on where yo% deter.ine theslo-e*

or test 1#, fiad e for the log (y(le Yroro $ 43 $ <Pa

.e 1*$ 5 *"! *#@ so ce / *#*

Ihe slo-e of the virgin (o.-ression (%rve w:en the test Ies%lts are -lotted as -er(ent (onsolidation r verti(al strain vers%s /ogarith8 of effe(tive stress ig* 7*aB is (alled the 8odified co8pression inde, CeY> andit is e+-iessed as D

757B o'

log5

o.eti.es @N is (alled the cornpceuion ratio Toe relationshi- :e5tween the .odified (o.-ression inde+ CeY and the (o.-ression inde+ Ce,is



a* ettle.ent C6lGl63n #1

given :y

756B

E+AMPLE 8.8

??'??'? ,.

1he (onsolidat1on (tata ot l31g* I*9?a*

R5FG25=:

'eter.ine the .odified (o.-ression inde+ of this soil :y aB EF* 757 and:B gra-hi(ally* (B Che(< the Ce fro. E+a.-le 7*" :y EF* 756*

S3lG423n:

nn tl,@(, J.*t lile,** E+a.nle 7*"*

a* Consider the virgin (o.-ression (%rve to :e a--ro+i.ately astraight line over the stress range 1 to 7 <Pa* Th%s, %s.g r*F*

757 we have 5 X X . .*#7 5 *1#7

*$!2log @

et# gra-hi(ally, (hoose any (onvenient this(ase %9s( ,11 =*= 1v ,v 11 11..r a.> ***************** ****** ****,* *****,* 'J '·' i*i#7 5 l8 $7], or Cet# *$7, whi(h (he(<s -art aB adeF%ately*

(* Ass%.e e / $*" fro. l31g* 7*:* Use tF* l5* nerefore

ce (et9l e> B / *$!21 $*"B *67

whi(h (he(<s the C fro. E+a.-le 7*"*

E+AMPLE 8.9

(215n:

The void ratio vers%s log effe(tive -ress%re data shown in ig* E+* 7*6*

:* To find C 5

lo5g (y ( le@ in



;.`

----

;.

318 Con8olldatlon and Con&olldatlon Sett1entenl8

J

3'.;:;

=3C¡;?

1 100 300 1000

E54215 3n>3l2=6423n >45>>, a e P6

R5FG25=:

$2. EY. 8.9

'eter.ine aB the -re(onsolidation -ress%re o4, :B the (o.-ression inde+Ce, and eB the .odified (o.-ression inde+ Ce.B

S34G423n:

a. Perf or. the Casagrande (onstr%(tion a((ording to the -ro(ed%reo%tlined in e(* 7*2, and f.d o4 1$1 <Pa*b. 4y definition EF* 75!B,

C e o3

log51*o

1'

Using the -oints a and of ig* E+* 7*6, $N *7!, $ *", 1<Pa, and , # <Pa* Therefore

ce $a - $ *7! 5 *" *$1 / *21a1,

log5@,5a

# 0."og 1

55555 555 55555 5555555555555555



4.M &ettleent Calculatlon !

log

A seeond gra-hieal D6 is to find $e ovbr one (y(le@ for e+a.-le,/ log l 8 / l* When this is done, Ce / tie. In ig* E+* 7*6 the

::

verti(al s(ale is not s%ffi(ient for Ilo3 / 1 log (y(le, :%t it (an :e done intwo ste-s, $ to $ and $$ to $d . To e+tend the line $$ to one f %ll log (y(leon the sa"$ gra-h, (hoose $$ at the sa.e -ress%re as $. Toen draw the line$$$d -arallel to $ $. This se(ond line is .erely the e+tension of $$ if thegra-h -a-er e+tended lower than shown*B 8r,

tie ce F ea 5 eb : ` ee 5 ed B

/ *7! 5 *"B *6 5 *""2B

*$1 *$#" / *21 , or sa.e as a:ove

(* The .odified (o.-ression inde+ Ce> isce *21

ce. / 1 $X 1 *7" / $2$

To (al(%late (onsolidation settle.ent, EFs* 75, 75", or 75! and 757.ay :e (o.:ined with EF* 752* or e+a.-le, %sing EFs* 75! and 752 weo:tain

se / ce l oe log o4 751B

I the soil is nor.ally (onsolidated, then o4 wo%ld :e eF%al to thee+isting verti(al over:%rden stress 0 , and wo%ld in(l%de theadditional stresstio a--lied :y the str%(t%re, or

7511B

When (o.-%ting the settle.ent :y .eans of the -er(ent (onsolidationvers%s log effe(tive stress (%rve, EF* 757 is (o.:ined with EF* 752 to get

751$B

or, analogo%s to EF* 7511, for nor.ally (onsolidated (lays,0 1 tio1

se cc.Zo log +

>>>

751#B

8ther si.ilar settle.ent eF%ations (an :e derived %sing a and 8 > In

this (ase the average stress for a given stress in(re.ent .%st :e %sed sin(ethe (o.-ression (%rves are nonlinear*

2,J

1

D

1



E9A3PE 8.O

(215n:

:ility of a 1 . layer of nor.ally (onsolidated an ran(is(o 4ay G%d*. .

R5FG25=:

Esti.ate the (onsolidation settle.ent of a large fill on the site if the

S3lG423n:

irst esti.ate the -re(onsolidation stress to :e a:o%t ! <Pa* in(e the (layis nor.ally (onsolidated, o@99999 0 > Use the res% ts oC is *67" and C is *$!2* Use E * 7511*

1/ .,9 m

e

! 1e !

/This sli t diff eren(e is the res%lt of o:tainin data fro. the s.all gra-hs*Toe settle.ent wo%ld :e re-orted as DDa:o%t 1 .*= With a high water ta:le,

large, fill that was a:ove the water ta:le wo%ld now :e s%:.erged* Th%s

trial and error (o.-%tations are reF%ired*

ere are a (o%-le of reasons or t e -o-% anty . eng.eenng -ra(ti(e of %sing the -er(ent (onsolidation or verti(al strain vers%s log

effe(tive stress (%rve to (o.-%te settle.ents* irst, esti.ating field settle5. .

gra-h, on(e yo% have a good esti.ate of the in sit% verti(al over:%rdenstress*

Another reason the -er(ent (onsolidation vers%s log eff e(tive stress -lots are -o-%lar is that d%ring the (onsolidation test it is often desira:leto <now what the sha-e of the (o.-ression (%rve loo<s li<e, so as to :e

318

.



8.7 &etueent Calculatlona 319

a:le to o:tain an early eval%ation of the -re(onsolidation -ress%re* Toevoid ratio vers%s log effe(tive stress (%rve (annot :e -lotted d%ring the testas it is ne(essary to <now :oth the initial and final val%es of the void ratio*This (al(%lation reF%ires the deter.ination of the dry .ass of solids, whi(h(an only :e deter.ined at the end of the test* Therefore the e vers%s log ac(%rve (annot :e -lotted d%ring the test* However the -er(ent (onsolidation3et s%s log -ress%re e%r*e ean :e -lotted while the test is :eing -erfor.ed*Another advantage is that when the -re(onsolidation -ress%re is :einga--roa(hed, the load in(re.ents -la(ed on the sa.-le (an :e red%(ed soas to define .ore (aref %lly the transition :etween the reloading (%rve andthe virgin (o.-ression (%rve* Also, the test (an :e sto--ed when two or

three -oints define the straight line -ortion of the virgin (o.-ression(%rve* inally, as Ladd 16!1aB -ointed o%t, two sa.-les .ay show verydiff erent e vers%s log o c -lots :%t .ay have si.ilar verti(al strain vers%slog effe(tive stress (%rves :e(a%se of differen(es in initial void ratio*

E9A3PE 4.11

(215n:

Toe data of E+a.-le 7*1*

R5FG25=:

Esh.ate the settle.ent d1rectiy fro. ig* 7*a*

S3lG423n:

l the -re(onsolidation stress is a:o%t ! <Pa, the final stress after loading is

1! <Pa* Ref er to ig* 7*a* At the a4, whi(h is eF%al to 0 sin(e it isnor.ally (onsolidated, the E is a:o%t *]* $t a 1! <Pa, the E9 is a:o%t$$]* Therefore the i9lE is 1"*], so the esti.ated settle.ent will :e

se *1"1 .B 1*" .Toe settle.ent is .ore in this e+a.-le :e(a%se the slo-e of the virgin(o.-ression (%rve is stee-er fro. ! to 1! <Pa than it is fro. 1 to 7 <Pasee E+a.-le 7*"B*

All the eF%ations for settle.ent -resented a:ove were for a single(o.-ressi:le layer* When the (onsolidation -ro-erties or the void ratio

* J

1

00

0



Í '1

32, Coneolldatlon and Conolldatlon &ettleent

vary signifi(antly with de-th or are different for distin(t soil layers, thenthe total (onsolidation settle.ent is .erely the s%. of the settle.ents of the individ%al layers, or

n

e e,2-

where se4 is the settle.ent of the ith layer of n layers as (al(%lated :y EFs*

o far in this se(tion we have only dis(%ssed settle.ent (al(%lations

Toe first thing to do is to (he(< whether the soil is -re(onsolidated*

then yo% have

str%(t%re, Xv D -l.%s the

e+(eeds the -re(onsolidation -ress%re

settle.ent (al(%lated, as is shown in ig* 7*1*= A = 5 p 3

then %se either EF* 7511 or 751#, :%t with the re(o.-ression indi(es Cr or r> in - a(e o e an e>3 res-e(tive y* e reco8press(n + e, r> 1s

defined 0%st li<e Ce, e+(e-t that it is for the average slo-e of the re(o.-res5sion -art of the e vers%s log o#c (%rve ig* 7*!B* I the data are -lotted inter.s of E9 vers%s lo o3 then th l D D(alled the 8odified reco8pression inde Cr, so.eti.es (alled the reco8pres5

751B

E9A3PE 4.1

(215n:

Toe void ratio vers%s log effe(tive -ress%re data shown in ig* E+* 7*6*

.



- ? ----- --- ..- - D5D5 --- . 55 . 55555DD5555DDD *** .-- '?----- . -- ?------------------ -- 5 5D

a K Aa*

e a:o a

2 2¡

- Ae

T 45Aa*555

1

n'

aB a Aa*

ve

W5 P'

.. 8 vn

a3..5 Aav

a. .

2 2

e> --- 3 Ae 1-

tAe$

e, 5 ?? T 6

'1

1

o,

:B 8vo Aav a

. v(

$2. 8.0 P2n2N25 3 >544l55n4 6lGl6423n> 3 3153n>3l2=645= >32l>.

%1

- -

#

.

.



55

...

5555555



crt: D --C,-

`-]`a )

<1

322 Con4811datlon and Conaolldatlon &ettleenta

!euired:

Cal(%late aB the re(o.-ression inde+ Cr and :B the .odified re(o.-res5sion inde+ 5n.

S3lG423n:

a* The re(o.-ression inde+ Cr is fo%nd in a si.ilar .anner to the CeEF* 75!B* Using the -oints e and J over llog (y(le, we find that

@ / e 5 e / *!6 5 *!" / *#

b. The .odified re(o.-ression inde+ Cr, is fo%nd fro. EF* 751*

/ *1"o

Note that neither of these ter.s has %nits*

To (al(%late settle.ents %f %ver (onsolidated (lays, EFs* 8- and 751# :e(o.e

751"B

when 4

75X!B

:v s o4. in(e Cr is %s%ally .%(h less than Ce, the settle.entso((%rring when4

:v s o4 are .%(h less than if the soil were nor.ally

(onsolidated*I the added stress (a%sed :y the str%(t%re e+(eeds the -re(onsolida5

tion stress, then .%(h larger settle.ents wo%ld :e e+-e(ted* This is:e(a%se the (o.-ressi:ility of the soil is .%(h greater on the virgin(o.-ression (%rve than on the re(o.-ression (%rve as was shown, for

e+a.-le, in ig 7 ! or the (ase, then, where 0 :v a4 the settle5.ent eF%ation (onsists of two -arts9 1B the (hange in void ratio or strainon the 1e(o.-1ession (%IMe fw. the %1iginal in sita (onditions of ( $

, 0 B

or iv ,

B to o44 and $B the (hange in void ratio or strin on the virgin

(o.-ress1on (%rve fro. o4 to the hnal (ond1:ons of F eW,;W: or F iv1 ,o41 ). Note that ,,& , .,. These two -arts are shown gra-hi(ally in ig*7*1:* The (o.-lete settle.ent eF%ation then :e(o.es

' I` eo o p3

1

1



8.7 &eltleent Calculatlon- 323

This eF%ation red%(es to

7517:B

4oth EFs* 7517 and 7516 give the sa.. e res%lts* 8ne

(o%ld.

arg%e that in the

sC3lidation -ress%re on the tr%e virgin (o.-ression (%rve sho%ld :e %sed*.

feren(e in the answer*o.ett.es t e egree o over(onso atton vanes t ro%g o%t e

(o.-ressi:le layer* o% (o%ld a--ly EF* 751" or 751! to the art where

into several layers, a--ly the a--ro-riate eF%ation to (al(%late the average

What is the :est way to get Cr and Cr. for %se in EFs* 751" thro%gh

o:tained fro. la:oratory .eas%re.ents9 dist%r:an(e d%ring sa.-ling,

:%::les in the voids@ and #B errors 2n test -ro(ed%res and .ethods of in er-re ing es res% s* is a er e. .e % es e -ro e. o re-r %( ingthe in sit% state of stress in the s-e(i.en* Leonards re(o..ends thatthe 0 1 :e a--lied to the s-e(i.en and that it :e inn%ndated andallowed to (o.e to eF%ili:ri%. for at least $2 ho%rs :efore starting thein(re.ental loading* Any tenden(y to swell sho%ld :e (ontrolled* Toenthe (onsolida5

as (losely as -ossi:le the in sit% stress state, Leonards re(o..ends that thesa.-le :e (onsolidated to slightly less than the o4 and then :e allowedtore:o%nd* This is the first (y(le shown in ig* 7*11* l yo% dont have a good ea o t e o4, then (onsolidate initially to0

dov orily, whi(h is

-res%.a:ly less than

o4.Toe deter.ination of cr or cr. is over the range of

0 1 ; v> as shown in ig* 7*11* I4 is (o...on -ra(ti(e to ta<e.the average

yo% (an see that the a(t%al val%es of the re(o.-ression inde+ de-end on

the stress at whi(h the re:o%nd5reload (y(le starts, es-e(ially whether itstarts at a stress less than or greater than the o4. ee the di*fferen(e2n

. _

.

1

.



324 Conolldallon and Oonolldatlon Settlementa

V5426l 5 54215 >45>> l3 >6l5

QQ 1

15555551

(%

$2. 8. TN26l 3n>3l2=6423n G15 >3D2n 45 535n=5= N35

=G5 6 =5452n2n 4J5 e 6445 I53n6=> 9

slo-es of the re:o%nd (%rves shown in the fig%re* The C, also de-ends onthe 8CR to wfO(h re:o%nd.g and reload.g ta<e -la(e, for e+a.-le, theratio of o3 / o4 in ig* 7*11* The final (onsideration affe(ting the val%e of C,is the -resen(e of gas :%::les in the -ores of the soil* Use of :a(< -ress%reCha-ter 11B (an so.eti.es ta<e (are of this -rohle.

E9A3PE 4*1#

(215n:

The data in E+a.-le 7*1 and ig* 7 ! is re-resentative of a Iayer of silty(lay 1 . thi(<*



5555 55 5555 55555555 55555



D 5D5 5D555555 DD5DDDDDDD5 555D55DD5DD55D5555555555 55

7*! ettle.ent Cl(%ltlon #$

R5FG25=:

Est;.ate the (onsolidation settle.ent if the str%(t%ral loads at the s%rfa(ewill in(rease the average stress in the layer :y # <Pa*

ro. E+a.-le 7*1, we <now that the 0 1

is 7 <Pa and the o4 is a:o%t 1#<Pa@ $

is a:o%t *72* in(e the a--lied stress is # <Pa, the 0 1 dov / 11<Pa 1# <Pa* Therefore %se EF* 751"* To get Cr , we will ta<e the averageslo-e of the two (%rves DE and E9 near the :otto. of ig* 7*!* Cr

isa--ro+;.ately *#* Now %se EF* 751"*1 . 7 #

se *# *1 72

log7

/ *$" . or $"

ro. the -re(eding d;s(%ss;on, the Cr in this e+a.-le is -ro:a:ly too largesin(e we deter.;ned it fro. a re(y(le well :eyond the l4 is thereforevery l;<ely that the settle.ents in the field will :e less than the -redi(tionof $" ..*

E+AMPLE 8."

Toe data in E+a.-le 7*1#, e+(e-t that the str%(t%ral Dengineer .ade anerror in (o.-%ting the loads@ the (orre(t loads now will -rod%(e anaverage stress in(rease of 6 <Pa in the silty (lay layer*

A G25=:

Esti.ate the (onsolidation settle.e% t d%e to the new loads*

S3lG423n:

Now the ,a--lied stress is .%(h greater than 41 liov , or 7 6 5 1!

1# <Pa* Therefore we .%st %se EF* 7517* In addition to the Cr, we needthe (o.-ression inde+ Ce. ro. ig* 7*! we find that Ce is a:o%t 8* $*%:stit%tion into EF* l : gives

1 2 1# $1 la 7 6

e *w 1 *72 og 7 l *72 g 1#

*#2 . 8 17 ./ *16#

o4

1



Í '

328 Conolldatlon and Conaolldatlon &ettleent4

As in E+a.-le *1, this val%e wo%ld :e re-orted as **a:o%t $ (.= d%e tothe %n(ertainties in sa.-ling, testing, and in esti.ating the a4, thea--liedstress in(rease, and e, and ce.

8.8 *ACTO!& A**ECTING THE(ETE!3INATION O* a

4r%.%nd, Jonas, and Ladd 16!"B dis(%ss three fa(tors whi(h signifi5

(antly infl%en(e the deter.ination of f ro. la:oratory (onsolidationtests* We have ahead9y .en ti%ned %ne, the ef fe(l %f sa.-le dist. :an(e on thesha-e of the (onsolidation (%rve ig* 7*!B* We showed how the =:rea<= inthe (%rve :e(a.e less shar- with in(reasing dist%r:an(e* o% (an see theseeff e(ts in ig* 7*1$a* With sensitive (lays es-e(ially for e+a.-le, igs* 7*7dand eB, in(reasing sa.-le dist%r:an(e lowers the val%e of the At thesa.e ti.e the void ratio is de(reased or the strain

in(reasedB for any given val%e o; ocB As a (onseF%en(e, the (o.-ressi:ilityat stresses less than the o4 are in(reased, and at stresses greater than theo4the (o.-ressi:ility is de(reased*

A load in(re.ent ratio LIRB of %nity is %sed in (onventional(onsolidation testing for e+a.-le, ATG ' $2#B* Toe LIR is defined asthe (hange in -ress%re or the -ress%re in(re.ent divided :y the initial

-ress%re :efore the load is a--lied* This relationshi- is as follows9

LIR oinitial 75$B

where Y is the in(re.ental stress, and oinitiaI is the -revio%s stress* An LIR of %nity .eans that the load is do%:led ea(h ti.e* This -ro(ed%re res%ltsin evenly s-a(ed data -oints on the void ratio vers%s log effe(tive stress(%rve s%(h as shown in ig* 7*:*

E+-erien(e with* sof t, sensitive (lays ig* 7*7dB, has shown that as.all stress (hange or even vi:ration .ay drasti(ally alter the soil str%( t%re*

or s%(h soils a load in(re.ent ratio of %nity .ay not a((%ratelydefine the val%e of the -re(onsolidation stress, so an LIR of less than oneis of ten %sed* The infl%en(e of varying the LIR on the (o.-ressi:ility aswell as on the o4 of a ty-i(al (lay is shown in ig* 7*1$:* The effe(t of thed%ration of the load in(re.ent is shown in ig* 7*1$(* Toe (o..onATG ' $2#B -ro(ed%re is for ea(h in(re.ent to :e lef t on the sa.-le

o

o4



555555555DDDDDDDDD5555 DD

j

e9

.Z

.Z

.Z

5Z?ZZ' Cl

In >24G a

55-&*1

·e oDCl ;:;

=DCo ----In >24G G15

- --- 6 643 G15 3n2 FG6l24 >6Nl5

- ---L6J3643 G15 3nN33 FG6l24 >6Nl5

E54215 3n>3l2=6423n >45>>, a c l3 >6l5

(5)

> e

In >24G

S6ll LIR

---- n >4G G15

l6J3643 G15 D24 >6ll

LIR 2n 122n24 3 a

---- L6J3643 G15 D24 >46n=6= LIR / 1*

E54215 3n>3l2=6423n >45>>, a#.C log >6l5

J

$2. 8.* $643> 6542n 45 l6J3643 =5452n6423n 3 6 554 3 >6Nl5 =2>4GJ6n5: J 554 3 l36= 2n55n4

6423;

327

D

a



328Conaolldetlon end Con811datlon Settlementa

a 3 3N5>>23nG15 J6>5= 3n

R 1 D24 4 tP>55 C. 9.

---- C3N5>>,3n G15 64 4 tP-- C3N5>>23n G15 64 4 / =6

5

$2.8.* 5 554 3 l36= 2n55n4 =G6423n 645 BGGn=, 3n6>, 6n= L6==, 9.

for $2 ho%rs* Note how this -ro(ed%re aff e(ts the a4. orne of theter.inology %sed for these fig%res will :e(o.e (learer af ter yo% read

4. P!E(ICTION O* *IE( CON&OI(ATION

C'!2E&

in(e the (onsolidation test really is a reloading of the soil shown :y(%rve CD of ig* 7*!B, even with high5F%ality sa.-ling and testing thea(t%al re(o.-ression (%rve has a slo-e whi(h is so.ewhat less than thelo e of the* ield vir in co ression curve A$D in ig* 7*!B*

(h.ert.ann 16B develo-ed a gra-hi(al -ro(ed%re to eval%ate theslo-e o t e 1e virgin (o.-ression (%rve* The -ro(ed%re for this(onstr%(tion te(hniF%e is ill%strated in ig* 7*1#, where ty-i(al void ratiovers%s log effe(tive stress



-K

- 2

K

B

Effe(tive (onsolidat*ion stress, ac log s(aleB

6

Eff e(tive (onsol idation stress, o log s(aleB

(T)

$2. 8.! lllG>46423n 3 45 S546nn 9)) N35=G5 433J462n 45 25l= 122n 3N5>>23n G15: 6 n36ll 3n>3l2=645= >32l; J 3153n>3l2=645= >3l.

!*9



## C3n>3ll=54l3n 5n= C3n>3ll=54l3n S544l55n4>

(%rves are -lotted* To (orre(t the la:oratory virgin (o.-ression (%rve fora nor.ally (onsolidated soil in the field, -ro(eed as follows9

l. Perfor. the Casagrande (onstr%(tion and eval%ate the -re(onsolidationD-ress%re o4.$* Cal(%late the initial void ratio e * 'raw a hori&ontal line fro. e ,

-arallel to the log ef fe(tive stress a+is, to the -re(onsolidation -ress%re o4. This defines (ontrol -oint l, ill%strated :y triangle lin ig* 7*1#a*

#* ro. a -oint on the void ratio a+is eF%al to .e , draw ahori&ontal line, and where the line .eets the e+tension of thela:oratory virgin (o.-ression (%rve L, define another (ontrol

-oint, as shown :y triangle $* o% sho%ld note that the (oeffi(ientof e is not a 33.agi( n%.:er,= :%t is a res%lt of .any o:serva

tions on diff erent (lays*2* Conne(t the two (ontrol -oints :y a straight line* The slo-e of this

line, 9, defines the (o.-ression inde+ Ce that .ost -ro:a:ly e+istsin the field* Line 9 is the field virgin co8pression curve. The(h.ert.ann (orre(tion allows for dist%r:an(e of the (lay d%e tosa.-ling, trans-ortation, and storage of the sa.-le -l%s s%:se F%enttri..ing and reloading d%ring the (onsolidation test* DD

E+AMPLE 8.)

(215n:

The e vers%s log o data of ig* E+* 7*1* This (onsolidation data is fro. an%ndist%r:ed (lay sa.-le ta<en fro. the .id-oint of a (o.-ressi:le layer 1 . thi(<* The 8CR 1*

R5FG25=:

Using the (h.ert.ann -ro(ed%re deter.ine aB the slo-e of the fieldvirgin (o.-ression (%rve* :B Co.-%te the settle.ent of this (lay layer if the stress is in(reased fro. $! to 7 <Pa* Cal(%late, %sing :oth thela:oratory and field virgin (o.-ression (%rves* (B Co..ent on thedifferen(e, if any*

S3lG423n:

a* irst, esta:lish the field virgin (o.-ression (%rve a((ording to the(h.ert.ann -ro(ed%re o%tlined a:ove* Perfor. the Casagrande (on5

1

1



4. Predlctlon ot *leld Conolldatlon Cur/e 331

@

-3' *!

3

*"

*

Ef fe(tive (onsol idation stress, oc <PaB

$2. EY. 8.)

str%(tion on the (%rve shown in ig* E+* 7*1 to o:tain the -re(onsolidation -ress%re* o3 is fo%nd to :e $! <Pa* 'raw a hori&ontal line fro. e0 /

*61$ to the -oint where it interse(ts the -re(onsolidation -ress%re toesta:lish (ontrol -oint 1 * shown :y triangle 1* E+tend the virgi*n (o.-res5

sion (%rve to *2$ e *2$ + *61$B or *#7, to esta:lish (ontrol -oint $*Conne(ting the two (ontrol -oints l to $ (reates the field virgin C.-ression (%rve*

Toe val%e of Ce fro. the field virgin (6.-ression (%rve is deter.ined 0%st li<e yo% did for the la:oratory (onsolidation (%rve see E+a.*-les 7*",7*!, and 7*6B* or the log (y(le f ro. 1 to 1 <Pa, e%. / *! ande1 / *#$6@ therefore Ce C *! 5 *#$6 / *#!"* Toe slo-e of thela:oratory virgin (o.-ression (%rve is fo%nd 2n the sa.e way and 5FG6l>*#1* We3ll need this val%e later*

.j

?O



!!* Con3Ulldetlon and Con4ollda'on Settlen....a.

b. To (o.-%te the settle.ent, we .ay %se either EF* 752 or 7511* UseEF* 752 first9

$.ee $X o

The ehange in void ratio, Ile, is .erely the differen(e in void ratio for o $! <Pa and o / 7 <Pa* These val%es are *61$ at -oint a and *!22at -oint b in ig* E+* 7*1 on the field virgin (o.-ression (%rve* Therefore,

*61$ 5 *!22 1.

K

77 .

e 1 U*61$

Using EF* 75ll 9

*#!" 1 .B log7

*61 555 5

The slight differen(e in the (al(%lated val%es of the (onsolidation settle5.ent se is d%e to s.all errors in reading data -oints fro. ig* E+* 7*1*

I we (al(%late the (onsolidation settle.ent %sing the la:oratory virgin (o.-ression (%rve to esta:lish Ce, we wo%ld o:tain EF*7511B

se 1 ' K 1 .B log *! ., or 1"] lower 61$ $!

(* Co.rnent on the differen(e* i+teen -er(ent (o%ld :e signifi(ant inso.e (ases, es-eeially if the -ro-osed str%et%re is -artie%larly sensitive tosettle.ents* Ladd 16!1aB has fo%nd the (h.ert.ann (orre(tion will.(rease (o.-ress1n .d1(es a:o%t 1] for fairly good sa.-les of sof t to.edi%. (lay* in(e the -ro(ed%re is si.-le, it wo%ld see. -r%dent to %seit to .a<e the :est -ossi:le esti.ates of field (o.-ressi:ility* 8n the other hand, :eware of too .%(h -re(ision in settle.ent (al(%lations* Whenfo%ndation engineers -resent their res%lts in an engineering re-ort, thee+-e(ted settle.ent wo%ld :e stated as =a--ro+i.ately 8 6 .=, :e(a%se

in(l%ding .ore signifi(ant fig%res wo%ld i.-ly .ore than the a(t%al

The (h.ert.ann -ro(ed%re for an over(onsolidated soil is il5l%strated in ig* 7*1#:* I it is s%s-e(ted that an over(onsohdated s1I 1s :eing tested, then it is good -ra(ti(e to follow the test -ro(ed%re s%ggestedin e(* 7*! and ig* 7*11* A (y(le of -artial %nloadint and reloading isshawn in Eig 7 J #: aod in Eigs 7 7a, :, aod e Ihe average slo-e of the

s U



8.9 Predlctlon of Al4Et Cll9,lrclallon Cur)N

re:o%nd5reload (%rve esta:lishes C,* Toe re.aining ste-s in the (h.ert.ann -ro(ed%re are as follows9

t. Calettlate the initial void ratio e > 'raw a hori&ontal line fro. e1 , -arallel to the log effe(tive stress a+is, to the e+isting verti(alover:%rden -reKss%re

> This esta:lishes (ontrol -oint l, as shown

:y triangle 1 in ig* 7*1#:*

$* ro. (ontrol -oint 1, draw a line -arallel to the re:o%nd5reload(%rve to the -re(onsolidation -ress%re o4. This willesta:lish(ontrol -oint $, as shown :y triangle $ in ig* 7*1#:*

#* In a .anner si.ilar to that %sed for the nor.ally (onsolidatedsoil, draw a hori&ontal line ro. a void ratio eF%al to *2$e*Where this line interse(ts the la:oratory virgin (o.-ression(%rve L, esta:lish a third (ontrol -oint, as shown :y triangle # inig* 7*1#:* Conne(t (ontrol -oints I and $, and $ and # :ystraight lines* The slo-e of the line 9 0oining (ontrol -oints $ and# defines the (o.-ression inde+ C*, for the field virgin(o.-ression (%rve* The slo-e of the line 0oining (ontrol -oints 1and $ of (o%rse re-resents the re(o.-ression inde+ C,* Ane+a.-le of a field (o.-ression (%rve is shown in ig* 7*7(*

E9A3PE 4.16

(215n:

Toe void ratio vers%s -ress%re data shown :elow* Toe initial void ratio is*!$, and the e+isting verti(al effe(tive over:%rden -ress%re is 1# <Pa*

Moid Ratio Press%re <PaB

*!7 $*"61 *"! 1*"#$ $*"# 1*" $*"2$

*"$# $*!2 2*1 7*22 1"*2" "00*26$ 1*# $

************K,K5d******9****** K 3 * 555555

1



--------e,D ;.;22

Z

334 Coneollda'on and Coneolldatlon &etlleenta

R5FG25=:a. Plot the data as e vers%s log a4c5b. Eval%ate the over(onsolidation ratio*(* 'eter.ine the field (o.-ression inde+ %sing the (h.ert.ann

-ro(ed%re*d. I this (onsolidation test is re-resentative of a 1$ . thi(< (lay

layer, (o.-%te the settle.ent of this layer 2 an additional stress of $$ <Pa were added*

S3lG423n:

a* The data is -lotted in ig* E+* 7*1"*

Effe(tive (onsolidation stress, o4,., <PaB

$2. EY. 8. &646 3=225= >l24l 3 S3=56n 6n= K2, 90.



8.3 S3ll P3ll5> 33+

:* The given val%e of is -lotted on the gra-h, and the Casagrande (onstr%(tion -erf or.ed to eval%ate o4. A val%e of 16 <Pa is fo%nd*o4 16

8CR / , / -/ 1*2"Rv 1#

Th%s the soil is slightly over(onsolidated*(* Using the (h.ert.ann -ro(ed%re for over(onsolidated (lays as given

-revio%sly, (ontrol -oints 1, $@ and # are esta:lished, as shown 2n ig* E+*7*1"* The val%es of Cr and Ce are eval%ated dtre(tly fro. 1g* E+*7*1" over one log (y(le* cr *"11 ......# *76 *$$, and ce *#25 *$!$ / *$"$* Note that cr 1] of ce.:

d* Using EF* 7517: , the settle.ent is (o.-%ted9

*$$ 1 B.log

16 *$"$ l B l 1# ` $$ 1

*!$ 1$ 1# *!$ . og 16

/ *$ .

*272 .

5 * ,.X, *

8.O SOIL PRO$ILES

In Ta:le 751 we list sorne of the (a%ses of -re(onsolidation 2n soilde-osits* In this se(tion, we st%dy sorne ty-i(al soil -rofiles fro. vario%s

-arts of the world and indi(ate their -re(onsolidation stresses as well as

their effe(tive verti(al over:%rden stresses with de-th* These over:%rdenstress -rofiles were (al(%lated 0%st li<e those of Cha-ter !, %sing thedensities and thi(<nesses of the soil layers as well as the de-ths to thewater ta:le* To -erfo.1 a detailed settle.ent analysis, ty-i(al -rofiles s%(has these are esta:lished for the -ro-osed site and are :ased on s%:s%rfa(e.vestigahons, %ndist%r:ed sa.-ling, and la:oratory testing* The ty-i(alsoil -rofiles are -resented in igs* 7*12 thro%gh 7*17*

.j

0

$



W.-- -+0 -10$0 1 +0 2_0$0 --

ill

si l ts, (l ays

tiff yel lowBday D - #] avg*

B

of t :l %e (lay9

enses

'ense sand, gravel til l

la B late or shale :edro(<

+0 100 1+0 200

ilty sand

*

2oft sensitive

E gray silty (lay@

*.e..B

"

o(*(as* shellsand sand sea.sI -1+

n

7

ilty sand

$2. 8." O15JG=5n 6n= N53n>3l2=6423n >45>> N32l5> 3 62n5l6> 3 45 B3>43n 656: 6 M>42 N3D5 >46423n 645 C6>66n=5 6n= $6=G,9""; J A 9) 45>4 >5423n, P34>3G4, %H 645 L6==, S*.

331

a

(*a



@;

r7 r/st

laI, Gss/re

an silt7-la7P9 -`-12w -1;;-1`;\

;

a1 > a P6

o $ 2 60

$

"

*.e..,B

Cl

7

1

ln36n2 l626l 6n=N3>4-l626l l6PI 5257W 5251]

6

$2. 8.) O15JG=5n 6n= N53n>3l2=6423n N32l5> 3 4D3 SD5=l>l6>: 6 S6-E=5J 45>4 5l= n56 S43n3l 645 H3l 6n= H3l4,16!!B@ J K6l2Y 45>4 >245 645 H3l4 6n= H3l, 16!6B*

.



o 1

9

,

<Pa B20 30 2 +0

Q W.11

_2

*.e.. #

'@

'"

a

Mery sof tf iss% redgreyish5green

7 (lay shel l (ontentin(reases withde-th B

U

'4<

PI -90 'a B

90 , < Pa B

o +0 100 1+0 200 2+0

(lay@ silt sea.s

E

*(e*

@ of t, dar< ra

si lty (layPI 525"

:B (lay

$2. 8. O15 JG =5n 6n= N53n>3l=643n >45>> N3l5> 3 62n5l6> n56 B6n3, T62l6n=: 6 B6n3-S266 2D6 645 E2=56n= H6lnJ5 l9* J A>26n ln>424G45 5 T55l6l6 645 M3, B6n=,6n= %5l>3n, 9*.

2

o

'



* 5 D55 55**t5 D5DDDDDD **** D5D 5D55555555 D 55555DD



9 P6

o $ 2 " 7 1

PP QSP & G>4

$ :.>

· ·E

2 !" S34, >5n>24215***

'. >2l4 l6o * l65 >2l46. 6n2n 43

" . PP D24 =5N4

7 <

1

,Q .6P .X

6

PI 515$

, a P63 1 1 $

S6n=

$ (6-J3Dn>2l4 l6

2 S34 6 Dn 5"57]

------.2 HQ >2l4 l6"

E7 el., a

*ae* 1

tel

(6 >2l4 l6

(6 l6

PI 5$Dn 5]

C1B PI 5$!5#2o

1$ -Tl

12

Dn 5!56]

(6 >2l4 l61" 51 5$2Dn 52!5"]

17 .X

$

:

$2. 8. O15JG=5n 6n= N53n>3l2=6423n >45>> N32l5> 3 L65C6Nl62n =5N3>24> L6G5n426n 3 L5=6 l6> 3 E6>45n (6n6=6: 6S62n4-AlJ6n, @GgJ5, 45>4 ll> 645 L53G52l, 54 6l., 986; J C. $. S.(l3G5>45 45>4 645 B33G 6n= L53n6=>, 9*.

.Q

,*C1B

'le

-



< vo 1 6N3 ;OPaV

o +0 100 1 +0 200 2+0 RGJJl5 2lU

6n >6n

f55525555551

1 f55`51 5

Z C263>2l4 l6I -11-16

*.e., < >3o

oCJ

Dn -8-*

20

30

6

0 ,a lP6

3 1 200 300 2 +00

S6n=

10

E

*e

H.,

20

30

< >3o

M5=2G 6>2l4 l6Dn -*" 61.

55555R5555559U

J

$2. 8.8 O15JG=5n 6n= N53n>3l2=6423n >45>> N32l5> 3 l626ll65 l6> 5D35= 42lld 3 45 C263 656: 6 C263 ?L33N? 645 =646 3 P3. J* O. O>45J5'> 6=G645 >32l 56n2> l6>>, %34D5>45n n215>24, 9; J H63n=, In=26n6 645 O>45J5, 9!.

#a*

0

H.o



8. APPRO+I MATE METHO&S A%O T7PICAL VALES O$ COMPRESSIO%I%&ICES

4e(a%se of the ti.e and e+-ense involved in (onsolidation testing, itis so.eti.es desira:le to :e a:le to relate the (o.-ression indi(es to thesi.-le (lassifi(ation -ro-erties of soils* These relationshi-s are also (o..only %sed for -reli.inary designs and esti.ates and for (he(<ing thevalidity of test res%lts*

Ta:le 75$ is a list of sorne -%:lished eF%ations for the -redi(tion of (o.-ression indi(es A&&o%&, /ri&e<, and Corotis, 16!"B*

TABLE 8-* S3n5 EN26U EFG6423n> 3 Ce 6n= CeY>

EF%ation Regions of A--li(a:ility

Ce *! LL 5 !BCp - *$7e0 *7#Ce 1!*"" S 1 5 w,,$ ` *6# S 1 5# wn

l*# + 1 5 t *ce 5 l*1eo 5 *#Bce /- *#$X - *$!B

ce 5 .12F eo 5 *B

Cp ?? .12e1 *1!ce *l wn

Re.olded (laysC:i(ago (laysC:i(ago (lays

Al2 (laysInorgani(, (ohesive soil@ silt,

so.e (lay@ silty (lay@ (lay8rgani( soils5.eadow .ats, -eats,

and organi( silt and (lay

oils of very low -lasti(ityAli (laysC:i(ago (lays

As s%..ari&ed :y A&&o%&, /ri&e<, and Corotis 16!"B* Note9 (n 5 nat%ral water (ontent*

Ter&aghi and Pe(< 16"!B -ro-osed the following eF%ation, :asdon resear(h on %ndist%r:ed (lays of low to .edi%. sensitivity9

Ce / *6 LL 5 1B 75$1B

whi(h has a relia:ility range of a:o%t k#]* This eF%ation is widely %sed,des-ite its wide relia:ility range, to .a<e initial (onsolidation settle.entesti.ates* Toe eF%ation sho%ld not :e %sed where the sensitivity of the (layis greater than 2, if the LL is greater than 1, or if the (lay (ontains a high

-er(entage of organi( .atter* orne ty-i(al val%es of the (o.-ressioninde+, :ased on o%r e+-erien(e and the geote(hni(al literat%re, are listed inTa:le 75#*

8f ten, C, is ass%.ed to :e ] to 1] of Ce. Ty-i(al val%es of C,range fro. *1 to *# Leonards, 16!"B* Toe lower val%es are for (laysof lower -lasti(ity and low 8CR* Mal%es of C, o%tside the range of * to* sho%ld :e (onsidered F%estiona:le*

#21



#2$ C3n53ll=54l3n 5n= C3n>3ll=54l3n S544l55n4>

TA,E 8-! TN26l V6lG5> 3 45 C3N5>>23n ln=5Y Ceoil

Nor.ally (onsolidated .edi%. sensitive (laysChi(ago silty (lay CLB4oston :l%e (lay CLBMi(<s:%rg :%(<s:ot (lay CHB *

wedis: .edi%. sensitive (lays CL5CHB1

Canadian Leda (lays CL5CHB ,

Ge+i(o City (lay GHB8rgani( (lays 8HBPeats PtB8rgani( silt and (layey silts GL5GHBan ran(is(o 4ay G%d CLB

an ran(is(o 8ld 4ay (lays CHB

*$ to **1 to *#*# to *O 5 to*" 1 to# lto 2! to 12 and %-1 to 11* to 2**2 to 1*$

*! to *64ang<o< (Jay CAB 04

8 * STRESS &ISTRIBlTIO%

In the -revio%s se(tions of this (ha-ter when we (al(%lated settle.ents, the in(rease in stress Qlo (a%sed :y an a--lied load was given* Inthis se(tion, we shall show yo% how to est;.ate the stress in(rease in thesoil d%e to :o%ndary or s%rfa(e loads*

%--ose a very large area s%(h as a s%:division or sho--ing .all is to

:e filled with seve1al .et1es %f sele(t (o.-a(ted .aterial* In this instanee,the loading is one di8ensional, and the stress in(rease felt at de-th wo%ld :e 1] of the a--lied stress at the s%rfa(e* However, near the edge or endof the filled area yo% .ight e+-e(t a (ertain a.o%nt of atten%ation of stress with de-th :e(a%se no stress is a--lied :eyond the edge* Li<ewise,with a footing of li.ited si&e, the a--lied stress wo%ld dissi-ate rather ra-idly with de-th*

8ne of the si.-lest .ethods to (o.-%te the distri:%tion of stresswith de-th for a loaded area is to %se the to 1 F#1: 8ethod. This is ane.-iri(al a--roa(h :ased on the ass%.-tion that the area over whi(h theload a(ts in(reases in a syste.ati( way with de-th* in(e the sa.e verti(al

for(e 1s s-read over an in(reasingly Iarger area, the %.t stress de(reaseswith de-th, as shown in ig* 7*16* In ig* 7*16a, a stri- or (ontin%o%sfooting is seen in elevation view* At a de-th M , the enlarged area of the

faating in(reases :y &Q$ oo ea (: side I:e width at de-th M is then ` *and the stress <M at that de-th is

loadF1/ -----

M 4 ` & B S laoF + 1B

4 ` & B S l

75$$B



!

DD D 55D 55 D 5555DDDDWD wWWDDWDWDDDWDD5DW 5DDDDD5 5D 5DD5DD5WD55D D 555 D=3=3===DD 55D 5DDD

a 1 tre (ltrl#utlon 343

-

8 +

B +

al tri- 3342n.

-

3 o 4L

4

t, ess 11 th 2> -lane at de-th , o, 4 ` &l L ` &l

$2. 8.9 T5 *: 6NN3Y26423n 3 45 =2>42JG423n 3 15426l>45>> D24 =5N4.

where o is the s%rfa(e or (onta(t stress*4y analogy, a re(tang%lar footing of width and length % wo%ldhave an area of = ` B 6 ` B at a de-th M , as shown in Eig 7 16h The(orres-onding stress at de-th M wo%ld :e

load

4 M :F % M : 4 M :F % M :75$#B

E+a.-le 7*1! ill%strates the %se of the $9 1 .ethod*

tG



2 8Gl! 2 B

...f.

oC9)

1

lnitial

2; stress, aS

No *E=

E9A3PE 4.1M

(215n:

Two .etres of fill F p / $*2 GgQ .#B are (o.-a(ted over a large area* 8n

to- of the (o.-a(ted fill, a # + 2 . s-read footing loaded with 12 <N is -la(ed* Ass%.e that the average density of , the soil -rior to -la(e.ent of the fill is 1*"7 GgQ.# The water ta:le is very dee-*

a* Co.-%te and -lot the effe(tive verti(al stress -rofile with de-th

-rior to fill -la(e.ent* : Co.-% te and -lot the added stress, I#J.a , d%e to the fill(* Co.-%te the additional stress with de-th d%e to the # S 2 .

footing w hen the footing :ase is -la(ed 1 . :elo w the to- of thefilled gro%nd s%rfa(e* Use the $9 1 .ethod* Ass%.e weight of footing -l%s :a(<fill eF%als weight of soil re.oved*B

$2. EY. 8.6



8.12 Stre-- Flatrlbutlon 345

---B # . ooting withload 12 < N@ area # + 2.

&

&Q$ 55t K # . 55515,1$51

# & 5D55555555

1B

&

$BD #B 2B

Area

B

*ia&B

. B 4 &B L &V ;2l < Pa B

o # 2 1$ 11!1 2 $ !

# " ! 2$ ##2 ! 7 " $ 7 6 * * !$ 16" 6 0 6 1"! 0 11 11 1#7 11 1$ 1#$ 116 1$ 1# 1" 6

1 1# 12 17$ 7

Note9 & ta<en :elow :otto. of footing*

$2. EY. 8.J

S3lG423n:

a* J%st as yo% did in Cha-ter !, the initial effe(tive stress distri:%tion is(al(%lated and -lotted in ig* E+* 7*1!a* Toe stress is &ero at &ero de-th and## <Pa at a de-th of $ . ( p[ / 1*"7 + 6*71 + $ / ## <PaB*

b. The added stress d%e to the $ . fill is $ + $*2 + 6*71 / 2 <Pa* This is shown in ig* E+* U !a :y the line -arallel to the in sit%

verti(aleffe(tive stress line* Noti(e that at any de-th, the additional stress d%e tothe fill is a (onstant 2 <Pa :e(a%se the fill is large 2n areal e+tent and th%s1] of its infl%en(e is felt thro%gho%t*



Z1

Conolldatlon and Conolldatlon &ettleenta

(* The (onta(t stress :etween the footing and the soil eF%als the(ol%.n load, "00 <N, divided :y the footing area, ! + 2 ., or 1$ .$, or

o K 5 load K 5 12 <N K 5 l l <NQ.$ or <Pa> area 1$ .$

Using the $9 l .ethod, a ta:%lation of how the stress (hanges with de-th [ is shown in 1 ig* E+* 7*1!:* The (hange in stress, a&B, in (ol%.n 2 isadded to the (hange in stress d%e to the fill in ig* E+* 7*1!a* l4 (an :e seenthat the stress d%e to the footing di.inishes F%ite ra-idly with de-th*

Toe theory of elasticity is also %sed :y fo%ndation engineers toesti.ate stresses within soil .asses* Toe soil does not ne(essarily have to

:e elasti( for the theory to wor<, at least for verti(al stresses@ only the ratioof stress to strain sho%ld :e (onstant* As long as the added stresses are well

:elow fail%re, the strains are still a--ro+i.ately -ro-ortional to stresses*In 177, 4o%ssinesF develo-ed eF%ations for the state of stress within

a ho.ogeneo%s, isotro-i(, linearly elasti( half5s-a(e for a point load a(ting -er-endi(%lar to the s%rfa(e* Toe val%e of the verti(al stress is

#& #B

aM 555555

31& F r & $ BQ$

75$2B

where \ -oint load, M de-th fro. gro%nd s%rfa(e to the -la(e where aM is desired, and

h1i&ontal distan(e f ro. -oint load to the -la(e where aM isdesired*

EF%ation 75$2 .ay also :e written as

75$B

where 0 is an infl%en(e fa(tor whi(h (o.:ines the (onstant ter.s in EF*75$2 and is a f %n(tion of r Q M.

These terrns are ill%strated in ig* 7*$a@ val%es of ' 0 vers%s r Q M areshown in ig* 7*$:* 4o%ssinesF also derived eF%ations for the radial,tangential, and shear stress@ these (an :e fo%nd in .ost advan(ed te+t:oo<son soil .e(hani(s* Note that the eF%ation for M is inde-endent of the

* .aterial@ the .odl%s does not enter into the eF%ation at all*4y integrating the -oint load eF%ation along a line, the stress d%e to a

fine load for(e -er %nit lengthB .ay :e fo%nd* In this (ase, the val%e of the



o,

;.2o D -S- N

;.BN

;.2

Na D

Nw D

B23

g,+ i)2 J'2 13

g, + 2 i)2 JB'2

;.1

555555 D5D5DDDDD55 5**------- **-?-? ?''? ?? 555 5555 55 5

--0--al

rQ&

J

$2. 8.*0 6 &52n2423n 3M5> G>5= 2n EF. 8-*) 6n= EF. 8-*;

J 5l6423n>2N J54D55n ' 0 , '( , 6n= r/ M 3 6 N32n4 l36= \645T6l3, 9"8.

!"

* J



348 C3n>3ll=54l3n 6n= C3n>3ll=64l3n S544l55n4>

verti(al stress is

75$"B= $

n ,. X X , , X X -'* *** K*** K $ *****K ***K*K 5, 5*5*W5

x & $ r $B1$ see ig* 7*$aB*

tFUali8ll i8f Lile ** a*J*J* *3*Bl**,a*l :SL .!,! a.1 v a**#M K

11

** **

The ne+t logi(al ste- is to integrate a line load over a finite area* New.ar< 16#B -erfonned the integration of EF* 7*$: and denved thefollowine9 ea%ation for the verti(al stress %nder the (o.er of a C%i!"v /ad$d !$ca%Ca! a!$a:

X'a 2!!

8nF 8 n 1B11$F 8

n $B

+------"E %E "E %E ( "E %E

8nF 8 n 1B11$

ar(tan K 75$!B

where L/ s%rfa(e or (onta(t stress,/ v .. QL3l

+ '

n y / M , and** ** ,* , 3I *,* 'I .. 'I

75$6B

, #..

V , R %@@110%1 ailU W lU lfl Ml lh= ,J '?'?'?' l W L.

The -ara.eters 8 and n are inter(hangea:le* ort%nately EF* 75$! .ay :erewritten as

, where 1/ an infl%en(e val%e whi(h de-ends on 8 andn.

F \ Q 3lf

8 7

Mal%es of + for vario%s val%es of 8 and n are shown in ig* 7*$1*

E+AMPLE 8.8

(215n:

The ! S " . re(tang%lar footing of E+a.-le 7*1! is loaded %nifor.ly :y <Pa*

R5FG25=:

a* ind the verti(al stress %nder the (o.er of the footing at a de-thof $ .*



- 5 5555555 555555DD5555D5D5D5D5D5

-

y *" 1 $ # 2 " 7 1 *$7 *$7

S - L.

S 8 *$" / $*g

*$" / oo

a, - 1*7K - / #*

L36= 6X N5 Gn24 3 656 *$2,,2 *

-,*

-1*$ $ - 1*"

& y11 .,,. 1*2S

/ ; n / *$$ 3===

1-

/

*$$

6n= n 65 2n456n56Jl5 -*,*** 9n / ,2.

/ *7

n

a. / Fn

I

n-nA'QQQQ

* - -- '26 n nn

1 1 1

. IH

*1 *$ *2 *1 *$ *# * =/ / 0. 1 I' 11

*1" Q / *" *1"=

2 ****** *****12

Q / * *12iZ, Q

9 1 =Q *1$

/ *2 *1$.

- U f 'UU- *1 5 111 1 .. *14l

<TI T,U # ? ¡.,......-

/ $*% n.n2:2n nA

a*, + + . .:;:¡

3@99 'Q Q + / *$ -V--

rJ/ + #'

!J ...2

v*vv

*2 + + , ... *2

!P 1!*,Q= .... -*$ ..-- / * 5 5^5 #

*$

3 l , '#

/ 8*8 o*1 *$ *2 *1 *$ *# * *71 $ # 2 " 7 1

V6lG5 3 n

$2. 7*$1 lnlG5n5 16lG5 3 15426l >45>> ,Gn=5 35 3 6 Gn23ll36=5= 546nGl6 656 645 .S. %61, 16!1B*

55

DE

--

Z

a*, 3J

5:

=/ y / *1



341

¡: 5 5 ,._

-

5 55 5555 5 5 ...,,, 55 ---- .



%78 Conollclatlon ancl Conollclatlon &ettleenta

b. ind the verti(al stress %nder the (enter of the footing at a de-tho .*(* Co.-are res%lts with ig* E+* 7*1!a*

S3lG423n:

a. #

y $ 4%

M / $ .9 therefore fro. EFs* 75$7 and 75$6,

8= -; = * = 1*

' = - = -4 = 2

ro. ig* 7*$1, find + / *$$#* ro. EF* 75#,M / FoQ

/ $" <Pa

b. To (o.-%te the stress %nder the (enter, it is ne(essary to divide the # + 2. re(tang%lar f oot.g .to to%r se(ttons of 1* + $ . . st&e* ind thestress %nder one (o.er and .%lti-ly this val%e :y 2 to ta<e into a((o%ntthe fo%r F%adrants of the %nifor.ly loaded area* We (an do this

:e(a%se* for an elasti( .aterial, s%-er-osition is valid* V & 1* 2

y $ 2 %

V 1*

n $ &$ &$ M $

Toe (orres-onding val%e of + fro. ig* 7*$1 is *16* ro. EF* 75#,

o M 5 L1 l 5 2 + 11! + *16 5 !2 <Pa

I:%s the verti(al stress %nder the (enter for this (ase is a:o%t three ti.esthat %nder the (o.er* This see.s reasona:le sin(e the (enter is loadedfro. ali sides :%t %ndet the (ornet i t is not*

(* At a de-th of $ . :elow the # + 2 . footing, the verti(al stressa((ord.g to the $9 I theory 1s 2! <Pa see 1g* E+* 7*1!:B* Th1s val%ere-resents the average stress :eneath the footing at 5$ .* The average ofthe (o.er and (enter stress :y elasti( theory is $" !2*$BQ$ / *1 <Pa*



4.1 &tre..(lalrl#utlon %71

Th%s the $9 l .ethod %nderesti.ates the verti(al stress at the (enter :%toveresti.ates oM at the (o.ers*

%--ose we want to find the verti(al stress at sorne de-th M outside

the loaded area* Under these (onditions we .erely fa:ri(ate other %ni5for.ly loaded re(tangles, ali with (orners a:ove the -oint where theverti(al stress i s desired, and s%htra(t and add lheir stress (ontri:%tions asne(essary*

E9A3PE 4*16

(215n:

A 2 + 1 . area %nifor.ly loaded with 1 <Pa*

R5FG25=:

a* ind the stress at a de-th of . %nder -oint A in ig* E+* 7*16*b. ind the stress at -oint $ if the right half of the 2 + 1 . area

were loaded with an additional 1 <Pa*

S3lG43n:

a* Refer to ig* E+* 7*16 and the n%.:ered -oints as shown* Add there(tangles in the following .anner for loaded areas and 5 for %nloaded areasB9 A 1$# 5 A 1"2 5 A!# A72 res%lt in the loadedre(tangle we want 7"$!* ind fo%r se-arate infl%en(e val%es fro. ig*7*$1for ea(h re(tangle at a de-th of .* then add and s%htra(t t:e (oro-%ted stresses* Note that it is ne(essary to add re(tangle A72 :e(a%se itwas s%:tra(ted twi(e as -art of re(tangles A IG and A!#*

ind stress % nder -oi nt A

$2. EY. 8.9

.j



Z

#$ C3n>3ll=64l3n 6n= C3n>3ll=64l3n S544l55n46

The (o.-%tations are shown in the following ta:le*

?1t).` A I $# 5Al"2 5A!# ` A72

Iora l o M 5 $# 7 $ 6 5 $ " k 17 8 5 8 # <Pa

:* Wnen re(tangle !761 is loaded with 1 <Pa and re(tangle 6"$1 is loadedwith $ <Pa, re-eat -art aB a:ove to o:tain the stress %nder -oint A at . de-th for the entire re(tangle 7"$! loaded with1 <Pa* Ne+t, a se(ond set of fo%r re(tangles wo%ld have to :e (al(%lated

0%st as for -art aB a:ove :%t only re(tangle 6"$1 wo%ld :e loaded with 1 <Pa@ the others wo%ld :e 51 <Pa* The total oM eF%als *# <Pafro. -art aB -l%s $#*7 5 $1* 5 $#*$ ` $*" or * <Pa*

Th%s it is -ossi:le to find the stress at any de-th M , in or aro%nd a%nifonnly loaded at ea or even %nder a ste- loaded at ea, :y %sing the -ro(ed%res o%tlined in E+a.-les 7*17 and 7*16* Re.e.:er that a new setof (al(%lations is reF%ired for ea(h de-th where >& is desired*

i.ilar -ro(ed%res are availa:le for verti(al stresses %nder unifor8ly

loaded circular areas. Use ig* 7*$$ to o:tain infl%en(e val%es in ter.s of Q r and M Q r , where M de-th,

r / radi%s of %niforrnly loaded area, / hori&ontal distan(e fro. the (enter of the (ir

(%lar area, and/ s%rfa(e (onta(t -ress%re, in <Pa*

E+AMPI E 8 *0

(215n:

A (ir(%lar tan< #*61 . in dia.eter is %nifor.ly loaded with 11! <Pa*

V 1 1 1 2 y 1 2 2 2&8 .., / M # # $ I% > y / M $ I 1 I+ *$#7 *$6 *$" *1711, $#*7 5 $*6 5 $*" ` 17*

L



·

h-1

1

I, stress i -er(ent of s%rfa(e (onta(t -ress%re

*1 *$ *# *2 *" *71* $ # 2 " 7 1 $ # 2 " 7 11

o 1 1 1 1 -( 11 1 *.l- ---- .... X

****J r5. +

r5*** 54,,,.

5 # 35R $* l*K. K

.......2.... $* ! 'F 1 ) Q .,. ... :2= +; o o

.......... l?--,.. I'... . Q /= 0*J**JK3

*.... 55r55*** ***K 2* ', ' .- ' **** r55***** *1 ? '- 1 Q Q e_ 5 1,B,5**,

=3= ,r55** l t5 313 3 /,Y, '?T# = 9 *!

0-...... # "* W **************

- ?' -U?'- I ., 1 1 1 12 13= 1 1 5 Note9 N% .:ers on (%rves

'.. 2 ) Q 11 X i nd i(ate offset distan(esD5 3 1 7*B ? ) ,X i n radi i +Qr 5 3 I ? ' 1 ,D , D, , , 1 1 1 11 11

[t * R ' + 2, J 5-U

e::

v9

9*K

OD9@ , , , J J Slv.S

! 1'(')

N 1* U 1 Q , 1 1 1

W r55 ! 35! , * ? Q '

7 Q r J 3f/J

6 nK0nnKl AB P? ? ? ??'??

... J599 5Fo

;.?, ?,',&''4?S'?? a,+

,a l 1 1U 1 ll l AlU0l8lUV 1 1 1 1 1 11 11 1 1 1 11111a,& I S F

DCII

$2. 8.** lnlG5n5 16lG5>, 5YN5>>5= 2U N55n465 3 >G65 3n464 N5>>G5, L , 3 15426l>4 Gn=5 Gn23l l36=5= 2Gl6 656 64 $3>45 6n= Al12n, 9)", 6> 245= J .S. %61,9.

o Q '-. ,.? ¡

! Q . O

M

T Q Q

1

D



354 Con4811detlon end Con4811detlon &etlleenta

!euired:

a. Co.-%te the stress %nder the (enter of the tan< at a de-th of $ .

b. Co.-%te the stress %nder the edge of the tan<, also a de-th of$ .*

S3lG423n:

a. Ref er to ig* 7*$$*& $ .! / #*61Q$ 1*6

/ 8@ then M / r / $Q1*6 / 1*$

/ r / Q1*6 8* ind + / *"#* Using EF* 75# we o:tain,

oM L / / 11! S *"# !2 <Pa

This (o.-ares e+a(tly with o& / !2 <Pa at the (enter for a ! + " .re(tang%lar area in E+a.-le 7*17* In :oth (ases, the area is 1$ . *

b. Again, ref er to ig* 7*$$* or the edge of the (ir(%lar loaded area9

& $ .r / 1*6

/ r / 1*6 . M / r / $Q 1*6 / 1*$

/ r /

1* ind + / *##@ then %sing EF* 75

#,

M 5 B I 5 11! + *## 5 #6 <Pa

This (o.-ares with oM / $" <Pa at a (o.er for a # S 2 . %nifor.lyloaded re(tang%lar area* In :oth (ases, the area of the loaded area is thesa.e*B

Another %sef%l integration of the 4o%ssinesF eF%ations is thetra-e&oidal loading shown in ig* 7*$#, whi(h .odels the loading (a%sed :y a long e8ban!8ent. Infl%en(e val%es are in ter.s of the di.ensions a

and , as shown . the fig%re* I the e.:an<.ent 1s not .f1r%tely long,then %se ig* 7*$2 together with ig* 7*$1 to re-resent different load(onfig%rations*

1

.



aQ&*1 *$ *2*" *1 *$ *2 *" 1* $ # 2 " 71*

*T r1

5$*

1*$(*5 5

5*

?? .... % ***on - 1*2 9@Z 3! .

... . :Q& 5 1* X ...

***** ., .,*6

*, 1,&77&& 113

*2

*7*! ..... 5

, ***?

*, X7. . ,,,

*2

5 55 , 1?' 1, 9 9'=/L

*fl**** 1Q + j *#

, Q +

- :Q& 8*.... + +

:;Q , +

a*,3 *# . - .., ,+

+ *#

a*,a, *$

* ****

5*2 == ?

., ,, +

,*,, Q

,,

*$

F.:L 1Q

999i

5

e

1!

*# l..., J + Q 1

*$ 55 .+

*$Q J $ # 2 " 71*

*$ + ( .,

C'*1.... +

*1L i** J

*1 3Q*1 *** .Q , c

I J- 0 1

,

ZZZ = ==33353535 ,v,,*,, % ni t load of

* :Q& 8*

e.:an < .ent&-

e,

,

%&

.' ? 5

a, 1

=> %J 3 3*1 *$ *2 *" *1 *$ *2 *" 1*

Mal%e of aQ&

$2. 8.*! lnlG5n5 16lG5> 3 15426l >45>> Gn=5 6 15 l3n5J6n- 5n4; l5n4 33 3 .S. %61, 9, 645 O>45J5,9).

355

., ., ,,,,

--= 1*13

?

?'+

5L,

'

L#05

K



*J



*1 *$ *# *2 *" 1* $ # 2 " 7 115555

5t55515 5P l

r 11

QQ**** i3 *55*K , K **o*$ ,---,--,--,---,-¡l --,--,--...---:--------,---.-:::::::::::.::::..-T'?'T-?'I o*$

V6lG5> 3 n X .--

4g.vB K51515Q`5 5 1,,* 5

?55FoI 6 L / = *$ 5 >3*l.450@ + '44-5,**5!36r #5-4---4--4::/.-;;.. r5@t@@t*ai5i551 *$

& . LQ& 3! @

,*n BQ 1, + Q $ 55

55 a , l S F - - 'Q 6 9 ! 1* 555555D`5Dt55t55t5=1

o* 1 5 Q@3Q 9 ?? / *1

DJ1Q ,+ ' Q

ai::¡

5ZZ@*1CG

1*--*-----*-*--t-----K-*--*-O

e9C::¡

;¡::

5e9

, Q 7 / 1! .R ZK

/7,·) / 1 / lQ 1 l.- -- 1

- .,X P. - ' - ' -

*----. ,.?'2?',:,I@L:1l? QW/ ., # UQL.,,, B5n564 3n5, o *

1 6G5> 3 n .G ------*--*--*--*--*---*--*--*-O-*-*---&&-*--*--*-*---4-*-*-*-*-*-G

B5n564 3n5, O ' .,,.,,.... K*5P t Q

¡,,,U:: - .Q 5

*#5 K

D55.¡5

..4: X:4:4jj4:4::2

*7

*"5 1 *, K K @@,,**K **5 K25$*o

*"

*2 55 5 5 5 --P::.::.,,....... :..-:;.... *5*$ 5 >KZ, *2-- Q*519*

' Z,,***, *****5 3=

*****5=3 * *

,5*******,K K* r9@955*$ *,** *5 5 i *1 `55*9*9**5`5555`55155`5`5`5`5I *$

555 5 *9999,***i*5- 0.0-.,l.-------------l---

--- -- .... - .......... - l0:;: .1....-------.._-----....0..G --------. ._......._.8--8--_. & >

*1 *$ *# *2 *" 1* $ # 2 " 7 1

V6lG5 3

$2. 8.*" lnlG5n5 16lG5> 3 15426l >45>> Gn=5 45 3n5> 3 6426nGl6 l36= 3 l2245= l5n4 645 .S. %61, 9.

358

1

-?

55s5 5

55

, 5



, -- . 55555555555D5555 5D5D555DDDDD5D555DDDDD55D5D5555555555

E9A3PE 4.1

,ven9

A highway e.:an<.ent, as shown in ig* E+* 7*$1* Ass%rne the averagedensity of the .aterial in the ern:an<rnent is $* GgQ.#

R5FG25=:

Co.-%te the verti(al stress %nder the (enterline at de-ths of # and " rn* *

irst, (al(%late the a--lied s%rfa(e stress B and the dirnensions of thee.:an<.ent in ter.s of a and b.

L pgh / $* GgQ .# S 6*71 .Qs$S # . 6 <Pa

ro. ig* 7*$#, and ig* E+* 7*$1,

b 2 8

a $ S # . " .

Ne+ t, (al(%late the verti(al stress for M / # .*a/ M "Q# $

b/ M Q# 1*"!

15555s5 5s5501

* 1

! K

X2X l

$2. EY. 8.*

k2



Z1

358 Conolldatlon and Conolldatlon &ettleenta

ro. ig* 7*$#, + *26,M B / / 6 <Pa S *277 $6 <Pa

for one5half of the e.:an<.ent, ^fr 7 <Pa for the entire e.:an<.ent*Th%s at this shallow de-th oM is al.ost the sa.e as the (onta(t stress*

inally, (al(%late the verti(al stress for [ / " .*

a/ M "Q" / l

b/ M 5 Q" 5 *7#

ro. ig* 7*$#, + *22,

oM / B / / 6 <Pa S *22 S $ $ <Pa

Now and then it :e(o.es ne(essary to (o.-%te the verti(al stressd%e to an irreg%larly sha-ed loaded area at vario%s -oints inside andQor o%tside an area* To fa(ilitate (o.-%tations, New.ar< 162$B develo-edinfluence charts fro. whi(h the verti(al stress and even the hori&ontal andshear stressesB .ay :e (o.-%ted* These infl%en(e (harts are :ased on4o%ssinesF3s theory, altho%gh si.ilar (harts have :een -re-ared for theWestergaard theory, to :e dis(%ssed shortly* E+a.-les of infl%en(e (harts.ay :e fo%nd in fo%ndation engineering te+t:oo<s, for e+a.-le, Leonards

16"$B and Pe(<, Hanson, and Thorn:%rn 16!2B* ig%re 75$ shows the New.ar< infl%en(e (hart for the (o.-%tation of verti(al stresses d%e to aloaded area* Thin< of the (hart as a (onto%r .a- that shows a vol(ano, theto- of whi(h is lo(ated at the (enter 8B of the infl%en(e (hart* I it were -ossi:le to loo< nor.al to a three5di.ensional s%rfa(e of the (hart, yo%wo%ld see th a t ea(h of the =areas= or =:lo(<s= has th sa8e surface a.E$.

We see only the -ro0e(tion on the (onto%r .a-@ the :lo(<s grow s.aller asthe (enter is a--roa(hed*

The (harts are s(aled with res-e(t to de-th so that they .ay :e %sedfor a str%(t%re of any si&e, in the following .anner* 8n the (hart is the lineA\. This line re-resents the distan(e :elow the gro%nd s%rfa(e M for whi(hthe verti(al stress is desired, and this distan(e is sed as the s(ale for adrawing of the loaded area* The verti(al stress is (o.-%ted :y .erely(o%nting the n%.:er of areas or :lo(<s on the (hart, (ithin the :o%ndaryof the loaded area that is drawn to the -ro-er s(ale and then -la(ed %-onthe (hart* Toe n%.:er of areas is .%lti-lied :y an infl%en(e val%e Q,s-e(ified on the (hart, and :y the (onta(t -ress%re to o:tain the stress atthe desired de-th* The -oint at whi(h the verti(al stress is desired is -la(edover the center of the (hart* E+a.-le 7*$$ ill%strates the %se of the (hart*

0



I / *1

3

S6l5 3 =2>46n5 00 /=5N4 & 64 D2 >45>> 2> 3NG45=

$2. 8.*) 4nlG5n5 64 3 15426l >45>> 3n 323n46l Nl6n5> 645 %5D6, 9"*.

359



<

E9A3PE 8.**

(215n:

A %nifor. stress of $ <Pa is a--lied to the loaded area shown in ig* E+*7*$$a*

Co.-%te the stress at a de-th of 7 . :elow the gro%nd s%rfa(e d%e to theloaded area %nder -oint R.

'raw the loaded area s%(h that the length of the line A\ is s(aled to 7 .*or e+a.-le, the distan(e $ in ig* E+* 7*$$a is 1* ti.es the distan(eA\. A\ 7 . and $ 1$ .* Ne+t, -la(e -oint A3, the -oint wherethe stress is re %ired, over the (enter of the infl%en(e (hart as shown inig* E+* 7*$$: to a slightly s*.aller s(aleB* Toe n%.:er of :lo(<s and -artial :lo(<sB are (o%nted %nder the loaded area* In this (ase, a:o%t eight :lo(<s are fo%nd* The verti(al stress at 7 . is then indi(ated :y

ov / ]1 + No* of :lo(<s 75#1B

+ infl%en(e val%e -er :lo(< *$ in ig* E+* 7*$$:B*Therefore,

31 / $ <Pa + *$ + 7 :lo(<s / 2 <Pa

All of the -re(eding stress distri:%tion sol%tions were integrations of

isotro-i( linearly elasti( half5s-a(e* Nat%ral soil de-osits do not a--roa(he&e i ea ma e 1

de-osits were fonned* :y the aggradation of alte.ate hori&ontal layers of silts and (lays* These de-osits are (alled varved c/ays, and the sol%tion for stresses at a -oint develo-ed :y Westergaard 16#7B .ay :e .ore a--li(a :le*In this theory, an elasti( soil is inters-ersed with inf initely thin :%t

.ove.ent* Westergaard3s sol%tion for the verti(al stress for a point load

380

3



ni3or8 loa, 2; IPa

,.,-

$11N

_F00

.o

11;

i,.2;

t1;

t

1 ?'0,-

a,

-2;---; - . .K @;--1o'

,**,***

A 'i.ensions in .etresB B

6

$2. EY. 8.**6 A45 %5D6, 9"*.

(T)

$2. EY. 8.**J A45 %5D6, 9"*.

* J



382 Comolldatlon end Con&olldetlon &ettleenta

for Poisson3s ratio v / 8B iso / -- -------

& ` -&

Y75#$B

is defined as the the ratio of the hori&ontal strain, T O , to the verti(al strain,

for dense .aterials* Mal%es for sat%rated (lays vary fro. a:o%t *2 to (hange

when stressed %ndrainedB is **e wntten as

(

f%n(tion of r Q M. Mal%es of ' ( are -lotted in ig* 7*$:*

7*$:* or r Q M less

:oth theories are :ased on ass%.-tions whi(h are far fro. reality* I4 of ten

tions of the Westergaard theory -ro:a:ly are (loser to reality for a layeredsoil de-osit* Toe $9 1 .ethod, (r%de as it .ay :e, is -ro:a:ly %sed a:o%t as Dof ten in -ra(ti(e as the sol%tions f ro. the theory of elasti(ity for esti.at5.g ver 1(a stresses*

A gra-h si.ilar to ig* 7*$1 for infl%en(e val%es for verti(al stress%nder a (o.er of a unifor8ly loaded rectangular area has :een -re-ared for the Wester aard (ase for Poisson3s ratio / 8 and is shown as i * 7*$"*o% %se 24 as yo% wo%ld %se ig* 7*$1*

Ta:les 752 thro%gh 75" -resent the infl%en(e val%es for verti(al stress%nder the (enter of a sLuare load, %nder the (enter ^f an infinitely long

uni or8 oa e rec angu ar area,

res-e(tively* These ta:les -resent infl%en(e (oeffi(ients for :oth the4o%ssinesF and Westergaard ass%.-tions* o% .ay find these (harts%sef%l in engineering -ra(ti(e*

I4 .%st :e -ointed o%t that on(e yo% have fo%nd the verti(al stressesfro. the eF%ations and (harts -rovided in this se(tion, they .%st :e added

to the e+isting in sit% over:%rden effe(tive stress, as was done in E+a.-le7*1!* This -ro(ed%re is ne(essary :e(a%se the elasti( sol%tions (onsider the

:alf5s-a(e to :e weightless and only the stress d%e to an e+terna loading is



.0 $

*$ *2 *" *7

%345:. 7Q&, n LQ&

a

P32>>3n'> 6423 O

0.0 0.0* *2 *" 1* $ 4 6

n

$2. 8.* lnlG5n5 16lG5> 3 15426l >45>> Gn=5 3n5> 3 6 Gn23l l36=5= 546nGl6 656 3 45 W5>4566= 453 645 &Gn6n6n= BG2n6n2, 9.

.j



TA,E 4"+ lnlG5n5 V6lG5> 3 V5426l S45>> 6 SFG65 n23l L36=5= A56

F%are area load,F -er % nit area

Q

55,,%55,,%#5

;L---P---??T

/ 'e-

L

n=5 45 C5n45 3

555 a & FI>

th, &

l lo

a/ M 4o%ssinesF Westergaard

$ *666$ *6#"1" *6672 *61661$ *66"7 *76221 *6622 *7!#2

7 *676$ *72#

2 *6"2 *!$2 *6# *"6!1#*" *66" *""6#*$ *771$ *"#6$*7 *727 *7"#$*2 *!7#$ *#$7$* *!7 *2"2!1*7 *"2!" *2$2"1*" *722 *#!621*2 *17 *#$611*$ *2$!" *$771* *##" *$1"

*" *1262 *666

*$ *177 *1$!3 * *



!8"

After '%n(an and 4%(hignani 16!"B*



<tri5 loa,Z 5er / nit area

'()*+ 8-) lnlG5n5 V6lG5> 3 V5426l S45>> n=5 45 C5n45 3 6n ln2n245l L3n S42N L36=

Width of l oad

Jo

*+, 4o%ssinesF Westergaard

00 1* 1*1 1* *66

1 *66! *616 *66" *617 *662 *777

! *661 *7!2

"* *67" *7#5"5 *67# *7#* *6!! *7$22* *6! *7!2* *6" *!72#* *62# *!"#* *6$ *!16$* *776 *"!$$* *71! *"71* *!1" *161*$ *"$2 *2271* * *#6$

*7 *2"$ *#$7* *#" *$1"*$ *1$! *76*1 *"2 *23 * *

After '%n(an and 4%(hignani 16!"B*

315

,. _



TA,E 8- lnlG5n5 V6lG5> 3 V5426l S45>> n=5 C3n5

3 6 n23l L36=5= R546nGl6 A56

o, W Fl Q \DDDDDDDDDDD::XE EE) ) E T- B --l

5

4o%ssinesF Case

%/

/ M *1 *$ *2 *" *7 1* $*

*1 * *6 *1! *$$ *$" *$7 *#1 *#$*$ *6 *17 *## *2# o*oso * *"1 *"$*2 *1! *## *" *7 *6# *11 *11# *11*" *$$ *2# *7 *1! *1$ *1#" *1# *1"*7 *$" o*oso *6# *1$ *12" *1" *171 *171* *$7 * *11 *1#" *1" *1! *$ *$$* *#1 *"1 *11# *1# *171 *$ *$#$ *$2 *#$ *"$ *11 *1" *17 *$ *$2 *$

Westergaard Case

%/

/ *1 *$ *2 *" *7 1* $*

*1 *# *" *11 *12 *1! *17 *$1 *$$*$ *" *1$ *$1 *$7 *## *#" *21 *22*2 *11 *$1 *#6 *$ *" *"" *!! *7$*" *12 *$7 *$ *"6 *71 *76 *12 *11$*7 *1! *## *" *71 *6 *1 *1$ *1#1* *17 *#" *"" *76 *1 *11" *12 *1$$* *$1 *21 *!! *12 *1$ *12 6*1!2 *16" *$$ *22 *7$ *11$ *1# *1$ *16" *$

Af ter '%n(an and 4%(hignani 16!"B*

!8



Pro#lea387

(onsidered* %rther, for sites where a layered s%:soil e+ists, that is, wherethere are large variations in the .od%l%s of elasti(ity, other sol%tions .%st

:e %sed to ta<e into a((o%nt the relative rigidities of the layers* ol%tionsto these <inds of stress distri:%tions .ay :e fo%nd in Harr 16""B andPo%los and 'avis 16!2B* These referen(es also s%--ly eF%ations andeharts for esti.ating tite h. i&ontal and shear stresses in elasti( .edia*

P!O,E3&

751* or the e vers%s log o (%rves of ig* 7*7a, (o.-%te the (o.-ressionindi(es* E+-lain why it is -ossi:le to get slightly different answers

than those shown at the :otto. of the fig%re* 75$* Merify the val%es of the -re(onsolidation stress shown in ig* 7*7a*

75#* 'eter.ine the over(onsolidation ratio 8CRB for the five fine5grainedsoils of ig* 7*7a*

752* Merif y that the val%es for the -re(onsolidation stress and the virgin(o.-ression inde+ shown in ig* 7*7: are (orre(t*

75* What is the 8CR of the (lay till in ig* 7*7(

75"* Estt.ate the -re(onsolidation stress for aB the %ndist%r:ed Leda(lay in ig* 7*7d, :B %ndist%r:ed Ge+i(o City day in Eig 7 7e eB

%ndist%r:ed Chi(ago (lay in ig* 7*7f, and dB the swelling (lays fro.Te+as in ig* 7*7g*

75!* 'eter.ine the (o.-ression indi(es for the fo%r soils of Pro:le. 75"*

757* The -ress%re vers%s void ratio data deter.ined fro. a (onsolidationtest on an %ndist%r:ed (lay s-e(i.en are as follows9

Press%re <PaB Moid Ratio

$ *6#2 *6277 *6#7

1" *6$

#$ *7!7"2 *!76

1$7 *"61#$ *!16

7 *!2$ *!61

*76

.j



3$8 Conaolldatlon and Conaoldatlon &ettleent

aB Plot the -ress%re vers%s void ratio (%rve on :oth arith.eti( and

:B 'eter.ine the eF%ations for the virgin (o.-ression (%rve andrve r %n oa ing s ar ing a a*

eB What are the (orres-onding .odified (o.-ression and re(o.5 -ression . i(es for this soil

d Est;.ate the stress to whi(h this (la has :een re(onsolidat Af ter A. Casagrande*B

%ilding is to :e (onstr%(ted on a " . thi(< strat%. of the (lay forwhi(h (onsolidation data are iven in Pro:le. 757* Toe avera e+isting effe(tive over:%rden -ress%re on this (lay strat%. is 1$ <Pa*

:%ilding is $! <Pa*

f %ll (onsolidation %nder the :%ilding load*

ay ra %. (a%se y

sti.ate t e e(rease in thi(<ness d%e to the :%ilding load if the(la had never :een re(onsolidated %nder a load eater than the e+isting over:%rden*

%sed for .a<ing the esti.ates in -arts aB and :B* Af ter A.

se.ilogarith.i( -lot, and it -asses thro%gh the -oint e 1*$1, oc /, . . .

relationshi-* Af ter Taylor, 1627*B

751 l. how that EFs* 756 and 751 are valid*

751$* The following (onsolidation test data were o:tained fro. %ndis5

tress 'ial ReadinglP6 ..B Moid Ratio

2 1$*#$ $*7$1 1$*$62 $*!6#$ 1$*1#1 $*!"62 11*$$2 $*"#17 6*# $*#1

1" "*"" 1*6#6#$ 2*$!$ 1*!""0 $*27 1*#121" $*61 1*#!2 #*## 1*2"22 2*# 1*76



Pro#lea 389

t%r:ed an ran(is(o 4ay G%d* or thts (lay, LL 5 77, PL 5 2#, Ps / $*! GgQ .# and (n / 1*!]* lnitially, the s-e(i.en heightwas $*2 (. arid its vol%.e was !*12 (.# Plot the data as -er(ent(onsolidation vers%s log -ress%re* Eval%ate the -re(onsolidation -ress%re and the .odified virgin (o.-ression inde+*

$51J* Plot the data of Pro:le. 1$, on a void ratio vers%s log -ress%regra-h* Eval%ate the -re(onsolidation -ress%re and the virgin (o. -ression inde+* 'o these val%es agree with what yo% fo%nd inPro:le. 751$ Co..ents

7512* The initial water (ontent of the sa.-le in Pro:le. 751$ is 1*!],and the density of the solids, Ps , is $*! GgQ .#

Co.-%te the wetand dry density and degree of sat%ration of the (onsolidation testsa.-le if the dry weight of the sa.-le is $*7 g* I the final water (ontent is 6*"], (o.-%te the degree of sat%ration and dry density atthe end of (onsolida tiao

751* A !* . thi(< layer of sof t an ran(is(o 4ay G%d is to :e loadedw ith a gran%lar fill # . thie<, on the a*erage* The total density of thef ill is a:o%t 1*6 GgQ .#

Ass%.e the test data in Pro:le. 751$ is

ty-i(al of the (lay layer, and that the layer is nor.ally (onsolidated*What (onsolidation settle.ent will ta<e -la(e )foe to the weight of the fill Ga<e these (al(%lations %sing aB the CeY deter.ined inPro:le. 751$, :B the Ce deterrnined in Pro:le. 751#, and (B dire(tlyfro. the -er(ent (onsolidation vers%s log -res51*1re diagra. yo% -lotted in Pro:le. 1$*

751"* Ass%.e the la:oratory test res%lts in Pro:le. 751$ are ty-i(al of another an ra n(is(o 4ay Gnd site, :%t where t:e (lay is slight1yover(onsolidated* The -resent verti(al effe(tive over:%rden stressis (al(%lated to :e a:o%t 1$ <Pa, and the thi(<ness of the (lay is 2

.* At, this lo(ation, the gran%lar fill F p / 1*6 GgQ.#B will J5 onlya:o%t 1 . thi(<* Est;.ate the (onsolidation settle.ent d%e to theweight of the fill*

7 1!* What settle.ent wo%ld yo% e+-eet at the overeonsolidated site inPro:le. 751" if the fill to :e (onstr%(ted were # . thi(< 'o this -ro:le. aB dire(tly fro. the -er(ent (onsolidation -lot and :B%sing EF* 7517 or 7516* How do the res%lts (o.-are

,



%M8 Conolldetlon end Conolldetlon &ellleen..

7517* Plot the following data and deter.ine the -re(onsolidation -ress%reand the .odified (o.-ression inde+*

] Consolidation Press%r((o.-r(ssion is ` B <PaB

*7 2*1 18*l l $*$2 2*76 7l*!2 1"#*71 #$!*#$ "2

!*# #$!*1$ 1""* 7"*"! 1""*61 #$!*6 "2

11* 1$71*7# $"$*1" 1$16*"7 1$717*! 1"1!*1 21#*6

-e(i.en height is $*2 .., (n / $6*#], pd 1* GgQ.#

a.-leis fro. a de-th of 5 1*! .*

7516* At the site where the sa.-le of Pro:le. 7517 was ta<en, the soil -rofile (onsists of a:o% r " ro of saod aod .::le filB and then 7 .of (lay* The water ta:le is a:o%t $ . :elow the gro%nd s%rfa(e*Average densities of the sand and r%::le fill are 1* GgQ .# a:ovethe water ta:le and 1*" GgQ .# :elow the water ta:le* Esti.ate the(onsolidation settle.ent if the average stress in(rease in the (o. -ressi:le layer is aB <Pa, :B 1 <Pa, and eB $ <Pa* Use :othEF* 7516 or EF* 751!B and yo%r -er(ent (o.-ression -lot fro.Pro:le. 7517, and (o.-are the res%lts* Co..ents

75$* Plot the following void ratio vers%s -ress%re data, and eval%ate the(o.-ression inde+ and the re(o.-ression inde+* 'eter.ine the

-re(onsolidation stress*

-



DD555D5D55555 555D55555..- -- .

55555555555555555555

Problema 371

Moid Ratio, e Press%re <PaB

l.>179 o1*6 11*26 $1*$6 21*1 7*66 1"*62 $*771 !00

*"6 7

*! *"$ 1"*!1! $

75$1* Use the (onsolidation data fro. Pro:le. 75$ to (o.-%te thesettle.ent of a str%(t%re that adds 1 <Pa to the already e+istingover:%rden -ress%re of *0 <Pa at the .iddle of a " . thie< layer*

75$$* What wo%ld :e the settle.ent of the sa.e st.(t%re in Pro:le. 8-* if the over(onsolidation ratio of the (lay were 1* and 0

1 <v /$! <Pa at the .idde-th of the (lay layer how yo%r wor< and

ass%.-tions on the e vers%s log a (%rve of Pro:le. 75$*

75$#* The (onsolidation (%rve of ig* E+* 7*6 is ty-i(al of a (o.-ressi:lelayer . thie<* I the e+isting 83e1:%1den -1ess1e is <Pa,(o.-%te the settle.ent d%e to an additional stress of 1 <Pa added

:y a str%(t%re*

7 $2* or the test data of P1o:le111 751$, (onstr%(t the field virgin (o.-res5sion (%rve %singD the (h.ert.ann -ro(ed%re for an 8CR of %nity*

75$* 'o Pro:le. 75$2 for an OCR / $**

75$"* At the .id-oint of a ! . thi(< soil layer, the void ratio is $*2* ind

t :is -ain t an t:e field virgin (o.-ression t%ve deter.ined2n

Pro:le. 75$2* What is the (orres-onding -ress%re I this -ress%re isdoubled ^her the entite site, (o.-%te the (onsolidation settle.ent of the layer*

75$!* how that the field virgin (o.-ression (%rve shown on ig* 7*7(Ce *16B is (o11e(t*

75$7 how that the -oint of intersetion where the laooratoey and fieldvirgin (o.-ression (%rves .eet for the -er(ent (onsolidation vers%s

.j1




log o3 gra-h is eF%al to *7eQl e

B*

This interse(tion is eF%iva5lent to t e * e -o.l on e e vers%s og o

singthe (o.-ression and re(o.-ression indi(es and :oth .odif ied in5di(es for as .any of the e ays o 1g* * as yo% (an* ow we o

iri(al relationshi s a ree with the la:oratory data

75#* 'o Pro:le. 75$6 for the (lays in Pro:le.s 757, 751$, 7517, and 75$*Again, how good is the agree.ent* D

75##* Co. %te the data and draw a (%rve of oM / vers%s de-th for -ointsdire(tly :elow a -oint load . 8n the sa.e -lot draw (%rves o Mw the (enter of s %are footin swith :readths of . and 1 ., res-e(tively, ea(h (arrying a

. . . . .

state.ent relative to the range within whi(h loaded areas .ay :e(onsidered to a(t as -o.t oa

(oordinates 8, 8B, and the (orners have (oordinates ", 1B* Alldi.ensions are in .etres* e area (arnes a %ni or. -r 1 <Pa* Esti.ate the stresses at a de-th of $ . :elow gro%nds%rfa(e at ea(h of the following lo(ations9 8, 8B, 8, 1B, ", 8B, ", 1B,

aard.ethods, and also deter.ine the ratio of the stresses as indi(ated :y

.ents

75#"* Cal(%late the stress distri:%tion with de-th at a -oint # . fro. the

# . with a %nifor. load of " <Pa* 'o :y aB the 4o%ssinesFtheory, B 4 e

75#!* How far a-art .%st two $ . dia.eter tan<s :e -la(ed s%(h, that

555555555555555555555



. DDD5D5555D5D55DDDDDDD55 5DDD5D55555DDDDD 5555555555555 5555555555555 555555DDD55 55

Pro#lea 373

their stress overla- is not greater than 1] of the (onta(t stress atde-ths of 1, $, and # .

75#7* Co.-%te the stresses for the data of E+a.-le 7*16, -arts aB and :B,%sing the New.ar< (hart, ig* 7*$*

75#6* Wor< E+a.-le 7*$1, %sing s%-er-osition of the res%lts of igs* 7*$2and 7*$ I * How does yo%r answer (o.-are with the sol%tion for E+a.-le 7*$1

752* iven the data of E+a.-le 7*$$* Instead of a load on the s%rfa(e,(o.-%te the de-th of an e+(avatton to (a%se a red%(tion . stress atthe :otto. of the e+(avation of $ <Pa if p / $ GgQ.#

Toee+(avation -lan area is shown in ig* E+* 7*$$a*

7521* or the e+(avation of Pro:le. 752, esll8ate the stress (hange at ade-th of " . :elow the :otto. of the e+(avation at -oint R.

752$* Is the $9 1 .ethod %sa:le for e+(avations Why

752#* A stri- footing # . wide is loaded on the gro%nd s%rfa(e with a -ress%re eF%al to 1 <Pa Cal(%late the stress distri:%tion at de-thsof #, ", and 1$ . %nder the (enter of the footing* l the footing restedon a nonnally (onsolidated (ohesive laye1 whose LL was 72 andwhose PL was , est;.ate the settle.ent of the footing*

7522* How wo%ld the esti.ated settle.ent %nder the (enter of a # S # .sF%are footing (o.-are with the settle.ent of the # . wide stri-footing in the -revio%s -ro:le., [ss%.ing soil (onditions were thesarne Ass%.e the foot.g 1s fle+i:le eno%gh to -roMIde %r%for.(onta(t -ress%re to the soil*

752* How .%(h diff eren(e in the (o.-%ted settle.ents is there in Pro:5le. 7522 if the Westergaard theory is %sed instead of 4o%ssinesFtheory

752"* A large oil storage tan< 1 . in dia.eter is to :e (onstr%(ted onthe soil -1file shown in ig* P72"* Aveiage de-th of the oil in titetan< is $ ., and the s-e(ifi( gravity of the oil is *6$* Consolidation

tests fro. the (lay Vayer are s1.*I1ar to those given . Pro:le. 7517*Est;.ate the .a+i.%. total and differential (onsolidation settle5.ent of the tan<* Negle(t any settle.ents in the sand* Wor< this -ro:le. ass%.ing aB (onditions at the .idde-th the (lay are ty-i(al of the entire (lay layer, and :B dividing the (lay layer intofo%r or five thinner layers, eo.-%ting the settle.ent of eaeh thinlayer and s%..ing %- :y EF* 7512* Hint9 ee E+a.-le 6*1$*



< '


&5N4 2

0=---- 7O7BGOCB77O7 -.-.-.-.$....-\.\4]

&5n>5 >6n= Psa, .8 MQ#

M5=2G >42 l6

p d / *) MQ#

S5'ig* P52"

1 . thi(< reinfor(ed(on(rete, and the average stress on the s%rfa(e of the sla: 1s

2l is shown in i * P752!* 8edo.eter tests on sa.of the (lay -rovide these average val%es9

F1 p

7+ Y5

4

+ S5'1

p & .9 MQ

Cl6

10 Dn "*

4 S5' P,at / .9 GgQn,#

ig* P52!

F

#



WWWt tttt t t t s

Problem- %M7

7527* Three %nifor.ly distri:%ted Ioads of 1 <Pa ea(h are a--lied tol8 + 18 . sF%are areas on the soil -rofile shown in ig* P7527*Undist%r:ed sa.-les of the (lay were ta<en -rior to (onstr%(tion*and (onsolidation tests indi(ated that the average -re(onsolidationstress is a:o%t 11 <Pa, the average (o.-ression inde+ is *, andthe average re(o.-ression inde+ is *$* Esti.ate the total (onsolidation settle.ent for the (lay layer only %nder the (enter of the.iddle loaded area*

Pl6n:

P32l5: F

00 P6 . F 00 P6 00 P6

0 . sand P sat / *.0 MQ#

! . S34 l6 P sat / .8! MQ#

@AB

A Ged dense a

$2. PB-"8

7526* A series of oil storage tan<s are to :e (onstr%(ted near Gysti( River -ower station in 4oston, GA* The ty-i(al tan< is $ . in dia.eter,and 24 e+erts an average fo%ndation stress of a:o%t 00 <Pa* Toe soil

-rofile at the site is very si.ilar to that shown in ig* 7*12a* Est;.ate :oth the total and differential (onsolidation settle.ent %nder theaverage ta o< H0n tD ee E+aro-Be 9 B $

75* A new highway to ira(ha, Thailand, is to :e (onstr%(ted east of 4ang<o<, a(ross a region of dee- de-osits of very soft .arine (lay* Aty-i(al soil -rofile is shown in ig* 7*1"a* Toe average Ce.# / *7 :elow the drying (r%st* Toe -ro-osed e.:an<.ent is 1 . wide atthe to-, has three hori&ontal to one verti(al side slo-e and is $ high* Esti.ate the %lti.ate (onsolidation settle.ent 3 the (enterlineof the e.:an<.ent*

F



Í '

nine

Tie !ate af Can§alidatian

.1 INT!O('CTION

In Cha-ter 7 we showed how to (al(%late the .agnit%de of (onsolidation settle.ent that a (lay layer %nder a str%(t%re will %ndergo :efore itrea(hes eF%ili:ri%. with the e+ternal load* We des(ri:ed how the -orewater -ress%re in e+(ess of hydrostati( dissi-ates with ti.e (onsolidationBand how the ef f e(tive stress %lti.ately :e(o.es eF%al to the a--lied load*It was .entioned that the rate of (onsolidation wo%ld de-end, a.ongother things, on the -er.ea:ility of the soil*

o.eti.es (onsolidation is (alled pri8ary consoIidation to disting%ishit fro. the other ti.e5de-endent (o.-onent of total settle.ent, secondary

co8pression. o% will re(all fro. e(* 7*$ that se(ondary (o.-ressiono((%rs af ter essentially all of the e+(ess -ore water -ress%re has dissi-ated@that is, it o((%rs at (onstant effe(tive stress* In sorne soils, es-e(iallyinorgani( (lays, -ri.ary (onsolidation is the largest (o.-onent of totalsettle.ent, whereas se(ondary (o.-ression (onstit%tes a .a0or -art of thetotal settle.ent of -eats and other highly organi( soils* In this (ha-ter, thetheones for esh.ating the ti.e rate of :oth -ri.ary (onsolidation andse(ondary (o.-ression of fine5grained soils are dis(%ssed*

Why is it i.-ortant to <now how fast a str%(t%re will settle %nder thea--lied load or e+a.-le, if the design life of a str%(t%re is years, andit is esti.ated that 24 will ta<e years for ali the settle.ent to o((%r,then the fo%ndation engineer wo%ld e+-e(t only rninor settle.ent -ro:le.sd%ring the lif e of the str%(t%re* 8n the other hand, if the settle.ent ise+-e(ted to ta<e a:o%t the ti.e reF%ired to :%ild the str%(t%re, then .ostif not ali of the settle.ent will have o((%rred :y the ti.e the str%(t%re is(o.-leted* I the str%(t%re is sensitive to ra-id settle.ents for e+a.-le,

%M4

/

?



9.2 The Conolldatlon Procea 377

re.for(ed (on(rete t ra.es or (on(rete -ave.entB, then str%(t%ral da.age(o%ld res%lt* Gost str%(t%res on (lay fo%ndations e+-erien(e grad%alsettle.ents d%ring their lifeti.es, whi(h .ay or .ay not i.-air the -erfor.an(e of the str%(t%res* This (ha-ter -resents -ro(ed%res for esti.ating the rate of fo%ndation settle.ent* The engineer then (an de(idewhat eff e(t, if any, the settle.ent .ay have on the str%(t%ral integrity aswell as the intended %se of the str%(t%re*

The ;ollowing notation is introd%(ed in (his (ha-ter*


r erondary ro.-ression inde+ EF 651B

>Wvg or u

&

L$ r5 1 . $ QsL .L ..L ..L .

]B5or ]B

Godified se(ondary (o.-ression inde+EF* 6D1"BCoeffi(ient of (onsolidation EF* 65#BLength of drainage -ath EF* 65BInitial dial reading EF* 651#B'ial reading at ti.e t , n 5 1, $,*** Consolidation settle.ent atti.e Ti.e fa(tor EF* 65B'egree of (onsoiidafionConsolidation ratio EF* 656B'e-th fa(tor EF* 656B

. THE CON&OI(ATION P!OCE&&

I4 is %sef%l to ret%rn to the s-ring analogy as -resented in Cha-ter 7ig* 7*$B* ig%re 6*la shows a s-ring with a -iston and a valve in a single

(ylinde1* A -1ess%1e ve1s%s de-th diagia. is shown in ig* 6*l:* Tite soil,re-resented :y the s-ring, is at eF%ili:ri%. with an initial effe(tive stress

> or the ti.e :eing, we shall ass%.e that all of the a--lied load on the -iston, do, is initially transferred to the e+(ess -ore water -ress%re d

u

e+(ess a:ove hydrostati( or initial % B* This is the (ase for one5di.ensionalJoadi ng, hnt Ja ter we shall see that this is not tr%e for three5di.ensional loading*

With ti.e, water is sF%ee&ed3, o%t thro%gh the valve, and the e+(ess -ore water -ress%re de(reases* T-%s there is a grad%al transfer of stressfro. the -ore water to the soil s<eleton and a (on(%rrent in(rease ineffe(tive stress* ig%re 6* l shows the initial effe(tive stress

, the (hange

.(reaseB . effe(ttve stress, , and the -ore -ress%re st;ll to :e d1s si-ated, d u, at t / t The verti(al dashed lines, la:eled 4 , t 2 , et(*, re-resentti.e f ro. the start of load a--li(ation* These lines are (alled

,j

G



55555 5555 5555 5555555 55.. 5 5 5 5 55 555 ----,--- 555555 - 5 5555

5

<5 55

# fA

3;V6l15

,K : .:

L.

P5>>G5 -,--- P5>>G5-----

R 1 1

_&2----

...

3

1

51..e# *> .c. ^ VO 1 LlU

H.5::

t t / 3..... 5 1 1

1

1 1

t, t$ tK 1 1

aB J ll 5 5

1 A

, ****

# V6l15

, % e

i.a '''''''K' 2l.G-P5>>G5 -G ;6

5L.

1 /l ¡:::::V a#o 2l.G a#o: . 1g

K**K i55 - ''1' +

$ lb.,

.....

- .'-

*U t l

? / # .c.

5EB %*

B

o 1 3. n 1

... R - .V

3339999 <: 4 4*

\b 35 tK

V6l15

= 5

$2. 9. SN2n 6n6l3 3 3n>3l2=6423n: 6^-, 3=5l 3 6 >2nl5 >32l 5

l65; =-, 3=5l 3 Gl42Nl5 >32l l65>.

5 5

%M4

5 5

: : W

j . -1QZ

, 5

e .



55 555*5D 5 555555D5DD -- - 55D5 5 - - . -------- % 5 ,K 5 55WWWWW 55 555WW55D55555WWWWW55WWW5WW 5

5 5 -----



6*$ 'he Con&olldatlon Proce&a %M

isochrones :e(a%se they are lines of eF%al ti.es* 6sobars are either ar(ti(taverns or (onto%r lines of eF%al -ress%re fo%nd on a weather .a-@isopachs are lines of eF%al thi(<ness of a geologi( de-osit@ and isotachs arelines of eF%al velo(ity on wind .a-s*B inally, at - oo all of the e+(essore water res %r flu wD Dthe initial stress @ -l%s the a--lied stress in(re.ent o. '%ring this ti.e,

. 0 . .

water is sF%ee&ed o%t of the (ylinder*y-i(a soi ayer 1s .%e .ore (o.- e+ t an e s1.- e . e

shown in igs* 6* la5(* Let %s in(rease the n%.:er of s-rin s, istons, andvalves as shown ig* 6*ld* As :efore, we (an show the initial effe(tivestress o3 within the soil -ress%re flu, d%e to the e+ternal load on the -istons, Ilo, in ig* 6* le* Let %s

:oth internaV as well as to- and :otto. drainage* In order for the water tosF%ee&e o% o (y in ers , , an , i is ne(essary or sorne o e

water in (ylinders I and 3to es(a-e :eforehand* Li<ewise, :efore the water (an :e sF%ee&ed o%t of the soil in (ylinder #, it is ne(essary that sorne of the water in e linders * and " :e s %ee&ed o%t first tare o-en, %-on a--li(ation of the e+ternaV stress Ao, water will start to flow

i..ediate red%(tion of the e+(ess -ore water -ress%re and an in(rease ini ers an , e (* s s own in ig* * , wi 1.e

the -ore -ress%re iso(hrones .ove to the right, and they are seg.entedlines :e(a%se of the finite n%.:er of -istons and valves* With an infiniten%.:er of istons the iso(hrones wo%ld :e s.ooth (%rves whi(h ra((%rately re-resent what is -hysi(ally o((%rring with ti.e in a (onsolidat5. .

:y igs* 6* l d5f, it (an :e seen that the de(rease in the ind%(ed -ore water 1, an

:otto. of the layer* This is :e(a%se the drainage path for the (enter (y . er 1s (ons1 era y onger t an or (y . ers 1 and * A> a res%lt, itta<es a longer ti.e for the (enter of a do%:ly drained layer or the :otto.of a singly drained layerB to dissi-ate its e+(ess -ore -ress%re*

the gradient i, whi(h eF%als O/1 F tlu/ p( g :/ tl M. Toe slo-e of the seg.ented iso(hrones in ig* 6*lf is flu/ tlM. At the e+a(t (enter of the (laylayer, the flow is &ero :e(a%se the gradient A%Q A& is &ero* At the ends, thegra 1en a--roa( es . 1.ty an t %s t e ow 1s t e argest n t at edrainage s%rfa(es*

Toe -ro(ess 0%st des(ri:ed is (alled consolidation. The a.o%nt of settle.ent the s-ring5-iston syste. or (lay layerB e+-erien(es is dire(tlyrelated to how .%(h water has sF%ee&ed o%t of the (ylinders or voids in

.



38, Tie !ate of Conolldatlon

the (layB* How .%(h water has sF%ee&ed o%t and th%s the (hange in voidratio of the (lay is in t%rn dire(tly -ro-ortional to the a.o%nt of e+(ess

-ore water -ress%re that has dissi-ated* Th%s the rate of settle.ent isdire(tly related to the rate f e+(ess -ore -ress%re dissi-ation* What weneed in order to -redi(t the rate of settle.ent of a fo%ndation is aneF%ation or theory that -redi(ts the -ore -ress%re and void ratio at any -oint in ti.e and s-a(e in the (onsolidating (lay layer* Then the (hange inthi(<ness or settle.ent of the ayer af ter any ti.e of loading (an :edeter.ined :y integration of the eF%ation over the thi(<ness of the (laylayer* The theory of (onsolidation whi(h is .ost (o..only %sed in soil.e(hani(s is a one5di.ensional theory* l4 was first develo-ed :y Ter&aghi

in the l6$3s and its derivation and sol%tion are s%..ari&ed in thefollowing se(tions*

.% TE! RAGHl$& ONE"(I3EN&IONACON&OI(ATION THEO!)

In this se(tion, we will -resent the Ter&aghi 16$B one5di.ensional(onsolidation eF%ation and dis(%ss sorne of the ass%.-tions ne(essary toderive the eF%ation* A detailed derivation and the sol%tion to the eF%ationis given in A--endi+ 45$* In 1de1 to %se the Ter&aghi theory with sorne

(onfiden(e, it is i.-ortant that yo% %nderstand the ass%.-tions andtherefore the li.itations of the theory*The (o.-ressi:le soil layer is ass%.ed to :e :oth ho.ogeneo%s and

(o.-letely sat%rated with water, and the .ineral grains in the soql and the1

water in the -ores are (o.-letely in(o.-ressi:le* 'ar(y3s law is (onsidered to govern the egress of water fro. the soil -ores, and %s%ally :othdrainage and (o.-ression are ass%.ed to :e one di.ensional* Us%allydrainage is -rovided at :oth the to- and :otto. of the (o.-ressi:le layer,

:%t we (o%ld 0%st as easily ass%.e drainage at only one s%rfa(e* TheTer&aghi theory is a s8a/1 strain theory in that the a--lied load in(re.ent

-rod%(es only s.all strains in the soil@ therefore :oth the (oeffi(ient of (o.-ressi:ility, a , and the 'ar(y (oeffi(ient of -er.ea:ility, , re.ain

essentially (onstant d%ring the (onsolidation -ro(ess* l av is a (onstantover the in(re.ent of a--lied stress, then there is a uniLue relationshi-

:etween the (hange in void ratio, ll.e, and the (hange in effe(tive stress,ll*o3* This i.-lies also that there is no secondary co8pression4 if se(ondary(o.-ression o((%rs, then the relationshi- :etween ll.e and ll.o3 wo%ld not

:e %niF%e, :y definition* Re(all that se(ondary (o.-ression is the (hangein void ratio that o((%rs at (onstant effe(tive stress*

1



555 ------- .... 5

9.3 Ter>aghl$ One"(lenlonal Conolldatlon Theor@ 311

The derivation of the Ter&aghi eF%ation (onsiders the vol%.e of

law, we <now the F%antity of flow de-ends on the hydra%li( gradient as

well as on the -er.ea:ility of the soil* Toe hydra%li( gradient (a%sing flow(an :e related to the e+(ess -ore water -ress%re in the ele.ent :y u/ P(0Bin(e the water is ass%.ed in(o.-ressi:le, :y (ontin%ity the vol%.e(han e in the ele.ent .%st :e the differen(e in flow in nele.ent in a differential ti.e dt. This -art of the eF%ation (an :e written

as -revio%sly defined* Partial differentials .%st :e %sed :e(a%se u is a%ne ion o o e -osi ion M an i.e *

Toe other -art of the eF%ation is o:tained :y relating the vol%.e(hange or (hange in void ratio of the soil s<eleton to the (hange ineffe(tive stress : .eans of the (oeffi(ient of (o. r s D 'l2deter.ined in the oedo.eter test* Th%s a

. . 33 ,,

is really the stress5strain. .

we (an eF%ate the (hange in effe(tive stress to the (hange in -ore -ress%re* n o er wor s as ong as e o a s ress is (ons an , as e e+(ess -ore -ress%re dissi-ates with ti.e, there is a (on(%rrent in(rease in

effe(tive stress, or *9lo3 / -.:6 C . As :efore, C is a f%n(tion of :oth [ and t.This half of the e %ation is %s%all written as

5av5a#dt dM

e t

5&/5 5a 2G 5av a#

D P(0 5/2 e1 a1

Rearranging, we o:tain

where

Toe (oeffi(ient (

52G a##5/2 51

e 65#

#

is (alled the coefficient of consolidation :e(a%se it (ontains the .aterial -ro-erties that gove. the (onsolidation -ro(ess* l yo%

asdi.ensions of L$ r5 1 or .$

Q s*

2

DJ

5



#7$ Tie !ete of Conolldetlon

EF%ation 65$ is the &erMaghi one5di8ensiona/ eo8olidation eLuation.

l4 (o%ld 0%st as easily :e written in three di.ensions, :%t .ost of the ti.e ineng.eenng -ra(t1(e one5 11nens1ona (onso i a ion is ass%rn asi(a y,the eF%ation is a forrn of the diff%sion eF%ation fro. .athe.ati(al

-hysi(s* Gany -hysi(al diff%sion -heno.ena are des(ri:ed :y this eF%ation, for e+a.-le, heat flow in a solid :ody* The =diff %sion (onstant= for the soil is the ev . Note that we (alled the ev a (onstant* l4 really isn3t, :%t

.

.a<e the eF%ation linear and easily solva:le*o ow o we so ve e er&ag i (onso i a ion eF% ion * %

solve ali other se(ond5order -artial differential eF%ations with (onstant(oeffi(ients* There are a variety of ways@ sorne are .athe.ati(ally e+a(t@others are only a--ro+i.ate* or e+a.-le, Harr 16""B -resents an a-

-ro+irnate sol%tion :y %sing the .ethod of finite differen(es* Taylor 1627B,

ter.s of a o%rier series e+-ansion, and this is what we do in detail inA--endi+ 45$* Here we shall 0%st give an o%tline of the sol%tion* irst, the

:o%ndary and initial (onditions for the (ase of one5di.ensional (onsolidation are9

-ressi:le layer*$* The initial ecess hydrostati( -ress%re tiu / u4 is eF%al to the

a--lied in(re.ent of stress at the :o%ndary, tio.

We (an write these :o%ndary and initial (onditions as follows9When [ 8 and when M Z , u 8

When t / 8, tiu ^ & Ilo oS 5 o@B

We %s%ally ta<e the thi(<ness of the (onsolidating ayer to :e Z , so thatthe length of the /ongest drainage pat 1s eF%a to or = (o%rse att oo, tiu 8, or (o.-lete dissi-ation of the -ore -ress%re will haveo((%rred*

Ter&aghi 16$B was o:vio%sly fa.iliar with the early wor< on heattransfer, and he ada-ted those (losed5for. sol%tions to the (onsolidation

the for.

u oS D5 oiB f ,F ` :JiF & :

n$

652B

where and G are di.ensionless -ara.eters see also Taylor, 1627B* Thr*first ter., , is a geo.etry -ara.eter, and it is eF%al to M / U. The se(ond

.



6*# Ter>eghl$ One"(lenlonal Conolldatlon Theor@ 383

(onsolida tion ( :y

t

where t /ti.e, and Zdr / length of the longest drainage -ath*

We have already .entioned that c

.*Qs or eF%ivalentB* has di.ensions of L$ T- 1 or %nits of

ro. EF* 65#, the ti.e fa(tor (an also :e written asG / ( e : Q7Q 6 " K B

Note that t has the sa.e ti.e %nits as . That is, if is in eenti.etres -er se(ond, then t .%st :e in se(onds* The drainage -ath for do%:le drainagewo%ld :e eF%al to half the thi(<ness Z of the (lay layer, or Z / / Zdr . I we had only a singly drained layer, the drainage -ath wo%ld still :e Zdr , :%t then it wo%ld :e eF%al to the thi(<ness U of the layer*

The -rogress of (onsolidation af ter sorne ti.e t and at any de-th M inthe (onsolidating layer (an :e related to the void ratio at that ti.e and thefinal (hange in void ratio* This relationshi- is (alled the consolidation ratio,and it is e+-ressed as

u 5e

B 5 e

65!B *

where e is sorne interrnediate void ratio, as shown on ig* 6*$* What we areloo<ing at gra-hi(ally in that fig%re is the ratio of ordinales (orres-ondingto $ and $ C. In terrns of stresses and -ore -ress%res, EF* 65! :e(o.es

o3 5 o4 a3 5 (ri u . 5 u u M 5 3 3 - --- / / l --

*- >J + a ^9 ^9

657B

where o3 and u are interrnediate val%es (orres-onding to e in EF* 65!, andu4 is the initial ecess -ore -ress%re ind%(ed :y the a--lied stress da3.

o% sho%ld satisfy yo%rself that these eF%ations are (orre(t fro. therelation5 shi-s shown in ig* 6*$ and f ro. ll.a 5 5 %l u. ee alsoA--endi+ 45$*B

rorn EFs* 65! and 657, it is evident that is &ero at the start * -f loading, and it grad%ally in(reases to 1 or 1]B as the void ratiode(reases fro. e 1 to e2 D At the sa.e ti.e, of (o%rse, as long as the totalstress rernains (onstant, the eff e(tive stress in(reases fro. ai to a as thee+(ess hydrostati( stress -ore water -ress%reB dissi-ates fro. C to &ero*The (onsolidation ratio is so.eti.es (alled the degree or percent

consolidation , and it re-resents (onditions al a point in the (onsolidatinglayer* I4 is now -ossi:le to -%t o%r sol%tion for C in EF* 652 in ter.s of the

*J

M

A



e

a D -D e, - e2o·a' - a'

e

21

!8" Tie !ete ot Conolldatlon

a a

Ila3 / tl% / %,

J

15a 55 a 555/ 5511 1

$2. 9.* L6J3643 3N5>>23n G15. %345: o3 5 oS F oS 5 oS : 5 G /

;- .

(onsolidation rat;o, EF* 657, or 00

l L f1F ` :JiF & :n&0

656B

Toe sol%tion to this eF%ation is shown gra-hi(ally in ig* 6*# in ter.s of the di.ensionless -ara.eters already defined* Toe tedio%s (al(%lationsinvolved in solving EF* 656 are no longer ne(essary* ro. ig* 6*# it is -ossi:le to find the a.o%nt or degree of (onsolidation and therefore u

and o3B for any real ti.e af ter the start of loading and at any -oint in the(onsolidating layer* All yo% need to <now is the c., for the -arti(%lar soilde-osit, the total thi(<ness of the layer, and :o%ndary drainage (onditions*With these ite.s, the ti.e fa(tor G (an :e (al(%lated fro. EF* 65* It isa--li(a:le to any one5di.ensional loading sit%ation where the soil -ro-er ties (an :e ass%.ed to :e the sa.e thro%gho%t the (o.-ressi:le layer*

ig%re 6*# also is a -i(t%re of the progress of consolidation. Toe

isochrones lines of (onstant TB in ig* 6*# re-resent the degree or -er(ent



.% Ter>aghl$ One"(lenlonal Conolldatlon Theor@ 385

o

B = >

,,,o*8-?'-$4-3

- - == - .. ., 5****-**

1 >D3e9 3G3#, 55

50,?''l,.WL ***

,

*725575

****># >: ,... *** -

>::J ) ;3t ...

^;3U

,,*** *

oH3

D

J,, J

+

& = I#.. 1 AH

1*

..l

1U*

*** ' *******

*** 1* '? ' - **** ?2

- - ==,...?'*** ' 5 -- - -r=I

- '

$

o *1 *$ *# *2 * *" 8* ! *7 *6 1*C3n>3l2=6423n 6423, U,

$2. 9.! C3n>3l2=6423n 3 6n l36423n 6n= 425 643 2n 6 =3GJl=62n5= l65 645 T6l3, 9"8.

(onsolidation for a given ti.e fa(tor thro%gho%t the (o.-ressi:le layer* or e+a.-le, the -er(ent (onsolidation at .idheight of a do%:ly drainedlayer total thi(<ness / Z : for a ti.e fa(tor eF%al to *$ is a--ro+i.ately$#] see -oint A in ig* 6*#B* However at the sa.e ti.e and ti.e fa(torBal othe1 lo(ations within the soil hrye1, the degt ee of (onsolidation is

diff erent* At $] of the de-th, for e+a.-le, M QU /

and / 22]*

1.tlarly, near the dra.age s%rfa(es at M / Z / *1, f or the sa.e ti.efa(tor, :e(a%se the gradients are .%(h higher, the (lay is already 7"](onsolidated, whi(h .eans that at that de-th and ti.e, 7"] of the originale+(ess -ore -ress%re has dissi-ated and the effe(tive stress has in(reased :ya (orres-onding a.o%nt*

E9A3PE 6*1

(215n:

A * . thi(< layer of Chi(ago (lay is doubly drained . This .eans that avery -ervio%s layer (o.-ared to the (lay e+ists on to- of and %nder the 1$. (lay layer*B The (oeffi(ient of (onsolidation c / 7* + 15s .*Qs*

55$

,

-



^3 0



5 555 5 555 55 5

5555

< ,2

-,.. X -?

-

15 5 55

R5FG25l:

.d tne degree or -er(ent (onsolidation for the (lay 2 yr af ter loading atde-ths of #, ", 6, and 1$ .*

S0lG43n:

irst, (o.-%te the ti.e fa(tor* ro. EF* 65,

& v3

Z15

7* + 15s .$ Qs #*1#" + 1! sQvrB (5

vrB

"B$

G..,:,

Note that Z 1$ . and Hdr " . sin(e there is do%:le drainage*... ... -- T?'' n *, %Q .

. 55 ' .... - ---- .# 3 ,,.X - 55 <J . 5, .. K *** **** v*K** ***** *

At M # ., M / Z *, ^ & "1] $t M / " ., M / Z 1*, 2"]

A t ! Z 9 Q %!

G+ 9 BQ1 =3=' &

At M 1$ ., M / Z / $*, 1]

E+AMPLE 9.*

(215n:

Toe soil (onditions of E+a.-le 6*1*

- .1 1=331==3**==3****

I the str%(t%re a--lied an average verti(al stress in(rease of 1 <Pa to the(lav laver, est;.ate the e+(ess nore water nress%re re.aining in the (lavaf ter yr for the de-ths in the (lay ayer of #, ", 6, and 1$ .*

S3lG423n:

Ass%.ing one5di.ensional loading, the ind%(ed e+(ess -ore water -ress%reat the :eginning of (onsolidation is 1 <Pa* ro. EF* 657,

^ & 1 5u

& ^9

. 3 ***** n == =3D

5



5 D 55 5 5 5555 D55 55DD55555D5 5 55555D5 5D55DD5 55 55D ... . 5 555555 D5D55555



.% Ter>aghl$ One"(lenlonal ConllOlldatlon Theor@ 387

S32l N32l5 &5N4

G P6

p 9a M Q. #-* -$ .---

1-

&-

5

1,

,,,-

$-

.

....

+-

/ *"$w / $#*$]

oh 15(lay

P, $"" <gQ. #

5n>5 sand

$2. EY. 9.*

^ & 4F l 5 ^.)

ro. the sol%tion in E+a.-le 6*1 we o:tain9

At M # .,At M / " .,

. "1],^ 2"]

u #6 < Pau 2 <Pa

At M / 6 ., J. / "1], u #6 <Pa

-ore -ress%res, that is, they are a:ove the hydrostati( water -ress%re*

layer has (onsolidated* 8f .ore -ra(ti(a interest is the average degree or

percent conso/idation of the entire layer* This val%e, denoted :y or U*vs isa .eas%re of how .%(h the entire la er has (onsolidated and th%s it (an :e dire(tly related to the total settle8ent of the layer at a given ti.e after

loading* Note that ^ (an :e e+-ressed as either a de(i.al or a -er(entage* Too:tain the average degree of (onsolidation over the entire layer

(orres-onding to a given ti.e fa(tor we have to find the area %nder the &

2

e



DJ



o-t-

1

a 0 o a0 + a .

2W1

1

1

388 Tie !ate of Conaolldatlon

At t / 8

a , t a 4 5 a 4 5 % &, tE +(ess -ore

-ress%re re.ai ni ngQ

+

E +(ess -ore -ress% re d issi -ated

/ a 5 % ,, ,

% avg /---- + 00 55555+ 1

$2. 9." A1565 =555 3 3n>3l2=6423n, Uavg , =52n5=.

(%rve of ig* 6*#* A(t%ally we o:tain the area o%tside the G (%rve asshown in ig* 6*2*B How the integration is done .athe.ati(ally is shown inA--endi+ 45$* Ta:le 651 -resents the res%lts of the integration for the (asewhere a linear distri:%tion of e+(ess -ore water -ress%re is ass%.ed*

The res%lts in Ta:le 651 are shown gra-hi(ally in ig* 6** In ig* 6*athe relationshi- is shown arith.eti(ally, whereas in ig* 6*:, the relationshi- :etween ^ and G is shown se.ilogarith.i(ally* Another for. of the

relationshi- is fo%nd in ig* 6*(, where is -lotted vers%s MT * Asdis(%ssed in the ne+t se(tion, igs* 6*: and 6*( have :een fo%nd to show(ertain (hara(teristi(s of the theoreti(al ^'G relationshi- to :etter ad vantagethan ig* 6*a* Note that as G :e(o.es very large, ^ asy.-toti (allya--roa(hes 1]* This .eans that, theoreti(ally, (onsolidation never sto-s :%t (ontin%es infinitely* l4 sho%ld also :e -ointed o%t that thesol%tion for ^ vers%s G is di.ensionless and a--lies to ali ty-es of -ro:le.s where lo / Ilu varies linear/y with de-th* ol%tions for (ases



-- 55 D5555555D55D55 - - -----D ,.,..-.--------- D55 55,5D5DD5555D5555 ---- 5 -- --- 5 55

T

o *$ *2 *" *7 1* 1*$ 1*2

o

=i***

'?******

T:::, =5

1

.......... X r55

,-

Log Tn ,* ,, ,,

G.G --- '?'-- V& G,, V&V ,M &.%

o

o=5

?'

K,^11

555 --........

,,, Tangent

'=r3****''5********

**,***K

1 ;;J ?

=35 uDsy.-tote

yQ3To *$ *2 *" *7 1* 1*$ 1*2

o **********

******Q

:::,

55, ,

5=5=vv

()Asy. -tote

$2. 9.) Uavg 15>G> T: 6 624542 >6l5; J l3 >6l5; 5 >FG65 334>6l5.

389

5

55 5

' -

- - n -- n -- n n ? n

-

?' --

=3

00



DD5DD5D5 5 5 ==5555 55(DK,9@il==5D ,D5D59,^



390 Tie !ate of CO3Olldatlon

Uavg

*1

G

*7*$ *#1*# *!1*2 *1$"* *16!*" *$7!

*7 *"!

*6 1*1"#.0 00

where the initial -ore -ress%re distri:%tion is sin%soidal, half sine, andtriang%lar are -resented :y Leonards 16"$B*

Casagrande 16#7 B and Taylor 1627B -rovide the following%sef%l a--ro+i.ations9

$

G 3&6 ^ $ ^_ B$2 2 1

651B

or ] "],

G 1*!71 5 *6## log 1 5 ^_) 6511B

E9A3PE 6*#

(215n:

G /: * for a (o.-ressi:le (lay de-osit*

Av erage deg1ee of (onsolida tion and the -er(ent (onsolida%on at the(enter and at M / U / *1*

S3lG423n:

ro. Ta:le 651 and ig* 6*, l3*i*vg / $"]* Therefore the (lay is $"](onsolidated, on the average* 1. ig* *# yoa (an see that the (enter of



.% Ter>aghl$ One"(lenlonal Conollda'on Theor@ 391

the layer 1s less than *] (onso:dated, wh;le at the **1]= de-th ( [/ U / *1B the (lay is !#] (onsolidated* 4%t, on the average thro%gho%t thelayer, the (lay is $"] (onsolidated*

What does the average (onsolidation .ean in tenns of settle.ents%avg (an :e e+-ressed as

651$B

where sF t : is the settle.ent at any ti.e, and se is the final * or %lti.ate(onsolidation -ri.aryB settle.ent at t / oo*

E9A3PE .+

(215n:

The data of E+a.-le 6*#*

R5FG25=:

ind the settle.ent when Uavg is $"], if the final (onsolidation settle.entis 1 .*

S3lG423n:

ro. faZ* 6 1$, sFt : ,v s(B* Therefore

sF t : $"] YI .B / *$" .

E9A3PE 6*

(215n:

Toe soil -rofile and -ro-erties of E+a.-les 6*1 and 6*$*

R5FG25=:

Co.-%te the ti.e reF%ired for the (lay layer to settle *$ .*



0

392 Tie !ete of Coneolldatlon

S3lG423n:

To (o.-%te th average degree of (onsolidation, yo% first .%st esti.atethe (onsolidation settle.ent se , as yo% did in Cha-ter 7* or Chi(ago (lay,a reasooa :le va B%e of Ce is a:o%t 8 $ Ta:les 75$ aod 75#B ro. ig E+6*$, U

/ 1$ . and e

/ *"$* 'eter.ine p for the sof t (lay and (al(%late

a at the .idde-th -f layer fro. EFs* !512( and !51* Ass%.e the (lay isnor.ally (onsolidated* o

>1 1*7 + 6*71 + 1* 1*7 5 1B + 6*71 + #

$*$ 5 1B S 6*71 S "

/ 11 <Pa

* . 0 00 se / *$ *

"$log

11/ *$ .

The average degree of (onsolidation Mavg when the (lay layer settles *$ .is EF* 651$B9

Io o:taio & we (an %se either Ta:le 651 or ig* +.2. 8r sin(e Uavg "], we (an %se EF* 651*

ro. EF* 6*, t / &ZJrl c

G / *27B$ / *17$

, where Hdr / " . for do%:le drainage@ or

*17$ + " .B7 /

7 + 15s .* Qs + #*1#" + 1 sQyr

/ $*" r

E9A3PE 6*"

(215n:

Toe data of E+a.-les 6*1 and 6**

A5FG25=:

How .%(h ti.e wo%ld :e reF%ired for a settle.ent of *$ . to o((%r if the (lay a yer were siogly draioed

1



D555555D5D55D555555555 55**5D5DD .5595..

.% Ter>aghl$ One"(lenlonal Conolldatlon Theor@ %%

S3lG423n:

Use EF* 65 dire(tly*

/ 7 S 15s .$Qs S #*1#" S 1! sQyr $*$# .$Qyr

*

where Hdr / 1$ . for single drainage*

*17$ + 1$ .B*

t / :/ 1*2 yr $*$# .$Qyr

or four ti8es as long as with do%:le drainage*

E9A3PE 6*!

(215n:

A 1 . thi(< (lay Vayer with single drainage settles 6 (. in #* yr* Toe(oeffi(ient of (onsolidation for this (lay was fo%nd to :e *22 + 15

*

(.* Qs*

. . R5FG25=:

Co.-%te the %lti.ate (onsolidation settle.ent, and find o%t how long itw ill ta<e to settle to 6] of this a.o%nt*

S3lG423n:

ro. EF* 65 solve for T9tcv

G & 2

$$

/ #* yr *22 15 B (. $ 1 .

B#.#" + 1, B

5 o*1 .*

s 1 (.* yr

(o. Ta:le 651 we see that the average degree of (onsolidation is :etween*7 and *6* Therefore we (an %se either EF* 6511 or ig* 6*a, or we (aninter-olate fro. Ta:le 651* Using EF* 6511, we have

*" / 1*!71 5 *6## log 1 5 O:

1*$! / log 1 5 O:

1

DJ

c1

+



394 Tie(- of eon.olldatlon

or 71*"], or 7$]

Th%s if 6 (. of settle.ent re-resents 7$] of the total settle.ent, then thetotal (onsolidation settle.ent is EF* 651$B9

sF t : 6 (. s 55 55 11 (.

e %avg *7$

or the ti.e for 90 settle.ent to o((%r, find G / *727 for Uava / *6,fro. Ta:le 651* Using EF* 65 and solving for t, we find that9

&ZJr *727 1 .B$ 1 (.$

t / -- / ------'---?'---

$X *22 + 3-$

(.$

Qs .$

1*6 S 18 s yr #*1#" S 1 s

/ 2*62 yr

E9A3PE 6*7

(215n:

The data of E+a.-le 6*!*

R5FG25=:

ind the variation . the degree of (onsolidation thro%gho%t the layerwhen t #* yr*

S3lG423n:

When t #* yr, the (orres-onding ti.e fa(tor *", fro. E+a.-le 6*!*

ind the (%rve for G / *" in ig* 6*#* or a layer with single drainage, we%se the to- half or :otto. half, de-ending on where the layer is drained*Ass%.e for this -ro:le. that the layer is drained at the top.: Toe (%rve for G *" re-resents the degree of (onsolidation at any de-th M. in(eG *" and %sing EF* 65 we find that this iso(hrone shows the variationof for t / #* yr* I4 (an :e seen that at the :otto. of the layer, where M / U 1, !1]* At .idheight of the I8 . thi(< layer, where M / U *, !6*]* Th%s the degree of (onsolidation var;es thro%gh the de-thof the (lay layer, :%t the average degree of (onsolidation for the entire



9." &545ln64l3n 3 45 C35ll5n4 3 C3n>3ll=64l3n ., #6

layer is 7$] E+a.-le 6*!B* Another interesting -oint a:o%t ig* 6*# is thatthe area to the lef t of the (%rve & / *" re-resents 7$] of the area of theentire gra-h, Z vers%s , whereas the area to the right of the (%rveG / *" re-resents 17], or the a.o%nt of (onsolidation yet to ta<e -la(e*ee also ig* 6*2*B

9." &ETERMI%ATIO% O$ THE COE$$ICIE%TO$ CO%SOLI&ATIO% cv

How do we o:tain the (oeffi(ient of (onsolidation cvU This (oeffi (ientis the only -art of the sol%tion to the (onsolidation eF%ation that ta<es intoa((o%nt the soil -ro-erties whi(h govern the rate of (onsolida tion* InCha-ter 7 we des(ri:ed the -ro(ed%re for -erfor.ing (onsolida tion or oedo.eter tests to o:tain the (o.-ressi:ility of the soil* We .entioned thateaeh load inere.ent %s%ally re.ains on the test s-eei.en an ar:itrarylength of ti.e, %ntil we ho-eB essentially ali of the e+(ess -ore -ress%re hasdissi-ated* 'efor.ation dial readings are o:tained d%ring this -ro(ess, and the(oeffi(ient of (onsolidation cv is deter.ined fro. the ti.e5defor.ation data*

The (%rves of a(t%al defor.ation dial readings vers%s real ti.e for agiven load in(re.ent of ten have very si.ilar sha-es to the theoreti(al ^'G (%rves shown in ig* 6** We shall ta<e ad%antage of this o:servation to

deter.ine the cv :y so5(alled **(%rve5fitting .ethods= develo-ed :yCasagrande and Taylor* These e.-iri(al -ro(ed%res were develo-ed to fita--ro+i.ately the o:served la:oratory test data to the Ter&aghi theory of (onsohdation* Gany fa(tors s%(h as sa.-le d1st%r:an(e, load .(re.entratio LIRB, d%ration, te.-erat%re, and a host of test details have :eenfo%nd to strongly affe(t the val%e of cv o:tained :y the (%rve5fitting

-ro(ed%res Leonards and Ra.iah, 166@ Leonards, 16"$B* 4%t resear(h :yLeonards and ira%lt 16"1B has shown that the Ter&aghi theory isa--li(a:le to the la:oratory test if large LIR3s EF* 75$B, %s%ally aro%nd%nity, are %sed*

The (%ne5fitting -w(ed . es o%tlined in this se(tion witl ena:le yoao deter.ine val%es of the (oeffi(ient of (onsolidation cv fro. la:oratory

test data* In addition, the -ro(ed%res will allow yo% to se-arate these(ondary (o.-ression fro. the -ri.ary (onsolidation*

Pro:a:ly the easiest way to ill%strate the (%rve5fitting .ethods is towor< wi th ti.e5deforrna tion da ta 3 an a(t%a l (onsolida tion test Wewill %se the data for the load in(re.ent fro. 1 to $ <Pa for the testshown in ig* 7** This data is shown in Ta:le 65$ and -lotted in igs* 6*"a,

:, and (* Note how si.ilar the sha-es of these (%rves are to the theoreti(al(%rves of igs* 6*a, :, and (*



,

!9 Tie !ate ol Conolldatlon

TA,E " T25-&536423n &646 3 L36= ln55n4 0 43 *0 P6 $2. 8.)

n M.in B ..B ..B

o*1*$

1$27

1#"

1$24027

1#7$

6 C6>66n=5'> L3 624 3 T2 M543=

In this .ethod, the defor.ation dial readings are -lotted vers%s thelogarith8 of ti8e, as shown in ig* 6*": and to larger s(ale in ig* 6*!* Theidea is to find ) 2 and th%s

2 , whi(h is the ti.e for ] (onsolidation, :y

a--ro+i.ating ) 100 , the dial reading (orres-onding to the ti.e for 1]D onso I ahon, 1100 or P . Refer to ig* 6* , t e t eoret1(a

(%rve, for a .o.ent* Note that the interse(tion of the tangent and theasy.-tote to the theoreti(al (%rve def ines / l ]* The ti.e for 1]

5%:

(onsolidation, of (o%rse, o((%rs at t / * Casagrande 16#7B s%ggestedthat )(o (o%ld :e a--ro+i.ated rather ar:itrarily :y the interse(tion of

. . .

6*!B* Later resear(h for e+a.-le, Leonards and ira%lt, 16"1B has shownthis -ro(ed%re defines to a good a--ro+i.ation the dial reading at whi(hthe e+(ess -ore water -ress%re a--roa(hes &ero, es-e(ially when the LIR islarge and the -re(onsol dation stress is e+(eeded :y the a--lied loadin(re.ent* 8n

s, on(e we find ) , the initial dial reading*How do we deter.ine ) , the dial reading (orres-onding to &ero

1

-er(ent (onsolidation, on a se.ilog -lot in(e G is -ro-ortional to Ma g %-to ^ & "] EF* 651B, the first -art of the (onsolidation (%rve .%st :e a -ara:ola* To find ) , (hoose an two ti.es, ! and t , in the ratio of 2 to

, an note their (orres-onding dial readings* Toen .ar< off a distan(ea:ove ) e %al to D D D rre(ted &ero

3 "*"$! o*#1" "*$7 *66* "*27 *12!

1* "*##! *$6

$* "*2 *7!$*7# *71$ *71#*7! *276 l*1#7

*27 *171*16

!*! 2*!! 1*7$1*6 2*#2 $*6#1* 2*#" $*$!1$1*6 2*$6 $*217#!*$ 2*21 $*7"



-

3E *

*%**

T25 2n

o $ 2 " 7 1 1$ 12

5: 1*B

EB 1*

a?'*(?i' $*

$*

a l

o*

5E

L3 425 2n

*1 1* 1 1 1

5: 1 *B

EBG

?'$*

3

$*

J

o*

5E

Q4 2n 1 $B

3 1 $ # 2

5:1*

\:

E\:G

a?'*o?'$*

$*

5l

$2. 9. &5436423n-425 G15> 3 =646 3 T6Jl5 9-*: 6 624542>6l5; J l3 425 >6l5; 5 >FG65 334 3 425 >6l5.

397

G

E

1*

E

1*



D

"*7

"*"

"*2 113 t,

"*$

"*

*7E

U R, U a

4* 2t, -4 R# t#

12t &55R

2

* *"Cl

3o(a *2

2j *$3

4 / !. 2n

*

2*7

2*"

2*2

2*$

-P-- R ,oo

U 1]

.

tZ-

2* *11* 1 11 1 1

T25 2n

$2. 9. &545''l2n6423n 3 ro J 45 C6>66n=5 T2543=; =6 3nUI T6Jl5 9-*.

:

e



t.+ (eterlna'on ot the Coefflclent ot Conolldatlon c., 3%

-oint W>

In eF%ation for.,

evera trials are %s%ally advisa:le to o:tain a good average val%e of R0 ,

or

and ) ) 5 ) 5 ) 651#(

In ig* 6*!, three different trials are shown for deter.ining )1

fro.W 1 , W

, W

* , and W

> Toe distan(es , y , an M are .ar e

o a * ve t eordinates (orres ondin to ti.es t , t , and 7 , res (tively* o% sho%ld

satisfy yo%rself that :oth the gra-hi(al -ro(ed%re and %sing EFs* 651#. . .

8n(e the initial and 00 -ri.ary (onsolidation -oints have :een

U 1 U 1 5 1U $1*7! 5 $*6 16*$7 ..

Th%s th average height of s-e(i.en d%ring the in(re.ent is $*7 ... . .

do%:ly drained, so %se Zdr / $*"Q$ in EF* 65* Th%s we have

GUJ, G 2 UJ,$ & '' &

$*16!

0

(.$

1#*" .in " 55B

..

*7l .$Qyr

.$

12 (.$

Re(all that the Casagrande fitting -ro(ed%re fo%nd ) 2 and th%s 2

:y a--ro+i.ating ) 1 This -ro(ed%re did not find 1 sin(e the ti.e for any other degree of (onsolidation .%st :e o:tained fro. the (lassi(al(onsolidation theory in whi(h 4 1 / oo* 4%t the -ro(ed%re does define a 7

(alled 7P for **-ri.ary=B whi(h is a -ra(ti(a*ti.e reF%ired to o:tain a

1



4,, Tie !ete of Conolldetlon

R ,oo

EYN525n46l

T562 453 P26;3n>3 I 643n

S53n=63N5>>23n

4NL3 425

$2. 9.8 T562 3n>3l2=6423n 453 6n= 6 4N26l 5YN525n46l G15G>5= 43 =52n5 7 .

good %sa :Be vaB%e of W 100 8f ten, in -ra(ti(e, P is (alled t 1 The de1iationof the e+-eri.ental (%rve* fro. the theoreti(al (%rve is shown in ig* 6*7*'iff eren(es in the (%rves are the res%lt of se(ondary (o.-ression andother effe(ts s%(h as the rate of effe(tive stress in(rease Leonards, 16!!Bnot (onsidered :y the Ter&aghi theory*

J T6l3'> SFG65 R334 3 T25 $2442n M543=

Ta ylor 1627B also develo-ed a -ro(ed%re for eval%ating ( , %si ng the

sF%are root of ti.e* As with Casagrande3s fitting .ethod, the -ro(ed%re is :ased on the si.ilarity :etween the sha-es of the theoreti(al and e+-eri.ental (%rves when -lotted vers%s the sF%are root of T and t. Refer to ig*6*( and (o.-a1 e it with ig* 6*"(* Note that in ig* 6*( the theoreti(al(%rve is a straight line to at least ^ &:::: 0 or greater* Taylor o:served thatthe a:s(1ssa of the (%rve at 6] (onsolidation was a:o%t 1*1 ti.es thea:s(issa of the e+tension of the straight line ig 6 (B He thns(o%Bd deter.ine the -oint of 90 (onsolidation on the la:oratory ti.e(%rve*

We will %se the sa.e data as :efore Ta:le 6 $B to ill%strate the ,QZfitting .ethod* These data are -lotted in ig* 6*6* Us%ally a straight line(an :e diawn tln o%gh the data -oints in the initial -art of the (o.-ress1on(%rve* The line is -ro0e(ted :a(<ward to &ero ti.e to define ) * The(o..on -oint at ) 1 .ay :e slightly lower than the initial dial reading at&ero ti.eB o:served in the la:orato(y d%e to i..edia te (oro-ression of thes-e(i.en and a--arat%s* 'raw a se(ond line fro. W wOh ali a:s(issas1*1 ti.es as large as eorres-onding val%es on the 3 st line* l11e interse(5tion of this se(ond line and the la:oratory (%rve defines )

+and is the

-oint of 6] (onsohdat1n* lts h.e 1s, of (o%rse, t D

1

9



.+ (eterlnetlon of the Coefflclent of Conolldetlon c. +81

5ZZ@

o

*

R33 90

2=

4 90 / !*$B * / $*" 2n 2*

3 1 1 $ $

2n*

$2. 6*6 &5452n6423n 3 Cv, G>2n T6l3'> >FG65 334 3 425 543=;=646 3 T6Jl5 65$*

The (oeffi(ient of (onsolidation is, as :efore, deter.ined :y %singEF* 65* ro. la:le 651, G 90 / *727* Toe average height of s-e(i.en isalso %sed, as :efore* Therefore

*727 $*"Q$B$ (.$

M $*" .in " sQ.inB

5 $*7 S 1 2 (.$Q s or *6 .$Q yr

This val%e is reasona:ly lose to the D1al%e o:tained %sing theCasagrande .ethod* 4e(a%se :oth fitting .ethods are a--ro+i.ations of the1y, yo% sho%ld not e+-e(t the. to agree e+a(tly* 8f ten (

0 as deter.ined :y the V4 .ethod is slightly greater than ( :y the log t fitting

.et o *

55



"0* T25 R545 3 C3n90ll=64l3n

o% sho%ld also note that c is not a (onstant for a test on a givensoil, :%t it de-ends greatly on the load in(re.ent ratio and whether the

-re(onsolidation stress has :een e+(eeded or not Leonards and ira%lt,16"1B* or load in(re.ents less than t e -re(onso ation stress, (onsolidation o((%rs %ite ra idl and e val%es (an :e rather hi * However deter.inations of P for these in(re.ents is of ten diffi(%lt :e(a%se the. '' . '' .

6*6* or %ndist%r:ed (lays ( is %s%ally a .;ni.%. for in(re.ents near the. . . .

deter.inedK witho%t going to ar :eond P . I dial readigs are -lotted as

as soon as t +

is rea(hed* Not only is the ti.e for testing signif i(antly. .

re %(e (o.-are o w en e o 1 , %also the (ontri:%tion of se(ondary (o.-ression to the e vers%s log o3 (%rve(an :e effe(tively .ini.i&ed see Leonards, 16!"B*

4 now o% sho%ld have noti(ed thatDD the data do not e+a(tl(oin(ide with the initial starting -oint in either of igs* 6*! or 6*6@ that is,

o

the differen(e :etween the initial la:oratory dial reading and R , the

o

1* Merti(al elasti( (o.-ression of the soil s-e(i.en, -oro%s stones,and a--arat%s*

$* Lateral e+ ansion of the soil s (i.en if it is not tn..ed e to the dia.eter of the ring*

. .

ring*

o% will have the o--ort%nity to %se the two (%rve5fitting .ethods todeter.ine ( in the -ro:le.s at the end of this (ha-ter*

9.) &ETERMI%ATIO% O$ THE COE$$ICIE%TO$ PERMEABILIT7

o% .ay re(all fro. ig* !*" that the (oeffi(ient of -er.ea:ility, ,of the soil .ay also :e o:tained indire(tly fro. the (onsolidation test* l yo% ta<e EF* 65# and solve for , yo% o:tain

1

0

.



9.) &545ln64l3n 3l 45 C35ll5n4 3l P5n56Jlll4 "0!

6512B

1he val%e 3 e 1s the v1d ratio at the start of the ti.e rate read.gs for 6given load in(re.ent*

E+AMPLE 9.9

(215n:

The ti.e5defor.ation data for the load in(re.ent 1 to $ <Pa of the test

in ig* 7*2* ro. Ta:le 65$ and ig* 6*!, a cv val%e of *71 .*

Qyr $*" + 152 (.$QsB (an :e deter.ined*

R5FG25=:

Co.-%te the (oeffi(ient of -er.ea:ility, ass%.ing the te.-erat%re of thewater is $>C*

S3lG423n:

l4 is first ne(essary to (o.-%te the (oeffi(ient of (o.-ressi:ility fro. EF*

75 and %sing ig 7 2hD $*1$ 5 1*!"

$ 5 1B <Pa

/ *#"Q<Pa / #*" + 15

ro. EF* 6512,! / cvp( gav

e1

$*" S 1 2 5S 15555 S 6*71 5 S #*" S

1

s

r n$ K X ro K

s 4n# s$

1 $*1$ N 1 (.

5 $*6 + 1 (. 5 $*6 + 1 9 .s s

Note that the e %sed . the eF%a%on 1s the vo1d r[tlo at the start ofthe load in(re.ent rather than the original or in sit% void ratio*

,j



TA,E 9-! TN26l V6lG5> 3 45 C35225n4 3 C3n>3l2=6423n Cv

c.,

oil

4oston :l%e (lay CLBLadd and L%s(her, 16"B

8rgani( silt 8HBLowe, a((heo, and eld.an, 16"2B

la(ial Jalee (lays CLBWalla(e and 8tto, 16"2B

Chi(ago silty (lay CLBT(r&aghi and Pe(<, 16"!B

wedish .(di%. sensitiv( (lays CL5CHB

(.$ Qs, + 1 52 $ Qyr

2 k $ 1$ k "

$51 *"5#

"*57*! $*5$*!

7* $*!



Holt& and 4ro.s, 16!$B1* la:oratory *25*! *15*$$* field *!5#* *$51*

an ran(is(o 4ay G%d CLB $52 *"51*$Ge+i(o City (lay GHB *651* *#5*

Leonards and ira%lt, 16"1B

5@@,%

E

+0

1 $30

20

,J

e9D

5o111

o #?e9'o,J

oE

XCo

I?

.

1 52

n=2>4GJ5= >6Nl5>:cv 2n 6n5 3 122n 3N5>>23n

K,*,,

cv 2n 6n5 3 53N5>>23nl25> 6J315 42> l3D5 l224

C3Nl545l 53l=5=>6Nl5>: cv l25> J5l3D 42> GNN5 l224

1

+.0

2.0

1.0

0.+

0.3

0.2

%

E

,J

*0 40 " 7 1 *0 140 1" *1

L2FG2= l224 LL

$2. 9.0 ANN3Y2645 35l6423n> 3 45 35225n4 3 3n>3l2=6423n Cv

D24 45 l2FG2= l224 645 .). %61, 9.

4,4

-

1

-



9.$ T)PICA 2A'E& O* Cv

Ty-i(al val%es of t e (oe 1(1ent o (onso 1 a ion c or a vils are listed in Ta:le 65#* A ro+i.ate (orrelations of cv with the liF%id

li.it are -resented in ig* 6*1*

.M WE2A'ATION O* &ECON(A!)

Th%s far we have dis(%ssed how to (o.-%te the (onsolidation or -ri.ary settle.ent se , an ow 1t vanes w1t 1.e* e o er wo (o.-onents of total settle.ent as Dven : EF* 751 were the i..ediate settle.ent

s4 and se(ondary settle.ent ss. I..ediate settle.ent is (al(%lated fro. sti(it

and Poisson3s ratio of the (o.-ressi:le soils* In addition, the (onta(t stressis ri % ion i

esti.ation of i..ediate settle.ents is treated in fo%ndation engineeringte+t:oo<s and will not :e dis(%ssed ere.*

ression is a (ontin%ation of the vol%.e (hange thatstarted d%ring -ri.ary (onsolidation, on.ly it %s%ally o(.(%rs at a

..%(h

tion in that it ta<es -la(e at a constant effective stress, that is, afteressent1a y a e e+(ess -ore -ress Dsettle.ent see.s to res%lt fro. (o.-ression of the :onds :etween individ5%al (lay -arti(les and do.ains, as well as other e e(ts on t e .1(ros(a e

od* Another (o. li(atin fa(tor is that

in the field it is diffi(%lt to se-arate se(ondary (o.-ression fro. . (on.soli5

thi(<* Parts of the layer near the drainage s%rfa(es .ay :e f%lly (onsoli5dated, an t ere ore %n ergo.g se(on ary D D Dnear the (enter of the layer are still in **-ri.ary*= 4oth ty-es of settle.ents

(ontri:%te to the total s%rfa(e settle.ent, and se-arating t e e e(ts .D D ettle.ent is not a si. le .atter*

However, in this se(tion we sha.ll -resent a -ra.(ti(al wor<ing hy-othesis,

and we shall show yo% how to .a<e esti.ates of se(ondary settle.ent forsorne si.-le (ases*

There is %nf ort%natel , a lot of (onf%sion in the geote(hni(al litera5 t%re as to the :est way to des(ri:e the .agnit%des and rates of se(on ary(o.-ression* In this se(tion, we shall follow Ray.ond and Wahls 16!"B

+87

,J1

.



<

+86 Tie !ate of Conolldetlon

and Gesri and odlews<i 16!!B, who define the secondary co8pression

inde (** as

( /--

.. A log t 651B

where $e the (hange in void ratio along a -art of the void ratio vers%s thelogarith8 of ti.e e%nDe :etween ti.es 1 and 1* , and

$t /the ti.e :etween t $ and t 1

This def inition is analogo%s, of (o%rse, to the -ri.ary(o.-ression inde+ Ce, defined as $e Q A log o3 EF* 75!B* In addition,we will define the 8odified secondary co8pression SndeC,, analogo%s

to EF* 756, as

(*** /1

**e 651"B

where (**/ the se(ondary (o.-ression inde+, EF* 651,eP / the void ratio at the start of the linear portion of the e vers%s

log t (%rve* 8ne (o%ld also %se e , the in sit% void ratio, with

no a--re(ia:le loss of a((%ra(y*B

o.eti.es (*** is (alled the secondary co8pression ratio, or the rateof secondary consolidation. As Ladd et al* 16!!B note, (*** / AQA log t.

The se(ondary (o.-ression inde+, (**, and the .odified se(ondary(o.-ression inde+, .... (an :e deter.ined fro. the slo-e of the straightline -ortion of the dial reading vers%s log ti.e (%rve whi(h o((%rs after

-ti.a1y (onsolidation is (o.-lete see, fo1 e+a.-le, ig* 6*!B* Us%allythe AW is deter.ined over one log (y(le of ti.e* The (orres-onding (hangein void ratio is (al(%lated fro. the settle.ent eF%ation EF* 75#B sin(e yo%<now the height of s-e(i.en for that in(re.ent and e *

To -rovide a wor<ing hy-othesis for esti.ating se(ondary settle.en ts, we shaH .a<e the foBlowing a! ""pi" ahont the hehavior of fine5grained soils in se(ondary (o.-ression* T:ese ass%.-tions, :ased onthe wor< of Ladd 16!1aB and others and s%..ari&ed :y Ray.ond andWahls 16!"B, are as follows9

l. (** is inde-endent of ti.e at least d%ring the ti.e s-an of in5

2. .. is inde-endent of the thi(<ness of the soil layer*3. (** is inde-endent of the LIR, as long as sorne -ri.ary (onsolida

tion o((%rs*4. The ratio (**Q Ce is a--ro+i.ately (onstant for .any nor.ally

(onsolidated (lays over the nor.al range of engineering stresses

Ty-i(al dial reading vers%s log ti.e :ehavior (%rves ill%strating theseass%.-tions for a nor.ally (onsolidated (lay are shown in ig* .11. o%

0

1



55555

5 --- 5555555555 5555D 55 5D D5 5 5D55555555--- D 5DDD-5



.M E/aluallon ol &econdar@ &ettleent 4,7

a9 5di e2:2?'

o

aB# 00 - *00 P6 LI R l B

555L3 425, 4 --------.

S53n=6 G15> n34n55>>62l N66ll5l

6 E54 3 =62n65 =2>46n5.

a9H:2

, e2:2?'5o

6: *00 - !00 P6LI R / 0.)

N

L3 2

J E54 3 l36= 2n55n4 6423 6n= 3n>3l2=6423n >45>>

$2. 6*11 TN26l >53n=6 3N5>>23n J56123 3 45 D3-2n N345>> J R63n6 6n= W6nl> 16!"B*

(an see that the rate of se(ondary (o.-ression e+-ressed in ter.s of settle.ent ( aW) -er log (y(le is ass%.ed to :e iode-endent of the 3 thi(<ness of the s-e(i.en as well as the load in(re.ent* There is sorne effe(thowever of the eonsolidation stress, and as Ges12 and 8odlews<i 16!!B

-oint o%t, C is strongly de-endent on the final effe(tive stress*The wor<ing hy-othes1s 1s %sef %l as a hrst a--ro+i.at1on for

esti.at ing se(ondary settle.ents* However yo% sho%ld e+-e(t sornea:errations in the a(t%al long5ter. settle.ent res-onse of thefo%ndation :e(a%se the

55



408 Tie !ate of Conolldatlon

ass%.-tions are ad.ittedly an oversi.-lifi(ation of real :ehavior* or e+a.-le, the se(ondary (o.-ression (%rves of ig* 6*11 .ay not :ea(t%ally -arallel or even have a (onstant slo-e* There is sorne eviden(e thatC< .ay (hange with ti.e, :oth in the la:oratory Gesri and odlews<i,16!!B and in the field Leonards, 16!#B* Also, the d%ration and thereforethe .agnit%de of se(ondary settle.ent is a f%n(tion of the ti.e reF%iredfot (o.-letion of -ri.ary eonsolidation P , and fro. earlier vZor< in this(ha-ter yo% <now that the thi(<er the (onsolidating Vayer, the longer is theti.e reF%ired for -ri.ary (onsolidation* Even tho%gh the strain at the endof -ri.ary (onsolidation for :oth thin and thi(< layers is a:o%t the sa.eas shown in ig* 6*1 laB, there is li.ited eviden(e A:oshi, 16!#B that the

slo-es .ay not :e -arallel and that C< .ay de(rease as the thi(<ness of thesoil layer in(reases*Ass%.-tions # and 2 are a--ro+i.ately (orre(t* Ass%.-tion # was

verified :y Leonards and ira%lt 16"1B and Gesri and odlews<i 16!!B,e+(e-t that the load in(re.ent .%st :e s%ffi(ient to go well :eyond the -re(onsolidation stress* The fo%rth ass%.-tion, that the ratio C Q Ce isa--ro+i.ately a (onstant, has also :een verified :y Gesri and odlews<i16!!B for a wide variety of nat%ral soils* Their wor< is s%..ari&ed inTa:le 652* Toe average val%e of C Q Ce is a:o%t *, and in no (ase ^lidthey find a val%e of that ratio to e+(eed 8* l. The range for inorgani( soils is*$ to *", while the range for organi( soils and -eats is so.ewhathigher* They also showed that this ratio holds at any ti.e, effe(tive stress,

and void ratio d%ring se(ondary (o.-ression* Toe only e+(e-tion, asshown :y Leonards and ira%lt 16"1, ig* #B s)e.s to :e the loadin(re.ent that straddles the -re(onsolidation stress, o. 8:vio%sly, .any F%estions re.ain to :e answered (on(erning the to-iof se(ondary (o. -ression*

TA,E "+ V6lG5> 3 C QC( 3 %64G6l S32l>

oil C,*QC,

8rgani( siltsA.or-ho%s and fi:ro%s -eatCanadian .%s<egLeda (lay CanadaBPost5gla(ial wedish (layoft :l%e (lay Mi(toria, 4*C*B8rgani( (lays and siltsensitive (lay, Portland, GEan ran(is(o 4ay G%d New Lis<eard CanadaB varved (layGe+i(o City (layH%dson River silt

New Haven organi( (lay silt

*#5*"*#5*7*65*1*#5*"

*5*!*$"

*25*"*$5**25*"*#5*"*#5*o#D*#5*"*25*!

kGodified after Gesri and odlews<i 16!!B*

555555555D

0

0

0



e·FF0

6*! E/eluatlon of &econder@ &ettleent 409

I, for sorne reason, yo% do not want to or (annot deter.ine @N fro.la:oratory test data, yo% (an %se the Ca Q Ce data of Ta:le 652 for si.ilar soils, or si.-ly %se an average Caf Ce vah1b of *, whi(h is a((e-ta:le for -reli.inary (al(%lations* Gesri 16!#B has -rovided another .ethod too:tain the se(ondary (o.-ression inde+, a(t%ally the .odified se(ondary(o.-ression inde+, and it is shown in ig* 6*1$* Here the Ca, is -lottedvers%s nat%ral water (ontent of the soil*

We will ill%strate how to est;.ate se(ondary settle.ent in E+a.-les6*1, 6*11, and 6*1$*

W6n 662n3 l6 %5Dl6n= 6n= All5l, 90

M5Y23 C24 l6 L53n6=> 6n= (26Gl4, 9

C6l653G> 36n2 >2l4 W6l>, 9*

5 m L5=6 l6 C6D3=, 9)3D56n N 6> 2

A3N3G> 6n= 2J3G> N564 L56 6n= B6Dn5, 9!

(J) C6n6=26n G>5 A=6>, 9) O6n2 62n5 =5N3>24> K56n5, 9)

.----------,"

Q

Q :a

Zl*E

oG

o

O O6n2 >2l4, 54. M36n, 54 6l., 9)8

%64G6l D645 3n45n4 \

$2. 6*1$ M3=225= >53n=6 3N5>>23n 2n=5Y 15>G> n64G6lD645 3n45n4. A45 M5>2, 16!#* S55 M5>2, 16!# 3 =5462l> 3 45555n5> 2nlG=5= 2n 42> 2G5.

Q Q

Q



'

E9A3PE .18

(215n:

Toe data for Pro:le. 751$ -l%s the following ti.e rate of (onsolidationdata for the load in(re.ent of 2 to 7 <Pa* This load in(re.entre-resents the anti(i-ated load in the field*B Ass%.e the (onsolidationsettle.ent, se , is # e. and that it oee%rs af te1 $ . TI1e thi(l.ess of the(o.-ressi:le layer is 1 .* The initial void ratio $ is $*7, and the initialheight of the test s-e(1.en 1s $*2 .., and the .1t1al dial reading is 1$*!..*

1B'ial Reading

$BEla-sed Ti.e

.ioB

#BVG2= 3Ratio

11*$$2 o $*"#111*11 *111*1$# *$ $*"1"11*7$ * $*"611*16 1* $*"1*62$ 1*7 $*771*76 #* $*!"1*!11 " $*#1*"" 1 $*#B1*21 1" $*"1 *17 # $*2!#6*616 " $*2##

$*216*"12 17 $*#7!6*276 # $*#"76*#!# $ $*#

6*1!$ 17 $*#$

6*# 2$6 $*#1

Co.-%te the a.o%nt of se(ondary (o.-ression that wo%ld o((%r fro. $to years af ter (onstr%(tion* Ass%.e the ti.e rate of defor.ation fart:e load range in the test a--ro+i.ates that o((%rring in t:e field*

41,

1



6*! E/aluatlon of &econdar@ &ettleent +11

S3lG423n:

The sol%tion 43 this -ro:le. 1eF%ites an eval%ation of C EF* 51B* o avoid ratio vers%s log t (%rve .%st :e -lotted fro. the given data* We (anreadily (al(%late the void ratio at any height or thi(<ness of the s-e(i.end%ring the (onsolidation test :y %sing the following .ethod* 4y definition,e = / =, and, for a (onstant s-e(i.en area, e Z / Zs , whi(h is theratio of height of voids to the height of solids* Toen, fro. the -hasediagra. ig* E+* 6*1aB, the void ratio at any dial reading ) .ay :eo:tained fro.

F Zo 5 Zs : 5 F )o 5

R^

Zs

Y651!B

where H*, the height of voids at ti.e t, Zs the height of solids,U 5t:e origioa l :eig:t oY s-e(iroeo,1

the initial dial reading, and ) dial reading at ti.e t.

ro. the -hase diagra. and the initial (onditions of this -ro:le.,2$

U UX D "*76 ..o

or the load in(re.ent 2 to 7 <Pa, the initial dial reading is 11*$$2@ thedial reading ) at the very :eginning of the test (orres-onding tos-eei.en height U : is 1$*!* Tlrns for the :eginning 3 this loadin(re.ent, e fro. EF* 651! is

K $*2 5 "*76B 5 1$*! 5 11*$$2B K e 5 "*76 5

$ D"#1

V3lG5 H524

T 5

¡ 4

!!,3!!!!3J1 55555`5Z

H 3n>3l 2=6423n>6Nl5 524 64

1 H =26l 56=2n R

2

$2. EY. 9.06 $3 2n2426l 3n=2423n>, 5 /- 50 , U ... U 0 , 6n= W ' W 0 D

*DJ

W

e

5

1



Í '1

%

oLO

o

Go

t=

G=

e9o

1

Cl.::-

o(o73=13

oo

eE *e

,**=

E oi2/

D

ZZ

o

3.=

.555 .. D55555 555555555D5555555 55555 5 5D5 55555555 5555555555 5555555D555555555D5DD55 5555

?'

o



.M E/aluatlon of &econdar@ &ettleent +1%

This val%e of e at W 11*$$2 is shown in (ol%.n # of the given data* Toe

of ) into EF* 651!* Ne+t, -lot the void ratio, (ol%.n #, and the ela-sed ti.e, (ol%.n $,

on se.ilo a er, as shown in ig* E+* 6*1:* @ is then fo%nd to :e *$* Note that C< de when d log (overs one f%ll log (y(le* The (orres-onding .odif ied se(ondary (o.-ression inde+ CaE EF* 651"B is *$Q1 $p )/ *$QKl $*#!$B *12@ $P is o:tained f ro. ig* E+* 6*I8: at the

To (al(%late se(ondary settle.ent ss , %se o%r :asi( settle.ent eF%a5

de s e

Now, however, de is a f%n(tion of ti8e and not stress* %:stit%ting de fro.

e s

/ *2" . / 2*" (.

i..ediate settle.ent s that .ay also have o((%rred*The se(ondary sett e.ent .ay a so e (o.-%te y .eans o Fs*

752 and 651" where

C (aE Ho d log t B 6516B

/ *12 1 .B log

$/ *2" ., as :efore

A detailed e+a.-le ill%strating the (o.-%tations for :oth se and ss is

E9A3PE .11

(215n:

'ata given in E+a.-le 6*1 Pro:le. 751$B* Toe initial water (ontent ofthe s-e(i.en is 1*!]*

o1



414 '!me 6ate of Con8,lldatlon

!euired:

ro. the data listed in Ta:le 652 and ig* 6*1$, esti.ate the aB C and :BCajD (B Co.-are with the val%es (al(%lated in E+a.-le 6*1*

S3lG423n:

ro. Pro:le. 751$, the val%e of Ce is 1*$# and the val%e of CeY is *#$*

a. or an ran(is(o 4ay G%d, %se an average val%e of Ca/ Ce of ** Therefore

C * Ce B *1*$#B *"$b. ro. EF* 651", Ca, Ca Q1 $P . ro. ig* E+* 6*1:, $P $*#!$*

Therefore

*"$Caj 1 $*#!$ / *17

A se(ond way to est;.ate the .odified se(ondary (o.-ression inde+is to %se ig* 6*1$, where Ca, is -lotted vers%s nat%ral water (ontent* or o%r e+a.-le, the initial water (ontent was 1*!]* ro. ig* 6*1$, a val%eof Caj of a:o%t *1 or higherB is o:tained if yo% %se the dashed line*

(* Co.-are with the (al(%lated val%es* ro. E+a.-le 6*1, C *$ and Ca, *1* Toe agree.ent %sing the a--ro+i.ateval%es is (ertainly a((e-ta:le for -reli.inary design esti.ates*

.4 CO3P!EHEN&I2E E9A3PE O* A TI3E!ATE O* &ETTE3ENT P!O,E3

E9A3PE .1

(215n:

A :rown silty sand fill . thi(< was -la(ed over a 1 . thi(< layer of (o.-ressi:le gray silty (lay* Underlying the (lay layer is :rown sandygravel* The soil -rofile is shown in ig* E+* 6*1$a* Ass%.e for this -ro:le.that the settle.ent of the fill and the sandy gravel is s.all (o.-ared to the



.4 Co0rehenl/e E5e0le ol W Tie !ata ol &ettleent Pro#le 415

S32l N32l5

3 P5>>G5 P6

1 1 $....- --.-- --$- -&---

=3 / p[ / *.0 MQ# + 9.8 + )

/ 98. P6

-+

51

615l : >oi' (P ,.....A on

. 2n3N5>>2

E*e

@

51

!$*!-*0 -- ----- ----

.) ".

-*) o9o D,1o $ / > s P,at 5 P( Bg&

98. .)* - .09.8 S ) .

/ 98. .)

". P6

$2. EY. 9.*6 S32l N32l5 6n= 554215 >45>> 15>G> =5N4.

settle.ent of the silty (lay layer* Pro-erties of the nonnally (onsolidatedsilty (lay layer are9

Initial void ratio, e/ l.l.

Co.-ression inde+, Ce/ *#"*e(ondary (o.-ression inde+, @N *"*at%rated density, Psat / 1*$ GgQ.#

Coeffi(ient of (onsolidation, $,, / *77 .$

Qyr*The density of the silty sand fill, p, is $* GgQ.# and the gro%nd

water ta:le 2> at the interfa(e of the fill and (lay, at 52 .*

3.o

,



41$ Tie !ate of Conolldatlon

R5FG25=:Part l. Co.-%te the (onsolidation settle.ent of the silty (lay layer

d%e to the we1ght of the ) . of new ll:Part 11* Co.-%te the ti.e rate of settle.ent*

Part . Co.-%te andK -lot o3 & B when ^ / ]*Part IM* Co.-%te the se(ondary settle.ent

S3lG423n:

Part I9 The -ro(ed%re for this -art is l B (o.-%te the initial effe(tive

over:%rden -ress%res of soil layers, $B (o.-%te the in(rease in verti(alstress d%e to e+ternaV load, #B (o.-%te the final effe(tive verti(al stress,and 2B eo.-%te settle.ent*

1. Initial effe(tive stress9/ p3gM , -rior to fill -la(e.ent*

o,9aeo .B / oov F 51 .B 5 1*$ 5 1*B Gg 0

.#

/ !"* <Pa

$* In(rease in o d%e to fill / pgh rni*

S 6*71 8Ws2 S 1 .

A3 / $* GgQ .#+ 6*71 .Qs$ Y . / 67*1 <Pa

!. inal effe(tive stress / initial effe(tive stress A3

>( to- of silty (layB 5 8 Aa 5 67 l <Pa

a# :otto. of silty (layB / !"* 67*l / 1!2*" <Pa

The a:ove stresses are -lotted in ig* E+* 6*1$a* C%rve A re-resen tsthe initial ver ti(al effe(tive ovet :. den sll esses

-1io1 to the -la(e.ent

of the . of silty sand fill* C%rve = re-resents the final verti(al effe(tiveover:%rden stress d%e to the ll alter (o.-lete (onso:datton of the s1lty(lay layer has ta<en -la(e* C%rve eF%als

A3, where A3 is the

in(rease in -ress%re d%e to the fill* We will ass%.e that $u / A3 onedi.ensional (o.-ressionB and that the load is -la(ed ali at on(e* A(t%ally

. of fill .ay ta<e days to wee<s to -la(e and (o.-a(t :%t, for -%r-osesof o%r e+a.-le, let %s ass%.e it was -laeed instantaneo%sly in one loadin(re.ent*B

4. Re(all that the silty (lay is nonnally (onsolidated* Th%s the(onsolidation settle.ent of the layer is given :y EF* 7511*

7511B

or the .idde-th of the layer, 0 / #7*# <Pa and a# ` $a / 1#"*2 <Pa*

1

1 1



55555555D55D55DDD55



5

9.8 C3N55n>l15 EY6Nl5 3 6 T25 R545 3 S544l55n4 P3Jl5 4175

Th%s .:; 4'I 3X_@ ,t

se 0.J 1 1*1 log #7*#1*2$ .

in(e the silty (lay layer is 1 . thi(<, it is -r%dent to divide the totalthi(<ness into thinner layers to i.-rove the a((%ra(y of res%lts* A 1* .thi(< layer is (hosen* Toe settle.ent of ea(h of these layers is s%..ed %-to o:tain the total (onsolidation settle.ent of the silty (lay layer* To assistin the (o.-%tations, ig* E+* 6*1$: is e.-loyed, and the (orres-onding}G K*K* %vo %**%*%* uvo , **v %**1* ==3 5, ''.:% --... - ****** K

1, $B #B 2B B "B !1 7B 6B 1B 11B

&EPTH --

#

.:.3 LO( (e THICK%ESS

BELOW8EPTH

SOIL

(RO%& BELOW T7PE 3 A3 COL (eSR$ACE @H>IN> 1"1

av, 5WW

1 eO$ &EPTH SETTLEME%TI%CREME%T

. < Pa < Pa . .

....X

*! Cli #*7 67*111*6

1*2# *#"*#"

1* *#"!1 1*1

"* !*$ 11* .) *6!6 *$$

1

7

6*7*! Q 16*1 T 11!*$

*!77

1 *$#

1*$ U $"*71

1$2*6 *""7 2 *1!$

1 ?? ?

11 + 1 #2*2 *7" *11 3*12 2

1$* 1#*$ 1 2$*1 U

12*$*$$

UT *1#2 "3=

U2$*1 1

1212*! 1

26*!12!*7

*2!#Z

+

*1$$

1555 An , 1

1*i

1"*$1

!*21*

!*2

1"#*11!*! "* n

17*1!*7

16*$ !$*!!$*!

$

1555

555 e / AH / 1*!1 .

555 555 c,9 11]

555 555

555 555 555

$2. EY. 9.*J S544l55n4 3NG46423n>.

' ' '. . . . 5 . ** *,**** ***

>D>

#*7

T Q16*"

0

U

1#$* l11*!

:*2## U *111

*2

1 *1#

*#!1 *6



-- -- ... . - JD5 5

*,,3*KDKD9*ZK,, .,.;U., -- -:: ,,*?3* ' ,E 7 ., -D7.D)E

. . ' - 3 DD9D5 *T,3W,@ K, ** , ... . ¡J ? ?? ,,.;l. .. .. ;;



<

418 Tie !ete ot

Coneollc:latlon

layers* or e+a.-le, the average de-th of the si+th layer is 51#*$ .@while o3 A3 / 12*$ <Pa* These val%es are si. 1 s(aled

off of ig* E+* 6*1$a* Inserting the a--ro-riate val%es into EF* 7511, weo:tain

1* ..se 8 *#" l l l 1og12*$

*1#2 ., 1$*,512 ,

(onsolidation settle.ent of the 1 . thi(< layer is 1*!1 ., or a:o%t 11]stra.* 1s va %e o se 1s a o%t o arger an e se e.en (a (% a e a:ove for a single 1 . thi(< layer* Ali things (onsidered, it -ro:a:ly is a.ore a((%rate -redi(tion* Altho%gh the answer is given to two de(i.al -la(es, there is seldo. 0%stifi(ation for s%(h -re(ision in settle.ent (o.-%tations* An est;.ate of =a--ro+i.ately 1*! .= wo%ld %s%ally :e of s%ffi5

16!!B has shown that (onsolidation settle.ents (an :e -redi(ted within arange of a:o%t $]*

Note that a settle.ent of 1*! . .eans that 1*! . of the fill wo%ldsettle :elow the gro%nd water ta:le, whi(h is at the original gro%nd s%rfa(e,

r s in the densit of the fill d%e to :%o an( wo%ld res%lt*Th%s the a(t%al settle.ent will :e so.ewhat less than 1*! .* This (ondition has :een ignored in this e+a.-le*

In -art II of this e+a.-le yo% are as<ed to (o.-%te the ti.e rate of

settle.nt* We (an (onstr%(t Ta:le E+* 6*1$a in(or-orating Uavs G, se , d

(onstant at 1 . see e(* 6*# and A--endi*+ 45$B* in(e the (lay layer hasdo%:le drainage, the val%e of Hdr in EF* 65 is 1 .Q$, or !* .* Toe c., isgiven as *77 .$Qyr*

TA,E E9. .1a T25 R645 3 S544l55n4

1B $B #B 2B

1 & se t

2$ 1

yrB

*1 *7 *1! *$

*$ *#1 *#2 $*#*# *!1 8*I*2 *1$" *"7 7*$"

*" *$7! 1*# 17*7$*! *2# 1*$ $"*2$*7 *"! 1*#! #!*1!*6 *727 1*2 *6*6 1*1"# 1*"$ !"*$



.4 Co0rehenl/e E5e0le 3 Tie !ete of &ettleent Pro#le 419

Mal%es of G fer given val%es of Uavg fro. Ta:le 6 l are s%:stit%tedinto this eF%ation and solved for t, (ol%.n 2 in Ta:le E+* 6*1$a* Toesettle.ent in (ol%.n # is o:tained fro. EF* 651$ :y .%lti-lying the total(onsolidation settle.ent for this e+a.-le, 1*!1 ., :y (ol%.n l. Toe datain (ol%.ns # and 2 are -lotted si.ilar to ig* 6*"aB in ig* E+* 6*1$(*

o

*

EEC1B

EC1B

*99@C1B

MB

1*

3 1 $ #

T25

40 60 70

$*

$2. EY. 9.* &646 3 T6Jl5 EY. 9.*6.

In engineering -ra(ti(e, only esti8ates of the ti.e rate of settle.ent(an :e .ade :e(a%se of the great de-enden(e that the rate of settle.enthas on the drainage -ath* I there were continuous layers of -er.ea:le soil,for e+a.-le thin sand sea.s, inter:edded in the 1 . (lay layer, then therate of settle.ent wo%ld :e signifi(antly greater see for instan(e, E+a.-le6*"B* Another fa(tor is o%r ina:ility to a((%rately -redi(t c > I -ossi:le,esti.ates sho%ld :e field ehee<ed, es-eeially fer i.-ortant 0o:s*

In -art 111 of this e+a.-le yo% are as<ed to deter.ine the effe(tivestress with de-th when vg / ]* The (o.-%tations start with the

eval%ation of , fro. ig* 6*# and the (onstr%(tion of Ta:le E+* 6*1$:*Toe de-ths in (ol%.n 1 of Ta:le E+* 6*1$: re-resent evenly s-a(ed

elevations within the 1 . thi(< (lay layer* Col%.n $ is the ratio of thede-th to layer thi(<ness* Toe ti.e fa(tor for Uavg of ] is fo%nd fro.Ta:le 9 l to :e *16! %se *$ for (onvenien(eB 1Ising ig 6 # along theti.e fa(tor (%rve for & / *$ and the vario%s ratios of M Q Z in (ol%.n $ of Ta:le E+* 6*1$:, find the val%es of the degree of (onsolidation at theseratios* or e+a.-le, at M / U / 8 and $*B, the val%e of is 1*, or 1]

1*

***



42, Tie !ate of Conolldatlon

TA,E E9. .1# l>33n5 &646 3 Uavg / )01B

'e-th$B

M / Z #B 2B

I,,.a4 <PaB

5 o .00 67*15"*77 *$ *! "7*!57*! * *2 22*"

51*"# *! *$7 $7*51$* 1* *$# $$*"512*#7 1*$ *$7 $7*51"*$ 1* *2 22*"517*1# 1*! *! "7*!5$ $* .00 67*1

(onsolidation at the to- and :otto. of t he (lay layer* At a ratio of *$ M / Z and l*! M / Z : the degree of (onsolidation is -o/o, et(* These val%esare -la(ed in (ol%.n #* The effe(tive stress is fo%nd :y .%lti-lying in(ol%.n # :y the a.o%nt of a , the weight of added fill, or 67*1 <Pa* A -lotof the iso(hrone for vg / ] is shown in ig* E+* 6*1$d* o% sho%ld(o.-are this f ig%re with ig* E+* 6*1$a* ro. Ta:le E+* 6*1$a, yo% (an seethat it ta<es a:o%t 1# years to develo- this iso(hrone* Toe iso(hronere-resents the dividing line :etween the a.o%nt of a that has gone into

effe(tive stress and the a.o%nt of -ore -ress%re in the (lay layer thatre.ains to :e dissi-ated* I the (lay layer were sa.-led and a (onsolidation test were -erfor.ed at a de-th of 5 1$* . the .iddle of the (laylayerB, the val%e of the -re(onsolidation -ress%re, wo%ld :e "*6 <Paa1 a , #7*# $$*" <PaB* This val%e is o:tained fro. ig* E+* 6*1$d*

There are -ra(ti(a i.-li(ations D to :e derived fro. -art III* I afo%nda tiao eogioeer waoted to red%(e the (onsolidation settleli0ent of astr%(t%re, the site (o%ld :e preloaded with fill and the fill re.oved later*Toe ti.e the -reload sho%ld :e a--lied .ay :e (al(%lated as in thise+a.-le* Af ter the f ill was re.oved, if the stress distri:%tion of the newstr%(t%re was a:o%t the sa.e or less than the ] iso(hrone shown in ig*E+* 6*1$d, then the (onsolidation settle.ent wo%ld :e (al(%lated :y %sing

the re(o.-ression inde+ Cr , and the settle.ents wo%ld :e s%:stantially lesse(* 7*!B*

Part IM, the final -art, ill%strates the (o.-%tation for ti.e rate of se(ondary (o.-ression* irst -lot the (onsolidation settle.ent data inTa:le E+* 6*1$a, se vers%s log ti.e, shown in ig* E+* 6*1$e* Note that thisis a theoreti(al settle.ent5log ti.e relationshi-* olving for the se(ondary

o4



.4 Co0rehenl/e E5a0le or a Tie !ate of &ettleent Pro#le 421

S32lN32l51 P5>>G5 P6

1 1 $

DDDD9 @:: SM Q W At t / 1$*6$ ,

avg 5l>33n5 5N5>5n4> 63Gn4

.

5$

&62n65 5

$2.

*" .

*2$6 .Q log (y(le of ti.e

This slo-e is shown in ig* E+* 6*1$e* This sa.e rate of se(ondary(o.-ression starts at -oint a on the theoreti(al settle.ent5ti.e (%rve*Point a (orres-onds to the settle.ent at 1] -ri.ary (onsolidation F se 1*!1 .B* Note that the -ri.ary (onsolidation (%rve has :een e+tra-olated slightly to -oint a. Th%s, fro. ig* E+* 6*1$e, the total settle5

,.



o1

*$

*2

*"

, *7

1... 1 1*

@

I 1*$

A tN52 $l63f . - l5

4

E@

CJl , 1*2

1*"

1*7

$*

$*$

$*2*11

se at U 1 1*!1 1 . 5

1

T25

2. E. 9.:;l5 &646 3 T6Jl5E. 9. 6.

P26

1 $ 1

e



Pro#lea 423

.ent at the end of, say, $ years is e+-e(ted to J5 a:o%t 1*7 .* To J5.ore -re(ise than this in -redi(ting settle.ents is :eyond o%r a:ility toa((%rately eval%ate soil -ro-erties and field drainage (onditions*

The -re(eding e+a.-le ill%strates sorne of the (o.-%tational detailsof a ti.e rate of settle.ent analysis for the si.-le (ase of one5di.ensionalloading and for a nor.ally (onsolidated (lay* I the loaded area were of li.ited e+tent, then yo% wo%ld have to ta<e into a((o%nt the stressdistri:%tion with de-th ai <ey -oints %nder the loaded area* 7o% wo%ld %sethe te(hniF%es dis(%ssed in e(* 7*1$ to esta:lish (%rve in a diagra.,si.ilar to ig* E+* 6*1$a* o% .ight even have to do this for severa

se(tions %nder the fo%ndation, for e+a.-le in the (enter, at the edge, and%ndet the (o.er of the loaded atea*

4e(a%se the (lay in E+a.-le 6*1$ was nor.ally (onsolidated, (o.-%5tation of the (onsolidation settle.ent -art IB was rela:vely stra1ghtfor ward* I the (lay had :een over(onsolidated, that is, if '. ^ then yo%wo%ld %se EFs* 751" thro%gh 7516, as the (ase .ay :e* o.eti.es the%--er -art of the ayer is ove((oosolida ted, aod t:e lower -a(t is noanally(onsolidated, and yo% have to ta<e this into a((o%nt in yo%r (o.-%tations*Anothet (o.-li(ation that of ten oee%rs is that the soil and eonsolidation -ro-erties F Ce, e B vary thro%gho%t the soil -rofile* In that (ase, when yo% :rea< %- the -rohle .to s.aller layers, as we d1d . 1g* E+* 6*1$a, thelayers will not ne(essarily :e evenly s-a(ed* In this (ase, ta:les, s%(h asill%strated in ig* E+* 6*1$:, are very hel-f%l for .a<ing the a(t%al(o.-%ta tions

Pro(ed%res for handling (o.-le+ settle.ent -ro:le.s in engineering -ra(ti(e are treated in de-th in fo%ndation engineering te+t:oo<s*

When soil -er.ea:ility and therefore ( varies within the (o.-ressi :le layer, or when :o%ndar y layers i.-ede dt ainage, tite -1:le. %f ti.erate of (onsolidation :e(o.es very (o.-le+ and n%.eri(al te(hniF%ess%(h as fo%nd . (ott 16"#B and Harr 16""B are (alled for*

P!O,E3&

6 l* The ti.e fa(tor for a (lay layer %ndergoing (onsolidation is *$*What is the degree of (onsolidation (onsolidation ratioB at the(enter and at the F%arter -oints that is, M / Z 5 *$ and *!BWhat is the average degree of (onsolidation for the layer

65$* I the final (onsolidation settle.ent for the (lay layer of Pro:le. 651

.j

,WUUX

o#0

8



424 Tie !ate of Conolldatlon

is e+-e(ted to :e 1* ., how .%(h settle.ent has o((%rred when theti.e fa(tor is aB *$ and :B *!

65#* I the (lay layer of E+a.-le 6*1 were s.gly dra.ed, wo%ld there :eany differen(e in the (al(%lated val%es l so, how .%(h dif feren(e

652* Plot a gra-h of e+(ess -ore -ress%re vers%s de-th, si.ilar to ig* E+*6*$, for the soil and loading (onditions given in E+a.-le 6*$, :%t for the (ase of single drainage* Ass%.e that %nder the (lay there isi.-ervio%s shale instead of a dense sand*

65* or the soil and loading (onditions of E+a.-les 6*1 and 6*$, esti.atehow long it wo%ld ta<e for *1, *$, and *2 . of settle.ent too((%r* Consider :oth single and do%:le drainage*

65"* 4y eval%ation of the series e+-ression EF* 45$5$# in A--endi+ 45$Bfor the sol%tion to the (onsolidation eF%ation, deter.ine the averagedegree of (onsolidation to the nearest *1 for ti.e fa(tors *$,*, *6 and inf inity* Merif y yo%r (o.-%tations :y referring to Ta:le 651 and ig* 6*a* Also (he(< :y EFs* 651 and 6511* After Taylor,1627*B

65!* How .%(h differen(e wo%ld there :e in the aB (o.-%ted %lti.atesettle.ent and :B the ti.e reF%ired for 6] (onsolidation for thesoil (onditions of E+a.-le 6*! if the (lay layer were do%:ly drained

657* A de-os1t of wedish (lay 1s 1$ . tfO(<, on the average, anda--arently drained on the :otto.* Toe (oeffi(ient of (onsolidationfor the (lay was esti.atd to :e 1 + 152 (.$ Qs fro. la:oratorytests* A settle.ent analysis :ased on oedo.eter tests -redi(ted an%lti.ate (onsolidation settle.ent %nder the a--lied load in the f ieldto :e 1*$ .* aB How long wo%ld it ta<b fer settle.ents of 2 and !(. to o((%r :B How .%(h settle.ent wo%ld yo% e+-e(t to o((%r in yr 1 yr yr (B How long will it ta<e for the %lti.atesettle.ent of 1*$ . to o((%r

656* A (onventional la:oratory (onsolidation test on a $ .. thi(< sa.-le gave a ti.e fo1 90_ (onsolidation eF%al to 1$ .in* Cal(%late

in (.$Qs, .$ Qs, and f t $ Qd*

651* List the ass%.-tions of the Ter&aghi one5di.ensional (onsolidationtheory* List the. in the order %f their i.-ortanee in ter.s of aB.athe.ati(al (onvenien(e and :B -ra(ti(aV engineering signifi(an(e*

6511* Toe ti.e rate of settle.ent data shown :elow is for the in(re.entfro. $ to 2 <Pa fro. the test in ig* 7** Toe initial sa.-le heightis $*2 (., and there are -oro%s stones on the to- and at the :otto.

(



Pro#lea 425

of the sa.-le* 'eter.ine ( :y aB the Jog ti.e5fitting -ro(ed%re and

:B the sF%are root of ti.e -ro(ed%re* (B Co.-are the res%lts of aB

and :B*

Ela-sed Ti.e 'ial Reading.inB ..B

3 2*21

*$ #*7!6* #*7#

l #*!!#*"

2 #*267 #*$7$

1 #*## $*!""" $*

1$ $*2$#$2 $*$!" $*172

651$* An oedo.eter test Taylor, 1627B was (ond%(ted on a sa.-le of sof tChi(ago silty (lay* 1he s-e(1.en had a dry weight of #$6*66 g and a

density of solids of $*! GgQ .#

The area of the ring was 6#*#1 (.

$

An old5fashioned dial indi(ator was %sed, whi(h .eas%red tentho%sandths of an in(h 0- 2 in* -er divisionB, and the in(re.entalstresses a--lied to the s-e(i.en were re(orded in <gf Q(.

* 'ire(t

.eas%re.ents of the thi(<ness of the s-e(i.en were as follows9

1*$2 in* when %nder 1Q7 <gQ(.* dial reading $72#B

1*$#7 in* when %nder 1Q$ <gQ(.* dial reading$"62B 1*$1 in* when %nder l <gQ(.* dialreading $27B

'ial readings in 152 in* re(orded d%ring the test are listed in Ta:leP651$*

aB Plot the $ vers%s log o3 andQ or the vers%s log o3 (%rve for thistest* 'eter.ine the -re(onsolidation , stress and the a--ro-riate(o.-ression inde+* 3

:B Plot dial reading vers%s 74 for eah in(re.ent and deter.ine( Plot ( vers%s log o3.

(B a.e as -ar t :B, only %se the Casagrande log ti.e fitting .ethod*dB or two in(re.ents, one :efore the -re(onsolidation stress and

one af ter the -re(onsolidation stress, (o.-are the val%es of ( asdeter.ined :y the two fitting -ro(ed%res*

,j



428 Tie !ate of Conolldaflon

TA,E P"1 &26l R56=2n> 2n 0-2

2n.5i' I'$'t (Y$ B

!5 Bi

.inB Ft t( =i 2 t !

! t 2 2t4 4t 8 8t 16

3 2843 2796 2694 24+8 1+00 3100 31022834 2780 2664 2421 14+1 3047 3040

2829 2768 2647 2379 1408 2999 298+

2 2824 2761 2629 2337 13+4 2946 2931

4 2820 27+1 2610 2288 1304 2896 2873

6

2817 2742 2+92 2239 1248 2841 2822

9 2813 273+ 2+76 2190 1197 2791 276812F 2811 2729 2+62 2142 1143 2743 2728

16 2809 2724 2++3 2098 1093 2701 2690

20F 2808 2720 2+46 2044 1043 2660 26+8

2+ 2807 2717 2+40 2013 999 2630 2636

30F 2806 271+ 2+33 1969 9+6 2602

36 280+ 2713 2+29 1937 922 2+7+ 2602

42F 2804 2710 190+ 892

" 2803 2709 2+17 1837 830 2+2+ 2+68100 2802 2706 2+08 1740 76+ 2496 2+37200 2801 2702 2493 1640 722 2471 2+18"00 2799 2699 2478 1+8+ 693 2446 2499

1440 2796 2694 24+8 1+00 642 2399 2468

($6t t() 3100 3102

PHft$ B5[!$ (1948).

651#* A (onsolidation test is -erfor.ed on the s-e(i.en with these (har5a(teristi(s9

Height of s-e(i.en #7*I8 ..Area of s-e(i.en 6*1 (.$

Wet weight of s-e(i.en / "$1*g 'ry weight of s-e(i.en /

2!*1 g 'ensity of solids / $*7GgQ.#

The (onsolidation data af ter A* CasagrandeB are s%..ari&ed inTa:le P651#*aB Plot the effe(tive stress vers%s void ratio (%rve for :oth arith5

.eti( and se.ilogarith.i( s(ales*:B Est;.ate the -re(onsolidation -ress%re*(B Co.-%te the (o.-ression inde+ for virgin (onsolidation*dB Plot the ti.e (%rve for the load in(re.ent fro. $" to 1$ <g for

:oth arith.eti( and se.ilogarith.i( s(ales* K eB Co.-%te the (oeffi(ient of (orn-ressi:ility a , the (oeffi(ient of

-er.ea:ility, and the (oeffi(ient of (onsolidation c

in(re.ent fro. $" <g to 1$ <g* , for the load



55 55555 555 55555 55



P3Jl56 427

'IABI E *9-?! Coasolidatioa Iest 'ata

kGodified af ter A. Casagrande*

6512* A (ertain (o.-ressi:le layer has a thi(<ness of 2 .* Af ter l yr whenthe (lay is ] (onsolidated, 7 (. of settle.ent has o((%rred* or asi.ilar (lay and loading (onditions, how .%(h settle.ent wo%ldo((%r at the end of l yr and 2 yr if the thi(<ness of this new layer

651* In a la:oratory (onsolidation test on a re-resentative sa.-le of (ohesive soil, the original height of a do%:ly drained sa.-le was $*2..* 4ased on the log ti.e vers%s dial reading data, the ti.e for ](onsolidation was 6 .in* Toe la:oratory sa.-le was ta<en fro. asoil layer whi(h is 1$ . thi(< in the field, do%:ly drained, and iss%:0e(ted to a si.ilar loading* aB How long will it ta<9e %ntil thelayer (nsolidates 2OU :B I the final (onsolidation settle.ent is

-redi(ted to :e 17 (., how long will it ta<e for a settle.ent of 2 (.to ta<e -la(e

Te.-*5 fiate Ti.e

Load<

Ela-sed Ti.e*wi%*

&26l Reading%%%

Q1"Q72 o o1" *!7!#$ 1*1!"" 1*72

1$7 $*76"$" 2*$2

$#* Q$$Q72 6## 1$ %dden 2*#*1 2*#2#

2* 2*""#

$75 *$#72- *27117$5 *67

$$*! 1!## 275 *""6$$*" $$2 *!$# 2 1$#'Q72 1 *!#$$*7 Q$2Q72 II88 *!#

Q$2Q72 1$2 !*#""Q#Q72 1$2 !*22!

1$ !*$#6$" "*626

#$ *7!7"Q!Q72 *$! 2*11"Q#Q72 *$! #*"6#



+4 Tie !ate of Conolldatlon

651" A Bayer of nor.ally (onsolida ted day # . thi(< has an average void ratio of 1*#* Its (o.-ression inde+ is *" and its (oeffi(ient of (onsolidation is .* Qyr* When the e+isting verti(al -ress%re on the(lay Vayer is do%:led, what (hange in thi(<*ness of the (lay Vayer will res%lt

6 1!* The settle.ent analysis for a -ro-osed strn(t%re indi(ates that " (.of settle.eht will o((%r in 2 yr and that the %lti.ate total settle.entwill :e a:o%t $ (.* The analysis is :ased 11 the ass%rn-tion that the(o.-ressi:le (lay Vayer is drained at :oth its to- and :otto.s%rfa(es* However it is s%s-e(ted that there .ay not :e drainage atthe :otto. s%rfa(e* or the (ase of single drainage, esti.ate aB the

%lti.ate total settle.ent and :B the ti.e reF%ired for " (. of settle.ent* Af ter Taylor, 1627*B

6517* The str%(t%re of Pro:le. 651! was (onstr%(ted and -erfor.ed essen tiallyas e+-e(ted d%ring the first 2 yr that is, the settle.ent of the :%ildingwas a:o%t " (.B* Toe owner de(ides to :%ild a d%-li(ate of the firststr%(t%re near:y* '%ring fo%ndation ;nvestigations, it is dis(overnd thatthe (lay layer %nder the new :%ilding wo%<l :e a:o%t $] thi(<er than %nder the f irst str%(t%re* 8therwise, the -ro-erties of the (lay arethe sa.e* Esti.ate for the new str%(t%re aB the %lti.ate totalsettle.ent, and :B the settle.ent in 2 yr* Af ter laylor, 1627*B

6516* A (ertain do%:ly drained (lay Vayer has an e+-e(ted %lti.ate settle

.ent se of 1 (.* The (lay Vayer, whi(h is 1! . thi(<, has a(oeffi(ient of (onsolidation of S 15! (.* Qs* Plot the se5ti.e relationshi- to aB an arith.eti( ti.e s(ale and :B a se.ilog ti.e s(ale*

65$* iven the sa.e soil data as for Pro:le. 6516* Af ter # yr, an ident;(alload 1s -la(ed, (a%s.g an addihonal 1 (. of (onsolidation settle.ent* Co.-%te and -lot the ti.e rate of settle.ent %nder these(onditions, ass%.ing that the load (a%sing (onsolidation settle.entis -la(ed instantaneo%sly*

65$1* iven the sa.e data as for Pro:le. 6516* Toe load (a%sing the 1(. %lti.ate settle.ent was -la(ed over a -eriod of $ yr* Altho%gh

we haven3t dis(%ssed how to handle this <ind of -ro:le., des(ri:ethe a--roa(h yo% wo%ld %se to (o.-%te the ti.e history of settle.ent*

65$$* A s-e(i.en of (lay in a s-e(ial oedo.eter with drainage at theto- onlyB has a height of $*" (. when f%lly (onsolidated %nder a -ress%re of <Pa* A -ress%re transd%(er is lo(ated at the :aseof the sa.-le to .eas%re the -ore water -ress%re* aB When another stJ ess in(1e.en t of <Pa is a--lied, what wo%ld yo% e+-e(t the



Pro#lea429

initial reading on the transd%(er to :e :B I, af ter 1 .in hadela-sed, the transd%(er re(ords a -ress%re of $ <Pa, what wo%ld yo%e+-e(t 1t to read 2 .in later total ela-sed ti.e 3 l hB Af ter C* A*Leonards*B

65$#* Toe total (onsolidation settle.ent for a (o.-ressi:le layer ! thi(< is esti.ated to :e a:o%t # (.* Af ter a:o%t " .o 17 dB a -oint $ .

:elow the to- of the singly drained layer has a degree of (onsolida5tion of "]* aB Co.-%te the (oeffi(ient of (onsolidat1n of the.aterial in .$

Q d* :B Co.-%te the settle.ent for 17 d*

65$2* A $ .D thi(< nor.ally (onsolidated (lay layer has a load of 00 <Paa--lied to it over a large areal e+tent* The (lay layer is lo(ated :elow

a gran%lar fill F p $ 8 GgQ .# B # . thi(<* A dense sandy gravel isfo%nd :elow the (lay* The gro%nd water ta:le is lo(ated at the to- of the (lay layer, and the s%:.erged density of the soil is *6

#

Consolidation tests -erfor.ed on $*$ (. thi(< do%:ly drainedsa.-les indi(ate t 9 .in for a load in(re.ent (lose to that of theloaded (lay layer* Co.-%te the effe(tive stress in the (lay layer at ade-th of 17 . :elow the gro%nd s%rfa(e 2 yr af ter a--li(ation of theload*

65$* iven the sa.e data as for Pro:le. 65$2* At t / " yr, what is theaverage degree of (onsolidation for the (lay layer

65$"* Again, given the sa.e data as for Pro:le. 65$2* l the (lay layer were

singly drained fro. the to- only, (o.-%te the eff e(tive stress at ade-th of 17 . :elow the gro%nd s%rfa(e and 2 yr af ter -la(e.ent of the e+ternaV load* Co..ents

65$!* 'eter.ine the average (oeffi(ient of -errnea:ility, (orre(ted to $>C,of a (lay s-e(i.en for the following (onsolidation in(re.ent9

1

1 <Pa, e l.

o$ / !00 <Pa, e$ / 1*17Height of s-e(i.en / $ ..'rainage at :oth to- and :otto. fa(esTi.e reF%ired for ] (onsolidation / $ 2nTest te.-eiat. e $#>c

Af ter A* Casagrande*B

65$7* Toe following data were o:tained fro. a (onsolidation test on an%ndist%r:ed (lay s*a.-le9

a , 5 1" <Pa,

a2 / #1 <Pa,

e1 *76

e* / *!#$

Toe average val%e of the (oeffi(ient of -errnea:ility of the (lay in

.j

GgQ.



43, Tie !ete ot Conaolldetlon

this -ress%re in(re.ent range is #* + 156 (.Qs* Co.-%te and -lotthe de(rease in thi(<ness with ti.e for a 1 . layer of this (laywhi(h is drained aB on the %--er s%rfa(e only and :B on the %--er s%rfa(e, and at a de-th of . :y a thin hori&ontal sand layer that -rovides free drainage* Af ter A Casagrande B

65$6* iven the data of Pro:le. 6511* Eval%ate aB the se(ondary (o.-ression inde+ and :B the .odified se(ondary (o.-ression inde+ if

o

/ $*2 (. Ps / $*! GgQ.#

At t 8, e / 1*!2, U 1*6$7 (.

At t 127 .in, e l*2, U 1*!$7 (.Weight of te(hni(ian / ! stone@ .oon -hase / f%ll

6 J8*h

ow that 6p l

Ca$p "5

9-E t .

va1D,.2

3# log l l%*

65#1* how that ss / H B"* log t is tr%e* e

65#$* Est;.ate the se(ondary (o.-ression -er log (y(le of ti.e for Pro:5e. 5

65##* Toe liF%id li.it of a soil is 7* Est;.ate the val%e of the .odified

se(ondary (o.-ression inde+*

65#2* iven the infor.ation of E+a.-le 6*1$* What wo%ld :e the settle .entof the silty elay Vayer if one layer were ehosen instead of the 1 layersa(t%ally %sed What wo%ld :e the settle.ent if $, , and ! layersre-resented the ) . thi(< layer3 Plot se vers%s the n%.:er of layers*

65#* iven the data and infor.ation of E+a.-le 6*1$* Af ter 1 yr of (onsolida tion, an additional areal fill load of 26 <Pa is -la(ed on thesite* Co.-%te the a.o%nt of additional settle.ent, and -re-are a

-lot of settle.ent si.ilar to ig* E+* 6*1$(*

65#"* iven the data and inf. .ation %f E+a.-fo 6*1$* %:seF%en t s%:5

s%rfa(e investigation reveals a thin -ervio%s layer at a de-th of 56*. that 1s, 2* . .to the silty (lay layerB, whi(h -rovides drainagethro%gho%t the silty (lay* Co.-%te the ti.e rate of settle.ent for these new (onditions, and -lot the res%lts on a gra-h si.ilar to ig*E+* 6*1$(*

U

1



ten

The 3ohr Circle=*ailureTheorie=§tre Path

18.1 INT!O('CTION

4efore we dis(%ss the stress5defor.ation and shear strength -ro-er ties of soils, we need to introd%(e sorne new definitions and (on(e-ts a:o%tstress and fail%re* ro. Cha-ers 7 and 6, yo% <now so.ething a:o%t theload5settle.ent5ti.e (hara(teristi(s of (ohesive soils, at least those d%e toone5di.ensional loading* In this (ha-ter and the ne+t, we shall des(ri:ethe rea(tion of sands and (lays to ty-es of loading other than one

d1.ens1onal*I the load or stress in a fo%ndation or earth slo-e is in(reased %ntil

the defor.ations :e(o.e %na((e-ta:ly large, we say that the soil in thefo%ndation or slo-e has =failed*= In this (ase we are referring to the

strength of the soil, whi(h is really the .a+i.%. or %lti.ate stress the.aterial (an s%stain* In geote(hni(al engineering, we are generally (on(erned with the shear strength of soils :e(a%se, in .ost of o%r -ro:le.s info%ndations and earthwor< engineering, fail%re res%lts fro. e+(essivea--lied shear stresses*

Toe following notation is introd%(ed in this (ha-ter*

y.:ol 'i.(nsion Unit

a ML-,* <Pa

e ML > ri <Pa

D

cC

'(finition

Int(r(e-t of th( 1line on the p'B diagra. EF* 15$#B

Interee-t of the Go:r fail%reenvelo-e EF* l57B

Consolidated drained tria+ialtestB

Consolidat(d %ndrained 426Y26l testB

a1

._



432 The 3ohr Clrcle= *allure Theorle= &tre Path


Y5L <Pa

uu

degreeBdegreeBdegreeB]B

0 L

0 degreeBF1 <PaF1 <Pa

<Pa<Pa

F av a,*BQ$ EF* 1516B( a., - a,*BQ$ EF* 1517BUn(onsolidated %ndrained

tria+ial testB An angleAngle of the fail%re -lane A46n ( B/p) EF* 15$1B:ear strain angle of rotation

in ' testBHori&ontal dis-la(e.entAn angle

Nor.al stressGa0or -rin(i-al stressInter.ediate - (i-al stressGinor -rin(i-al stress

Y5 Nor.al stress on the %re -lane at fail%re EF* 15!B

<Pa<Pa

degreeB

degreeB

ear stress:ear stress on t:e fail%re

- ane a %relo-e of t:e S 1line on t:e p' .

lo-e of the Gohr fail%re

the angle of interna/ friction :

18. &T!E&& AT A POINT

the (on(e-t of stress at a -oint in a soil is really fO@titio%s* Toe -oint ofa--li(ation of a for(e within a soil .ass (o%ld :e on a -art1( e or . a

D t s% ort an for(e :%t if the for(e were a--lied to a -arti(le. , the stress (o%ld :e e+tre.ely large* Th%s when .we

a:o%t a for(e -er %nit area, in whi(h the area %nder (onsideration is thegross (ross5se(tlona or eng.eenng area* is area

ain (onta(ts as well as voids* Toe (on(e-t is si.ilar to the =engineering area=D%sed in see-age and flow -ro:le.s Cha-ter !B*

r(es F F

2, D D D , F,,, as shown in ig* 1*1* or the ti.e :eing, let3s ass%.e that these



18 &tre al a Polnt

\&

433

4

$2. 0. A .>32l 6>> 645= GN3n J >5156U 35>.

for(es a(t in a two5di.ensional -lane* We (o%ld resolve these for(es into(o.-onents on a s.all ele.ent at any -oint within the soil .ass, s%(h as -oint R in that fig%re* The resol%tion of these for(es into nor.al and shear (o.-onents a(ting, for e+a.-le, on a -lane -assing thro%gh -oint R at anangle a fro. the hori&ontal is shown in ig* 1*$, w:i(: is an e+-anded

view of a s.all ele.ent at -oint R. Note that for (onvenien(e o%r sign(onvention has co8pressive forces and sFresses positive :e(a%se .ost nor.alstresses in geote(hni(al engineering are (o.-ressive* This (onvention thenreF%ires that a positive shear stress -rod%(e countercloc!(ise (o%-les on o%r ele.ent* P%t another way9 positive shears -rod%(e cloc!(ie .o.entsa :o%t a -o.t J Ust outside the ele.ent, as shown :y the insert in ig* 1*$*Cloc!(ise angles are also ta<en to :e positive. These (onventions are theopposite of those nor.ally ass%.ed in str%(t%ral .e(hani(s*

To :egin, let3s ass%.e that the distan(e $C along the in(lined -lanein ig* 1*$ has %nit Iength, and that the fig%re has a %nit de-th -er-endi%la1 to the -lane of the -a-er* Th%s the verti(al -lane =@ has thedi.ension of I sin a . and the hori&ontal di.ension $. has a dirnensioneF%al to 1 (os a. At eF%ili:ri%., the s%. of the for(es in any dire(tion

.%st :e &ero* o s%..ing in the hori&ontal and verti(al d;re(tions, weo:tain

#.9h Z &eos a Nsin a 8 15IaB

1:F., = Tsin a ' (os a 5 8 15I:B

'ividing the for(es n EF* 151 :y the areas %-on whi(h they a(t, weo:tain the nor.al and shear stresses* We shall denote the hori&ontal

- A .



+%+ The 3ohr Clrcle= *allure 'heorl0. &IN44 Pathe

o

S2n 3n15n423n>

H / 3Y >2n a

A56 / 1 >2n a

M v 3> 6

$2. 0.* R5>3lG423n 3 45 35> 3 $2. 0. 2n43 3N3n5n4> 3n 6>6ll 5l55n4 64 N32n4 A. S2n 3n15n423n> 65 >3Dn 2n 45 >6ll 2n>542G5.

nor.al stress :y a and the verti(al nor.al stress :y the stresses on thea5-lane are the nor.al stress < and the shear stress T*B

o+ sin a 5 3Ta C8 a 5 oa sin a/ m

y

15$aB

15$:

olving EFs* 15$a and 15$: si.%ltaneo%sly for < and Ta, we o:tain

15#B

a

I yo% sF%are and add these eF%ations, yo% will o:tain the eF%ationfor a circle with a radi%s of F a 5 oy BQ$ and its (enter at o+ oy :/ , 8X*When this (ir(le is -lotted in T5o s-a(e, as shown in ig* 1*#: for the

D D i <nown as the " ohr circle o stress Gohr 177! *I4 re-resen.ts the state of . stress al a point at eLuilibriu8, and it a--lies to

sa.e to o:tain a (ir(le fro. these eF%ations*in(e the verti(al and hori&ontal -lanes in ig* 1*$ and ig* 1*#a

have no shearing stresses a(ting on the., they are :y definition principal

planes. Th%s the stresses K and ` are really principal stresses. o% .ay

re(all fro. o%r st%d of stren th of .aterials that rin(i al stresses a(t on -lanes where T 8* Toe stress with the largest .agnit%de is (alled the

.



=

o a

o - o

----- a , + aB

6ai/s D ---2

=

#$%

(5)

5

$2. 1*# T5 M3 l5 34 >45>>: 6 5l55n4 64 5FG2l2J2G, J 45M3 2l5; 5^ M3 2l5> 2nlG=2n 3*.

, . _



436 The 3ohr Clrcle= *allure Theorlea= Stre-- Pathe

8a@or principal stress, and denoted :y the sy.:ol o Toe s.allest -rin(i-alstress is (alled the 8inor principal stress, o#, and the stress . the thirddi.ension is the inter8ediate principal stress, o$ In ig* 1*#:, o$ isnegle(ted sin(e o%r derivation was for two5di.ensional -lane stressB(onditions* We (o%ld, however, (onstr%(t two additional Gohr (ir(les for o1 and o$ and o$ and o# to .a<e a (o.-lete Gohr diagra., as shown in

Now we (an write EFs* 15# and 152 1 in ter.s of -rin(i-al

stresses*

AW E # AW 5 #

a &$ $

(os $a 15BAW 5 # *

$s. $ a Y155"B

Het e we have a1:itta1ily ass%.ed tha t < 1 and o# o% sho%ldverif y that the (oordinates of XN 3TB in ig* 1*#: (an :e deter.ined :yEFs* 15 and 15"* ro. these eF%ations, also verify that the (oordinatesof the (enter of the (ir(le are o1 # BQ$, 8X, and that the radi%s iso1 5 # BQ$*

I4 is now -ossi:le to (al(%late the nor.al stress > and shear stress GN

on any -lane a, as long as we <now the -rin(i-al stresses* In fa(t, we (o%ldal.ost as easily derive eF%ations for the general (ase where and arenot -rin(i-al -lanes* These eF%ations are <nown as the double angle

eLuations, and they are the ones generally -resented in strength of .ateri als

te+t:oo<s* The analyti(al -ro(ed%re is so.eti.es aw<ward to %se in -ra(ti(e :e(a%se of the do%:le angles@ we -erfer to %se a gra-hi(al -ro(ed%re :asedon a %niF%e -oint on the Gohr (ir(le (alled the pole or the origin of

planes.Q&his -oint has a very %sef%l -ro-erty9 any straight fine

dra(n through the pole (ill intersect Fhe "ohr cirde at a point (hich

represents the state of stress on a plane inc/ined at the sa8e orientation in

space as the line. This (on(e-t .eans that if yo% <now the state of stress, o

and G , on sorne -lane in s-a(e, yo% (an draw a line -arallel to that -lanethro%gh the coordinares of o and G on the Gohr (ir(le* Toe -ole then is the -oint where that line interse(ts the Gohr (ir(le* 8n(e the -ole is <nown,the stresses on any plane (an readily :e fo%nd :y si.-ly drawing a line fro.the -ole -arallel to that -lane@ the (oordinates of the -oint of interse(tionwith the Gohr (ir(le deter.ine the stresses on that -lane* A f ewe+a.-les will ill\strate how the -ole .ethod wor<s*

E9A3PE 1O .1

(215n:

tresses on an ele.ent as shown in ig* E+* 1*1a*



a IPa)

ig* E+* 1*1



2#7 T5 M3 Cll5, $6llG5 Theorl5* S45>> P646

R5FG25=:

The nor.al stress > and the shear stress T on the -lane in(lined at a #>fro. the hori&ontal ref eren(e -lane*

S3lG423n:

l* Plot the Gohr (ir(le to so.e (onvenient s(ale see ig* E+* 1*l:B*>1 # $ 1$

(enter of (ir(le $ $

#$ <Pa

radi%s of (ir(le >1 5 #

*

$ 5 1$

$ <Pa

$

$* Esta:lish the origin of -lanes or the -ole* I4 is -ro:a:ly easier to %se thehori&ontal -lane %-on whi(h o1 a(ts* The state of stress on this

* -lane is indi(ated :y -oint $ in ig* E+* 1*l:* 'raw a line -arallel to the -lane %-on whi(h this state of stress o1, 8B a(ts the hori&ontal -laneBthro%gh the -oint *re-resenting oI and 8* 4y definition, the -ole P. is wherethis line interse(ts the Gohr (ir(le* 4y (oin(iden(e, it interse(ts at o* , 8BX* A line thro%gh the -ole in(lined at an angle1 a #> fro. the hori&ontal -lane wo%ld :e -arallel to the -lane on the ele.ent in ig* E+* 1*la, andthis is the -lane on whi(h we reF%ire the nor.al and shear stress* Theinterse(tion is at -oint C in ig* E+* 1*l:, and we find that XN #6 <Paand GN / 17*" <Pa*

o% Dsho%ld verif y these res%lts :y %sing EFs* 15 and 15"* Notethat GN is -ositive sin(e -oint @ o((%rs a:ove the a:s(issa* Th%s the senseof GN on the #> -lane is deter.ined as indi(ated in igs* E+* 1* l and d,whi(h re-resent the to- and :otto. -arts of the given ele.ent* or :oth

-arts, the dire(tion vr sense of the shear stress GN is eF%al and o--osite asit sho%ld :eB* However, they are :oth -ositive shear stresses, whi(h is(onsistent with 8UI sign (onvention ig* 1*$B*

E+AMPLE O .*

(215n:

The sa.e ele.ent and stresses as in ig* E+* 1*la, e+(e-t that the ele.entis rotated $> fro. the hori&ontal, as shown in ig* E+* 1*$a*

R5FG25=:

As in E+a.-le 1*1, find the nor.al stress XN and the shear stress GN on the -lane in(lined at a #> fro. the :ase of the ele.ent*



. 555555555DDDD DD .. DDDDD555555555555D5 .. --



= IPa)B;

o, a

H323n46l al

$2. EY. 0.*

2#6

.j



22 T5 M3 Cll5, $6llG5 T53l5>, S45 P646

l* Plot the Gohr eirele ig* f%* 1*$:B* inee the -rin(i-al stressesare the sa.e, the Gohr (ir(le will :e the sa.e3 as in E+a.-le l*1*

$* ind the -ole of the (ir(le* As in the -revio%s e+a.-le, draw a line -arallelto a -lane on whi(h yo% <now the stresses* I we again :egin with the .a0or -rin(i-al -lane, this -lane is in(lined at an angle of $> to the hori&ontal*tart at -oint A, and where this line interse(ts the Gohr (ir(le, defines the -ole P of this (ir(le*

#* Now find the stresses on the a5-lane, whi(h as :efore is in(lined at #> tothe :ase of the ele.ent* ro. line AP, t%. an angle in the sa.e direetionas in the ele.ent, #>, and the stresses on that -lane are defined :y the

-oint of interse(tion of the line with the Gohr (ir(le in this (ase at -o.tCB* (ale off the (oordinates of -oint C to deter.ine > and GN. Note thatthese stresses are the sa.e as in E+a.-le 1*1* Why is this 4e(a%senothing has (hanged e+(e-t the orientation in s-a(e of the ele.ent*

or ste- $, we (o%ld 0%st as well have %sed the .inor -rin(i-al -lane as o%r starting -oint* In this (ase a line fro. o#, 8B (o%ld :e drawnat !> fro. the hori&ontal -arallel to the o#5-laneB, and it wo%ld interse(tthe Gohr (ir(le at the sa.e -oint as :efore, -oint P. We now have a(he(< on the ste-5if we have done everything (orre(tly, we sho%ld o:tainthe sa.e -ole* in(e line AP is -arallel to the .a0or -rin(i-al -lane, we(an showthe dire(tion of o right on this line in ig* E+* 1*$@ si.ilarly, the dashedline fro. the -ole to o3 is -arallel to the o#5-lane*

Now yo% -ro:a:ly (an :egin to see what is really ha--ening with the -ole* I4 is 0%st a way of relating the Gohr (ir(le of stress to the geo.etry or orientation of o%r ele.ent in the real world* We (o%ld 0%st as well rotatethe G' a+es to (oin(ide with the dire(tions of the -rin(i-al stresses ins-a(e, :%t traditionally G vers%s a is -lotted with the a+es hori&ontal andverti(al*

E****+* * AMPLE O .!

(215n:

Toe stress shown on the ele.ent in ig* E+* 1*#a*

R5FG25=:

a* Eval%ate XN and GN when a 5 #>* :* Eval%ate o1 and o3 when a 5 #>*

,



G 5$'

Q

a- -

. $ **n

5 52 G Pa %

'-* GPa

* GPa

" GPa

6

! G PaB .8, r,, ).! GPa

/ /

a!

&a o G Pa B

J

*ig. EY. 18.%

441

$

a0



442 The 3ohr Clrcle= *allure Theorle= &tre Patha

e 'eter.ine the orientation of the .a0or and .inor -rinei-al -lanes*d. ind the .a+irn%. shear stress and the orientation of the -lane

on whi(h it a(ts*

S3lG423n:

Constr%(t the Gohr (ir(le, as shown in ig* E+* 1*#, a((ording to thefoBBowi ng ste-sD

1. Plot the state of stress on the hori&ontal -lane ", $B at -oint A. Note that the shear stress .a<es a (lo(<wise .o.ent a:o%t a

and therefore is -ositive*$* In a si.ilar .anner, -lot -oint = -2, 5$B* The shear stress on theverti(al -lane is negative sin(e it .a<es a (o%nter(lo(<wise .o.ent*

#* Points A and = are two -oints on a (ir(le a dia.eter in this (ase sin(e their -lanes are 6> a-artB@ the (enter of the (ir(le has (oordinates of <3 o,, BQ$, 8X * Constr%(t the Gohr (ir(le with (enter a t 1, @

4. To find the -ole, re.e.:er that a line drawn -arallel to the -lanehori&ontal in this e+a.-leB %-en 3Nhi(h a <nown state of stress aets, -oint

A , interse(ts the Gohr (ir(le at the -ole P. As a (he(<, yo% (o%ld also drawa line in the verti(al dire(tion fro. -oint = -2, 5$B and f ind the sa.e

-ole*

* To find the state of stress on the -lane in(lined at angle a #> fro. the

hori&ontal* draw the Jine PC a t a n angle # fro. the hori&ontal see ig*E+* 1*#:B* The state of stress on ihis -lane is given :y the (oordinates at -oint C 1*7, *#B GPa*

"* Lines drawn fro. P to o and o* esta:lish the orientation of the .a0or and.inor -rin(i-al -lanes* I he val%es of I and o# are deter.ineda%to.ati(ally on(e the (ir(le is drawn@ here they are "*2 and 52*2GPa, res-e(tively* 8f (o%rse oI and o* are -er-endi(%lar to their

res-e(tive - lanes, whi(h are oriented a t 1 X > a nd 11> to the hori&ontal, res-e(tively*

!* The .a+i.%. shear stress (an :e (al(%lated :y EF* 0- when $a 6>*This is (r 1 #BQ$ 1 ...U.. *2 GPa see -oints M ! M). o% (an also si.-lys(ale off the .a+i.%. val%e of 5r fro. the Gohr diagra.* Toe

orientation of 5r.a+ 1s the I.e PM or PM, de-ending on whi(h .%t%ally -er-endi(%lar -lane yo% desire* A(t%ally 5r 5 5 *2 GPa is the.;ni.%. shear stress*B

E9A3PE 1O .+

Two -lanes, a and O, are se-atated :y an %nl.own angle (J. 8n -lane a,XN 1 <Pa and '!N $ <Pa* Plane a lies 1> fro. the hori&ontal, as



55555 D5D5555DDDD .. .. ----- 555



18. &tre at a Polnt

shown in ig* E+* 1*2a* The stresses on -lane area /

6 <Pa andG / 5# <Pa*

R5FG25=:

a* ind the .a0or and .inor -rin(i-al stresses and their orientation*b Eiod the stresses on the hori&ontal -lane*(* ind the angle :etween -lanes a and .

S3lG423n:

l. Plot the (oordinates of the stresses on -lanes a and . l yo%

ass%.e the :ody or ele.ent is in eF%ili:ri%., then these (oordinates are onthe (ir(%.feren(e of the Goln (it (le* To find the (enter, (onstr%(t a

-er-endi(%lar to the line $ , whi(h 0oins the two -oints* The interse(tionof the hori&ontal %5a+is and the -er-endi(%lar :ise(tor to $ is the (enterof the (ir(le C.

$* Esta:lish the -ole :y drawing a line fro. -oint A -arallel to the -lane 1>fro. the hori&ontalB %-on whi(h the stresses at -oint A a(t towhere it interse(ts the Gohr (ir(le* Toe interse(tion of this line and theGohr (ir(le is the -ole P.

#* Lines fro. the -ole P to 3 and 6! indi(ate the orientation of the .a0or and.inor -rin(i-al -lanes* The -rin(i-al stresses a(t -er-endi(%lar to these -lanes* The s(aled5off val%e of a1 is eF%al to 1*" <Pa, and a is

6 K%nd to :e #*" I <Pa* #

4. The stresses on the hori&ontal -lane are fo%nd :y drawing ahori&ontal line fro. the -ole %ntil it interse(ts the Gohr (ir(le at -oint Z 4the stres ses on this -la oe a re 7 ", # 17B <Pa*

* To find the angle :etween the two -lanes a and b, draw the line P fro. the -ole to . This line is the a(t%al orientation in s-a(e of -lane . The angle A then re-resents the tr%e angle :etween -lanes $ and , or A 2"*

E9A3PE 1O *

(215n:

The stresses oo an ele.ent shown in ig* E+* I*a*

R5FG25=:

ind the .agnit%de and dire(tion of the .a0or and .inor -rin(i-alstresses*

,_



< -'

0 P6

Pl6n56

On Nl6n5 J: 6J 9 P6, TJ -! P6, 3 Nl6n5 6

6

r P6

4

$

-2

-4

-6J

*ig. E5. 18.+

444



r IPa)

2

o1; a IPa)

-2

-

S

(5)

J

ig* E+* 1*

.j



""8 The M3 Cll5, $6llG5 T53l56, S4566 P646

S3lG423n:

Ref er to ig* E+* 1*: for the following ste-s*

l* Plot the two -oints V and ` frorn the given stress (oordinates*These two -oints lie on the (ir(%.feren(e of the (ir(le* W here the hne V ` interse(ts the o5a+is esta:lishes the (enter of the Gohr (ir(le at ", 8B*

$* Lo(ate the -ole :y drawing a line frorn -oint ` -arallel to the -lane on whi(h the stress at R a(ts* This line is at 2> fro. the hori&ontal,and it interse(ts the Gohr (ir(le at the -ole P, whi(h is the sa.e -oint as -oint V.

#* To find the dire(tion of the -rin(i-al stresses, draw a line fro. the -%le to o 1and o# , tltese lines ate shown dashed %n ig* E+* 1*:* The dire(tionarrowsB of o and o! are shown in the fig%re* The val%es of o and o# ares(aled off the fig%re and fo%nd to :e 7*7 <Pa and #*$ <Pa,res-e(tively*

4y now yo% (an see that the Gohr (ir(le of stress re-resents the(o.-lete two5dirneosiaoaX sta te of stress a eLuilibriu8 i n a o eleroen t or at a -oint* The -ole si.-ly (o%-les the Gohr (ir(le to the orientation of theele.ent in the real world* The Gohr eirele and the eon(e-t of the -ole arevery %sef %l in geote(hni(al engineering@ we shall %se the. thro%gho%t therest of this te+t*

O ! STRESS-STRAI % RELATIO%SHIPS A%& $AILRE CRITERIA

Earlier, in the introd%(tion to Cha-ter 7, we :(ie;ly .entionedsorne stress5strain relationshi-s* Now we want to ela:orate on, aswell as ill%strate, so.e of those ideas* The stress strain e%rve fer .ildsteel is shown in ig* 1*2a* Toe initial -ortion %- to the -ro-ortionalli.it or yield -oint is linear/y eia.stic. This .eans that the .aterial will ret%.43 its original sha-e when the stress is released, as l.g as the a--lied stressis :elow the y1eld -o.t* I4 1s -ossi:le, however, for a .aterial to have anonlinear stress5strain (%rve and still :e elasti(, as shown in ig*1*2:* Note that :oth these stress5strain relationshi-s are inde-endent of ti.e* I ti.e is a varia :le, t:en t:e .aterial is (alled 7isco e/astic. o.e real.aterials s%(h as .ost soils and -oly.ers are vis(o5elasti(* Why, then, don3twe %se a *iseo5elastie theory to des(ii:e tite :ehaviot of soils 11te -ro:le. isthat soils have a highly nonlinear stress5strain5tirne :ehavior, and%nfort%nately only a .athe.at1(ally well5develo-ed I.ear theory of vis(o5elasti(ity is availa:le*



a a

a

'P3N3423n6l l224

E E

6 M2l= >455l J %3nl2n56 5l6>42

a a

A A

5 P554l Nl6>42 = El6>43-Nl6>42

a

q

5 B244l5 W3 6=5n2n 6n=D3 >345n2n

$2. 0." EY6Nl5> 3 >45>>->462n 5l6423n>2N> 3 2=56l 6n= 56l64526l>: 6 2l= >455l, J n3nl2n56 5l6>42, 5 N554l Nl6>42,= 5l6>43-Nl6>42, 5 J244l5, 6n= D3-6=5n2n 6n= D3->345n2n.



< '1

++4 The 3ohr Clrcle= *ellure Theorle= &tre Path

Note that so far we3ve said nothing a:o%t fail%re or yield@ Evenlinearly elasti( .aterials yield, as indi(ated in ig* 1*2a, if s%ffi(ient stressis a--lied* At the -ro-ortional li.it, the .aterial is said to :e(o.e plastic

or to yield p/astica/ly. Toe :ehavior of real .aterials (an :e ideali&ed :yseveral -lasti( stress5strain relationshi-s, as shown in igs* 1*2(, d, and f* Per@ect/y plastic .aterials ig* 1*2(B, so.eti.es (alled rigid5p/astic, (an :etreated relatively easily .athe.ati(ally, and th%s are -o-%lar s%:0e(ts of st%dy :y .e(hani(ians and .athe.ati(ians* A .ore realisti( stress5strainrelationshi- is e/asto5plastic ig* 1*2dB* The .aterial is linearly elasti( %-to the yield -oint oR 4 then it :e(o.es -erfe(tly -lasti(* Note that :oth -erfe(tly -lasti( and elasto5-lasti( .aterials (ontin%e to strain even witho%tany additional stress a--lied* The stress5strain (%rve for .ild steel (an :e

a--ro+i.ated :y an elasto5-lasti( stress5strain (%rve, and this theory isvery %sef%l in, for e+a.-le, wor<ing, -%n(hing, and .a(hining of .etals*o.eti.es .aterials s%(h as (ast iron, (on(rete, and a lot of ro(<s arebrittle, in that they e+hi:it very little strain as the stress in(reases* Then, atsorne -oint, the .aterial s%ddenly (olla-ses or (r%shes ig* l*2eB* Gore(o.-le+ :%t also realisti( for .any .aterials are the stress5strain relationsshown in ig* l*2f* or!5hardening .aterials, as the na.e i.-lies, :e (o.estiffer higher .od%l%sB as they are strained or =wor<ed*= The little h%.- inthe stress5strain (%rve for .ild steel af ter yield ig* 1*2aB is an e+a.-leof wor<5hardening* Gany soils are also wor<5hardening, for e+a.-le,(o.-a(ted (lays and loose sands* or!5softening .aterials ig* l *2fBshow a de(rease in stress as they are strained :eyond a -ea< stress* ensitive(lay soils and dense sands are e+a.-les of wor<5sof tening .ateri als*

At what -oint on the stress5strain (%rve do we have fail%re We (o%ld(all the yield -oint =fail%re= if we wanted to* In sorne sit%ations, if a.aterial is stressed to its yield -oint, the strains or defle(tions are so largethat for all -ra(ti(aV -%r-oses the .aterial has failed* This .eans that the.aterial (annot satisfa(torily (ontin%e to (arry the a--lied loads* Thestress at =fail%re= is of ten very ar:itrary, es-e(ially for nonlinear .aterials*With :rittle5ty-e .aterials, however, there is no F%estion when fail%reo((%rs5 it3s o:vio%s* Even with wor<5sof tening .aterials ig* 1*2fB, the -ea< of the (%rve or the .a+irn%. stress is %s%ally defined as fail%re* 8nthe other hand, with sorne -lasti( rnaterials it .ay not :e o:vio%s* Where

wo%ld yo% define faO%re if yo% had a wor<5hardening stress5strain (%rveig* l*2fB With rnaterials s%(h as these, we %s%ally define fail%re at sornear:itrary -er(ent strain, for e+a.-le, 1 or $], or at a strain or defor.ation at whi(h the f%n(tion of the str%(t%re .ight :e i.-aired*

Now we (an also define the strength of a .aterial* I4 is the .a+i.%.or yield stress or the stress at sorne strain whi(h we have defined as=fail%re*=



18.+ The 3ohr"Coulo# *allure Crlterlon***

As s%ggested :y the a:ove dis(%ssion, there are rnany ways of defining fail%re in real .atetials, or -%t another 3Nay, there are .any failure criteria. Gost of the (riteria don3t wor< for soils, and in fa(t the onewe do %se, whi(h is the s%:0e(t of the ne+t se(tion, doesn3t always wor< sowell either* Even so, the .ost (o..on fail%re (riterion a--lied to soils isthe " ohr5Cou/o8b failure criterion.

18.+ THE 3OH!"CO'O3, *AiX'!EC!ITE!ION

Goln is the sa.e 8tto Gohr of Golir (ir(le fa.e Co%lo.: yon<now fro. (o%lo.:i( fri(tion, ele(trostati( attra(tion and re-%lsion,a.ong other things* Aro%nd the t%rn of this (ent%ry, Gohr 16Bhy-othesi&ed a (riterion of fail%re for real .aterials in whi(h he stated that.aterials fail when the shear stress on the failure p/ane at failure

reaches so8e uniLue

funetj 8 >8J t he nor8al stress on that plane , or

G? / ?( 66 ) 15!B

where G is the shear stress and o is the nor.al stress* The first* s%:s(ri-t J

ref ers to the -lane on whi(h the stress a(ts in this (ase the fai/ure plane :and the se(ond J*ri9ieans =at fail%re*=G q (alle ^t:e shear trength 8f the .aterial, and the relationshi-

e+-ressed :y EF* 15! is shown in ig* 1*a* ig%re 1*: shows anele.ent at fail%re with the -rin(i-al stresses that (a%sed fail%re and theres%lting nor.al and shear stresses on the fail%re -lane*

or the -resent, e will ass%.e that a fail%re -lane e+ists, whi(: isnot a :ad ass%.-tion for soils, ro(<s, and .any other .aterials* Also, wewon 3t worry now a:o%t how the -rin(i-al stresses al fail%t e are a--lied tothe ele.ent test s-e(i.en or re-resentative ele.ent in the IieldB or howthey are .eas%red*

Anyway, if we <now the -rin(i-al stresses at fail%re, we (an (onstr%(t

draw, s<et(hB a Gohr (ir(le to re-resent this state of stress for this -ar ti(%lar ele.ent* i.ilarly, we eo%ld ond%(t severa tests to fail%re ar .eas%re fail%re stresses in several ele.ents at fail%re, and (onstr%(t Gohr (ir(les for ea(h ele.ent or test at fail%re* %(h a series is -lotted 2n ig*

1*"* Note that only the to- half of the Gohr (ir(les are drawn, whi(h is(onventionally done in soil .e(hani(s for (onvenien(e only* in(e theGohr (ir(les are deter.ioed at fail%re, it is -ossi:le 3to (onstr%(tthe li.iting or fail%re envelo-e of the shear stress* This envelo-e, (alled the "ohr failure envelope, e+-resses the f%n(tional relationshi- :etween theshear stress .,. and the nor.al stress a11at fail%re EF* 15!B*

11

.j



1

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&

o6

QQ

Q

i b Q ;

Q $62lG5 Nl6n5

Q Q

Q

... .

.

J

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Note that any Gohr (ir(le lying :elow the Gohr fail%re envelo-es%(h as (ir(le $ in ig* 1*"B re-resents a sta:le (ondition* ail%re o((%rs

Gohr (ir(le is tangen/ to the Gohr fail%re envelo-e* Note also that (ir(leslying a:ove the Gohr fail%re envelo-e s%( as (ir( e . 1g* (annote+ist* Toe .aterial wo%ld fail :efore rea(hing these states of stress* I thisenvelo-e is %niF%e for a given .aterial, then the -oint of tangen(y of theGohr fail%re envelo-e gives the stress (onditions on the fail%re -lane atfail%re* Using the -ole .ethod, we (an therefore deter.ine the angle of the

Q



18.+ The 3ohr"Coulo# *allure Crllerlon

&

M3, 4,;lG,5 5n,3l3N5T

A 555****Q 555*=33 \

a

$2. 0. T5 M3 2l5> 64 62lG5 =52n5 45 M3 62lG5 5R.-5l5N5.

fail%re envelo-e* Toe hy-othesis, that the -oint of tangen(y defines theangle of the fail%re -lane in the ele.ent or test s-e(i.en, is the "ohr

failure hypothesis. o% sho%ld disting%ish this hy-othesis fro. the Gohr fail%re theory* The Gohr fail%re hy-othesis is ill%strated in ig* 1*!a for the ele.ent at fail%re shown in ig* 1*!:* tated another way9 the Gohr fail%re hy-othesis states that the -oint of tangen(y of the Gohr fail%reenvelo-e with the Gohr (ir(le at fail%re deter.ines the in(lination of thefail%re -lane*

Another thing yo% sho%ld note fro. ig* 1*!a is that even tho%gh2n soil .e(hani(s we (o..only draw only the to- half of the Gohr (ir(le, there is a :otto. half, and also a **:otto.5half= Gohr fail%re

envelo-e*This also .eans, if the Goh fail%re hy-othesis is valid, that it is eF%allyli<ely that a fail%re -lane will for. at an angle of a. , as shown in ig*11*!a* In fa(t, it is the non%nifor. stress (onditions on the ends of a tests-e(i.en and s.all inho.ogeneities within the s-e(i.en itself that wethin< (a%se a single fail%re -lane to of teo fa(. in a test s-e(i.en* ,er wonder why a (one forras at fail%re in the to- and :otto. of a (on(rete(ylinder when it is failed in (o.-ression hear stresses :etween thetesting .a(hine and s-e(i.en (a-s (a%se non%nifor. stresses to develo-within the s-e(i.en* I everyth.g 1s ho.ogeneo%s and %nif or. stress(onditions are a--lied to a s-e(i.en, then .%lti-le fail%re -lanes for.at (on0%gate angles, k a

1

, as shown in ig* 1*!(* Now we are goiog to invoBve Gonsie%r 'r Co%lo.: in o%r story* Inaddition to his fa.o%s e+-eri.ents with (ats3 f%r and e:ony rods, G*Co%lo.: 1!!"B w as also eoneerned with .iiitat y defense wor<s s%(h asrevet.ents and fortress walls* At that ti.e, these (onstr%(tions were :%ilt :y r%le of th%.:, and %nf ort%nately for the ren(h .ilitary defenses .anyof these wor<s failed* Co%lo.: :e(a.e interested in th e -ro:le. ofthe lateral -ress%res e+erted against retaining walls, and he devised asyste.for aoalysis of ea (t: -ress%res against retaining strn(t%res that is stiH %sed

D5 5B>& D (,w3== ==5 ,,K

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today* 8ne of the things he needed for design was the shearing strength of the soil* 4eing also interested in the sliding fri(tion (hara(teristi(s of diff erent .aterials, he set %- a devi(e for deter.ining the shear resistan(eof soils* He o:served that there was a stress5inde-endent (o.-onent of shear strength and a stress5de-endent (o.-onent* Toe stress5de-endent(o.-onent is si.ilar to sliding fri(tion in solids, so he (alled this (o.-onent the angle of interna/ friction, denoting it :y the sy.:ol >8. Toe other

******* K* 5 55D5DDD555555555555D55555



18.+ The 3ohr"Coulo# *allure Crlterlon453

(o.-onent see.ed to :e related to the intrinsi( cohesion of the .aterialand it is (o..only denoted :y the sy.:ol c. Co%lo.:3s eF%ation is,titen,

5r 1 / o tan B, e 157B

where G is the shear strength of the soil, o is the a--lied nor.al stress, andB, and e are (alled the strength para8eters of the soil as defined a:ove* This,elationshi- gives a straight l.e and ,s, therefore, easy to wor< with* As ise+-lained in the ne+t (ha-ter, neither B, nor e are inherent -ro-ertit9s of the.aterial@ on the (ontrary they are de-endent on the (onditions o-erativein the test* We (o%ld, .%(h as G* Co%lo.: -ro:a:ly did, -lot the res%lts

of a shear test on soil to o:tain the strength -ara.eters L, and e ig* 1*7B* Note that either st,ength -aia.eter (o%ld :e &ero for any -arti(%lar stress(ondition @ that is, 5r / e when B, / 8, or G / o tan L, when e 8* As weshall see in Cha-ter 11, these relationshi-s are valid for (ertain s-e(ifi( test(onditions for sorne soils*

Altho%gh who first did so is %n<nown, it wo%ld see. reasona:le to(o.:ine the Co%lo.: eF%ation, EF* 157, with the Gohr fad%re (ntenon,EF* 15!* Engineers traditionally -refer to wor< with straight lines sin(eanything higher than a first5order eF%ation straight lineB is too (o.

-li(ated o the nat%ral thing to do was to straighten o%t that (%rved Gohr fail%re envelo-e, or at least a--ro+i.ate the (%rve :y a straight line over sorne giveo stress ra nge@ then the eF%ation for that line in ten%s of theCo%lo.: strength -ara.eters (o%ld :e written* Th%s was :o. the "ohr

Coulo8b strength criterion , whi(h is :y far the .ost -o-%lar strength(riterion a--lied to soils* The Gohr5Co%lo.: (riterion (an J5 written as

&ff / X JJ tan L, e 156B

the ter.s having :een defined -revio%sly* This is a si.-le, easy5to5%se(riterion that has .any distin(t advantages over other fad%re entena* l4 1sthe only fail%re (riterion whi(h -redi(ts the stresses on the fail%re -lane atfail%re, and sin(e soil .asses have :een o:served to fail on rather distin(ts%rfa(es, we wo%ld li<e to :e a:le to esti.a te t:e state of stress on

&

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+7+ The 3ohr Clrcle= *allure Theorl..= &tre Path

-otential sliding s%rfa(es* o the Go r5 o% o. (ntenon 1s very %se % or analyses of the sta:ility of earth slo-es and fo%ndations*

4ef ore we dis(%ss the <inds of tests %sed to deter.ine the Gohr5

5D sorne Gohr (ir(les, :oth :efore fail%re and at fail%re* They have severaVD .terest.g ( ara(tenstl(s t a w1 e %se % a er on*

irst, if we <now the angle of in(lination of the Gohr fail%reenvelo-e or have deter.ined it fro. la:oratory tests, then it is -ossi:le to

D D D of the slo e of the Gohrfail%re envelo-e* To do this, we have to invo<e the Gohr fail%re hy5

-rin(i-al stress is a / 2> * 1*1B

A roof of this e %ation is re %ested in one of the ro:le.s at the end of the (ha-ter*

whi(2* are /ess than the stresses reF%ired to (a%se fail%re* %(h a state of s ress .ig e re-resen e y(ase !3* is the 8obi/iMed shear resistan(e on the potential fail%re -lane, and ,,f.f

is the shear strength availa:le shear stress on the fail%re - ane at a1 %re *in(e we haven3t rea(hed fail%re et there is sorne reserve stren th re.ain5ing, and this really is a definition of the factor of safety in the .aterial* 8r

1*11B

Now if the stresses in(rease s o that fail%re o((%rs , the n the Gohr (ir(le :e(o.es tangent to the Gohr fail%re envelo-e* A((ording to the

shear stress on that -lane of ! . Note that this is not the largest or

the -lane in(lined at 2 > and is eF%al to

!3* 1*1$B

Then why doesn3t fail%re o((%r on the 2> -lane Well, it (annot, :e(a%se on that -lane the shear strength availa:le is greater than r.a+, so

D D D the di tan(e fro.the .a+i.%. -oint on the Gohr (ir(le %- to the Gohr fail%re envelo-e inig* 1*6:* That wo%ld :e the shear strength availa:le when the nor.alstress XE on the 2> -lane was o1 0#1BQ$*



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The only e+(e-tion to the a:ove dis(%ssion wo%ld :e when the shearstrength is inde-endent of the nor.al stress@ that is, when the Gohr fail%reenvelo-e is hori&ontal and cf, 8* I sit%ation I s own . 1g* * e, an it is valid for s-e(ial (onditions whi(h are dis(%ssed in Cha-ter 11* %(h.aterials are (alled pureFy cohesive for o:vio%s reasons* or the (ase shown

really, as is e+-lained in Cha-ter 11B* The shear strength is 3& W, andthe nor.al stress on the theoreti(al fail%re -lane at fail%re is o11#1BQ$*

Another %sef %l thing that we sho%ld do :efore going on is to writet e Go r5 o% o. aI %re (ntenon . ter.s o -nn(1-a s resses a a1 %re, rather than as in EF* 156 in ter.s of 3& and o * Loo< at ig* 1*1 and note thatsin cf, W/ , or

151#B

Rearran in , we have

1512B

G

5 Q 55>Jr

#1

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o5( (ot ^t? 5`51

-------0---------4

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Hure Crlterlon457

or

o 1 ` sin V

Using sorne trigono.etri( identities we (an e+-ress

X ?U tan* 151"B

5 tan$ 2>AW

E %ations 1512 thro%gh 151! are (alled the obliLuity relationships :e(a%sethe .a+i.%. in(lination, or o:liF%ity, of the Go r a1 %re enve o-e o((%rs

D These fo%r e %ations are, of (o%rse, onl validwhere e / 8* Ins-e(tion of these eF%ations and ig* 1*1 shows that the

Gohr (ir(le ;JJ> r ) are the stresses on the -lane of .a+i.%. o:liF%ity in11

t e s1 e e.en * n o er wor s, D 11 3ff D D

lane* As we -ointed o%t :efore, this -lane is not the -lane of .a+i.%.shear stress* 8n that -lane a 2>V, the o:liF%1ty w1 e ess t an e

io of : to o o $ is less than 'T'. o *

The o:liF%ity relationshi-s are very %sef%l for eval%ating tria+ial test dataThe last fa(tor we sho%ld (onsider is the effe(t of the inter.ediate

-nn(1-a stress ^Ji on (on 1 1ons a ai %r * $

so.ewhere :etween the .a0or and .inor -rin(i-al stresses, the Gohr (ir(les for the three -rin(i-al stresses loo< li<e those shown . 1g* * (

t a (an have no infl%en(e on the

G

o

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. j



5 - K @ @ K,K K ,X . , K*9K*99 .. K5 *



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(onditions at fail%re for the Gohr fail%re (riterion, no .atter what .agnit%de it has* Toe inter.ediate -rin(i-al stress o -ro:a:ly does have aninfl%en(e in real soils, :%t the Gohr5Co%lo.: fail%re theory does not(onsider it*

0.) TESTS $OR THE SHEAR STRE%(TH O$SOILS

In this se(tion we shall :riefly des(ri:e sorne of the .ore (o..ontests for deter.ining the shearing strength of soils* orne of the tests an

rather (o.-li(ated, and for f%rther details yo% sho%ld (ons%lt rnan%als and :oo<s on la:oratory testing, es-e(ially those :y the ATG 167B, U**Arrny Cor-s of Engineers 16!B, U** 4%rea% of Re(la.ation 16!2B, and4isho- and Hen<el 16"$B*

&254 S56 T5>4

This test is -ro:a:ly the oldest strength test :e(a%se Co%lo.: %sed a ty-eof shear :o+ test .ore than $ years ago to deter.ine the ne(essary -ara.eters for his strength eF%ation* Toe test in -rin(i-ie is F%ite si.-le*4asi(ally, there is a s-e(i.en (ontainer, or 33shear :o+,= whi(h is se-arated

hori&ontally into halves* 8ne5half is fi+ed@ with res-e(t to that half theother half is either -%shed or -%lled hori&on tally* A nor.al load is a--liedto the soil s-e(i.en in the shear :o+ thro%gh a rigid loading (a-* Toeshear load, hori&ontal defor.ation, and verti(al defonnation are .eas%redd%ring the test* 'ividing the shear for(e and the nor.al for(e :y theno8inal area of the s-e(i.en, we o:tain the shear stress as well as thenor.al stress on the fail%re -lane* Re.e.:er that the fatl%re -lane 1s forced to :e hori&ontal with this a--arat%s*

A (ross5se(tional diagra. of the essential feat%res of the a--arat%sis shown in ig* 1*1$a, while ig* 1*1$: shows sorne ty-i(al testres%lts* Toe Gohr5Co%lorn: diagra. for (onditions at fail%re a--ears inig* 1*1$(* As an e+a.-le, if we were to test three sarn-les of a sand at

the sa.e relative density 0%st :efore shearing, then as the nor.al stressX% was in(reased, we wo%ld e+-e(t fro. o%r <nowledge of slidingfri(tion a (on(%rrent in(rease in the shear stress on the fail%re -lane atfail%re the shear strengthB* This (ondition is shown in the ty-i(al shear stress vers%s defor.ation (%rves for a dense sand in ig* 1*1$: for X%i ^% ^ %J· When these res%lts are -lotted on a Gohr diagra., ig* 1*1$(@the angle of interna fri(tion L, (an :e o:tained*



= D -A

=

1 1----- - --

11

------ ; nJ D PB A

S2 D P2 Aa n, D P1 A

AW ..

=

6 ANN664G>

J T5>4 5>Gl4>

5 M3 =266

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=e9 3 *



4$, The 3ohr Clrcle= *aHure Theorl..= &tre Pathe

Ty-i(al res%lts of verti(al defor.ation U for a dense sand areshown in the lower -ortion of ig* 1*1$:* At first th)re is a slightred%(tion in height or vol%.e of the soil s-e(i.en, followed :y a dilationor in(rease in heighl or vol%.e* As the nor.al stress on in(reases, theharder it is for the soil to dilate d%ring shear, whi(h see.s reasona:le*

We do not o:tain the -rin(i-al stresses dire(tly in the dire(t shear test* Instead, if they are needed, they .ay :e inferred if the Gohr5Co%lo.:fail%re envelo-e is <nown* Toen, as is shown in E+a.-le 1*", the angle of rotation of the -rin(i-al stresses .ay :e deter.ined* Why is there rotationof the -rin(i-al -lanes Initially, the hori&ontal -lane -otential fail%re -laneB is a -rin(i-al -lane no shear stressB, :%t af ter the shearing stress isa--lied and at fail%re, :y *definition, it (annot :e a -rin(i-al -lane*Therefore, rotation of the -rin(i-al -lanes .%st o((%r in the dire(t shear test* How .%(h do the -lanes rotate I4 de-ends on the slo-e of the Gohr fail%re envelo-e, :%t it is fairly easy to deter.ine, as is shown in E+a.-le1*", if yo% .a<e sorne si.-le ass%.-tions*

E9A3PE 1O .6

(215n:

The initial and fail%re (onditions in a dire(t shear test, as shown in ig* E+*

1*"*

R5FG25=:

Plot the Gohr (ir(les for :oth initial (onditions and at fail%re, ass%.ing cpis <nown* ind the -rin(i-al stresses at fail%re and their angles of rotationa a1 %re*

(3lG423n:

The Gohr (ir(les for :oth initial (onditions and at fail%re are shown on

the right side of ig* E+* 1*"* At fail%re, yo% <now the nor.al stress onthe fail%re -lane, 11, is the sa.e as the initial nor.al stress, <nB in(e cp is<nown ass%.e e is s.all or &eroB, fro. the Gohr fail%re hy-othesis ig*1*!B the shear stress on the fail%re -lane at fail%re is deter.ined :y the

-oint of tangen(y of the Gohr (ir(le at fail%re* The (enter of the fail%re(ir(le (an :e fo%nd :y drawing a -er-endi(%lar to the Gohr fail%reenvelo-e fro. the -oint of tangen(y* The radial distan(e is, of (o%rse,eF%al to o15 o#BQ$1J* Another way to find the Gohr (ir(le at fail%re is



18.7 Teat lor the &hear &trength ol Son- +11

ln2426l E? / a ,;555 555

aO & /o 01 & a30

G

P325

M3 =266>

a

X / ,

,/

Q

$2. EY. 0.

gra -hi(alXy :y t(ial and error ind the only (ir(le whi(h is tangent at

N 5r : and whose dia.eter lies on the o5a+*is* 8n(e the fail%re (ir(le is11d1awn, the val%es of 11 and *1 ean :e sealed off* ro. the -ole .ethod,the angles of rotation of these stresses are readily fo%nd, as shown in ig*

Ihere are, 3 (o%rse, severaV advantages and disadvantages of thedire(t shear test* Pri.arily, the test is ine+-ensive, ast, and si.-le,es-eeially for gran%lar .aterials* We do o:serve shear -Ba oes and thinfail%re &ones in nat%re, so it see.s alright to a(t%ally shear a s-e(i.en of soil along sorne -lane to see what the stt esses ate on that -lane* 'isadvantages in(l%de the -ro:le. of (ontrolling drainage5 it is very diffi(%lt if

not i.-ossi:le, es-e(ially for fine5grained sods* ConseF%ently, the test 1snot so s%ita:le for other than (o.-letely drained (onditions* When 9wefor(e the fail%re -lane to o((%r, how (an we :e s%re that it is the wea<*estdireetion or even at the sa.e (riti(al dire(tion as o((%rs in t:e fieJd Wedon3t <now* Another flaw in the dire(t shear test is that there are rather seno%s stress (on(entra%ons at the sa.-le :o%ndaties, wlri(h lead tohighly non%nifor. stress (onditions within the test s-e(i.en itself* Andfinally, as shown :y E+a.-le 1*", an %n(ontrolled rotat1on of -nn(1-al

.j

3n=2423n>:



482 The 3ohr Clrcle= *ellure Theorle= &tre.a Patha

-lanes and stresses o((%rs :etween the start of the test and fail%re* Toa((%rately .odel the in sit% loading (onditions, the a.o%nt of this rotationsho%ld :e <nown and a((o%nted for, :%t it isn3t* The Gohr (1r(les for thedire(t shear test are f%rther ill%strated :y E+a.-le 1*!*

*** *** ****** *

(215n:

A dire(t shear test is r%n on a .edi%. dt.se sandy silt, with the nor.al

stress an/

" <Pa* K

/

** At fail%re, the nor.al stress is still " <Paand the shear stress is 21 <Pa*

R5FG25=:

'raw the Gohr (ir(les for the initial (onditions and at fail%re andeter.ine9

a* The -rin(i-al stresses at fail%re*b. The orientation of the fail%re -lane*(* The orientation of the .a0or -rin(i-al -lane at fail%re*d. The orientation of the -lane of .a+i.%. shear stress at fail1*1re*

3 G43n:

a. l he initial (onditions are shown in ig* E+* 1*! :y (ir(le i. in(e K *, the initial hori&ontal stress is #$ <Pa The nor.a l stress on thes-e(i.en is held (onstant at " <Pa d%ring the test, so a 1 is also

a. in(e

11the shear stress at fail%re is 21 <Pa, the fail%re -oint as in ig* 1*1$(B is

-lotted as -oint F. Toe cp is deter.ined to :e #$>* What ha--ens :etweenthe initial Gohr (ir(le , and at fail%re B 1s %n<nown* I he (onstr%(tion of

(ir (le was des(ri:ed in E+a.-le 1*"* Toe (enter of (ir(le is fo%nd to :eat 61 <Pa, 8B* o a11 1#6 <Pa and a

*1 2# <Pa*

b. The state of stress at faih1re -oint F is ", 21B <Pa, and the fail%re -lane isass%.ed to :e hori&ontal, a good ass%.-tion for the dire(t shear

(* A line drawn hori&ontally fro. the <nown state of stress at -oint 9 interse(ts the Gohr (ir(le at P, the -ole* Line Pa

11indi(ates the

orientation of the .a0or -rin(i-al -f aoe I4 .a<es an angle of a:o%t "*>with the hori&ontal* D

E9A3PE

@



18.7 Teta tor lhe &hear Stntn@lh of &olla

80

-¡;¡a*

Z**

*,,D

.?.'.?..'.

*?@e'l

"2-----0----

2

fJB $

o

&11

8ZZ 80 00 *0

Nor.al stress, o <Pal

X11

" $2. EY. 0.

d. Line P" is the orientation of the -lane of .a+i.%. shear stress@it is a:o%t 1"> fro. the hori&ontal*

Note that in this e+a.-le, if we didn3t ass%.e that t-*e Gohr fatl%reenvelo-e -assed thro%gh the origin of the Gohr diagra., .ore than onetest at different oZ3s wo%ld :e reF%ired to esta:lish the Gohr envelo-e*

'%ring the early history of soil .e(hani(s, the dire(t shear test was the.ost -o-%lar shear test* Toen, a:o%t 16#, A* Casagrande while at G*I*T* :egan resear(h on the develo-.ent of (ylindri(al (o.-ression tests in anatte.-t to over(o.e sorne of the serio%s disadvantages of the dire(t shear

test* Now this test, (o..only (alled the triaial test, is :y far the .ore -o-%lar of the two* The tria+ial test is .%(h .ore (o.-li(ated than thedire(t shear* :%t also .%(h .ore versatile* We (an (ontrol drainage F%itewell, and thete is no rotation of o and o! tress (on(entrations still e9+ist, :%t they are signifi(antly less than in the dire(t shear test* Also, the fail%re -lane (an o((%r anywhere* An added advantage* we (an (ontiol the stress -aths to fail%re reasona:ly well, whi(h .eans that (o.-le+ stress -aths in



+4+ The 3ohr Clrcle= *ellure Theorle= &tre Path

the field (an .ore effe(tively :e .odeled in the la:oratory with the tria+ialtest* tress -aths are e+-lained in the ne+t se(tion*

The -nn(1-le of the tria+ial test is shown in 1g* 1*1#a* l:e soils-e(i.en is %s%ally en(ased in a r%::er .e.:rane to -revent the -ress%ri&ed (ell fl%id %s%ally waterB fro. -enetrating the -ores of the soil*A +i a l load is a--lied t:ro%g: a -istan, aod of ten t:e vol %roe (:aoge of t:e s-e(i.en d%ring a drained test or the ind%(ed -ore water -ress%re d%ring 1an %ndrained test is .eas%red* As .entioned a:ove, we (an (ontrol the 3

-

S32l >N525n

RGJJ55J6n5

05ll

T3 13lG5 6n5 3 N35D645 N5>>G5 56>G55n46 =5125 A V3l 3 AG

J

$2. 0.! 6 S5642 =266 3 45 426Y26l 6NN664G>; J 6>>G5=>45>> 3n=2423n> 3n 45 426Y26l >N525n.

5D5555555555555 555555 D55'-5 _ . 5



18.7 Tet lor the &hear &trength of &oll 485

drainage to and fro. the s-e(i.en, and it is -ossi:le, with sorneass%rn- tions, to (ontrol the stress -aths a--lied to the s-e(i.en*4asi(ally, we ass%.e the stresses en the :o%ndary of the s-e(i.en are -rin(i-al stresses ig* 1*1#:B* This is not really tr%e :e(a%se of sornesrnall shear stresses a(ting on the ends of the s-e(i.en* Also, as.entioned :efore, the fail%re -lane is not for(ed5 the s-e(i.en is free tofail on any wea< -lane or, as so.eti.es o((%rs, to si.-ly :%lge*

o% will note that the 6Y26l in ig* 1*1#: is the differen(e :etweenthe .a0or and .inor -rin(i-al stresses@ it is (alled the principal

stress

d if@erence or so.eti.es wrongJy t:e devia tar stressB Note a Jso t:a t for the (onditions shown in the fig%re, o* / o! o((%D o.eti.es we will

ass%.e that >((n o1 o$ for s-eeial ty-es of stress -ath* tests* Co..on tria+ialstress -aths are dis(%ssed in the ne+t se(tion*The tria+ial test is far .ore (o.-le+ than the dire(t shear test@ entire

:oo<s have :een written on test details and inter-retation of the res%ltssee, for e+a.-le, 4isho- and Hen<el, J 6"$B* Gost of the data and testres%lts des(ri:ed in Cha-ter 11 were derived fro. tria+ial tests*

'rainage (onditions or -aths followed in the tria+ial test are .odels3 s-e(ifi( (riti(a design sit%ations reF%ired for the analysis of sta:iJi ty inengineering -ra(ti(e* These are (o..only designated :y a two5letter sy.:ol* The first letter ref ers to what ha--ens before shear5 that is,whether the s-e(i.en is (onsolidated* Toe se(ond letter ref ers to thedra.age (ond1t1ons dur8g shear. he three -er.iss1:le dra.age -aths .

the tria+ial test are as follows9

'rainage Path4efore hear5'%ring hear y.:ol

O n(onsohdated5O ndra.ed O OConsolidated5Undrained CUConsolidated5'rained C'

or reasons e+-lained in Cha-ter 11, the %n(onsolidated5drained testdefies inter-retation and is therefore rneaningless* Tria+ial test res%lts for the three drainage -aths are des(ri:ed in detail in Cha-ter 11*

E9A3PE 18.4

(215n:

A (onventional (onsolidated5drained C'B tria+ial test is (ond%(ted on asand* Toe eell -ress%re is I <Pa, and the a--lied a+ial stress at fail%re is$ <Pa*

AH, * * + 4 4 5

J '



555

277 T5 M3 Cll5, $5llG5 T53l56. S4566 P646

R5FG25=:

tions*a*Plot the Gohr (ir(les for :oth the initial and fail%re stress (ondi5

:* 'eter.ine L, ass%.e e 8B*(* 'eter.ine the shear stress on the fail%re -lane at f ail%re 5r

11, and

find the theoreti(al angle of the fail%re -lane in the s-e(i.en* Alsoe er.ine e orien a 1n o e - ane o .a+i.%. o 1F%1 y* 1

d* 'eter.ine the .a+i.%. shear stress at fail%re -6Y and the angle of the -lane on whi(h it a(ts@ (al(%late the availa:le shear strength on this -lane andthe fa(tor of safety on this -lane*

S3lG423n:

a* Ref er to ig* 1*1#: and ig* E+* 1*7* Toe initial (onditions are shown atthe to- of ig* E+* 1*7 for the (onventional tria+ial test* Toe inilK tr5

T al Kl**the (eKllK*1*r* 5 5rt 9*>, 11 U KiKl**9*619l inKan iKr(t1s1 or e .1 1a s ress (on 1 1ons 1s a

point at 1 <Pa, as shown in the Gohr diagra. of ig* E+* 1*7* Atfail%re, the 6Y26l/ o ' .. l.: % / $ <Pa* o

-1W o1 5 a* :W a*WQC $ 1 # <Pa

Now we (an -lot the Gohr (ir(le at fail%re@ a 1W # and 0 31/ 1* Toe

(enter is at o1 # BQ$

/$, and the radi%s is o1

5 # BQ$

/1* Toe

:* We ind cp gra-hi(ally to :e #>* We (an also %se EF* 151# if we -refer ananalyti(al sol%tion* Th%s

L, * AWW5 *War(s.* $

ar(s.5olf 3*W "00

(* ro. the Gohr fail%re hy-othesis, the (oordinates of the -oint of tangen(y of the Gohr fail%re envelo-e and the Gohr (ir(le at fail%re are11, -W; WB* ro. EF* 156, we <now that &WW/ NJ+ tan cp, :%t %nli<e thedire(t shear test we don3t <now XJ+ in the tria+ial test* Loo< (aref %lly at ig*1*1*

Toe s.all angle near the to- of the Gohr (ir(le is L, :y a theore. fro.1 se oo geo.etry * ere ore, s.(e $ , s. cp. ov.g for 11, we o:tain

Alf 3*W ! l - 3*W *

XJ+ / $ 5$

s. cp $ 5 1 sin #> / 1 <Pa

& WW X J + tan L, 1 tan #> 7"*" <Pa

an e of in(lination of the fail%re -lane (an :e fo%nd

. . . . .

#>



2;; o

At 3ail/re

;; a IPa)

1,.5 T....for the &hear &trenglh of &olla 487

e5ll a3 00 P6

ln2426l3n=2423n>:

a11 !00 P6

A4 62lG5:e5ll 0! 00 P6

M3 =266:

$2. EY. 0.8

gra-hi(ally :y the -ole .ethod or analyti(ally* ro. the stress (onditionsat fail%re shown in ig* E+* 1*7, the -ole is at 1, 8B, and a (an :e.eas%red to :e ">* or the analyti(al sol%tion, %se EF* 151

a / 2> ^Q? / ">

Toe -lane of .a+i.%. o:lig%ity is oriented at this angle also sin(e the.a+i.%. in(lination of the Gohr fail%re envelo-e is #> and the -oint of

2

, J

*****,

1



tangen(y deter.ines the (ondition of .a+i.%. o:liF%ity* In other words,the ratio - / o is a .a+i.%. at this -oint on the Gohr (ir(le and on the -lane in the s-e(i.en in(lined at "> fro. the hori&ontal*

=. T.a+ / ) /X DJ - *W

$/ 1 <Pa* ro. the -ole, the -lane of G"ax

1Q$ ** The .a+i.%. o:liF%ity -art (B is 7"*"Q1 ro.

$ tan #> 11* <Pa

whi(h is greater than 5r.a+ 1 <Pa* Therefore the fa(tor of safety on the

**

Note that the fa(tor of saf ety on the a1

/ "> -lane is

1=availa:le 7"*"

either the .a0or or .inor -rin(i-al stress5 nothing in :etween* With these2&

(onditions in real -ro:le.s .ore a((%rately* Today, however, these tests

are -ri.arily %sed for resear(h rather than for -ra(ti(a engineeringa--li(ations*

A (o%-le of other tests of the dire(t shear ty-e .%st also :e.entioned* &orsional or ring shear tests ig* 1*1aB have :een develo-ed

so that the test s-e(i.en .ay :e sheared to very large defor.ati.s*This

. . . . .

strength of (ertain .aterials, whi(h is easier to o:tain with a ring shear devi(e than :y re-eatedly reversing the dire(t shear :o+* A .ore (o..on



:::.. X - - X -------------- 5555 5555555 ...

55555555555



aell insie)

D a

An7 stress an 4e

6

E nds are f i+ed so that

lo'Q Q

+

, Q Q

Any stress (an :e a1 , a$ , or a#

5

$2. 0." S5642 =266> 3 45: 6 3ll3D l2n=5 45>4; J Nl6n5>462n 45>4; 6n= 5 4G5 426Y26l 3 GJ32=6l >56 45>4.

D . ...... .. . ,9@999@* - 5//

Q Q



47, The 3ohr Clrcle= *allure Theorle= &tre Patha

T T3N Nl645n 34645>

S32l >N525n

H323n46l >56 Nl6n5 B3443 Nl645n 2> 2Y5=

6l

a!

T

,..... 3 K a,

J535 >56

K , 1

1C3n>46n4 >N525n =26545

62n462n5= J:. W25-52n35=GJJ5 5J6n5%(I 4N5

*. A >46 3 15 42n3n2n2n 2n> S(I 4N5

!. R22= Nl645> N2>642 R3>35-C6J2=5 4N5

J

$2. 0.) S5642 =266> 3: 6 43>23n6l 3 2n >56; J =254>2Nl5 >56 6NN664G>.

test %sed . :oth (andinavia and in the United tates for stati( anddyna.i( testing is the direct si8ple shear 'B test ig* l*1:B* In thistest, a fairly ho.ogeneo%s state of shear stress is a--lied, there:y avoidingt:e stress (an(en tra tians whi(: e+ist io t:e a(dioa(y di(e(t s:ea( a--a( at%sin(e stress (onditions in the ' test are not the sa.e as those shown inE+a.-les 1*" and 1*! for the dire(t shear :o+, they are des(ri:ed inE+a.-le 1*6*



U

E9A3PE 18.

(215n:

Toe ' test*

R5FG25=:

Ill%strate the stress (onditions in the test, and draw the Gohr (ir(les for

:oth initial and fail%re (onditions*

S3lG423n:

Toe initial (onditions for the ' test shown in ig* E+* 1*6a are the sa.eas those for the dire(t shear :o+ test shown in ig* E+* 1*" and ig* E+*

1*!* The sides of the soil sa.-le are for(ed to rotate thro%gh an angle y :y thea--li(ation of a hori&ontal shear stress, '!Ov· These stress (onditions areshown in ig* E+* 1*6:* Note the a:sen(e of (o.-le.entary shear stresseson the outside of the soil sa.-le@ this is ne(essary for si.-le shear* 6nside

the sa.-le, however, the a--lied stress syste. is ass%.ed to :e pure shear,and (o.-le.entary stresses are ne(essary for eF%ili:ri%.* With thea--li(ation of '!Ov D and and O (onstant, the Gohr (ir(le enlarges a:o%tthe sa.e (enter as the initial Gohr (ir(le i. At fail%re, the Gohr (ir(le is

0%st tangent to the Gohr fail%re envelo-e, and the Gohr (ir(le loo<s li<e(ir(le J of ig* E+* 1*6(*

or this (ondition, the -ole P is fo%nd :y e+tending a line fro.0

0, --E

0 hori&ontally the -lane on whi(h these stresses a(tB to where it

interseets the Goln (it (le* Lines dtawn fro. the -ote re-resent theorientations of different states of stress within the soil sa.-le* Toe line P"

re-resents the -lane of .a+i.%. a:sol%te val%eB shear stress@ the line P9

re-resents the orientation of the fail%re -lane5 it is not hori&ontal as in

the dire(t shear test* The line Po 11 re-resents the orientation of the o1 -lanes when '!Ov is negative on the hori&ontal s%rfa(e* When and 2 thesign of '!O v :e(o.es -ositive on the hori&ontal -lane, as in a cyclic si8ple

shear test, then the -ole is lo(ated at P for that -art of the (ir(le* Toe line P3o 11 :e(o.es the new orientation of the -rin(i-al -lane with a negative J,the angle of -rin(i-al stress rotation*

471

*J

******* @@@@@@*****.6j

0



<oil

6 n2426l3n=2423n> J W24 6NNl26423n 3 >56

>45>>5> 3n 43N 6n=J3443 3nl >55 45Y4

***,,,5

J

*eMB

3

5 M3 2l5>

+M



5555555555 5 55555



$25l= T5>4>

4e(a%se of all the -ro:lerns asso(iated with sa.-ling and la:oratorytesting, it so.eti.es is :etter to .eas%re the strength dire(tly in the field*The .ost (o..on f ield tests for sof t (lays are the vane shear test and the

Dutch cone penetro8eter. The latter test is also very effe(tive when %sed for sandy soils* The standard penetration test PTB is %sed for gran%lar .atenals and so.etl.es for (ohes1ve so;ls, :%t 1t is less a((%rate ines-e(ially sof t (lavs* Toe /o(a borehole shear test has :een develooed for %se in loess soils* The pressure8eter and scre( plate tests are also :e(3o.ingin(reasingly -o-%lar for deter.ining, a.ong other things, the strength anddefor.ation -ro-erties of soils* ield test eF%i-.ent and test .ethods are

des(ri:ed :rieflyD in Cha-ter 11 and in detail in .ost te+t:oo<s onfo%ndation engineering* Ladd, et al* 16!!B have a good dis(%ssion of thea--lt(a:1ltty ot :oth la:oratory and fteld tests . geote(h.(al eng.eenng -ra(ti(e*

18.6 &T!E&& PATH&

As yo% <now fro. the first -art of this (ha-ter, states of stress at a -oint in eF%ili:ri%. (an :e re-resented :y a Gohr (ir(le in a '!'a (oordi5nate syste.* o.eti.es it is (onvenient to re-resent that state of stress :yl.

. stress point , whi(h has the (oordinates o1 5 #BQ

.$ and o1 #BQ$, as

55 UlD ** 5 - - -

*l3loW Wv,l U, l 3Ul

Uli99UlJ

I' 5 -ring, we

&

>1 5 #

--------- -

Q S45>> N32n4

1 $ *Q ' ***********

1

11

# 1 # & .$

$26. 0. A M3 2l5 3 >45>> 6n= 3AS??nn2n ?'4 ..??'' ...........

473

5

55

F



5D DD D ----'---/---- D 9 **,,- ,,

. 55 5 55D



=

a, inreasin$

474 T5 M3 Cll5, $5llG5 Theorlea, tresa P86

ass%.e a1 and o# a(t on verti(al and hori&ontal -lanes, so the (oordinatesof the stress -oint :e(o.e F av 5 a,,BQ$ and F av a,,BQ$, or si.-ly L and -,res-e(tively@ or

v 5 a, , &

$

v P a ,, &

$

1517B

1516V

4oth B and p (o%ld, of (o%rse, :e defined in ter.s of the -rin(i-al stresses*4y (onvention, L is (onsidered -ositive when av a,.4 otherwise it isnegative*

We of ten want to show s%((essive states* of stress whi(h a test

s-e(i.en or a ty-i(al ele.ent in the field %ndergoes d%ring loading or %nloading* A diagra. showing the s%((essive states with a series of Gohr (ir(les (o%ld :e %sed ig* 1*1!aB, :%t it .ight :e (onf %sing, es-e(ially if the stress -ath were (o.-li(ated* Therefore it is si.-ler to show only thelocus of the stress -oints* This lo(%s is (alled the stress path, and it is -lotted on what we (all a p5L diagra8 ig* 1*1!:B* Note that bothp and L

(o%ld :e defined either in ter.s of total*stresses or effe(tive stresses* As :efore, a -ri.e .ar< is %sed to indi(ate effe(tive stresses* S3 fro. EFs* 1517 and 1516 and the effe(tive stress eF%ation EF* !51#B, we <now thatL3 5 L while p3 p 5 u, where u is the e+(ess hydrostati( or -ore water -ress%re*

Altho%gh the (on(e-t of a stress -ath has :een aro%nd for a longti.e, Prof* T* W* La.:e of G*I*T* de.onstrated its %sef %lness as atea(hing devi(e La.:e and Whit.an, 16"6B and develo-ed the .ethodinto a -ra(ti(aV engineering tool for the sol%tion of sta:ility and defor.ation -ro:le.s La.:e, 16"2 and 16"!@ La.:e and Garr, 16!6B* Mery oftenin geote(hni(al engineering -ra(ti(e, if yo% %nderstand the (o.-lete stress

a N6 J

$2. 0. 6 SG5>>215 M3 2l5>; J >45>> N64 6 3n>46n4 As6n= 2n56>2n a, 645 L6J5 6n= W246n, 99.

555 555 5555 555 ----?'--



18.4 &...... Path +M7

-ath of yo%r -ro:le., yo% are well along the way towards the sol%tion ofthat -ro:le.*A si.-le ease to ill%strate stress -aths is the eo..on tria+ial test in

whi(h a* re.ains fi+ed as w in(rease a orne Gohr (ir(les for this testare shown in ig* 1*1!a along with their stress -oints* The (orres-ondingstress -ath shown in ig* 1*1!: is a straight line at an angle of 2> fro.the hori&ontal :e(a%se the stress -oint re-resents the state of stress on the

. n2426l 3n=2423n>:

ND & aO =3>4642 3N5>>23n

f N·

*. &G2n l36=2n 3Gnl36=2n

!. S45>> N64>

6 6

vv

F

'

E P64 A: A6 $a.

79 A6 / .U $a.C: A6 O, $a. 2n56>5>

&: A6 5$a. - E: A6 =556>5>, $a. / O

$: A6 2n56>5>, $a. =556>5>

$

-;

$2. 1*17 &255n4 >45>> N64> 3 2n2426ll =3>4642 >45>> 3n=2423n>645 L6J5 6n= W246n, 16"6B*

. j




-lane %lqented 2> f1o. the -1in(i-al -lanes* Note that this is the -lane ofrna+i.%. shear stress*B

orne e+a.-les of stress -aths are shown in igs* 1*17 and 1*16* Inig* 1*17 the initial (onditions are / O, an eF%al5all5aro%nd or hydrostati( state of stress* Those in ig* 1*16, where the initial verti(al stress isnt the sa.e as the initial hori&ontal stress, re-resent a non5hydrostati(

av ,( aO ,( 8 nonhydrostati((o.-ression B

$* '% ring loading ar % nloadi ngB

a Aa

#* tress -athsF

A61 in(reases, A6 / 8

49 A61 i n(reases, A6 de(reases

C9 Aa de(reases Aa 8

'9 A61 de(reases, A6 in(reases

-

e

-;

$2. 0.9 O255n4 >45>> N64> 3 2n2426ll n3n-=3>4642 >45>>3n=2423n> 645 L6J5 6n= W246n. 99.



1o 8 S1re.. Pa-b- 477

state of stress* o% sho%ld verif y that ea(h stress -ath in igs* 1*17 and1*16 has in fa(t the dire(tion as indi(ated in the fig%res* We shall showyo% how to do this in E+a.-le 1*18*

E9A3PE 18.18

ig%res 1*17 and 1*16*

R5FG25=:

Merify that stress -aths A , =, and C of ig* 1*17 and A and of ig*1*16 are (orre(t as shown*

The initial eonditions for ali stress -aths in ig* 1*I are - F av a,*BQ$ ov oh and L 8* inal (onditions are EFs* 1517 and 1516B

or stress -ath $ , Ao= / $oh 4 so

Th%s the stress -ath $ .oves o%t on the -5a+is :y an a.o%nt $ov / $oh.

or stress -ath =, -2.oh 5 Ufo=@ so',

4 #PJ / -------- / v 5Aoo

These val%es are the ( p, FB (oordinates of the end of stress -ath =. Th%sthe L and p :oth in(rease :y an a.o%nt llL 5 llov and Ilp Ilov ,whi(h

.j



P1D

¡

478The 3ohr Clrcle= *allure 'heorle8: &treea Petha

.eans that the stress -ath has a slo-e of or is in(lined at 17*2> as shownin i * 1*17*

or stress -ath C, tia,. 8 and I1; in(reases :y sorne a.o%nt*

o IiL I1; and Ii p tio Therefore the slo-e of t:e stress -ath .%st :e I or .(hned at 2 >* This sol%tion also holds for stress -ath $ in ig*1*16* Here initial (onditions are noo5:ydrosta ti(, so

The final (oo1dinates for -ath $ are

>> Iiov 5 a,.B1& *

1 a,.PJ &

S3 AF

J A3and tip /

J1, whi(h is the sa.e as for stress -ath C in

ig* 1*17*or stress -ath D in ig* 1*16, 1 de(reases while ti.o,. in(reases*

Initial ( p , B : are the sa.e as -ath $ in this fig%re, while the final val%esof

5 Aa B 5 o,* A o ,*B

B1& $

O0 5 tio B o,. I1.o, . :

PJ & *

S3

I1.L / -.$Utia 5 $

tia+,

and Iip /-$I1

$ti.a

h

J:e a(t%al slo-e of the stress -ath de-ends %n the relative .ag.t%des ofAo and Ao,*, :%t in general it trends down and o%t as shown in ig* 1*16*

l4 is of ten (onvenient to (onsider stress ratios. In Cha-ter ! wedefined a lateral stress ratio S, whi(h is the ratio of hori&ontal to verti(al

#

#



1,.8 Slrff& Path& 479

stress,

K $ & (7-18)

In ler.s of effective stresses, this ratio isoS,

K $ & 7-19

o

(onditions of no lateral strain* inally, we (an define a ratio S 1 for theai %re*

o3 S '

'

2 -v

where 1,1/ the hori&ontal eff e(tive stress at fail%re, and

Xv / e ver i(a e e( ive s re s DUs%ally S is defined in ter.s of effe(tive stresses, :%t it .ay 0%st as

well :e in ter.s of total stresses* Constant stress ratios a--ear as strai t i * l *$ * These lines (o%ld also :e stress aths

for initial (onditions of Xv aO 8 with loadings of S eF%al to a (onstant h =

s%(h as those shown in igs* 1*17 and 1*16*

F K1 3N5>>23n

] K !

P, -3

-;

$2. 0.*0 &255n4 3n>46n4 >45>> 6423> 6n= 5Y6Nl5> 3 >45>> N64>,>4642n 3 v O // O 645 L6J5 6n= W246n, 16"6B*

.j

a



2



Z

27 T5 M3 Cll5, $6llG5 T53l56, S4566 P5l6

Note that

or in ter.s of S

L ' S - / tan Q# /-

p l K

S l 5 tan Q#

l tan Q# 15$$Bwhere /* is the slo-e of the line of (onstant K when K ^ K . At fail%re, the

1slo-e of the S 1 line is indi(ated :y the sy.:ol ip. Note also that for any

-oint where yo% <now p and B, for e+a.-le -oint $ in ig* 1*$B, aO and0 (an readily :e fo%nd gra-hi(ally@ that is, lines at 2> fro. the stress

-oint interse(t the a5a+is at aO and a inall , there is no reason wh.%st always :e greater than NO· I4 %s%ally is, :%t there are .any i.-ortantsit%ations in eote(h D D D

(onvention L is negative and K l, as shown in ig* 1*$*D D in

geote(hni(al engineering* When soils are de-osited in a sedi.entary en5D i e a a e or e sea, t ere 1s a gra %a %1 %- of over:%rden

stress as additional .aterial is de-osited fro. a:ove* As this stress in5(reases, the sedi.ents (onsolidate and de(rease in vol%.e Cha-ters 7and 6 * l the area of D

of the. de-os.it, then it s.ee.s reasona:le that the (o.-ression is essentially

an an eF%a to S , and the stress -ath d%ring sedi.entation and (onsolidation wo%ld

s1.1 ar o -al . 1g* y-i(al val%es of S 1 for gran%lar

.aterials range fro. a:o%t *2 to *" whereas for nor.all ((lays S (an :e a li ttle less than * %- to *7 or *6* A good average val%eis

stress de(rease o((%rs :e(a%se the over:%rden stress0 1

has to :e re.oved

o ows a--ro+i.a e y .e . 1g*1*$1, and the soil s-e(i.en ends %- so.e-la(e on the hydrostati( a a or a+is* 1s stress -ath and its relation to the strength of (lays isdis(%ssed in Cha ter 11*

I, instead of sa.-ling, the over:%rden stress was de(reased :y

C wo%ld :e followed* l the verti(al stress (ontin%ed to :e re.oved, thei we e ow e -5a+is* t en :e

over(onsolidated and S wo%ld :e greater than 1**o.ett.es in engineering -ra(ti(e a test s-e(i.en is re(onsolidated

in the la:orato %nder S sit% stresses* %(h (onditions are shown in ig* 1*16 and at -oint A in ig*

. . . . o

Y15$1B



F

o

BS5=25n46423n 6n= ,3n>3l2=6423n S6Nl2n

Q =,,,?

-3

SN525n 2n l6J J535 45>42n

$2. 0.* S45>> N64> =G2n >5=25n46423n 6n= >6Nl2n 3 n36ll3n>3l2=645= l6, D55 S ^ 1*

F K1 3N5>>23n

------- Kj

N'

-; K 5Y45n>23n

SJ3l (5345n26l En2n552n 5Y6Nl5

AC9 A+ial Ce.1#ressieA $:l6425n l66:l2n 2n556>5 v , h eenstant

LE:

AE:

LC:

L6456l EY45n>23n

AY26l EY45n>23nL6456l C3N5>>23n

A4215 564 N5>>G5- =556>5 3, 31 3n>46n4

nl36=2n 5Y616423n - =556>5 31 , 33n>46n4 P6>>215 564 N5>>G5 - 2n56>5 3,

XD 3246n4

$2. 0.** S45>> N64> =G2n =62n5= l36=2n> 3n n36ll 3n>3l2=645= l6> 6n= >6n= 645 L6J5, 9.

.j



Í '

"8* T5 M3 Cll5, $6llG5 TE53l-. >45..P646

fail%re de-ends on the f ield loading (onditions oile wishes to .odel* o%ri n 1 1 n n e a ora ory s ress -a s w De .o e

the. are shown in ig* 1*$$* Note that these stress -aths are for drained

loading dis(%ssed in the ne+t (ha-terB in whi(h there is no e+(ess -orewater -ress%re@ therefore total stresses eF%al effe(tive stresses and the totalstress -ath TPB for a given loading is identi(al to the effe(tive stress -ath

As s%ggested :y EF* 15$, we are of ten interested in (onditions at

2 e 1 ine an the Gohr5Co%lo.: fail%re envelo-e* Consider the two Gohr (ir(lesshownin ig* 1*$#* The (ir(le on the lef t, drawn for ill%strative -%r-oses only,

re-resents fail%re in ter.s of the p'B diagra.* Toe identi(al (ir(le on theright is the sa.e fail%re (ir(le on the Gohr &5 1 diagra.* To esta:lish the. .

-aths, deter.ined over a range of stresses, were %sed* The eF%ation of the K 1line is

B1 a p1tan ip

where a / the inter(e-t on the F5a+is, in stress %nits, andres-e( o

15$#B

degrees*

Toe eF%ation of the Gohr5Co%lo.: fail%re envelo-e is

.1,.1 / e X JJ tan B, 156B

ro. the eo.etries of th

and

o, ro. a p'B :e (o.-%ted*

sin cp tan 2N 15$2B

a

(os F, 15$B

ear s rengt -ara.eters B, an $ .ay rea y

F &

a e

N a

$2. 0.*! R5l6423n>2N J54D55n 45 S , l2n5 6n= 45 M3-C3Gl3J62lG5 5n15l3N5.

c &



18.4 &treaa Patha

A nother %sef %l as-e(t of the p'B diagra. is t:at it .ay :e %sed toshow :oth total and effe(tive stress -aths on the sa.e diagra.* We said :efore that for drained loading, the total stress -ath TPB and theef fe(tive stress -ath EPB were identi(al* This is :e(a%se the -ore water -ress%re ind%(ed :y loading was a--ro+i.ately eF%al to &ero at all ti.esd%ring shear* However, in general, d%ring undrained loading the TP is noteF%al to the EP :e(a%se e+(ess -ore water -ress%re develo-s* or a+ial(o.-ression ACB loading of a nor.ally (onsolidated (lay ( S ^ 1B * a

positive e+(ess -ore water -ress%re d u develo-s* Therefore the EP lies tothe left of the TP :e(a%se o3 / o 5 d u. At any -oint d%ring the loading,the -ore water -ress%re d u .ay :e s(aled off any hori&ontal line :etweenthe TP and EP, as shown in ig* 1*$2*

F

N, N'

$2. 0.*" S45>> N64> =G2n Gn=62n5= 6Y26l 3N5>>23n l36=2n 3 6n36ll 3n>3l2=645= l6.

I a (lay is over(onsolidated / ? 1B, then negative -ore water -ress%re 5 % B develo-s :e(a%se the (lay tends to e+-and d%ring shear, :%t it (an3t* Re.e.:er9 we are tal<ing a:o%t %ndrained loading in whi(hno vol%.e ehange is allowed*B or AC loading on an overeonsolidated(lay, stress -aths li<e those shown in ig* 1*$ will develo-* i.ilarly, we(an -lot total and eff e(tive stress -aths for other ty-es of loadings and%nloadings, for :oth nor.ally and over(onsolidated soils, and we shallshow sorne of these in Cha-ter 11*

In .ost -ra(ti(a sit%ations in geote(hni(al engineering, there e+ists a

stati( gro%nd water ta:le@ th%s an initial -ore water -ress%re C , is a(tingon the ele.ent in F%estion* o there ar really three stress -aths we sho%ld(onsider, the EP, the TP, and the* T 5 % BP* These three -aths areshown in ig* 1*$" for a nor.ally (o9nsolidated (lay with an initial -orewater -ress%re C %ndergoing AC loading* Note that as long as the gro%ndwater ta:le re.a.s at the sa.e elevation, u

or the (onditions at fail%re*does not af fe(t e1ther the EP

.X

0

1

1



<

$2. 0.*) S45>> N64> =G2n 6Y26l 3N5>>23n 3 6 5612l 3153n>3l2=645= l6.

F

', Q ', ::::=- ---- --,-S _:. ....

-, -3

2. 0.645 L6J5, 9.

6

272



P!O,E3&

151* iven an ele.ent with stresses as indi(ated in ig* PI51* ind9aB The .a0or and .inor -rin(i-al stresses and the -lanes on

whi(h they a(t*:B The stresses on a -lane in(lined at #> fro. the hori&on5

eB The .a+i.%. shear stress and the in(lination of the -laneon whi(h it a(ts*

rooP6

!)

*0 P6

*0 & H323n46l

!) P6

$2. P0-

15$* Wor< Pro:le. 151 with the ele.ent rotated #> (lo(<wise fro.the hori&ontal*

15#* With tlte ele.ent 3 Pro:le. 1 $ rotated J8>, 2n= the .agnit%deand dire(tion of the stresses on the horiMontal -lane*

152* Wor< E+a.-le 15# with the ele.ent rotated $> (lo(<wise fro.the hori&ontal* In addition, find the stresses .agnit%de and dire(tionB on the verti(al -lane*

15* EF%ations 15 and 15" were derived fro. ig* 1*$, with a and ayas -rin(i-al stresses* 'erive the .ore general eF%ations for theGohr (ir(le when a and ay are nol a(ting on -rin(i-al -lanes*

15"* Toe state of -lane stress in a :ody is des(ri:ed :y the following*

stresses* o 6 <NQ.* eo.-ression, a! $ <NQ. tension'eter.ine :y .eans of the Gohr (ir(le the nor.al stress and shear stress on a -lane .(hned at 1 to the -lane on whi(h the nnot

-rin(i-al stress a(ts* Che(< the res%lts analyti(ally* After A*Casagrande*B

+17

- ll

L..



--------3---

Woriontal 5lane

W-5laneoriontal)

Í'

"88 T5 M3 Cll5, $6llG5 T53l5>, S45>6 P64>

15!* At a (ertain (riti(aV -oint 2n a steel :ea., on a verti(al -lane the(o.-ressive stress is 1$" GPa and the shearing stress is #2* GPa*There is no nor.al stress on the longit%dinal hori&ontalB -lane*ind the stresses a(ting on the -rin(i-al -lanes and the orientationof -rinei-al -lanes ,vith the hori&ontal* Af ter Taylor, 1627*B

157* A soil sa.-le is %nder a :ia+ial state of stress* 8n -lane 1, the stressesare $", 7B, while on -lane $, the stresses are 11*", 52B* ind the.a0or and .inor -rin(i-al stresses*

156* or the ele.ent shown in ig* PI569 aB ind the .agnit%de of the%n<nown stresses O and GO on the hori&ontal -lane* :B ind theorientation of the -rin(i-al stresses@ (learly in di(ate their orienta

tion in a s.all s<et(h* eB how the orientation of the -lanes of .a+irn%. as well as .;ni.%. shear*

151 iven the ele.ent wi th stresses as s:own in Eig PHJl@ aB indthe .agnit%de and dire(tion of X% and ;( :B ind the .agnit%deand direetion of o1 and o# 4e s%re to elearly indieate these stressesand their dire(tions on a se-arate s<et(h*

ig* P151

1511* iven the data of E+a.-le 1** aB ind the .agnit%de aoddire(tion of the stresses on the hori&ontal -laae* :B ind the

5 555D 55 555 D5555555555555555555555*---***----- =555D55D555D5 5555555D55D5D555



Problema "8

.a+i.%. shear stress and deter.ine the angle :etween the -laneon whi(h it a(ts and the .a0or -rin(i-al -lane*

f stress on a s.all ele.ent is a / $7 <Pa o / 12 <Pa,and the shear stress on the hori&ontal -lane is ` 2 <Pa* aB ind the

:B I the .aterial is a loose sand, (an yo% say whether the ele.ent

151#* iven the verti(al and hori&ontal nor.al stresses of Pro:le. 1"1$*. e .a+i.%. va %es o

verti(al -lanes to (a%se fail%re in a .edi%. dense sand* Ass%.e the

angle of internal f ri(tion for the sand is #">*e s a e - ane s ress in a .ass o ense (

des(ri:ed :y the following stresses9

Nor.al stress on hori&ontal -lane / #!<Pa Nor.al stress on verti(al -lane / $<Pa

v r i(al lanes / 7 <Pa

'eter.ine : .eans of the Gohr (ir(le the .a Dt%de and dire(5tion of the -rin(i-al stresses* Is this state of stress safe against

.inor -rin(i-al stressesD are , #, and $ GNQ.*, res-e(tively*

shearing stresses and the o:liF%ity angles on -lanes at #>, 2>, ">,

its to- and :otto. fa(es, <Pa on one -air of verti(al fa(es, anda on e o er -air o ver i(a a(es* re i

on any fa(e* ill in the n%.eri(al val%es for ea(h stress and angle 2nthe following ta:le* Af ter Taylor, 1627*B

Ga0or -rin(i-al -lane 9Inter.ediate -rin(i-al -lane9

.or -nn(1- - an( 9Plane of .a+i.%. shearing stress9Plane of .a+i.%. o:liF%ity9

a<PaB T<PaB a

Note9 a is the angle of orientation of the reF%ired -lane with res-e(t tothe hori&ontal -lane*

151!* In Pro:le. 151" what is 48, ass%.ing $ && 8




1517* how that on a -lane in(lined at 2> with res-e(t to the -rin(i-al -lanes, the ratio of ' 6Y to o1 #BQ$ is in fa(t less than G/ 99·Hint9 Ass%.e a a and a *

1516* Prove that EF* 151 is tr%e, ass%.ing that the Gohr5Co%lorn:fail%re (riterion is valid* 'oes it .atter 2 e / 8 Hint9 'erive thee %ation first with e / 8 then with e / 8*

15$* how that EF* 151# is identi(al to EF* 1512*

15$1* EF%ation 1512 is tr%e if e / 8* 'erive the e+-ression for the6"

15$#* how that E s* 151" and 151! are identi(al to E s* 1512 and151* fhis is a good review of trigono.etri( identitiesB

n a ire(t s ear test on a s-e(1rnen o (o es1on ess sand, theverti(al nor.al stress on the s e(i.en is !00 <N .$ and the

hor .i&ontal shear . str .ess .at fail%re is *00. <NQ .*

aB

Ass%..ing

line fail%re envelo-e whi(h goes thro%gh the origin, deter.ine :y. . .

-rin(i-al stresses at fail%re* :B E+-lain why it is not -ossi:le to

to (a%se

e stress

At fail%re9F1 /

#

=

(. , (.

aB 'raw the Gohr (ir(les for :oth initial and final stress (onditions*:B how (learly the lo(ations of the oles of these (ir(les*(B 'eter.ine the .agnit%de and orientation of the -rin(i-al

stresses at fail%re*dB What is the orientation of the fail%re -lane

* * * o

are the stresses os and 13s on the sides of the s-e(i.en at fail%re Note9 13Q. 6 &hvB

15$"* Two (onventional C' tria+ial (o.-ression tests were (ond%(ted ona dense ang%lar dry sand at the sa.e void ratio* Test $ had a(onf ining -ress%re of 00 <Pa, while in test = the (onfining

-ress%re

.



Pro#lea 419

was 2 <Pa@ these stresses were held (onstant thro%gho%t the test*. .

of 2 and 1! <Pa, res-e(tively*

aB Plot the Gohr (ir(les for :oth tests at initial (onditions andat re*

:B Ass%rning e / 8, deter.ine fQ,*eB What is the shear stress on the fail%re -lane at fail%re for :oth

testsdB 'eter.ine the theoreti(al orientation of the fail%re -lane in

eB What is the orientation of the -lane of .a+irn%rn o:liF%ity 15$!*

how that stress -aths , T, and in ig* 1*17 are (orre(t*

are (orree *

15all5aro%nd h drostati(state of stress of <Pa* <et(h the stress -aths for the loading

h V

<Pa@ :Bov is held (onstant while oh in(reases to 1 <Pa@ eB :oth oh

an ov are .(rease o a@ ov rernains (ons n D i eoh de(reases to 1 <Pa@ and eB ov is in(reased :y $ <Pa at the sa.eti.e that oh is de(reased :y $ <Pa*

iven e sa.e ini ia (on i 2 nstress -aths for loading when aB Iloh Ilov/ * and :B $oh Ilov/ .

15#$* I the initial stress (onditions in a soil sa.-le are ov 1 GPa andJh / #

aB oh in(reases to 1 GPa and :B oh de(reases to 8 GPa*

15##* Eval%ate the / and /3 for the (onditions shown in ig* 1*$1* Are

15#2* A tria+ial sa.-le of loose sand is tested in lateral e+tension LEBsee ig* 1*$$B* The sa.-le is first (onsolidated non5

hydrostati(ally,. . . .1 5 # 5

and the angle of interna fri(tion is #> e 8B* aB 'raw the Gohr (ir(les for :oth initial and =at fail%re= (onditions* :B What will :ethe rna0or and .inor -rin(i-al stresses at fail%re eB 8n a p'Bdiagra. draw the stress -aths for :oth the (onsolidation see ig*1*$1B and shearing -hases of this test* how the K 1line*

15#* Another sa.-le of the sa.e sand tested in Pro:le. 15#2 is testedin lateral (o.-ression LCB* Co.-lete -arts aB thro%gh eB re5

. .

. .

0



ele/en

7hear 7trengthaf 7andi andCla@i

11.1 INT!O('CTION

The shear strength of soils is a .ost i.-ortant as-e(t of geoted.i(alengineering* The :earing (a-a(ity of shallow or dee- fo%ndations, slo-e

* sta:ility, retaining wall des1gn and, .d1re(tly, -ave.ent des1gn are aliaffe(ted :y the shear strength of the soil in a slo-e, :ehind a retaining wall,

or s%--orting a fo%ndation or -ave.ent* tr%(t%res and slo-es .%st :esta:le and se(%re against total (olla-se when s%:0e(ted to .a+i.%.anti(i-ated a--lied loads* Th%s /i8iting eLuilibriu8 .ethods of analysis are(onventionally %sed for their design, and these .ethods IeF%ile detennina5

tion of the %lti.ate or li.iting shear resistan(e shear strengthB of the soil*In Cha-ter 1, we defined the shear strength of a s.l as the %lti.ate

or .a+i.%. shear stress the soil (an withstand* We .entioned thatso.eti.es the li.iting val%e of shear stress was :ased on a .a+i.%.allowa:le strain or defor.ation* Mery of ten, this allowa:le defor.ationa(t%ally (ontrols the design of a str%(t%re :e(a%se with the large safetyfa(tors we %se, the aet%al sheat sttesses in the soil -wd %(ed :y the a--liedloads are .%(h less than the stresses (a%sing (olla-se or fail%re*

The shear strength (an :e deter.ined in several diff erent ways@ wedes(ri:ed sorne of the .ore (o..on la:oratory and field tests in e( 1 In sit% .ethods s%(h as the vane shear test or -enetro.eters avoid sorne of the -rohle.s of dist%r:a n(e asso(iated with the e+tration of soilsa.-les fro. the gro%nd* However, these .ethods only deter.ine theshear strength indireetly thro%gh eortelations with la:oratory res%lts or ha(<(al(%lated fro. a(t%al fail%res* La:oratory tests, on the other hand,yield the shear strength dtre(tly* In add1tton, val%a:le infor.ation a:o%tthe stress5strain

:ehavior and the develo-.ent of -ore -ress%res d%ring shear (an often :e



11.1 lntrocluctlon 411

o:tained* In this (ha-ter, we shall ill%strate the f%nda.ental stressdefor.ation and shear strength res-onse of soils with the res%lts of la:oratory tests for ty -ieal soils* In this way, we ho-e yo% ean gain so.e%nderstandine of how soils a(t%allv :ehave when sheared*

A word a:o%t the s(o-e of this (ha-ter* l4 is -%r-osely <e-t as si.-leas -ossi:le* 8nly test res%lts of ty-i(al =well5:ehaved= sands and (lay soilsare ill%strated@ s-e(ial soils s%(h as (e.ented sands, stiff fiss%red (lays,highly sensitive **F%i(<=B (lays, and organi( soils are not (onsidered indetail herein* -e(ial to-i(s s%(h as strength anisotro-y, the Hvorslev -ara.eters, (o.-le+ stress syste.s, and (ree- are not in(l%ded in this(ha-ter* Toe a--roa(h is ad.ittedly (lassi(al and we ho-e not oversi. -lified* The interested st%dent .ay wish to (ons%lt advan(ed te+t:oo<s

and the geote(hni(al literat%re on soil :ehavior for additional 2n onnationa:o%t the real :ehav1or of sands and (lays*

In this (ha-ter we draw heavily on the wor< of o%r tea(hers and(olleag%es* We gratef %lly a(<nowledge the i.-ortant (ontri:%tions .ade :y A Casagrande, R @ Hirs(hfeld, @ @ Ladd, / L Lee, A. Leonards, J* 8* 8ster:erg, * J* Po%los, and H* 4* eed* 8%r dis(%ssion of shear strength of soils starts with sands and is followed :y the strength -ro-erties of (ohesive soils*

The following notation is introd%(ed in this (ha-ter*


A , A, = <e.-ton3s -ore -ress%re -ara.etersa Hen<el3s -ore -ress%re -ara.eter A , A, L2 .l Initial s-e(i.en area and area at so.e

strain, res-e(tively EF* 1157Bc ,/ D c .,. c ... " 1 L1 1 1Q<Pa Co.-ress1:ility of the soil s<eleton, -ore

fl%id, and water, res-e(tively EF* 11511B6! 67 ML' 1G'2 <Pa =Cohesion= or inter(e-t on ,,* a+is when a - 8E ! ML' 1 r52 <Pa e(ant .od%l%s

E ! ML' 1r52 <Pa Initial tangent .od%l%s

E8ML- 1!5l <Pa Undrained .od%l%s of linear defor.ation

o%ng3s .od%l%sBEP Effe(tive stress -athe de(i.alB Mnid ratio aft(r ronsnlidatinn

$c!i de(i.alB Criti(al void ratio

e6d de(i.alB e(n(densee61 de(i.alB e(ri5looseed de(i.alB e5densee! de(i.alB e5looseh An e.-iri(al e+-onent EF* 115

s, ens1tivity EF* 1156BTP Total stress -ath

,WML' 1r52 <Pa Initial -ore water -ress%re@ :a(< -ress%re

.j

'



492 &hear &trength of &ancl and Cla@


?ML'

1r5

2 <Pa Resid%al (a-illaryB -ore water -ress%reaf ter sa.-ling

L# .# Initial vol%.e EF* 1152B

strainsCorre(tion fa(tor to vane shear strength

Ahc ML' 1 r52 <Pa Total hori&ontal (onsolidation stressvc

ML' 1

r52

<Pa Total verti(al (onsolidation stressAoct ML' 1r52 <Pa 8(tahedral nor.al stress EF* 115$#B*c ML' 1 r52 <Pa Effe(tive (onsolidation -ress%re,3 cr!t

ML' 1 r52 <Pa Criti(al effe(tive (onfining -ress%re

*W ML' 1 r52 <Pa Effe(tive (onfining -ress%re at fail%re

oS / o* Prin(i-al effe(tive stress ratio EF* 1151B 1 5 #B ML' 1r52 <Pa Prin(i-al stress differen(e EF* 115$BTZ ML' 1r52 <Pa Undrained shear strengthTo(t ML' 1 r52 <Pa 8(tahedral shear stress EF* 115$2Bet?, degreeB Angle of interna fri(tion fro. C' tests

2?3, (Q?r degreeB Angle of interna fri(tion in ter.s of effe(tive stress and total stress, res-e(t5ively

c/]p,3 ],K degreeB Angle of interna fri(tion fro. -lanestrain tests and tria+ial tests,

res-e(tively EF* 115B

Note9 A -ri.e .ar< on an angle or stress indi(ates effective stresses. %:s(ri-tso, e, and indi(ate initial, (onsolidation, and fail%re (onditions, res-e(tively*

11. ANGE O* !EPO&E O* &ANO&

I we were to de-osit a gran%lar soil :y -o%ring it fro. a single -ointa:ove the gro%nd, 1t wo%ld for. a (or%(al -ile* As .ore and .oregran%lar .aterial was de-osited on the -ile, the slo-e for a short -eriod of

ti.e .ight a--ear to :e stee-er, :%t then the soil -arti(les wo%ld sli- andslide down the slo-e to the angle of repose. Th;s angle of the slo-e withres-e(t to the hori&ontal -lane wo%ld re.ain (onstant at sorne 8ini8u8val%e* Refer for a .o.ent to ig* "*! for an ill%stration of the angle of re-ose* in(e this angle is the stee-est stable slo-e for very loosely -a(<edsand, the angle of re-ose re-resents the angle of inte.al fri(tion of thegran%lar .aterial at its /oosest state*

and ^l%nes are an e+a.-le fro. nat%re of the angle of re-ose*ig%re 11*1 shows how :oth a stationary d%ne 'B as well as a .igratingd%ne G'B are for.ed* 8n the leeward side LB, the slo-e of the d%ne

.:1# L# .# Change in vol%.e EF* 1152BV ]B Merti(al or a+ial strain1 , $ , # ]B Ga0or, inter.ediate, and .inor -rin(i-al

=



O5N.3>2423n 3 >6n= J D2n=.. I=.56l >.4G4G5 3 >46423n6

63D> 2n=2645 45 =25423n 3 62 G5n4> W. E >3D>=25 WS 2> 45 D2n=D6= >l3 5 3 45 =Gn5, LS 45

l55D6=, 3 =3Dn-D2n= >l3N5. R 6> 2NNl5>, 6n= C

2> 45 5>4 3 45 =Gn5. &6>5= l2n5> >3D 45 35

$2. . $36423n 3 >6n= =Gn5> 6n= 2llG>46423n 3 45 6nl5 3 + J H3>4 $. 13n B6n=64. C3N24 9* :y

(Gl PGJl2>2n C3N6n, H3G>43n, T+. >5= D24 N52>>23n. AII 4>5>515=.

will have an angle of re-oseB whi(h varies fro. #> to #>, de-ending onfa(tors that are dis(%ssed later in this (ha-ter* l t e s o-e on e eewar

> then the slo e is %nsta:le and sand

grains will roll down the slo-e %ntil the angle of re

. -ose is rea

.(hed* A

.n

11*1@ event%ally a s.ooth slo-e at the angle of re-ose will 3. Toe angleo re-ose e-en s on t e ty-e o .a eria sre resents the an le of interna fri(tion or shearing resistan(e B, at itsloosest state* Re(all that the ter.s loase or dense are only relative ter.s

vior in shear* As we shall the stress5strain and vol%.e (hange res-onse de-ends on the

11.% ,EHA2IO! O* &AT'!ATE( &ANO&

To ill%strate the :ehavior3 of sands d%ring shear, let3s start :y ta<ingwo &amp e& o &an : one a a ve D ** D , = ,

the other at a very low void ratio, the **dense= sand* We (o%ld -erfor.dire(t shear tests ig* 1*1$B, :%t to :etter .eas%re the vol%.e (hanges weshall %se the tria+ial a--arat%s, as shown in ig* 1*1#a and ig* 11*$* Weshall r%n the two tests %nder (onsolidated drained C'B (onditions, whi(h

.j



5 5 55555 5 5

,1r

494 &hear &trength of &ld and Cla@

o15 o# W645 l515l

6n5:

e

.P P 3l.Q

TV3lG5 =556>5

-'

2 V3lG5 2n56>5

--2,

-.X

-- X

--

-

-

5 :, -5--#555

,

.,##,#, ,B,#

EY6Nl5: S6Nl5 =556>5>in =W=u ,...,, GG l./C2 *615 65 35l l lt:le<

D645 2>5> 2n 15426l 4GJ5

lt

1 1

'- .:

$2. .* C3n>3l2=645=-=62 n5= 426Y26l 45>4 D24 13lG5 6n5 56->G55n4>.

..ea.ns we will allow water to freely enter or leave the sa.-le d%ring shear

A .UU- t** - 5... ,.. **** 1 .' , --- 555 555=5the. a.o%nt of water that enters or leaves the sa.-le and eF%ate this tothe

' 5 i9lllU' %,%*,.. . .

v v,% li9lllU 5 in Li1e sa.-1e* nDaier 1eav.gthe sa.-le d%ring shear indi(ates a vol%.e de(rease, and vi(e versa* In

:oth o%r tests the (onfining -ress%re, oc eF%als o# , is held (onstant and thea+ial stress is in(reased %ntil fail%re o((%rs* ail%re .ay :e defined =3==

.*.** 9 . .,..?'

??

5 .55

,

, '- #J.a+

2.Ga+i.%. -rin(i-al effe(tive stress ratio, o4/ o#B.a+*

53D -- L4 3 - o* : *LJ at a -res(n:ed stra.*

Gost of the ti.e, we will define fail%re as the 8ai8u8 principal

scress aifference, wni(n is .e sa.e as co8press,ve screng8 0 .es-e(i.en* Ty-i(al stress5strain (%rves for loose and dense sand are shownin ig* 11*#a, while the (orres-onding stress vers%s void ratio (%rves areoresented in i$* 11*#:*

When the loose sand is sheared, the -rin(i-al stress differen(e grad%5ally in(reases to a .a+i.%. or %lti.ate val%e o - o! B%1tD Con(%rrently,as the stress is in(reased the void ratio decreases fro. e1 e5looseB down toect e(5looseB, whi(h is very (lose to the criticaI void ratio e(ntD

Casagrande16#"aB (alled the %lti.ate void ratio at whi(h (ontin%o%s defor.ationo((%rs with no (hange in -rin(i-al stress differen(e the critica/ void ratio.

s

--

..

lllC

3

.e



55 5 555 5 5 5555 55 DD55 D5D55 .

.-.. 55 K ,



-e

)

...

e,

o··F:0

l!

el

e rit

t:l·o>

e

Prin(i-al stress differen(e, o 15

o#B

6

Prin(i -al stress d1fferen(e, 31 5 3# B

X $ 2 , X .! T26Y26l 45>4> 3n ? l33>5? 6n= ?=5n>5? >N5 2 5n > 3 6 4N 2 6 lsand9 aB >45>>->462n G15>; J 132= 6423 6n5> =G2n >56 645H2>5l=, 9!.

495

".



496 S55 S45n4 3 S5n=6 5n= Cl5>

When the dense s-e(i.en is sheared, the -rin(i-al stress differen(erea(hes a -ea< or .a+i.%., af ter whi(h it de(reases to a val%e very 5loseto o

- o! B%lt for the loose*sand* Toe void ratio5stress (%rve shows that thedense sand de(reases in vol%.e slightly at first, then epands or dilates %-to ecd e(5denseB* Noti(e that the void ratio at fail%re ecd is very (lose to ec1.Theoreti(ally, they :oth sho%ld :e eF%al to the critica/ void ratio e(ritDi.ilarly, the val%es of o - o! B%it for :oth tests sho%ld :e the sa.e* Toediff eren(es are %s%ally attri:%ted to diffi(%lties in -re(ise .eas%re.ent of %lti.ate void ratios as well as non%nifor. stress distri:%tions in the tests-e(i.ens Hirs(hf eld, 16"#B* Eviden(e of this latter -heno.enon is il l%strated :y the diff erent ways in whi(h the sa.-les %s%ally fail* Toe loose sa.-le j %s tbulge.s , while the dense sa.-le of ten fails along a distin(t -laneoriented a--ro+i.ately 2> B, Q$ fro. the hori&ontal B, is, of (o%rse,the effective angle of sheanng res1stan(e of the dense sandB* Note that 1t1sat least theoreti(ally -ossi:le to set %- a sa.-le at an initial void ratio s%(hthat the vol%.e (hange at fail%re wo%ld :e &ero* This void ratio wo%ld, of (onrse, he the (riti(aX void ra tio euit

." E$$ECT O$ VOI& RATIO A%OCO%$I%I%( PRESSRE O% VOLMECHA%(E

Th%s far, in des(ri:ing the :ehavior of the two drai%ed tria+*ial testson loose and dense sands shown in ig* 11*#, we have .entioned thefollowing -hysi(al F%antities*

-rin(i-al stress differen(estrainvol%.e ehange(riti(aX void ratio e(rit and, indire(tly,relative density EFs* `$ and 25#B

We ha%e -%r-osely a%oided defining the ter.s loose and dense :e(a%se thevol%.e (hange :ehavior d%ring shear de-eds not only on the initial voidtalio and 1elati ve density :%t also %n the (onfining -t ess.e* In this se(tionwe shall (onsider the eff e(t of (onfining -ress%re on the stress5strain andvol%.e (hange (hara(tens:(s of sands . dra.ed shear*

We (an assess the effe(ts of o# and, re.e.:er, in a drained testo* / o* , as the e+(ess -ore water -ress%re is always &eroB :y -re-aringseveraB sa.-Bes a t the sa.e void ra tio and testing the. at different(onfining -ress%res* We wo%ld find that the shear strength in(reases witho# A eonvenient way to -lot the -rinei-al stress differenee vers%s strain



11*2 E54 3 V3l= R6423 6n= C3nlnln P5>>G5 3n V3lG5 C6n6 26!

data is to nor8aliMe it :y -lotting the principal stress ratio a1 / a3 vers%s strain*or a drained test, of (o%rse, a1 / a3 / ai/ a* . At fail%re, the ratio isoiQa#B.a+D ro. EFs* 1512 and 151",

1 si*n "V,' tan* O2 ` "V'

1151B

1 5 s. Q? $

where "' is the ef@ective angle of inte.al f ri(tion* Toe -rin(i-al stressdif feren(e is related to the -rin(i-al stress ratio :y

I15$B

.a+

Let3s loo< first at the :ehavior of loose sand* Ty-i(al drained tria+ialtest res%lts are shown for loose a(ra.ento ver san 1g* * a* e

ress ratio is lotted vers%s a+ial strain for different effe(tive(onsolidation -ress%res o9i(D Note that none of the (%rves has a distin(t

Toe vol%.e (hange data is also nor..ali&ed :y divid.ing th.e vol%.e (hange

To :etter a--re(iate what is going on in ig* 11*2a, let %s (o.-%te t eD D D train of ] for o3 #*6 GPa

and a3c / *1 G.Pa* The

** -rin(i-al stress ratios for these (onditions are $*

an * ,115$, we o:tain the following res%lts9

GPaBGPaB GPaB

*1 #* *$ *# #*6 !*7

l4 is interesting to loo< at e s a-es o e vo %.e e s rainvers%s %rves in i * 11*2:* As the strain in(reases, thevol%.etri(

strain de(reases for the .ost -art* This is (onsistent with the :ehavior of a

,j

. . .



Z

498 &hear &trength ot &end end Cle0

Ge

'jH MP6

5 ??' 0.8, ', 99,, !8

*2.+

+ 1 1+ 20 2+ 30 3+ 40

AY26l >462n, E 6l

* * &2l6423no

g 0 C3N5>>23no *22

??^J -+eD

D.Z*.

Z*.*Z

?G'D@9

CI?

51

::, 3 MP6

o? -1+

o + 1 1+ 20 2+ 30 3+ 40

AY26l >462n, T

J

$2. ." TN26l =62n5= 426Y26l 45>4 5>Gl4> 3n l33>5 S665n43 R215 >6n=: 6 N2n2N6l >45>> 6423 15>G> 6Y26l >462n; J 13lG542 >462n15>G> 6Y26l >462n 645 L55, 9).

e+a.-le, *1 and *$ GPaB, the olti.etrie strain is -ositi **e or dilation ista<*ing -la(e Th%s even an initially loose* sand :ehaves li<e a dense sand@

that is, it dilates if o#(

is low eno%gh Now, let3s loo< at the :ehavior of dense sand* Toe res%lt of severaldrained tria+ial tests on dense a(ra.ento River sand are -resented in ig*

11** Altho%gh the res%lts are si.ilar in a--earan(e to ig* 11*2, there aresorne signifi(ant differen(es* irst, definite -eales are seen in the o o9'strain (%rves, whi(h are ty-i(al of dense sands (o.-are with ig* 11*JaB*e(ond, large increases of vol%.etri( strain dilationB are o:served* However, at :igher (onfining -ress%res, dense sand e+hi:its the :ehavior of loose sand :y showing a decrease in vol%.e or (o.-ression with strain*

4y test.g sa.-les of the sa.e sand at the sa.e v1d rat1os or densities :%t with different effe(tive (onsolidation -ress%res, we (an de5

55

...



tt

A99 sa85les ense

ilation

- Co85ression

·s9>

/'

- 2.L

o:,

>-1;

.`

-1'-- -H.

o.J..._ 1;

-H1

.J..._ --..l ......H...B;

H-1 B - ,J

B ;

oZ9Z

??I?

'',?2' j

.¡:;e;::a*

6

AY26l >462n, c

J

$2. 11.) TN26l =62n5= 426Y6l 45>4 5>Gl4> 3n =5n>5 S665n43R215 >6n=: 6 N2n2N6l >45>> 6423 15>G> 6Y26l >462n; J 13lG542>462n ,5>G> 6Y26l >462n 645 L55, 16"B*

D

-



Z

&hear &trength of &and and Cla@a5,,

ter.ine the relationshi- :etween vol%.etri( strain at fail%re and voidratio or relative density* We (o%ld define fail%re as either the.a+i.%. a15 a#B

or .a+i.%. o@Qa#* or drained tests, fail%re o((%rs at the sa.e straina((ording to :oth (riteria* Points at fail%re are shown as s.all arrows inig* 11** Mol%.etri( strain at fail%re vers%s void ratio at the end of (onsolidation, fro. the data in igs* 11*2: and 11*: for vario%s (onf ining

-ress%res other data have :een added as wellB, are shown ig* 11*"* or e+a.-le, -oint l in ig* 11*: is -lotted as -oint 1 in ig* 11*"* l4 (an :eseen that for a given (onf ining -ress%re the vol%.etri( strain de(reases:e(o.es .ore negativeB as the density deereases void ratio in(reasesB 4y

definition, the (riti(al void ratio is the void ratio at failure when thevol%.etri( strain is &ero* Th%s for the vario%s val%es of o*c in ig* 11*", e(ritis the void ra tio when $=/ 8* or e+a.-le, e(rit for o*c $* GPa is

**We (an see how e(rit varies with (onfining -ress%re :y ta<ing the (riti(aV

void ratios of ig* 11*" and -lotting the. vers%s o*c, as is done in ig* 11*!*Here we have (alled o#( the crilic83 (onf ining -ress%re a9# (nt

R5l64215 =5n>4, , o

80 60 40 $ o

o^Iai

DZZZ

...?e9'5...?G'D

.Z

.9

.E 51999,

3

*.9

Al2 >6Nl5>:S665n43 R215 >6n=

o ( GPaB

-1+ **" *! *7 Z.9 l 8

V32= 6423 64 end 3 3n>3l2=6423n, e(

$2. . V3lG542 >462n 64 62lG5 15>G> 132= 6423 64 5n= 3 3n >3=6G3n 3 =62l,ed t, 26Y26l 45>4> at 1623G> 3342323 N5>>G5> 645

L55, 9).



;.`....f)

o·.:0..a

-e·o ;.

>'Fic

-.9

·.::/ ;.@

A99 sa85les: <ara8ento 6 ier san0 ata 3ro8 #i$. 11.@

.6._ ---8--- --- ...G- .E..--===-1 ...G8 * 1* 1* $* $* #* 3.+

Criti(a (onfining -ress%re, 24 GPaB

$2. . C2426U 132= 6423 15>G> N5>>G5 3n=2423n> 3 =62n5=426Y26l 45>4>. &646 3 $2. . 645 L55. 9).

AII sa.-les9a(ra.ento R iver sand

aiX¡¡;

...

5e4: 5

.4

oK -1Z 0- -... -- -- --- _._ --

3 * 1* 1* $* $* #*

Effe(tive (onsolidation stress, o0( GPaB

$2. .8 V3lG542 >462n 64 62lG5 15>G> 554215 3n>3ll=6423n>45>> 3 =255n4 2n2426l 132= 6423> 645 L55, 9).

-(a



$ &hear &lrength ot &enda and Cla@a

:e(a%se this is the effe(tive (onfining -ress%re at whi(h &ero vol%.etri(strain o((%rs at fail%re for a given void ratio*A se(ond and 0%st as interesting a--roa(h is to %se the data shown io

igs* 11*2: and 11*: -l%s other data at inter.ediate void ratiosB and -lotthe relationshi- :etween vol%.etri( strain at fail%re and (onfining -ress%refor vario%s val%es of void ratio af ter (onsolidation* %(h a gra-h is showoin ig* 11*7, altho%gi1 the void ratios indi(ated are initial void raios aod notthe void ratios af ter (onsolidation* Note that the val%e of o3c at

:.#/ #., && 8 is the (riti(aV (onfining -ress%re, o# (ritD in(e they are drainedtests, o*c / 0 *1. This relationshi- (o%ld also :e o:tained fro. ig* 11*" :ynoting the val%es of vol%.etri( strain at (onstant void ratios and -lotting

:.#? VG vers%s a#,

(5)

ln56>2n 132= 6423

$2. .9 l=56l25= 13lG542 >462n =646 3 =62n5= 426Y26l 45>4>: 6

= =.. 15>G> $c J =/=.. 15>G> 3#*



11.4 Elfect of 2old !atio and Conflnlng Preaure on 2olue Change #

We (an show the relatioashi-s of igs* l I *" and 11*7 in ig* 11*6ideali&edB* in(e :oth igs* . and .8 have a (o..on a+is, it is -ossi:le to w.:ine the. in a single three5di.ens 1onal gra-h <nown as the Peacoc! diagra8 af ter Willia. H%:ert Pea(o(< who first (onstr%(ted s%(ha diagra. in 16"!B, as shown in ig* 11*l8*

With the Pea(o(< diagra., we a re a:le to -red*i(t the :ehavior of sand at any void ratio af ter (onsolidation ec and at any (onfining -ress%reo#* or e+a.-le, if the effe(tive (onfining -ress%re is given at -oint C in

ig* 11*1, whi(h is higher than o# (rit for this given void ratio ec# , then wewo%ld e+-e(t a de(rease in the vol%.e or a .in%s :..# Q M , whi(h is eF%al

to the ordinate . 8n the other hand, if o# is less than o# (rit s%(h as -oint $ for the given val%e of ec , then a dilation or -ositive vol%.e (hange will

ta<e -la(e eF%al to 4,:ordinate )D. As the void ratio af ter (onsolidation

varies to5and5fro along the void ratio a+is, o#(rit varies, and so will the vol%.e(hanges at fail%re* or a real sand, the Pea(o(< diagra. has(%rved s%rfa(es* or e+a.-le, the Dtine KP in ig* l l*1 sho%ld loo< li*<eone of the (%rves in ig* 11*7* The line P] in ig* 11*1 is also (%rved* eeline P] in ig * 11*!9 here yo% are loo<iog a t a -lane on the Pea(o(< diagra. where :..# Q # / 8*

$2. .O P563 =266, D2 3J2n5> $2>. .96 6n= J 2n 6n2=56l26= 6N 43 >3D 45 J56123 3 =62n5= 426Y26l 45>4> 3n >6n=.

,. _

9 ***,K5

1



11.7 ,EHA2IO! O* &AT'!ATE( &ANO&('!ING 'N(!AINE( &HEA!

The .ain differen(e :etween drained and %ndrained tria+ial shear isthat in an %ndrained test no vol%.e (hange is allowed d%ring a+ial

loading* Iloweve1, %nless the (onfining -t ess1e j %st ha--ens to :e at o#(rit,the soil will tend to change volu8e d%ring loading* or e+a.-le, referring tothe Pea(o(< diagra., ig* 11*1, again, if a soil at ec is tested undrained at

a o# at -oint C, then the sand sa.-le wo%ld tend to de(rease in vol%.e, :%t it (an3t* As a res%lt, a positive -ore -ress%re is ind%(ed, whi(h (a%ses a

reduction in the eff e(tive stress* Toe li.iting or .ini.%. effe(tive -ress%reat fail%re is o#(rit :e(a%se at this -ress%re = Q = is &ero* I no tenden(ytowards vol%.e (hange ta<es -la(e, then no e+(ess -ore -ress%re isind%(ed* o the .a+i.%. -ossi:le -ore -ress%re in this e+a.-le is eF%al

to o*c5 o# (rit W or the distan(e 4H in ig* 11*1* Toe Gohr (ir(les at fail%refor this (ase are shown in ig* 11*1la* Toe dashed (ir(les T re-resent theeffe(tive stress (onditions, whereas the solid (ir(le & is in ter.s of total

stresses9 in(e EF* !51# always holds, the two (ir(les are se-arated :ythe val%e of au ind%(ed at any ti.e d%ring the test* in(e the vol%.e(hange tendency is to red%(e, a -ositive (nange in(reaseB in -ore -ress%reis (a%sed, whi(h in t%rn res%lts in a reduction in the effe(tive stress* Th%s,for this e+a.-le,* au / 5 Z / o*c 5 *1 / o*c 5 o# (ntD The o1 5 o# is

given :y EF* -! when the (onfining -ress%re at fail%re is o# (ritD

Also, if we were to r%n a drained test with the (onfining -ress%reeF%al to o* c at -oint C, the drained strength wo%ld :e .%(h larger than the%ndrained strength sin(e its Gohr (ir(le .%st :e tangent to the effe(tiveGohr fail%re envelo-e* J%st loo< at th( relative si&es of the two effe(tiveGohr (ir(les in ig* .lla*

A different res-onse o((%rs when we r%n a test with the effe(tive(onfining -ress%re less than 9, (nt s%(h as -oint . in ig* 11 1 ro. the

Pea((< diagra., we wo%ld e+-e(t the sa.-le to tend to dilate ordinate )D B* in(e the s-e(i.en is -revented fro. a(t%ally e+-anding, a negative -ore -ress%re is develo-ed whi(h increases the eff e(tive stress fro. D ABtowards U oJ (ri, B* I h%s, as . the -rev1%s e+a.-le, the l.%t.g eff e(ttvestress is the (riti(aV (onfining -ress%re o9i (ritD The sit%ation .ay arise wherethe negative -ore water *-ress%re a--ro[(hes 51 <Pa or 51 at.os-here,and (avitation ta<es -la(e, :%t we will ignore this -ossi:ility in this(ha-ter*B Toe whole -oint of this e+er(ise is that we .ay -redi(t the

5,4

----------- ------., -



11.S ,eha/lor of &aturated &and (urlng 'ndralned &hear 5,5

&

e( / (onstant

`

E, T5********** / ...............

'ra ined test

,**5555555 U nd rained test

?

H C, 4

6

=3\ B

T

a

&

1

1

-.:lG ;X1 1

e( (onstant Q

< e ^ a erot QQ ,5

QQ Q

QQ

U E, T, 'rainedtest

3 aJ

$9. . T5 M3 2l5> 3 Gn=62n5= 6n= =62n5= 426Y26l3N5>- >3n 45>4>: 6 6>5 D55 a#e o# e,*,@ J 6>5 D55 a *e o#(rii D

undrained :ehavior of sands fro. the drained :ehavior when we <now thevol%.e (hange tendencies as ideali&ed in the Pea(o(< diagra.*

The Gohr (%ele re-resentation for the (ase where o*3 eo

*

* 1s3(nt

-resented in ig* l l.l l :* The %ndrained test starts o%t at o*c, -oint A, andsin(e the ind%(ed -ore water -ress%re is negative, the effe(tive (onfining -ress%re in(reases %ntil fail%re is rea(hed at -oint U. Note that theeffe(tive stress Gohr (ir(les E at fail%re in igs* 11*1la and : are the sa.e

L

T



786 &heer Stren@th of &enda encl Cle@

'()*+ 1101 ( SG6 3 C3n5N4> S3Dn 2n $2. .

Eff((tive Gohr Cir(lesConsolidationPress%re 'rained, Effe(tive / Total Undrained, Effe(tive Undrained, Total

Larger than%ndrained

.aller than drained9 .aller than drained9Left of total Right of eff((tivestress (ir(le stress (ir(le

.aller than%ndrained

Larger than drained9 Larger than drained9Right of total Left of effe(tive

stress (ir(le

*W #ic

stress (ir(le

Ali (ir(les wo%ld :e the sa.e@ :e(a%se no vol%.e (hange. . ?'

.....,......., ' -- 2 00- ---e **K*** ************ *

si&e :e(a%se, for this void ratio ec , the effe(tive stress at fail%re is the sa.e,

o# (rit * l the effe(tive stress and void ratio are the sa.e, then the sa.-leswo%ld have the sa.e (o.-ressive strength, o415 *14 th%s the (ir(les havethe sa.e dia.eter* Note that the total stress (ir(le G. at fail%re, is also thesa.e si&e as the effe(tive stress (ir(le :e(a%se o - o! is the sa.e for :oth & and E 4 also & l;es to the left of E. This (ase is the o--osite of ig*11*1la* The total stress Gohr fail%re envelo-es have :een o.itted fro.the fig%re to si.-lify things*B Note also that the drained Gohr (ir(le for this9se(ond (ase is s%:stantially s8aller than the effe(tive stress (ir(le for

the %ndrained (ase* As :efore, the (ir(le starts at o*c, and it .%st :e tangentto the eff eetive Gohr fail%re envelo-e* inee the oid ratio af ter (onsolidation ee is a (onstant for all the tests shown in ig* 11*1 1, all theeffe(tive Gohr (ir(les .%st :e tangent to the effe(tive stress fail%reenvelo-e*

A s%..ary of the .ain -oints 0%st dis(%ssed and shown in ig* 11*11is -resented in Ta:le 1151* or a .ore (o.-rehensive treat.ent of the%ndrained strength (hara(teristi(s of sands see eed and Lee 16"!B*

E9A3PE 11 .1

(215n:

A :attery filler r%::er sF%ee&e :%l: -l%s glass t%:eB (ontains dense sand*Toe :attery filler :%l: and sand are (o.-letely sat%rated with water*

. .



.) B551l3 3 S54G545= S6n=> &Gln n=5ln5= S55 !

R5FG25=:

I the :%l: is sF%ee&ed, des(ri:e what ha--ens to the water level in theglass t%:e* Will it go %-, down, or re.ain the sa.e

S3lG423n:

4e(a%se the sand is dense, it will tend to dilate or e+-and when sheared*This a(tion will (reate a slightly negative -ress%re in the water, whi(h D2lldraw water into the voids and (a%se the level in the glass t%:e to .ovedownward*

E+AMPLE .*

(215n:

Toe sa.e a--arat%s as for E+a.-le 11*1, only now the :%l: is filled with /oose sand*

R5FG25=:

Predi(t the :ehavior of the water level in the glass t%:e when the :%l: is

sFlee&e *

S3lG423n:

When loose sand is sheared, the soil will tend to de(rease in vol%.e* Thisa(tton w1ll (reate a -ositive -ress%re in the water, whi(h will sF%ee&e water o%t of the voids* Th%s the water level in the t%:e will .ove %-ward* l4follows that if the sand in the :attery filler :%l: is at its (riti(al void ratio,then %-an sF%ee&ing shea riogB t:e :%l:, t:e wa ter leveB roay at firstde(rease slightly, :%t with (ontin%ed sF%ee&ing it will ret%. to its originallevel@ that is, no net vol%.e ehange will oee%r when the sand is at 5:2 ,

E+AMPLE .!

(215n:

A C' tria+*ial test is (onda(ted on a gran%lar soil* At fail%re, eiQe! 2**Toe effe(tive .inor -rin(i-al stress at fail%re was 00 <Pa*

D J

E K KZZgKg21gggL



508 &hear &trength ol &ancl and Cla@

r P6

!00

*00

00

O 00 *00 !00 "00 )00 a P6

$2. EY. .!

R5FG25=:

a. Co.-%te B,.b. What is the -rin(i-al stress differen(e at fail%re(* Plot the Gohr (ir(le and the Gohr fail%re envelo-e*

S3lG423n:

a. ro. EFs* 1512, 151", or 1151, we <now that1 sin WIV ' i 2 WIV' 2 8

*1 5 s. , tan *^Q?

olving for B,, we o:tain B, / #!>*b. ro. EF* 115#,

o - o! 9 / o*3 o4,W 5 1B / 1 <Pa 2 5 / # <Pa

3*

(* ee ig* E+* 11*#*

E9A3PE 11 .+

(215n:

ig%re 11*"*

R5FG25=:

What is the (riti(aV void ratio for a(ra.ento River sand when the(onfining -ress%re is 1* GPa

$



.) B551l3 3 S64G645= S6n= &Gln n=6ln5= S56 6

S3lG423n:

ro. ig* 11*", inter-olating :etween@the (%rves for o* 5 1*# and $* GPa,we find that ec for o3 - 1*B is a:o%t *"1 for a(ra.ento River sand*

E+AMPLE .)

(215n:

ig%re 11*7*

R5FG25=:

What is the (riti(al (onfining -ress%re for a(ra.ento River sand if thevDoid ratio eF%als *!

S3lG423n:

ro. ig* 11*7, we (an inter-olate :etween the (%rves for $ - *!1 and

*!7 fo1 the val %e of o# w hen $=/ = is &ero We o:taio a of aho%t *!GPa*

E+AMPLE .

(215n:

ig%re 11*1, :%t s(aled to the ideali&ed :ehavior of a(ra.ento Riversand a (o.:ination of igs* 11*" and 11*7B@ o# (rit5 *2 GPa and ec e(rit

R5FG25=:

'es(ri:e :oth the drained and %ndrained :ehavior of this sand if the testvoid ratios af ter (onsolidation at a*c *2 GPa are aB 8 7 a nd J 8 !

S3lG423n:

in(e o*c and ec are at (riti(al, there is :y definition no vol%.e (hanged%ring shear* Th%s o%r test -lots at -oint H in ig* 11*1, with the val%esof u4 (nt and ec as given o% (an verify these val%es 2n igs* 11*" and 11*7*B



51, Shear Stren@th of Smd& and Cla&

a* When ec e(rit *7 *7B, then at o*c / *2 GPa the (oordinates of o%r test wo%ld have to -lot belo( the AP -lane, whi(h .eans $=/ = is negative*'%ring drained shear, o* is (onstant no e+(ess -ore -ress%re develo-sB, andthe s-e(i.en wo%ld (onsolidate and de(rease in vol%.ed%ring shear* Its (oordinates wo%ld :e on the e+tension of -lane KP.

. .

:%t sin(e it is %ndrained it (annot3* Therefore the s-e(i.en wo%ld develo- -ositive -ore water -ress%re along with a (on(%rrent de(rease in o#* In ig*11*1, the test (oordinates .%st re.ain on the e *7 line and in the

-lane AP. Toe only way this (an ha--en is for o* to de(rease, w 1(ense in view of the in(rease in ore water ress%re*

b. When ec e(rit *! *7B the o--osite of aB will ha--en9 in

(oordinates of o%r test to re.ain on -lane KP, the $=/ = .%st in(rease*

-ore water -ress%re to de(rease and the o# to in(rease* This is what

in(reases*

E9A3PE 11 .!

(215n:

ra.ento River sand i s* 11*"and 11*7B, with e(rit *" and o# (rit / 1*" GPa*

'es(ri:e the :ehavior, :oth in drained and %ndrained shear, if we .ain tainthis void ratio of *" :%t test the s-e(i.en with o3c of aB 1* GPa and

a*

S3lG423n:

a* When o*c o*(rit? then the s-e(i.en will dilate and a -ositive $=/ i,#, will o((%r* This :ehavior is si.ilar to what ha--ens to -oint $ inig* 11*1* Toe dilation is .eas%red :y the ordinate )D so that the(oordinates of o%r test re.ain on -lane KP.

In %ndrained *shear, the tendency will :e for dilation whi(h is -revented@ we .%st re.ain at ec / *" and on -lane AP. Therefore o# .%stin(rease, whi(h .a<es sense -hysi(ally sin(e the ind%(ed -ore water -ress%re tends to de(rease*



11.7 ,eha/lor ot &lltureted &enda (urlng 'ndralned &hear 711

b. When a*c a# (rit? the :ehavior wo%ld :e si.ilar to -ath inig* 11*1 in drained shear* In %ndrained shear, the tenden(y towards(o.-1ession wo%ld res%lt in -ositive e9+eess -are -ress%re and a deerease in

E9A3PE 11*7

(215n:

A drained tria+ial test on sand with o# / 1 <Pa and ai Qa#B.a+ / #*!*

a* ai1,

b. a15 # B, and(* B,.

S3lG423n:

a* a@Q#B #*!* olve for aiWB ai1 #*!1B <Pa*b. a1 5 a# B ai 5 a* :1 5 1 2 <Pa*

(* Ass%.e for sand that e3 / 8* o, fro. EF* 151#,et,9 ar(s1 n

a3 lf 5 a#3 J B ar(s1W n

2 #8

, ,a *1

!

Note9 We (o%ld also deter.ine et,3 gra-hi(ally fro. the Gohr (ir(le -lotted for fail%re (onditions, as shown in ig* E+* 11*7*

r P6

#

$

1

o

4 400

Center at #$

800 a P6

$2. EY. .8

,j



X , --



E9A3PI E 11

(215n:

Ass%.e the test s-e(i.en of E+a.-le 11*7 was sheared undrained at thesa.e total (ell -ress%re 1 <PaB* The ind%(ed e+(ess -ore water -ress%reat fail%re :..C1is eF%al to ! <Pa*

R5FG25=:

a* oiW,b. F o15 * :1,e* F, in ter.s of total stress, andd. the angle of the fail%re -lane N!

a*, b. in(e the void ratio af ter (onsolidation wo%ld :e the sa.e for this test as for E+a.-le 11*7, ass%.e cp3 is the sa.e* o% (an do this -ro:le. e1ther 1B analyti(ally or $B gra-hi(ally*

l. $na/ytica//y# We <now that

*1 *15 :..C1 1 5 ! 7 <Pao

These are the answers to -arts aB and :B*e* We ean write EFs* 151# and 1151 in ter.s of total stresses* Using

EF* 151#,. R9 !

s. 3Ptotal *2$R W! $6" !B 1

3Ptotal / $2 *7o

Using EF* 11"1=

11 * $6" ` !B F? Bo 1 * $

olving for 3PtotaJ , we o:tain 3Ptotal / $2*7>*

5no -n.esB $ 22 tan$ 2>



.) B561l3 3l S64G645= S6n= &Gln n=6ln5= S56 )!

r P6

2

QT IPtotal / $3

300 Q

200 555Effe(tive stresses

555Total stresses

00

400 " 800 , P6

o, / 7 P6

$2. EY. .9

$* 7raphically# Plot the Gohr fail%re envelo-e with cp / #> on aGohr diagra. ig* E+* 11*6B* There is only one (ir(le that is tangent to the

envelo-e and with *1 / 7 <Pa 1 5 !B* 8n(e the (ir(le is drawn trial and errorB,

1is a%to.ati(ally deter.ined . 1 $6" <PaB as is o - * :1,

the dia.eter of the fail%re (ir(le / $1" <PaB*The Gohr (ir(le at fail%re in ter.s of total stresses has the sa.e

dia.ete1 sin(e o1 o# B ( o#B* o% (an* -lot the total stress (ir(lestarting *W 1, the total (ell -ress%re, and deter.ine (f,totaJ Co.-areigs* E+* 11*7 and 11*6 with ig* 11*lla*

d* ro. EF* 151, a, 2> (-3Q$ / "$*>*

E+AMPLE .0

(215n:

Toe sa.e sand as for E+a.-le 11*6 e+(e-t, that the (ell -ress%re is #

5.

R5FG25=:

S3lG423n:

There are severa a--roa(hes to this -ro:le.* ra-hi(ally, we (o%ld(onstr%(t a total stress (ir(le tangent to the total fail%re envelo-e shown in

i5^*5 , ** ,,,,5D5*TJi >. ,a ,M .......

at



12 S56 S45n4 3l S5n=6 6n= Claya

ig* E+* 11*6 :%t starting at o*c / *1 / # <Pa* Toen shif t yo%r (o.-ass or (%ele .a<er to the lef t %nttl the (1r(le 1s JUt tangent to the eff e(tiveGohr fail%re envelo-e*

$uW/ o*W5 o*W # <Pa 5 1" 12 <Pa

Analyti(ally, %se EF* 1151 and o1Qo#Btotai fro. E+* 11*6*

X+J #1 9 / #$*22B !#$ <Pa# total

o1W5 o3W/ !#$ 5 # / 2#$ <Pa

ro. EF* 115# and F oif o* :1& #*! E+a.-le 11*7B,

ll u1/ *1 5 o*W/ # 5 1" / 12 <Pa

Che(<9 ll u1/ 11 - o41/ !#$ 5 #*!1"B / 12 <Pa

. $ACTORS THAT A$$ECT THE SHEARSTRE%(TH O$ SA%OS

in(e sand is a =fri(tional= .aterial we wo%ld e+-e(t those fa(torsthat in(rease the fri(tional resistan(e of sand to lead to in(reases in theangle of internal fri(tion* irst, let %s s%..ari&e the fa(tors that infl%en(eB.

1* Moid ratio or relative density$* Parti(le sha-e#* rain si&e distri:%tion2* Parti(le s%rfa(e ro%ghness* Water "* lnter.ediate -rin(i-al stress!* Parti(le si&e7* 8ver(onsohdation or -restress

Moid ratio, related to the density of the sand, is -erha-s the .osti.-ortant single -ara.eter that affe(ts the strength of sands* enerallys-ea<ing, for drained tests either in the dire(t shear or tria+ial testa--arat%s, the lower the void ratio higher density or higher relativedensityB, the higher the shear strength* Toe Gohr (ir(les for the tria+ial testdata -resented earlier are shown in ig* 11*1$ for vario%s (onfining

D5 5555D 5D 555555555555 555555555555555



S665n43 R215 >6n=,-- -P ----':...- -,,?'-::.//--P- -....- -PL33>5, O / !8

5; / 0.8

T5>4 nGJ5

$ 2 8 0 * " 8

S665n43 R215 >6n=,2 G 33>5,

5¡ / 0.8

*

5@*@a**

?' o****?' "J

*eQ

7 1 * 8

S665n43 R215 >6n=,

2 M5=2G =5n>5, &, / 85; / *!1

$

o 7 1 1$

"

S665n43 R215 >6n=,2 &5n>5, &, / 00

5; / *"1

$

%36l >45>> MP6

$2. .* M3 2l5> 6n= 62lG5 5n15l3N5> 3 =62n5= 426Y26l 45>4>,2llG>4642n 4l?l5 554> 3 732= 6423 3 5l64215 25n>24 3n >56 >45n4645 L55, 9); 6l>3 645 L55 6n= S55=, 9.

?



1" S56 S45n4 3 S6n=6 6n= Cl

-ress%res and fo%r initial void ratios o% (an see tha t as the void ratiode(reases, or the density in(reases, the angle of internaV f ri(tion or angle of shearing resistan(e cf, in(reases*

Anther thing yo% sho%ld noti(e is that the Gohr fail%re envelo-es inig* 11*1$ are (%rved@ that is, cf,3 is not a (onstant if the range in (onfining

-ress%res is large* We %s%ally s-ea< of cp3 as if it were a (onstant, :%t we%nderstand that the Gohr fail%re envelo-e really is (%rved*

The eff e(ts of t elative density or void ratio, grain sha-e, grain si&edistri:%tion, and -arti(le si&e on cp are s%..ari&ed :y Casagrande in Ta:le115$* Mal%es were deter.ined :y tria+ial tests on sat%rated sa.-les at.oderate (onfining -ress%res* enerally s-ea<ing, with all else (onstant, cf,in(reases with in(reasing ang%larity ig* $*B* I two sands have the sa.e

TABLE -* Anl5 3 In45n6U $2423n 3 C35>23nl5>> S32l>

'1 Loose 'ense No*

eneral 'es(ri-tion rain :a-e ..B 5,, e (f?degB e (0?degB

$

#

2

2

" lig:tly silty sand f ro.the sho%lders of t* Pe(<

%:ang%lar tos%:ro%nded

*1# 1*7 *72 #2 .)" "*

'a., GT! (reened gla(ial sand, %:ang%lar *$$ 1*2 *7 ## *" 2#

Gan(hester, %H7t and fro. :ea(h of %:ang%lar

h dra%li( fill da.,

*! $*! *71 # *2 2"

%a::in Pro0e(t, GA6 Artifi(ial, well5graded %:ro%nded t *1" "7 *21 2$ *1$ !

.i+t%re of gravel with s%:ang%lar

1 and for reat alt La<e * Ang%lar *! 2* *7$ #7 *# 2!

Well5graded, (o.-a(ted Ang%lar *17 "

(r%s:ed ro(<

4y A* Casagrande*tThe angle of internal fri(tion of the %ndist%r:ed t* Peter sandstone is larger than ">

and its eohesien se s.all t:at slig:t finger -ress%r( a( r%::ing or even stiff :lowing at as-e(i.en :y .o%th, will destroy it*

iAngl( of internal fri(tion .eas%red :y dire(t shear test for No* 7, :y tria+ial tests for 6l2

othen*

555555D5D555D5DDD

8ttawa standard sand Well ro%nded *" 1*$ *! $7 *# #

and f ro. t* Peter sand5 Ro%nded *1" 1*! *"6 #1 *2! #!t

stone4ea(h sand fro. Ply.o%th, Ro%nded *17 1* *76 *9

GAilty sand fro. ran<lin %:ro%nded *# $*1 *7 ## *" #!

alls 'a. site, NH

ilt sand fro. v;(init%:ang%lar to *2 2*1 *" #" *2 2"

of Jo:n Gartin 'a., C8 s%:ro%nded



11.6 *actora That Affect the &hear &trength of &and 517

relative density, the soil that is :etter graded for e+a.-le, an W soil aso--osed to an P soilB has a larger >8. As a re.inder, two sands at thesa.e void ratio .ay not ne(essarily have the sa.e relative density*BParti(le si&e, at (onstant void ratio, does not see. to infl%en(e >+8 signifi (antly*Th%s a fine sand and a (oarse sand at the sa.e void ratio will -ro:a:ly havea:o%t the sa.e *Z,*

Another -ara.eter, not in(l%ded in Ta:le 115$, is s%rfa(e ro%ghness,whi(h is very diffi(%lt to Jneas%re* l4 will, however, have an effe(t on *Z,*enerally, the greater the s%rfa(e ro%ghness, the greater will :e ,P. lt has also :een fo%nd that wet soils show a 1> to $> lo(er >8 than 2 the sandswere dry*

o far we have only dis(%ssed res%lts fro. dire(t shear or tria+ialtes s . w i( o$ o# or 0 1D

-rin(i-al stress, other ty-es of tests li<e -lane strain or (%:oidal shear tests.%st :e %sed ig* 1*12B* Resear(h s%..an&e y a , et a *

lane strain is lar er than in tria+ial shear :y 2> to 6>in dense sands and $o to 2> for loose sands* A (onservative esti.ate of the

psres%lts >68 %sing the following eF%ations af ter Lade and Lee, 16!"B9

>68ps 6.5>28,x - 1!> ( >28,x ? #2>B ll5aB

has :een fo%nd to not tgnifi(antly affe(t el?, :%t it strongly aff e(ts the

D Ta:le 115#* orne (orrelations :etween >8) and dry density, relative density, and soil (lassifi(a ion are s own ifor esti.ating the fri(tional (hara(teristi(s of gran%lar .aterials* I yo%

TA,E 11"% SG6 3 $643>

Moid ratio e e t, HjV ,

Ang%larity Arain si&e distri:%tion%rfa(e ro%ghness )

Water ] Parti(le si&e

Inter.ediate -rin(i-al stress8ver(onso at1on or -restress

( 9@@99999999a .

R t, `t] t, `J* slig:tly



.--.......- -r--+· ----r ,-- -,- -,- --,.-----:B1..---,

--6elatie ensit7

B , 1

B; 1--- -1-- - 4,'- -= Z,' o4taine 3ro8 eetie stress 3ail/re enelo5es. A55ro&i8ate orrelation is 3or oesionless 8aterials wito/t 5lasti3 ines.

2 1---+--+----+--+-1-----+----t--

Porosit7, n 3ar P, D 2.@` M$8 B )

1.2 1.B 1.1. 1.@ 1. 1 . 1.L 2.; 2.1 2.2 2.B 2.

?r7 ensit7 M$8B )

#i$. 11.1B%rrelations 4etween te eetie 3rition an$le in tria&ialo85ression n te r7 ensit7, relatie ensit7, an soil lassiGationa3ter .<. Na , 1L1).

..I

IB

'-5.r##3 oD@@

9E¡;;e

.U:35Z@,e

8* * *2 *# I *# *$ *$ I*1

$1*$ 1*1 1* *6 *! *" * * *2 *2 *# *# *$ *$ *1

5B



-1L)

. T5 C35l l5n4 3 E64 P5>6G5 64 R564 3 S6n=6 )9

have a (o.-lete vis%al (lassifi(ation of the .aterials at yo%r site, together with sorne idea of the in sit% relative density, yo% already have a -rettygood idea a:o%t the shear strength :ehavior of the soils in advan(e of ala:oratory testing -rogra.* or s.all -ro0e(ts, s%(h esti.ates .ay :e allyo% need for design*

. THE COE$$ICIE%T O$ EARTHPRESSRE AT REST $OR SA%OS

In e(* !*" we defined the (oeffi(ient of earth -ress%re at rest as

where oS,0

/ the hori&ontal effe(tive stress in sit%, andthe v ertieal effeeti e stress in sit%*

We .entioned that a <nowledge of S is very i.-ortant for the design of earth5reta..g str%(t%res and .any fo%ndations@ it also infi%en(es liF%efa(tion -otential, as we shall soon see* Th%s, if yo%r assess.ent of theinitial in sit% stresses in the soil is ina((%rate, yo% (an :e way off in yo%r -redi(tion of the -erfor.an(e of s%(h str%(t%res*

o% already <now fro. Cha-ter ! e(* !*B how to esti.ate 0 1 fro.

the densities of the overlying .aterials, the thi(<nesses of the vario%slayers, and the lo(ation of the gro%nd water ta:le* A((%rate .eas%re.entsof oS, are not easy, es-e(ially in sands* I4 is vit t %ally i.-ossi:le to installan earth -ress%re (ell in sit%, for e+a.-le, witho%t (a%sing sorne dis5t%r:an(e and dens1fl(allon of the sands aro%nd the (ell, and tfOs (hangesthe stress field at the very -oint of .eas%re.ent* ConseF%ently, thea--roa(h %s%ally ta<en is to est;.ate S fro. theory or la:oratory tests,and t:eo (al(nBa te aho and af.

fro. EF !516

The :est <nown eF%ation for esti.ating S was derived :y J[<y 1622,1627B,D*vh*ieh* is a th*eoretieal relationshi- :etween S and the angle of inte.al fri(tion 18: or

/ - sin (-3 115"B

This relationshi-, as shown in ig* 11*12, see.s to :e a*% adeF%ate -redi(tor of S for nor.ally (onsolidated sands* in(e .ost of the -ointslie :etween *# and * for these sands, S

of *2 to *2 wo%ld :e a

reasona:le average val%e to %se for -relirninary design -%r-oses*I the sand has :een -reloaded, then S is so.ewhat greater* (h.idt

16"", 16"!B and Al-a n 16"!B s%ggested tha t t:e io(rease in (o%ld J5

.j

5.# , 555 5 TK 5 K 3555 55

1

1

K

1



Z

52, &hear &trength ot &anda and Cla@a

0.8

o

**,D 0.

*?*'

*

L55n=

O 6n63n >6n >G 6nG 6 W6J6> >6n= >GJ6nGl6 C6463355 >6n= >GJ6nGl6 B6>45= >6n=O S6n= S23n>, 9)8

?*B'9?'

a*B

*.5....

?*'B

0.

0.)

B5l2G >6n=t##,. M2nn5>346 >6n= 3Gn=5= P5nn>l16n26 >6n= 6nGl6

3

o 0."e:-

*B

5

o*B

G

0.!

0.*

3.* *9 ! !! !) ! !9 21 43 2 2!

$2. ." R5l6423n>2N J54D55n S 0 6n= ,p 3 n36ll 3n>3l2=645= >6n=> 645 AI-HG>>62n2 6n= T3Dn>5n=, 9).

related to the over(onsolidation ratio 8CRB :y

115!B

where S Q c &S for the over(onsolidated soil,S . ,.c S for the nor.ally (onso 2 ate

h an e.-iri(al e+-onent*Mal%es of O range :etween *2 and * Al-an, 16"!@ (h.ert.ann, 16!B

and even as high as *" for very dense sands Al5H%ssaini and Townsend,16!B* Ladd, et al* 16!!B -ointed o%t that this e+-onent itself var;es With

e+a.-le, Al5H%ssaini and Townsend 16!B fo%nd a signifi(antly lower S d%ring reloa ing t an %r.g %n oa .g . a oratory tests on a %r% or..edi%. sand* Th%s S history of the de-osit*

a--ears to :e very sensitive to the -re(ise stress

(lays*We shall have .ore to say a:o%t this s%:0e(t when we dis(%ss S for

e#.

1

1



11.4 ID'E*ACTION ANO C)CIC3O,IIT) ,EHA2IOA O* &AT'!ATEO &ANO&

o% .ay re(all that we .entioned the -heno.enon of liF%efa(tiond%ring o%r des(ri-tion of the F%i(<sand tan< e(* !*7B* We des(ri:ed the :ehavior of the very loose sands in the tan< d%ring the %-ward flow of water ig* !*1$aB or when a sho(< load was a--lied to the side of the tan< ig* !*1$(B* We also gave a -hys1(al e+-lanat1on for this -heno.enon* Wesaid that when loose sat%rated sands are s%:0e(ted to strains or sho(<s,there is a tenden(y for the sand to de(rease in vol%.e* This tenden(y(a%ses a -ositive inerease ifl -ore -ress%re whi(h res% lts in a de(rease in

ef fe(tive stress within the soil .ass* 8n(e the -ore -ress%re :e(o.es eF%alto the effe(t1ve stress, the sand loses all its strength, and 24 is said to :e in astate of liLuefaction.

E+a.-les of liF%efa(tion :riefly .entioned in e(* ! *7 in(l%ded thefaih%e of t* Pe(< 'a., Gon ta na, a nd the flow slides that have o((%rredalong the :an<s of the lower Gississi--i River* Here, liF%efa(tion ta<es -la(e %nder (onditions of large statieally ind%(ed strains Casagrande,16#"a, 16B* We will (all this stati(ally .onotoni( loadingB ind%(ed(ondition /iLuefaction. River :an<s (o.-osed of loose %nifor. fine sands(an liF%efy when s%:0e(ted to large strains, s%(h as .ight :e (a%sed :ystee-ening of the :an<s d%e to erosion, and the strains -rod%(e in(reased -ore -ress%res* %(h a sit%ation is s:own io ig* 11*1* Initially a soil

ele.ent at A, sorne distan(e fro. the slo-e, is %nder a .%(h safer state of initial stress ( S (onditions5 dis(%ssed in the -revio%s se(tionB than theele.ent at =. As erosion starts at the :ase of the slo-e, the soil stresses arein(re-*sed, the -ore water -ress%re rises, and a li.ited &one shown in ig*11 l aB (an liF%efy As this .aterial Hlo(s o%t into the river, additionalstresses are a--lied to the ad0a(ent soils, and they also (an liF%efy ig*11*1:B* In this way, liF%efa(tion progresses inland %ntil the .aterial (o.es toeF%ili:ri%. on a very flat slo-e angle ig* 11*1(B* orne i.-ortant(hara(teristi(s of different ty-es of flow slides are listed in Ta:le 1152*8ther ty-es of soils whi(h .ay :e affli(ted :y flow slides sho%ld :e addedto (ol%.n $9 hydra%li(ally -la(ed fills of sands and s1lty sands s%(h as.ine waste or tailings da.s* As .entioned in e(* !*7, these str%(t%res are

:%ilt with very little engineering design or (onstr%(tion s%-ervision, andliF%efa(tion5ty-e fail%res are relatively (o..on* Noti(e also 2n Ta:le 1152the (hara(ter of the strains ne(essary to start flow (ol%.n #B* Thesestrains (an :e (a%sed :y a sta:( in(rease in stress, li<9e the (ase of theriver:an< erosion leading to -rogressive liF%efa(tion, or they (an :e(a%sed :y dyna.i( or vi:ratory loads* E+a.-les of this se(ond ty-e of

521

1



*ro/n water s/r3ae

Abone o3 initial liZ/e3ation

522 &hear &trength of &and and Cla@a

S6ll3D 45n>23n 6>

6 S464 34 l2FG56423n

P35>>215 45n>23n 62n

(3Gn= D645 >G65

J P35>>215 l2FG56423n

$2n6l >6N D55l2FG56423n >43N>

S6n= 6>> 2n13l15= 2n N35>>215l2FG56423n 5Y45n=> 43 6 l2245==5N4 J5l3D 2n6l 5FG2l2J2G >l3N5

S6ll3D 3n5 3 l3D 3n2n2n N5>>G5n34 >G>5N42Jl5 43 l2FG56423n

!o 43 )o

5 S5423 4lG3G >l2=5 6 56 645 62lG5

V5426l >6l5 6J3G4 * + 323n46l >6l5

$l. .) L2FG56423n 2n l33>5 >6n= 6=j65n4 43 6 D6453n4

645 C6>66n=5, 9).

loading are -ile driving, :lasting, traffi(, rotating .a(hinery, stor. waves,and earthF%a<es* 4e(a%se .a0or earthF%a<es affe(t large areas, they (anand have (a%sed large de-osits of loose sat%rated sand to liF%efy for e+a.-le, eed and Idriss, 16"!@ eed and Wilson, 16"!B*

A diffe1ent <ind %f liF%efa(tion than that whi(h o((.s d%e to stati(stresses is (alled cyc/ic 8obility. Here (y(li( loads, li<e those fro. anearthF%a<e, (a%se a :%ild%- of -ore -ress%res in .edi%. to high density



A

Q1

as9les, e+5 %tes *(nt

Ra-d not af, %tes

)



Z

524 &hear &trength ot &and and Cla@

sat%rated sands and ind%(e .eas%ra:le strains in sa.-les that ordinarilye+hi:it a dilative res-onse %nder stati( loads@ this -heno.enon is o--ositeto the :ehavior -redi(ted :y the Pea(o(< diagra. of ig* 11*1* Th%s cyclic

stresses, if they are large eno%gh and for a s%ffi(ient d%ration that is,n%.:er of (y(lesB, (an (a%se .edi%. dense to very dense sat%rated sandsto liF%efy %nder the right (onditions of density and (onfining -ress%re*Loose sands, of (o%rse, fail at the least n%.:er of (y(les*

Let3s :egin o%r dis(%ssion of the :ehavior of sands %nder (y(li(loading :y f irst st%dying sorne test res%lts whi(h showed liF%efa(tion %nder stati( stresses* These tests, fro. Castro 16"6B, -resented in ig* 11*1",show the res%lts of three CU tests and one C' test, all hydrostati(ally

(onsolidated to 2 <Pa* The reJa tive densities

of ea(h s-e(i.en af ter (onsolidation are also indi(ated on the fig%re ne+t to the stress5strain (%rvefor ea(h s-e(i.en* The s-e(i.ens were loaded a+ially .onotoni(allyB :ys.all dead5load in(re.ents of weight a--lied a:o%t every .in%te to the soil sa.-le*

In test A, the one with the lowest ,, the -ea< stress differen(e of $ <Pa was rea(hed in 1 .in, whi(h (orres-onded to an a+ial strain of a:o%t 1]* Then, when the ne+t s.all inere.ent of load was a--lied, the

s-e(i5 .en s%ddenly (olla-sed5 liF%efied5 and in a:o%t *$ s the stressde (reased fro. $ to # <Pa at ] strain, where 24 re.ained as the

s-e(i.en ti(e how the ore ress%re for s-e(i.en $ re.ainedthe sa.e d%ring flow* At this .a+i.%. val%e of -ore -ress%re, t e

effe(tive .inor -rin(i-al stress was only a:o%t 1 <Pa, and if yo% (al(%latethe B, fro. these stresses %se EF* 151# or 1151B, yo% get B, #>*The total and eff e(tive Gohr (ir(les at the -ea< and d%ring flow after

liF%efa(tion are shown in ig* 11*1!* Also shown for (o.-arison are theres%lts of the C' test on the sa.e sand at the sa.e ,. 4oth tests indi(atethat ^Q? #> for this loose sand, at:o%g: as -ointed o%t :y Casagrande16!B, the agree.ent .ay :e only a (oin(iden(e* In any event, theeffe(tive stress (ir(le at the -ea< on .a+i.%. stress differen(e l;es :elowthe effe(tive fail%re envelo-e*

ig%re 11*1! is another good ill%stration of the very large diffe1en(esin the strength of sands, de-ending on the drainage (onditions we dis (%ssedin the -revio%s se(tions of this (ha-ter* Here yo% see the res%lts of* C'

vers%s CU tests on the sa.e sand at the sa.e relative deosity and at thesa.e effe(tive (onsolidation stress* The differen(es are even greater whenyo% (onsider the strength of the sand af ter liF%efa(tion* In a flow slide, thissaod wonXd si.-ly flow o%t li<e a very dense liF%id, and its eF%ili:ri%.slo-e angle .ight :e only a very few degrees*

Now let3s loo< at the res%lts of tests on s-e(i.ens and C in ig*11*1* -e(i.en = ig* 11*1"B at , / 22] also liF%efied af ter a -ea< stress differen(e of $ <Pa was rea(hed at a:o%t $] strain5then the



800 &--.&-&-&--&---&- .- --.

555-----:--:::-;5--&..-

,@a*

:/. 00M

Qc + @V- +

C' 45>4; ', / !0

CU 45>4; ', / "Y" 2n 43 /

)

Ge9

+ +

"00 +

+

CU 45>4; ', / ""0." > 3 N56

3o + Y?' + ...

5Z=

Z@3

o*e9

43 E / 8

CU 45>4; ', / !00.* > 3 N56

Y43 E / *)

a, !0 P6 A

oo 0 * ) *0

AY26l >462n, E

ln2426l a c / "00 P6a 1 / ) P6

0 ) *0

AY26l >462n, E

AII 3G 45>4> 2n2426ll 3n>3l2=645= 43 a c / "00 P6.

$2. . C3N62>3n 3 455 =3>46426ll 3n>3l2=645= C 45>4>6n= 3n5 C& 45>4 3n J6n=2n >6n= l36=5= 2n55n46ll 43 62lG5 645 C6>66n=5, 9), 3 C6>4c, 99.

525

,.

?''

¡:; *00



+ PeaI stre

1

00

555555.=

00-¡;l*

CZ*

5**,Z

?'?..'.lllC1B

*eQ

00

E 5 215 >4 5>> 2l5 W64 N56

511 Q

554215>45n4 $2l5 3 COI

45>4 >3Dn N3N62>n

346l >45>> 42l54 N56

...... ?-- A QQ

A

34lll 45>> "2l5G2nFl l3D

W1141.F.-.-.!F..:.._ &--!-420=----- -i--:-!:E-:::-..i.*-t-+001-- --100:-----t 700 -,----F- 800;:-N-01 X 6 X l X > X 4 X 5>>

P6lQ a1 / # P6

a +, / ) P6 P35 5>>G5 64 N 6, G, ll1M3l 2H > 2n 5 3 46l

d$2i. .

4215 >45>5> 3 45

T ln=G = N3 5 N5> G5 = 2n l3D, ;, 1

2 n A n= 4 5 C 45>4 3 5AA¡. C3n=242 n 64 J34

6Y2?G >5>> 255 5 6 = =G 2n l w 6 >3 n 645 C >66n=5,6!B*

'

W



11.8 luefactlon and C@cllc 3o#lllt@ ,eha/lor ol &aturated &enda 527

s-e(i.en flowed ra-idly to a strain of 17] and sto--ed flowing* To get it.oving again, additional s.all weights had to J5 added to the -iston* Noti(e that the -ore -ress%re ind%(ed in this sa.-le d%ring liF%efa(tion was.ore than # <Pa, and if yo% (al(%late B,,yo% get a val%e of a:o%t #$>*in(e it was denser than s-e(i.en A, a higher fri(tion angle is reasona:le*-e(i.en @ was slightly denser than =, and it never e+-eri en(edliF%efa(tion* The s-e(i.en o:vio%sly lt ied to dilate as the a+ial stress wasin(reased sin(e the -ore -ress%re decreased af ter the .a+i.%.* Thesetests show how liF%efa(tion o((%rs %nder stati( or .onotoni(loading* Their lig%efa(tion :ehavior (an :e e+-lained :y the (riti(aV voidratio (on(e-t, and the Pea(o(< diagraIl (an :e %sed to -redi(t their :ehavior*

The o((%rren(es of the 9" Niigata, Ja-an, and the An(horage,Alas<a, ea1thF%a<es sti.%lated .%(h researeh into the -ro:le.s of g+ owtds%:siden(e and fail%re d%e to earthF%a<e dyna.i(B loading of sat%ratedsands* Prof* H* 4* eed and fOs st%dents at the U.versity of Cahfor.a at4er<eley :egan to st%dy this -ro:lern, %sing :oth hydrostati(ally and non5hydrostati(ally (onsolidated %ndrained (y(li( tria+ial tests to si.%lateearthF%a<e loadings* Insight .ay :e gained fro. a series of tests where thevaria:les tho%ght to gove. the (y(li( :ehavior of sands are tested in asyste.ati( .anner* ro. the Pea(o(< diagra., it is evident that initialrelative density and effe(tive (onfining -ress%re are two <ey -ara.eters* Inaddition, the .agnit%de %f the (y(li( st+ ess and n%rn:et %f (y(les to (a%sefail%re were st%died* everal definitions of fail%re were %sed, s%(h as

vario%s -er(ent (y(li( strains and when the -ore -ress%re ratio $u Qo@Je %aled one*

Ty-i(al res%lts fro. a hydrostati(ally (onsolidated (y(li( %ndrainedt(ia +ia l test ao loase sa od a re s:awn in Eig 8 eed and I ee, 9Mery little strain develo-ed d%ring the first nine (y(les of (y(li( stressa--lieation, even tho%gh the -ore -ress%res grad%ally inereased* Then :etween the nioth and tenth (y(les the -ore -ress%re s%ddenly in(reased toa val%e eF%al to the (onfining -ress%re, and the s-e(i.en devel%-ed verylarge strains in the ne+t (o%-le of (y(les* I4 was o:served that the s-e(i.enwas in a fl%id (onditioo over a w1de range of stra.s* 3I:e s%ddenness of the (olla-se or liLueaction was also of interest* In several tests, thes-e(i.ens showed very little strain, after even a relatively large n%.:er of (y(Jes t :eo they wo%Bd s%ddeoly liF%efy af ter aoBy ane ar two .ore(y(les were a--lied* Ali in all, it was fo%nd that loose sands :ehaved a:o%t

When dense sands were tested, however, the res%lting :ehavior wasF%ite s%r-ns.g* 1y-1(al res%lts of (y(h( tna+tal tests on the sa.e sand as%sed in ig* .8 and at the sa.e effe(tive (onsolidation -ress%re areshown in ig* 11*16* 8nly the relative density is !7] now instead of the

1

* J



Í'

!0 1

eo **,**555A+ial strai n at tJ.a / #6 < Pa·99

?a

o*',*

$ 1 55

eD...

, ,o -- -(.)

o 5 5 5- -- 55 5 ?'

,n Test No* 112 ***** A+ial stra i n at tJ.a / 8+ e 55 5 -

·9955D5 a - ,*K

5,,

- -?- 1

ea*, 5,n

eZ 0.8, d, !85 1nn Ln-

?^ ., 5,5* A+ial strain at tJ.a 5k !9 <Pa

N%. :er of (y(les

aB A+ial strain vs* n % . :er of (y(les

1

00

3a*

*(onf i ni ng -ress%re Q -ore water -ress%re

555555at tia !9 <PaCorre(ted (hange i n -ore

5

$ 2 1 20 2 1

N%.:er of (y(les

J Cl'l6n5 2n N65 D645 N5>>G5 1> nGnJ5 34 (y(les

(orre(ted to .ean e+tre.e -rin(i-al stress (onditionsB

$2. .8 TN26l l2 426Y26l 45>4 3n l33>5 >6n= 645 S55= 6n= L55,9.

E1

.

V

55

**D

5 t^t3a

$ 2 1 20 2 1

1 1



......

A&ial strainat Aa D - ; IPa _ ,'

a..'.:,. ,.. , l n i tial eetie Can$e i n 5ore water

....

a.

/

/-; '---

)5:o

@

(

*

,, 3A+ial strain

·99&

'E

5:G

5 K K .--

,, I'

,- at ea / ` ! <Pa

o - 55 5-

5-5- 5-5- 5-

1#giA+ial strainat Aa / 8 -

e9o

·995:

Test No* 1 16a(ra .ento R iver sande, *!1, ', / !7] .... 38***3o** *,,,

+ 1UJ

) ,a* & 1 < Pa

'O.. Aa & ! <Pa 3^1 1

$ 2 1 $ 40 1

N % .:er of (y(les

a B A+ial strain vs* n % . :er of (y(les

999,^X

::,5 1 ,**

(@

*

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-revio%s #7]* '%ring the first 1 or so (y(les, very little a+ial straino((%rred, :%t the ind%(ed -ore water -ress%res grad%ally in(reased* At(y(le 1#, the -ore -ress%re .o.entarily :e(a.e eF%al to the total (ell -ress%re when the -rin(i-al stress differen(e was &ero d%ring the (y(le@that is, the effe(tive (onfining -ress%re was .o.entarily &ero* Even tho%ghthe effe(tive stress was &ero d%ring -art of the (y(le, the s-e(i.en was stilla:le to withstand additional (y(li( stress* As (an :e seen in ig* 11*16, thestrain a.-lit%de was less than I ] even af ter $ (y(les, and the sa.-le didnot (olla-se as was the (ase for the loose sand* 4ased on other tests, eedand Lee 16""B also fo%nd that the lower the (onfining -ress%re, the .oreeasily liF%efa(tion, or cyc/ic 8obi/ity as it is now (alled, wo%ld develo-* Inother words, in(reasing the eff e(tive (onfining -ress%re wo%ld de(rease the

-otential for (y(li( .o:ility*The varia:les that af fe(t the (y(li( .o:ility of sat%rated sands areshown in ig* 11*$a, where -ea< (y(li( stress vers%s log n%.:er of (y(lesis shown* l4 (an :e seen that as the -ea< stress is lowered, .ore (y(les arereF%ired to fail the sa.-le* I the relative density andQor the effe(tive(onfining -ress%re is in(reased, it ta<es a higher (y(li( stress to fail thesa.-le for a given n%.:er of (y(les to fail%re* aid in another way, it willta<e a larger n%.:er of (y(les to (a%se fail%re for the sa.e (y(li( stress*The definition of (y(li( stress is ill%strated in ig* 11*$: for :oth (y(li(tria+ial tests and (y(li( si.-le shear tests* Cy(li( si.-le shear tests see.to .ore (losely re-resent a(t%al field stress (onditions* The differen(es instress (onditions :etween these two <inds of tests have :een the s%:0e(t of

.%(h resear(h for e+a.-le, eed and Pea(o(<, 16!1@ inn, et al*, 16!1@Par< and ilver, 16!@ and Castro, 16!B*

8ther fa(tors have :een fo%nd to infl%en(e the res%lts of (y(li(testing of sat%rated sands* The .ost signifi(ant fa(tor is -erha-s the.ethod of sa.-le -re-aration and the res%lting soil str%(t%re G%lilis, etal*, 16!@ Ladd, 16!!B* 8ther fa(tors in(l%de -revio%s (y(li( strain historyfro. -rior earthF%a<es, for e+a.-leB, the (oeffi(ient of earth -ress%re atrest, S , and the over(onsolidation ratio of the soil de-osit eed, 16!6B*As the val%e of K or 8CR in(reases, a larger n%.:er of (y(les to (a%sefail%re is reF%ired for a given (y(li( stress* Prior (y(ling or -restraining(a%ses the sa.e res%lt*

I4 is diffi(%lt to -er(eive that an initially dense sand (o%ld liF%efyd%ring (y(li( loading* ro. o%r -revio%s dis(%ssion in this (ha-ter, densesands tend to in(rease in vol%.e dilateB, whi(h .eans the -ore -ress%resho%ld de(rease and the effe(tive stresses sho%ld in(rease* Is 24 really -ossi:le that the o--osite rea(tion (an o((%r %rther, as was shown in thePea(o(< diagra. ig* 11*1B, in(reasing the effe(tive (onfining stress onan initially dense sand tends to (a%se =loose=5ty-e :ehavior@ that is, itwo%ld in(rease rather than de(reaseB the -otential for liF%efa(tion*



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$2. .*0 6 (5n56l25= 5l6423n>2N J54D55n N56 l2 >45>> 6n=nGJ5 3 l5> 43 6G>5 l2 3J2l24 62lG5; 554> 3 2n2426l =5n>246n= 3n2n2n N5>>G5 65 2n=2645=; J =52n2423n 3 l2 >45>> lio 2n45 426Y26l 45>4 3 TOv 2n 45 l2 >2Nl5 >56 45>4.

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Additional wor< :y Castro 16"6 and 16!B see.ed to answer theseano.alies* 4y very (aref%1 .eas%re.ents of the failed (y(li( tria+ia1s-e(i.ens, he fo%nd a radi(al water (ontent and void ratio redistri:%tionin the sa.-les at fail%re* They were alte.ately ne(<ing down and :%lgingo%t at the to-, and he fo%nd the relative densities varied signifi(antlythro%gho%t the s-e(i.en* The reaons for this :ehavior are (o.-le+ andare dis(%ssed at sorne length :y ^@99asagrande 16!B and Castro 16"6 and16!B* In any even t, Castro3s wor< see.ed to e+-lain that we were seeingtwo :asi(ally different -heno.ena9 1B (lassi(al 1iF%efa(tion of loosesands, whi(h we des(ri:ed earlier and whi(h we all %nderstand, and $B the -heno.enon (alled cyclic 8obility whi(h o((%rs in the la:oratory d%ringcyclic tria+ial or si.-le shear tests*

These two -heno.ena are ill%strated in ig* 11*$1, whi(h is si.ilar toig* 1 1*!* This fig%re is li<e loo<ing %-ward fro. :eneath the Pea(o(< diagra. on the ]RP -1ane* The =steady5state 1ine= re-resen ts the (riti(avoid ratio and effe(tive stress rela tionshi- af ter liF%efa(tion* oils withvoid ratios and effe(tive stresses lying a:ove and to the right of the steady5state line are (ontra(tive or loose and th%s are s%:0e(t to liF%efa( tion* or e+a.-le, a sa.-le starting at -oint C when stressed or vi:rated

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9



11.4 luefactlon and C@cllc 3o#lllt@ ,eha/lor of &aturated &enda 7%%

develo-s a la1ge a.o%nt of -ositiv e e+eess -ore -ress%re and ends %- at -oint A on the steady5state line, where the sa.-le has no f%rther tenden(yto (hange vol%.e* 8n the other hand, a dense dilative s-e(i.en originallyat -oint :elow the steady5state line, if s%:0e(ted to (y(li( shear, will.ove towards -oint =, a (ondition of &ero effe(tive stress* This is the(ondition of (y(li( .o:ility defined a:ove* l the sa.e sa.-le were loaded.onotoni(ally or stati(ally in an ordinary tria+ial test, then it wo%ld go inthe o--osite dire(tion towat ds the steady5state line* This sa.-le wo%ld

:ehave 0%st as we des(ri:ed in e(* 11* for dense sat%rated sands %nder %ndrained loading* Note that there 1s noth.g (ontrad1(tory a:o%t th1s

:ehavior* A state diagra. showing the steady5state lines for several ty-i)alsands is shown in ig* 11*$$* Toe differen(es :etween liF%efa(tion and

(y(li( .o:ility have :een s%..ari&ed :y Castro and Po%los 16!!B inTa:le 115*

However, the (ase is not (losed on this s%:0e(t* We (an still %se theres%lts of the (y(li( tria+ial test and ali o%r e+-erien(e with it* G%lilis, et al*

16!B (ond%(ted (y(h( tna+ial tests where relattve densities varied fro.] to 6] and the (y(li( stress ratios 5rQa,@ B fro. *$ to ** Theseval%es of density and stress ratios adeF%ately (over .ost (onditions to :ee+-e(ted in the field*B They fo%nd that =** *there was no a--arent effe(ton non%nifonn strains or water (ontent redistri:%tion in the sa.-les -rior to the develo-.ent= of fail%re eed, 16!6B* Af ter fail%re, the sa.enon%nifonn (onditions ne(<ing, :%lgingB as Castro o:served were no5ti(ed* These res%lts Ds%ggest that the (y(h( tna+ial test (aref%lly -er

35= (an in fa(t :e %sed to eval%ate the :ehavior of field (onditions :y.a<ing a--ro-riate (orre(tions for / or :y %sing the (y(li( si.-le shear test with eorreetions eed, 16!6B*

What (an yo% do to avoid a liF%efa(tion fail%re or the stati( (aseof nat%ral slo-es, .onitoring of the field -ore water -ress%res with -ie&o.eters .ay give sorne indi(ation of i.-ending insta:ility* 8:servations of erosion and s.all slides along rivers .ay also hel-* I the -ro:le. .volvesearthF%a<es, 24 is i.-ossi:le to (ontrol the n%.:er of (y(les or the a--lied(y(li( stresses* However it .ay :e -ossi:le to in(rease the in sit% density

:B re.o @al and re-laee.ent of the loose soil or :y (o.-a(tioo of t:eloose soils :y te(hniF%es des(ri:ed in Cha-ter * Li<ewise, the addition of a s%r( harge hll or :er. over a sat%rated sand layet will in(rease the

effe(tive stresses whi(h sho%ld red%(e the liF%efa(tion -otential or at leastthe (y(li( .o:ilityB* inally, it .ay :e -ossi:le to -er.anently lower thegro%od wa ter ta:le :y .eans of drains and Qor -%.-ing, whi(h wo%ldred%(e the -ossi:ility of liF%efa(tion*D Clearly, the -ro:le. of a liF%efaetion fail.e in a de-osit of loose

sat%rated sands is real and sho%ld not :e overloo<ed, es-e(ially for1.-ortant str%(t%res s%(h as da.s and -ower -lants* W5 don3t have ali the

,. _



'()*+ 1105 &255n5> B54D55n L2FG56423n 6n= Cl2 M3J4L;F%efa(tion Cy(li( Go:ility

eneral

Effe(t of a*e

at (onstant void

ratio for aSe /a*e

Effe(t of oScf o#ieat (onstantvoid ratio and a*e

Gost li<ely in %n;for.,fine, (fean, loose sand*tati( load (an (a%seliF%efa(tion* Cy(li(loads (a%sing shearstresses larger thanthe steady5statestrength also 6n(a%seliF%efa(tion*

In(reased a*e .eans larger defor.ations liF%efa(tion is ;nd%(ed*The .agoit%de andQorn%.:er of (y(li( loadsneeded to (a%se liF%e5fa(tion in(reases withXJ$· Cy(li( loadss.aller than the steadystate strength (annot(a%se liF%efa(tion :%t.ay (a%se (y(li(.o:ility*

.aller additional loadsare needed to (a%seliF%efa(tion as aS ,/o*ein(reases* WhenoSe / a#_ e is large, asoilis .ore %nsta9:le and .ay,qn the e+tre.e, :es%s(e-ti:le to=s-ontaneo%s liF%efa(tion*=

Any soil in any state (andevelo- (y(li( .o:ility2n the la:oratory the(y(li( stresses are largeeno%gh*

In(reased a*e

.eaos in(reased (y(li( load to(a%se (y(li( .o:ility*4%t the (y(li( .o:ilityratiot %s%ally de(reaseswith ;n(reas;ng <#_e.

In soils that have low

-er.ea:ility, in(reasedaS ,/ a*e see.s to res%ltin so.ewhat s.aller(y(li(.o:ility stresses, whi(his a reasona:le trend*In (lean sands,(y(li( .o:ility stressin(reases with aSe l<#_eBThis %n%s%al res%lt for (leansands is -ost%lated to :ed%e to the s%:stant;altest error d%e toredistri:%tion of void

ratio in the la:oratorys-e(i.ens*

After Castro and Po%los 16!!B*

t <> 5 ,< * 8 , where o - o B 1*s the dynan%*( -n*n(1* -al stress = eren(e, or the

!*e

(y(li( .o:ility stress*



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answers, :%t fort%nately resear(h (ontin%es and -ra(ti(a design -ro(ed%res are .at%ring eed, 16!6B* In .ost (ases, however, the -resentdesigns await the %lti.ate test of their adeF%a(y %nder field loading

earthF%a<eB (onditions*

.9 STRESS-&E$ORMATIO% A%O STRE%(TH CHARACTERISTICSO$ SATRATE& COHESIVE SOILS

What ha--ens when shear stresses are a--lied to sat%rated (ohesivesoils Gost of the re.ainder of this (ha-ter (on(erns this F%estion* 4%t

first, lef s :riefly review what ha--ens when sat%rated sands are sheared*

ro. o%r -revio%s dis(%ssion, for e+a.-le, yo% <now that vol%.e (hanges(an ta<e -la(e in a drained test, and that the dire(tion of the vol%.e(hanges, whether dilation or (o.-ression, de-ends on the relative density

as well as the (onfining -ress%re* I shear ta<es -la(e %ndrained,then the vol%.e (hange tenden(ies -rod%(e -ore -ress%res in the sand*

4asi(ally, the sa.e things ha--en when (lay soils are sheared* Indrained shear, whether the vol%.e (hanges are dilation or (o.-ressionde-ends not only on the density and the (onfining -ress%re :%t also on the



11. &tre"(eforatlon and &trength Characterltlc 7%M

stress history of the soil* i.ilarly, in %ndrained shear the -ore -ress%resdevelo-ed de-end greatly on whether the soil is nonnally (onsolidated or over(onsolidated*

Ty-i(ally, engineering loads are a--lied .%(h faster than the water (an es(a-e fro. the -ores of a (lay soil, and (onseF%ently e+(ess hydro5stati( or -ore -ress%res are -rod%(ed* l the load.g 1s s%(h that fail%redoes not o((%r, then the -ore -ress%res dissi-ate and vol%.e (hangesdevelo- :y the -ro(ess we (all consolidation Cha-ters 7 and 6B* The -ri.ary differen(e in :ehavior :etween sands and (lays, as .entionedwhen we dis(%ssed the (o.-ressi:ility of soils Cha-ter 7B, is in the ti8e itta<es for these vol%.e (hanges to o((%r* The ti.e as-e(t stri(tly de-endson, or is a f%n(tion of, the differen(e in -er.ea:ility :etween sands and

(lays* in(e (ohesive soils have a .%(h lower -er.ea:ility than sands andgravels, it ta<es .%(h longer for the water to flow in or o%t of a (ohesivesoil .ass*

Now, what ha--ens when the loading is s%(h that a shear fail%re isi..inent in(e :y definitionB the -ore water (annot (arry any shear stress, all the a--lied shear stress .%st :e resisted :y the soil str%(t%re* P%tanother way, the shear strength of the soil de-ends only on the effective

stresses and not on the -ore water -ress%res* This does not .ean that the -ore -ress%res ind%(ed in the soil are %ni.-ortant* 8n the (ontrary, as the totalstresses are (hanged :e(a%se of sorne engineering loading, the -ore water -ress%res also (hange, and %ntil eF%ili:ri%. of effe(tive stresses o((%rsinsta:ility is -ossi:le* These o:servations lead to two f%nda.entally differ(nt

a--roa(:es to the sol%tion of sta:ility -ro:le.s in geoteehnieal engineering91B the total stress approach and $B the effective stress ap proach. In the totalstress a--roa(h, we allow no drainage to ta<e -la(e d%ring the shear test, andwe .a<e the ass%.-tion, ad.ittedly a :ig one, that the -ore water -ress%reand therefore the effe(tive stresses in the test s-e(i.en are identi(al to thosein the field* Toe .ethod of sta:ility analysis is (alled the total stressanalysis, and it %tili&es the total or the undrained shear strength G? , of the soil*The %ndrained strength (an :e detennined :y either la:oratory or field tests* I field tests s%(h as the vane shear, '%t(h (one -enetro.eter, or -ress%re.eter test are %sed, then they .%st :e (ond%(ted ra-idly eno%gh so that %ndrained(onditions -revail in sit%*

The se(ond a--roa(h to (al(%late the sta:ility of fo%ndations, e. :an<.ents, slo-es, et(*, %ses the shear strength in ter.s of effe(tivestresses* In this a--roa(h, we have to .eas%re or esti.ate the e+(esshydrostati( -ress%re, :oth in the la:oratory and in the field* Toen, if we3<now or (an esti.ate the initial and a--lied total stresses, we .ay(al(%late the effe(tive stresses a(ting in the soil* in(e we :elieve thatshear strength and stress5defor.ation :ehavior of soils is really(ontrolled or

* J

X:.: ?- ?:/:/;??-? X:,:X ???--:/-/--/--/--/---/-,----- ------ - X X - X: X :-- Q' Q B5 5 555B 55 C C # .#3# C # C #C #C # # - .## # , B.. . . , . , , ; ! ; 6 > 5 Q ,. . 9 . , , , ,; .. , 5,5,,,5,5,* =3DW*, K***,5D **@*,=e=D===D3===3=3=5=5 55=D=D9



#7 S56 S45n4 3 S6n=> 6n= Cl66

detennined :y the effe(tive stresses, this se(ond a--roa(h is -hiloso 2-(ally .ore satisfying* 4%t, it does have its -ra(ti(al -ro:le.s* or e+a.-le,esti.atin or .eas%rin the ore ress%res es e(iall in the fiel Deasy to do* Toe .ethod of sta:ility analysis is (alled the effective stress

analysis, and it %tili&es the drained shear strength or the shear strength intenns of effe(tive stresses* Toe drained shear strength is ordinarily onlydetennined :y la:oratory tests*

o% -ro:a:ly re(all, when we des(ri:ed tria+ial tests in e(* 1*,that there are li.iting (onditions of drainage in the test whi(h .odel realfield sit%ations* We .entioned that yo% (o%ld have (onsolidated5drainedC'B (onditions, (onsolidated5%ndrained CUB (onditions, or %n(onsolidated5%ndrained UUB (onditions I4 is aBso (onvenien t ta des(ri:e the

:ehavior of (ohesive soils at these li.iting drainage (onditions* I4 is notdiffi(%lt to translate these test (onditions into s-e(ifi( field sit%ations withsi.ilar drainage (onditions*

We .entioned in e(* 1* that the %n(onsolidated5drained test U'Bis not a .eaningf %l test* irst, it .odels no real engineering designsit%ation* e(ond, the test (annot :e inter-reted :e(a%se drainage wo%Xdo((%r d%ring shear, and yo% (o%ld not se-arate the effe(ts of the (onfining -ress%re and the shear stress*

As we did with sands, we shall dis(%ss the shear :ehavior of (ohesivesoils with ref eren(e to their :ehavior d%ring tria+ial shear tests* o% (anthin< of the sa.-le in the tria+ial (ell as re-resenting a ty-i(al soil ele.entin the field %nder different drainage (onditions and %ndergoing different

stress -aths* In this .anner, we ho-e yo% will gain sorne .s1ght .to how(ohesive soils :ehave in shear, :oth in the la:oratory and in the field*/ee- in .ind that the following dis(%ssion is so.ewhat si.-lified, and

D that real soil :ehavior is .%(h .ore (o.-li(ated* Towards the end of the(ha-ter we shall indi(ate sorne of these (o.-le+ities* 8%r -ri.ary refer en(es are Leonards 16"$B, Hirs(hfeld 16"#B, and Ladd 16"2 and 16!1:B,as well as the le(t%res of Professor H* 4* eed and * J* Po%los*

.9. C3n>3l2=645=-&62n5= C& T5>4 B56123

We have aheady des(ti:ed this test when we dis(%ssed the strengt: of

sands earlier in this (ha-ter* 4riefly, the -ro(ed%re is to (onsolidate the tests-e(i.en %nder sorne state of stress a--ro-riate 43 the field or designsit%ation* Toe (onsolidation stresses (an either :e hydrostatic eF%al in alldire(tions, so.eti.es (alled isotropic: or non5hydrostatic different in dif ferent dire(tions, so.eti.es (alled anisotropic :. Another way of loo<ing atthis se(ond (ase is that a stress differen(e or fro. the Gohr (ir(lesB ashear stress is a--lied to the soil* When (onsolidation is over, the =C= -artof the C' test is (o.-lete*



a ' S

11. &lreaa"(eforatlon and &trength Characterlatlca 539

'%ring the ='= -art, the drainage valves re.ain open and the stressdiff eren(e is a--lied very slowly so that essentially no e+(ess -ore water -ress%re develo-s d%ring the test* Professor ,ft**** Casagrande ter.ed this testthe 5test for =slow= testB*

In ig* 11*$#, the total, ne%tral, and effe(tive stress (onditions 2n ana+ial (o.-ression C' test at the end of (onsolidation, d%ring a--li(ationof a+ial load, and at fail%re are shown* The s%:s(ri-ts v and O refer tov ertieal and hori&ontal, res-e(tively@ e .eaos (onsolidation* or (onven5

tional a+ial (o.-ression tests, t:e initial (onsolidation stresses are hydrostati(* Th%s v / o,. / o4c (ell -ress%re, whi(: is %s%ally held (onstantd%ring the a--li(ation of the a+ial stress Ilo. In the a+ial (o.-ression test,Ila o 5 o , and at fail%re Il.o / a15 a#BZ5 The a+ial stress (an :e

1 # 1

a--Bied either hy in(reasing the load on the -iston in(re.entally F stress5controlled loadingB or thro%gh a .otor50a(< syste. whi(h defor.s thesa.-le at a (onstant rate (alled a constant rate of strain testB*

Note that at ali the ti.es d%ring the C' test, the -ore water -ress%reis essentially &ero* This .eans that the total stresses in the drained test areD

TOTAL, u %ETR AL, G 5` AA $ECTIVE,

a#.C / dve

At the end of (onsol idation h ydrostati( (onsolidation,3 / a 1 , or non5hydrostati((onsol idation, a 5 a 15 :

(onstant9

0-

t ª

i< >c

5

3 c a hc

At fai l %re9

tress diff eren(e is a--l iedvery slowly so that e+(ess -ore water -ress%re

% 9,,, 8 thro%gh the test

l at / a 1 5 a# B t

<>e

0-?' E$2. .*! S45>> 3n=2423n> 2n 45 3n>3l2=645=-=62n5= C& 6Y26l 3N5>>23n 426Y26l 45>4.

55555 5 5 D K,*,K, K 3 .. ,,,K* 5 95,* . 5



54, &hear &trength of &and and Cla@a

al(ap eF%aB to the effe(tive stresses Th%s e/ a4 / n , / n ,, and

11 / o41 / oc ` do1. I non5hydrostati( (onsolidation stresses were a-5 -lied to the s-e(i.en, then 11 / o41 wo%ld :e eF%al to o4c ` d o1.

Ty-i(al stress5strain (%rves and vol%.e (hange vers%s strain (%rvesfor a re.olded or (o.-a(ted (lay are shown in ig* 11*$2* Even tho%ghthe two sa.-les were tested at the sa.e (onfining -ress%re, the over(onsolidated s-e(i.en has a greater strength than the nor.ally (onsolidated(lay * Note also that it has a higher .od%l%s and that fail%re the .a+i.%.do, whi(h for the tria+ial test is eF%al to o1 5 o# B_ o((%rs at a.%(h lower strain than for the nor.ally (onsolidated s-e(i.en* Notetoo the

analogy to drained :ehavior of sands* Toe over(onsolidated (lay epandsdt% ing shear w hile the no11nally eonsolidated (lay co8p,esses or eonsoli5dates d%ring shear* This is analogo%s to the :ehavior des(ri:ed earlier for

O1553n>3 I2=645=

a e / 3n>46nU

%36ll 3n>3l2=645=

%36ll3n>3l2=645=

$2. .*" TN26l >45>>->462n 6n= 13lG5 6n5 15>G> >462n G15>3 C& 6Y26l 55N5>>25l 45>4> 64 4l?l5 >65 5554215 53l2A2A >45>>.

e # #



11. &tre"(eforatlon and &trenglh Characterla'ca 7+1

sands9 nor.ally (onsolidated (lays :ehave si.ilarly to loose sands,whereas over(onsolidated (lays :ehave li<e dense sands*

In the C' tria+ial test, the stress -aths are straight lines sin(e we%s%ally <ee- one of the stresses (onstant and si.-ly vary the other stress*Ty-i(al drained stress -aths are shown in ig* 1*$$ for fo%r (o.*.onengineering sit%ations whieh ean :e .odeled in the tria+ial test The stress -ath for the a+ial (o.-ression test ill%strated in ig* 11*$# is the straightline A@.

The Gohr fail%re envelo-es for C' tests of ty-i(al (lay soils areshown in igs* 11*$ and 11*$":* Toe envelo-e for a re.olded (lay as wellas a nor.ally (onsolidated %ndist%r:ed (lay is shown in ig* 11*$* Eventho%gh only one Gohr (ir(le re-resenting the stress (onditions at fail%rein ig* 11*$#B is shown, the 1es%lts of three or .ore C' tests en identi(als-e(i.ens at different (onsolidation -ress%res wo%ld ordinarily :e reF%iredto -lot the (o.-lete Gohr fail%re envelo-e* I the (onsolidation stressrange is large or the s-e(i.ens do not have e+a(tly the sa.e initial water (ontent, density, and stress history, then the three fail%re (ir(les will note+a(tly define a straight line, and an average :est5fit line :y eye is drawn*The slo-e of the line deter.ines the Gohr5Co%lorn: strength -ara.eter et,3,of (o%rse, in ter.s of ef fe(tive sliesses* When the faih%e enD*ZeVo-e ise+tra-olated to the shear a+is, 24 will show a s%r-risingly s.all inter(e-t*Th%s it is %s%ally ass%.ed that the $ -ara.eter for norrnally (onsohdatednon5 (e.ented (lays is essentially &ero for ali -ra(ti(a -%r-oses*

or over(onsolidated (lays the e3 -ara.eter is greater than &ero, asindi(ated :y 1g* 11*$":* Toe over(onsolidated -ortion of the strengthenvelo-e 'ECB l;es above the nor.ally (onsolidated envelo-e A4CB*This -ortion 'ECB of the Gohr fail%re envelo-e is (alled the preconsolida

tion hu8p. Toe e+-lanation for this :ehavior is shown 2n the e vers%s o3

G

T346l / E54215

a

$2. .*) M3 62lG5 5n15l3N5 3 6 n36ll 3n>3l2=645=l6 2n =62n5= >56 .



542 &hear &trength of &3d and Cla@

5 3 w, if S / 00

V22n 3N5>>23n G15

(5) a

'

G

J

6n 3153n>3l 2=645= l6.

(%rve when -lotted arith.eti(ally is (on(ave %-ward*B Let %s ass%.e that

on enand high void ratio* As we (ontin%e to in(rease the verti(al stress we rea(h

i on e virg. (o.-ress1on (%rve an (ond%(t a C' tria+ial test*We (o%ld, of (o%rse, do the sa.e thin with a C' dire(t shear test*strength of the sa.-le (onsolidated to -oint $ on the virgin (%rve wo%ld(orres ond Din ig* 11*$":* I we (onsolidate and test another otherwise identi(al



.9 S4,.>-&5364l3n 6n= S45n4 C6645l>4l> )"!

s-e(i.en whi(h is loaded to -oint =, then we wo%ld o:tain the strength,again nor.ally (onsolidated, at -oint = on the fail%re envelo-e in ig*11*$":* lf we re-eat the -ro(ess to -o.t C o@, the -re(onsolidation stressB,then re:o%nd the s-e(i.en to -oint , then reload it to -oint T and shear,we wo%ld o:tain the strength shown at -oint E in the lower fig%re* Notethat the shear strength of s-e(i.en T is greater than s-e(i.en =, eventho%gh they are tested at e+a(tly the sa.e effe(tive (onsolidation stresses*The reason for the greater strength of T than = is s%ggested :9y the faetthat T is at a lower water (ontent, has a lower void ratio, and th%s isdenser than 4, as shown in ig* 11*$"a* lf another s-e(i.en were loaded to@, re:o%nded to , reloaded :a(< -ast T and C and on to F, it wo%ld havethe strength as shown in the fig%re at -oint F. Note that it is now :a(< onthe virgin (.n-t ession e%ne and the nor.ally (onsolidated *failnre eo5velo-e* The effe(ts of the re:o%nding and re(onsolidation have :een 2n

effe(t erased :y the in(reased loading to -oint 9. 8n(e the soil has :eenloaded well -ast the -re(onsolidation -ress%re o4,it no longer =re.e.:ers=its stress history* D

.9.* TN26l V6lG5> 3 &62n5= S45n4 P66545>

or the Gohr fail%re envelo-es of igs* 11*$ and 11*$" we did notindi(ate any n%.eri(al val%es for the effe(tive stress strength -ara.etersB,.Average val%es of B, for %ndist%r:ed (lays range fro. aro%nd $= for

33n6 (onsolidated highly -lasti( (lays %- to #> or .ore for siltyandsandy (lays* The val%e of >J8 for (o.-a(ted (lays is ty-i(ally $> or #> and

o((asionally as high as #>* As .entioned earlier, the val%e of e3 for nor.ally (onsolidated non5(e.ented (lays is very s.all and (an :e

negle(ted for -ra(ti(aV wor<* I the soil is over(onsolidated, then B, wo%ld :e less, and the e3 inter(e-t greater than for the nor.ally (onsolidated -artof the fail%re envelo-e see ig* 11*$": againB* A((ording to Ladd 16!1"B,

for nat%ral over(onsolidated non5(e.ented (lays with a -re(onsolidationstress of less than to 1 <Pa, e3 will -ro:a:ly :e less than to 1 <Paat low stresses* or (o.-a(ted (lays at low stresses, e3 will :e .%(h greater d%e to the -restress (a%sed :y (o.-a(tion* or sta:ility analyses, the Gohr5

Co%lo.: eff e(tive stress -aa.eters cp and e 3 ate dete.rined 83l er therange of eff e(tive nor.al stresses li<ely to :e en(o%ntered in the field* l4

has :een o:served for e+a.-le, /enney, 166B that there is not.%(h differen(e :etween B, deter.ined on %ndist%r:ed or re.oldedsa.-les at the sa.e water (ontent* A--arently, the develo-.ent of the.a+i.%. val%e of cJ]3 1eF%ires so .%(h strain that the soil str%(t%re is :ro<en down and al.ost re.olded in the region of the fail%re -lane*

E.-iri(al (orrelations :etween 54' and the -lasti(ity inde+ for nor .ally (onsolidated (lays are shown in ig* 11*$!* This (orrelation is :ased



E)0

215

o

& & 0.

L55n=

K5nn5 9)9Bj5G 6n= S23n> L6==, 54 6l. 9

&

90 o A

5@@@ --- 5 , o5 5 ? o .

6...l*'

>> **** K K > I >?e g *** *** ---o

*******

----------2. - ------------

M o o=ro551@@55 3

3 5 T 55

(a $35e*

-- ---o-------------

1

5555555oo5555

Q LQ A1565 Bj5G 6n= S23n>, 90

1 L k >46n=6= =5126423n .S. %61, 9

8 0 $3< 2 )0 0 70 7 90 1

Pl6>4224 2n=5Y, PI

$2. 11*$! EN226l 35l6423n J54D55n >, 6n= PI 3 426Y26l 3N5>>23n 45>4> 3n n36 l 3n>3l2=645= Gn=2>4GJ5= l6> 645 .S. %61,16!1, 6n= L6==, 54 6 ., 16!!B*

.>..

:

o



11. &treaa"(eforatlon and &trength Characterlatlca 545

on wor< :y /enney 166B, 40err%. and i.ons 16"B, U** Navy 16!1B,and Ladd, et al* 16!!B* in(e there is (onsidera:le s(atter aro%nd the=average line,= yo% sho%ld %se this (orrelation with (onsidera:le (a%tion*However ig* 11*$! is %sef %l for -reli.inary esti.ates and for (he(<ingla:oratory res%lts*

9 ! se 7 C& S45n4 2n En2n552n P6425

Where do we %se the strengthsD deter.ined fro. the C' test As .entioned -revio%sly, the li.iting drainage (onditions .odeled in the tria+ialtest refer to real field sit%ations* C' l3*(nditions are the .ost (riti(al for the

long5ter. steady see-age (ase for e.:an<.ent da.s and the long5ter.sta:ility of e+(avations or slo-es in :oth sof t and stiff (lays* E+a.-les of C' analysis are shown in ig* 11*$7* How yo% a(t%ally go a:o%t .a<ingthese analyses for sta:ility (an :e fo%nd in te+t:oo<s on fo%ndation ande.:an<.ent da. engineering*

o% sho%ld :e aware that, -ra(ti(ally s-ea<ing, it is not easy toa(t%ally (ond%(t a C' test on a (lay . the la:oratory* To ens%re that no -ore -ress%re is really ind%(ed in the s-e(i.en d%ring shear for .aterials withvery low -er.ea:ilities, the rate of loading .%st :e very slow* Toe ti.ereF%ired to fail the s-e(i.en ranges fro. a day to several wee<s 4isho-and Hen<el, 16"$B* %(h a long ti.e leads to -ra(ti(al -ro:le.s in thela:oratory s%(h as lea<age %f vahes, seals, and the .e.:rane that s%rro%nds

the sa.-le* ConseF%ently, sin(e it is -ossi:le to .eas%re the ind%(ed -ore -ress%res in a (onsolidated5%ndrained CUB test and there:y (al(%late the ef fe(tive stresses in the s-e(i.en, CU tests are .ore -ra(ti(aV for o:tainingthe eff e(tive stress strength -ara.eters* Therefore C' tri a+ial tests are notvery -o-%lar in .ost soils la:oratories*

.9." C3n>3l2=645=-n=62 n5= C T5>4 B56123

As the na.e i.-lies, the test s-e(i.en is first (onsolidated drainagevalves o-en, o:vio%slyB %nder the desired (onsolidation stresses* As :efore,these (an either :e hydrostati( or non5hydrostati( (onsolidation stresses*

Af ter (onsolidation is (o.-lete, the dra.age valves are (losed, and thes-e(i.en is loaded to fail%re in %ndrained shear* 8f ten, the -ore water -ress%res develo-ed d%ring shear are .eas%red, and :oth the total andeffe(tive stresses .ay :e (al(%lated d%ring shear and at fail%re* Th%s thistest (an either :e a total or an eff e(tive stress test* This test is so.eti.es(alled the )5test. D

Total, ne%tral, and effe(tive stress (onditions in the s-e(i.en d%ringthe several -hases of the CU test are shown in ig* 11*$6* The sy.:ols are

*5 J

* 5K5 * 55 ,J



- -

548 &heer &trength of &enda end Cle@

Q 55 5555 K 5 Q':'-?-

6l EJ6n5n4 3n>4G45= 15 >l3Dl, 2n l65>,

r =62n5= >56 >45n43 l6 35

J E64 =6 D24 >456=->4645 >55N65

T 2n >24G =62n5=>56 >45n4

3

5 E Y616423n 3 n64G6l >l3N5 2n l6

$2. .*8 S3n5 5Y6Nl5> 3 C& 6n6l>5> 3 l6> 645 L6==, 9J.

the sa.e as we %sed :efore . ig* 11*$#* lhe general (ase of %neF%al(onsolidation is shown, :%t ty-i(ally for ro%tine tria+*ial testing the s-e(i5

.en is (onsolidated hydrostati(ally %nder a (ell -ress%re whi(h re.ains(onstant d%ring shear* Th%s,

Lil(e the C' test, the aSIal stress (an :e in(reased in(re.etally or at a(onstant rate of strain* At fail%re, then, the test in ig* 11*$6 is rather (onventional in that the a+ial stress is in(reased to fail%re a+ial (o.-res5

Q -



TOTAL, a %ETRAL, G E$$ECTIVE, a3

A4 45 5n= 3 3n>3l2=6423n a e / e5=3>4642 3 n3n-=3>4642 :

o#H Ive + o + (u

&G2n >56 6Y26l

A4 62lG5:

k AG

e

a a AG

a ave $a 1 AG

/ a4 ,

k AG1

In N6425, 43 5n>G5 00 >64G6423n, D2 2> n55>>6 333= 56>G55n4> 3 45 N35 D645 N5>>G5, 6 ac p!$ssC!$2> 6NNl25= 43 45 N35 D645. T3 55N 45 554215 3n>3l2=6423n>45>>5> 3n>46n4, 45 4346l >45>>5> =G2n 3n>3l2=6423n 6563=2nl 2n56>5= J 6n 63Gn4 5Y64l 5FG6l 43 45 6NNl25=J6 N5>>G5, D2 2> 45 >65 6> 62>2n 643>N52 N5>>G5J 6 3n>46n4 63Gn4-45 554215 >45>>5> 3n 45 l6 =3 n346n5.

EY6Nl5: IA2426l 55A=2425A>.'24l'l J65 N5>>G5:

$2. .*9 C3n=2423n> 2n >N525n =G2n 6 3n>3l2=645=-Gn=62n5= 6Y26l3N5>>23n C 45>4.

.j

<^- 54<:NO



=9993*9$9E92A9 9 w ;<.pa<t **B..:::..;. K



548&hear &trength of &enda and Cla@a

sion testB* Note that the e+(ess -ore wate1 -t ess.e mu develo-ed d%ringshear (an either :e -ositive that is, in(reaseB or negative that is, de(reaseB*This ha--ens :e(a%se the sa.-le tries to either (ontra(t or e+-and d%ringshear* Re.e.:er, we are not allowing any vol%.e (hange an %n(tr[ined

testB and therefore no water (an flow in or o%t of the s-e(i.en d%ringshear* 4e(a%se vol%.e (hanges are -revented, the tendency towards vol%.e

(hange ind%(es a -ress%re in the -ore water* I the s-e(i.en tends toeontraet or (onsolidate d . ing shear, then the ind%(ed -ore water -ress%re

is positive. I4 wants3 to (ontra(t and sF%ee&e water o%t of the -ores, :%t(annot@ th%s the ind%(ed -ore water -ress%re is -ositive* Positive -ore

-ress%res o((%r in nor.ally (onsolidated (lays* I the s-e(i.en tends to

e+-and or swell d%ring shear, the ind%(ed -ore water -ress%re is negative.T4 wa nts to e+-and and draw DNater into the -ores, :% t (annot, th%s the -ore water -ress%re de(reases and .ay even go negative that is, :elow&ero gage -ress%reB* Negative -ore -ress%res o((%r in over(onsolidated

(lays* Th1@s, as noted in ig* 11*$6, the direction of the ind%(ed -ore water -ress%re au is i.-ortant sin(e it dire(tly affe(ts the .agnit%des of theeff e(tive stresses*

Also yo% .ight note that in a(t%al testing the initial -ore water -ress%re ty-i(ally is greater than &ero* In 0de1 to ens%1e f%ll sat%ration, a bac!

pressure u is %s%ally a--lied to the test s-e(i.en ig* 11*$6B* When a :a(< -ress%re is a--lied to a sa.-le, the (ell -ress%re .%st also :ein(reased :y an a.o%nt e F%al to the :a(< -ress%re so that the ef

fe(tive (onsolidation stresses will re.ain the sa.e* in(e the effe(tivestress in thes -e(i.en does not (:aoge, l:e slrength of tl%9 s-e(i.en is not s%--osedto :e (hanged :y the %se of :a(< -ress%re* In -ra(ti(e this .ay not :ee+a(tly tr%e, :% t the advantage of having 00 sat%ration for a((%rate.eas%re.ent of ind%(ed -ore water -ress%res far o%tweighs any disadvantages of the %se of :a(< -ress%re*

Ty-i(aJ stress5strain, ilu, and oW@o3 (%rves for CU tests are shown inig* 11*#, for :oth nor.ally and over(onsolidated (lays* Also shown for (o.-arison is a stress5strain (%rve for an over(onsolidated (lay at loweffe(tive (onsolidation stress* Note the -ea<, then the dro-5off of stress as

strain in(t eases wor<5sof tening .aterial, 1g* 1*2B* l he -ore -ress%revers%s strain (%rves ill%strate what ha--ens to the -ore -ress%res d%ringshear* l:e nor.ally (onsolidated s-e(i.en develo-s -ositive -ore -res s%re*In the over(onsolidated s-e(i.en, after a slight initial in(rease, the -ore -ress%re goes =negative=5in this (ase, negative with res-e(t to the

:a(< -ress%re C > Another F%antity that is %sef %l for analy&ing test res%lts isthe -rin(i-al effe(tiveB stress ratio o;Qo#* Note how this ratio -ea<s eatly,

0%st li<e the stress d;fferen(e (%rve, for the over(onsolidated (lay*i.ilar test s-e(i.ens having si.ilar :ehavior on an eff e(tive stress :asis willhave si.ilarly sha-ed o;Qo# (%rves* They are si.-ly a way of nor.al5



11. &tre"(eforatlon and &trength Characterltlc 549

8ver(onsol idatedat h igh a c

Nor.all y(anso 1dated

55K K 8ver(onsol idatedat l ow a c

*1*% Nor.al l y

T .

XX 55

XX

X 5

XX 8ver(onsol idated

8ver(onsol idated

(onsol idated

Note9 or hydrostati( (onsol idation, a4 la at the start of the test@for non5hydrostati( (onsol idati on , a4 la 1*

$2. .!0 TN26l a, il.u, 6n= a4/ a G15> 3 n36ll 6n= 3153n>3l2=645= l6> 2 G= 625= >2,56 C 45>4.

i&ing the stress :ehavior with res-e(t to3 the effe(tive .inor -rin(i-al stressd%ring the test* o.eti.es, too, the .a+i.%. of this ratio is %sed as a(riterion of fail%re* However, in this te+t we will (ontin%e to ass%.e fail%reo((%rs at the .a+i. %. -rin(i-al stress differen(e (arn-ressive strengt:B

What do the Gohr fail%re envelo-es loo< li<e for CU tests in(e we(an get :oth the total and effe(tive stress (ir(les at fail%re for a CU testw:en we .eas%re the ind%(ed -ore water -ress%res, it is -ossi:le to define

,* X

?''

G



-- ---- --?- ::Q:Q&''.Q ':''·



S56 S45n4 3 S6n=> 6n= Cl6>

the Gohr fail%re envelo-es in ter.s of :oth total and effe(tive stressesfro. a series of tria+ial tests (ond%(ted over a range of stresses, asill%strated in ig* 11*#1 for a nor.ally (onsolidated (lay* or (larity,only one set of Gohr (ir(les is shown* These (ir(les are si.-ly -lottedfro.* the stress (onditions at fail%re in ig* 11*$6* Note that the effe(tivestress (ir(le is dis-la(ed to the left, towards the origin, for the nor.ally(onsolidated (ase, :e(a%se the s-e(i.ens develo- -ositive -ore -ress%red%ring shear and o3 o 5 Il.u. Note that :oth (ir(les have the sa8e

dia8eter :e(a%se of o%r definition of fail%re at .a+i.%. o1 5 o# B oi 5 oB* o% sho%ldverify that this eF%ation is tr%e* 8n(e the two fail%re envelo-es are drawn,the Gohr5Co%lo.: strength -ara.eters are readily defina:le in ter.s of

:oth total e, L, or so.eti.es @!, (=!B and effe(tive stresses e3, F,3B* Again, aswith the C' test, the envelo-e for nor.ally (onsolidated (lay -asses

G or -ra( i(a -%r-oses e (an eta<en to :e &ero, whi(h is also tr%e for the total stress e -ara.eter* Note

T

' ''''&!:>181

5', c 1 == 8 a a

T1 555555 A% 5 1 ***55 5"----

>45>>5> 3 6 n36ll 3n>3l2=645= l6.

the total stresses, and the effe(tive stress (ir(le at fail%re is shifted to the2 ig* e s o e

effe(tive stress (ir(le at fail%re to the right so.eti.es .eans that the ,' isess an ^IJrD y-1(a y, t e (o.-lete Gohr fail%re envelo-es are de ter.ined :y tests on several s (i.ens (onsolidat



11. &lreu"(eforetlon end &trength Characterltlc 771

G

o, o'

$2. .!* M3 2l5> 64 62lG5 6n= M3 62lG5 5n15l3N5> 3 J344346l TB 6n= 554215 EB >45>>5> 3 6n 3153n>3l2=645= l6.

stress range of the field -ro:le.* ig%re 11*## shows the Gohr fail%reenvelo-es over a wide range of stresses s-anning the -re(onsolidationstress* Th%s sorne of the s-e(i.ens are over(onsolidated and others arenor.ally (onsolidated* o% sho%ld note that the =:rea<= in the total stressenvelo-e -oint M : o((%rs ro%ghly a:o%t twi(e the a4 for ty-i(al (laysHirs(hf eld, 16"#B* The two sets of Gohr (ir(les at fail%re shown in ig*

G W55 *C*55555r 5 N

CQ

-555Q

T

Q 5********

5a

5t &

555@,, T

QQ

+ G +

O, o'

$2. .!! M3 62lG5 5n15l3N5> 315 6 6n5 3 >45>>5> >N6nn2n 45N53n>3l2=6423n >45>>

5

o4



77&hear &trength of &and and Cla@

1 1 ## (orres-ond to the hvo tests show n in ig* 11*# 0 the =nonnally(onsolidated= s-e(i.en and the s-e(i.en **over(onsolidated at low oc.33

o% .ay have not;(ed that an angle a was indi(ated on the effe(tivestress Gohr (ir(les of igs* 11*#1, 11*#$, and 1I9##* 'o yo% re(all the Gohr fail%re hy-othesis where;n the -oint of tangen(y of the Gohr fail%reenvelo-e with the Gohr (ir(le at fail%re defined the angle of the fail%re

-lane in the s-e(i.en l not, reread e(* 1*2* in(e we :elieve that theshear strength is (ontrolled :y the effe(tive stresses in the s-e(i.en atfail%re, the Gohr fail%re hy-othesis is valid in ter.s of effective

stressesonly.

tress -aths for the two tests of ig* 11*## are shown in ig* 11*#2* Toetests are F%ite (onventional, hydrostati(ally (onsolidated, a+ial (o. -ressiontests* Let3s loo< first at ig* l l*#2a, the shess -aths for the test on nor.ally(onsolidated (lay* Toree stress -aths are shown, the eff e(tivestress -ath EPB, the total stress -ath TPB, and the total5%

stress -aths,

T 5 % B P* The -aths :egin on the hydrostati( a+is at val%es of p eF%al tothe total and effe(tive (onsolidation -ress%res, res-e(tively* Note that

p p3 C > The total stress -a t: for a+ial (o.-ression and (onstant eell -ress%re is the straight line in(lined at 2> as shown* in(e -ositive -ore -ress%res develo- in the nor.ally (onsolidated (lay, the EP lies to theleft of the TP :e(a%se o3 / o 5 $u. Toe sit%ation is dire(tly analogo%sto that

shown in ig* 1*$2* Note that B1 is the sa.e for ali three stress -aths :e(a%se we define the fail%re at the .a+i.%. a1

a#

B ig%re 1 1 #2a issi.ilar to ig* 1*$2, e+(e-t the initial (onsolidation in that (ase wasnon5hydrostati( ( S 1B*

in(e the over(onsolidated (lay was tested in a+ial (o.-ression witha (onstant hydrostati( (ell -ress%re, the two total stress -aths of ig*11*#2: are e+a(tly li<e those of ig* l 1*#2a5strai t lines in(lined at 2>to t e y rostati( a+is* 4%t the sha-e of the EP is signifi(antly different*Loo< :a(< at the dev elo-.en t of -ore -ress%re with a+ial strain for this test in ig* 11*#* ee how it starts o%t slightly -ositive, then goes waynegative a(t%ally, less than %0 , as was e+-lained -revio%slyB* Toe sa.ething ha--ens to the EP in ig* 11*#2:* l4 goes slightly to the left A % B

of the T 5 C ) P at first, then as the -ore -ress%re :e(o.es in(reasinglynegative, the EP (rosses the T 5 u :P %ntil .a+i.%. L or L is

rea(hed* Again, :e(a%se of the way we define fail%re, B1

1is the sa.e for ali

three stress -aths* 7o% .ay re(all that the EP in ig* 11*#2: for theover(onsolidated (lay has a sha-e si.ilar to that shown in ig* 1*$,e+(e-t that the latter sa.-le was (onsolidated with S

1? 1*

I yo% are still %n(lear a:o%t stress -aths, it wo%ld :e a good idea toreread e(* 1*"*

1

1



-- 2 l'Zll




F

3N & a < N a N, N

P

6

F K l2n5

J

$2. .!" S45>> N64> 3 45 =3>46426ll 3n>3l2=645= 6Y26l 3N5>>25A 45>4> 5A 6 A56ll (5A>6l2El645EI (l6>; :B 515(5A>5l2 El645=l6>.

.9. TN236l V6lG5> 3 45 n=62n5= S45n4 P66545>

Earlier in this se(tion, we gave s%.e ty -i(al val%es fo1 e3 and et,3 de5

ter.ined :y C' tria+ial tests* The range of val%es indi(ated is ty-i(al for ef fe(tive stress strengths deter.ined in CU tests with -ore -ress%re .eas%re.ents, with the following reservation* In o%r dis(%ssion so far, we haveta(itly ass%.ed that the Gohr5Co%lo.: strength -ara.eters in ter.s of effe(tive stresses deter.ioed J CI tests wit: -ore -ressnre Fieas%re.eotswo%ld :e the sa.e as those deter.ined :y C' tests* We %sed the sa.e

*D J

1



%nelo5e at

o - oAt a0 Jo l8a, % nelo5e at

o0 Jo l 8a

Z D

1eronsol ia!e Nor8all7 aosaliate

554 &hear &trength of &and and Cla@

sy.:ols, e3 and 2?3, for the -ara.eters deter.ined :oth ways* This ass%.-5tion is not stri(tly (orre(t* Toe -ro:le. is (o.-li(ated :y alte.ativedefinitions of fail%re* We have %sed the .a+irn%. -rin(i-al stress dif feren(eo - o! B.a+ to define fail%re thro%gho%t this (ha-ter, :%t of ten inthe literat%re and so.eti.es in -ra(ti(e yo% will find fail. e defined inter.s of the .a+irn%. -rin(i-al effe(tive stress ratio oUo9'.a+ whi(h isthe sarne as the .a+i.%rn o:liF%ity EFs* 1512 thro%gh 151!B* 'e-endingon how the stress differen(e and the -ore water -ress%res a(t%ally develo-with strain, these two definitions .ay indi(ate different (3s and F,3s* This ises-e(ially tr%e for sensitive (lays, as shown in ig 11 #

sa.-le N' /---

$

sa.-le

$2. .!) TN26l 62lG5 5n15l3N5> 3 C 45>4> 3n 6 >5n>24216 l6,2llG>4642n 45 554 3 =255n4 62lG5 24526 3n 45 >l3N5 6n= 2n455N43 45 M3-C3Gl3J 62lG5 5n15l3N5 645 L6==, 9J.

40err%rn and irnons 16"B st%died this -ro:lern in sorne detail, and

their res%lts are s%..ari&ed in ig 11 #" Here, "V' as defined at o;Qa#B.a+ and o1 5 o#B.a+ are -lotted vers%s 3Pd, the effe(tive stress -ar a.eter

deter.ined in drained tests* Note that tf,3 fro. the .a+i.wn -riaei-aleffe(tive stress ratio the dotsB is frorn 8> to #> greater than L,d. Also notethat (- at .a+i.%rn -rin(i-al stress differen(e the sF%aresB is less than :oth L,d and L,3 at the rna+i.%. -rin(i-al effe(tive stress ratio* In one (asethe differen(e is a:o%t !>*

Toe -oint is that yo% sho%ld :e (aref %l when st%dying -%:lished dataor engineering test re-orts to deter.ine e+a(tly how the strength tests were(ond%(ted, how fail%re was defined, and how any re-orted Gohr5Co%lo.: -ara.eters were deter.ined*

, *,5D55*t55DD5DDD 55 5



t3>' at o0 oB ) 8a&1

t3>' at o0 - oB l 8a&

.

12

B@`L1;11121B111@1

1`1L

Cla7

Cornwall Cornwall ersi8is Eeal Honon ?slo #reriIsta Hoalen #orne4/ ra88enIern4raten <een <isters Nort 6i$e ?r$ani oston 4l/e Ee78o/t New Waen Wasle8ere

Eiener =e$el

<tate

/6 6 6 6

// / / / / / / / / / /66

6e3erene

enne7

WenIel N.*.9.

Casa$rane an 6iarCasa$rane Wirs3el

<Ie85ton an iso5Worsle

1 $ # 40>, =555>

/ Gn=2>4GJ5= R 53l=5=

$2. .! R5l6423n>2N J54D55n =5452n5= 3 C& 45>4> 6n= '=5452n5= 43 C 45>4> D24 N35 N5>>G5> 56>G5=. TD3 62lG524526 65 2n=2645= 3 45 Gn=62n5= 45>4> 645 Bj5G 6n= S23n>,90.

+++

* D a u a* , s e K



" S56 S45n4 3 S5n=6 6n= Cl66

or the Gohr5Co%lo.: strength -ara.eters in ter.s of total stresses,the -ro:le. of definition of fail%re doesn3t (o.e %-* ail%re is defined atthe .a+i.%. (o.-ressive strength o - 'J B.a+D or nor.ally (onsoli5dated (lays, >/8 see.s to :e a:o%t half of >18) th%s val%es of 1> to 1> or .ore are ty-i(al* The total stress e is very (lose to &ero* or over(onsolidated and (o.-a(ted (lays, >/8 .ay de(rease and e will of ten :e signifi(ant*When the fail. e envelo-e straddles the -re(ons,olida tion stt ess, -1-er inter-retation of the strength -ara.eters in ter.s of total stresses isdiff i(%lt* This is es-e(ially tr%e for %ndist%r:ed sa.-les whi(h .ay havesorne variation in water (ontent and void ratio, even within the sa.egeologi( strat%.*

In the se(tion on ty-i(a l val%es of d(a ioed streogt: -ara roete(s, we

-rovided an e.-iri(al (orrelation for >/8 and PI ig* 11*$!B* These were for nor.ally eonsolidated %ndist%r:ed elays tested in tria+ial eo.-ression,and in fa(t .ost of the tests %sed to develo- this fig%re were CU tests with -ore -ress%res .eas%red* ig%re 11*$! still (an :e %sed for -reli.inaryesti.ates and for (he(<ing la:oratory test res%lts :e(a%se the diff eren(esin >/8 , de-ending on how fail%re is defined, et(*, are less than the s(atter inthe fig%re*

.9. >5 3 C S45n4 2n En2n552n P6425

Where do we %se the CU strength in engineering -ra(ti(e As .entioned

:bfoH, this test, with -ote -ress%res .eas%red, is (o..only %sed todeter.ine the shear strength -ara.eters in ter.s of :oth total and effe( tivestresses* CU strengths are %sed for sta:ility -ro:le.s where the soils havefirst :e(o.e f %lly (onsolidated and are at eF%ili:ri%. with the e+istingstress syste.* Then, for sorne reason, additional stresses are a--hed F%i(<ly,with no drainage o((%rring* Pra(ti(aV e+a.-les in(l%de ra-id drawdown of e.:an<.ent da.s and the slo-es of reservoirs and (anals* Also, in ter.s of effe(tive stresses, CU test res%lts are a--lied to the field sit%ations.entioned in the earlier dis(%ssion of C' tests* orne of these -ra(ti(ae+a.-les are ill%strated in ig* 11*#!*

J%st as wi th C' tests, there are sorne -ro:le.s with CU tests on (lay*or -ro-er .eas%re.ent of the -ore -ress%res ind%(ed d%ring shear,

s-e(ial (are .%st :e ta<en to see that the sa.-le is f %lly sat%rated, that nolea<s o((%r d%ring testing, and that the rate of loading or rate of strainB iss%ffi(iently slow so that the -ore -ress%res .eas%red at the ends of the s-e(i.en are the sa.e as those o((%rring in the vi(inity of the fail%re -lane* As we .entioned, the %se of :a(< -ress%re is (o..on to ass%re1] sat%ration* The effe(ts of the other two fa(tors (an :e .ini.i&ed :y -ro-er testing te(hniF%es, whi(h are des(ri:ed at length :y 4isho- and J5Yen<el 16"$B*

5D5555555D K K,

...



r-

--- ,

11.9 &tre"(eloratlon and &trength Characterltlc 557

J13J#R,-J5. /i/.l3 + JF 6 EnJ6nn5n4 62>5= * >GJ>5FG5n4 43 3n>3l2=6423n

Gn=5 24> 322n6l 524, .

s& 0,,of (o(o eo,(e,-ond@ng 43 3n>3l2=6423n Gn=5steady5state -do,43 =6D=3Dn

J R6N2= =6D=3Dn J52n= 6n 564 =6. %3 =62n653 45 35. R5>5132 l515l 6ll> 3 B - .

r 1 2n>24G Gn=62n5= >56>45n4 3 l6 2n n64G6l>l3N5 N23 43 3n>4G423n3 2ll

5 R6N2= 3n>4G423n 3 6n 5J6n5n4 3n 6 n64G6l>l3N5.

$2. .! S3n5 5Y6Nl5> 3 C 6n6l>5> 3 l6> 645 L6==, 9J.

Another -ro:le., not of ten .entioned, res%lts fro. trying to de ter.ine9the long5ter. or eff e(tive stress strength -ara.eters and the short5te,r. or CU5total stress strength -ara.eters fro. the sa.e test series* Toe rates of loading or strain reF%ired for (orre(t effe(tive stress strength deter.ination.ay not :e a--ro-riate for the short5ter. or %ndrained loading sit%ation*Toe stress5defor.ation and strength res-onse of (lay soils is rate5de-endent@ that is, %s%ally the faster yo% load a (lay, the stronger it :e(o.es* In the short5ter. (ase, the rate of loading 2n the field .ay :eF%ite ra-id, and therefore for (orre(t .odeling of the field

,*,K &K* 5*,,595K,K@ 4 AL

,DD 55595 515==3P==




sit%ation, the rates of loading in the la:oratory sa.-le sho%ld :e (o.-ara5 :le* Th%s the two o:0e(tives of the CU5effe(tive stress test are reallyin(o.-ati:le* The :est thing to do, tho%gh rarely done in -ra(ti(e, wo%ld :e to have two sets of tests, one set tested C' .odeling the long5ter.sit%ation and the other CU set .o(leling the short ter. %n(lraine(l loa(liag*

E9A3PE 11 .11

(215n:

A nor.ally (onsolidated (lay was (onsolidated %nder a stress of 1 <Pa,

then sheared %ndrained in a+ial (o.-ression* The -rin(i-al stress dif ferenee at fail%re was 1 <Pa, and the ind%eed -ore -ress%re at fail.ewas 77 <Pa*

'eter.ine the Gohr5Co%lo.: strength -ara.eters in ter.s of :oth totaland effe(tive stresses aB analyti(ally and :B gra-hi(ally* Plot the total andeffe(tive Gohr (ir(les and fail%re envelo-es* (B Co.-%te F o4f o* :1 and6Q dB 'eter.ine the theoreti(a l a ogle 3 the fail.e -laoe in 45s-e(i.en*

To solve this -ro:le. we need to ass%.e that :oth e3 and cr are neghgt:le*Toen we (an %se the o:liF%ity relationshi-s EFs* 1512 thro%gh 151!B tosolve for B, and 3PrBa * T o %se these eF%ations, we nee^l o .., a4 .. , a

* .. and n , We <now

a*1 1 <Pa and a - a* :J ? J #

1 <Pa* Therefore

E62 / 0- o* :1

` *1 / 1 ` 1 / $ <Pa

a41 / E62 u1 $ 77 1"$ <Pa

ro. EF* 151#,

- C / 1 5 77 / "$ <Pa

B, / * 1arr,s.5

* 1

ar(s.2

12 *>

1

/



11.9 &....."(etoratlon ancl &trength Characterltlc 559

&

1

1

--5555

55T 1

1 1 $ $ # a, o'

$2. EY. .

b. The gra-hi(al sol%tion in(l%ding the fail%re envelo-es is shown in

ig* E+* 11*11* To -lot the total and effe(tive Gohr (ir(les, we wo%ld stillneed to (al(%late 11 , oi

1and *1. The (enters of the (ir(les are at $, 8B

for total stresses and at 11$, 8B for effe(tive stresses*(* The stress ratios at fail%re are

#

1"$ $ "1

"$ * > $

Another way to get these val%es wo%ld J5 to %se EF* 1512*

oi / 1 sin $"*> 1*2 $ "1o! 1 5 sin $"*> * D

-> / 1 si n 12*> 1*$ 1 "!l sin l2*> *! D

d. Use EF* 151, in ter.s of effective stresses9

a1/ 2> ` / 7> fro. the hori&ontal

.9. n3n>3l2=645=-n=62n5= T5>4 B56123

5In this test, the s-eei.en is -laeed in the tria+ial eell with the drainagevalves (losed fro. the :eginning* Th%s, even when a (onfining -ress%re isa--lied, no (onsolidation (an o((%r 2 the sa.-le is 1] sat%rated* Toen,

*J

\



560 &hear &trength of &and and Cla@a

as with the CU test, the s-e(i.en is sheared %ndrained* The sa.-le isloaded to fail%re in a:o%t 1 to $ .in@ %s%ally -ore water -ress%res arenot .eas%red in this test* This test is a total stress test and it yields thestrength in terrns of total stresses* A. Casagrande first (alled this test the\ test for =FK%i(<=B sin(e the sa.-le was loaded to faiB.e .%(h .oreF%i(<ly than in the 5test*

Total, ne%tral, and effe(tive stress (onditions in the s-e(i.en d%ringthe several -hases of the UU test are shown in ig* 11*#7* The sy.:ols areas %sed :efore in ig* 11*$# and 11*$6* The test ill%strated in ig* 11*#7 is

TOTAL a %ETRAL, G E$$ECTIVE, a3

l5=2645l 645>6Nl2n; J5356NNl 26423n 3 5llN5>>G5:

0-0

%,

5>2=G6l 6N2ll6N5>>G5.645>6N 2n

0 13 / ur

-N X & C ,

A45 6NNl26423n 3=3>4642 5llN5>>G5 S /

00:

5a c / %,

-G, .G / -G, Ac

00 S, :. B -

&G2n 6NNl26423n3 6Y26l l36=:

-G, Ac k uU

aa , a, # B ,

A t 62lG 5.

-G, 8( k uUZ

$2. .!8 C3n=2423n> 2n 45 >N525n =G2n 45 Gn3n>3l2=645=-.$=62$5:I 6Y26l 3N5>>23n 45>4



.9 S45>>-&5l364l3n 6n= S45n4 C6645l>4l> )

F%ite (onventional in that hydrostati( (ell -ress%re is %s%ally a--lied,and the s-e(i.en is failed :y in(reasing the a+ial load, %s%ally at a(onstant rate of strain* As with the other tests, the -rin(i-al stressdifferen(e at fail%re is o1 5 #B.a+D

Note that initially for %ndist%r:ed sa.-les, the -ore -ress%re isnegative, and it is (alled the residual pore pressure 5u,, whi(h res%lts fro.stress release d%ring sa.-ling* in(e the effe(tive stresses initially .%st :egrea ter t:ao &ero otherwise the s-e(i.en wo%ld si.-ly disintegrateB andthe total stresses are &ero at.os-heri( -ress%re / &ero gage -ress%reB, the

-ore -ress%re .%st :e negative* ee ig* 1*$1 for insight into thesa.-ling -ro(ess*B When the (ell -ress%re is a--lied with the drainagevalves (losed, a -ositive -ore -ress%re tS uc is ind%(ed in (he s-e(i.en,

whi(h is e+a(tly eF%al to the a--lied (ell -ress%re eB All the in(rease inhydrostati( stress is (arried :y the -ore water :e(a%se 1B the soil is 1]sat%rated* $B thl (o.-ressi:ility of the water and individ%al soil grains iss.all (o.-ared to the (o.-ressi:ility of the soil str%(t%re, and #B there isa %niF%e relationshi- :etweeo the effe(ti*ve :yd rosta ti( stress aod the vaidratio Hirs(hfeld, 16"#B* N%.:er 1 is o:vio%s* N%.:er $ .eans that novol%.e (hange (an oee%r ttnless w ater is allowed to flow o%t of or intoBthe sa.-le, and we are -reventing that fro. o((%rring* N%.:er # .eans :as1(ally that no se(ondary (o.-ression vol%.e (hange at (onstanteffe(tive stressB ta<es -la(e* o% .ay re(all fro. the dis(%ssion of theass%.-tions of the Ter&aghi theory of (onsolidation Cha-ter 6B that the

saroe assn.-tioo was reF%ired9 that is* that the void ratio and effe(tivestress were %niF%ely related* Th%s there (an :e noD (hange 2n void ratiowitho%t a (hange in effe(tive stress* in(e we -revent any (hange in water (ootent, the void ratio and effe(tive stress re.ain the sa.e*

tress (onditions d%t ing a+ial loading and al fail%te ate si.ila1 43

those for the CU test ig* 11*$6B* They .ay a--ear to :e (o.-le+, :%t if yo% st%dy ig* 11*#7 yo% w1Il see that the 8 8 (ase 1s as readliy %nder standa:le as the CU (ase*

Ty-i(ally, stress5strain (%rves for UU tests are not -arti(%larly dif fer ent froro CJ J ar C' stress5strain (%rves for the sa.e soils* or %ndist%r:edsa.-les, es-e(ially the initial -ortions of the (%rve initial tangent .od%l%sB, are strongly de-endent on the Luality of the %ndist%r:bd sa.-les*

Also, the sensitivity e(* $*!B affe(ts the sha-e of these (%rves@ highlysens.ve (lays have shar-ly -ea<ed stress5stra. (%rves* TI1e .a+i.%.stressD differen(e of ten o((%rs at very low strains, %s%ally less than *]*orne ty-i(al UU stress5strain (%rves are shown . 1g* 11*#6*

Toe Gohr fail%re envelo-es for UU tests are shown in ig* 11*2 for 1] sat%rated (lays* All test s-e(i.ens for f%lly sat%rated (lays are-res%.a:l y at the sa.e water (ooteot aod void ratioB, aod oooseF%entBythey will have the sa.e shear strength sin(e there is no oonsolidation



q

$2. .!9 TN26l >45>>->462n G15> 3 A 53l=5= 6n= >3n53N645= l6>, 8 5=2G >5n>24215 Gn=2>4GJ5= l6, 6n= C 2l>5n>24215 Gn=2>4GJ5= l6.

T

& Tt / C

M3 62lG5 5n15l3N5total stressB

555555555555*Z*9* *****,,K ****,* >O & o

1 --_._ _._ _. --I A6 - a total 6

a

& 5 ^ 1]55555^ 11 5555 1]5555

a

J

$2. ."0 M3 62lG5 5n15l3N5> 3 45>4>: 6 00 >64G645= l6; JN6426ll >64G645= l6.

7$



A/

(S

Qell


allowed* Therefore all Gohr (ir(les at fail%re will have the sa"$ dia.eter and the Gohr fail%re envelo-e will :e a hori&ontal straight line see ig*1*6(B* This is a very i.-ortant -oint* I yo% don3t %nderstand it, refer again to ig* 11*#7 to see that in the UU test the effe(tive (onsolidationstress is the sa.e thro%gho%t the test* I all the sa.-les are at the sa.ewater (ontent and density void ratioB, then they will have the sa.estrength* Toe UU test, as -revio%sly .entioned, gives the shear strength inter.s of total stresses, and the slo-e F,! of the UU Gohr fail%re envelo-e iseLual to Mero. The inter(e-t of this envelo-e on the T5a+is defines the totalstress strength -ara.eter e, or & W/ e, where & Wis %ndrained shear strength*

or -artially sat%rated soils, a series of UU tests will 5define aninitially (%rved fail%re envelo-e ig* 11*2:B %ntil the (lay :e(o.es

essentially 1] sat%rated d%e si.-ly to the (ell -ress%re alone* Eventho%gh the drainage valves are (losed, the (onf ining -ress%re will (o.-ressthe air in the voids and de(rease the void ratio* As the (ell -ress%re isin(reased, .ore and .ore (o.-ression o((%rs and event%ally, when s%ffi(ient -ress%re is a--lied, essentially 1] sat%ration is a(hieved* Toen, aswith the (ase for initially 1] sat%rated (lays, the Gohr fail%re envelo-e :e(o.es hori&ontal, as shown on the right side of ig* 11*2:*

Another way of loo<ing at the (o.-ression of -artially sat%rated(lays is shown in ig* 11*21* As the (ell -ress%re is in(reased in(re.entally,

$2. ." R5>Gl4> 3J462n5= 3 6 PH 45>4 3n 6 N6426ll >64G645=3N645= l6 645 S5N43n, 9)", 6n= H2>5l=, 9!.

5 - .. 55555 5 -



55555D5D555555555

5M &hear &trength of &anda and Cla0

the .eas%red in(re.ent of -ore -ress%re in(reases grad%ally %ntil at sorne -oint for every in(re.ent of (ell -ress%re added, an eF%al in(re.ent of -ore water -ress%re is o:served* At this -oint, the soil is 00 sat%ratedand the solid e+-eri.entalB (%rve :e(o.es -arallel to the 2> line shownin the fig%re*

In -rin(i-ie, 24 is -ossi:le to .eas%re the ind%(ed -ore water -res5s%res . a senes of 8 8 tests altho%gh 1t 1s not (o..only done* in(e theeffe(tive stresses at fail%re are independent of the total (ell -ress%resa--lied to the several s-e(i.ens of a test series, there is only one ## effe(tive stress Gohr (ir(le at fail%re* This -oint is ill%strated in ig* 11*2$* Note that no .atter what the (onfining -ress%re for e+a.-le, et> oc

,

et(*B, there is only one effe(tive stress Gohr (ir(le at fail%re* Toe .inor

effe(tive -rin(i-al stress at fail%re o4.1 ) is the sa.e for ali total stress(%eles shown . the fig%re* in(e we have only one effe(tive (ir(le atfail%re, stri(tly s-ea<ing, we need to <now :oth F,' and e3 in advao(e in order to draw the Gohr fail%re envelo-e in ter.s 3 effe(tive stresses for the UU test* We (o%ld -erha-s .eas%re the angle of the fail%re -lane inthe failed UU s-e(i.ens and invo<e the Gohr fail%re hy-othesis, :%t aswas dis(%ssed in e(* 1*2, there are -ra(ti(a -ro:le.s with this a--roa(h*I4 sho%ld also :e noted that the angle of in(lination of the fail%re -lane a, shown . 1g* 11*2$ is defined :y the effe(tive stress envelo-e* 8therwise9as indi(ated in ig* 1*6( and EF* 151, theory wo%ld -redi(t a to :e 2>

1

& Gohr fail% reenvelo-es9

TG7 / C Q

$

4 - ......... X. X.X .....X.....X .....X ,..

o4 (1 5 < t / -G, k 42.G >el

Note9 a t is the sa.e for all three total stress (ir(les

.. ,o, o3

$2. ."* 45>4 5>Gl4>, 2llG>4642n 45 GnlFG5 554215 >45>> M3



11. &tre"(eloratlon and &trength Characterletlca e

inee the strength %lti.ately is (ontrolled or gove.ed :y t:e effe(tivestresses, we :elieve that the -hysi(al (onditions (ontrolling the for.ationof a fail%re -lane in the test s-e(i.en .%st in sorne fashion :e (ontrolled :y the effe(tive stresses a(ting in the s-e(i.en at fail%re* Th%s EF* 151sho%ld :e in ter.s of B, instead of 3 r5

tress -aths for the UU tests of ig* 11*2$ are shown in ig* 11*2#*4ehavior is for a nor.ally (onsolidated (lay, and the val%es of p and B for all three tests are listed in the ta:le :elow the fig%re* R fer to ig* 11*#7 2 ne(essary to verif y Kthese val%es* I the (lay were over(onsolidated, thenfro. yo%r <nowledge of CU :ehavior yo% wo%ld e+-e(t the EP to have asha-e si.ilar to those of ig* 11*#2:*

F

K l2n5

, / 646n >2n 2?3B

a e r

1

- - Po1 Po$

ln2426l C3n=2423n> A4 $62lG5

T5>4 Pn Fo Pt ;&

A6 Aa,

n n o$ -

'5 A6 *6 A6

>45>>5> 1 e G* $

/0JK f ' :uc2 -,* OH* o * $

- - ; ;&

>45>>5>

AII %,

Aa *(%, ,-***%, -1,.o * *

$2. ."! S45>> N64>l3 45>4> 3n 6 n36ll 3n>3l2=645= l6.S65 45>4> 6> 2n $2. ."*.

.j

?

- .

1



.9.8 TN26l V6lG5> 3 S45n4>

The %ndrained strength of (lays varies widely* 8f (o%rse, 3Pr is &ero, :%tthe .Kagnit%de of 3&3 (an vary fro. al.ost &ero for e+tre.ely sof t sedi.entsto severa GPa for very stiff soils and soft ro(<s* 8f ten, the %ndrainedshear strength at a site is nor.ali&ed with res-e(t to the verti(al effe(tiveover:%rden stress 0

1at ea(h sa.-ling -oint* Toen the 9Q>1

1ratios are

analy&ed and (o.-ared with other data* This -oint is (overed in .oredetail later in this (ha-ter*

.9.9 n3n2n5= C3N5>>23n T5>4

We (an, thedreti(ally at least* (ond%(t ao 18confined co8pressj8 test 6n=o:tain the UU5total stress strength* This test is a s-e(ial (ase of the test with the (onfining or (ell -ress%re eF%al to &ero at.os-heri( -ress%reB*The stress (onditions in the %n(onfined (o.-ression test s-e(i.en aresi.ilar to tl.se of ig* 11*#7 for the 8 8 test, e+(e-t that oc is eF%al to&ero, as shown in ig* 11*22* I yo% (o.-are these two 2 %res o% Dt at t e e fe(tive stress (onditions at fail%re are identical for :oth tests*And if the effe(tive stress (onditions are the sa.e in :oth tests, then thestrengths will :e the sa.e

Pra(ti(ally s-ea<ing, for the %n(onfined (o.-ression test to y1eld thesa.e strength as the UU test, several ass%.-tions .%st :e satisfied* These

are as follows9l* The s-e(i.en .%st :e 1] sat%rated@ otherwise (o.-ression of

the air in the voids will o((%r and (a%se a de(rease in void ratioand an increase in strength*

$* The s-eei.en .%st n34 (ontain 6n fiss%res, s1lt sea.s, varves, or other defe(ts@ this .eans that the s-e(i.en .%st :e intact , ho.ogeneo%s (lay* Rarely are over(onsolidated (lays inta(t, and ofteneven nor.ally (onsolidated (lays have sorne fiss%res*

#* The soil .%st :e very fine grained@ the initial effe(tive (onfiningstress as indi(ated in ig* 11*22 is the resid%al (a-illa1y stress whi(his a f%ndion of the resid%al -ore -ress%re 5C! this %s%ally .eans

that on/y e/ay soils are s%ita:le for testing in %n(onfined (on9-ression*2* The s-e(i.en .%st :e sheared ra-idly to fail%re@ 24 is a total stresstest and the (onditions .nst he %odrained thro%gho%t the test* I the ti.e to fail%re is too long, eva-oration and s%rfa(e drying willin(rease the5 (onfining -ress%re and too high a strength will res%lt*Ty-i(al ti.e to fail%re is 2 to 1 .in*



A3ter sa85lin$ o

set/50 4e3orea55liation o3 a&ial loa: o -;o D /,

,

o D Ao + /, + A/

/ ri n$ a55l iation

o a D + /, + A/

11

o3 D Aa 1 + /, + A/3

D a 0,At 3ail/re:

o

.9 S45>>-&5364l3n 6n= S45n4 C6645l>4l> 7!

IZIHE a N I JTR A L % ` E ECTI M E a3

-<

-G, k AG

-G, k A% 1

$2. ."" S45>> 3n=2423n> 3 45 Gn3n2n56 3N5>>23n 45>4.

4e s%re to disting%ish :etween %n(onfined co8pressive strength e

e! and the %ndrained shear strength, whi(h is 3! To o! 1

E+AMPLE .*

(215n:

An %n(onfined (o.-ression test was (ond%(ted on a soft (lay* The

s-e(1.en was tn..ed fro. the %nd1st%r:ed t%:e sa.-le and was # ..in dia.eter and 7 .. high* The load on the load ring at fail%re was 12*# N, and the a+ial defor.ation was 11 ..*

R5FG25=:

Cal(%late the %n(onfined (o.-ressive strength and the shear strength of the sof t (lay sa.-le*



)8S55 S45n4 3 S5n=> 5n= Cl5>

S3lG423n:

To (al(%late the stress at fail%re, we have to <now the area of the s-e(1.en A.,. At fail%re it is not eF%al to the original area A , :%t is so.ewhat

greater* In (o.-ression, the s-e(i.en de(reases in height and in(reases india.eter as long as Poisson3s ratio EF* 75##B is greater than &ero*B o, firstto deter.ine the a(t%al area of the s-e(i.en at fail%re* in(e the s-e(i.en

is tested in %ndrained shear, we (an ass%.e t e vo %.e isas a 2 t (ir(%lar e linder*

Th%s $s at 6n strain e9 is

Now we (an (al(%late 4 e area o es-e(i.

1157B

I1%/ %

11 ..Q7 .. *1#!, or 1#*7]* Th%s $s 111 ..$* Now$

the (o.-ressive stress at fail%re is 12*# N Q111 ..$

/ 1$*7 <NQ. <PaB*l we had si.-ly divided :y the original area of the s-e(i.en, we wo%ldhave o:tained 12*6 <NQ.*

, a signifi(ant error*

l4 sho%ld :e noted that the a(t%al shear stress on the fail%re -lane atD D ed shear stren th G e

:e(a%se11

o((%rs on a fail%re -lane whose in(lination is deter.ined :y the11

e e(ttve s resses, as e+ D D D Dand the a--ro+i.ate .agnit%de of asso(iated error is indi(ated in ig*11*2a for the s-e(i.en at fail%re in ig* 11*2:* The .agnit%de of the

3 D D : the (al(%lations in E+a.-le 11*1#*

E+AMPLE .!

11*2a and 11*2:*

ReF%ired9

G



5 5 5 55555555 55555555555



11. &tre"(eforatlon end &trength Cherecterltlc 581

&

-4 ->G7 e Q

15 59@,5L**9**** J K

o, o'

P325

$a,

aG n34 >3Dn

J

$2. .") 6 &255n55 J54D55n G!, 6n= G,- e 6n J Gn3n45=3N5>>23n 45>4 >N525n 645 H2>5l=, 9!.

S3lG423n:

ro. EF* 15",

'.- $ $.oS

/ $ sin $af

ro. EF* 151, NJ - 2> ` F,3Q$* o NJ - ">* Therefore

N1

; J6 5 $ sin 1$> / *2##A*o

. j

******** K ** .& D5 * 5 * o5* 5 ** K a... ,,, 5D@ *K &@*@eK**e9999 5



57, &hear &trenglh of &and and Cla@8

Con(l%sion9 '! 9 / e strength is a:o%t 1] greater than )G 99for cp) / #>*

Note that the error is less for s.aller B, angles* Also note that.o o 5 =

)G 9 $ / $ $ / 3T.a+

The -oint ill%stated :y E+a.-le 11*1# is that the a(t%al shear strength of the fail%re -lane is overesti8ated :y the one5half %n(onfined(o.-ressive strength* The .agnit%de of the error is -ro:a:ly a:o%t 1]at .ost*

Why then does the %n(onfined (o.-ression test a--arently wor< satisfa(torily I4 is far and away the .ost (o..on la:oratory strength test

%sed today in the United tates for the design of shallow and -ilefo%nda%ons in (lay* Part of the answer hes . co8pensat8g errors. a.-ledist%r:an(e es-e(ially tends to red%(e the %ndrained shear strength* Anisotro-y also is a fa(tor, as is the ass%.-tion of -lane strain (onditions for .ost design analyses whereas the real stress (onditions are .ore threedi.ensional* These fa(tors tend to red%(e the %ndrained shear strength sothat the differen(e :etween '!9 / e and '! :e(o.es negligi:le in engineering -ra(ti(e* everal of these -oin ts are dis(%ssed :y Ladd, et al* 16!!B*

11*6*18 O45 W6> 43 &5452n5 45 n=62n5= S56S45n4

There are other ways :esides the %n(onfined (o.-ression test or the UUtria+ial test to o:tain the %ndrained shear strength of (ohesive soils* orneof the field .ethods were .en tioned :riefly at the end of e(* 1*@ other .ethods are %sed e+(l%sively in the la:oratory on %ndist%r:ed sa.-les* Inali the .ethods, loading to fail %re is ass%.ed to ta<e -la(e so ra-idly that%ndrained (onditions e+ist* The res%lt o:tained fro. the test is then (orrelatedwith the %ndrained shear strength '!9.

Ta:le 1 1 5" and igs* 1 1*2" thro%gh 1 1* ill%strate the .ethods(o..only %sed for deter.ining '!9. Ref eren(es are listed in the ta:le if yo%need additional details a:o%t these tests or their inter-retation*

E+(e-t for the P 1, all the held te(hr%F%es hsted . a:le 115" weredevelo-ed in E%ro-e, :%t there has :een in(reasing interest in the. inre(ent years in North A.eri(a Ladd, et al*, 16!!B* The (onditions for arelia:le %n(onfined (o.-ression test are not of ten .et* Gore so-histi(atedla:oratory testing te(hniF%es are attra(tive :%t in(reasingly e+-ensive*a.-ling of -oor VUality, %nfort%nately the r%le rather than the e+(e-tionin the United tates, (an signifi(antly affe(t the .eas%red shear strength*orne soils s%(h as stiff fiss%red (lays are diffi(%lt if nt i.-ossi:le to even



H524 M6Y2G3 16n5> G9

P6

16 # $

$

48 $

J

$2. ." T316n5 TV: 6 S46n=6= 3=5l >3Dn 3n 24> >2=5. T5345 4D3 16n5>, D2 6n J5 64465= 43 45 >46n=6= T316n5,65 3 15 >34 3 15 >42 l6>. J SN56G3n> 3 45 44n5516n5>. P3436N 3G45> 3 S32l45>4, ln., E16n>43n, lll2n32>.

.j



'()*+ 11"4 L6J3643 6n= $25l= M543=> 3 &5452n2n Gi

No* Test Use ig* No* Re.ar<s

Torvane La:, 11*2" Hand :eld@ (ali:rated s-ring@ F%i(<@TV field G>5= on t%:e sa.-les or the sides

of e+-loratory tren(hes, et(*a.-le tested is seen*

$ Po(<et La:, 11*2! a.e as a:ove, e+(e-t s-ring is 6l2-

PPB O- 211) 8·

(one test t%:e sa.-les* E de-ends on (one angleCB and .ass*

2 Mane shear La:, 11*26 Mario%s si&es and (onfig%rations avail5 test MTB field a:le for :oth field and la: %se* HeightQ

dia.eter ratio HQ'B 5 $ for fieldvanes@ HQ' 5 1 for la: vanes* 8nlyla: vane sa.-le is seen*

2 tandard ield 11*1 A standard =s-lit5s-oon= sa.-ler is -enetration driven :y a "#* <g ha..*er falling *!".*test PTB Toe n%.:er of :lows reF%ired to drive the

sa.-ler *# . is (alled the standard

'ist%r:ed sa.-le o:tained*" '%t(h (one ield 11*$ A "> (one with a -ro0e(ted area of 1 (.l

-enetro.eter is -%shed at 1 to $ .Q.in* Point resistan(eCP1B Lc and fri(tion on the fri(tion sleevef,

are .eas%red either ele(tri(ally or .e(hani(all *

Press%re.eter ield 11*# A (ylindri(al -ro:e is inserted in a =2llPGTB hole .ay :e seH5:oringB* Lateral

-ress%re is a--lied in(re.entally to sideof :ote*

7 (rew -late ield 11*2 Toe -late is s(rewed down to the desired (o.-resso5 testing de-th@ hydra%li( -ress%re is a lied.eter in(re.entally and the settle.ent is o:served@PCB (ontin%e loading %ntil the :earing

(a-a(ity of the soil is rea(:ed*6 Iowa :orehole ield 11* 'evi(e is lowered into a :ore:ole and e+5

shear test -anded against the side walls o,*B* Toen4=IB entire .e(:anis. is -%lled fro. gro%nd s%r5

E 1) . tagetest res%lts are G>5= to -lot Gohr diagra.

to 1 <Pa*

572



TA,E 11"6 3n4.4est or

Li.itations Referen(es

Mery sof t to stiff(lays

* Mery sof t to stiff

Cohesive soils witho%t -e::les,fiss%res, et(* Test only a s.alla.o%nt of soil near the s%da(e*8nlB ro%gh ealihratiea 'll'Í4 EJ .

a.e as a:ove*

# Mery softto

soft (lays

2 oft tostiff(lays

5 ran%lar soils

All soil 4N5>

e+(e-t verycoa1&e

gran%lar soils

a.e as a:ove, e+(e-t good (orrelation with *,* on soft, sensitive

(lays*Gay overesti.ate G 9 see Z59l,B

11*for (orre(tion fa(tor for very sof t(lays* Unrelia:le readings 2 vaneen(o%nters sand layers, varves,stones, et(*, or if vane rotated 433

ra-idly*Mery ro%gh (orrelation with *,* for

(ohesive soils* 4o%lders 6n(a%se -ro:le.s* Res%lts aresensitive to test details*

4o%ldets (a%se -,o:le.s* ReF%ireslo(al (orrelation for soft (lays*

Hans:o 16!B

Cadling and 8denstad 16B40err%. 16!$B(h.ert.ann 16!BATG 167B ' $!#Ladd, et al* 16!!B

AI G 167B ' 17"de Gello 16!1B(h.ert.ann 16!B/ova(s, et al* 16!!B

anglerat 16!$B

E8PT 16!2B(:.ert.ann 16!BLadd, et al* 16!!B

ITG 167B 8 #221

! All soil ty-es ReF%ires a (orrelation :etween

-1and 5r 1.

G)nard 16", 16!B(h.ert.ann 16!BLadd, et al* 16!!BRag%elin, et al* 16!7B

7 Ali soil ty-es Gostly %sed to st%dy th( (o.-ressi Jan:% and enneset 16!#Be+(e- t very h0l0ty of gran%lar soils*

(hwa:Git(hell and 8ardener 16!B

(oarse 16!"B fo%nd good agre(.ent

with

(hwa: 16!"B

gran%lar soils the s(r(w -iat( and the vane shear (h.ert.ann 16!B

6 LoessialsiltyB soils

test in -l%ti( w(dish (lays*Cannot J5 %s(d with soils D24 1]

or .ore grav(l or (aving sands*Un(ertain drainage (onditionsd%ring sh(ar .a<es the test diffi(%lt to inter-r(t* Is it C' or CUor so.(w:ere . :etweenB

Wineland 16!B(h.ert.ann 16!B



Z1

574 &heer Stren@th of &enda and Clea

Undrained (o.-ressivestrength read dire(tlyfro. s(ale at

* -res(ri:ed -enetrat ion

5..J3# Pres(ri:ed -enetrationinto (ohesive >32l sa.-le

$2. ." P354 N5n543545 PP, 6 6n=-5l= =5125 D2 2n=2 645>Gn3n2n5= 3N5>>215 >45n4 N3436N 3G45> 3 S32l45>4, ln.,E16n>43n, lll2n32>.

sa.-le* There are statisti(al advantages, too, for having lots of indire(ts%:s%rfa(e inf or.ation o:tained ra-idly and at relatively low (ost -aredwith a feD*v, e+-ensive la:oratory tests on what .a y not eveo :e the wea<estor the .ost (riti(a strata at the site* inally, sorne soil -ro-erties / , -er.ea:ility, defor.ation .od%l%sB (an only :e dete.ned relia:lyin the field*

Toe .a0or disadvantage of the in sit% .ethods is that '! 1 is o:tainedonly indire(tly thro%gh (orrelations with la:oratory tests or :y :a(<(al(%lation fro. theory or a(t%al fail%res* ig%re 1 1* is an e+a.-le of the(orre(tion fa(tor that .%st :e a--lied to the field vane test to o:tain the

:est est;.ate of the in sit% '! 1. 8ther (orrelations are -rovided in thereferen(es for ea(h test listed in Ta:le 115"* Es-e(ially %sef%l are the(orrelations -resented :y U** Navy 16!1B, de Gello 16!1B, and (h.ert.ann 16!B for the PT and '%t(h (one -enetro.eters* or the -ress%re.eter test, see G)nard 16!B and 4ag%elin, et al* 16!7B* In a realsense, then, these tests only give an inde of the a(t%al %ndrained shear strength of the soil*

(o.



>6l5 356>G2n

n =

- 0 eeN5n54643n $55

.rn

Penw at@on*5r 5 G

)<+J 9V

S6Nl5 X 4GJ5

S32l>6Nl5

M6>>

C3n5 6nl5j

=555>

R6n5 3 G+

P6

2 # 15$

1 # $5"#

" " *511

1 " *75$

$2. ."8 P2n2N25 3 45 SD542> 6ll-3n5 45>4 S$C. T5 Gn=62n5=>4256 >45n4 2> N3N3423n6l 43 45 6>> 3 45 3n5 6n= 2n15>5lN3N3423n6l 43 45 N5n546423n >FG65=. T5 45>4 G>4 J5 6l2J645=645 .H6n>J3, 9). S56 >45n4 6n5> 65 46JGl645= 3 45 43G >46n=6=53n5>.

575



A55lietorZ/e, = *ro/n s/r3ae

,,,,-- or to5 o3 sa85le

-

- 6o

---

W ane

--- -- &--------

6

-BIINt.e s.fa(e

J

5 TN26l >25> HI& : El n56542>6l 5ll6>:

L6J: * + *

$25l=: + !8 1 +

U::U / 19 G # r,,*,**

H " T.a+

1# + " & - *: G9 - 2&#

$2. ."9 6 P2n2N25 3 45 16n5 >56 45>4 VST; J 5n= 125D 3 4516n5, >3D2n 45 N3J6Jl5 3n5 3 =2>4GJ6n5 6n= 45 GN4G5 >G656l45 C6=l2n 6= O=5n>46=, 9)0, 5 4N26l 16n5 >5>; = 4535G6l3Gl6> 3 T1, 6>>G2n 6 Gn23 >45>> =2>42JG423n.

+78



r 1 1e / S r 1 vane

y.:ol Referen(e1*2 *55 *,**5 ,5 5`5 5t5 K9K*9*****99** 55l

8 e 40err%. 16!$B

" A Gilligan 16!$B

Ladd and tt 16!2

1*$ '1 laate and Pre:er 16!2B

o La Ro(helle, et al* 16!2B

+ Holt& and Hol . 16!6B Layered and varved (lays

>::

.:2.

G

*$ 40err%.3s 16!$B re(o..ended (%rve¡¡.o

.. 1 "G

*"

o1

o"

o Plasti(ity inde+, PI

$2. .)0 C35423n 643 3 45 25l= 16n5 45>4 6> 6 Gn3423n 3 PI,J6>5= 3n 5J6n5n4 62lG5> 645 L6==, 9), 6n= L6==, 54 6l.,

9.

577

** K *999*@ W 5 5* 55W,, 5*** K *,*,* ,W ** ,22525 *5 WWD5 D5W 5D ***, * D 555*

*o** 1*



W24l2n5

6 J

$2. .) S46n=6= N5n546423n 45>4 SPT: 6 ?>Nl24->N33n? >6Nl5; J=2ll 2 D24 >6Nl5 J52n 2n>545= 2n>2=5 3ll3D >45 6G5 64 . T5>l5515 5nl3>5> 45 !.) 65. H65 2n 45 62>5= N3>2423n 2>>3Dn 64 *. &6D2n 3G45> 3 M3J2l5 &2ll2n C3., ln=26n6N3l2>, ln=2-6n6. P3436N J W*8* K316>.

571



PG> 2nn5 3=> "0 -56>G5 N32n4 5>2>46n5 F(

PG> 2nn5 3=> "0 662n-56>G5N32n4 6n= >2=5 2423n 5>2>46n5, F(

PG> 3G45 3=>

N5n543545;45n NG> =3Dn 43

n5Y4

27 45>42n =5N4

80

"0

:;,.....---C3n5 0 $ B

15# ! ..6

$2. .)* &G4 3n5 N5n543545 CPTB9 6 B556nn 9)! 56n26l3n5 D24 2423n >l5515.

571

,* X



$2423n >l5515

--//-- O R2n >56l

!).

A56 0 $

J

$2. .)* 3n4. &G4 3n5 N5n543545: J C3>> >5423n 3 63=5n 5l5426l N5n543545 D24 >462n-65 l36= 5ll> 43 56>G5J34 45 N32n4 5>2>46n5 6n= 45 >l5515 2423n 645 H3l=5n, 9".

)80



Mise. 3 ill

Hoose sanan si

%.i:::.

<o3 t la7 'a.o

fJ

ense si lts an sans0 sorne $rael

- -

o 0 F( GPaB

1 < PaB

where p[ total over:%rden -ress% re at de-th & Ne (orrelatioo fa(tor l :eari ng (a-a(ity

fa(torB@ range fro. to as high as!, de-ending on the soil de-osit

5

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.9. S5n>242124

Earlier, in e(* $*!, we very generally defined sensitivity as the ratio of the%ndist%r:ed or nat%ral strength of a (lay to its re.olded strength* trength

was lef t -%r-osely vag%e* Now we (an define sensitivity .ore -re(isely, atleast within the -re(ision lirnits of the strength .eas%re.ents the.selves*Us%ally, sensitivity is :ased on the %n(onf ined (o.-ressive strength or the

%n(onfined shear strength &W / e, :%t the la:oratory or field vane shear tests or the wedish fall5(one test (o%ld also :e %sed* ensitivity , istherefore

/ %n(onfined (o.-ress1ve strength%nd1st%r:edB 3 %o(oofined (o.-ressive

strength re.oldedB

r %ndist%r:edB

T re.oldedB

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585

1



7" S56 S45n4 3 S6n=> 6n= Cl6>

I4 sho%ld :e noted that the re.olded strength deter.ination .%st :e at

the sa8e water (ontent5 the nat%ral water (ontent (n5as the water (ontent of the %ndist%r:ed s-e(i.en* Ta:le 115! indi(ates the range of sensitivity val%es (o..only %sed . the 8r%ted tates, where fOghlysens1ttve (lays are rare* ensitive (lays e+ist in other -arts of the world,es-e(ially easte. Canada and (andinavia* 8ther sensitivity s(ales areavaila:le :esidesthose listed in Ta:le 1 15! 6 e+a .-le, <e.-ton and Northey, 16$@40err%., 162B*

TABLE - TN26l V6lG5> 3 S5n>242124

Range of ,

ig%re $*6 shows what ha--ened to a sa.-le of Leda (lay fro.easte. Canada :efore and af ter re.olding* Leda (lays are of ten very stiff in their nat%ral state* Their %n(onfined (o.-ressive strengths .ay :egreater than 1 <Pa, :%t their liF%idity indi(es EF* $5$#B, are of ten $ or .ore* No wonder that their strengths are so low when they are thoro%gh1yre.olded The sa.-Je shown in ig* $*6 had a sensitivity of a:o%t 1Penner, 16"#B whi(h definitely F%alifies it as e+tra F%i(< or even greasedlightningB a((ording to Ta:le 115!* Note that with s%(h (lays, yo% have to%se either a la:oratory vane or fall5(one test to o:tain the re.olded;WEdeo aod / %:ota , 16"$B

Correlations :etween sensitivity and liF%idity inde+ have :een .ade :y several researehers, as show n in ig* 11*"*

.9.* >5 3 45 n=62n5= S56 S45n4 2nEn2n552n P6425

Li<e the C' and CU tests, the andiained 0 UU str ength is a--li(a:le to(ertain (riti(a design sit%ations in engineering -ra(ti(e* These sit%ationsare where the engineering loading is ass%.ed to ta<e -la(e so ra-idly thatthere is no ti.e for the ind%(ed e+(ess -ore water -ress%re to dissi-ate or for (onsolidation to o((%r d%ring the loading -eriod* We also ass%.e thatthe (hange in total stress d%ring (onstr%(tion does not affe(t the in sitn%ndrained shear strength Ladd, 16!1:B* E+a.-les shown in ig* 11*!in(l%de the end of (onstr%(tion of e.:an<.ent da.s and fo%ndations for

Condition

Low sensitive

%*s*

$52

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1Gedi%. sensitive 257 15#Highly sensitive 751" !0%i(< E+tra F%i(<

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11. &trea"(etoratlon and &trength Characterltlc 587

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* # "

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e.:an<*.ents, -iles, and footings on nor.ally (onsolidated (lays* or these (ases, of ten the .ost (riti(aV design* eondition is i88ediately afJer

the a--li(ation of the load at the end of construction : when the ind%(ed -ore -ress%re is the greatest :%t before (onsolidation has had ti.e to ta<e -la(e* 8n(e (onsolidation :egins, the void ratio and the water (ontentnat%rally de(rease and the strength in(reases* o the e.:ari<.ent or fo%nda:onhe(o.es in(reasingly safer with ti.e*

8ne of the .ore %sef%l ways to e+-ress the %ndrained shear strengthis in ter.s of the & W / ratio for nor.ally (onsolidated (lays* o.eti.esthis is (alled the e/ p ratio. In nat%ral de-osits of sedi.entary (lays the

.j

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<o3tela7

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,,55 555555*Q ?Q

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Q Q *Q Q

Q - Q Q K Q. VQ

G 1 Gn=62n5= >56 >45n43 45 3N645= l635

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5 $3342n Nl65= 6N2=l 3n l6 =5N3>24

$2. .) S3n5 5Y6Nl5> 3 6n6l>5> 3 l6 645 L6==, 9J.

%ndrained shear strength has :een fo%nd to in(rease with de-th, and th%sit is -ro-ortional to the in(rease in effe(tive over:%rden stress with de-th*l4 was first o:served :y <e.-ton and Hen<el 16#B and (onf ir.ed :y40err%. 162B that the & W / 1 ratio see.ed to in(rease with in(reasing

-lasti(ity inde+* 40err%.3s 162B res%lts are shown in ig* 11*7 along withthose of several other resear(hers@ in addition, several :est5fit (orrelationsare also shown in the fig%re* There is a lot of s(atter so ig* 11*7 sho%ldonly :e %sed with (a%tion* However, as with ig* 11*$!, s%(h (orrelationsare %sef%l for -reli.inary esti.ates and for (he(<ing la:oratory data*

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o 1 $ # 12

Plasti(ity ind+* PI

$2. .)8 1R5l 23n>2N J54D55n 45 6423 5rJ/ a#., n= Nl6>4224Q 2n=5Y 3n36ll Jn>3l2645= l6>

:

90



Z1

59, &hear &trength of &enda and Cla@

/enney 166B and 40err%. a od iroaos 16"B -resented sorne theoreti(al& W / a4 ratios vers%s PI :ased on the (orrelations of ig* 11*$!,

S 1 , and the

<e.-ton -ore -ress%re N66545 $ to :e dise%ssed in e(* 11*11B* Thesetheoreti(al relationshi-s tended to de(rease rather than in(rease with PI,

:%t the agree.ent was satisfa(tory for PI #* /enney 166B (on(l%dedt:a t 1:/ 0 was essentially inde-endent of PI af ter all@ rather, it -ro:a:lyde-ended on the geologi( history of the (lay*

40err%. and i.ons 16"B also -resented t:e reBa tionshi- :etween

&J/ a@ and liF%idity inde+ LIB for sorne Norwegian .arine (lays, as shownin ig* 11*6* As yo% <now fro. ig* 11*", the F%i(< (lays are those D24very high LI3s* Therefore it a--ears that Norwegian F%i(< (lays have a

&W/ a@ ratio of a:o%t *1 to *1**2

5 =1*5 13

*#

*$

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3o

* # 2

LiF%idi ty inde+, LI

$2. .)9 R5l6423n>2N J54D55n 5r, Qa.4, 6n= l2FG2=24 2n=5Y 3 %3D526nl6> 645 Bj5G 6n= S23n>, 90.

o% sho%ld :e aware of the fa(t that the & W / ratio de-ends strongly

on the total stress -ath* This -oint is dis(%ssed by 40err%. 16!$B 6n=

Ladd, et al* 16!!B, a.ong others* In other words, yo% -ro:a:ly will o:taindiff erent val%es of &W/ a4 , de-ending on whether yo% r%n field vane tests,a+ial (o.-ression or a+ial e+tension tria+ial tests, or dire(t si.-le sheartests*

o.eti.es it is :etter te nor.ali&e the %ndrained sheat strengt: wit:

res-e(t to the effe(tive conso/idatin -ress%re o ( or the -re(onsolidationstress a4 if the (lay is slightly over(onsolidated* or these soils the%ndrained strength is really (ontrolled :y the eff e(tive (onsolidation -ress%rerather than the e+isting effe(tive over:%rden stress* 40err%. 16!$B hy -othesi&ed that the ra tio :etweeo o4 and oe wo%ld vary with PI, as shownin ig* 11*"a* o5(alled yo%ng= (lays are nor.ally (onsolidated re(entsedi.ents, th%s they haven3t had ti.e to :e over(onsolidated :y any of the fa(tors listed 2n Ta:le 751* 8n the other hand, 33aged= (lays areslightly over(onsolidated, and 40err%. fo%nd that the a.o%nt of over(onsolida tion in(reased so.ewhat with the PI ig* 11*":B* Toeres%lting effe(t on

5 55555 5D5555555D5555D

1

1

1



11. &tren"(eforlon and &trength Characterlatlc 71

the strenhiwas indi(ated :y the dashed (%rves* la:eled **40err%. 16!$B=in ig* 11* 7*

Re(al fro. the dis(%ssion of the vane shear test that 40err%. 16!$B -ro-osed a (orre(tion fa(tor for the vane shear test :ased on a st%dy of a(t%al e.:an<.ent fail%res ig* 11*B* or (onvenient referen(e, thisfig%re is re-rod%(ed witho%t all the data -oints as ig* 11*"(*

Gesri 16!B dis(ovet ed a vet y inter esting relationshi- :etween all

these o:servations* Co.:ining igs* 11*"a and 11*": Gesri o:tained ig*11*"d, 5rW/ o4 vers%s PI, whi(h shows essentially the sa.e :ehavior for **aged= and =yo%ng= (lays* Now a--ly 40err%.3s (orre(tion fa(tor X. for the vane shear test to o:tain the in sit% strengths@ the res%lt is ig* l l *"e*In other words, & W / o4c Br@eld is al.ost a (onstant eF%al to *$$ and inde-en

dent of PI There is great %n(ertainty in s%(h a (on(l%sion :e(a%se of thes(atter in the e.-;ri(aV relationshi-s %-on whi(h it is :ased, and therelationshi-s shown in igs* 11*"d and l l*"e .ay :e only a (oin(iden(e*

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&hear &trength of &and and Cla@592

range for sof t sedi.entary (lays has tre.endo%s -ra(ti(a 1.- 1(a 1ons' ., .In Cha-ter 7 we :riefly .entioned that settle.ent analyses, to :e

(o.-lete, .%st also (onsider the i88ediate or distortion sett/e8ent of thestr%(t%re* Toe -ro(ed%res for (al(%lating i..ediate settle.ent %s%allyinvolve elasti( theory, and one o t e 1gges -ro e

the elasti( .od%l%s for the soil* Toe o:vio%s waywo%ld :e to ta<e the initial slo-e of the stress5strain (%rve, (alle t etangent 8odulus, as deter.ined in the tria+ial test* 8r, :e(a%se the stressstrain (%rves are so of ten (%rved, yo% (o%ld ta<e the secant 8odulus, whi(h

is the slo-e o a stra1 t .e rawn ro Ds level s%(h as ] of the .a+i.%. stress* These definitions areshown in ig* 11*"l. 4y the way, sin(e the i..e 1ate sett e.en a es

-la(e :efore any (onsolidation (an o((%r, the tria+ial tests sho%ld :e(ond%(ted undrained . Th%s the .od%l%s, however defined, is (alled theundrained 8odu/us E,..

However, as shown :y .any resear(hers, the %ndrained .od%l%s issignifi(antly aff e(ted :y sa.- e 1st%r anee* os ot%r:an(e tends to red%(e the E.., and th%s yo% wo%ld tend to over5-redi(tthe i..ediate settle.ents in the field* 4e(a%se of several other fa(tors

a

Et / 2n2426l 46n5n4 3=GlG>

8max

$ 6Y

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$2. . &52n2423n> 3 45 2n2426l 46n5n4 3=GlG> 6n= 45 >56n43=GlG> G>G6ll =52n5= 64 )0 3 45 6Y2G >45>>.

. -- -- - -- --'/



11. &tre .(eforatlon and &trength Characterltlc 513

5555555wr%*(h af fe(t the %ndrained .od%l%s in la:oratory tests IA--olonia, Po%los,and Ladd, 16!1@ i.ons, 16!2B, field loading tests are so.eti.es %sed for i.-ortant -roJe(ts* ettle.ents are .eas%red, and the .od%l%s is :a(<(al(%lated fro. elasti( theory* Load tests have shown that stress levelis one very i.-ortant fa(tor that strongly aff e(ts Eu. or e+a.-le, large s(aleloading tests (arried o%t in Norway and Canada Hoeg, et al*, 16"6@ Tavenas, etal*, 16!2B showed very little settle.ent sin(e the load was a--lied ra-idly%ntil a:o%t one5half the fail%re load was rea(hed Then settle.ents started toa((elerate as the load was in(reased* Th%s the :a(<(al(%lated Eu val%es werevery de-endent on the level of the shear stress a--lied :y the s%rfa(e loaJ*

4e(a%se of all the5 -ro:le.s with the la:oratory deter.ination of Eu

and :e(a%se large5s(ale field loadiog tests are e+-ensive* it is (o.rnon toass%.e that Eu is so.ehow related to the %ndrained shear strength* or e+a.-le, 40err%. 16!$B said that the ratio E@ &Wranges fro. to 1,with &W deter.ined :y the vane shear test* Toe lowest val%e is for highly -lasti( (lays, where the a--lied load is large (o.-ared to the val%e of o4 a that is, the added stress to the fo%ndation is relatively largeB* Toehigher val%e is for (lays of low -lasti(ity, where the added load is relativelys.all* '3A--olonia, Po%los, and Ladd 16!1B re-orted an average Eu/ &Wof 1$ for load tests at 1 sites, :%t for the (lays of higher -lasti(ity therange was 7 to 2* i.ons 16!2B fo%nd -%:lished val%es ranged fro. 2to # These (ases -l%s a few others we have ta<en fro. the literat%reare -lotted vers%s PI in ig* 11*"$ for sof t (lays* till hss%red soils and

gla(ial tills are not in(l%ded*DThere is .%(h s(atter for PI :%t not.%(h data for PI * I4 see.s reasona:le to si.-ly %se 40err%.3sre(o..endation E@ &W of to 1B and the -ro(ed%res develo-ed :y'3A--olonia, et al* 16!1B for esti.ating i..ediate settle.ents of soft(lays*

Another fa(tor whi(h strongly affe(ts the %ndrained shear strength of (lays is stress history* We .entioned this fa(tor when we -o.ted o%t thediff eren(e 2n :ehavior :etween nor.ally (onsolidated and over(onsolidated (lays see, for e+a.-le, igs* 11*# and 11*##B* Let3s first (onsider sorne data showing how the nor.ali&ed %ndrained strength &W/ o c varieswith the over(onsolidation ratio 8CRB* These data are shown for si+(lays in ig* 11*"#* l yo% ta<e the ratio of the 5r 1 / oc iatios, as shown in

ig* 11*"2, all these soils fall into a rather narrow :and, with only thevarved(lay so.ewhat lower* Ladd, et al* 16!!B showed that this ratio of ratios isa--ro+i.ately eF%al to the 8CR to the *7 -ower, or

F & W / o4c :oc

3& W / 1 c : ne8CRB

D7 ll5

1B

Relationshi-s s%(h as this (an :e %sef%l for (o.-aring strength data fro.different sites or even fro. the sa.e site*

--r - - .X...55

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$2. .* T5 6423 Eu/ & 1 15>G> Nl6>42241 2n=5Y, 6> 5nn45= J1 >5156U6G43>.

. Ladd, et al* 9 also showed how Eu/ 5rf varies with 8CR, :%t theW 11 .

*@** 55D 55 W ** ** W 3 *** 5

W K W , 55 K ******** %11*1, .@.

d.e-ends so.s.trongly on the level of shear stress* In general, however, it8 8

K ML*/ 5or a given stresslevel v1g* 11*:K9,B*

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.9.! SN526l P3Jl5> 3 45 S56 S45n643 C35>215 S32l>

All of the -revio%s dis(%ssion has :een li.ited to **well5:ehaved= (ohesivesoils* These are the relatively ho.ogeneo%s .arine and fresh water sedi5.entary (lays of low to .edi%. sensitivity whi(h are nor.*ally (onsoli5oate(t or or%y sllgnfly over(onsoll(tated* As yo% .ight s%r.ise, there are

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rFa: )or,a ) n

76 &hear &trength of &enda and Cla@

$2. ." R5l64215 2n56>5 2n Gn=62n5= >45n4 6423 D24 OCA 3=54 >2Nl5 >56 45>4> >32l> 1 43G " 65 2=5n4225= 2n $. 11*"#B@a$! L6== 54 6l. 9.

.any (ohesive soil de-osits thro%gho%t the world that are not =well :ehaved*= In fa(t, s%(h soils are -ro:a:ly the r%le rather than the e+(e-tion* In this list are in(l%ded stiff fiss%red (lays, -eats and other organi(soils, varved and layered soils, highly sensitive (lays, and resid%al andtro-i(al soils* 8f ten these -ro:le. soils -ossess fiss%res and other

defe(ts that .a<e the. diffi(%lt to sa.-le and test in the la:oratory*They .ay :e very heterogeneo%s and highly varia:le even within the(onfines of a s.all :%ilding site* In sit% testing te(hniF%es des(ri:edearlier are a good way to o:tain sorne s%:s%rfa(e infor.ation as well asan idea of the statisti(al s-read or varia:ility of the .aterial at the site*In addition to the %s%al geote(hni(al literat%re, two E%ro-ean(onferen(es have :een (on(e.ed with -ro:le. soils5the eote(hni(alConf eren(e 8slo, 16"!B and the eventh E%ro-ean Conferen(e on oilGe(hani(s and o%ndation En gineering held in 4righton, England, in16!6* Toe latter (onferen(e had as



`;;

@;;

;;

2;;

11. &treaa"(eforatlon and &trength Characterlatlca 74M

3 ------..-----,---.-------1.....G....G

1 $ 2 7 1

OCR

$2. .) E54 3 OCA 3n Eu/ 5r,, 3 =254 >2Nl5 >56 45>4> 3nB6n3 l6. A45 L6== 6n= E=5>, 9*, 6n= L6==, 54 6l., 9.

its .ain the.e the deter.ination of design -ara.eters for a wide varietyof soil (onditions* o.eti.es the Asian and Af ri(an regional (onferen(eshave sessions on -ro:le.s asso(iated with resid%al and tro-i(al soils*

There are sorne other fa(tors that strongly aff e(t the shear strength of (lay soils that are not related to a s-e(ifi( geologi( de-osit or region of the

world* We (o..only ass%.e that (lays are isotro-i(5 that is, their strength is the sa.e in all dire(tions* It has :een <nown for .any year9@that the %ndrained strength of .any (lays is dire(tionally de-endent for e+a.-le, Hvorslev, 16"B* Re(ently, even e and c, have :een fo%nd to :e

intrinsica/ly anisotropic for e+a.-le, aada and 4ian(hini, 16"B* There isalso eviden(e of an apparent anisotropy d%e to the stress syste., :oth

d%ring (onsolidation and d%ring shear* Anisotro-y is i.-ortant :e(a%se,

for sta:ility analyses, the variation of the shear strength with dire(tionalong a -otential sliding s%rfa(e signifi(antly affe(ts the (al(%lated safety

fa(tor* This variation is shown :y 40err%. 16!$B, and it is one of thedetails in(l%ded in the (orre(tion fa(tor to the vane strength ig* 11*B*

Another fa(tor in(l%ded in 40err%.3s vane shear (orre(tion fa(tor isthe strain rate effect. Taylor 1627B showed that the %ndrained strength of are.olded 4oston :l%e (lay in(reased a:o%t 1] -er log (y(le of ti.ein(rease in s-eed of shear ig* 11*""aB* 40err%. 16!$B showed a:o%t the

55D5D55D55 X D.D,5,*.,, 5 555 D X ' K .. 55555555 55



598 &hear &trength ot &ancl and Cla@

...B. 5555.$&= .5: *9

t<B 5

* 59*G, M

Re.olded 4oston :l %e (lay@%ndrai ned (yli ndr;(al (o.-ression tests@water (ontent of $6]

Y(

2* 3

E :::

: 2 L5 55L** 535 5351 2 1D# 1 $ 1 1

-eed of a+ial (o. -ression ]Q.in B

al

1*$

1*

r , *73 r,o*s

*"

*2

*$

o

5

*1 *1 *1 1*

Rate of shear strain ]Qh B

J

$2. . E54 3 645 3 l36=2n 3n 45 Gn=62n5= >45n4 3 6B3>43n JlG5 l6 645 T6l3, 9"8; 6n= J &65n, %3D6, Nl6>42l6. T5 >45n4 6423 2n 45>5 l6445 45>4> 2> D24 5>N54 43 45 >45n464 45 %(I >46n=6= 645 3 0. N5 645 Bj5G, 9*.

sa.e in(reaseD in CU tests on a Norwegian -lasti( (lay ig* 11*"":B*

'iff eren(e :etween the rate of loading in the la:oratory and in the field(an shar-ly affe(t the %ndrained shear strength* Ladd, et al* 16!!B alsodis(%ssed this -oin 4.

inally, we .ention :riefly the -ro:le. of the residual strength of soils* When stiff over(onsolidated (lays have wor<5sof tening stress5strain(%rves li<e those shown in ig* 11*$2, the %lti.ate strength at large strainsis (alled the residual strength of the soil <e.-ton, 5 16"2@ 16!!B* Atorsional or ring shear devi(e s%(h as shown in ig* 1*1a is %sed todeter.ine the resid%al strength*

")

- -I& 5

--- o5

? -..

5

f5

'ra..en -lasti( (lay@

%ndra; ned tria+ial (o.-ression tests@ 5(onsolidated to in sit% stresses

5 1 1 1

-A-



11*18 PORE PRESSRE PARAMETERS

I4 sho%ld now :e a--arent that when sat%rated soils are load -orewater -ress%res will develo-* In the (ase of one5di.ensional loadingsCha-ter 7B, the ind%(ed -ore water -ress%re is initially eLua/ to the.agnit%de of the a--lied verti(al stress* In three5di.ensional or tria+ial ty-eloadings, -ore water -ress%res are also ind%(ed, :%t the a(t%al .agnit%dewill de-end on the soil ty-e and 4> stress fOstory* O (o%rse the rate of loading a9s well as the soil ty-e deter.ines whether we have drained or %ndrained loading*

I4 is of ten ne(essary in engineering -ra(ti(e to :e a:le to esti.ate 0%st

how .%(h e+(ess -ore water -ress%re develo-s in %ndrained loading d%e toa g1ven set of stress (hanges* Note that these stress (hanges are in tenns oftotal stresses, and they (an :e either hydrostati( eF%al all5aro%ndB or non5hydrostati( shearB* 4e(a%se we are interested in how the -ore water -ress%re d

u res-onds to these (hanges in total stress, =6, A6* , and A6!, it is(onvenient to e+-ress these (hanges 2n ter.s of pore pressure coefficients .

para8e1e1s , w hi(h were first introd%ed in 162 J Prof* A* W* <e.- tonof I.-3erial College in England*

In general, we (an vis%ali&e the soil .ass as a (o.-ressi:le soils<eleton with air and water in the voids* I we in(rease the -rin(i-alstresses a(ting on a soil ele.ent, as in the tria+ial test for e+a.-le, thenwe

will o:tain a de(rease in voB%roe of t:e ele.ent and an in(rease in -are -ress%re* Refer again to ig* 11*#7, whi(h re-resents the stress (onditionsin the UU test* C%nside1 what ha--ens when we a--ly the h9Bdrostatie eell -ress%re ac and -revent any drainage fro. o((%rring* l the soil is 1]sat%rated, then we will o:tain a (hange in -ore -ress%re A% / d uc in ig*11*#7B, n%.eri(ally eF%al to the (hange in (ell -ress%re dacF / ac in ig*11*#7B we 0%st a--lied* In other words, the ratio d u/ $ac eF%als l.I the soilwere less than 1] sat%rated, then t:e ra tio of t:e indn(ed "11 d%e to t:ein(rease in (ell -ress%re $oc wo%ld :e less than l. I4 (an :e shown seeA--endi+ 45# for detailsB that this ratio for the ordinary tria+ial test is

d u' ' '''' & =

dC1* 5 n53c s!

where n -orosity, (o.-ressi:ility of the voids, and

Cs! / (o.-ressi:ility of the soil s<eleton*

or (onvenien(e, Prof* <e.-ton (alled this ratio =. Toe -ore -ress%re -ara.eter = e+-resses the in(rease in -ore -ress%re in %ndrainedloading d%e to the in(rease in hydrostati( or (ell -ress%re*

*J

11511B

C



$,, &hear &trength of &anda and Cla@a

I the soil is (o.-letely sat%rated with water, then C C(, and for .ost soils C(/ Cs! - 8 sin(e the (o.-ressi:ility of water C( is so s.all(o.-ared with the (o.-ressi:ility of the soil s<eleton* Therefore, for satrated soils, / l. I the soil is dry, then the ratio of C / Cs1c a- -roa(hes inf inity sin(e the (o.-ressi:ility of air is vastly greater than thesoil str%(t%re@ hen(e = 8 for dry soils* Partially sat%rated soils haveval%es of = ranging :etween 8 and 1* 4e(a%se in general :oth C*, and Cs1care nonlinear for soils, the relationshi- :etween and the degree of sat%ration is also nonlinear, as shown in ig* 11*"!* This relationshi- willde-end on the soil ty-e and stress level, and the e+a(t relationshi- willhave to :e deter.ined e+-eri.entally*

EF%ation 11511 is very %sef%l in the tria+ial testing to deter.ine if thetest s-e(i.en is sat%rated* Toe -ore -ress%re res-onse to a s.all (hange in(ell -ress%re is .eas%red, and is (al(%lated* I / 1 or nearly so, thenfor sof t (lays the test s-e(i.en is sat%rated* However if the soil s<eleton isrelatively stiff, then it is -ossi:le to have = less than l and still have 1] see Ta:le 1157B* This (ondition is -ossi:le :e(a%se as Cs! getss.aller a .ore rigid soil s<eletonB, the ratio C(/ Cs1c :e(o.es larger@ th%s de(reases* Wissa 16"6B and 4la(< and Lee 16!#B s%ggest -ro(ed%res toin(rease sat%ration and there:y in(rease the relia:ility of -ore -ress%re.eas%re.ents in %ndrained tests*

Now let3s a--ly a stress differen(e or a shear stress to o%r soil sa.-lesee ig* 11*#7 again for the UU testB* In this (ase, a -ore -ress%re d u is

ind%(ed in the s-e(i.en d%e to the (h9ange in stress differen(e do do1 5

do#, or we (an write, as Prof* <e.-ton did for tria+ial (o.-ression

TA,E 11"4 T535426l 8-V6lG5> 3 &255n4 S32l>64 C3Nl545 3 %56l C3Nl545 S64G6423n

oil Ty-e * - 1] * 99

oft, nor.allyD (onsolidated (lays *6667 *67"

Co.-a(ted silts and(lays@ lightly over

(onsolidated (lays *6677 *6#8ver(onsolidated stiff

(lays@ sands at .ostdensities

Mery dense sands@ very*67!! *1

stiff (lays at high(onfining -ress%res *61# >.G>

Af ter 4la(< and Lee 16!#B*

0

1



1* .......--i.--.--- ---$------$-t----$--t$--t-- 11-

*7 :,Co. -a(t r (layey slt the etial

N= l .a+ 5 11 l :Qf t > 112 $

S 1 in lQl : I P I

H:3 Wet..: V Corr -a(ted ti ll

'ryCIB

G / 7 -si

*lo# 1 :si

Y # 1

E *" #

?('*:l

??C..IB''..

8tt wa sand theoreti al B9

Y', 1], W,, W $ -, @

*2 Cs< $*" S 15 in l :

3# 0 PÍ \ *lo# / 1

C

oIB % 1, *lo# 1 -si

o** % 1, *lo# $ - i

*$

o I j 1 J ,, 2 J***Z***K***J* ..¡......... ,,,,,:999999999999Tt999955W " " ! ! 7 7 90 6 11

'egree of sat %rf ion,

$2 . . T5 N3 5 N5>>G5 N66 545 = 6> 6 Gn23n 34 =555 3 >6426423n 3 >5156 >32l> 6445

Bl6j 6n9!.

*=e



¡,

68 &hear &trength of &enda and Cla@

1151$B

if the soil s<eleton is elastic. in(e soils in general are not elasti( .aterials,the (oeffi(ient for the -rin(i-al stress differen(e ter. is not 1Q#* o<e.-ton %sed instead the sy.:ol A for this (oeffi(ient* Now we (an

1

(o.:ine EFs* 11511 and 1151$ to ta<e into a((o%nt the two (o.-onents of -ore -ress%re9 1B that d%e to (hange in average or .ean stress and $B thatd%e to (hange in shear stress, or

1151#B

EF%ation 1151# is the well5<nown <e.-ton eF%ation for relating theind%(ed -ore -ress%re to the (hanges in total stress in %ndrained loading* l = / 1 and * 1], then we nor.ally write EF* 1151# as

11512B

o.eti.es it is (onvenient to write EF* 11512 as

1151B

where $ =A.EF%ations 1151# thro%gh 1151 are derived in detail in A--endi+ 45#*

There we show that these eF%ations are tr%e for :oth tria+ial (o.-ression63$ 63# B and tria+ial e+tension 63$ 631B (onditions, altho%gh thes-e(ifi( val%e of is de-endent on the stress -ath, as dis(%ssed in e(*11*1$*

Li<e the -ara.eter =, the -ara.eter A also is not a (onstant@ it .%st :e deter.ined for ea(h soil and stress -ath* Toe -ara.eter A is veryde-endent on the strain, the .agnit%de of o$ , the over(onsolidation ratio,anisotro-y, and for nat%ral (lays tested in the la:oratory, on sa.-ledist%r:an(e* Ta:le 1156 relates the ty-e of (lay to different val%es of the $

-ara.eter at fail%re, $1 in tria+ial (o.-ression* 8f (o%rse $ (an :e

(al(%lated for the stress (onditions at any strain %- to fail%re, as well as atfail%re*The <e.-ton -ore -ress%re (oeffi(ients are .ost %sef%l 2n engineer

ing -ra(ti(e sin(e they ena:le %s to -redi(t the ind%(ed -ore -ress%re if we<now or (an est;.ate the (hange in the total stresses* In the field, the<e.-ton eF%ations are %sed, for e+a.-le, when we want to est;.ate the -ore -ress%re res-onse d%ring %ndrained loadings that .ight J5 a--lied :y



.3 P35 P5>>G5 P66545> 80!

TABLE -9 V6lG5> 3 $ ,3 V623G> S32l TN5>Ty-e 3 Clay $W

Highly sensitive (lays

Nor.ally (onsolidated (lays

Co.-a(ted sandy (lays

Lightly over(onsolidated (lays

Co.-a(ted (lay5gravels

` to ` F

` 2 to ` l

` to ` #

8 to ` 1

5to `1

Heavily over(onsolidated (lays 5 2 to 8

After <e.-ton 162B*

a highway e.:an<.ent (onstr%(ted on a very sof t (lay fo%ndation*Ty-i(ally, the e.:an<.ent is (onstr%(ted .ore ra-idly than the e+(ess -ore water -ress%re (an dissi-ate, and th%s we ass%.e that %ndrained(onditions a--ly* Toe in(rease in e+(ess -ore -ress%re (an res%lt ininsta:ility if the -ore -ress%re gets too high ConseF%en tly, i t is i.-artantto :e a:le to est;.ate 0%st how high the -ore -ress%res are li<ely to get andthere:y o:tain sorne idea %f how (lose to fail. e the e.:an<.ent .ight :e* I 24 is too high, stage (onstr%(tion .ight :e %tili&ed@ then field.onitoring of the -ore -ress%res wo%ld :e advisa:le* <e.-ton3s -ara.e tershave also :een %sed for the design and (onstr%(tion (ontrol of (o.-a(ted

earthfill da.s*

E+AMPLE ."

(215n:

Toe CU test of E+a.-le 11*11*

R5FG25=:

; "

S3lG423n:

Use EF* 1151#* in(e -ore -ress%res were .eas%red, the s-e(i.en.%st have heen sat%rated* Th%s ass%.e = - l. o A at fail%re is

tlu 5 tlo Q tl Qo Q Q Q t Q l o.4..

l #

¡

*

¡

A /#



8,4 &hear &trength of Sancf& and Cla@

In an ordinary tria+ial (o.-ression test, A3# / 8 sin(e the (ell -ress%reis held (onstant thro%gho%t the test see ig* 11*$6B* ro. E+a.-le11*11, $o

11/ o

15 o

* :1/ 1 <Pa and $u1/ 77 <Pa* Therefore

A -77

5 *77

ro. Ta:le 1156 yo% (an see that the (lay was -ro:a:ly so.ewhatsensitive*

As shown :y Law aod HaBt& 16!7B and in A--endi+ 45#, whererotation of -rin(i-al stresses o((%rs, it is :etter to define the -are -ress%re -ara.eter A in te1.s of -tin(i-al stress inere.ents whieh* are inde-endentof the initial stress syste.* I this is done, then the eF%ations for A for ea(hof the (o.rnon tria+ial stress -aths dis(%ssed in e(* 11*1$B are

$u

$ac / $a 1151"B

$u ll51!B

$u A / 1 5 5ae $ov l l517B

le 11516B

l4 is also shown in A--endi+ 45# that

and

le

115$1B

o% will find these eF%ations %sef%l in e(* 11*1$ and for the -ro:le.s atthe end of this (ha-terB*

A .ore general -ore -ress%re eg%ation was -ro-osed :y Hen<el16"B to ta<e into a((o%nt the effe(t of the inter.ediate -rin(i-al stress* lt

115$$B

$ /



where

t for Cla I0)

and a is the Zen!el pore pressure para8eter. o.eti.es t e e e -ara.nd so.eti.es aQ #a* E %ation 115$$ is

deriv. ed in A--endi+ * 45#* Also in 45#, the eF%ation.s f .or getting t.he

and e+tension (onditions are develo-ed* These relationshi-s are for tria+ial (o.-ression A

ll5$B

or tria+ial e+tension AE and LCB (onditions

$ 52

a5 115$"B

These eF%ations .ean, of (o%rse, that a / 8 for elasti( .aterials sin(e $ / in tria+ial (o.-ression and $ / # in tria+ial e+tens1on *

i ea of what the inter.ediate rin(i 6l stress is in the field, then yo% -ro:a:ly sho%ld %se EFs* 115$$ thro%gh ll5$2 to

. . . . .

-ress%res fro. la:oratory test res%lts, -ri.arily :e(a%se the -ore -ress%re -ara.eters arevery sensi ive o sa. ,'3A -olonia, et al* 16!1B, and Lero%eil, et al* 16!7a and :B -rovide.ethods for esti.ating -ore -ress%res %nder e.:an<.ents on so t e ays*

P!E&&'!E AT !E&T *O! CA)&

s 1s tr%e or san s, a nowat rest, S , for a (lay de-osit is of ten very i.-ortant for the design of earth5retainingstr%(t%res, e+(avations, and sorne o%n at1ons* n e(@5 * ,

D D 1 val%es of S for sands* We said that S wase.-iri(ally related to cp) EF* 115" .and ig* 11*12B, and w. e also .entioned

nor.ally (onsolidated sands EF* 115!B*

* J

DD ,K5 G ** 5,* ,e B 5,.,B

.,

.



$,$ &hear &trength of &and and Cla@

H53l=5= n=2>4GJ5= H5455n5

o B335 6n= l5l6n= 9)

o R. L6== 9)

B2>3N 9)8

**** e,, K ¡nH3

... C6N6n5ll6 6n= V62= 9*

b C3N2l5= J W34 9*

AJ=5l62= 6n= K25 9

. - K - >2n 9' 0.0)

*"

o

0.)

*2

>.G .._ ...._ ...._ ---! ----1. ----!. -G1$ $ 24 28 32 #"

$2423n 6nl5, > =555>

$2. .8 S 0 15>G> ,' 3 n36ll 3n>3l2=645= l6> 645L6==, 54 6l., 9.

are shown in ig* 11*"7* 4roo<er and Ireland 16"B also fo%nd a tenden(yf-r the nor.ally (onsolidated S to in(rease with -lasti(ity inde+* Gassars(h 16!6B has (olle(ted the res%lts fro. 1$ inyestigations, in(l%ding the(o.-ilation :y Ladd, et al* 16!!B, and they are shown in ig* l l*"6* Theinter(e-t of the :est5fit line of ig* 11*"6 is very (lose to the average of S

for sands shown in ig* 11*12*The effe(t of in(reasing the over:%rden stress and s%:seF%ent %nloading on oS, and S is shown in igs* 11*!a and :, res-e(tively* '%ringsedi.entation, the effe(tive hori&ontal stress oS, in(reases in -ro-ortion tothe in(rease in effe(tive verti(al stress, so S is (onstant* I %nloadingoee%rs :eea%se of erosion, for e+a.-le, then there is a hysteresis effeet,and the val%e of S in(reases* 'e-ending on how .%(h %nloading a(t%allyta<es -la(e, it is -ossi:le for the lateral stresses to approach a state of

55555555555555D5555

0

1



0.8 5

o 0. .X 799,_

.... o 5:::, 0.

.X >5?: '. 5 o 5

a* 0.) Uo

el

?s o K

/ 0."" 0."*PIQ00." -

3 -a,?.;::: 0.* 5 o &2>4GJ5 3 l6J3643?22 53n>366456 3 6o >5=25n4

0.

Z -.& .& .& .1& .1 &

.1& ---81- .._ --8-

---

n **** D5 en C9*n 5,n on nn 1nn 11n

Plt>4224 2n=5Y, PI

$2. 11*"6 C35l6423n J54D55n Ka 3 l6J3643 45>4> 6n= Nl6>42242n=5Y PI 645 M6>>6>, 16!6B*

*)0 .X! 53 LQ

J

" .X -

# - -]W

R5l36=2n

* - '.. 5

5 E3>23n 5

, S5=25n46423n

3 1 1

o l UUU ::W

0

P6

$2. 11*0 R5l6423n>2N> >3D2n 45 554 3 6 6n2n 315JG=5n>45>> =G2n >5=25n46423n, 53>23n, 6n= 5l36=2n 3n 6 323n46l>45>> 3,; 6n= J 35225n4 3 564 N5>>G5 64 5>4, Ka 645 M35n>45n 6n= E2n>452n, 90.

0

*J

e9 .... n=2>4GJ5=

CJ 5



$,8 &#ear &trenglh of &anda and Cla@a

1*"

1*$

.0

*7Q R5l36=2n

Q-3 OCA / 0

*2 L- - --'-- ---'---'-...................,.. .

1 * " 8 0 *0

5OCA /-

a

$2. . E54 3 3. 153n>3l2=6423n 3n S 0 3 6 >5n>2421.6 l6

=G2n 5Nl3445= J L6==, 54 6l. 9.

' #> or #> EF* 1512B* I there is s%:seF%ent relo(91*ding, then ihe S tends to de(rease, as shown in ig* 11*!:*

The eff e(t of over(onsolidation on the K of a sensitive (lay is shownin ig* 11*!1* Again, there is sorne hysteresis when the (lay is re:o%ndedfrorn a high 8CR* There is lirnited eviden(e that the relationshi- :etweenS and 8CR de-ends to sorne e+tent on the -lasti(ity of the (lay ig* . .

several (lays d%ring %nloading and re(orn-ression* or (lays with a PI of a:o%t $, a val%e of h / *2 is reasona:le* Toen h de(reases slightly as PIin(reases, with the lowest val%e of h *#$ at PI 7* These val%es of h

are sornewhat lower than those for sands e(* 11*!B* /ee- in .ind too thatall these data are for la:oratory (onsolidated sa.-les* ield :ehavior isrn%(h .ore errati(, as shown :y Gassars(h, et al* 16!, ig* 17B* Thesea%thors as well as Tavenas, et al* 16!B and Wroth 16!B des(ri:ete(hniF%es for estirnating the S in sit% in de-osits of soft (lays* Wroth16!B also dis(%sses the effe(ts of erosion and a fl%(t%ating gro%nd water

In ter.s of lateral 564 -ress%res, this is (alled a passioe state of failure, and the stressratio K P is (alled the coefficient of passioe earth pressure.

5 555555555 555 5D5D555555555555555555555

1

1



B.;rooIer an lrelan 1L@)

2.` <784ol

2.@ -----

-·-

P91;2;B;@;

2. 6. Ha 1L@)oston 4l/e la7, P9 D 2B

2.2

-o _$ 1-oo

2.;

,

a ve$2. 11*!$ S

115>G> OCA 3 >32l> 3 =55n4 Nl6>G5>.

T5 =646 :y B335 6n= l5l6n= 16", $2. 11B D6> 5Nl3445= J L6== 96.

.j

55 5 5 *@a K 5 5



81, &hear &trenglh of Sana and Cla0

ta:le on the variation of S with de-th* enerally, the %--er few .etres of a soft (lay de-osit are over(onsolidated the dry crust : and K (an :e F%itehigh* Toen it will de(rease with de-th as the 8CR de(reases, %ntil it iseF%al to the nor.ally (onsolidated val%e when 8CR / 1.

11.1 &T!E&& PATH& ('!ING 'N(!AINE(OA(ING" NO!3A) CON&OI(ATE(CA)&

We show e+a.-les of stress -aths for %ndra.ed Ioad.g of nor.ally

(onsolidated (lays in igs* 1*$2, 1*$", 11*#2a, and 11*2#* Undrainedstress -aths for over(onsolidated (lays are shown in igs* 1*$ and 11*#2:*ro. o%r (o..ents (on(erning those fig%res yo% sho%ld now %nderstandwhy these stress -aths have the sha-es they do have* Toe stress -aths weshowed for %ndrained shear were for the .ost (orn.on ty-e of tria+ial test%sed in engineering -ra(ti(e, the a+ial (o.-ression ACB test* Gost of theti.e the initial (onsolidation stresses are hydrostatic / 5 lB :e(a%sela:oratory -ro(ed%res are si.-ler* However, a :etter .odel for 2n sit%stress (onditions wo%ld :e non5hydrostatic (onsolidation@ that is, the a+ialstress wo%ld :e different than the (ell -ress%re ( S $/&' 1B* As we.entioned in e(* 1*", there are stress -aths other than a+ial (o.-ressionthat .odelrea l e%gi%eeriog desigo sit%ations o.e of these are shown 2n ig 11!#, along with their la:oratory .odel* A+ial (o.-ression ACB .odelsfo%n dation loading s%(h as fro. an e.:an<.ent or footing* Laterale+tension LEB .odels the * a(tive earth -ress%re (onditions :ehind retainingwalls* A+ial e+tension AEB .odels %nloading sit%ations li<e e+(avations,and lateral (o.-ression LCB .odels -assive earth -ress%re (onditions s%(has .ight o((%r aro%nd an earth an(hor*

I yo% thin< a:o%t it, the ordinary tria+ial test is not the :est .odelfor the design (onditions ill%strated in ig* 11*!#* lt wo%ld :e ali right for (ases aB and (B if the fo%ndation or e+(avation were (ir(%lar in sha-e for e+a.-le, an oil tan<, .issile silo, or rea(tor -itB* Toe .ore %s%al (ase is

whete %ne di.ension -et -endi(%lar to the -age in ig* 11*!#B is very long(o.-ared to the others* This is the (ase for plane strain. E+a.-les are longe.:an<.ents, stri- footings, and long retaining walls* In these (ases,stri(tly s-ea<ing, the shear strengths sho%ld :e deter.ined :y %sing -lanestrain tests ig* 1*12:B* Toe la:oratory .odelsD of ig* 11*!# (an alsoa--ly to stress (onditions in t:is test 0%st as weH as in t:e t(ia +ial test in(e the -lane strain test is .ore (o.-li(ated in several res-e(ts thanthe tria+ial test, it is not of ten %sed in engineering -ra(ti(e* Tria+ialstrengths are still (o..only o:tained for design -ro:le.s that areo:vio%sly -lan strain*



H% )

e) #o/nation /nloain$ e&aation) A&ial

e&tension

.-/'

$25l= S24G6423n L6J3643 M3=5l

6 $3Gn=6423n l36=2n

J A4215 564N5>>G5

AY26l3N5>>23n

3

L6456l5Y45n>23n

= P6>>215 564 N5>>G5 L6456l3N5>>23n LC

$2. .! S3n5 33n 25l= >46J2l24 >24G6423n> 6l3nD24 452 l6J3643 33=5l



0

"1$ S56 S45n4 3 S6n=> 6n= Cl6>

I t is i.-o1tant that 9yo% <now how to .a<e the oo.-%tationsne(essary to -lot %ndrained stress -aths@ the -ro(ed%res for doing so are11I%strated :y the follow.g e+a.-les*

E+AMPLE .)

(215n:

Toe o5 and C'( data of ig* E+* 11*1a were re(orded when the nor.ally(onsolidated (lay of E+* 11*11 was tested in a+ial (o.-ression*

a 5 a P6

3

G P6

00

80

0

"0

* # c

*0ac / )0 P6

oo * # q

$2. EY. .)6



.* S4566 P646 &Gln n=6ln5= L36=ln-

'raw the total and effe(tive stress e

ara.eters*

several strains in order to -lot the stress . -aths* Us%ally fiv. e or si+ -oints

D%st fill in the a

o o 5 o $o 115$!B

an

---* $

# #

115$7B

115$6B

1' #' 5 Now 0%st (hoose the val%es of o - a* :

andstra.s, an Note that

a

.% at severa (onven.ient

L C p ' 2'

1 # J

$ $' J'

*

¡

l

!# 51 6# #"* 17"* 1$6* 7" !

62 !6* "7 2!* 16!* 11*

ail%re I2l 1 77 "$ * $* 11$*

Il 6" 6$ 7 27* 167* 1"*

$ 76 66 1 22* 162* 6*



o

@;

;

2;

? i.-::0._. -'---'--_.._...._-H--H----_._.........

o

--------------

1;; 2;; 5, 5' IPa)

5 555 555 5 555 55555555555 5 5 55555

* * 5

Í'1

712 S55 trength 3 enda end Cleya

F P6

$2. EY. .)J

Total and effe(tive stress -aths are shown in ig* E+* 11*1:* Thefail%re lines are also drawn, ass%.ing a3 a 8*

.(e ,v / $2*l > , N' / $"*">

#+G / 12*1> , cl]r / 12*>

Note that the -ro:le. (o%ld :e solved gra-hi(ally :y -lotting the TPfirst, then s(aling off the (orres-onding ilu val%es hori&ontally to the left

of the TP@ one -oint done this way is shown in ig* E+* 11*1:*

E+AMPLE .

(215n:

A*long e.:an<.ent shown in ig* E+* 11*19@a is to :e (onstr%(ted ra-idlyon a de-osit of soft organi( silty (lay in northe. weden* Toe soil -rofileand -1o-e1ties a1e also shown in ig* E+* 11*1"a* Ass%.e S *"* Also

ass%.e $ :efore fail%re is a:o%t *#@ at fail%re, $1/ * after Holt& andHol., 16!6B*

'eter..e the TP, T 5 % BP, and EP for a ty-i(al ele.ent . :elowthe (enterline of the e.:an<.ent*

S3lG423n:

irst, (al(%late the initial stress (onditions for the ele.ent* Use EFs* !51# *

0



P9 - 1;

11.1 &treN Path (urlng 'ndralned oadlng"Norall@ Conolldated Clan 117

p .*" MQ! ----,

¡ $ ` . Q ¡ - W $*1 GgQ.3 3

. 1555555551! . 55555555

f 1 " p / .! MQ#

K ZDn - "0LL - 0

8rgani(sil ty (lay

$2 . EY. .6

!512, and !51*

0,,5 1*$26*71B1B 1*#6*71B2B 5 "# <Pa 1*6*71B2B #6 <Pa

/ vo 5 u1 / $2 <Pa

0 5 0.6a,( S 5 8 "B 5 12 <Pa

e(ond, (al(%late the :,. d%e to the e.:an<.ent*

ao at the s. fa(e $*16*71B$*!B ! <Pa

o,, at 52 .@ %se ig * 7*$# ,

6 / *2 + $ / *6O' / *6 + ! / 1 <Pa

This is ao#., on the ty-i(al ele.ent*To deter.ine the in(rease in hori&ontal stress :,.O, there are eF%a

tions* and sorne (hat ts availa:le fot a li.ited n%.:et %f geo.elt ies see,

for e+a.-le, Po%los and 'avis, 16!2B* In this (ase, ass%.e the in(rease inhon&ontal stress 1s one5tfOrd of the .(rease . verti(al stress*

:,.a,, 8 ##1B 1! <Pa

Ne+t, %se EFs* 1517 and 1516 to deter.ine B, p, and p for :othinitial and final (onditions* 'on3t forget the (on9ditions for the T 5 u :

P* T o get the final effe(tive stresses, we need to est;.ate the ind%(ed -ore -ress%res* Use the -ore -ress%re -ara.eter infor.ation given* Ass%.einitially that the soil is not stressed to fail%re@ so A *#* = l :elow

!

C



X ¡X , . X '.. X ---



< 1

$1$ &hear &trength ot &and and Cla@

the water ta:le* Use EF* 11512*Ilu lo Alo 1 5 lo#B 1! *#1 5 1!B $6 <Pa

I the e.:an<.ent was overstressing the %nderlying soil, then the ;nd%(edIlu wo%ld :e #2 <Pa :e(a%se $ / *B* I we %sed Hen<el3s -ore -ress%reeF%ations, EFs* 115$$ alBd 115$, we wo%ld -redi(t Ilu to :e a:o%t #$ <Pa*As we said in e(* 11*J8, -redi(ting in sit% -ore -ress%res is not easy*

I4 is so.eti.es hel-f %l when (al(%lating stress -aths to draw littleele.ents with the a--ro-riate total, total 5 u , ne%tral, and effe(tivestresses indi(ated si.ilar to ig* 11*$6B* This te(hniF%e is shown in ig*E+* 11*1": :oth for initial (onditions and af ter loading* Note thatstresses on the ele.ents for initial (onditions are those we (al(%lated

at theor final stresses the verti(al total stress

in(reased :y 1 <Pa and the hori&ontal total stress in(reased :y 1! <Pa, as. . . .

shown are those we fo%nd fro. the -ore -ress%re eF%ation* Toe (al(%la5tions or p, p , anthe ele.ents*

a G a

ln2426ln=2423n>:

F "# 5 # <Pa

N"# #

/ 7 < Pa Po 5 %/ P / 16 <Pa

o

$2n6l 703n=2423n>:

/ $$ <Pa P,5 G / # <Pa

/ 9* <Pa -@ / $2 <Pa

$2. EY..J

#



---------- ----

.* S45>> P64> &Gln n=6ln5= L36=ln-%36ll C3n>3ll=645= Cl66 8

F P6

#G *9 G #6 555

*0

0

0 *0 "0 )0 0 0 80 90 ,00 N, N P6

$2. EY. .

inally, -lot the stress -aths on the p B diagra., as shown in ig* E+*11*1"(* <et(h the EP so as to have a sha-e si.ilar to those shown

-revio%sly for e+a.-le, igs* 11*#2 and 11*2#B for nor.ally (onsolidated(lays*

The ne+t e+a.-le is a little .ore (o.-li(ated* irst, we shall (onstr%(t the stress -aths and deter.ine the strength -ara.eters for an a+ial(o.-ression test@ then we shall %se the AC test and o. <9nowledge of stress -aths to deter.ine the -ore -ress%re res-onse of a lateral e+tensiontest* We will see that the effe(tive stress -aths for :oth tests are 1dent1(al,

even t:o%gh the total stress -aths are very different*

E+AMPLE .

(215n:

Two identi(al s-e(i.ens sa.e (, e, et(*B of a nor.ally (onsolidatedsat%rated (lay were hydrostati(ally (onsolidated ( S / 1B and then sheared%ndrained* In test 2, the a+ial (oro-ressiao ACB test, the (ell -ress%re washeld (oostant while the a+ial stress was in(reased %ntil fail%re* -e(i.en =was failed :y latetal e+tension LEB in whieh the verti(al stress was held

(onstant while the (ell -ress%re was de(reased %ntil fail%re o((%rred*tress5stra. and -ore -ress%re data 9 ror test $ are show% in Ta:le E+*11*1!a*

6. Co.-%te and -lot the stress5strain and -ore -ress%re5strain (%rvesfor test A.

:* Plot the TP and EP for hoth tests*

o



818 &hear &trenglh of &and and Cta@

(* 'eter.ine cp3 and 3Pr for :oth tests*d. how that the stress5strain (%rve for the test A ACB is identi(al to

that for the test LEB*e* Eval%ate the -ore -ress%re5strain data for test = fro. the LE

stress -aths*f. Co.-%te the -ore -ress%re -ararneter $ for :oth tests*

'()*+ +>. 11 .17a T5>4 A AC 45>4 =646

e

oI

o*#

o*16

$ *2 *$62 *$ *21" *2 *2!7 *" *1

1 *! *#1$ *7 *

After Ladd 16"2B*

S3lG423n:

a* Plot ': and .: C': (%rves for test A ACB, as shown in ig* E+*l l.l !a* Note that the data in Ta:le E+* 1 1*1!a is n or.ali&ed with res-e(tto the effe(tive (onsolidation stress o4 in the test* We (o%ld ass%.e a o4inwha tever %ni ts t:e test was (ond%(tedB, or we (an 38r< eMefBthing o%t inter.s of the nor.ali&ed stresses*

b. As fot the -1evio%s e+a.-le, 24 is hel-f%l 43 s<et(h ele.entsshowing the total, ne%tral, and effe(tive stresses for the initial (onsolidation (onditions, d%ring shear, and at fail%re, as is done in ig* E+* 11*1!:*Use these stresses to (o.-%te the TP for :oth tests and the EP farthe AC test* in(e at this ti.e we don3t <now anything a:o%t the -ore -ress%res develo-ed in the LE test, we (annot -lot its EP*

Cal(%lations for p. p, and B for test A ACBD

Initial (onditions9

p -

Lo /-*- O



11.1 tr ...Path (urlng 'ndralned oadlng"Norall@ Conolldated Cla0 61

0.6

$62lG5

0.4

0.2

o o " 7 12 16 c

A%a 0.6

0.4

16 c

$2. EY. .6 S45>>->462n 6n= N35 N5>>G5->462n G15> 3 45 AC

45>4.

At fail%re9 K 1*7 1 K l $6P 9 ' $ 5 *

PY / P9 - u / *!2

Che(<9 PY .3 D *!2B

K 1*7 5 1 K 8 $6B9 ' * - .

Che(< 9 l# 2@ D

/ *$6B

#@

*



Z

X ,e9

¡¡;e9

+

22j

K t,i

e

3'

e9oo11B11B

U22

=fi1Bt

?e

'O9 111

222 .

G

e9o¡¡;

a?o'*E

oG

+

^t

:::,^X

(l

5l 5

o1

-QB

-

1B B

e9 5- W222 **J

***

111

*o O,**** e

**** *e....

M

Z,@

e9o X .;:;- 225 ee9- G

8*0

F

o

-559 1B

3

o



;.@

-Qe, D -;.;B ) -.::l,/-1

.:'.l/F

D +;.;. -K . -Q----D- .-J

;.2

1.; 2.;_%_ i_

.* S45>> P64> &Gln n=6ln5= L36=ln-%3nn6ll C3n>3ll=545= Cl66 *

or Test LEB91 1

Po p $5 1

1 51

Lo / $5/ 8

1 2$ $

*!1

B 1 5$*2$ *$6

Now -lot the TP3s for :oth test $ ACB and test LEB* We <nowthat the TP3s will :e stra;ght lines in(lined at 2> fro. the stress(onditions in :oth tests sin(e one of the -rin(i-al stresses re.ains (onstantd%ring the test* Therefore we need only (al(%late and -lot the end -oints], p , and L

0 1on ig* E+* 11*1!(, and (onne(t these -oints with straight

lines*Inter.ediate -oints for :oth the I P and EP .ay :e (al(%lated

fro. the stress5strain and -ore -ress%re5strain infor.ation of Ta:le 11*1!aand ig* E+* 11*1!a* This -ro(ess is e+a(tly li<e that shown in E+a.-le11*1* Us%ally it is easier to do the -ro:le. gra-hi(ally :y si.-ly -lottingthe inter.ediate L val%es on the TP L / .oQ$B at several (onveniently

s-a(e d stra.s* lhts deter.ines the inter .ediate p val%es* Then, seale off the .u val%es hori&ontally to deter.ine the inter.ediate p3 val%es at thesesa.e strains* This -ro(ess, shown in ig* E+* 11*1: and ig* E+* 11*1!(,deter.ines the (orres-onding EP*

: :

$2. EY. . S45>> N64> 3 45 AC 6n= LE 45>4>.

,._



<,U

822 S56 S45n4 3 S6n=> 6n= Cl6>

Note that only %ne EP is shown fot both tests* This is so :e(a%se theeffe(tive stress (onditions in :oth tests are the sa.e* Why Note thatd%ring shear the stress differen(e 63, whi(h is eF%al to 3 - 3! , is thesa.e Cor :oth tests* Loo<ing at it another way9

or the AC test,

or the LE test,

63AC / ^ 63 - / 63

=3LE V 5 V ao / 63

Therefore at every strain in(l%ding at fail%reB 63A / 63LE Th%s the

stress5strain (%rves for :ath tests . nst he the (8e o, if we -lotted theLE stress5strain (%rve, it wo%ld loo< e+a(tly li<e the AC (%rve shown inig* E+* l l*1!a* 4y the way, this is the answer to -art d*

I the two s-e(i.ens have e+a(tly the sa.e stress5strain (%rve andidenti(al strengths, then the effe(tive stress (onditions in the s-e(i.ens.%st :e identi(al, :oth at fail%re and d%ring loading* This .eans that theEP3s .%st also :e the sa.e*

Another way of loo<ing at this is that in the LE test, the (hange instress differen(e ao is -rod%(ed :y a (hange, a de(rease, in (ell or hydrostati( -ress%re* When the hydrostati( -ress%re (hanges, in an %ndrained test, only a (hange in -ore -ress%re res%lts, not a (hange ineffe(tive stresses* I there is no (hange in effe(tive stresses, then the

stress5strain and stren gth :ehavior .%st :e the sa.e Hirs(hfeld, 16"#B *The only differen(e at fail%re :etween the tests .%st :e in the a.o%nt of -ore -ress%re au that develo-s* I this is tr%e at fail%re, then it is tr%ethro%gho%t the test* Therefore we (an (onstr%(t the -ore -ress%re5strain(%rve -art e* of this e+a.-leX for the test = LEB fro. the stress -ath -lots*

As with test A ACB the a.o%nt of -ore -ress%re develo-ed in test =

LEB is si.-ly the hori&ontal distan(e :etween the TP and the EP Corthat test* Note that for the LE test ali val%es of au are negative. The

TA,E E+. .J T5>4 B LE 45>4 =646

E $a/ a4 $u/ a4

o 3 ol *# 5 *1"$ *2 5 *1"2 *$ 5 8*ll" *2 5 *!7 *" 5 *

1 *! 5 *21$ *7 5 *#



11.1 &tren Path (urlng 'ndralnecl oadlng"Nonnell@ Conolldeted Cla@a 1%

(onstr%(ted -ore -ress%re5strain (%rve for the LE test is shown in ig* E+*11*1!d along with the stress5strain (%rve for :oth tests and the -ore -ress%re5strain (%rve for the AC test* or easy (o.-arison, n%.eri(alval%es of the -ore -ress%re are listed in Ta:le E+* 11*1!:* ig* E+* 11*1!dand Ta:le E+* 11*1!: are sol%tions to -art e*

Now yo% (an see where the effe(ttve stress val%es for the LE test iniZ* E+* 11*1!: (arne frorn* Another (%rio%s fa(t a:o%t the AC and LEtest is that the n%.eri(al differen(e :etween the two -ore -ress%re(%rves at a

a*" $62lG5

AC 6n= LE

7 * 1" E

.UlG

a *"

*2

*$

1"

E

5*$T5>4 B LE

5*2

$2. EY. .= S45>>->462n 6n= N35 N5>>G5->462n =646 3 J34

2

DJ



3

824 &heer &trength ot &enda end Cle@a

given strain is e+a(tly eF%al to the -rin(i-al stress differen(e at that straino% (an (he(< this state.ent :y %sing the val%es of Ta:les E+* 11*1!a and : 3 s(aling off A3 val%es :etween the two $u (%rves of ig* E+* 11*1!d*Also the hori&ontal distan(e :etween the two TP3s in ig* E+* 11*1!( iseF%al to do al a given shain*

Now that we <now the TP3s and EP3s for :oth tests, we (an(o.-%te 48 ,and >68! for the two tests -art eX* ro. ig* E+* 11*1!( we (an.eas%re the angles ,*fQ, 1QlrACB and 1QlrLE? with a -rotra(tor, or we (an %seEF* 15$1* in(e the (lay is nor.ally (onsolidated, we shall ass%.e thate3 ,***, 8 and t:is is why we drew the inter(e-ts a and a3 oo the p&> diagra.to :e essentially &ero* ro. EFs* 15$2 and 15$ we .ay readily (o.-%teet,3, ^l?rACB and (l? rLEBD These val%es are shown in Ta:le E+* 11*1!(*

'()*+ +>. 11 .17c S45n4 P66545> 3 $. EY. . 2n =555>

Angle Test $ ACB Test LEB

1$* $$3P& ,'

1$*7$1

$#*7$1

f. Let %s now (o.-%te the -ore -ress%re -ara.eter A for :oth tests*

Io o:ta. the stress (hanges d%nng the test, 1t 1s %s%ally eas1er to ref er tothe ele.ents of ig* E+* 11*1!:, and sele(t the (hanges in total stress fro.the initial (nditions to the (onditions at fail%re*

ar t:e test A A, Aa# 5 8 and Aa 15 NJJ a1 5 1 7 1 8 5

*7@ $u1/ ** o,

or L*ae test = LEB, A3 / O and*7@ $u

1

5 *#* o,

$W5*# 5

5*7B

**6

8 5 5*7B *7

I this is (onf%sing, it .ight :e easier to %se EF* 1151! for the LE test,

8f (o%rse we <new fro. EF* 115$ that $i sho%ld eF%al .A c.: The tenn1



11*1$ tre% P545 &Gln n=5ln5= L36=ln-%35ll Coneolldeted Cl65 1$

Ilo,. is negative :e(a%se it is de(reased d%ring the LE test refer again toig* E+* 11*1!:B*

What (on(l%sions (an we draw fro. this e+a.-le irst, :oth thea+ial (o.-ression and * lateral e+tension tests have identi(al stress5strain (%rves and their (o.-ressive strengths $a1 are the sa.e* I the

stress5strain(%rves are the sa.e, then they have the sa.e E .od%l%s* They also have

the sa.e EP* However they have .ar<edly different TP3s and .ar<edlydiff erent -ore -ress%re res-onses, :%t $Wand th%s $W: is the sa.e for :othtests* We (an s%..ari&e these o:servations as follows9

arne Ila and .a1arne a'T (%rves and E .od%l%sarne EPa.e et,3

a.e $1and $1 :'ifferent TP'ifferent 3Pr 'iff erent llu

In E+a.-le 11*1! we showed the stress (onditions and -lotted thestress -aths for the AC and LE tests, where yo% will note that the -rin(i-alstresses at fail%re had the sa.e orientation as they did at the :eginning of the test* or the a+ial e+tension AEB and lateral (o.-ression LF tests

see igs* 1*$$ and 11*!# for a review of these testsB, the -rin(i-al stressesrotate d%ring shear, and the stress -aths go belo( the hori&ontal a+is* Inthis (ase, L :e(o.es negative* I we went thro%gh a si.ilar e+er(ise as wedid in E+a.-le 11*1!, we wo%ld rea(h the sarne (on(l%sions as for the ACand 1 E testsD they have t:e sa.e strength* EP* A,. and el, :%t differentTP and .u. Toe stress (onditions for the AE anl LC tests are shown inig* 11*!2@ yo% .ight (o.-are these stresses with those shown 2n ig* E+*11*1!: and see what is .eant :y the rotation of -rin(i-al stresses* ig%re

11*! then shows ty-i(al test res%lts fro. AE and LC tests* The stress -aths for :oth tests are shown in ig* 11*!"*

Toe differen(e :etween the AC5LE and the AE5LC tests is reallya f%n(tion of the inter.ediate -rin(i-al stress a$ Note that for the first

two ty-es of tests we ass%.e that o$ 5 F#, and there is no rotation of -rin(i-al stresses fro. the :eginning of the test %ntil fail%re* 0n theother hand, for the 5AE5LC tests a2 / a, and a rotation of -rin(i-alstresses o((%rs* T2> rotation wo%ld :e even .ore dra.ati( if, for initial(onditions, we haddifferent verti(al stresses than hori&ontal stresses9 that is, 2

11 K ,.1 5 >(enDor this initial (ondition, 00 / a10 and a,.0 / *o / ((nD or :oth the AEand LC tests, the hori&ontal stress at fail%re :e(o.es the .a0or -rin(i-al stress, as shown in ig* 11*!2*

.j



<,

626 &hear &trenglh ol &and and Cla@

AY26l EY45n>23n AE L6456l C3N5>>23n LC

a G * o3 oG '55

:

ln2426l3n=2423n>:

a

A4 62lG5:

/ a - A3 - G ::¡: AG / a / a - % 5 A% /

$2. ." S45>> 3n=2423n> 3 45 6Y26l 5Y45n>23n AE.

N2n2N6l >45>> 2> n3D 323n46l 3 J34 45>5 45>4> 64

orne a(t%al test data on nat%ral (lays is shown in igs* J 1*!! and11*!7* These res%lts verify the assertions .ade a:ove that the EP, o5t , and

$1res-onses of C and LE, nd AE and LC tests ar esKsentiallyThe sa.e

:y the sign and .agnit%de of the -rin(i-al stress differen(e, o / o., 5ah , and is inde-endent of the -arti(%lar sha-e of the total stress -ath4isho- and Wesley, 16!B*

ote t at t e P for the AE and LC tests in igs* 11*!! and 11*!7did not (ross the AE5TP as it did in ig* 11*!"* This .eans that theind%(ed -ore -ress%re in these tests did not go slightly negative, in (ontrast

to the :ehavior of ig* 11*!"* Toe s-e(ifi( EP (hara(teristi(s for any givensoil .%st :e deter.ined :y la:oratory tests*Toe angle of in(lination of the fail%re -lanes as deter.ined a((ording

to the Gohr fail%re hy-othesis dis(%ssed in e(* 1*2B is dif ferent for theAE and LC tests :e(a%se of the rotation of -rin(i-al stresses* We .aydeter.ine this an le : %sin the ole .ethod* This ro(ed%re is shown 2n

ig* 11*!6 for the AC and AE tests@ si.ilar res%lts wo%ld :e fo%nd for theLE and LC tests* In s%..ary, then, for9

or AC and LE, no rotation of o1 and o#9 a.1/ 2> B, Q$

.



--------A% an HC

o q

A%

LC

AE

oE

$2. .) S45>>->462n 6n= N35 N5>>G5->462n G15> 3 AE 6n= LC

45>4> 3n 6 n36ll 3n>3l2=645= l6 645 H2>5l=, 9!.

F

'','

5A%, 503 , A%,555 W I

P, -3

'' K l2n5 5Y45n>23n

-; '$2. . S45>> N64> 3 45 AE 6n= LC 45>4>-n36ll 3n>3ll=645= l6.

7$!

1



## K1 l i ne 3(o.-ressio

!) -

!0

3

o# (onsant , o1 in(1easi*ng

a , (onsant , a * de(feasing

,,..,,..,,..$

1+ 5tarting -oint

1H..

10 K*,,,* 1 _

+

Ttal s*tre,ses -ress%re 3.

o*e

1

o

I%o

-+

'1

o

W llo** >=*r,*L;t

'..I LC

D :*

1+01 1 + 10 1 a.K*

!) 40 252 5# -2 o * #

trairl

O fB T346l

0-3n>3l2= 45= n=6 n5= 4 26Y26l4j

>4>>-> 62n G15> 3 554215,>454> N64> 6¡= J45 4> 3 6 n 6ll 3 >3l2=645= l6 45 2>3 6n=W >l5, 9) .

.Q

#3

6

dI



"

2 E ffe(tive stress

Tota stress N6of AC test

42 -ath of AC test

a**

$M

o %

1$

11

O? o@ o

5$ -3 /

$<Pal

52 -ath

o'f AE??a'n?d

===5***** Total stress -ath

LC test of LC test

6

42a**

0-- -- -- '$,.555 55o55a*****

-

F X X *i,X % X A+ial (o.-ression ACB

''L1.' A+ial e+ tention AE B

Lateral (o.-ression LCB

5$ * -. 51*$ *2 o*a 1*$A+ial strain

52

-e(i.en /oTest Ty-e

(T)

wn w, t 1#&

a5<Pal A

$ .a+

/ars (lay9!*2 1*$ *#6

!$* #2*6 *!#

!*# #2* *!#

A, is the -ore -ress%re -ara.eter flt fail%re :ased on e+-ressions in Ta:le 45#5$*

$2. .8. 6 T346l 6n= 554215 >.45>> N64> 6n= :B

3n>3l2=645= Gn=62n5= 426Y26l 45>4> 3n Gn=2>4GJ5= >6Nl5> 3 L5=6 l6 3 K6>, On4623 645 Law 6n= H3l4,

98.29

.j

o

#

&

--5

165$$5 *! AC !1*5t565$$5! *! LC !#*165$$5# *! AE !1*



o85ression:

a

Z1

83, &hear &trength of &and and Cla0

El55n4 64 $62lG5 M3 Cl5> 64 $62lG5

83*Z 2 78) /2

a 1 / 2 5 78) /2

$2. .9 Anl5 3 2nl2n6423n 3 45 62lG5 Nl6n5 3 AC6n= AE 45>4>.

11.1% &T!E&& PATH& ('!ING 'N(!AINE(OA(ING" O2E!CON&OI(ATE( CA)&

All of the -revio%s se(tion on %ndrained stress -aths (on(e.ed the :ehavior of norrnally (onsolidated (lays* or over(onsolidated (lays, the -rin(i-les are the sa.e :%t the sha-es oY t:e stress -a t:s a re diYferent :e(a%se the develo-ed -ore -ress%res are diff erent* E+a.-les of stress -aths for a+ial eo.-ression tests on overeonsolidated elays are shov. 2nigs* 1*$ and 11*#2:* /nowing how the e+(ess -ore water -ress%resdevelo- along with the sha-es of the total stress -aths for the vario%s ty-esof tests, yo% (an readily (onstr%(t the EP3s for over(onsolidated (lays*



.! S45G P54> &Gln n=6ln5l L36=ln-O153n>3l l=6l5= Cl6N !

F

''P, N'

'

K, l2n55Y45n>23n

-

$2. .80. AE 6n= LC >45>> N64> 3 6n 3153n>3l2=645= l6.

As dis(%ssed in e(* 11*11, over(onsolidated (lays %s%ally have a S.>1

.%(h greater than one* Therefore the stress Pslths for over(onsolidated(lays in sit% or for sa.-les re(onsolidated to 2n sit% stresses in thela:oratoryB will start fro. :elow the hydrostati( ( S lB a+is, as shownin ig* 1*$* ig%re 11*7 shows how the stres*s -aths for AE and LC testson an over(onsolidated (lay .ight a--ear*

E+AMPLE .8

(215n:

Consolidated %ndrained tria+tal (o.-ression tests are (ond%(ted on anover(onsolidated (lay with -re(onsolidation stress o4 of 7BB <Pa, whi(hiseF%ivalent to an* 8CR of 1*3 Toe res,*%lts are shown in ig* E+* 11*17a*Another CU test is (ond%(ted on the sa.e (lay at the sa.e 8CR and th%sthe sa.e o4. In the latter test, the lateral stress is not held (onstant, :%t isin(reased at the sa.e ti.e as the a+ial stress is in(reased so that Ao#5

*$ a1 > ee ig* E+* l l*17:*B Ass%.e that the test res%lts on this (lay

1



55 5555555555555555555 5 55555555DD -------

55

Í ' ,1

632 S56 S45n4 3 S5n=6 6n= Cl66

a , 5 a

a .,?'--- *QQ .

--G:6- ail %re

*"

Q*2:Q*$

1 1 1 1 1 1

n " R R 1 1$

.

%-*%-

5 .*$ 5 l a ,

5*2

o $ 2 " 7 1 1$ iaal --H--n ' H -

$2. EY. .86 I L* I

$2. EY. .8J

shown in ig* E+* 11*17a are valid for all ways of (hanging the :o%ndarystresses in (o.-ression, that is, :oth o and o* in(reasing d%ring the test*

R5FG25=:

Predi(t the :ehavior of the se(ond CU test*

a* Cal(%late the F%antities and fill in the (ol%.ns of Ta:le E+* 11*17for 8, *, $*, , and !*] strain*

:* 'raw the TP and the EP for this test*

-

#

Q

'-

e .j



11.13 &...... Patha Furln@ Kndralned *oaclln@0verconeolldatacl Clap

S3lG423n:

a. Ta:le E+* 11*17, filled in*

'()*+ +>. 11.11-

j ]B , Ao#

o o oo.s 1" #*$. SS 11*"

s.o 7 1"*1. 62 17*7

0¡ #

7 76" 7#*$

1#7 61*"1" 6"*1!2 67*7

$ A%

*1 o o*os #*"5 *11 . 59K**$# .!5 *#$ 5 .*

Ali stresses 2n <Pa*

b. ig* E+* 11*l e* Note that a4 aQ8CR B fro. EF 75$ Th%s7

Also

4%t, a4 7 <Pa* Therefore

F P6

40

&&e

// 7 <Pa

40 0 -, -3 P6

i * E+* 11*17(

0



8!" S55 S45n4 ol S6n=> 6n= Cl5>

Toe F%antity in -arentheses is what is -lotted in ig* E+* 11*17a* Now theval%es for ao1 and ao3 / *$ ao (an :e deter.ined fro. the fig%re andinserted a--ro-riately in Ta:le E+* 11*17* 8n(e the initial val%es are<nown* o and o* at ea(h strain are also readily o:tained*

or (al(%lation of au, %se EF* 11512 ass%.e / 1] for a tria+ialtest with -ore -ress%res .eas%redB or

au / ao3 $F ao1 - ao# B

/ *$ ao ` $F $o 1 - *$ ao

/ *$ *7A B Ao

Th%s val%es of C in Ta:le E+* 11*17 at e ieadily deternrined*

tress -aths are either (al(%lated fro. EFs* 1517 and 1516 or(onstr%(ted gra-hi(ally ig* E+* 11*17(B*Af ter C* W* Lovell*B

E+a.-le 11*17 1Il%strates two 1.-ortant -o.ts* hrst, the EP has thety-i(al sha-e of an over(onsolidated (lay (o.-are with igs* 1*$ and11*#2:B* e(ond, yo% (an %se the -rin(i-ies develo-ed -revio%sly for si.-le ordina ry tria +ial tests (onstan t (ell -ress%reB to -lot the res%lts of.ore (o.-le+ stress -ath tests*

." APPL ICATIO%S O$ STRESS PATHSTO E%(I%EEBI%( PRACTICE

In this se(tion, we offer sorne e+a.-les of how a <nowledge of thestress -aths hel-s to e+-lain what is ha--ening to the stresses in the gro%ndd%ring a given engineering loading or %nloading sit%ation* I yo% (an drawthe (o.-lete stress -ath for so.e (riti(al ele.ents in yo%r engineering

-ro:le., then yo% will have a .%(h :etter %nderstanding of the entire -w:le.* This <nowledge will ena:le yo% to design an a--w-1iate la:ota5tory test -rogra., to esti.ate the in sit% load5defor.ation res-onse of thes1I and str%(t%re, and f .ally to -lan a s.ta:le o:servahon and .str%

.entation -rogra. for .onitoring the (onstr%(tion o-erations and final -erfor.an(e of the str%(t%re*

I et3s loo< first a t wha t ha-- ens when we ta<e a sa.-le of nor.aHy (onsolidated (lay* We showed -art of the stress -ath d%ringsa.-ling in ig* 1*$1* The .ore (o.-lete stress -ath d%ng ali theo-erations ne(essary :efore the s-e(i.en is ready for testing is shown 2nig* 11*71* No wonder then that the %ndrained shear strengths are of tenvery .%(h less than in sit% strengths if the sa.-les are -oor*



11*12 A--ll(etlon ot tre% Pelh 43 Englneerlng Pra(tl(e !)

ND - 6

F /--$

AP 9 =Perfe(t= sa.-l ing

4C 9 T% :e sa.-lingC'9 E +tr%sion fro. t%:e'E9 Cavitation and water (ontent

redistri :%tionE 9 Tri..ing and .o%nting in the

tria+ial (ell

B

3n>3l2=645= l6 645 L6== 6n= L6J5. 9!.

Pro(ed%res for eval%ating sa.-le dist%r:an(e and (orre(ting the.eas%red shear strength are s%ggested :y Ladd and La.:e 16"#B

and

Ne+t, we shall (onsider the (ase of fo%ndation loading, for e+a.-le,a highway e.:an<.ent (onstr%(ted on a soft (lay fo%ndation* Let %sass%.e that the (lay is very nearly 1] sat%rated and is nor.ally(onsolidated* This (ase, as shown :y ig* 11*!#a, .ay :e .odeled :y a+ial(o.-ression stress (onditions* tri(tly s-ea<ing, as .entioned -revio%sly,the loading sho%ld :e -lane strain t9$ 8B for a long e. a nt, %t weshall %se the (o..on tria+ial test, with whi(h yo% are fa.iliar, for ill%strative -%r-oses* The stress -aths for this (ase are shown in ig* 11*7$(o.-are with ig* 1*$"B*

Let3s loo< a little .ore (losely at these stress -aths and their en5. . . .

; ' 3

,than 1 a:o%t *"B, so that the initial stress (onditions in the gro%nd are - otte as -o.t on t e 1g%re* n a o%n tton ing, e on&onstresses -ro:a:ly in(rease slightly, as we ass%.ed in E+a.-le 11*1", :%tfor this (ase we will ass%.e that they are essentially (onstant* Then, theT 5 % BP is the straight line A@. The total stresses re-resented :y -ointC are a--lied at the end of (onstr%(tion* Toe ind%(ed -ore -ress%res are

. .



- 1J

Z

5, 5'

.........

.........

'.........

,............

-Z

1 line

--r-J0e&tension)

F K1 2n5

6

J

$2. .8* S45>> N64> 3 6 3Gn=6423n l36=2n 6n= J3Gn=6423n 5Y616423n 3 n36ll 3n>3l2=645=X l6.

831



11*12 A--ll(atlon ol tre Path to Englneerlng Pr7Ctl(e 7#!

the ty-i(ally sha-ed EP hoo<ing off to the lef t, as is ill%strated :y (%rve A=. The distan(e =@, then, is n%.eri(ally eF%al to the e+(ess -ore -ress%re ind%(ed :y the e.:an<.ent loading* Note that the shear stresson a ty-i(al eleroeot %nder the e.:an<.ent in(reases fro. its initial val%eof F to F Had loading (ontin%ed to the level of L , the EP wo%ld have

1 1interse(ted the S line and fail%re wo%ld have o((%rred*

or this e+a.-le, let3s ass%.e that we were good designers, that we(orre(tly esti.ated the in sit% shear strength of the soil, and that no fail%reo((%rred* Then we are at -oint on the EP at the end of construction, the.ost (riti(al design (ondition for fo%ndatioo loadings on nor.ally (onsolidated (lays* Why is this Well, loo< at what ha--ens after we rea(h -oint =. The a--lied loading is (onstant thereaf ter ass%.ing no additional(onstr%(tion o((%rsB, the (lay starts to (onsolidate, and the e+(ess -orewater -ress%re that was (a%sed :y the load dissi-ates* This e+(ess -ore -ress%re is* re-resented :y the distan(e =@. Th%s the EP -ro(eeds alongline =@. Ulti.ately at u 1], all the e+(ess -ore -ress%re will J5dissi-ated and o%r ele.ent will :e at -oint C in eF%ili:ri%. %nder thee.:an<.ent load* lt will still have a shear stress F 1 a(ting on it, and p / p / p 1 in(e there is no e+(ess -ore water -ress%re re.aining in theele.ent, the total stresses will eF%al the eff e(tive stresses at -oint C. Nowyo% (an see why -oint = at the end of (onstr%(tion was the .ost (riti(alfor this (ase* Point was the (losest -oint to the fail%re line K 1. Af ter that, :e(a%se of (onsolidation, the fo%ndation soil :e(a.e stronger withti.esaferB %ntil at -oint C we were at the farthest -o.t fro. the K + hne for

this -arti(%lar loading sit%ation* That is why the end of (onstr%(tion is the.ost (riti(a for fo%ndation loading of nor.ally (onsolidated (lays* Theengineering lesson here is that if yo% .a<e it thro%gh the end of (onstr%( tion -eriod for this ty-e of loading, then (onditions :e(o.e safer with ti.e*

or the fo%ndation loading of an over(onsolidated (lay, the TP andEP wo%ld loo< so.ething li<e the -aths shown in igs* 1*$ and 11*#2:*As the negative e+(ess -ore -ress%re dissi-ates, the stresses on the ele.ent.ove (loser to the S 1line, whi(h .eans that the long5ter. (onditions area(t%ally the least safe after dissi-ation of the -ore -ress%re has o((%rred*4%t in .ost (ases, we are so far fro. the K 1 line anyway that long ter.(onditions are %s%ally not (riti(al*

- 5YAMPLE .9

(215n:

The e.:an<.ent of E+a.-le 11*1"* Tria+ial (o.-ression tests indi(ate"V' / $#> and e3 / ! <Pa*

1

DJ



4%4 &hear &trength ot &and and Cla@

F P6

!0

K1 l2n555599JLK

1/1) / $1*#

*0

O 0 *0 !0 "0 )0 0 0 80 90 -, -3 P6

$2. EY. .9

!euired:

Constr%(t the S line and deter.ine whether the e.:an<rnent will :esta:le*

, a1 %re wo

Another i.-ortant engineering sit%ation (on(e.s an e+(avation for a o%n a 1n . nor.a y (onso I ate ( ay* 1s s1t%at1on 1s 1 %strate .ig* 11*!# as an e+a.-le of a+ial e+tension* We already <now f ro. ig*

11*!" what the TP and EP loo< li<e for this (ase, they are also in ig* 11*7$:*in(e the verti l r

stress -ath goes f ro. the initial (onditions at -oint $ to -oint C. As withthe (ase of fo%ndation loading, the hori&ontal stresses .ay also de(rease

slightly, :%t for ill%stration -%r-oses, we shall ass%.e that they re.ain iy %ne ange * in(e nega ive -ore -ress%res o((%r %e o % oa 5ing the EP .%st lie to the right of the T 5 % BP* or the (ase shownwith %nloading fro. L down to F 1 , the EP then follows (%rve A=, and

-oint = re-resents (onditions at the end of (onstr%(tion* or this (ase,fail%re did not o((%r, and we are safe at the end of (onstr%(tion* Now, thee+(ess -ore -ress%re starts to dissi-ate5it is negative in this (ase, and nowit starts to :e(o.e .ore and .ore -ositive, following line DC. At -ointC, of (o%rse, ali the e+(ess negative -ore -ress%re wo%ld :e dissi-ated andthe total stresses wo%ld eF%al the effe(tive stresses* 4%t, this wo%ld never

0



." ANNll64l3n> 3l S45>> P64 43 Enln55ln P64l5 !8

o((%r :e(a%se w:eo the EP rea(hed -oint , it wo%ld interse(t theS 1line in e+tension and fail%re wo%ld o((%r* Therefore the long5ter.(onditionsare the .ore (r iti(al for the (ase of an e+(avation in nor.ally (onsolidated(lays* In (ontrast to the (ase of fo%ndation loading, 0%st :e(a%se yo% getthro%gh (onstr%(tion witho%t a fail%re doesn3t .ean that yo% are free of a -ossi:le fail%re* No, the e+(avation will :e(o.e less and less safe withti.e* ield .eas%re.ents for e+a.-le, La.:e and Whit.an, 16"6B haveshown that the rate of dissi-ation of this negative -ore -ress%re o((%rsrelatively fast, .%(h faster than in the (ase of fo%ndation loading* There forethe engineering i.-li(ation for this (ase is to get that e+(avation filled andthe (lay loaded as fast as -ossi:le* 8therwise yo% ris< a fail%re o((%rring at

sorne ti.e, -erha-s only a few wee<s af ter (orn-letion of the e+(ava tionThis is another e+a.-le of the long5ter. (onditions :eing .ore (riti(althan the end of (onstr%(tion (onditions*

These e+a.-les ill%strate the val%e of t:e stress -ath .ethod* o%(an (onstr%(t si.ilar TP and EP diagrarns for the other (ases shown inftg* .Q#, for :oth nor.alty and over wnsolidated elays, and see what the(riti(al design sit%ations are* orne of the (riti(al (onditions for sta:ilityare s%..ari&ed in Ta:le 1151 Ladd, 16!1"B*

TABLE -0 C2426U C3n=2423n> 3 45 S46J2l24 3 S64G645= Clays

o%ndation Loading9

eil Ty-(9 S34 %@ (lay tiff Chighly OC (lay

Criti(a(ondition9

(aseno drainageB

Pro:a:ly UU (ase :%t(he(< C' (ase drainageD24 eF%ili:ri%. -ore

-ress%resB

Re.at<9s* Use ` W 8, e 10

D24 a--ro-riate(orre(tionse(* 11*6B*

ta:ility %s%Uy nota .a0or -ro:le.

E+(avation or Nat%ral lo-e9

oil ly-e9 of t %F(lay tiff highly OC (lay

Criti(a(ondition9

Co%ld :e eitherUU or C' (ase

C' (ase

(o.-lete drainageB

Re.ar<s9 I soil is very 1ensiti@@e,2l.a9,(hang( fro. drain(dto %ndrain(d(onditions*

Use effe(tive stressenslysis wida(F%ili:l3i%. -ore

-r(ss%res* l (lay2> fiss%red, e3 and -erha-s

.ay de(reas( D24 ti.e*

After Ladd 16!1:B*

,¡



P!O,E3&

1151* A gran%lar .aterial is o:served :eing d%.-ed fro. a (onveyor :elt* I4 for.ed a (oni(al -ile with a:o%t the sa.e slo-e angle, 1*7hori&ontal to 1 verti(al* What (an yo% say a:o%t the .aterial

115$* A :attery filler 1s f11led w1th a .edrn. ro%nded sand . the1

densest state -ossi:le* Every effort is .ade to <ee- the sandsat%rated* A trans-arent t%:e allows o:servation of the water levelin the :attery filler* What will ha--en to the water level, if anything, as the :%l: is sF%ee&ed very hard Why Wo%ld it.atter if the sand were loose E+-lain*

115#* o% are (li.:ing %- a large sand d%ne west of %.a, Ari&ona*The slo-e angle is ##>* In what (o.-ass dire(tion are yo% traveling 'on3t forget the de(lination

1152* The -rin(i-al stress ratio for a drained test at fail%re was 2*"*What was the -ro:a:le relative density of the sand

115* 'enve EF* 115#*

115"* A dire(t shear test is (ond%(ted on a fairly dense sa.-le of ran<lin alls sand fro. New Ha.-shire* The initial void ratiowas *""7* he shear :o+ was !" .. sF%are, and 1r%t1ally the

height of the s-e(i.en was 11 ..* The following data were(olle(ted d%ring shear* Co.-%te the data needed and -lot the%s%al (%rves for this ty-e of test*

Ti.e Merti(al Hori&ontal Thi(<ness Hori&ontalEla-sed Load 'is-la((.ent Change Load.inB <NB ..B ..B E%

o $*$ 7*76 #*" o* (onstantB 7*7$ #*2 #" 7*"# #*$ !$1$ 7*22 #*1 112# !*6$ #*# 12$72 !*17 #*6 1" "*#7 #*"# 1no" *26 #*" 1!22

Alter Taylor, 1627*B

1151* A (onventional tria+;al (o.-ression test is (ond%(ted on asa.-le of dense sand fro. t* Pe(< 'a., Gontana* The initialarea of the test s-e(i.en was 1 (.$ and its initial height was! ..*lnitial void ratio was *"* The following data were %:served

14,



=est No. 1o -

=est No. 2

A&ial<train\)

ol.1 B.22

;1 - ;B)

IPa)

oB21

@.1`.1;.

BL;B;

ol/8tri<train

\)

o- ;.1;

+ ;.@;

+ 2.L+ .1;+ .1;

A&ial<train

\)

o;.`22.;

o1 - oB)

IPa)

o

ol/8tri<train \)

o

@.;;.@L.@

1`.B2;.

B1`B;`

+ .;+ .B

1@.`1`.@2;.

A3tr A. Casa$ran.)

.F

Pro#le141

d%ring shear* irst* (al(%late the average area of the s-e(i.en*ass%rr%ng 1t 1s a nght (ir(%lar (ylinder al all ti.es d%ring the test*Then .a<e the (al(%lations ne(essary to -lot the a+ial stressvers%s a+ial strain and vol%.etri( strain vers%s a+ial strain (%rvesfor this test* Ass%.ing e3 / 8, what is ^QB3

Cha.:er train 'ial

Ti.e Press%re giving A H B 4%ret A+ial Load

Ela-sed <Pase(* -siB ..

o $"*7 *7

s*

*##

2 *"6"*1

6 !*"7*16*1$

$2 1*$11$*6

2" 1*#$

giving AM B

After Taylor, 1627*B

1157* The res%lts of two C' tria+*ial tests at d1fferent (onf .ing

-ress%res on a .edi%. dense, (ohesionless sand are s%..ari&ed inthe ta:le :elow* The void ratios of :oth s-e(i.ens werea--ro+i.ately the

$6 5 *"72$6* 5 1*7

9)0 5 #*#"!!1@V 5 #*777# 5 2*$!

5 2*#5 2*!15 4.84

612 5 2*6$61 5 2*6"

9090 5 *1

5 # inB (e % l:fB

$B $* o$B 1*61 17$ 21B

$1B 1*7" #!2 72B

$$2B 1*6$ "21 122B$2B $*1# !7! 1!!B

$!7B $*7 6$1 $!B

#16B #*"" 6! $17B

#6B 2*" 67# $$

2$B *2 6!

7B !*# 767 $$B

"#B 7*6 712 17#B



842 &hear &trength of &enda and Cla0

sa.e at the start of the test* Plot on one set of a+es the -rin(i-alstress diff eren(e vers%s a+ial strain and vol%.etri( strain EF* 1152B vers%s a+ial strain for :oth tests* Est;.ate the initial tangent.od%l%s of defor.ation, the =]= se(ant .od%l%s, and the strainat fail%re for ea(h of these tests*

1156* or the two tests of Pro:le. 1157, deter.ine the angle of internafri(tion of the sand at aB -ea< (o.-ressive strength, :B at%lti.ate (o.-ressive strength, and eB at ] a+ial strain* Co.5.ents*

1151* A sand is hydrostati(ally (onsolidated in a tria+ial test a--arat%sto 2$ <Pa and then sheared with the drainage valves o-en* At fail%re,

o1 5 o# B 1s 0" <Pa* 'eter..e the .aJor and ..or -rin(i-alstresses at fail%re and the angle of shearing resistan(e* Plot theGohr diagra.* This -ro:le. sho%ld :e followed :y the

11511* The sa.e sand as in Pro:le. I 151 is tested in a dire(t shear a--arat%s %nder a nor.al -ress%re of 2$ <Pa* The sa.-le failswhen a shear stress of $7 <Pa is rea(hed* 'eter.ine the .a0or and .inor -rin(i-al stresses at fail%re and the angle of shearingresistan(e Plot the Gohr diagra. E+-la in the d ifferen(es, if any,of these val%es with those o:tained in the -re(eding -ro:le.*

1151$* Indi(ate the orientations of the .a0or -rin(i-al stress, the .inor

-rin(i-al stress, aod the ailnre -la ne a t:e tests in Pra:le.s1151 and 11511*

1151#* A gran%lar soil is tested in dire(t shear %nder a nor.al stress of # <Pa The si&e af the sa.-le is ! "$ (. in dia.eter* l the soilto :e tested is a dense sand with an angle of interna f ri(tion of "* >, deter.ine th*e si&e of the load eell reF%ired to .eas%re theshear for(e with a fa(tor of safety of $ that is, the (a-a(ity of theload (ell sho%ld :e twi(e that reF%ired to shear the sandB*

11 12* The stresses ind%(ed :y a s%rfa(e load on a loose ho.onta1sandlayer were fo%nd to :e 2*"$ <Pa, != 1*#$ <Pa, o,. $*6

<Pa, and 1E1, - 1*#$ <Pa* 4y .eans %f Gohr (it (les, detennine if s%(h a state of stress is safe* Use EF* 1511 for the definition offa(tor of safety*

1151* l the sa.e shess (onditions as in P1o:le. 11512 aet on a 5verydense gravelly sand, is s%(h a state safe against fail%re

1151"* The effe(tive nor.al stresses a(ting on the hori&ontal and verti(al -lanes in a siltB gra*el soil are 1*61 GPa and #*17 GPa, res-ee



Pro#lea

tively* Toe shear stress on these -lanes is k *"2 G Pa* or these(onditions, what are the .agnit%de and dire(tion of the -rin(i-alstresses Is this a state of fail%re

1151!* A sa.-le of dense sand tested in a tria+ial C' test failed along a well5defined fail%re -lane at an angle of ""> with the hori&ontal* ind theeff e(tive (onf ining -ress%re of the test if the -rin(i-alstress differen(e at fail%re was 1 <Pa*

11517* A dry loose sand is tested in a va(%%. tria+*ial test in whi(h the -ore air -ress%re of the sa.-le is lwered :elow gage -ress%re towi thin a:o% t 6] of 5 1 a t.* Est i .ate t he -ri n(i -al stress d i fferen(e and the .a0or -rin(i-al stress ra*tio at fail%re*

11516* or the data shown in ig* 11*2a, what is aB the -rin(i-al stressdifferen(e and :B the -rin(i-al stress ratio at an a+ial strain of 1] for an effe(tive (onfining -ress%re of $ GPa

115$* or the (onditions given in Pro:le. 11516, -lot the Gohr (ir(le*

115$1* 'o Pro:le.s lDl516 and 115$ for the data shown in ig* 11*a*

115$$* A sa.-le of a(ra.ento River sand has a (riti(al (onfining -ress%re of 1 <Pa* l the sa.-le is tested at an ef fe(tive(onf ining -ress%re of 1 <Pa, des(ri:e its :ehavior in drainedand %ndrained shear* how res%lts in the for. of %ns(aled Gohr (ir(les*

115$#3 * or the sand of Pro:le. 115$$, des(ri:e the :ehavior in drained and%ndrained shear in a tria+*ial test if the effe(tive (onfining -ress%re is! <Pa*

115$2* A drained tria+ial test is -erfor.ed on a sand with o#(5 // *1

<Pa* At fail%re, T.a+ / 0 <Pa* ind 1, o 1 5 #B, and (-3*

1 15$* I the test of Pro:le. 115$2 had :een (ond%(ted %ndrained,deter.ine o15 # B1, (-3, (f?totat and the angle of the fail%re -lanein the s-e(i.en* u1/ 1 <Pa*

115$"* I the test of Pro:le. 115$ were (ond%(ted at anD initial (onfining -ress%re of 1 <Pa, esti.ate the -rin(i-al stress differen(e and

the ind%(ed -ore water -ress%re at fail%re*1 15$!* Ass%.e the sand of Pro:lern -*" is a(ra.ento River sand at a

5 void ratio of *7* I the initial vol%.e of the s-e(i.en was 0(.#, what (hange in vol%.e wo%ld yo% e+-e(t d%ring she@ir

115$7* What vol%rne (hange wo%ld yo% e+-e(t d%ring the test of Pro:le. 115$



5555555555555555555

6++ &hear &trength of &anda and Cla@a

l l 5$6* A silty sand is tested (onsolidated5drained in a tria+ial (ell where :oth -rin(i-al stresses at the start of the test were <Pa* l thetotal a+ial stress at fail%re is l *"# G Pa while the hori&ontal

-ress%re re.ains (onstant, (o.-%te the angle of shearing resistan(eand the theoreti(al orientation of the fail%re -lane with res-e(t tothe hori&ontal*

l l 5#* The silty sand of Pro:le. 115$6 was inadvertently tested (onsolidated5%ndrained, :%t the la:oratory te(hni(ian noti(ed that the

-ore -ress%re at fail%re was $6 <Pa* What was the -rin(i-al stressdifferen(e at fail%re

1 15#1* I the (onsolidation -ress%re in the CU test of Pro:le. 115# were1 <Pa instead of <Pa, esti.ate the -ore -ress%re at fail%re*

115#$* A sa.-le of sand failed when o - o! was 6 <Pa* l thehydrostati( (onsolidation stress were # <Pa, (o.-%te theangle of shearing resistan(e of the sand* What else (an yo% saya:o%t the sand

1 15##* I the sa.-le of Pro:ie. 1 15#$ were sheared %ndrained and theind%(ed -ore -ress%re at fail%re were $ <Pa, esti.ate the -rin(i-al stress differen(e at fail%re* What wo%ld :e the angle of shearing resistan(e in ter.s of total stresses

115#2* A sa.-le of sand at the field density is <nown to have a oQo! B.a+of 2** I s%(h a s-e(i.en is hydrostati(ally (onsolidated to 1$1<Pa in a tria+ial test a--arat%s, at what effe(tive (onf ining -ress%re o4Wwill the sa.-le fail if the verti(al stress is held (onstantI:is is a l a tera l e+tensian test B

115#* Two C' stress -ath tria+ial tests are (ond%(ted on identi(al

A B

)0 P6

ln2426l3n=2423n>:

o

l**9la 1 80 P6 i..:6a, i **9la#

A4 62lG5:

59@T**9la, 9 #

$2. P-!)

<);' i

'5@@

CE CE



Problem-145

sarn-les of the sa.e sand* 4oth s-e(i.ens are initially (onsoli5a e y

shown in ig* Pl 15#* -e(i.en A failed when the a--lied a, was17 <Pa* Ga<e t e ne(essary (a (% a ion(ir(les at fail%re for :oth tests, and :B the stress -aths for :othtests* eB 'eter.ine ' for the sand* Af ter C* W* Lovell*B

115#"* Plot a gra-h of o4 a, vers%s B, . en yo% s wo%ld have :een hel f %l for solving sorne of these

-ro:le.s*B What range of val%es of 9, sho%ld :e %sed

1**@#!* Est;.ate the shear strength -ara.eters of a fine :ea(hB sand PB*nd .a+i.%. void ratios*

%:ro%nded to s%:ang%lar sand has a 0 of a:o%t *1 .. anda %nif or.ity (oeffi(ient of #* The angle of s eanng res1stan(e.eas%red in the dire(t shear test was 2!>* Is this reasona:le Why

115#6* Esti.ate the B, val%es for aB a well5graded sandy gravel WBal a density of $*1 GgQ.#

@ :B a -oorly graded silty sand with afield

#* *

density@ and dB a -oorly graded gravel with an in sit% void ratio

of *2*

1152* The res%lts of a series of C' tria+ial tests on a .edi%. dense,

(ohesionless sand are s%..ari&ed in the ta:le :elow* Toe voidratios for all t e test s-e(1.ens wer the start of the test* Plot the strength (ir(les and draw the Gohr fail%re envelo-e for this series of tests* What angle of inte.alf ri(tion sho%ld :e %sed in solving sta:ility -ro:le.s in whi(h therange of nor.al stresses is aB 5 <Pa@ :B 151 <Pa@

Confining Press%re C*o.-ressive trength

Test No* P6 <PaB

$ 2 17!

2 177 0SO

s *990 1$

#7 1$"6

Alter A* Casagrande*B

11521* Est;.ate the val%es of the (oeffi(ient of earth -ress%re at rest,S , for the fo%r soils of Pro:le. 115#6*

.j



$48 &hear &trength of &and and Cla@

1152$* l the sands of Pro:le. 1152l had :een -reloaded, wo%ld yo%r esti.ate of S Why

:e any different l so, wo%ld 24 :e higher or lower

11 2#* Est;.ate K for sands l, 2, 2, ", , and 1 in Ta:le 115$ for relative,densities of 2] and 7]*

115223* or f%t%re referen(e, -la(e a s(ale of S on the ordinate of ig*

11*1#* o% sho%ld -ro:a:ly also indi(ate a range of val%es of S >

1152* E+-lain the diff eren(e :etween IiF%efa(tion and (y(li( .o:ility*

1152"* The Pea(o(< diagra. ig* 11*18B has :een %sed to -redi(t the -ore -ress%re res-onse of %ndrained tests on sands, :ased on thevol%.e (hanges o:served at fail%re in dra ;oed tests A4 a giveovoid ratio a sa.-le (onsolidated at an effe(tive (onfining -ress%reless than >9q (nt wo%ld :e e+-eeted to offer 88e resistanee toIiF%efa(tion sin(e it sho%ld have a dilative tenden(y and thereforedevelo- negatlve -ore water -ress%reB than a sa.-le (onsohdated

at a (onfining -ress%re higher than o#(rit as this one sho%ld tendto de(rease in vol%.e d%ring shearB* This is (ontrary to what has

:een fo%nd in the la:oratory in (y(li( tria+ial tests* E+-lain thea--arent (ontradi(tion*

1152!* ig%re 11*17: shows that at the tenth (y(le, the (hange in -orewater -ress%re is a:o%t "" <Pa 0%st at the :egiooing of thea--li(ation of the -rin(i-al stress differen(e* et, at a F%arter of a(y(le latet as well as slightly :eforeB the -ore water -ress%re is 0%st a:o%t eF%al to the eff e(tive (onfining -ress%re* At this ti.ethe -r.(1-al stress d1ff eren(e 1s Mero E+-la. th1s o:serva%on* I4will hel- if yo% %nderstand the answer to Pro:le. 1152"*B

11527* A Iarge -ower -lant is to :e (onstr%(ted at a site i..ediatelyadJa(ent to the 8h1 River* 1he soils at the s1te (ons1st of . of Ioose to .edi%. dense gran%lar .aterials, and the gro%nd water ta:le is near the gro%nd s%rfa(e* in(e there are severa -otential

ea rthF%a<e sonr(e areas that (o%ld infl%en(e the site , list sorne.eas%res that (o%ld :e ta<en to -rote(t the fo%ndation of thisi.-ortant st.et%re fro. liF%efaetion andQor eyeli( .o:ility*

B B 526 We sta ted io e(s O aod 1 1 6 tha t the irn(oosalida red5d rainedtest was .eaningless :e(a%se it (o%ld not :e -ro-erly inter-reted*WhB is this so 'ise%ss in ter.s of la:oratory tests as weH as

-ossi:le -ra(ti(a a--li(ations*

1



Pro#le 1+M

115* A C' a+ial (o.-ression tria+ial test on a nor.ally (onsolidated(lay failed along a (learly defined fail%re -lane of !>* The (ell -ress%re d%ring the test was $ <Pa* Esti.ate 48 , the .a+i.%.

oS / o* , and the -rin(i-al stress differen(e at fail%re*

1151* %--ose an identi(al s-e(i.en of the sa.e (lay as in Pro:le. 115 was sheared %ndrained, and the ind%(ed -ore -ress%re at fail%rewas 7 <Pa* 'eter.ine the -rin(i-al stress differen(e, totalan d eff e(tive -rin(i-al sliess I atios, B,, 2?,otal , A+ 6n= a f for this test*

115$* A series of drained dire(t shear tests were -erfor.ed on a sat%rated(lay* The res%lts, when -lotted on a Gohr diagra., gave e3 /1 <Pa and 46n N' ** Anothe1 san1-le of this (lay was (onsoli5

dated to an effe(tive -ress%re of 00 <Pa* An undrained dire(tshear test was -erfor.ed, and the .eas%red val%e of &ff was" <Pa* What was the -ore water -ress%re at fail%re3 Was thesa.-le nor.ally (onsolidated3 Why3

115#* Toe follow.g .for.a:on was o:ta.ed fro. la:oratory tests on *s-e(i.ens fro. a (o.-letely sat%rated sa.-le of (lay9

aB The sa.-le had in the -ast :een -re(o.-ressed to at least $5.

:B A s-e(i.en tested in dire(t shear %nder a nor.al stress of "<Pa, with (o.-lete drainage allowed, showed a sheanng

strength of # <Pa*(B A s-e(i.en whi(h was first (onsolidated to " <Pa, and thens%:0e(ted to a dire(t shear test in whi(h no drainage o((%rred,showed a shearing strength of 1! <Pa*

Co.-%te et,3 and (t,y for the %ndrained (ase* <et(h the Gohr enveln-es whi(h yo% wo%ld e+-e(t to ohtain fro. a series of %ndrained and drained tests on this (lay* After Taylor, 1627*B

1152* Tria+ial tests were -erfor.ed on %ndist%r:ed sa.-les fro. thesa.e de-th of organi( (lay whose -re(onsolidation load, de5ter.ined fro. (onsolidation tests, was in the range 6 to 1" <Pa*The -rin(i-al stresses at fail%re of two C' tests were

Test No 1D a*5 $ <Pa ,Test o* $9 a# // *8 <Pa, o / 6!6 <Pa

loaded in a+ial (o.-ression* D

D J




tress 'ifferen(e<PaB

train]B

Pore Press%re<PaB

o o o# *" 1" *1 #$6 *# 49

1$ *# !#1 *6 117 1*"7 122$1 2*2 17!$2 1* $#7

aB Plot the Gohr (ir(les at fail%re and deter.ine ' fro. the C'tests for the nor.ally (onsolidated -ortion of the fail%reenvelo-e*

:B or the CU test, -lot (%rves of -rin(i-al stress differen(e and -ore -ress%re vers%s strain*

eB 8n a p5L diagra., -lot the stress -aths for the C' and CUtests* What is the 8CR of the nor.al stresses on the fail%re

-lane at fail%redB Ass%.ing that the single CU test for whi(h data are given is

re-resentative for CU tests r%n at -ress%res well a:ove the -re(onsolidation stress9 aB What is V in ter.s of total stressesa:ove the effe(ts of -re(onsolidation :B What is V' de ter.ined

:y the CU test a:ove the effe(ts of -re(onsolidationAf ter A* Casagrande*B

115* In Pro:le. 1152, fail%re in the CU test was ass%.ed to haveo((%rred when the .a+i.%. -rin(i-al stress differen(e wasrea(hed* Cal(%late and -lot the -rin(i-al effe(tive stress ratiovers%s strain for this test* What is the .a+i.%. u4 / u3U Is thereany differen(e in ' for the two fail%re (riteria Hint9 t%dy hg*11*#*

115"* A CU tria+ial test is -erforrned on a (ohesive soil* Toe effe(tive(onsolidation stress was ! <Pa* At fail%re, the -rin(i-al stressdifferen(e was 1$ <Pa, and the .a0or effe(tive -rin(i-al stress

was 17 <Pa* Co.-%te <ern-ton3s -ore -ress%re (oeffi(ient $ atfail%re*

115!* %--ose another s-e(i.en of the soil in the -re(eding -ro:le.develo-ed a .a0or effe(tive -rin(i-al stress of $$ <Pa at fail%re*

What wo%ld <e.-ton3s -ore -ress%re (oeffi(ient $ at fail%re :e,if a4 / 6 <Pa D



12@-

;@2;

+ ;

Pro#le 1+

1157* Two sa.-les of a slightly over(onsolidated (lay were tested intria+ial (o.-ression, and the following data at fail%re were o: tained*The -re(onsolidation stress for the (lay was esti.ated fro.oedo.eter tests to :e a:o%t 2 <Pa*

-e(i.(n + P6 7 P6

aB 'eter.ine the <e.-ton -ore -ress%re -ara.eter $ at fail%re

for :oth tests*:B Plot the Gohr (ir(les at fail%re for :oth total and ef fe(tive

stresses*eB Est;.ate (-3 in the nor.ally (onsolidated range, and $ and 48

for the over(onsolidated range of stresses*

1156* Two identi(al s-e(i.ens of sof t sat%rated nor.ally (onsolidated(lay were (onsolidated to 1 <Pa in a tria+ial a--arat%s* 8nes-e(i.en was sheared drained, and the -rin(i-al stress diff eren(eat fail%re was # < Pa* The other s-e(i.en was sheared %ndrained, a nd the -rin(i-al stress differen(e at fail%re was $ <Pa*

'eter.ine aB 48 and 3Ptotal@ :B u1 in the %ndrained s-e(i.en@ eB $1 in the %ndrained s-e(i.en@ and dB the theoreti(al angle of fail%re -lanes for :oth s-e(i.ens*

115"* A (lay sa.-le is hydrostati(ally (onsolidated to 1* GPa andthen sheared %ndrained* The a1 5 a#B at fail%re was also eF%alto 1 GPa* I drained tests on identi(al sa.-les gave 48) / $$,eval%atethe -ore -ress%re at fail%re in the %ndrained test and (o.-%te<e.-ton3s $ -ara.eter*

l l5"1* An %ndrained tria+ial (o.-ression test was -erfor.ed on a

sat%rated sa.-le of nor.ally (onsolidated (lay* The (onsolidation -ress%re was 1 <Pa* The s-e(i.en failed when the -rin(i-alstress differen(e was 7 <Pa and the ind%(ed -ore* water -ress%rewas "! <Pa* A (o.-anion %ndrained test was -erf or.ed D on anidenti(al sa.-le of the sa.e (lay, :%t at a (onsolidation -ress%reof $ <Pa* What .a+i.%. -rin(i-al stress differen(e wo%ld yo%e+-e(t at fail%re for this se(ond test s-e(i.en What are "V' and

.l



85, &hear &trength of &and and Cla@

l3462d Predi(t t:e aogle af the failnre -lanes far the two %ndrainedtests* 'eter.ine $Wfor this (lay*

115"$* The following data were o:tained fro. a CU test with -ore -ressnres .eas%red on an %ndist%r:ed s-e(i.en of sandy silt*The (onsolidation -ress%re was 7 <Pa and the s-e(i.en wassheared in a+ial (o.-ression*

aB Plot (%rves of -rin(i-al stress diff eren(e and -ore -ress%resvers%s strain Plot on one sheet

:B Plot the stress -aths on a p'B diagra.*eB W11at is the .a+i. %. dfe(tive -rin(i-al stress ratio de**elo-ed

in this test Is it the sa.e as the .a+i.%. o:liF%ity for thiss-e(1.en*

dB Is there any differen(e in B, as deter.ined when the -rin(i-alstress differen(e or t:e -rin(i-al effe(tive stress ratio is a

After A. Casagrande*B

115"#* Ty-i(al (onsolidated5drained :ehavior of sat%rated nor.ally (onsolidated sa.-les of Ladd3s 16"2B si.-le (lay are s:own in ig*PI 15"#* o% are to (ond%(t another a+ial (o.-ression C' tria+ialtest on the sa.e (lay with the effe(tive (onsolidation stress eF%alto 00 <Pa* or this test esti.ate aB the water (ontent and :B the

-rin(i-al sltess diffet etlCe at an a+ial sttain of ]* Af te1 C* W*Lovell*B

Prin(i-al tress'i ffer(n(e train

Ind%(edPore Press%re

<PaB ]B <PaB

o$$" o*11 o71

"6! *2 #$#]7 *66 2

12! $*$ #"

$7$ *!7 - 009#6 7*21 5 $7121" 11*17 5 #22# 1#*6# 5 !#2#1 1"*7$ 5 !"!2$1 16*!1 5 !76



1;;

o 2 @ ` 1; % \)

aw \l

#i$. P11-@B

111

D ^

28

*

22

20

18-- .. .......... -- ........ ---

D,o $ )0 00 *00 )00 000 L3




115"2* The (onsolidation :ehavior of the si.-le (lay of Pro:le. 115"# isshown in ig* PI 15"#* Est;.ate the water (ontent of a sa.-le of this (lay at an 8CR of 1, if the .a+i.%. (onsolidation stress is <Pa instead of 7 <Pa* Af ter C* W* Lovell*B

115"* Tria+ial (o.-ression tests were r%n on s-e(i.ens fro. a large%ndist%r:ed :lo(< sa. le of (la * 'ata are iven :el w*thro%gh 2 were r%n so slowly that (o.-lete drainage .ay :e

.

Gohr fail%re envelo-es for this soil* 'eter.ine the Gohr5Co%lo.:strength -ara.eters in ter.s of :oth total and eff e(tive stresses*Af ter Taylor, 1627*B

a*1 , Y5 246c,c , Y5

76 36 "481 231 1#1 #

What (an yo% say a:o%t the -ro:a:le in sit% 8CR and S ( ay * s 1t -oss1 e to esti.ate the E; and &f of this soil of this

115""* trength tests (ond%(ted on sa.-les of a stiff over(onsolidated(lay gave lower strengths for C' tests than for CU tests* Is thisreasona:le Why Af ter Taylor, 1627*B

<Pa* In whi(h of the following tria+ial tests wo%ld yo% e+-e(t the(o.-ressive strength to :e larger Why

aB A C' test -erfor.ed at a (ha.:er -ress%re of 1 <Pa*:B A CU test -erfor.ed at a (ha.:er -ress%re of 1 <Pa*

115"7* An %n(onfined (o.-ression test is -erfor.ed on a dense silt*Previo%s drained tria+ial tests on si.ilar sa.-les of the silt gavecp / #>* I the %n(onfined (o.-ressive strength was 2! <Pa,est;.ate the hei ht of (a illa rise in this soil a:ove the ro%nd

water ta:le* Hint9 ind the effe(tive (onfining -ress%re a(ting on

115"6* Est;.ate the in sit% val%e of S of the silt of Pro:le. 115"7* Is thisval%e reasona:le in ter.s of the (orrelation shown in ig* 11*"6

115!* Another s-e(i.en of the dense silt of Pro:le. 115"7 is tested in%n(onf ined (o.-ression* Ass%.e the avera e ore si&e of the siltis $ X ., and esti.ate the (o.-ressive strength of the sa.-le*

.

Test No*9 * # 2 2 " ! 7

(51 5 a* )9,Y5 22! 167 6 37 331 1 133 116

1



Pro#lea 1#

115!1* What wo%ld ha--en if the s-e(i.en of Pro:le. 115"7 was -re5

-ared in a loose state, then sheared What wo%ld :e 1ts %n(onhned(o.-ressive strength

115!$* The res%lts of %n(onf ined (o.-ression tests on a sa.-le of (lay in :oth the %ndist%r:ed and re.olded states are s%..ari&ed :elow*'eter.ine the (o.-ressive strength, the initial tangent .od%l%s of defor.ation, and the se(ant .od%l%s of defor.ation at ] of the(o.-ressive strength for :oth the %ndist%r:ed and re.olded s-e(i.ens* 'eter.ine the sensitivity of the (lay* or the sol%tion of a -ra(ti(a sta:ihty -ro:le. involving this (lay in tite andistar :edstate, what shear strength wo%ld yo% %se if no (hange in water (ontent o((%rs d%ring (onstr%(tion* Af ter A. Casagrande*B

Undist%r:ed tate Re.olded tate

A+ial train :..a A+ial train

:..a

]B <PaB ]B l(PaB

o o o.* o-

$ 61 2 $

" 133 " 32

7 149 7 212 160 12 47

G: '?'' l f, so20 1"1 20 1

115!#* aB how that EF* 1157 in E+a.-le 11*1$B is (orre(t for undrained

tria+ial or %n(onfined (o.-ression tests* :B 'erive a s.%lar e+-ression \6 the area of the s-e(i.en in a drained tria+ial test*

Hint9 $., / fF $ , Z , t, LlV.

115!2* In ea(h of the following (ases state whi(h test, V or , sho%ldshow t:e greater shearing strength* E+(e-t for the differen(e stated :elow, the two tests are the sa.e ty-e in ea(h (ase tria+ial, dire(ts:ea1, et(*B anti fer identieal elay sa.-les*

aB The tests are r%n with no drainage allowed, and test R 2> r%n.%(h aster than test 9S *

:B a.-le ` is -re(onsolidated to a larger -ress%re than sa.-le V the -ress%res d%ring the tests are ali<e for the two (ases*

eB Neither saro-le is -re(onsolidated@ test V is allowed to draind%ring shear and test ` is not allowed to drain*

dB 4oth sa.-les are highlB overeo.olidated@ test V is not allowed to drain and test ` is allowed to drain*

DJ

*****



$54 &hear &trength of &and and Cla@

eB Test R is on a sa.-le that is essentially in the %ndist%r:edstate, and test V is on a s-e(irnen with a--re(ia:ly dist%r:edstr%(t%re :%t with the sa.e void ratio as R.

Af ter Taylor, 1627*B

115!* List the advantages and disadvantages of ea(h of the field testslisted in Ta:le 115" for deterrnining the %ndrained shear strengthof (ohesive soils*

115!"* Whi(h of the tests in Ta:le 115" are a--ro-riate to rneas%re the%ndrained shear strength for aB a :%ilding fo%ndation and hB a (%t slo-e for a highway in ea(h of the following five (ases9

iB ensitive (andinavian (lay*iiB 8rgani( .arine (lay fro. the U** %lf Coast*iiiB tiff fiss%red (lay till fro. the .;dwest United tates*ivBCanadian fi:ero%s -eat*vB Heavily over(onsolidated swelling (lay fro. New Ge+i(o*

l l5!!* Esti.ale the .a+i.%. e+-e(ted val%e %f tire -or e -1ess1e -ara5.eter = for the following soils9

aB Co.-a(ted gla(ial till at / 6]*:B oft sat%rated nor.ally eonsolidated 4oston :l%e day* (B oil aB at / 1]*dB %ff over(onsohdated (lay at 5 66]*

eB Loose 8ttawa sand at / 6] and 1]*fB Co.-a(ted (layey silt at / 6] and s%:0e(ted to high(onfining -ress%res*

gB 'ense 8ttawa sand at / 66] and 1]*

115!7* A $ . thi(< fill is (onstr%(ted at the s%rfa(e of the soil -rofile of E+a.-le !** I the (lay is slightly over(onsolidated, est;.ate the(hange in -ore -ress%re at -oint A of ig* E+* !**

115!6* A s1l sa. -le is ta<en fro. the rnid-oint of the (lay layer of E+a.-le !*, that is, fro. a de-th of " .* I the -ore -ress%re

-ara.eter $u for %nloading is *6, est;.ate the effe(tive verti(alaod :ari&anta J stresses a(tiog an the sa .-le 0%st :efore testing in

the la:oratory* Ass%.e cf,3 for the (lay is $>* Hint9 'raw ele.entswith stresses si.ilar to ig* 11*#7, and %se the def;nition of sttessincre8ents in A--endi+ 45#* Af ter * A. Leonards*B

1157* What wo%ld yo%r answer to Pro:le. 115!6 :e if yo% %sed EF*11 $$ instead of 11 1#

11571* A sa.-le of nor.ally (onsolidated (lay is re.oved fro. 51 . :elow the gro%nd s%rfa(e* The effe(tive verti(al over:%rden stress



Problema

is $ <Pa, and S is *7* l the -ore -ress%re -ara.eter d%e tosa.-ling is 8*!, esti.ate the (hange in -ore -ress%re 2n the sa.-lewheri it is re.oved f ro. the (lay layer* What effe(tive stresses a(ton the s-e(i.en af ter e+tr%sion fro. t he sa.-le t%:e Ass%.ethe gro%nd water ta:le is at the s%rfa(e*

1157$* how that u in E+a.-le 1 151" is a:o%t #$ <Pa, as -redi(ted :yEFs* 115$$ and 115$*

1157#* Pre-are a listing of those relationshi-s in Cha-ter 11 and elsewherethat (an :e %sed to -redi(t a soil -ara.eter or -ro-erty na.ely,L,, e, / B when sorne other -ro-erty w, PI, et(*B is <nown* List the -age and fig%re n%.:er, ordinate, a:s(issa, and varia:les of the

gra-h, if any* This listing will J5 hel-f %l for solving the ne+t fo%r -ro:le.s*B

11572* or the data shown in ig* 7*, esti.ate the %n(onfined (o.-res sivestrength and the sensitivity of this soil* Ty-i(al val%es for the (lay areLL // 77, PL / K2#, and PI // 2*

1157* The data -resented in ig* 7*1: are for a :la(< fiss%red organi(silty (lay or (layey silt* At a de-th of " ., esti.ate the e+-e(tedval%e or range of val%es of the %ndrained .od%l%s*

1 157"* A (ohesive soil with a liF%idity inde+ of 1 has a nat%ral water (ontent of ]* Est;.ate as .any soil -ara.eters 6> yo% (an*In(l%dt, if yo% (an, (o.-ressi:ility and rate of (o.-ression -ara.eters as well as those related to shear strength*

1157!* The .edi%. gray silty (lay of ig* 7*17: at a de-th of $ . hadan LL of #7 and a PL of $#* Esti.ate the following -ara.eters for this soil9 aB (oeffi(ien t of earth -ress%r e al test, :B effe(tie angleof internaB fri(tion@ eB ratio of 5r 1 J a4

4 dB a(tivity@ eB sensitivity@

and & the %ndrained o%ng3s .od%l%s* Are there any in(onsisten(ies in the val%es yo% o:tained l so, dis(%ss the -ossi:lereasons*

11577* A nor.ally (onsolidated (lay has a "' of #>* Two identi(als-e(i.ens of this (lay are (onsolidated to $ <Pa in a tria+ial (ell*Predi(t the .a+i.%. and .;ni.%. -ossi:le a+ial stresses in the

s-e(i.ens for a (onstant (ell -ress%re* Hint9 The *first test is ana+ial C8IJ1-ression test, the se(ond test is an a+ial e+tension test*What ass%.-tions are ne(essary to solve this -ro:le.

1 1576* The effe(tive stresses at fail%re for three identi(al tria+ial s-e(i.ens of an over(onsolidated (lay are shown in ig* PI 1576* Plotthe Gohr (ir(les at fail%re and deter.ine "' and e3* 'eter.ine the

1



6+6 S56 S45n4 3 S6n=> 6n= Cl6>

d@oo P6

2 < Pa

21$#

<Pa

o(@@@< Pa

L E B AC

$2. P-891

theoreti(al angle of in(lination of the fail%re -lanes in ea(h tests-e(i.en, and show these on a s.all s<et(h* Also s<et(h the

eff e(hve stress -aths for the three tests* Af ter C* W* Lovell*B1156* Tht ee identi(al s-e(i.ens sa.e e, (: of a (lay are nonnally

(onsolidated and sheared (onsolidated5drained C'B 2n :oth (o. -ression and e+tension* Toe stresses at fail%re for the three s-e(i.ens are as shown in ig* Pl l56*aB Plot the Gohr (ir(les at fail%re, and deter.ine cp and (f?totalD

:B 'eter.ine the in(lination of the -redi(ted fail%re -lanes fro.the Gohr fail%re hy-othesisB* <et(h the failed s-e(i.ens,showing their fail%re -lanes*

(B <et(h the three stress -aths* After C* W* Lovell*B

A AC B LC

8."C AE

$2. P-90

11561* A series of (onventional tria+ial (o.-ression tests were (ond%(tedon three identi(al s-e(i.ens of a sat%rated (lay soil* Test res%ltsare ta:%lated :elow*

-e(i.en 21%,<PaB

A 1 1! 2

e # 360 1#

aB <et(h the total and effe(tive stress -aths for ea(h test, anddeter..e the Gohr5Co%lo.: strength -ara.eters in ter.s of



Pro:le.a 1!

:oth total and effe(tive stresses* :B Est;.ate the theoreti(al angleof the fail%re -lanes for ea(h s-e(1.en* (B 'o yo% :eheve this(Jay is nonnally or over(onsolidated Why

1156$* Ass%.e that the ind%(ed -ore -ress%res at fail%re for Pro:le.11561 were9 s-e(i.en A, - 1 <Pa@ s-e(i.en =, 52 <Pa@ ands-e(i.en C, 7 < Pa@ and that everything else was the sa.e* Now do -arts aB and :B a:ove, and then answer -art (B*

1156#* An a+ial (o.-ression CU test has :een -erfor.ed on an %nd1s t%r:eds-e(i.en of 00 sat%rated organi( (lay* Toe data for the test aregiven in Pro:le. 1152* A lateral e+tension test is to :e -erfor.ed onan identi(al s-e(i.en at the sa.e (onsolidation -ress%re and with the

sa.e ti.e of (onsolidation and ti.e of loading as in the a+ial(o.-ression test*

aB Plot the total and effe(tive stress -aths* 'eter.ine the (%rve of -ore -ress%re vers%s 1B -rin(i-al stress differen(e and $B a+ialstrain that yo% wo%ld -redi(t theoreti(ally for the laterale+tension test*

:B 8n the p'B diagra., draw the line (orres-onding to &eroind%(ed -ore -ress%re and the line along whi(h the .agnit%deof the ind%(ed negative -ore -ress%re is eF%al to the -rin(i-alstress dif feren(e*

(B What is $, for :oth the AC and LE test

Af ter A* Casagrande and R* C. Hirs(hfeld*B11562* The following data were o:tained fro. a (onventional tria+ial(o.-ression test on a sat%rated ( = / 1B, nor.ally (onsolidatedsi.-le (lay Ladd, 16"2B* The (ell -ress%re was held (onstant at 1<Pa, while the a+ial stress was increased to fail%re a+ial (o.-res5

sion testB*

C D64 ]B A(r%ial <PaB 211 <PaB

o 3 3l #* 1*6* 2*2 *$ #*

" *2#*6

7 *" 2*1

1 .1 2*#

1$ *7 fail%re 2*2

6 Plot t:e s and llu vers%s a+ial strain (%rves* 'eter.ine .$.1.:B Plot t:e total and effe(tive stress -aths for the AC test*

(B What is 2?3 Ass%.e e3 8 for nor.ally (onsolidated (lay*B

1

DJ



$58 &hear &trength of &anda and Cla@a

A lateral e+tension LEB test was (ond%(ted on an identi(al sa.-leof the sa.e (lay sa.e e,wB* In this test, the a+ial or verti(al stresswas held (onstant at 1 <Pa, while the (ell -ess%re was decreased

to 2*$ <Pa, at whi(h ti.e the s-e(irnen failed*

dB Plot :oth the total and eff e(tive stress -aths for the LE test*eB 'eter.ine uW, a41, a4Wand $W for this test*fB ind 3Ptotal for :oth the AC and the LE tests*gB ind the theoreti(al in(linations fro. the Gohr fail%re hy

-othesisB of the fail%re -lanes in ea(h test* <et(h the s-e(i.enat fail%re, indi(ating the effe(tive stresses at fail%re and thefail%re -lane in(lination*

1 156* A (onventional tria+ial (o.-ression ACB test was (ond%(ted on asat%rated sarn-le of over(onsolidated (lay, and the following data,nor.ali&ed with res-e(t to the effe(tive (onfining -ress%re, wereo:tained*

ca+ial ]B $o/ o4 $u/ o4

o o o* *! *!

1 *6$ P o.os$ 1*#" 5 *#2 1*!! 5 *$$" 1*6! 5 *#7 $*1 5 *2"

1 $*1! 5 *$1$ $*$# 5 *712 $*$7 5 *"$1" $*## fail%r( D5 *"!

A lateral e+tension LEB test was (ond%(ted on an identi(als-e(i.en of the sa.e (lay* While the verti(al stress was .aintained eonstant, the eell -ress%re was de(r eased %ntil fail%r e o(5(%rred at the sa.e -rin(i-al stress differen(e as the AC s-e(i.enF IJ.a/ a4 / $*##B* ro. yo%r <nowledge of stress -aths and soil :ehavior, deter.ine aB the effe(tive and total stress -aths for :oth

tests and :B the -ore -ress%re vers%s strain res-onse of the LEtest* (B Can the Gohr5Co%lo.: strength -ararneters :e de terrninedWhy After C. W* Lovell*B

1156"* A S (onsolidated5%nd rained t ria+ial (o.-1ession o((ll /(onstant Btest was (ond %(ted on an %ndist %r:ed s-e(i .en of sensitivewedish (lay* The i nitial (onditions were as shown i n ig*Pl 156"a* The stress5strain and -ore -ress%re res-onse of thes-e(i.en is shown i n ig* PI I 56":*



·B;;

jo

:2;;Mt)

1

:i1;;

total ne%tral effe(tive

3 280P6

ig* P1156"a

train, E

$

:100

$ #train, E

ig* P1156":

.j



660&hear &trength ol &and and Cla@

aB ind the stress (onditions at fail%re and sy.:oli(ally show thetotal, ne%tial, and ef feetive stresses li<e the =initial (onditions=shown a:oveB*

:B <et(h the total and eff e(tive stress -aths*eB Plot $ vers%s c* What is $WU What are cp and (- T

1 156!* I an LE test were (ond%(ted on a sa.-le of wedish (layidenti(al to that tested . Pro:le. 1 156", -redi(t the -ore -ress%revers%s strain res-onse of the (lay* What is C1 and $WU What is (-T

11567* The data shown in ig* Pl 1567 were o:tained fro. several CUtests on a sat%rated (lay whi(h has an 8CR of 1 and a -re(on(*

*.0

1 q

5*2

$2. P-98



N1Pro:le.

solidation stress of 7 <Pa* It is ass%.ed that these res%lts areD,alid for all (o.-ressioo stress -aths on this (lay* o% are goingto r%n a s-e(ial stress -ath test on this (lay* Af ter (onsolidation at0 , the (ell -ress%re will :e in(reased in s%(h a way that *91o# /

*$ *91o1 %ntil fail%re o((%rs* or this s-e(ial stress -ath test, fill in

the ta:le :elow and -lot the total and eff e(tive stress -aths* Af ter

]B 2o1 <PaB 2o# <PaB o1 <*PaB o# <PaB u <PaB $

o*$*

*!*

11566* A series of CU (o.-ression tests on a si.-le (lay Ladd, 16"2B

-rovided the following test res%lts9

%ial ]B $5r,lo@ A

o o1 *# *#

$ *2 *"2

2 *$ *!"

" *2 *77

7 *" *6$1 .21 *6#

1$ fail%re *7 *62

aB In an a+ial (o.-ression test, if o4 / $ <Pa, deter.ine B1,P9, and P_ . :B ind 54' and e3. A s-e(ial lateral e+tension stress -ath testwas (ond%(ted on this (lay in whi(h the de(rease in lateral stresswas e+a(tly eF%al to the in(rease 2n a+ial stress@ that is,5Ao

#/ Ao or this (ase, if o4 / 2 <Pa, deter.ine *91o 1, L,p, p3,

and A% when eB the a+ial strain is 2] and dB at fail%re* After C* W* Lovell*B

1151* ig%re Pll51 shows nor.ali&ed data fro. an a+ial(o.-ression AF tria+ial test and a lateral (o.-ression LF

tria+ial test on sat%rated si.-le (lay Ladd, 16"2B* Ga<e thea--ro-riate (al(%lations, and -lot the (o.-lete total and effe(tive stress -aths for J34 tests* What are the Gohr5Co%lo.: strength -ara.eters'eter.ine $ 6 for ea(h test*

ZJ

1



Í '1

662 &hear &trength ol &and and Claa

$ 2 " B 1 1$ c a+ial

.lG

a *"

,*,* 555*"$B

*B

*2QQK LC AC

Q*$

o $ 2 " B 1 1$

a4

a4 LC ? K

K K $*$6B $*$6B

ca+ial

$Q AC

Q

3$ 2 " B 1 1$

c a+ial

ig* P1151

11511* Two s-e(i.ens of a sof t (lay fro. the <a5Ede:y test field inweden were re(onsolidated to their initial in sit% effe(tive stress(onditions and then sheared to fail%re* 8ne s-e(i.en was loadedin a+ial (o.-ression ACB, while the other was failed :y a+iale+tension AEB* Toe nor.ali&ed stress5strain and -ore -ress%restrain data for :oth tests are shown in ig* Pll511 after i..ie,16!#B* Pertinent s-e(i.en data is given in the a((o.-anying ta:le*aB 8n a p5L diagra., s<et(h he total, total 5 u , and effe(tivestress -aths for :oth tests* :B 'eter.ine 54V' and (f?totat 2n :oth

1



*& a ve

ot testsstart here

-4

5*1

$ # (%)

7 a'

GH2 AE *$ #1* 8 *9 72*$ *" 1*!

kAss%.ed*

o e9sit% -ore water -ress%re

6. In

ig* P11511

(o.-ression and e+tension* eB Cal(%late the <e.-ton -ore -ress%re -ara.eter A at fail%re for :oth tests* dB how in a s<et(h the

s-e(i.ens*

115l8i* Ar the val%es given and (al(%lated for K1 ,

&W/a1B,,et(*, for the

si.-le (orrelations with PI, LI, et(*, given in this (ha-ter

1151#* or the oil tan< -ro:le. in Cha-ter 7 Pro:le. 752"B, -lot the(o.-lete total, total 5 u , and effe(tive stress -aths d%e to (onstr%(tion and filling of the tan< for an ele.ent %nder the (enter lineof the tan< and at the .id-oint of the (lay layer* Ass%.e that

1




K at the site is *! and that the average val%e of the $ -ara.eter 1

:efore fail%re is *2@ ass%.e A1 ** Ga<e reasona:le esti.atesof the strength -ara.eters, and esti.ate the fa(tor of safet9against fail%re*

1 1512* What is the .a+i.%. saf e height of the e.:an<.ent for E+a. -les11*1" and 1 1*16 Plot a gra-h of fa(tor of safety vers%s height of the e.:an<.ent*

1151* How wo%ld yo% re(o..end the shear strength :e deter.ined for the following design sit%ations 7o%r answer (an in(l%de :othla:oratory and f ield tests or, in sorne (ases, no tests :%t sorneother design a--roa(h that .ay :e a--ro-riate* 4e as s-e(ifi( as

aB Long5ter. sta:ility of a (o.-a(ted (lay earth da.*:B ta:ility of a hydra%li( f ill sand da. %nder seis.i( loading*eB End of (onstr%(tion of a (o.-a(ted (lay earthf ill da.*dB o%ndation on a sof t sat%rated nor.ally (onsolidated (lay*eB hall %w fo%ndation on a loose dry sand*fB DDEnd of (onstr%(tion of an e+(avation in sof t nor.ally (on5

solidated (lay*gB C%t slo-e in an over(onsolidated stif f fiss%red (lay*hB Highway e.:an<.ent on a stiff fiss%red (lay*

. W5555D555D5 55555555 5



a00endi5 a

A00lication of the71 7@ite of'nitita Geatechnical En@ineering·

A. I%TRO&CTIO%

Within the s(ientifi( and engineering (o..%nity, there has always :een se.e eoaf %sion as to the -ro-e( syste. of %nits for -hysi(al.eas%re5 .ents and F%antities* Gany syste.s have :een advan(ed d%ringthe last few (ent%ries and sorne, s%(h as the I.-erial or 4ritishEngineering syste., the so5(alled **.etri( syste.,= and a few hy:rids,have a(hieved -o-%lar %sage* Re(ently, with the growth of international(oo-eration and trade, it has :e(o.e in(reasingly a--arent that one,single, (o..only a((e-ted syste. of %nits wo%ld :e not only (onvenient :%t also of tre.endo%s -raetieal val%e*

Altho%gh the field of geote(hni(al engineering .ay not (lai. thegreatest (onf %sion in the %se of %nits, it %ndo%:tedly ran<s near the to- of all fields in the n%.:er of diff erent syste.s in (o..on %sage* La:oratoryengineers, following their (o%nter-arts in the -hysi(al s(ien(es, have attern-t(d to %se sorne sort of .etri( syste., %s%ally the (gs (enti.etre5 gra.5se(ondB syste., for the si.-le la:oratory tests* They, with ease, a--ly the.<s .etre5<ilogra.5se(ondB syste. to .eas%re.ents of -res s%re andstress in (onsolidation and tria+ial tests, and, with sorne i.-%nity, they %se

4n:sh Eng.eering %nits Cor (o.-a(tion tests* As anB teaeher ef soil.e(hani(s (an testify, the (onf %sion to the %ninitiated is tre.endo%s* Atleast, -ra(ti(ing geote(hni(al engineers in North A.en(a have :eenso.ewhat (onsistent in the %se of the 4ritish Engineering syste. for la:oratory and field densities, stress .eas%re.ents, et(*, altho%gh they(o..only alte.ae :etween -o%nds -er sF%are foot, <i-s -er sF%are foot,

this a--(nd;+ has :een ada-ted O" an 642l5 written J R* '* Hell at Nerthwest(. University, Nov(.:er 16"6* ee also Holt& 167B*

DJ



' -- 555 555 - 5 5

Z51

$$$ A00llcatlon of the &I &@te of 'nlt to Geotechnlcal Englneerlng

tons -er sF%are foot, and -o%nds -er sF%are in(h, de-ending on how theyor their (lients feel a:o%t the s%:0e(t* ort%nately, ton5for(eQf t* is within$] of 1 <g5for(eQ(. $

, a (o..on la:oratory %nit for stress and -ress%re,and the fo%ndation engineer %tili&ing (onsolidation test data (an (onvertdire(tly with s.all error* tri(tly s-ea<ing, %sing for(e as a :asi( %nit isin(orre(t@ roass s:o%Bd :e the :asi( %oit, wi t: for(e derived a((ording to Newton3s se(ond law of .otion* Use of the <ilogra. as a %nit of for(e isone of the diff <%lties with the so5(alled =.etri( syste.,= a .odifiedversion of the .<s syste., whi(h was (o..on a.ong (ontinentalE%ro-ean eng.eers* At least they tried to <ee- the distin(tion :etween.ass and for(e :y (alling the <iBogra.5for(e a !ilopond <-B*

A .oderni&ed version of the .etri( syste. has :een develo-ed over the -ast # years The syste. is <nown as 6 , whi(h stands for =Le yste.e International d3Unit)s= =The International yste. of Units=B@it is deseri:ed in detail in the ATG l 6)"B "etric hactice 7uiNe and in the

$&" tandard for "etric Practice 167B, 'esignation E #75!6,availa:le . the :a(< of every (%rrent ATG Ann%al 4oo< of tandards*The syste. .ay event%ally :e(o.e the (o..on, and -erha-s the onlylegal, syste. %sed in the United tates, Canada and a few other (o%ntriesstill %sing theI.-erial or 4ritish Engineering syste.* In fa(t* reat 4ritain itself (on5 verted (o.-letely to I in 16!$, and A%stralia and New ealand

followed s%it shortly thereaf ter* Gost E%ro-ean (o%ntries already have defa(to (onversion to I, es-e(ially in engineering -ra(ti(e*

A. THE &I 3ET!IC &)&TE3

The I .etri( syste. is a f %lly (oherent and rationali&ed syste.* l4 isfo%nded on seven :asi( %nits for length .etre or .eterB, 8ass <ilogra.B,ti8e se(ondB, electric current a.-ereB, tber8odJ,narnic te8perature <elvinB,lu8inous intensity (andelaB, and a8ount of substance .oleB* Ali these :asi(%nits ha e -re(ise definitions, na.es, and sy.:ols* Units for ali other

-hysi(al F%antities (an :e derived in ter.s of these :asi( %nits* o.eti.esthe denved F%an:t1es are given s-e(1h( na.es, s%(h as the ne(ton for for(eand the (att for -ower* The derived %nit of for(e re-la(es the <ilogra.5for(e<gfB of the .<s syste., so that the na.e of the %nit indi(ates that it is a%nit of for(e, not .ass* A great advantage is that one and only one unit

eists @o, each physical Luantity, and all other .e(hani(al F%antities s%(h asvelo(ity, for(e, and wor< (an :e derived fro. the :asi( %nits* In addition,the I %nits for for(e, energy, and -ower are independent of the nat%re of the -hysi(al -ro(ess, whether .e(harri(al, ele(tr i(al, 0 (henri(al*



A.! B6>l 6n= &5l15= SI M54l nl4> 8

As -revio%sly .entioned, a .a0or advantage of I is that it is a f %lly

(oherent syste., whi(h .eaos that a -rod%(t or F%otient of any two %nitF%antities is a %nit of the res%lting F%antity* or e+a.-le, %nit lengthsF%ared sho%ld :e %nit area, and %nit for(e sho%ld :e %nit .ass ti.es %nita(l9eleration* 8:vio%sly, .any of the engineering %nits in (o..on %se for e+a.-le, a(re, l:5for(e, <g5for(eB are not (oherent %nits* Also, %nits whi(h.ight :e rela ted to :asi( %oi ts J -owers of 0 are not (onsistent withinthe I syste.* A good e+a.-le is the litre, or liter, whi(h is a (%:i(de(i.etre* The eF%ivalent vol%rne of the litre has :een defined as e+a(tly15# .# 1 (.#

B* Additional advantages of I in(l%de the %se of %niF%eand well5defined sy.:ols and a::reviations and the (onvenient de(i.alrelation :etween .%lti-les and s%:.%lti-les of the :asi( %nits*

In the ne+t two se(tions of this a--endi+ we des(ri:e in detail the I%nits of -arti(%lar interest in geote(hni(al engineering and -resen t a-5 -ro-riate (onversion fa(tors for sorne of the (orn.on .<s and 4ritishEngineering %nits* in(e yo% are li<ely to en(o%nter 0%st a:o%t anything inyo%r engineering -ra(ti(e, it is i.-ortant that yo% <now how to (onvert :etween these syste.s and I, and that yo% have sorne feel for -hys1(alF%antities in :oth sets of %nits*

A.! BASIC A%& &ERIVE& SI METRIC %ITS

Ihe three hove unit r of ioterest to geote(:oi(al eogioeers are lt8gth ,8ass, and ti8e. The I %nits for these F%antities are the 8etre, ., the!ilogra8, <g, and the second , s* Te.-erat%re, whi(: .ight also J5 of interest, is e+-ressed in !elvins /B, altho%gh the syste. does allow for %seof the degree Celsi%s >CB, whi(h has the sa.e interval* Ele(tn( (%rrent 1se+-ressed in a8peres AB* %--le.entary %nits in(l%de the radian and steradian , the %nits of -lane and solid angles, res-e(tively*

As .entioned, these :asi( I %nits have -re(ise -hysi(al definitions*or e+a.-le, (ontrary to a -o-%lar .is(on(e-tion, the .etre is not thedistan(e :etween two :ars in Paris, :%t rather it has :een defined ase+a(tly eF%al to a (ertain n%rn:er of wavelengths of radiation (orres-onding to a s-e(ifi( llansition level of* <9t y-ton 7"* T:e standard <;logra. is

eF%al to the .ass of the ;nte.ational -rototy-e <ilogra., a (ylinder of -latin%.5iridi%. alloy -reserved in a va%lt at Le 4%rea% InteD.ational desPoids et Ges%res at evres, ran(e* i.ilar standard <ilogra.s (an also J5fo%nd at the National 4%rea% of tandards near Washington, '*C* These(ood :as :eeo def;oed as t:e dnra tion of a (ertain o%ro:er of -eriods of the radiation (orres-onding to a s-e(ifi( transition state of (esi%. !!.

.j



5 DD555 ** X .., - ---- - .. 5555 5 5 ***555555D5 555 555D D5 555555 5 55 5555 55 --- D555555 5 55 555 555 5DD555555 5 5 5 55D55555 5

5-

I ,1

$$8A0011cat1on 0 .. .. :::, .. .. ..... ?'

.;, X

.. 5 5-

Derived units geote(hni(al engineers %se in(l%de those listed in Ta:le.

A. 1*

Prefies are %sed to indi(ate .%lti-les and s%:.%lti-les of the :asi(and derived %nits* I -refi+es are listed in Ta:le A5$*

The nref i+es sho%ld :e a--lied to indi(ate orders of .agnit%de ofthe :asi( or derived %nits and to red%(e red%ndant &eros so %1at n%.1i=3a*1

,. FG 1 5 . *X l fMM TE?'? sho%ld not :e aoolied to the=t L1K/.#! .0 -

'()*+ (01

55 . Unit I y.:ol or.%la

.$********leration .etre -er se(ond sF%ared .Qs

area sF%are .etre .$

=rea he(tare ha h.

density <ilogra. -er (%:i( .etre /gZ

/ 12 .$

$

for(e newton N <gD.QslJ o

freF%en(y hert& .CJ.% $ $.o.ent or tora%e newton .etre ND. <gD. Qs

5 -ower watt w '!

$

oress%re -as(al Pa N5 Q.

$ ..stress -as(al ra E J E

%nit wei ht newton -er (%:i( .etre NQ.

velo(ity .etre -er se(ono .,volta$ e volt V

vol%.e (%:i( .etre ll

WQA# # #

vol%.e litre L d.5 15 .

wor< energyB 0o%le *J - ***

IAttC A$it.

a(tor Prefi+ y.:ol

I834 e+a E11s -eta I'

11$ tera T19 giga 1" .ega M

1# <ilo1$ he(to

1 de<a da151 de(i =15$ (enti (15# .illi 15" .i(ro

156 nano n151$ -i(o -151s fe.to 1517 atto a

Q?

53

5

111

55 3

.# <gQs$ D.$

.



5555555 5 55 5555555 5555555 555555555555 D555555 55 5 D5=355



A." SI Unl46 3l ln45564 43 (5345nl6l Enln55 6n= T5l C3n156l3n $6436

deno8inator of (o.-o%nd %nits <ilogra. is an e+(e-tion sin(e <g is a :asi( %nit in the I syste.B* Note that spaces, not (o..as, sho%ld :e %sedto se-arate gro%-s of &eros a (on(ession to the E%ro-eans to -ers%adethe. to sto- %sing a (o..a as a de(i.al *-ointB*

o .a.tain the (oheren(e of the syste., it is t e(orn.ended that 3,Q

basic units be used to for8 derived units. or e+a.-le, the %nit of for(e, thenewton, is derived a((ording to Newton3s se(ond law, 9 / "a, where the.ass " is in <ilogra.s and the a((eleration a is in .Qs*

, ali :asi( %nits*or derived (o.:inational %nits s%(h as -ress%re or stress -as(als or newtons -er sF%are .etreB, .%lti-les and s%:.%lti-les of the :asi( .etri(

%nits in this (ase .etresB sho%ld :e avoided* or e+a.-le, NQ(.$

and N Q ..$ are wrong@ the a--ro-riate -ref;+ sho%ld :e %sed with the n%.era5

tor to indi(ate larger or s.aller F%antities, for e+a.-le, <NQ .

$

or GNQ.$

for <ilonewtons -er sF%are .etre or .eganewtons -er sF%are .etreB*

A." SI %ITS O$ I%TERESTTO (EOTECH%ICAL E%(I%EERS A%OTHEIR CO%VERSIO% $ACTORS

Length* o% sho%ld already :e fa.iliar with the I %nit for lengththe .etre, .B* 4y the way, tfOs 1s the A f G re(o..ended s-elling*BUsef %l I length .%lti-les and s%:.%lti-les are the <ilo.etre <.B, .illi.etre ..B, .i(ro.etre *.B, and nano.etre n.B* Conversion fa(torsfor the (o..on 4ritish Engineering and .<s syste.s are9

1 in(h, in* $*2 - *$2 1 foot, f t / *#27 .1 yard, yd *6122 .1 .ile U ** stat%teB / 1*"6 Y 1# - 1*"6 1 .ile na%ti(alB 1*7$ S 1# // 1*7$ 1 angstro., A ** 1 + 1 - *1 n1 .il ** $*2 + 15s . 5 *$2 .. 5 $*2 'M

ood I -ra(ti(e s%ggests that .%lti-le and s%:.%lti-le .etri( %nits :e %sed . .(re.ents of l888, for e+a.-le, .., ., <.* Use of the

(enti.etre, es-e(ially for lengths %nder # .., sho%ld J5 avoided*Gass* o% .ay re(all fro. -hysi(s that the inertia or .ass I %nit9

<;logra., <gB of a -hys1(al o:0e(t is a ri%@as%re of the - o-e1ty whi(h(ontrols the res-onse of that o:0e(t to an a--lied for(e* lt 2> (onvenient to

.eas%re the .ass in tenns of the a((eleration of an o:0e(t -rod%(ed :y a%nit for(e, as reJa ted :y Newton3s se(ond law of .otion* Th%s a %nit for(e(a%ses <g .ass to a((elerate .Qs$

Toe .ass then is an a--ro-riate.eas%1e of the a.o%nt of .atter an e:0et entains* The .ass rernaios the



670 ANNll64l3n 3 45 SI S>45 3 nl4> 43 (5345nl6l Enln55ln

sa.e even if the o:0e(t3s te.-erat%re, sha-e, or other -hysi(al attri:%tes(hange* Unli<e weight, whi(h is dis(%ssed later, the .ass of an o:0e(t ^loesnot de-end on the lo(al gravitational attra(tion, and th%s it is alsoinde-endent of the o:0e(t3s lo(ation in the %niverse*

A.ong ali the I %nits, the <ilogra. is the only eneDNhose na.e, for histori(al reasons, (ontains a -refi3+* Toe na.es of n@i%lti-les and s%:.%lti -lesof the <ilogra. are for.ed :y atta(hing -rtZfi+es to the word gra8 rather than to !ilogra8. In other words, 15" <g is not a .i(ro5<ilogra., :%t a.illigra. / 15# g* i.ilarly, 1 <g is not l <ilo5<ilogra. :%t is eF%ivalent to1 .egagra. GgB@ 1 <g is also the .etri( ton tB, so.eti.es s-elled=tonne= to avoid (onf %sion with the 4ritish ton / $l: A TG re(o. .ends that the .etri( ton :e restri(ted to (o..er(ial%sage and that the ter. tonne :e avoided altogether* Pra(ti(a %nits of .ass in enginee1 ing -1 a(ti(e a1e the .egag1a. GgB, the <ilog1 a. <gB,and gra. gB, the latter two %ni ts :eing -ri.arily %sed in la:oratory wor<*

orne %sef %l relat1nsfO-s and (onvers1n a(tors are9

l -a%od roass, l :ro avaird % -aisB 8 2#" <gl 4ritish shortB ton / $ l:. / 6! *$ <gl gra.* g / J8 5# <gl .etri( ton, t / 1# <g / " g / l Ggl sl%g l l:5for(eQf tQs$

B 12*6 <g

Ti.e* Altho%gh the se(ond sB is the :asi( I ti.e %nit, .in%tes.inB, ho%rs hB, days dB, et(*, .ay :e %sed where (onvenient, even tho%gh

t:ey a (e oat de(iroa lly (ela ted Gay:e so.e day we will even have ade(i.al ti.e syste.@ see Carrigan, 16!7*B

or(e* As .entioned, the I %nit of for(e is derived fro. 9 / "a ,

and it is ter.ed the ne(ton % whi(h is eF%al to l <g D.Qs$ Conversionfa(tors for (o..on engineering for(e %nits are9

1 l:5for(e 2*227 Nl 4ritish short ton5for(e 7*76" + 1# N / 7*76" <Nl <g5for(e 5 l <- 5 6*7! Nl <i- / 1 l:5for(e 2*227 + 1# N 2*227 <N .eh i( ton5fo1(e 000 <g5f. (e 6*71 S0# N 6*7! <N l dyne gD(.Qs$

B /15 N / I8 X.'

I4 is o:vio%s that the n%.:ers in newtons for s%(h ite.s as (ol%.nloads wo%ld :e very large indeed and (onseF%en tXy so.ewha t aw<wa rdTherefore, (onsistent with the r%les for a--li(ation of -refi+es, it is si.-leto ad0%st these rather large n%.:ers to .ore .anagea:le F%antities forengineering wor<* Toe (o..on -refi+es wo%ld :e <ilo 1#

B, .ega 1" B,

and giga 16B, so that engineet ingK fot (es wo%ld :e <ilonewtons, <N,

.eganewtons, GN, and giganewtons, N* Toe sy.:ol for .ega is G, toavo1d (onf %s1on w1th the sy.:ol for .dh, .*B Th%s, sin(e l ton5for(e is 7*6<N, 1 tons wo%Xd :e 7*6 GN*



5555555 5



A.+ &I 'nlt ol lntereat to Geotechnlcel Englneera and Thelr Con/eralon *actora 1M1

orne %sef %l relationshi-s of these -ref i+es are9

l <ilonewton, % 1# newton 1 Nl .eganewton, M% / 1" newton 1# % / 1 %

l figanewton, $% 17 newton / 1 % 1$ M% / 1 M%l giganewton, (% / 16 newton 1" % / 1# M% / 1M% # giganewtons / # figanewtons / 1 :o+afiganewtons

12*2 giganewtons / 1 grossafiganewtons

kThis %nit is only a (onstant -rior to o-ening th( :o+*

Toe (orre(t %nit to e+-ress the (eight of an o:0e(t is the newton sin(ethe weight is the gravitational for(e that (a%ses a downward a((elerationof the o:0e(t* 8r, weight eF%als "g, where " is the .ass of the o:0e(t

and is the a((eleration d%e to gravity* o% will re(all that the a((elera tiond%e to gravity var;es with latit%de and elevation and* in faet, I re(o..endsthat weight :e avoided and that .ass :e %sed instead* I weight .%st :e%sed, it is s%ggested that the lo(ation and gravitational a((eleration also :estated* However, for .ost ordinary engineering -%r5 -oses, the differen(e ina((eleration a:o%t *]B (an :e negle(ted, and aslong as we e+-ress the weight in newtons, the %nits will J5 (onsistent*

Another -ro:le. with weight is that it is (o..only %sed when wereally .ean the .ass of an o:0e(l Eo( e+a.-le, in the la:o(alory when we=weigh= an o:0e(t on a la:oratory :alan(e, we really are (o.-aring two.asses, the .ass of the %n<now n o:0eet w ith o:0e(ts of <now n .ass*Eyen s(ales or :alan(es whi(h dis-la(e linear s-rings are (ali:rated :y

%sing o:0e(ts of <nown .ass*%rther a.:ig%ity o((%rs, of (o%rse, :e(a%se (o..on %nits of .asss%(h as the -o%nd or <ilogra. are of ten %sed in engineering -ra(ti(e as a%nit of for(e* I -o%nd is %sed as a %nit of for(e, then de-ending on theres%lting a((elerations, different .ass %nits are defined* or e+a.-le, if a l: for(e (a%ses an a((eleration of l f tQs$

, then the .ass is l l:5for(eDs$Qf t,whi(h is (alled a slug. In other words, 1 l:5for(e 1 sl%g + 1 ftQs$

Usingsl%gs as %nits of .ass a5v oids the eonf %sion with -o%nds5.ass, and this %nithas :een (o..only %sed in aerodyna.i(s and fl%id .e(hani(s*

I we wanted to %se .stead a -o%nd5.ass syste., we (o%ld def .e a%nit of for(e (alled the poundal, where 1 -o%ndal 1 l:rn S 1 ftQs$

Po%ndals are a--arently %sed only in -hysi(s :oo<s*

E9A3PE A.1

(215n:

A for(e of 1 l: a(ts on an o:0e(t weighing 1 l:*

j



672 ANNll64l3n 3l 45 SI S>45 3l nl4> 43 (5345nl6l Enln55ln

R5FG25=:

ind the res%lting a((eleration*

S3lG423n:

ro. Newton3s se(ond law,

9C "a / 4 :aor

/ 9g / l l:f B#$*1! f tQs

$

B /

< l l:f

#$ 1!Df Q $t s

E+AMPLE A.*

(215n:

Toe o:0e(t in E+a.-le A* l, whi(h weighs 1 l:f*

R5FG25=:

ind its .ass when a 1 l:f (a%ses an a((eleration of 1 f tQs$*

S3lG423n: 9 C "a C F 4 :a

" l l:f *#1 l:f Ds$ // *#1 sl%

#$*1! f tQs$ ft g

E+AMPLE A.!

(215n:

Neil Ar.strong weighs 1 l: on earth*



A." SI nll> 3 ln455>4 43 (5345nl6l Enln556 6n= T5l C3n156l3n $6436 !

R5FG25=:

How .%(: does :e weigh on the s%rfa(e of the .oon3

S3lG423n:

irst, we have to (al(%late Gr* Ar.strong3s .ass on earth* Unless he hadhealth -w:le.s d%r ing the *oyage, his .ass Mill :e the sa.e on t:e .oon

1 1:f l:f Ds*

M / - / / 2*""55, or 2*"" sl%gs #$*1! f tQs$ f t

in(e 1 sl%g / 12*6 <g, :is .ass is "7*# <g* Another way to (al(%late :is

.ass is to eonvert his weight to newtons@ t:en divide :y .

] / 1 l:f 2

D fN B / ""!*$ N or ""!*$ < D.

M / ] // ""! *$ <g D.Q s2

/

g 6*7! .Qs*

"7*8J <g

Ne+t, D5 have to eit:er as< an astrono.er or loo< %- in the Zandboo!

of Che8istry and Physics 16!!B or sorne other referen(e the gravitational

*

a((eleration on the s%rfa(e of the .oon* We find that 7.oon / 1*"! .Qs Th%s,

W.oon Gg.oon / "7*# <g 1*"! . Qs$

V 11#*"$ N 8r, sin(e 2*227 N / l:f,

W.oon 11#*"$ N K

ll:f N

B$*2 l:f 2 227

Che(<9 8n earth, ""! N U: // 11#*" N on the .oon*

ee how (onf %sing the old 4ritish Engineering syste. (an :e3 However, if yo% thin<* this is :ad, wait %ntil yo% try to (onvert densities and%nit weights3

tress 6nl Press%re* Toe I %nit for stress and -ress%re is the pascal *

PaB, whi(h is e+a(tly eF%al to newton -er sF%are .etreDNQ. .

There has :een sorne o:0e(tion, es-e(ially in E%ro-e, to the %se of the -as(al as the :asi( %nit of stress and -ress%re :e(a%se it is so s.all* Theer.ans and ren(h, for e+[.-le, often %se the b^ir , whi(h is e+a(tly tosPa* However the -as(al is .ore logi(al sin(e it 1s a (oherent %r%t@ that1s,

$

/



674 ANNll64l3n 3 45 SI S>45 3 nl4> 43 (5345nl6l Enln55ln

eF%ations involving the -as(al with other I %nits (an :e written witho%t(oeffi(ients of -ro-ortionality :eing reF%ired*

Conversion fa(tors for sorne (o..on engineering %nits are9l -si J:5for(eQin* $

B / "*76 + 1# Pa or "*76 <Pal at. at TPk / 1 *1# + 1 Pa or 11*# <Pal <g5for(eQ(. $ / 6*7! + 12 Pa or 67*! <Pal .etri( ton5for(eQ .$ / 6*7! + 1# Pa or 6*7! <Pal :ar / l + 1 Pa or 1 <Pal <si <i-Qin*$ B / "*76 + 1" Pa or "*76 GPa1 4ritish ton5for(eQf t $ / 6*!" + 1# Pa or 6*!" <Pal l:5for(eQf t $ / 2!*77 Pa

tandard te.-erat%re and -ress%re, not a .otor oil additive or oil Test Pro:e*

It is o:vio%s that the -as(al is a s.all %nit, :%t as with I for(e %nits,1t 1s easy to add -refi+es to .a<e the large n%.:ers .ore .anagea:le*Th%s, -si in the a:ove ta:le is .ore (onveniently e+-ressed as "*6 <Pa<NQ .$

B than as "*6 + 0# Pa* or ordinary tria+ial testing of soils, for e+a.-le, hydrostati( (ell -ress%res rarely e+(eed *00 or !00 -si 1#!6 or $"7 <PaB* 8r, if ali the -ress%res in a test series are in this range, it .ight

:e (onvenient to %se ." or *. GPa* And, as with* other syste.s of %nits, aro%nded or even interval rnay :e .ore (onvenient@ for e+a.-le, in this(ase, 1* and $* G Pa*

i.ilar e+a.-les (o%ld :e given for engineering stresses* Either <ilo-as(als or .ega-as(als, <Pa or GPa, or <ilo5 or .eganewtons -er

sF%are .etre, < N Q .$

or GN Q .$

, will :e(o.e (o..only %sed for fo%nda tion stresses, lateral earth -ress%res, allowa:le :earing val%es, et(*In the la:oratory, for(e is .eas%red :y a -roving ring or load (ell and then(onverted to stress for e+a.-le, in the %n(onf ined (o.-ression or dire(ts:ear testsB, so the (o.-%tational -ro(ess will :e no .ore (o.-li(atedthan it is now* i.ilarly, with ele(tri(al -ress%re transd%(ers, a (ali:rationfa(tor .%st :e %sed to (onvert .illivolts .MB o%t-%t to -ress%re inwhatever %nits are %sed*

A (onvenient a--ro+i.ation, -art of whi(h is already in %se .geote(hni(al engineering -ra(ti(e, is the following9

* 1 4ritish shortB ton5for(eQf t $ 1 <g5for(eQ(.$ 1 at.os-here

1 .etri( ton5for(eQ.$ / 1 <Pa / 1 <NQ.$

The error involved is :etween $] and 2], whi(h is (ertainly less thanordinary engineering a((%ra(y reF%irernents*

E+AMPLE A."

(215n:

The -ress%re or stress is 00 <Pa*



A*2 I Unlts of lnlereal lo eole(hnl(al Englneera n= Thelr Converlon $8Cl3n 1!

R5FG25=:

Convert this -ress%re or stress to aB -si l:5for(eQin$*B, :B <si <i-sQ in$

*B,eB tsf 4ritish ton5for(eQf t$ B, dB <g5for(eQ(.$ , eB :ar, fB .etri( tonfor(eQ .$, gB .. of .er(%ry, hB f t of water, and iB . of water*

S3lG423n:

A si.-le way to (onvert fro. one set of %nits to another is to set %- aneF%ation with the eF%ivalents in either the n%.erator or deno.inator of th( eF%ation so that the a--ro-riate (an(ellations o((%r*

a* P 1 <Pa / 1<N l l:f V 1 N V *$2 . B$.$ 2*227 N <N 1 in*

// 12* -si

Note9 The e+a(t (onversion val%e is 12*# !!# !! <N Q.$ , whi(h (o.esa:o%t if yo% %se the e+a(t val%e for 1 l:f / 2*227 $$1 "1 $" N* in* ise+a(tly eF%al to *$2 .*

:* p // 1 <Pa

@,** l88 <N 1 l:f B 1 N B 1 <i- B *$2 $

.$ 2*227 N <N 1 l:f in*

/ *12 <si

Again, as in -art aB, the e+a(t (onversion val%e is slightly different*(* p // 1 <Pa

1 <N ll:f B 1 N B 1 tonf B *#27 . B$

.$ 2*227 N <N $ l:f 1 ft K / 1*2 tonf Q f t $

d* P l88 <Pa / 1<N l l:f B 1 N B . B$D .$ 6*7! % <N 1 (.

/ 1*$ <gf Q(.$

Note9 The e+a(t (onversion for <gf to N is 6*7" "*#

e* P // 1 <Pa 5 1 <Pa 1 :ar BY I Pa V 1 :ar 1 Pa D 1 <Pa D

. P l88<Pa 1 <N 1 <gf B 1 N B 1 tonf B.$ 6*7! N <N l888 <gf

/ 1*$ .etri( tonf Q.$

g* or p in .. of .er(%ry, we need to re.e.:er or loo< %- thedensity of Hg* I4 is 1#*" gQ(.# Also re(all fro. hydrostati(s that p 5



"!" ANNll64l3n 3 45 SI S>45 3 nl4> 43 (5345nl6l Enln55ln

pgM , where M 1s the de-th of the fl%id* Th%s for -t ess. e in (. of

.er(%ry, M / p Q p. o#

M K 1 <N 1 N B (. B 1 g B . B#5 .$ <N 1#*" <g 1 (.

B 000 .. Bs$

D 6*7!

/ ! .. Hg

. Again, %se M / p Q p

M /

l889 A 9 N B 1@ @ <g BY

6*7

. B *# . B/ ##* f t of water

i* M / l889 19 N B 1@ @ <g B 6*7 . B/ 1*$ . of water

'ensity and Unit Weight* 'ensity is defined as .ass -er %nit vol%.e*lts %nits ;n the I .etri( Bte. are <ilogra.s -er (%:i( .etre, <gQ ro

#T3.any (ases, it .ay :e .ore (onvenient to e+-ress density in .egagra.s

-er (%:t( .etre, Gg Z.#* Conversions 3 the (onnnon la:oratory and

field densities are9

1 l:5.assQf t # / 1"*17 <gQ.#

1 gQ(.# / 1# <gQ.#/ 1 GgQ .

#/ 1 tQ.

#

#o% will re(all that the density of water, p..,, is e+a(tly 1* gQ (. at

2>C, and the variation is relatively s.all over the range of te.-erat%resen(o%ntered in ordinary engineering -ra(ti(e* Therefore it is %s%ally s%ffi(iently a((%rate to ta<e p.., 1# <gQ.

#/ 1 GgQ.

#, whi(h si.-lifies

-hase (o.-%tations (onsidera:ly* l4 is also %sef%l to <now that 1

<gQ .# is eF%al to "$*2 l:5.assQ f t#*Ty-i(al den*sities that .ight :e en(o%ntered in geote(hni(al -ra(ti(e#

are 1*$ GgQ .#

!2*7 l:Qf t#

B, 1*" GgQ .

#

1 l:Qf t

#

B, and $* GgQ. 1$

l:Qf t # B* Ranges of dif ferent densities are also listed in Ta:le $51* Toe(o..only %sed density for (on(rete, 1 l:Q f t #

, is al.ost e+a(tly $*2g . *

o% sho%ld note that all .ass and vol%.e ratios (o..on in geote(h5ni(al engineering -ra(ti(e are not aff e(ted :y the %se of I %nits* 1e+a.-le, void ratio or water (ontent of any given soil still has the sa.en%.eri(al ,, al%e*

1



A." SI nl4> 3 ln455>4 to (5345nl6l Enln55> 6n= T5l C3n15>l3n $IICl3>

Unit weight or weight -er %nit vol%.e is still the (o..on .eas%re5.ent in geote(hni(al engineering -ra(ti(e* However, s.(e weight sho%ld :e avoided in te(hni(al wor< for all the reasons dis(%ssed earlier, then %nitweight also sho%ld :e avoided* ATG now re(o..ends that density :e%sed in -la(e of %nit weight* I yo% .%st (onvert fro. density to %nitweight, then si.-ly %se / p, whi(h .ea11,s yo% will have to (onsider thea--ro-riate val%e for the a((eleration d%e to gravity* The 33standard= val%eof g is 6*7! .Qs$ #$*1! f tQs$

B, whi(h as .entioned -revio%sly, (an :e%sed with s%ff i(ient a((%ra(y for ordinary eng.eenng wor< for .ost

-la(es on this earth* I yo% ever have a 0o: on the .oon or sorne other -lanet, then yo% .%st %se the lo(al val%e for . /ee- in .ind, also, to :every (aref%l whi(h =-o%nds33 yo% are wor<ing with, l:f or l:., in these

(onversions*

E+AMPLE A.)

(215n:

Toe density of water is 1 <gQ .#*

R5FG25=:

The density of water in aB gQ(.

#

and J 1:Qft

#

S3lG423n:

et %- an eF%ation as follows9

a* 1 < 5 1 < 1 g Bl . B# 5 l g #. . l <g 1 e. (.

:* 1 <g / 1 <g 1 l:. B *#27 . B# # *2#" <g lft

/ "$ 2# l:. #

Another way to do -art : is to re(all that l l:.Qf t#

1"*17 ,<Q. @ so

1 <g / 1 <g l l:.Qf t# DB# # 1"*17 <gQ .#

"$*2#5f t #

#



E9A3PE A.

15n:

'ensity of water, P( / 1 <gQ .#

R5FG25=:

%nits*

Re(all that l N / l 555

s$ N <N

/ 67! 5/ 6*7! 5

#. we <now that

1 <g "$*2# l:. f t

l lJ are %sed, fro. -art a* ,

'7 / 6*7#5.

.

"$*2 l:f 4

This is the (o..only %sed val%e for the %nit weight of water*

E9A3PE A.

(215n:

A soil has a dry density of 1*! GgQ.#

171



A." SI nl4> 3 ln455>4 43 (5345nl6l Enln55> 6n= T5l C3n15>l3n $6436 9

R5FG25=:

Convert this density into %nit weights, in ter.s of :oth aB I and :B

4ritish Engineering %nits*

S3lG423n:

a* 6 units#

Pd / 1*! GgQ.#/ 1! <gQ.

#

/ p

1! 5 6*71 5 / 1" "!! 5 1"*! 5.# s3 .# .#

:* ritish Engineering units, in ter.s of l:.9#

P / 1! <g 1 l:.Qf t

B / l"*l# l:.

.# 1"*17 <gQ .# f t#

p

7 / 1"*1# l:. #$*1! B / #212 l:.Df tf t# $ s$

f t#

In ter.s of l:f 9 ro. -art aB,#

/ 1" ! <N 1 N B l lhf B *#27 . B

/ 1"*# l:f Qf t #

Toe latter val%e in tenns of l:f is, of (o%rse, the .ore fa.iliar fig%re*

eostatie tress* or (o.-%tations of geostati( stresses, the %nitweights of the vario%s soil layers (an :e easily re-la(ed :y the p of thelayers* The %s%al for.%la

n

then :e(o.es n

< / P40`4

;-

!512(B

where ; 5 total verti(al stress at sorne de-th, P4 / density of ea(h layer,&@ thi(<ness of ea(h layer, and a((eleration of gravity*

<g . B * N <N

.



$8, A00llcatlon ot the &I &@te ot 'nlt to Geotechnlcal Englneerlng

l p is a (onstant thro%gho%t the de-th , then!512:B

4y analogy, (o.-%tation of the stati( -ore water -ress%re C at sorne de-thh( :elow the gro%nd water ta:le is

u / h !51

where P( / the density of water 1 GgQ .#B*

1.1larly, to o:ta. tfie eff e(tive verti(al over:%rden stress, the eff e(tive or :%oyant density p for ea(h layer :elow the gro%nd water ta:le (an :e %sed or, -erha-s .ore si.-ly, 0 1 0., 5 C

>

'i.en sional analysis of these eF%ations for stress shows that if the

densities are e+-ressed in GgQ .#, then stresses a%to.ati(ally res%lt in <Pa,or

Gg B . B . l888 <gD. 000 l <Pas$ , .$ .$

everaV e+a.-les of geostati( stress (o.-%tations %sing I %nits (an :efo%nd in Cha-ter !*



a00endi5 #"1

(eri/atian oa0lace$i tFYNuatianA

in e(* ! *6, a flow net is a(t%ally a gra-hi(al sol%tion

of La-la(e3s eF%ation, EF* !5$2* The ass%.- io riva5

tion of th1s eF%a 2

e / (1on]stant i*e*, n9o (onsolidation Cha-ter 7B or (o.-ression

of the .edi%. o((%rsl

'ar(y3s law EF* !5B is validConsider the flow of water into an ele.ent with di.ensions dx and

dy ig* 451*1B* Two5di.ensional flow is ass%.ed hete 3 si.-li(ity@ yo%(o%ld do the e+a(t sa.e thing in three di.ensions, :%t it wo%ld 0%st J5.ore (o.-li(ated* The ter. av+Q ihB d+ indi(ates the rate of change inve o(i D D D si.ilarly, #v Way : dy is the rate of (hange 2n

v; in the y5dire(tion* ro. (ontin%ity, we <now

=$1u,Bo

ese two eF%ations eF%al, we get

)h*R+ a v,* *5d dy 5d dy Oa+

.

1

DJ

a



&

7

1

+[ 7a

882 (erl/atlon or a0lace$ Euatlon

+

av

$2. B-. $l3D 2n43 6n= 3G4 3 6n 5l55n4 d J dy.

or

Q a v

K a vy

a+ )By

45151B

sin(e d and dy (annot :e &ero*ro. 'ar(y3s law EFs* !5$ and !5B, v / !i / !Il h/ L. Th%s we (an

write for o%r ele.ent9

%:stit%ting these ter.s into EF* 45151 we o:tain

! a$h ! aih o V 0V 2 y a 2

in(e ! was ass%.ed to :e isotro-i(, ! / !R . o we have6 $ 6 $-P -/ O)l+ $ )ly $

!5$2B

whi(h is l.$place3s eLuation in t(o di8ensions. or the eF%ation in threedi.ensions, si.-ly add the ter. )l $hQa& $ to EF* !5$2*

5



B-*. ASSMPTIO%S

i one5di.ensional (onsolidation theory, weneed to ass%.e the following9

1* The (lay is ho.ogeneo%s and 00 sat%rat *D D D t :oth the to and :otto. of the (o. ressi5 :le

layer*

2* The soil grains and water are in(o.-ressi:le*o.-ress1on an ow are one i.e i

"* The s.all load in(re.ent a--lied -rod%(es essentially no (hange in thi(<ness that is, s.all strainsB, and ! and a*, re.ain (onstant*

D D D nshi :etween the vol%.e (han ee and the effe(tive stress Iu,3.In other words, de 5 5a.,da3 and

.

i.? -ortant ass%.-tion also i.-lies that there is ! secondary

co8pression.

Now let %s :orrow a little ele.ent fro. ig* 6*1 and enlarge it 2nig* 45$*1* 8%r ele.ent C315ls at a e- M ow e o- o e (o.-ressi5

er has thi(<ness dM and has an area d ti.es dy. The vol%.eehange of the ele.ent is the differen(e :etween the a.o%nt of flow 2n and

kCha-ter 6*

11#

._

. . .



64+ (erl/atlon and &olutlon of Ter>aghl$e One"(lenelonal Conolldailon Theor@

> a4 : o%t

d% 5r5*

3 d& qQ 525 0 13

.( I 0K -4- d&

5525255 a 5551555% & Q O,n+ y

2?

=YS42ll 43 J5

dy

$2. B-*. S32l l65 Gn=532n 3N5>>23n, >22l6 43 $2. 9..

o%t of the ele.ent* in(e (onsolidation %nder these (onditions is dire(tly

in o%r

i / /- --& distan(e p( g

Toe (orres-onding hydra%li( gradient at the :otto. of o%r ele.ent dM isg1ven y

. a u6 M dM5

. P( g aM

ro. 'ar(y3s law, d\ !iadt , we .ay (o.-%te the F%antity of flow d\

Li<ewise we .ay (o.-%te t e F%antlty o ow . 1.einto the ele.ent :

B-*-"

We (an now (o.-%te the vo %.e e ange ro. t e eren(e in ra es o * Also we ass%.e the area d dy to :e a %nit area*

vol%.e (hange d0G- d\in

a

-



)02.2 Ferlvetlon 185

The vol%.e (hange .ay also :e deter.ined fro. the la:oratory

oedo.eter test* Re.e.:er, fro. Cha-ter 7, that we wo%ld o:tain ala:oratory (%rve si.ilar to ig** 7*2, whi(h we again show as ig* 45$*$*ro. EFs* 75a and :, the (oeffi(ient of (o.-ressi:ility a is

a 5de

e1 e$/45$5"B

5> da3 oS 5 o4

To :e (orre(t, we sho%ld write these eF%ations in ter.s of ef fe(tivestresses* ro. ig* 45$*$, yo% (an see that the slo-e of the e5o3 (%rve isnegative, and yo% <now that e 1 is n%.eri(ally larger than e2 D

ro. EF* 752, s tJ.eZ / F l e

B, or in ter.s of o%r ele.ent in ig*

1

45$ and the e5a3 relationshi- in ig* 75$*$* we o:tain

s $ dM5de dM 45$5!B

where e 1

(orres-onds to the initial void ratio e ro. EF* 45$5", 5de //d o3. Therefore 6 dM a

da3 :/ =

dM 45$57B

Now, fro. o. dis(%ssion in Cha-ter 6 , we <now that as the e+(ess -ore

e

&

e ,6 / - - /---

e oB o$ 5 o1

B

o

- G.

$2. B-*.* L6J3643 3N5>>l3n G15 >66 6> $2. 9.*.

aO

*,

.



L-B)

88 &5l164l3n 6n= S3lG4l3n 3 T56l'> On5-&l5n>l3n6l C3n53ll=63n Theory

water -ress%re dissi-ates, the effe(tive stress in the soil s<eleton in(reases*This is shown s(he.ati(ally in igs* 6* l( and f* Th%s we (an write that*a 3 5 5.u, he(a%se any change in effe(tive stress is n%.eri(ally eF%al tothe negative of the (hange in e+(ess -ore water -ress%re* Thisrelationshi- is tr%e, of (o%rse, as long as the total stress does not (hange* Now, EF* 45$57 (an :e written as

6 d[ / - # d[

e

and sin(e du / ( aC/ a ) dt , EF* 45$56 :e(o.es5 a aC d[ /

'd d[

45$56B

45$51B e a,

4y eF%ating the vol%.e (hangevol%.e (hange in EF* 45$51, we have

o:tained EF* 45$5 and the

` el a, at 45$511B

We (an (olle(t the soil -ro-erties ter.s as in EF* 65#,

where c is (alled the coefficient of conso/idation sin(e it gove.s the

(onsolidation -roeess* Note that it has %nits of L$ r51

We th%s o:tain

EF%ation 65$ is the Ter&aghi one5di8ensional conso/idation eLuation. I weass%.e c. , is a (onstant with res-e(t to ti.e and -osition, then Eg* 65$ is ase(ond5order -artial differential eF%ation with (onstant (oeffi(ients* Thereare a variety of ways to solve s%(h eF%ations@ so.e are .athe.ati(allye+a(t, others are only a--ro+i.ate* or e+a.-le, Harr 16""B -resents ana--1+i.ate sol%tion %sing the .ethod of finite differenees* Taylor 1627B,following Ter&aghi 16$B, -rovides a .athe.ati(ally rigoro%s sol%tion inter.s of a o%ner senes e+-ans1on* I he develo-.ent that follows 1sada-ted fro. Taylor 1627B and Leonards 16"$B*

B-*.! MATHEMATICAL SOLTIO%

The :o%ndary and initial (onditions for the (ase of one5di.ensional(onsolidation are as fo11ows D

1* There is (o.-lete drainage at the to- and :otto. of the (o.5 -ressi:le layer*

! a$ % dM dl



8-*.! M64564l6l S3lG3n

*. The initial ecess hydrostati( -ress%re flu u4 is eF%al to the

a--lied in(re.ent of stress at the :o%ndary, :..These :o%ndary and initial (onditions (an :e written

when [ O and when & Z , C && Owhen t 8, C C / flo F oS 5 o@B

The general sol%tion of EF* 65$, when the initial e+(ess -ore -ress%reu4 is a f%n(tion of the de-th M , is

When =@ is a (onstant or var;es linearly with de-th, the sol%tion :e(o.es

= , ' "n o F n

lB3IT

. n M B

$ 15 s. $ 31& U

3=

&35

3

+ e+- 5F n 1B $ < l e1B t

E+G -

45$51#B

2 < oP(0 Z2

$X

G

where o4 initial effe(tive stress, oS / o4 flo, and n 8, l, *, #, * * Thesol%tion -rovides tile instantaneo%s val%e of the -ore water -ress%re u atany s-e(ified ti.e and -oint in the soil .ass* The only N64 of EF* 45$51#that is a f%n(tion of the soil -ro-erties is c >

o% (an see that the sol%tion is in ter.s of 4D3 di.ensionlessF%antities, and G or as we wrote in EF* 652,

u o$ 5 o;B Q1BfiYTB

n5o

652B

o% will re(all that the di.ensionless F%antity & is (alled the ti8e factor,

and it is related to e EFs* 65 and 65"B :y

& e QtQ <l e>B QtQ 45$512B

ZJr \oP(0 ZJr

In this eF%ation Hdr is the longest drainage -ath a dro- of water has tofollow in a (o.-ressi:le soil de-osit to get to a free draining :o%ndary*In ig* 45$*1 yo% (an see that the height of a do%:ly =62n5= layer isZ. Therefore the drainage -ath Hdr is eF%al to U. I we had only asingly drained layer, we wo%ld only (onsider the to- half of ig* 45$* 1,

and again the drainage -ath wo%ld :e the height of U.

$

1

O



555 5 5 5D555 555555555555

88 &5l164l3n 6n= S3lG4l3n 3 T56l'> On5-&l5n>l3n6l C3n>3ll=64l3n T53

The consolidation ratio relates the (hange in vol%.e at de-th M andti.e t to the %lti.ate vo %.e e ange a e-

^ / vol%.e (hange at de-th M and ti.e 45$ K 1B M %lti.ate vol%.e (hange at de-th M

Toe (hange in vol%.e, of (o%rse, .eans a (hange in void ratio, or as we

wrote in EF* 65!,

u /e

5 e 65!B

M $ - $2

Toe (hanges in void ratio (an :e related to the stress in(re.ent thro%ghthe (oeffi(ient of (onsolidation a > These relationshi-s are shown in ig*

45$*$* 4e(a%se in ene5di.ensional (onsolidation, the initial e+(ess hydro5* t of a lied stress, E * 65!

:e(o.eso3 5o4

3 +

02 - R1

a3 5

o@::.)

^9 -

^ ^9

u657B

^9

in EF* 656, or

o%r sol%tion to the (onsolidation eF%ation EF* 652B as

u M / ^ - L f1F ` :JiF

& :n$

656B

This eF%ation is s:own gra-hi(ally in ig* 6*#, and we e+-lain in Cha-ter 6how to %se this fig%re to o:tain the a.o%nt of (onsolidation at any de-thand ti.e in the (onsolidating layer see E+a.-les 6*1 and 6*$B*

enerally in engineering -ra(ti(e we are interested in the vol%.e(hange of the entire soil layer* o we want the average degree or percent

consolidation , whi(h is defined as

M]B / totl vol%.e (hange at ti.e t + I88]B 45$ K 1"Bvol%.e (han e

or one5di.ensional (o.-ression, the (hange in vol%.e is, of (o%rse,

eF%al 5to the (hange in height of the layer* To o:tain the average degree of (onsolidation over the entire layer we have to find the area %nder the (%rve(orres-onding to a given ti.e fa(tor in ig* 6*#@ this is shown in ig* 6**

at e.a i(a y, DL dM l

1 Z

or fro. ig* 45$*1,

FO: / Z Z 8 dM 45$51!B

U]B _o ZY

+ +

OX2 - >19 -

-------+ 1 45$517BF a 5 a4: Z

u



B-*.! M64564l6l S3lG4l3n

Rewriting,U]B

00 F ` Z H , K ' ? F u 5 ai : 5 u dM

$ $ 1 8

45$516B

or

U]B l 3B f ` ZF o 5 a4: dM 5 f Zu

dM1

$ U %$ a I o o

45$5$B

%:stit%ting the val%e of u f ro. EF* 45$51# into EF* 45$5$ and integral* ing, we o:tain9

U]B 5 $H 5 a4: lO?:Í - a;B$ U - a4 5 eÍ J. $n @1Bw

$n 1B3!T $ H B$ H $n 1B31T

* $n ` 1B$3113 $ rBl$H1Y e+- 5

2 o

P%tting in the li.its, we o:tain

U]B / l 5 L 51B 51 5

1Bn5 $n 1B$3113

*

45$5$1B

Y e+- 5g

$n 1B 31! $ XV

2G

45$5$$B

or

U]B 1

7 $n - e+- 5 K*(**5

n>A $n 1B$3113 * 2

45$5$#

This sol%tion is for the s-e(ial (ase of (onstant or linear initial hydrostati(e+(ess -ress%re and is valid for all val%es of ^. ol%tions for other initial

-ore -ress%re distt i:%tions are -revided :y Taylor B627B and Leonards16"$B, :%t the differen(es are negligi:le for -ra(ti(aV K -%r-oses* Toes%..ation indi(ated :y EF* 45$5$# (an J5 (arried o%t on(e and for all andta:%lated Ta:le 651B or shown gra-hi(ally ig* 6*B* Casagrande 16#7Band Taylor 1627B give the following a--ro+i.ations for EF* 75$5$#, wfO(h

are %sef %l to <now9or ^ "],G 3;BuM

"651B

***

0 .

S 5 lB C8

"

$

L



DJ1



68 (erl/atlon and &olutlon ol Ter>aghl$ One"(lenlonal Conolldatlon 'heor

or ] "], & / 1*!71 5 *6## log1 5 O: 6511B

D or val%es of ] " ], the series in EF* 45$5$# (onverges e+tre.elyra-idly so tha t onBy the first ter. is signifi(an t Therefore, letting n 5 8,EF* 45$5$# :e(o.es

FO: / 1 l 5 * e+- 5 & : l 45$5$2B

Rearranging, EF* 45$5$2 gives EF* 6511*

*



a00endi5 J-!

Pare Preii're Paraeteri·

8-!. &ERIVATIO% O$ SKEMPTO%'S POREPRESSRE E@ATIO%

Toe -ore -ress%re -ara.eters e(* 11*18B, first defined :y <e.-ton 162B, relate the (hange in -ore water -ress%re to the (hange in total stressd%ring %ndrained loading*

irst, lef s derive EF* 11 11* This ean :e done in seve1al ways* 8nesi.-le way is to ass%.e for a start that we have a tria+ial s-e(i.en 2neF%ili:ri%. with the (ell -ress%re <e a(ting on it* Ass%.e for the .o.entthat the soil s<eleton is elasti( and isotr( -i(, and that there 65 :oth airand water in the voids that is, * 1]B* Now, when we a--ly a s.all(hange in the (ell -ress%re $ac to the sa.-le, J Ter&aghi3s -rin(i-ie of effe(tive stress EF* !51#B, the cOa%$ in effe(tive stress is

IJ.a# <<e nuThe vol%.e (hange $= (a%sed :y this (liange in stress is

$= 5 Cs1t MYAa@B 5 5C = 1

F $ac 5 A% B

where Cst is the (orn-ressi:ility of the soil s<eleton and # 1 is the original

vol%.e of the sa.-le*As .entioned in Cha-ter 7, the .ineral grains the.selves are rela5

t1vely .(o.-ressi:le, so any de(rease in the vol%rne of the soil s<eletonres%lts in a de(rease in vol%.e of the voids or

where n is the -orosity, and C*, is the (o.-ressi:ility of the -ore fl%id

Cha-ter 1l.

. ,



$92 Pore Preure Paraeter

air waterB* I 1], then C C(, the (o.-ressi:ility of water* l we allow no drainage to o((%r, then these two (hanges in vol%.e .%st :eeF%al, or

5 n=AC= $u / 5 cs!=oF $oc 5 $u :

olving for the ratio .uQ .ac, we o:tain EF* 11511*3 .u l-- & =.loe 5 nC

11511B

l ;(s<

where .oc / .* . We dis(%ssed in e(* 11*1 the val%es of = for differentsoils and test (onditions see Ta:le 1157B* A .ore general way to o:tainEF* 11511 is shown later in this a--endi+*

We (an follow a si.ilar develo-.ent for the (hange in -ore -ress%red%e to the (hange in the -rin(i-al stress differen(e or shear stress in o%r tria+ial test s-e(i.en in order to derive EFs* 1151# thro%gh 1151* Ass%.ethat the soil s<eleton still :ehaves elasti(ally@ then the vol%.e (hange(a%sed :y the (hange in effe(tive stresses is

l

$= 5(s< vo# Ao; $oS Aa9'

The sy.:ols were -revio%sly defined* or the (o..on tria+ial(o.-res sion test, "*$ / .* , so

$= 5 Cs< v Y"*o; $ Aa# B

Toe (oeffi(ient 1Q# (o.es a:o%t :e(a%se for elasti( isotro-i( .aterials thevol%.e (hange is d%e to the av$!a$ of the (hanges in the three -rin(i-alstresses* Now add and s%:tra(t !A3# to the righ t5hand side of the eF%ation,and invo<e Ter&aghi3s -rin(i-ie of effe(tive stress* We then o:tain

av 5(s< vo 1 "*oZ 5 "*# *.* 5 #"*% B

As :efore, the de(rease in voids is

av 5n=AC = .##Gu 45#51B

or %ndrained (onditions, the two vol%.es .%st :e eF%al* olving for .u

and noting that

we o:tain

= & '''' nC

(s<

11511B

45#5$B

Note that the (oeffi(ient I Q# for the stress differen(e ter. is for elasti(

#



8-!.* &5lnl3n 3 o, 5n= *1 43 R3454l3n 3l PlnlN5l S4,....> U#

.aterials and tria+ial (o.-ression (onditions* I we .a<e a si.ilar deriva5* et

45#5#B

Note that yo% have to add and s%:tra(t $"a # in this (ase*B Th%s for elasti(soil s<eletons, the -ore -ress%re -ara.eter in e+tension is twi(e that in(o.-ression*

in(e soils in general are inelasti( .aterials, <e.-ton 162B re -la(ed the two (onstants in EFs* 45#5$ and 45#5# :y the (oeffi(ient A, sothat

llu o* A Ao - "! _

8f ten it is (onvenient to write EF* 1151# as

1151#B

where $ =A. or sat%rated soils, we %s%ally write EF* 1151# as

ll u / "# $F llo1 - llo# B 11512B

1151# aregiven :y <e.-ton 162B* or tria+ial (o.-ression (onditions,

llu / l

llo $Ao!

*$ 5 1

"#

- llo

X

45#52B

And for tria+ial e+tension (onditionsll u / 4l l

$lo la *$ 5 $

lo- loX

45#5B

# ! # !

These eF%ations show that if soils :ehaved as -erfe(tly elasti( .aterialsthat is, A 1Q# in (o.-ression and A $Q# in e+tensionB, then the -ore -ress%re wo%ld de-end only on the average (hange in -rin(i-al stress,whi(h is the first -art of EFs* 45#52 and 45#5*

B-!.* &E$I%ITIO% O$ =31 A%O =3#$OR ROTATIO% O$ PRI%CIPAL STRESSES

Law and Holt& 16!7B showed that (ontradi(tory definitions o e -ore -ress%re -ara.eter $ e+ist in the literat%re :e(a%se c the la(< of a(onsistent definition of -rin(i-al stress in(re.ent for (ases where the -rin(i-al stresses rotate* They -ro-osed the following syste., to ta<e (are

= :le a.:i ities when the -rin(i-ie stresses rotate 6>*In this syste., Ilo1 and lo# are (alled the 8a@or a 8inor princ,pa

stress incre8ents, res-e(tively* A -rin(i-al stress in(re.ent is defined as the.a+i.%. or .ini.%. nor.al stress in(re.ent i.-osed on a given stress

# !



555 .. --?- --- .. 5555 D5 .. 5 -- 55 . . - 5 DDDD5

Z 1

694 Pora 0

T4 . . . ..,J 5 5555D 5 **** K ******>**** 55DD '?' ! --- 5 ,v, . ssion anO nega%ve tor tension* .loW is the algebraically largest nor.al (o.-onent of a given sysie. or stress.(re.ents, an(t llo# is the algebraically s8allest nor.al (o.-onent of that syste.*

The advantage of this syste. is that the stress in(re.ent I not tr . th , X =D5==* 33l .10 ; 11 + A n

the dire(tion the original or final o,, and so is NXJ· This -oint is @% !a%9 999@K9@5 i , w@,@,*, I *9?%vW sorne (o.oinations 1 llAW an(t ll^1#

:eing a--lied to ty-i(al e+isting stress syste.s re-resented :y o and

TA,E ,"%"1 5 l*,*@

S45>> ln55n4> Gn24> 3 `h^?

- - .. , K,,**K ,

>1>45 2> 6>>G5= >45>> 65 6J246, 6n= 6Y2>54 2n >45>>

l.tiJI tresstress

inal tress Ll.3, C1#

yste. ln(re.ent tate1 1 Ganit%de 'ire(t3nn n,** **,

l2 1 2 1 9

# #2--

2 y t o Ht

T> T* T.

# n5r

# 2 l I2 4 2 T #

0K2

155, 1 P

- H 52 M

t T2 T2*t M .& M(r1i(al9 H & .H.ori&onl

Da

5l

5555,* J

55 55 5 5 ,*, -,-

,****

"%5

.% *O!3'A& *O! PO!E P!E&&'!E0 .. . -- -- 1 en

PATH TE&T&u.. * 5D ·"··T &T!E&&

To aid in (al(%lating the (orre(t val%e of the -ara.eter A, Law and Holt& 16!7Bderived the a--ro-riate e+-ressions for A for the fo%r ty-es of tria+ial stress -ath tests, AC,

AE, LC, and LE e(s* 1*" and l l*1$B* These

. . .

=3 "" 1 ... .., . D

1

- . . 5D

5***

5 n J

+ % 5%5 o W 2

.

r



--- . 5 D DD 55555



B-!.! $3Gl6> 3 P35 P5>>G5 P66545> 43 &l55n4 S45>> P64 T?46 89)

TABLE B-!-* &52n2423n 3 P2n2N6l S45>> ln55n4> 6n= $3Gl6>3 P35 P5>>G5 P66545> 3 V623G> TN5> 3 T26Y26l T5>4>

Test Ty-e Aa Aa$ Aa# or.%la for .A EF%ation

Co.-ression test9A+ial (o. r(ssion, AC $a o o .A ,> A%QAa*, 1151"

' ... ....ion LE o Aa* Aa* $, 5 1 A% QAa** 1151!

E+tension test9A+ial e+tension, AE o o Aa*, $,. > l 5 A%QAa 11517

Lateral (o.-ression, LC Aa11 Aa11 o .A1, A%Q Aa11 l l516

Aft(r Law and Holt& 16!7B*

are shown in Ta:le 45#5$* The derivation of these e+-ressions is shown int:e follow ing e+a.-le*

E+AMPLE B-!.

(215n:

An a+ial e+tension AEB tria+ial test is (ond%(ted on a sat%rated (lay*

R5FG25=:

'eter.ine the (orre(t for.%la for the -ore -ress%re -ara.eter A.

S3lG423n:

In the AE test, the lateral (ellB -ress%re re.ains (onstant while the a+ialsliess is de%eased* Therefore

A((ording to the definition of -rin(i-al stress .(re.ents -ro-osed :y Lawand Holt& 16!7B, $a., is negative sin(e it de(reases* Th%s it is alge:rai(allythe s.allest (o.-onent of the stress in(re.ent* %:stit%ting these defini5tions for A6 1 and AeJ9s into EF* 11 l ass%.e = 1B, D5 o:tain

$u11517B

A - - - $a.,

This for.%la is the sa.e as shown for the AE test 2n Ta:le 45#5$*

l

<



- 1

,"%.+ P!OO* THAT $ac $ ,e ANO $ae $ ,c

I4 was shown :y e+a.-le in e*e* 1 1*1$ that the -ore -ress%re -a ra.eter $ was the sa.e in a+ial (o.-ression ACB as in lateral e+ten sionLEB* l4 was inf erred that $ in a+ial e+tension AEB was identi(al to $ i n lateral eo.-ression LEB* The state.ents a1e tr%e eJen tho%gh these sets of tests have diff erent total stress -aths* Toe -roof of this (ontention was given :y Law and Holt& 16!7B*

We f irst def ine p / o@ o@BQ$ as the average of the .a0or and.inor eff e(tive stresses and B o1 5 # BQ $ as half the -rin(i-al stressdifferen(e ( *$c. 1*"B * We (an e+-ress the slo-e at any -oint on

theeffe(tive stress -ath in a p 'B diagra. as

dB d( o - oJ dp3 / dF o o 5 $ % B

or the a+ial (o.-ression (ase do1 do,. and d a3 8* Hen(e

F ## , %e or the lateral e+tension (ase do 1 / 8 and do3 / d o,. Hen(e

in(e :oth tests have (he sa.e eff e(tive st1ess -a ths see, f. e+a.-le,E+a.-le 1 1*1!B then

Hen(e 115$B

1.1larly, we (an show that

ae e

,"%.7 (E!I2ATION O* THE HEN-E PO!EP!E&&'!E ED'ATION ANO COE**ICIENT&

Ass%.e an ele.en t of soil in eF%ili:ri%. with stresses >= o , and o* *

on it* When we a--ly stress in(re.ents .1.o , *1*o* , and *1*o! to the ele.ent,an e+(ess -are -ress.e IGu a od a (es%ltiog (haoge in eff e(tive stressbs

Af ter (ott 1 6"# B* and Perloff and 4aron l 6!"B

$9$

#1



8-!.) &5l164l3n 3 the H5n5l P35 P5 .G5 EFG64l3n 6n= CO5ll5n46 8

o((%rs* o, , //

Ass%.e for now that the soil s<eleton is elasti( and isotro-i(* Th%sit has a :%l< .od%l%s /s< / EQ#1 5 $vB* in(e the definition of :%lle.od%l%s is the vol%rnetri( effe(tive stress j a4 aS a#B divided :y thevol%.etri( strain = Q = ,

?( a NY 6:2 E /

# 1 5 =

Rearranging, the vol%rnetri( strain of the soil s<eleton is3 a3 a3

v 3 ` $ # (s< !3

where Cs< 1Q Ks! is (alled the co8pressibility of soi/ s!eleton, and 1, $,and

# are -rin(i-al strains* in(e T and v are diffi(%lt to deter.ine for areal soil, the general (oeffi(ient Cs< is .ore -ra(ti(aV (ott,516"#B* Now, if we state this eF%ation in terrns of total stress (hanges and -ore -ress%re,

This eF%ation states that the vol%.etri( strain is a f%n(tion only of D n effe(tive stress for a linear/y elastic .aterial or, in fa(t, for any non5dilative, no5vol%.e5(hange5d%ring5shear .aterialB* oweer soils do (hangevol%.e d%e to the (hange in shear stress, and this isa((o%nted for :y an e.-iri(al (orre(tion fa(tor, 'l "*,*o(I, where l *"*To(,I is

the a:sol%te val%e of the incre8ent in *,*o(,D Th%s we have

= (s<g .3.1aoe, 5 u Toe,o

:e(a%se, :y definition fro. (ontin%%. .e(hani(s,

1 N2 #

8o(t // !

115$2B

As Perloff and 4aron 16!"B -oint o%t, sin(e =o3 (, is a nonlinear f%n(tion of D D D D (al(%late it dire(tl fro. the

stress in(re.ents* Instead we .%st deter.ine "5ro(, fro. thedifferen(e To(,h 5 5roe,B1*

.j

115$#B



-B-L)

698 Pore Preaaure Pararnetera

Now, as we did in e(tion 45#*1, let %s loo< at what ha--ens to thevoids* Toe vol%.etri( strain in the voids is

avv-/ 5C 45#51B= = =

where C is the (o.-ressi:ility of the voids, and # , the vol%.e of voids, isn = > l / 1], then C / C(, the (o.-ressi:ility of water* And if there

0

is no (hange in vol%.e -er.itted that is, %ndrained (onditions -revailB,then setting EF* 45#51 eF%al to EF* 45#5" and solving for au, we have

au 1

aoo(t B Ia3To(t IJ 45#5!B

nF Cv : s<

(s<

in(e soils are not linearly elasti( .aterials, as :efore we %se e.-iri(al (oeffi(ients whi(h are to :e deter.ined :y e+-eri.ent,

and

= & '''' nC

l P(s<

11511B

o EF* 45#5 :e(o.es

Da &'

Cs<

45#57B

I I5$$BToe (oeffi(ient a is the Zen!el pore pressure -ara.eter*

Altho%gh this derivation for EF* 115$$ is rather elegant .athe.ati(ally, it .ay :e easier to si.-ly write the eF%ation as

This latter for.%lation is .ore (onsistent with the definition of -rin(i-alstress in(re.ents -resented in e(* 45#*$* With this definition, a syste.ati(

se-aration of the stress in(re.ents fro. the initial and final stress states is -ossi:le*EF%ations 1151# and 45#56 are %sef%l sin(e they allow the se-aration

of -ore -ress%re effe(ts o:served in soils into two (o.-onents, that d%e tolB the (hange in .ean or average stress, and $B the (hange in shear stress*

The Hen<el -ara.eter a is, li<e the <e.-ton -ara.eter A, nonlinear and .%st :e deter.ined for ea(h stress -ath* l4 is also very de-endent

a

1



B-!.) &5l164l3n 3 45 H5n5l P35 P5>>G5 EFG6ll3n 6n= C35ll5n46 89

on strain, on the .agnit%^le of o$ , on the over(onsolidation ratio, and on.aterial -ro-erties s%(h as anisotro-y* The -ara.eters a and are for

general (hanges in total stress* They ena:le the engineer to -redi(t the -ore -ress%re if the (hanges in the total stresses are <nown or (an :e esti.ated,theref ore they (an :e very %sef %l in engineering -ra(ti(e*

o.eti.es in the geote(hni(al literat%re the Hen<el -ara.eters aredenoted :y the sy.:ol a, where a / a/ #* In this (ase, EF* 45#56 wo%ld :e

Ao 1 ` Ao$ ` Ao#

$u #

45#51B

This is the way Hen<el 16"B originally wrote his eF%ation, :%t with thesy.:ol a for a. Th%s Hen<el3s original a or a was one5third o%r a. Later Hen<el and Wade 16""B s%ggested the notation %sed herein, along withEF* 115$$*

I4 is of ten %sef %l to :e a:le to (onvert :etween the Hen<el -ara.eter a and the <e.-ton -ara.eter A. or the s-e(ial (ase of tria+ial (o.-ression ACB, o$ o# and * 1] ( = 1B, we have

Aoo(t / # Ao $Ao!

and

so EF* 115$$B

:%t sin(e Ao$ / Ao# 8 (onstant (ell -ress%reB and Ao 1 $av ,

$u / \ .U. a v3$ B $o# # =

ro. EF* 1151# and for tria+ial (o.-ression (onditions in Ta:le 45#5$, we<now that $ac $u/ Aa*,* Therefore D

V* $ac / ! a *5 l 15$aB

or the lateral e+tension LEB test, ^Ji a#, and EF* 115$$ :e(o.es $

$u # Ao 1 $Aa# B

a5

- A6 1 5 Ao#B

1

DB

#



¡

M88 Pore Preure Paraeter

$ M$ $ M$ C /

*O - a5

*'6O

/# 5

5

*'O

ro. EF* 1151# and Ta:le 45#5$, we <now that $ 1e / 1 5 C/ O. There5 re D

1 * V* 7* $ / - - - a 55 / - a

55le # # # #

115$:B

whi(h is the sa.e as EF* l l5$a* This res%lt sho%ld not :e %ne+-e(ted sin(ewe have already shown that $ac / $ 1e EF* 115$B*

or the (ase of a+tal e+tension AEB, o$ o 1, and EF* 11 $$ :e(o.es V*

C / #

$Ao1 Ao# B

a5

4%t sin(e llo / flo* / 8 and Ao! / .,,

5Ao 1 5 Ao# B#

1 $ 1 $ u /-# #

- a #5Ilo / # -

a

5Ilo#

ro. EF* 1151# and Ta:le 45#5$, we <now that $ae / 1 5 C/ .,. There

fore $ 1 5 1

5 a55 5 a555

ae # l l5$"aB

# # #

or the lateral (o.-ression LC test, o$ == so EF. 115$$ :e(o.es

M$tGu $ Aa 1 floJ B ` a

# Ao 1 flo# B

in(e flo 1 / llo$ /:,,.O and llo# / 8, we have

C / * a M$5B 6O# # 1

ro. EF* 1151# and Ta:le 45#5$, we <now that $1c 5 7:i..C / 7:i..O.

Therefore$ M$

$,c / # a *5 l15$":B

As e+-e(ted EF* 115$1B, $ae $ 1c

Note t:a t for elasti( .aterials, A ( $ ,e l Q# and Aae $ 1c $Q#,and a 8* In general, sin(e $ac ':: $ 1c , then the a -ara.eters are notne(essarily the sa.e for the two (ases, -ri.arily :e(a%se the (o.-ressi

:ility of the soil s<eleton Cs< is not the sa.e in (orn-ression as ine+tension*

# #

#



!eferencei

A4'ELHAGI', G**, A%O /RIE/, R*J* 16!"B =Al Rest Lateral Earth Press%re of aConsolidating Clay,= Journal of the 7eotechnica/ Engineering Division , ACE,Mel* 1$, No (T, -- !$1 !#7*

A4ELEM, *G* 16!B =The ta:ili&ation of o%ndations of tr%(t%res on Loessoils,= Proceedings of the 9ourth lnternational Conference on oil "echanicsand 9oundation Engineering , London, Mol* 1, --* $65$"#*

A4os., H. 16!#B ''An E+-eri.ental Investigation on the i.ilit%de in the Consolidation of a of t Clay, In(l%ding the e(ondary Cree- ettle.ent*= Proceedings o the E1glnh l8erna1io1u.l Co11fe1 e11ce on oil $leeharaics and

9oundation Engineering , Gos(ow, Mol* 2*#, -* 77*

AL-HG>>AI%I,G*G* 16!!B =Contri:%tion to the Engineering oil Classifi(ationsof Cohesionless oils,= 9inal )eport , Gis(ellaneo%s Pa-er 5!!5$1, U**Ar.y Engineer Waterways E+-eri.ent tation, Mi(<s:%rg, Gississi--i, "1 --*

WNEN' *C* 16! =lnvestigation of S Testing 2nCohesionless oils,= &echnica/ )eport 5-2511, U** Ann Engineer ater5ways +-eri.ent tation* Mi(<s:%rg, Gississi--i, 0 --*

Al*PAN, l. 16"!B =The E.-iri(al Eval%ation of the Coeffi(ient S and S 1t ,; oil

and 9oundation , Mol* MII, No* I, --* #152*AGERICAN As8CIATI8N 8R TATE HIHWA A%& TRANP8RTATI8N 0$$ICIALS

16!7B tandard peufications for G!a%sp91E1ai9!i "aterials and "etbod5t a8pling and &esting, 1$th Ed*, Washington, 3.5.Part I, -e(ifi(ations, 7$7 --*@ Part 11, Tests, 667 --*

AGERICAN o(IET 8 CGL ENINEER 16!7B oil J8prove8ent5Zistory , Capabilities, and Autloo! , Co..ittee on Pla(e.ent and l.-rove.ent of oils,eote(hni(al Engineering 'ivision, ACE, 17$ --* 3

AGERICAN o(IET $OR TESTI%( A%& GATEIUAL 167B =Nat%ral 4%ilding to,nes@oil and Ro(<,= $nnual oo! of $&" tandards , Part 16, Philadel-hia, "#2 --*

AGElllCAN S3IET7 8R TETIN A%& MATEIALS 16""B $&" "etric Practice7uide, $nd Ed*, 2" --*

7,1

*J



702 !eterence

ARAMIN, M*I*, AN' NUGER8M, * 16B =ee-age Co.-%tations for Hydra%li(tr%(t%res,= tpoitel3 stvu i $r!hite!ture , Gos(ow, referen(ed in Harr, 16"$B*

AITER4ER, A* 16B ='ie Rationelle /lassifi<ation der ande %nd /iese,=Che8i!er5`eitung , Mol* $6, --* 165167*

AITER4ER, A* 1611B =Lerornas orhallande till Matten, ^leras Plasti(itetsgranser o(h Plasti(itetsgrader,= =The 4ehavior of Clays with Water, their Li.its of Plasti(ity and their 'egrees of Plasti(ity,=B Kungliga %antbru!sa!ade8iens

Zandlingar och &ids!rift , Mol* , No* $, --* 1#$517@ also in lnternationale "ittei/ungen fjr oden!unde , Mol* l, --* 152# =\:er die Physi<alis(he4oden%nters%(h%ng %nd O:er die Plasti&itat der Tone=B*

A&&o%&, A**, /RIE/, R*J* AN' C8R8TI, R*4* 16!"B =Regression Analysis of oilCo.-ressi:ility,= oils and 9oundations, Mol* 1", No* $, --* 165$6*

4AUELIN, *, JUEL, J**, AN' HIEL', '*H* 16!7B &he Pressure8eter and

9oundation Engineering , Trans Te(h P%:li(ations, Cla%sthal, er.any, andAeder.annsdorf, wit&erland, "1! --*

M8N 4AN'AT, H** 16"$B $erogeo/ogy , %lf P%:lishing Co.-any, Ho%ston, Te+as,# --*

4AR'EN, L*, A%& G(oWN, A* 16!#B =Gi(rostr%(t%ral 'ist%r:an(e in oft ClaysRes%lting fro. ite lnvestigation a.-ling,= Proceedings of the lnternational y8posiu8 on oil tructure, othen:%rg, weden, -* $1#*

4ARREIT, R*J* 16""B =Use of Plasti( ilters in Coastal Constr%(tion,= Proceedingsof the &enth lnternational Con@erence on Coastal Engineering, To<yo, --*12751"!*

4EEGANN, H*/**PH* 16#B =I.-roved Gethods of 'eter.ining Resistan(e toAdhesion :y o%nding thro%gh a Loase leeve Pla(ed 4ehind the Cone,= Proceedings of the &hird lnternational Conference on oil "echanics and 9oundation Engineering , %ri(h, Mol* I, --* $1#5$1!*

4E/8W, * 16#B =oil ree&ing and rost Heaving with -e(ial A--li(ation 43Roads and Railroads,= &he (edish 7eo/ogica/ ociety , eries C, No* #!,$"th ear 4oo< No* #@ translated :y J*8* 8ster:erg, Northwestern Univer5

4IH8P, A*W* 167B =Test ReF%ire.ents of Geas%ring the Coeffi(ient of E64 Press%reat Rest,= Proceedings of the Conference on Earth Pressure Proble8s, 4r%ssels,Mol* I, --* $512*

4IH8P, A*W*, A%& HEN/EL, '*J* 16"$B &he "easure8ent of oil Properties in the&riaial &est, Edward Arnold Ltd*, Lond-n, $nd Ed*, $$7 --*

4IH8P, A*W*, AN' WELE, L*'* 16!B =Tria+ial A--arat%s for Controlled tressPath Testing,= 7otechniLue , Mol* SSM, No* 2 --* "!5"!*

4JERRUG, L. 162B =eote(hni(al Pro-erties of Norwegian Garine 8ays,=

7otechniLue, Mol* IM, No* $, --* 265"6*4JERRUG, L. 16"!B 33Engineering eology of Norwegian Nor.ally ConsolidatedGarine Clays as Related to ettle.ents of 4%ildings,= 7otechniLue, Mol*SMII, No* $, --* 715117*

4JERRUG, L* 16!$B =E.:an<.ents on of t ro%nd,= Proceedings of the $CE pecialty Con@erence on Perfor8ance of Earth and Earth5upported tructures,P%rd%e University, Mol* 11, --* 152*



!#

4JERRUG, L*, AN' IG8N, N *E* 16"B **Co.-arison of hear trength Chara(teristi(s of Nor.ally Consolidated Clays,= Proceedings of the $CE )esearchConferehce on the hear trength of Cohesive oils , 4o%lder, --* !115!$"*

4LAC/, '*/*, A%& LEE, /*L* 16!#B =at%rating La:oratory a.-les :y 4a(< Press%re,= Journal of the oil "echanics and 9oundations Division, ACE,Mol* 66, No* Gl, --* !56#*

4%ss1NE, J* 177B $pplication des Potentiels a L3tude de L3Luilibre et due " ouve8ent des olides lastiLues, a%thier5Millars, Paris*

4o&o&U/, G* 16"#B =lhe Gd%l%s of Elast;(ity of L5=6 Ciay ield Geas%re.ents,= Canadian 7eotechnica/ Journal, Mol* 1, No* l, --* 2#51*

4o&o&UIC, G*, AN' LE8NAR', *A* 16!$B 3!he lo%(ester Test ill,= Proceedingso the $CE pecialty Conference on Perfor8ance of Earth and Earth5upported tructures,; P%rd%e University, o * , art , --*

4LA' L* l]6 33Mi:rato Co.-a(tion of Cohesionlessoils,= Proceedings of the pecialty ession 'o. $ on oil Dyna8ics, venlnte.ational Conferen(e on oil Ge(hani(s and o%ndation Engineering,Ge+i(o City, --* 115117*

4R88/ER, E*W*, OII IR*El N' H 16"B ?E64 Press%res al Rest Related totress History,= Canadian 7eotechnica/ Journal, Mol* II, No* l, --* 151*

4<8G8N8, W**, J8NA, E*, AN' Lld?', C*C* 16!"B =Esti.ating In itn Ga+i.%. PastPre(onsolidation Press%re of at%rated Clays fro. Res%lts of La:ora toryConsolido.eter Tests,= pecial )eport 1*, Trans-ortation Resear(h 4oard,

--* 251$*CA'LIN, L*, AN' 'ENTA', * 16B 3!:e Mane 4orer,= Proceedings 'o. 1,

Royal wedish eote(hni(al Instit%te, --* 1577*

CAGPANULA, R**, AN8 M AI', *P* 16 Q$B 3 A i.-le /*5Tria+ial 9H,= Canu8an

7eotechnical Journal , Mol* 6, No* #, --* $265$"*CAJtRIAN, R*A* 16!7B ='e(i.al Ti.e,= $8erican cientist, Mol* "", No* #, --*

#5#1#*

CAARAN'E, A* 16#$aB 'is(%ssion of =A New Theory of rost Heaving,= :y A*C*4en<eBroan and E R 8hlrnstead* Proceedings oF the Zigh(ay B)esearch oard , Mol* ll, --* 1"75 1!$*

CAARAN'E, A* 16#$:B =Resear(h on the Atter:erg Li.its of oils,= Publi )oads, Mol* 1#, No* 7, --* 1$151#"*

CAARAN'E, A* 16#$(B =The tr%(t%re of Clay and lts I.-ortan(e 2n o%ndationEngineering,= Journal of the oston ociety of Cioil Engineers, A-ril@ re -tinted 2n Conuibutio,rs to oiI "echanis 1+2 1+, 4CE -- 1 l J

CAARAN'E, A* 16#"aB =Chara(teristi(s of C*8hesionless oils Affe(ting theta:ility of lo-es and Earth ills,= Journal of the oston ociety \f Civil

Engineers, Jan%ary@ r(-rinted 2n Contributions to oil "echanics 1+251+,4CE, --* $!5$!"* *CAARAN'E, A* 16#":B =The 'eter.ination of the Pre5Consolidation Load and

lts Pra(ti(al ignifi(an(e,= ';s(%ss1on '5#2, Proceedings of dte 9i8 68ernational Conference on oil "echanics and 9or8dation Engineering ,Ca.:ridge, Mol* 111, --* "5"2*

CAARAN'E, A* 16#!B =e(-age l:ro%g: 'a.s,= Journal of the 'e( England

l1



Í '

0" !elerencea

ater or!s $ssociation , Mol* LI, No* $@ re-rinted in Contributions to oil

" echanics 1+251+, 4CE, --* $65##"*

CAARAN8E, A. 16#7B =Notes on oil Ge(hani(s5 irst e.ester,= HarvardUniversity %n-%:lishedB, J*$6 --*

CAARAN8E, A. 1627B =Classifi(ation and Identifi(ation of oils,= &ransactions,ACE, Mol* 11#, --* 6156#*

CAARAN8E, A. 16B =Notes on the 'esign of Earth 'a.s,= Journal of the oston ociety of Civil Engineers, 8(to:er@ re-rinted in Contributions to oil " echanics 1+151+2*, 4CE, --* $#15$*

CAARAN'E, A. 167B =Notes on the 'esign of the LiF%id Lirnit 'evi(e,=7otechniLue, Mol* MIII, No* $, --* 72561*

CAARAN8E, A. 16!B =LiF%efa(tion and Cy(li( 'efor.ation of ands, a Criti(alReview,= Proceedings of the 9ifth Pana8erican Conference on oil "echanicsand 9oundation Engineering , 4%enos Aires@ re-rinted as Harvard oil Ge(hani(s eries, No* 77, $! --*

CAARAN'E, A., AN8 A'UG, R*E* 1622B Clos%re to =A--li(ation of oil Ge(hani(s in 'esigning 4%ilding o%ndations,= &ransactions, ACE, Mol* 16, -* 2"!*

CATR8, * 16"6B =LiF%efa(tion of ands,= Ph' Thesis, Harvard University@re-rinted as Harvard oil Ge(hani(s eries, No* 71, 11$ --*

CATR8, * 16!B =LiF%efa(tion and Cy(li( Go:ility of at%rated ands,= Journal

of the 7eotechnical Engineering Division , ACE, Mol* 11, No* T", J%ne, --*1 5"6*

CATR8, *, AN' P8UL8, *J* 16!!B =a(tors Affe(ting LiF%efa(tion and Cy(li(Go:ility,= Journal of the 7eotechnical Engineering Division , ACE, Mol* 1#, No*

T", --* 151"*CATERPILLAR TRACT8R Co* 16!!B Caterpillar Perfor8ance Zandboo! , or. AE/

##1#, 7th Ed*, Cha-ter 12, Peor;a, Illinois, -* "*

CE'ERREN, H*R* 16!!B eepage , Drainage, and 9lo( 'ets , $nd Ed*, John Wiley #ons, ln(*, New or<, #2 --*

CLEMENER , W*A* 167B =E+-erien(es With Loess as a o%ndation Gaterial,=&ransactions, ACE, Mol* 1$#, --* 1151"6*

C8LLIN, /*, AN' G(oWN, A. 16!2B =The onn and %n(tion of Gi(rofa:ri(eat%res in a Mariety of Nat%ral oils,= 7otechniLue , Mol* SSIM, No* $, --* $$#5$2*

C8UL8G4, C.A. 1!!"B =Essai s%r %ne a--li(ation des regles de Ga+i.%s etGinirnis a F%elF%es Pro:le.es de tatiF%e, relatifs a l3Ar(hite(t%re,= "8oires de "ath8atiLue et de PhysiLue, Prsents a l3$cad8ie )oya/e des

ciences , par divers avans, et lús dans ses $sse8bles, Paris, Mol* !, vol%.efor 1!!# -%:lished in 1!!"B, --* #2#5#7$*'3APP8L8NIA, '*J*, W.TGAN, R*M*, AN8 '3APP8L8NIA, E*'* 16"6B =and Co.

-a(tion with Mi:ratory Rollers,= Journa/ of the oil "echanics and 9ounda

tions bivision , ACE, Mol* 6, No* G l, --* $"#5$72*

'3APP8L8NIA, '*J*, LAG4E, T*W*, A%O PoUL8, H** 16!1B =Eval%ation of PorePress%res 4eneath an E.:an<.ent,= Journal of the oi/ "echanics and

9oundations Division , ACE, Mol* 6!, No* G", --* 771576!*



0)

'3APP8L8NIA, '*J*, P8UL8, H**, AN' LA'', 5.5. 16!1B **lnitial ettle.(nt of tr%(t%res on Clay,= Journal of the oil "echanics and 9oundations Division ,

ACE@ Mol* 6!, No* , --*=ilter a:ri(s9 4ri 4 %t%re in Road and Highway Con5

str%(tion,= Civil Engineering , ACE, Mol* 2", No* , --* 15'3AR(, H* 17"B **Les ontaines P%:liF%es de la Mille de 'i0on,= 'al.ont, Paris*

8AW8N, R** 1622B 'is(%ssion of =Relation of Undist%r:ed a.-ling to

La:ora5tory es D D116#*

'E GELL8, M**4* 16!1B e tan ar ene ra io , , Proceedings of the 9ourth Pana8erican Conference on oil "echanics and 9oundation Engineering , Mol* 1, --* 157"*

'14ERNAR'8, A* 16!6B =The Ef fe(t of La:oratory Co.-a(tion on the Co.-ressi :ility of a Co.-a(ted Highly Plasti( Clay,= GCE Thesis, P%rd%e Univer5sit 17!

'141AI8, E*, AN8 TEl3^rIAGAR, P* 16!B =Prnvefylling til 4r%dd -a 4lt Leire,= Proceedings of the eventh candinavian 7eotechnical "eeting, Co-enhagen,Polyte<nis< orlag, --* 1!#517*

'UNCAN, J*G*, AN' 7UCHINANI, A*L* 16!"B ?An Engineering Gan%al for ettle.ent t%dies,= 7eotechnical Engineering )eport , University of California al

E'EN, W*J* 16!1B =a.-ler Trials in 8ver(onsolidated ensitive Clay,= a8pling of oil and )oc! , ATG -e(ial Te(hni(al P%:li(ation No* 27#, --* 1#$512$*

E&E%, W*J*, AN8 /%48TA, J*/* 16"$B =orne 8:servations on the Geas%re.ent of ensitivity of Clays,= Proceedings of the $8erican ociety for &esting and

"aterials, Mol* "1, --* 1$#651$26*EI'E, 3., AN' H8LG4ER, >. 16!$B =Test ills to ail%re on t e 4 an o

= roceedin s o the $CE pecialty Conference on Perfor8ance of Earth

and Earth5upported tructures, P%rd%e University, o * , art , -*E8PT 16!2B Proceedings of the European y8posiu8 on Penetration &esting,

to(<hol., wedish Co%n(il for 4%ilding Resear(h, Mols* t , $*1, $*$, and #*

INN, , n inTria+ial and i.-le hear Tests,= Journal of the oil "echanics and 9ounda5

LAATE, /*, AN8 PRE4ER, T* 16!2B **ta:ility of Road E.:an<*.ents,= Canadian

7eotechnical Journal , Mol* 11, No* l, --* !$577*R C*R* AN' AHLMIN, R** 162B 33tresses and 'efle(tions Ind%(ed :y aUnifor. Cir(%lar Load,= Proceedings o

## * 2"!52!*ARCIA54EN88CHEA, l*, L8MELL, .D., AN8 ALTCHAEL, A** 16!6B =Por(

'istri:%tion and Per.ea:ility of ilty Clays,= , Journal o@ the 7eotechnical Engineering Division , ACE, Mol* 1, No* T!, --* 7#657"*

I44, H*J* 16"6B 'is(%ssion, Proceedings of the pecia/ty ession 'o. J on Epansive oils and "oisture "ove8ent in Part/y aturated oils, eventh

D D D o%ndation En D eerin ,

Ge+i(o City*

,¡



- --5555555555

Z1

M86 !eference

RIG R*E* 166 =Ph si(o5Che.i(al Pro erties of oils9 Clay Ginerals,= Journal

of the oil "echanics and 9oundations Division , ACE, Mol* 7, No* G$, --*l 51!*

R8G/8, *J* 16!2B =Review of E+-ansive oils,= Journal of the 7eotechnical En ineerin Division ACE Mol* 1, No* T", * ""!5"7!*

Zandboo! of Che8istry and Physics 16!!B CRC Press, Cleveland, 7th Ed*

of Clay :y the all5Cone Test,= Proceedings 'o. 1, wedish eote(hni(al

HAN48, * 16"B =Consolidation of Clay with -e(ial .Referen(e to.Infl%en(.e of rains,

HAN48, * 16!B Jord8ateria/liira , Al.Fv1st$17 --*

HARR, G*E* 16"$B 7round(ater and eepage , G(raw5Hill 4oo< Co.-any, Newor<, #1 --*

HARR, G*E* 16""B 9oundations of &heoretica/ oi/ " echanics, G(raw5Hill 4oo< Co. an New or< #7 l

HARR, G*E* 16!!B " echanics of Particu/ate "edia , G(raw5Hill 4oo<

Co.-any, HAEN, A* 1611B 'is(%ssion of ='a.s on and o%ndations,= :y A*C*

/oenig, HEN/EL, '*J* 16"B =The hear trength of at%rated Re.o%lded

Clays@3 Proceed5

HIL, J*W* 16"1B =A Ra-id Gethod of Constr%(tion Control for E.:an<*.ents of Cohesive oils,= Engineering "onograph 'o. , revise , %rea% oRe(la.ation, 'enver, $6 --*

HIRCHEL', R*C* 16"#B =tress5'efor.ation and trength Chara(teristi(s of oils,= Harvard University %n-%:lishedB, 7! --*

HE, /*, AN'ERLAN', 8*4*, AN' RoLEN, E*N* 16"6B =Undrained 4ehavio%r i nder Load Tests at usr%. = 7otechni ue Mol* SIS No* l

--* 11511* *HoENT8LER, C*A*, AN' TERAHI, C. 16$6B =Interrelatio-shi- of Load,

Road, and %:grade,= Pub/ic )oads, Mol* 1, No* #, --* #!5"2*

y8posiu8 on Penetration &esting E8PlB,

'Mol*

l, --* 151"$*

HoLG, *, AN' Ho%&, R*'* 16!!B =A t%dy of Large 'ia.eter Piston a.-lers,= Proceedings of the pecia/ty ession 'o. , Ninth Inte.ational Conferen(eon oil Ge(hani(s and o%ndation Engineering, To<yo, -* !!@ also in

Proceed ings of the /nternationa/ y8posiu8 on oft Clay, 4ang<o<, -* #71*

H8LT, R*8* 167B =I Units in eote(hni(al Engineering,= 7eotechnical &esting

Journal , ATG, Mol* #, No* $, --* !577*



!eferencea 707

H8LT, R*8*, AN8 4R8G, 7*4* i6!$B =Long5Ter. Loading Tests at <A5Ede:y,weden = oceedinU ef the $CE peeiaHty Co1t.fe1ence on Perfor8ance of Earth and Earth 5upported tructures, P%rd%e University, Mol* 1, Part l, --*4 -

HoLT&, R*'*, A%O HoLG, * 16!6B =Test E.:an<.ent on an 8rgani( ilty Clay,= Proceedings of the eventh European Conference on oil "echanics and 9oundation Engineering , 4righton, England, Mol* #, --* !657"*

llo%&, W** 166B =E+-ansive Clays Pro-ert1es and Pro:le.s,= \uarterly of theColorado choo/ of "ines, Mol* 2, No* 2, --* 7651$*

Ho%&, W**, A%O \I44, H*J* 16"B =Engineering Pro-erties of E+-ansive Clays,=&ransactions, ACE, Mol* 1$1, pp. "215"!!*

HoUH,* B.K. 16"6B asic oils Engineering, $nd Ed*, The Ronald Press Co.-any, New or<, "#2 --* D

HowAR', A*/* 16!!B =La:oratory Classifi(ation of oils5Unified oil Classifi(a tiooyste.,= Ta! ciences G,'ai!ii!, Aa% #. 4, U** 4ttrea% 3 Re5 (la.ation,'enver, " --*

Hv8RLEM, G*J* 1626B ubsurface Eploration and a8pling of oSls Jor Civil

Engineering Purposes, U** Ar.y Engineer Waterways E+-eri.ent tation,Mi(<s:%rg, Gississi--i, $1 --@ re-rinted :y the Engineering o%ndation,16"$*

Ilv8RLE v, G*J* 16"B Physi(al Co.-onents of the hear trength of at%ratedClays,= Proceedings of the $ CE )esearch Conference on the hear trength of Cohesive oils, 4o%lder, --* 1"651!#*

INTERNATI8NAL 8CIET 8R 8IL GECHANIC AN8 f 8UN'ATI8N ENINEEIUN16!!B =List of y.:ols, Units, and 'efinitions,= %:(o..ittee on y.:ols,Units, and 'efinitions, Proceedings of the 'inth lnternational Conference onoil "echanics and 9oundation Engineering, To<yo, Mol* #, --* 1"51!*

lu/, J* 1622B =Toe Coeffi(ient of Earth Press%re at Rest= in H%ngarianB

"agyar "rno! s EpitsM Egylet KoMdonye Jo%.al of the o(iety of H%ngarian Ar(hite(ts and EngineersB, Mol* !7, No* $$, --* #5#7*

uK7. J* 1627B **Earth Press%re in ilos,= Proceedings of the econd 6nternalional Conference on oil "echanics and 9oundation Engineering , Rotterda., Mol* I,

--* 1#51!*

1AN4U, N , AN' ENNEI, / 16!#B =ield Ca.-resse.eter Prin(i-ies a%dA--li(ations,= Proceedings of the Eighth 6nternationa/ Conference on oil

"echanics and 9oundation Engineering, Gos(ow, Mol* 1*1, --* 1615167*

J8HN8N, A*W*, AN8 ALL4ER, J*R* 16"B DDa(tors that Infl%en(e ield Co.-a(tion of oils,= ulletin $!$, High w aB Resear(h 4a1d, $" --*

JoNEs, 8*E*, AN' Ho%&, W** 16!#B =E+-ansive oils5the Hidden ';saster,=

Civil Engineering, ACE, v ol* 2#, No* 7, --* 26 1*/ARLssoN, R* 16!!B **Consisten(y Li.its,= in (oo-eration D24 the La:oratory

Co..ittee of the wedish eote(hni(al o(iety, w(dish Co%n(il for 4%ilding Resear(h, 'o(%.ent '", 2 --*

/AUGAN, R*I*, AN' HERGAN, D..,JR*, 16"2B **Engine(@ring Geas%re.ents for Port Allen Lo(<,= Journa/ of the oil "echanics a%d 9o(u/atinns Division, ACE, Mol* 6, No* G, --* $$15$2!@ also in Design of 9oundations Jor Control of ettle8ent , ACE, --* $715#!*

l1



Í'

!eterence708

of la(ial La<e

Cl'ays,= :y T*H* W%, Journal of the oil "echanics a8i 9oundations Division ,

/*E NNE, T*C* 16"2B =ea5Level Gove.ents and the eologi( Histories of the Post5la(ial Garine oils at 4oston, Ni(olet, 8ttawa, and 8slo,= 7otech

niLue, Mol* SIM, No* #, --* $#5$#*/ENNE, T*C* 16!"B =onnation and ara( eris ;

Marved oils,= l.$urits @erru8 "e8orial =o/u8e5Contributions to oil

"echanics , Norwegian eote( .ea nstl % e, s o, --*/ovAC, W*'*, EvAN, J*C*, AN' RIITH, A*H* 16!!B DDTowards a Gore tan

dardi&ed PT,= Proceedings of the 'inth 6nternational Conference on oilndation En ineering, To<yo, Mol* $, --* $"65$!"*

LA'', C*C* 16"2B =tress5train 4ehavior of at%rated Clay and 4asi( trengthD D nt of Civil En D eerin , Gas5

sa(h%setts Instit%te of Te(hnology, "! --*LA'8, C*C* 16!1aB =ettle.ent Analyses far Cohesive oils,= )esearch )eport )-15

, oils P%:li(ation $!$, 'e-art.ent of Civil Engineering, Gassa(h% settsInst;t%te of Te(hnology, 1! --*

LA'8, C*C* 16! l :B =trength Pararneters and tress5train 4ehavior of at%ratedClays,= )esearch )eport , 0 s % i( D , D DEngineering, Gassa(h%setts Instit %te of Te(hnology, $7 --*

LA'8, C*C* 16!$B =Test E.:an<rnent on ensit;ve Clay,= Proceedings of the $CE pecialty Conference on Perfor8ance of Earth and Earth5upported tructures ,ACE, P%rd%e University, Mol* I, Part 1, --* 1# and 1!*

E.:an<rnents Constr%(ted on Con5

ne(ti(%t Malley Marved Clays,= )esearch )eport )-25-, eote(hni(al P%:li(a tion#2#, 'e-art.ent of Civil Engineering, Gassa(h%setts lnstit%te of Te(h5nology, 2#7 --*

LA'', C*C*, AN8 LAG4E, T*W* 16"#B =The trength of Undist%r:ed Clay 'eter.ined fro. Undrained Tests,= %aboratory hear &esting o@ oi/s, ATG

. . . .

LA'', C*C*, AN' L%s(HER, U* 16"B =Engineering Pro-erties of the oils Underly5ing t e a.-%s, esear D D D'e-art.ent of Civil Engineering, Gassa(h%setts Instit%te of Te(hnology*

LA'8, C*C*, AN' EoER, L. 16!$B =Consolidated5Undrained 'ire(t5i.-le hear Tests on at%rated Clays,= )esearch )eport )-5+, oils P%:li(ation $72,

LA'8, 5.5., AN' o8TE, R* 16!2B =A New 'esign Pro(ed%re far ta 11ty o o tClays,= J ournal of the 7eotechnical Engineering Division , ACE, Mol* l, No*T!, --* !"#5 !7"*

LA'', 5.5., ooTE, R*, IHIHARA, /*, (HL8ER, *, AN8 PoUL8, H** 16!!B=tress5'efor.ation and trength Chara(teristi(s,= tate5of5the5Art Re-ort,

D D D rence on oil "echanics and

9oundation Engineering, To<yo, Mol* $, --* 2$15262*

LA'', R** 16"B =Use of Ele(tri(al Press%re Transd%(ers to Geas%re oil Pres5



!eferenc:4!6

s%re,= )esearch )eport )250, oils P%:li(ation 17, 'e-art.ent of CivilEngineering, Gassa(h%setts lnstit%te of Te(hnology, !6 --*

LD3, R 9 =-e(i.en Pre-aration and Cy(li( ta:ility of ands,= Journal of

the oil "echanics and 9oundatSons Division , ACE, Mol* 1#, No* TI, --*#52!*

LA'E, P*M*, AN' LEE, /*L* 16!"B =Engineering Pro-erties of oils,= )eport ,UCL 25Es51"$ 12 --

LAG4E, T*W* 161B oil &esting for Engineers, John Wiley ons, In(*, New or<,

LAG4E, T*W* 16#B =The tr%(t%re of Inorgani( oil,= Proceedings, ACE, Mol* !6,e-arate No* #1, 26 --*

LAG4E, T*W* 167aB =The tr%(t%re of Co.-a(ted Clay,= Journal o@ the oil " echanics and 9oundations Division , ACE, Mol* 72, No* G$, X"251 to 1"25

#2* *LAG4E, T*W* 167:B =The Engineering 4ehavior of Co.-a(ted 8ay,= Journal o:

the oil "echanics and 9oundations Division , ACE, Mol* 72, No* G$, --* 1"51 to 1"5#*

LAG4E, T*W* 16"2B =Gethods of Esti.ating ettle.ent,= Journa/ of the oil " echanics and 9oundations Division , ACE, Mol* 6, No* G, --* 2#5"!@also io Design 9oundations For Control of ettle8ent , ACE, --* 2! !$*

LAG4E, T*W* 16"!B =tress Path Gethod,= Journal of the oil "echanics a%d 9oundations Division , ACE, Mol* 6#, No* G", --* #65## l.

LAG4E, T*W*, AN' GARR, W*A* 16!6B 33tress Path Gethod9 e(ond Edition,= Journal of the 7eotechnical Engineering Division , ACE, Mol* 1, No* T", --*!$!5!#7*

LAG4E, T*W*, AN' WHITGAN, R*M* 16"6B oil "echanics, John Wiley # ons,

ln(*, New or<, # --*LAG4RECHT, J*R*, AN8 LE8NAR', *A* 16!7B =Effe(ts of tress fOstory on

'efonnation of and,= Journal of the 7eotechnical Engineering Division,ACE, Mol* 12, No* TI 1, --* 1#!155,* 1#7!*

LAR8CHELLE, P*, AN' LEE4MRE, * 16!1B =a.-ling 'ist%r:an(e inCha.-lain Clays,= a8pling of oil and )oc! , ATG -e(ial Te(hni(alP%:li(ation No*27# * 12# 1"#*

LAR8CHELLE, P*, TRA/, 4*, TAMENA, *, A%& Ro, G* 16!2B =ail%re of a TestE.:an<rnent on a ensitive Cha.-lain Clay 'e-osit,= Canadian 7eotechni

ca/ Journal, Mol* 11, No* 1, --* 12$51"2*LAW, /*T*, AN' HoLT* R*8* 16!7B **A Note on <e.-ton3s A Para.eter D24

Rotation of Prin(i-ie tresses,= 7otechniLue, Mol* SSMIII, No* 1, --*

LEE, K.L. 16"B =Tria+ial Co.-ressive trength at%rated ands Under eis.i(Loading Conditions,= Ph' 'issertation, l,Jniversity of California al 4er<eley,$1 --*

LEE, K.L., A%& EE', H.B. 16"!B ='rained trength Chara(teristi(s 3 ands,= Journal of the oil " echanics and 9oundations Division , ACE, Mol* 6#, No*G", --* 1 11 121*

._



Í '

M18 !eference

LEE, /*L*, A%O INH, A* 16!1B =Co.-a(tion of ran%lar oils,= Proceedings of the 'inth $nnua/ y8posiu8 on Engineering 7eology and oils Engineering ,

4oise, Idaho, --* 1"151!2*

LE8NAR', *A*, Ed* 16"$B 9oundation Engineering , G(raw5Hill 4oo< Co.-any,

LE8NAR', *A* 16!#B 'is(%ssion of =The E.-ress Hotel, Mi(toria, 4ritish Col%.:ia9 i+ty5five ears of o%ndation ettle.ents,= Canadian 7eotechnica/

Journa/ , Mol* 1, No* 1, --* 1$51$$*

LE8NAR', *A* 16!"B Esti.ating Consolidation ettle.en ts of hailow o%%da5tions on 8ver(onsolidated Clays,= pecial )eport 1*, Trans-ortation Re sear(h4oard, --* 1#51"*

LE8NAR', *A* 16!!B 'is(%ssion to Gain ession $, Proceedings of the 'inth /nternationai Con@erence on oii "echanics arui 9ou8l(ion Enginee, ing ,

To<yo, Mol* #, --* #725#7"*LE8NAR', *A*, AN' AiTCHAEL, A** 16"2B Co.-ress1:il;ty of Clay,= Journal

of the oil "echanics and 9oundations Division , ACE, Mol* 6, No* G, --*1## 1", also in Design uf 9ound(ions fo, Co8,13 uf etdenre8 , AEE, --*1"#517*

LE8NAR', *A*, C%rrER, W*A*, A%O tt8LT, R*'* Y167B 3'yna.i( Co.-a(tionof ran%lar oils,= Journal of the 7eotechnical Engineering Division , ACE,Mol* 1", No* 1, --* #522*

LE8NAR', *A*, AN' IRAULT, P* 16"1B =A t%dy of the 8ne5'i.ensionalConsohdat1on Iest,= Proceed8gs o the h:th lnternat,ona/ Con@erence on o,I "echanics and 9oundation Engineering , Paris* Mol* , --* 11"51#*

LE8NAR', *A*, AN' RAGIAH, 4*/* 166B =Ti.e Effe(ts in the

Consolidat;on of Clay,= Papers on oils51+2+ "eeting , A.eri(an o(ietyfor Testing and Gaterials, -e(ial Te(hni(al P%:li(a:on No* $2, --* 11"51#*

LER8UEIL, *, TAMENA, *, TRA/, 4*, LAR8CHELLE, P*, AN' Rov, G* 16!7aB=Constr%(tion Pore Press%re in Clay o%ndations Under E.:an<.ents* Part19 The aint5Al:an Test ills,= Canadian 7eotechnical Journa/ , Mol* 1, No*1, -* "*

LER8UEIL, >., TAMENA, *, GIEUEN, ., AN' PEINAU', G* 16!7:B =Constr%(5tion Pore Press%res in Clay o%ndations Under E.:an<rnents* Part 119enerali&ed 4ehavio%r,= Canadian 7eotechnical Journal, Mol* 1, No* 1, --*

Lr%, T*/* 16!B =A Review of Engineering oil Classifi(ation yste.s,= pecial Procedures for &esting oil and )oc! for Engineering Purposes, th Ed*, ATG-e(ial Te(hni(al P%:li(ation 2!6, --*5 #"15#7$*

Loos, W* 16#"B =Co.-arative t%dies of the Effe(tiveness of 'ifferent Gethodsfor Co.-a(ting Cohesionless oils,= Proceedings of the 9irst lnternationa/

Con@erence on oil "echanics and 9oundation Engineering , Ca.:ridge, Mol*III, --* 1!251!6*

LoWE, J*, 111 16!2B =New Con(e-ts in Consolidation and ettle.ent Analysis,= Journal of the 7eotechnical Engineering Division , ACE, Mol* 1, No* T", --* !25"1$*

I 'WE, J , , $ACCHE, P E , AN8 EEI 'GAN, H 16"2B DeonsoBida*tion Testing with 4a(< Press%re,= Journal of the oil "echanics and 9oundations Division .



,

6elerencea !11

ACE, Mol* 6, No* G, --* "657"@ also in Design of 9oundations for Control of ett/e,,..Qent , ACE, --* !#56*

LKA>, R** F l:')0 =8ensifi(ation of Loose 'e-osits :y Po%nding,= Journal of the7eotechnical Engineering Division , ACE, Mol* 1", No* T2, --* 2#522"*

GAC'8NAL', A*4*, AN' AUER, E*/* 16!B =Toe Engineering ignifi(an(e of Pleisto(ene tratigra-hy in the as<atoon Ar(a, as<at(hewan, Canada,=Canadian 7eotechnical Journal , Mol* !, No* $, --* 11"51$"*

GANNHEIG, 4*R** 16!6B =A New Con(e-tion of the onnation of the /olaPenins%la A-atite 'e-osit9 The Co-rogeni( I.-a(t Theory5CIT,= &he Journal

of /rreproducible )esults, o(iety for 4asi( Irre-rod%(i:le Resear(h, Mol* $, No* 1, --* "5!*

GAARCH, /*R* 16!6B =Lateral Earth Press%re in Nonnally Consolidated 8ay,= Proceedings of the eventh European Conference on oil "echanics and 9oun

dation Engineering , 4righton, England, Mol* $, --* $25$* GAARCH, /*R*, H8LT, R*8*, H8I*G, 4**, AN' RE'RICIC8N, A* 16!B33Geas%re.ent of Hori&ontal In it% tresses,= Proceedings of the $CE pecialty

Conference on 6n itu "easure8ent of oil Properties, R et , North Carolina, Mol* I, --* $""5$7"*

G(oWN, A. 16!#B 33The Nat%re of the Gatri+ in la(ial A:lation Tills,=osiu8 on oil tructure, othen:%rg,

weden, -* 6*

' . . Ban

7eotechnical Journal, Mol* IM, No* #, --* #75#"*

NAR',GCE Thesis, University of Illinois*

GNAR', L* 1 ress%re.e er,

--* !52#*GNAR', L*, AN' 4R8IE, * 16!B =Theoreti(al and ra(: As-e(ts o

Consolidation,= 7otechniLue, Mol* SSM, No* 1, --* #517* GERI, * 16!#B =Coeffi(ient of e(ondary Co.-ression,= Journal of the oil

D 9oundations Division , ACE, Mol* 66, No* G l, --* 1$#51#!*GERI, * 16!B 'is(%ssion of =New 'esign Pro(ed%res for ta:ility of oft

No* T2, --* 26521$*

' .,terrelationshi-,= Journal of the 7eotechnical Engineering Division , ACE, Mol*

GILLIAN, M* 16!$B 'is(%ssion of 33E.:an<.ents on oft ro%nd,= Proceedings

GILL, W*T*, A%& 'EALvo, * * .-a( 0n 6n 33 ro i ,oils, newsletter of Converse, Ward, 'avis,3 and 'i+on, In(*, Pasad(na,Califorr%a, an ew ersey,

GITCHELL J*/* 16"7 =In5Pla(e Treat.ent of o%ndation oils,= Place8ent and

J8prove8ent of oil to upport tructures, A , --* @ .o the oil "echanics and 9oundations Division , ACE, Mol* 6", No* Gl, 16!B --* !#511*

l



55555555555555555 5 5555555555555

* !eference

GITCHELL, J*/* 16!"B 9unda8entals of oil ehavior , 3n Wiley # ons, ln(*, New or<, 2$$ --*

GITCHELL, J*/*, AN' AR'NER, W** 16!B =In it% Geas%re.ent of Mol%.eChange Chara(teristi(s,= tate5of5the5Art Re-ort, Proceedings of the $CE pecialty Conference on 6n itu "easure8ent of oil Properties , Raleigh, North Carolina, Mol* 11, -* ###*

GoH, *C*, 4RAN', E*W*, AN' NEL8N, J*'* 16!$B =Pore Press%res Under a 4%ndon of t iss%red Clay,= Proceedings of the $CE pecialty Conference on

Perfor8ance of Earth and Earth5upported tructures, P%rd%e University, Mol* I,Part 1, --* $25$2"*

GoHR, 8* 177!B =\:er die 4esti..%ng %nd die gra-his(he 'arstell%ng vonTragheits.o.enten e:ener la(hen,= Civilingenieur , (ol%.ns 2#5"7@ also in

$bhand/ungen aus de8 7ebiete der technischen "echani! , $nd Ed*, W* Ernst

%* ohn, 4erlin, --* 6 and 16 1612B*G8HR, 8* 16B =Wel(he U.stiinde :edingen die Elasti&itiitsgren&e %nd den

4r%(h eines Gateriales= `eitschrift des =ereines Deutscher 6ngenieure, Mol*22, --* 1$251#@ 1!$51!!*

G8RENTERN, N*R*, AN8 EIENTEIN, . 16!B =Gethods of Esti.atingLateral Loads and 'efor.ation,= Proceedings of the $CE pecialty Conferenceon %ateral tresses in the 7round and Design of Earth5)etaining tructures,Co.ell University, --* 15 1$*

G%%%s, J*P*, EE', H*4*, AN8 CHAN, C*/* 16!!B =Effe(ts of a.-le Pre-arationon and LiF%efa(tion,= Journal of the oil "echanics and 9oundations Divi sion

, ACE, Mol* 1#, No* T$, --* 61517*

NE3GAR/, N*G* 16#B =i.-lified Co.-%tation of Merti(al Press%res in Elasti(o%ndations,= niversity of 6llinois Engineering Eperi8ent tation Circular

, Ur:ana, Illinois, 16 --* NEWGAR/, N*G* 162$B =lnfl%en(e Charts for Co.-%tation of tresses in Elasti(

o%ndations,= niversity of 6llinois Engineering Eperi8ent tation ulletin ,eries No* ##7, Mol* "1, No* 6$, Ur:ana, Illinois, re-rinted 16"2, $7 --*

\TER4ER, J*8* 16!B =Infl%en(e Mal%es for Merti(al tresses in a e.i5inf initeGass '%e to a n E.:an<.ent Loading,= Proceedings o f the 9ourt h 6nterna5 tional Conference on oil "echanics and 9oundation Engineering , London,Mol* 1, --* #6#5#62*

\TER4ER, J*8* 16"#B =C%rrent Pra(ti(e in o%ndation 'esign511,= Chicagooil "echanics %ecture eries, ACE and Illinois Instit%te of Te(hnology, --*"5$$*

\IE4G A N T 16"B =Notes ao t:e :eariog R esistao(e af aft Clays = $cta Polytechnica candinavica , eries Ci5$, AP $"# 166B, --9 15$$*

PAR/, T*/*, AN8 ILMER, G*L* 16!B ='yna.i( Tria+ial and i.-le hear 4ehavior of and,= Journal of the 7eotechnical Engineering Division , ACE, Mol*J8I , No I", -- 1# $6

PAR8N, A*W*, /RAWC/, J*, A%& CR8, J*E* 16"$B ?An lnvestigation of thePerfer.anee en an 7 Ten Mi:rating Reller for the Co.-aetion ef eil,=Road Resear(h La:oratory, La:oratory Note No* LNQ"2Q AWP* J/* JEC*

PAML8M/, N*N* 16"B Collected or!s, Alead* Na%< UR, Leningrad*



6elerence-713

PEC/, R*4*, HAN8N, W*E*, AN' TH8RN4URN, T*H* 16!2V 9oundation Engineering ,

$nd Ed*, John Wiley # ons, ln(*, New or<, 12 --*PENNER, E* 16"#B =ensitivity in Leda Clay,= 'ature , Mol* 16!, No* 27", --*

#2!5#27* *PERL8, W*H*, AN8 4AR8N, W* 16!"V oil "echanics5Principles a8i $pplications,

The Ronald Press Co.-any, New or<, --* #65#"1*Po%L8, H**, AN8 'AMI, E*H* 16!2B Elastic olutions for oil and )oc! "echa5

8es, lohn Wiley # ons, ln(*, New or<, 211 --*PRo(roR, R*R* 16##B =%nda.ental Prin(i-ies of oil Co.-a(tion,= Engineering

'e(s5)ecord , Mol* 1 11, Nos* 6, 1, 1$, and 1#*PG>H, R* 16!#V eneral Re-ort on **Physi(o5Che.i(al Pro(esses whi(h Affe(t

oil tr%(t%re and Mi(e Mersa,= Proceedings of the lnlernational y8posiu8 on

oil tructure, othen:%rg, weden, A--endi+ -* ##*

UILE, R*G*, AN' TH8GP8N, C*'* 16""B =The a:ri( of Anisotro-i(allyConsolidated ensitive Garine Clay,= Canadian 7eotechnical Journal , Mol*lll, No* $, --* "15!#*

RAro, A*A* 16"B =The Pre(onsolidation Press%re in Clay oils,= GCE Thesis,P%rd%e University, 21 --*

RAG8N', *P*, ToWNEN', '*L*, A%O LoJ/ACE/, G*J* 13V!1B >The Effeets 5 a.-ling on the Undrained oil Pro-erties of the Leda oil,= Canadian

7eotechnical Journal , Mol* 7, No* 2, --* 2"5!*RAG8N', *P*, AN8 WAHL, H*E* 16!"B =Esti.ating 8ne5 'i.ensional

Consolidation, In(l%ding e(ondary Co.-ression of Clay Loaded fro.8ver(onsolidated to Nor.ally Consolidated tate,= pecial )eport 1*,Trans-ortation Resear(h 4oard, --* I Q $#*

REE8, G*A*, LoMELL, .D., ALTCHAEL, A**, AN' W333, L@E* 16!6B =rost

Heaving Rate Predi(ted fro. Pore i&e 'istri:%tion,= Canadian7eotechnical Journal , Mol* 1", No* #, --* 2"#52!$*

RUTLE'E, P*C* 1622B =Relation of Undist%r:ed a.-ling to La:oratory Testing,=&ransactions, ACE, Mol* 16, --* 11"$511"#*

AA'A, A**, A%& 4IANCHINI, ** 16!B =trength of 8ne 'i.ensionallyCon sohdated Clays, Journai uf tl,e 7eotechnieal Engineel3ing Diooion,

2CE, Mol* 11, No* Tll, --* 11l5ll"2*ANLERAT, * 16!$B &he Penetro8eter and oil Eploration , Elsevier, A.sterda.,

2"2 --*(HGERTGANN, J*H* 16B >The Undist%r:ed Consolidation 4(havtor of 8ay,3

&ransactions, ACE, Mol* 1$, --* 1$1 1$##*(HGERTGANN, J*H* 16!B =%ggested Gethod for (rew5Plate Load Test,=

pecial Procedures for &esting oil a8i )oc! Jor ingineering Purposes, th Ed*,ATG -e(ial Te(hni(al P%:li(ation 2!6, --* 7157*

(HGERTGANN, J*H* 16!B =Geas%re.ent of In it% hear tr(ngtht tat(5of5theArt Re-ort, Proceedings of the $CE pecialty Conference on 6n itu "ea sure8ent of oil Properties, Raleigh, North Carolina, Mol* 11, --* !51#7*

(HGI'T, 4* 16""B 'is(%ssion of =Earth Press%res at Rest Relat(d to tressHistory,= Canadian 7eotechnical Journal, Mol* 111, No* 4: --* $#65$2$

.j



5 55 5 55555555 DD 555 5555555555 5D555D555 5 55555

" 6eterence&

(HGI'T, 4* 16"!B =Lateral tresses in Unia+ial train,= ulletin 'o. *, 'anisheote(hni(al Instit%te, --* 51$*

CHWA4, E** 16!"B =4earing Ca-a(ity, trength, and 'efor.ation 4ehavio%r of oft 8rgani( %l-hide oils,= Ph' Thesis, Instit%tionen fOr Jord5 o(h4erg.e<ani<, /%ngliga Te<nis<a Hogs<olan, to(<hol., #"7 --*

(orr, R** 16"#B Principies of oil "echanics, Addison5Wesley P%:lishing Co. -any,In(*, Reading, Gassa(h%setts, --* $"!5$!*

EE8, H*4* 166B =A Godero A--roa(h to oil Co.-a(tion,= Proceedings of the Eleventh California treet and Zigh(ay Conference, re-rint No* "6, Thelnstit%te of Trans-ortation and Traffi( Engineering, University of Californiaat 4er<eley, -* 6#*

EE8, H*4* 16"2B Le(t%re Notes, CE $!1, ee-age and Earth 'a. 'esign,University of California at 4er<eley :y W*'* /ova(s, A-ril 1#B*

EE8, H*4* 16!6B =oil LiF%efa(tion and Cy(li( Go:ility Eval%ation for Levero%nd '%ring EarthF%a<es,= Journa/ of the 7eotechnical Engineering Divi

sion , ACE, Mol* 1, No* T$, --* $15$*

EE8, H*4*, AN8 CHAN, C*/* 166B =tr%(t%re and trength Chara(teristi(s of Co.-a(ted Clays,= Journal of the oil "echanics and 9oundations Division ,ACE, Mol* 7, No* G, --* 7!51$7*

EE8, H*4*, A%& loRI, I*G* 16"!B =Analysis of oil LiF%efa(tion9 NiigataEarthF%a<e,= Journal of the oil " echanics and 9oundations Division , ACE,Mol* 6#, No* G#, --* 7#5 17*

EE8, H*4*, A%& LEE, /*L* 16""B =LiF%efa(tion of at%rated ands '%ring Cy(li(Loading,= Journal of the oil " echanics and 9oundations Division , ACE,Mol* 6$, No* G", --* 151#2*

EE8, H*4*, AN8 LEE, /*L* 16"!B =Undrained trength Chara(teristi(s of Cohesionless oils,= Journal of the oil "echanics and 9oundations Division ,ACE, Mol* 6#, No* G", --* ###5#"*

EE8, H*4*, AN8 PEAC8C/, W*H* 16!1B =Test Pro(ed%res for Geas%ring oilLiF%efa(tion Chara(teristi(s,= Journal of the oi/ "echanics and.9oundations Division , ACE, Mol* 6!, No* G7, --* 16651116*

EE8, H*4*, AN8 WJL8N, *'* 16"!B =The T%rnagain Heights Landslide, An(hor age, Alas<a,= Journal of the oil " echanics and 9oundations Division , ACE,Mol* 6#, No* G2, --* #$5##*

EE8, H*4*, WooowAR', R*J*, AN8 LUN'REN, R* 16"$B =Predi(tion of wellingPotential for Co.-a(ted Clays,= Journa/ of the oil "echanics and 9oundations Division , ACE, Mol* 77, No* G2, --* 1!5 1#l.

EEGEL, R*G* 16!"B =Plasti( ilter a:ri(s Challenging the Conventional ran% lar ilter,= Civil Engineering , ACE, Mol* 2", No* #, --* !56*

ELI, E*T*, AN8 oo, T*5* 16!!B =%nda.entals of Mi:ratory Roller 4ehavior,= Proceedings of the 'inth 6nternational Conference on oil "echanics and 9oundatiorS Engineering , To<yo, Mol* $, --* #!5#7*

IG8N, N*E* 167B 'is(%ssion of =Test ReF%ire.ents for Geas%ring the Coeffi (ientof Earth Press%re at Rest,= Proceedings of the Conference on Earth Pressure Prob/e8s, 4r%ssels, Mol* 111, --* 5#*

IG8N, N*E* 16!2B **Nor.ally Consolidated and Lightly 8ver(onsolidated Cohe5



715

sive Gaterials,= eneral Re-ort, Proceedings o@ the Conference on ettle8enlof tructures, Ca.:ridge University, 4ritish eote(hni(al o(iety, --* 5#* *

/EGPT8N, A*W* 16#B **The Colloidal A(tivity of Clays,= Proceedings of the &hird Jnternational Conference on oil "echanics and 9oundation Engineering, Mol*, --* !5"1*

/EGPT8N, A*W* 162B =The Pore5Press%re Coeffi(ients $ and ,; 7otechniLve,

Mol* IM, --* 12#512!*/EGPT8N, A*W* 16"B =Effe(tive tress in oils, Con(rete and Ro(<s,= Pore

Pressure and uction in oils, 4%tterworths, London, -* *

D /EGPT8N, A*W* 16"2B =Long5Ter. ta:ility of Clay lo-es,= 7otechniLue, Mol*SIM, No* $, --* !!511*

/EGPT8N, A*W* 16!!B =lo-e ta:ility of C%ttings in 4rown London Clay,=

. . . '

9oundation Engineering, To<yo, Mol* #, --* $"15$!*

E* WILLIAG8N R*, A%& G8HNE, J* 16!!B =%idelines for Use of a:ri(s inConstr%(tion and Gaintenan(e of Low5Mol%.e Roa , nte )e ort U** orest ervi(e, Portland, 8regon@ also -%:lished as )eport 'o. 9Z$5&5-0552 :y the ederal H2 way n%r%stratlon, as ng on,3.5., 111 --*

TAL8R, '*W* 1627B 9unda8enta/s of oil "echanics, John Wiley # ons, ln(*,00

TAMENA, *A*, CHAPEAU, C*, LAR8CHELLE, P*, AN' Ro, G* 16!2B **I..ediateD la 33

Canadian

7eotechnical Journal , Mol* 11, No* 1, --* 165121*

' ' ., ., , .,

16!B,='iffi(%l.ties in the In it% '.etennination of S in. oft ensitive

of oi'l Properties, Raleigh, North Carolina, Mol* I, --* 252!"*

ERAHI,assr!aft, yo1* 1!, o* $2, PP9 225226@ re-riri*Jed in 9ro8 &heory to

TERAHI, K. 16$B Erdbau8echani! auf odenphysi!alischer 7rundlage, ran&1-&1g %n ein,

TERAHI /* 16$ =Con(rete Roads5 A Pro:le. in o%ndation Engineering*= Journal of the oston ociety of Civil Engineers, ay@ re-nnttions to oil "echanics / +251+, 4CE* --* !57*

l

Di

,



!eferenceM16

TERAHI, /* 162#B &heoretical oil " ecmanics , John Wiley ons, In(*, New

TERAHI, /*, AN8 PE(/, R*4* 16"!B oil "echanics in Engineering Practice, $ndEd*, John Wiley ons, In(*, New or<, --* !$6*

TURN4ULL, W*J* 16B =Co.-a(tion and trength Tests on oil,= -resented atAnn%al Geeting, ACE, Jan%ary, as (ited :y La.:e, T*W*, and Whit.an,R*M* 16"6B oil " echanics, John Wiley ons, In(*, New or<, -* 1!*

T%RN4ULL, W*J*, AN8 osTER, C*R* 16"B =ta:th&ahon of Gaterials :y Co.-a(tion,= Journal of the oil " echanics and 9oundations Division , ACE, Mol* 7$,

No* G$, --* 6#251 to 6#25$#@ also in &ransactions, ACE, Mol* 1$#, 167B, --* 15$"*

U** ARG C8RP 8 ENINEER 16!B =La:oratory oils Testing,= Engineer "anual , E" J 1551+.

%*s* ARG ENINEER WATERWA ESPERIGENT TATI8N 16"B =The Unified oilClassifi(ation yste.,= &echnical "e8orandu8 'o. *5*2-. A--endi+ A,Chara(teristi(s of oil ro%-s Pertaining to E.:an<.ents and o%ndations,16#@ A--endi+ 4, Chara(teristi(s of oil ro%-s Pertaining to Roads andAirf ields, 16!*

U** 4%REA8 8 RECLAMATIO% 16!2V Ea rth "anual , $nd Ed , 'e%ver 71 --

U** NAM 16!1B **oil Ge(hani(s, o%ndations, and Earth tr%(t%res,= '$=9$C Design "anual D"5-, Washington* '*C*

WALLACE, *4*, AN8 8rro, W*C* 16"2B ='ifferential ettle.ent at elfridge Air or(e 4ase,= Journal of the oil "echanics and 9oundations Division , ACE,Mol* 6, No* G, --* 16! $$@ also in Design of 9oundations for Control of

ettle8ent 4 ACE, --* $26 $!$*WARHAW, C*G*, AN' Ro, R* 16"1B =Classifi(ation and a (he.e for the

Identifi(ation of Layer ili(ates,= 7eological ociety of $8erica ulletin , Mol*!$, --* 125126$*

WETERAAR', H*G* 16#7B =A Pro:le. of Elasti(ity %ggested :y a Pro:le. inoil Geehanies9 A of t Gaterial R ein for(ed :y N%.ero%s trong Hori&ontalheets,= in Contributions to the "echanics of olids , tephen &i8oshen!o th

$nniversary =olu8e, Ga(.illan, New or<, --* $"75$!!*

WIL8N, *'* 16!B =%ggested Gethod of Test for Goist%re5'ensity Relations of oils Using Harvard Co.-a(tion A--arat%s,= pecia/ Procedures for &esting oi/ and )oc! for Engineering Purposes, th Ed*, ATG -e(ial Te(hni(alP%:li(ation 2!6, --* 11 1#*

WINELAN', J*'* 16!B =4orehole hear 'evi(e,= Proceedings of the $CE pe

cialty Conference on 6n itu "easure8ent of oil Properties , Raleigh, NorthCarolina, Mol* I, --* 115$$*

WIA, A*E** 16"6B 33Pore Press%re Geas%re.ent in at%rated tiff oils,= Journal of the oil "echanics and 9oundations Division , ACE, Mol* 6, No* G2, --*

1"#51!#*WR8TH, C** 16!$B =eneral Theories of Earth Press%res and 'efonnations,=

eneral Re-ort, Proceedings of the 9ifth European Conference on oil "echaBnics and 9oundation Engineering , "adrid , =ol. 66 , pp. ##5$*



!elerence

55? n n @'; .. n ;

5 5 n

lnitial tresses and 'efor.ationChara(teristi(s,= Proceedings of the $CE pecialty Conference on 6n itu0 1 nf :,..1 PrnnPrliP Ralei%h North Carolina, Mol* II, --* 171 $#*

o'ER, E*J*, AN8 WITCA/, G*W* 16!B Principies of Pave8ent Design , John,* .., - '..

**K K o. =3 T55* ,,K, M555 3!11 55

oN, R*N*, A** N' HEERAN, '*E*. 16-!#B =a:ri(. Unit lntera(tion and oil 4e5

...othen:%rg, wede@, --* 1!"517#*8N, R*N*, AN8 W AR/*ENTIN, H.. <1: JJ .2oi1 .ir.,

.

(ientifi( P%:lishing Co*, New or<, 226 --******* 5

D IGGIE, T** 16!#B =oil Tests on a Clay fro. <a5t99de:y, weden, Norwegian

eote(hni(al Instit%te, lnte.al Re-ort No* #"5#, $1 --*

1

.

¡;5 l

.L 5 .5 .

' -. ' .,

'i g: D5 - DJ

55 e,K,, 5

5'



lnde5

** ***99%Tn , H *9959a **lssifi(ation svste.s W 1@**,@,* +

A(tivity9defined* 21* 177ty-1(a1 vaa %es,Bu.

Allo-hane F see Clay .ineralsBW Q WW K L 3! 01<

Angle of internal fri(tion, 2$ Fsee a/so hear strenitthB

(orrelation with e* 17effe(t of test ty-e, 1!. - .w n, MI J I 8

s%..ary of fa(tors affe(ting* 1!t vnir**l v$1i,**** 3i l "

-lasti(ity inde+, #6range, #6snr./age 1i.i, *,**soil (lassifi(ation* %se in* 2

* 5 ,*K * $

to%ghness ide+, 2"- 5 . 5

(@. -ressi inde+* #2$(onsolidation :ehavior* ##7

4entonite* 1!* J 764erno%lli energy eF%ation* $$* $$!

- ,** - .Angle of re-ose, 1!!

definition* 26$sand d%ne* 26#

Anisot ro-y, 6!* "6.

Q --- 2l'.'IL ---

5D5555,1*

4ody stress F.ree tress J

4oiling F see %i(<sandB4orderline (lassifi(ation* #* "5!4oston :l%e (lay9

tests9 tria+ial testB (oern(aent 0 (onso11aat1on ****,**

A --arent (ohesion* 1 !"Artesia n -ress%re* $2$ACE* 6.-- n

A9 -%i te K Clay .ineralsBAtter:(rg li.its, #252

(ohesion li.it, #2effe(t of air drying* #7eng.eering -ro-enies9

relation to, 2ftow inde+* 2"liF%id li.it, LL, #25#6

devi(e* #!etTe(t of grooving tool, #75#6ftow (%rve* #7one -oint test, #7test des(ri -tion, #7

-lasti( li.it, #25#6test des(ri-tion* #7

-lasti(ity (hart, 1, 2

(o. -ression inde+, #2$ -rofile* ##"val%es of CnQC(, 2756

4o%lders, $!* 265* "%sed in dassifi(ation* 2, "

4o%ssinesF .ethod F see a/so tress

distri:%tionBinft%en(e (harts*

#7int**orated over ar(as 12"52 -oint load* #52"

4r%(ite Fsee Clay .in(ralsB4%l<ing, 1#* 1!2* 1!" *4%lldo&er* 1$"5$*! s% a/so

Co.-a(tton (F%i-.(ntB4%ll3s liv(r* 1!7

California 4earing Ratio* C4R, 1$, 15"C8R F see California 4earing RatioBCa-illarity, 1"!5!7

adh(sion for(es, 1"!height of ris(* 1"!5"6

M1

UDJ

.



72, lndex

Ca-i l l a ri t y F continued: Clay . i nerals F continued:t -i (a l va l %es* 1 !"

negat i e -ress% re* 1 !$i n s.a ll t % :es* 1 "!5!

Ca -i l l a r -ress% res* 1 !5!$

i n frost a(tion* 1 6$Ca -ill a n t % :es* 1 "!5!#Ca ;lil l a r v* ater * 1 ""Ca,1ta t ion* 1 !* 2C ' ( s$$ hear strengt h9 hea r st rengt h testsBC ' tests* 2#752* 2", 26#5#

toga -a rty* 1 7flo((%l at i on , fa(tors (a %si ng, 6gi h:site* !6hallo si t(* 7$57#* 76

E lt* 7$h dro%s al %. i no sil i(ates* !7 i

den t i fi(at1on* 77576'TA* 77elt9(t ron . i(roso-y* 77,5ra y d i ffra(t ion* 77

i lli te* 757"* 76* 61Goh r fail % re en velo-esD E G* 7"

nor .a l l y (onsol idated (lavs*21 8 erh (onsol i dated (lavs92$sa n d@* * 1 5

shea r strengt h -ara.eters* 1 "5 1 7* 2#* st ress (on d it ions #6st ress -at hs* 271 * 21test detai ls* 26#52, #756t y -i(a l :ehavior* 2625#

i on (on(ent ration* 6<aoli nite, 71 57$* 76* 61

ato. i( st r%(t %re* 71

E G * 7$. a ri ne* 6#. i ,ed ayer . i nerals* 7, 77.on t .ori ll on i te s.e(titeB, 7#57, 77576* 61

ato. i( st r %(t %re, 7#572

Cell -ress%re* 2" ( s$$ a/s Confini ng EG* 7 -a i , 6rti(le ntera(tion

-re11reBCh i(ago (lay9

(oeffi(ient of (onsolidation, 22(o. -resswn inde+, *121 52$(onsol idat i on :eha vior, #soi l r rel3ile* !"@val%e of C*,QC,* 26

Ch lorite (s$$ Clay . ineralsB

Cl assifi(ation syste.s ( s$$ oil (lassifi(ationsyste.sB

%sed i n (lassifi(at i on* , ", !!(onsisten(y "1(onsolidation :ehavior* $665#"defi ned, !!desi((atedZ or dry (r%st, 1 #", 1 7"frost s%s(e-t i :i l i ty* 1 6

sensi tive, #6sh ri n <age* 1 !756sta:tl1ty, (riti(a (ond1t1ons, "#6str%(t %re, d%e to (o. -a(tion, 1 1 !s **et li ng* $7 * #"

Clay .i nerals, $"* !7577

a:sor:ed water* 6$562a(tivity of, 6$atlo-ha ne* 77at(a -% lgite,7 EG* 7!

:oodiog ageotsD(o5valent* 17hyd rogen :ond* 6$Ja.es, 17 :r%(ite, 7

ehlorite, 7 7!, 76, 61(rystal str%(t% re9

o(tahed ral or al%.i na sheets, !7

%se ot J3last i(i ty Cha rt, 77571Vsta:iti&ation* li .e* 62ilic"1 &heet 94

soi t str %(t % re9dis-ersed, 656"flo((% lated, 656"

tet rahed rat si li(a B sheet, !75!6Clay soils, $ $", !! (s$ a.s ClaBs9 ClaV

. i nerals9 hear strengthBvan der Waal3s for(es, 7#, 6ver . i(%tite* 7

Cl %sters ( s$$ oil fa:ri(BCoa, se g, a i ned soils, $ $!, 26, "Co::les* $!* 265Coeffi(ient of (onsolidation (s$$

Consolidat ionBCoeffi(ient of (%rvat %re9

ty-i(al *,,aJ %es, #1Co(ffi(ient of lateral earth -ress%re ( s$$ /

0

Coeffi(ient of -er.ea:ility9deter.ination :v oedo.eter test* 2$5#

Coelh(1ent ol %.i3or.ily9defined, $6,

effeet 3A Ql, Hity-i(al val%(s* #1* 12

Co(ffi(ient of vol%.( (hange, #11, #1#Cofferda., $"Cohesion , defined, $Cohesio11less, 1 $Cohesive soil* defined, !!Colla -si ng soils 177Co. -a(ted (lays9

-erfor.a n(e of, 1#5"1PH test , es%l ts, "2 -ro-erties, 1 1 !5$2strengt h, 1$2

tet ra hed ral or si li(a sheets, !757$ %se in eart h da.s, 1756



lndell

Co. -a(ted (lays F continued:

Co.-a(tion eF% i -.ent F

continued:

721

%se in -ave.ent design* 1 25!Co. -a(tion9

:enefOs of* 1 1 1 :y :lasting* 1 #6(lays* -ro-erties of* 1 1!5$2of (ohesive soils* 1 1 !5$2(ont rol tests* 125#(% rve* 1 1#

line of o-ti.%.s, 1 1* 126.a+i. %. d1 y de11si ty * 1 1#o-ti.%. water (onten t* 1 1#

defin it ion* 1 1dry densities* ty-i(al val %es* 1 1 #, 15"dvna .i(* 1 #6521field vers%s la:oratory* 1 1"5 1 !i. -a(t* 1 1 1<11eadi11g* 1 1 1 51 #, 1 1"lift thi(< ness* 1$2* 1$!* 1 #, 1##, 1#75#6.ost effi(ient (onditions* 12#522o:0e(tives of* 1 1 1 -er((nt* 12$ -roofrolling* 1 $65#* 122ra-id (ontrol F see Co.-a(tion tests, ra-id

relative, 12$relati ve density* 12$sat% rat ion (%rve* 1 1 #512s-e(ifi(ations, 121 52stati(* 1 1 1 * 1 1 #

t heory, 1 1 151" ty -es 3,l1 1 vi:ratory9

elfe(t of freF%en(y* 1##5#2, 1#"elfe(t of lift thi(< ness* 1#"5#6effe(t of n %.:er of -asses, 1#"5#!effe(t of towing s-eed* 1 #"5#!6-ti.%. freF%en(y, 1##5#2,aria:les aTeeti ng* I JJ

vi:ratory insit %* vi:rofloation* 1#6vi:ratory s%rfa(e, -late (o.-a(tors, 1#$5#

Co.-a(tion (ontrol, 1215#Co.-a(tion (F%i-.ent, 1$252

:ovinas .as(%lini%s sona.:%lor%., 1$!draglines, 1$2d11. - tr%ZZ<s* 1$2, 1$12 + 2 and 2 + 2 rollers, 1 #grid or .esh rollers, 1#, 1#$.otor grad(r or =:lade,= 1$!

-ower shovels, 1$2rollers, 1$!r%::er tire roller, 1$7, 1#, 1"5!sera-ers e r =-ans,= 1$2, 1$" 1$6shee-sfoot rollers* 1$65#1, 1"5!s.ooth wheel rollers, 1$!5$7, 1"5!ta. -ing foot rollers, 1#5#1vi:ratory (o.-a(tors, 1#$5#

a--li(ations of, 1 #ty -es of, 1#2

vi:rating dr%., 1l$* 1#25#

vi:rating -lates and ra..ers, 1#$, 1#25#g.-a(tion -ro:le.s9 D

i9w([email protected](@tion, 122 -%.-ing or weaving* 122

Co.-a(tion s-e(ifi(ations, 12152end -rod %(t, 12$522.ethod s-e(ifi(ations* 12$* 12

o.-a( ion es(% rves* ty-i(al* 1 1 d(st r%(t ive 125#eF %i -.enl ty -e* 12"* 1$field (he(< -oint test* 127526field densit y tests* 1 #!, 125#%se of field drying* 1 nondestr%((ive, 12* 1 $5#n %(lear densitv .eters* 1#e.9 -gi nt Protor l est 127526Pro(tor test, 1 1 151Pro(tor test .odifiedB* test details* 1 1251Pro(tor test standardB, test details, 11151$ra-id .ethod* 1 51

Co.-a(ti ve effort, 1 1 151$* 12#522Co.-ressi :ility* $7576

(lays* $7"(oeffi(ient of* #151#, #7157$, "7, "7!(oeffi(ient of vol%.e (hange, #11(o. -a(ted (lays, 1 175$* 1$#effe(t of LI R on, #$"one di.ension* $757"saods $7"57!soil s<eleton* "6156$, "6!567

Co.-ression* $7#elasti(, in oedo.eter, 2$, 251i nde+* #1 #* #21 52$.od %l%s* #1 $ratio, #12se(nnda ry #!" #7t ria+ial, "6#

Co.-ression i nde+* #1#, #2152$a--ro+i.ations, #21(F%ations for, #21field, ##, ###.odified, #12.odified se(ondary, 2"se(ondary* 2"ty-i(al val%(s of, #2$

Co.-r(ssion ratio, #12, (s$$ a/sConsolidation -ara.eten@ Godifi(d(o.-ression ind(+B D

Co.-resso.eter F see (rew -late(o.-resso.et(r testB

Confining -r(ss%r( (s$$ Tria+ial testsBConfinl3ng -ress%r(9

(onsolidation, (riti(a,

(+a.-l(, 6elfe(t on (y(li( .o:ility, #tria+ial tests9

.j



!$$

Confining -ress%re ( c%i%C$d)hyd rostati(, #7, "1non5hyd rostati(, #7, "1

Conservation of .ass, law of, $$Consisten(y9

definition* "1des(ri -*tors, "1

Consisten(y li .its, #2, (s$$ a/s Atter:erg

lndex

Consolidation -ara.eters (c%i%C$d)

relation to .odified re(o. -ressioninde+, #$

se(ondary (o.-ression inde+, 2"ti.e fa(tor* #7$57#, #66, "7!

Consolidation ratio, #7#57!, "77Consolidation sett le.ent, $7

(al(%lation of, #65$"

Consolidtion 9(oeffi(ient of* #71 , #6, "7"57!

(orrelations, 22deter.ination of* #6, #66, 21relation to ti .e fa(tor, #7#

ty -i(al val %es, 22defined, #!6degree of, #7#, #7!, "7756effe(t of -er.ea:ility, $7"nat % ral soils :ehavior, $665#6

-er(ent, $61 , #7#, #7!, "77 -heno.ena e+-lained, $7" -ri .ary* #!"

-redi(tion of* 217 -ro(ess, #!!57ratio, #7#, "77s-ring analogy, $77, #!!57se(ondary, #!", 251settle.ents, #!"stress, $61Ter&aghi3s 1 5 ' Theory* #7

ass% . -tions, #7, "71derivation, #71 57$* "7#57"sol %tion, #7$57* "7"56

test, $76562t :eory #757# "7#57"ti .e rate of, #!"5!!%nder(onsolidated* $62

Consolidation -ara.eters9(oeffi(ient of

(o. -ressi :ility, #151#(onsolidation, #71vol%.e (hange, #1 1 , #1#

(o. -ression inde+, #1#512, #1!relation to .odified (o.-ression inde+,

#1(onsolidation ratio, #7#

degree of (onsolidation, #7#average degree of, #7!576, #6156$relation with ti.e fa(tor, #7756

.odified (o.-ression inde+, #12, #1!relation to (o. -ression inde+, #1

.odified re(o.-ression inde+, #$relation to re(o.-ression inde+, #$

.odified se(ondary (o.-ression inde+se(ondary (o.-ression ratio, rateof se(ondary (o.-ressionB, 2"

-er(ent of (onsolidation, #7#re(o. -ression inde+, #$

.ethod to eval%ate, #$#5$2

Consolidation testi ng, $765$6#data -resentation9

-er(ent (onsolidation vs* effe(tive stress,$61 56#

void ratio vs* effe(t ive stress, $6156#fi+ed ring, $6561

floati ng ri ng, $6561test details* $76561Consolidation tests9

effe(t of sa.-le dist % r:an(e, $6!567of ty -i(al soils, $665#6

Chi(ago and Indiana gla(ial (lay, #Leda (lay, ##Loessial soils, #!Ge+i(o City (lay, #2

NC (lays and silts* # Newfo%ndland -eat, #7 Newfo%ndland silt, #78C (la y tills, #1 5$swelling (lays, #"

Consol idation t heory9Ter&aghi3s theory

ass%. -tions, "7# :o%ndary (onditions* "757!derivation, "7#57"sol%tion* "7"56ti .e fa(tor, "7!* "7656

Consolido.eter, $76561Const rained .od %l%s, #1 151$ Conti n %lly eF%ation, $$(Q- ,51Wa, : ratio9

effe(t of age, 61defined, 7!577effe(t of over(onsolidation, 656$effe(t of stress -ath, 6relation with LI* 6relation with PI* 76

CU (s$$ a/s hear strength@ shear strength

testsBCU tests, 257, 225", 2"Gohr fail%re envelo-es9

nor.ally (onsolidated (lays, overQ(onsolidated (lays, 1

-re(onsolidation stress, 1sands, sensitive (lay, 2

shear strength -ara.eters, relation with C' tests, 555ty-i(al val%es, #52

stress (onditions, 2!



5

D555 *!

. 55 5 5 535 5D5

stress -aths, $5#* 7#572 'ilatan(y (s$$ oil (hara(teristi(sBCC3 ' ( (,K(l 'istortion settle.ent, $7#TP* $5# 'rainage -ath, #!6, #7$

T5U 0BP, $5# do%:le drainage, #!6, #7#, #7, #6#, #66test details, 2 sing,ee1rai11==D.117, -'j-' J > J

ty -i(al :ehavior* 26 ' (s$$ hea r strengt h tests, dire(t shearB

-G ????' ;E5 .- -Casagra nde3s, #6"52 'o.ains (s$$ oil fa:ri(B

T,*** 1 D 16! 252$ 'o%:le angle eF%ations* 2#"Cy(li .o:ility9 'ry strength ., oil (hara(tenst1(sB

definition, $$* $2 'TA (s$$ 'ifferentia l ther.al analysisB

d1neren(es oetween 11F%e1a(tion* J*,**%%t(n (one =3==D 9, 6 ,.'

55,

5;T?-3

fa(tors affe(ting* #

5 . K K .,

???' MI

Cy(li( strain history9 Earth -ress%re ( s$$ / 0

**ffert on (v(li( .o:ilit v* # ¡:...,i** 5D5ss% re (oeffi(ient of* $$Cy(li( st ress, definition* # Earth str %(t% res* e+a. -les* 1 1

Etfe(t ive (onsolidation stress, $61Effe(ti ve grain si&e* $1 1

'ar(y3s 3= $$52, "71* * * * ,n K,1

(*11e(*9ive Z*,%,=definition* $#52 Effe(tive si&e9

deviation fro.* $ - . . &'i n theory of (onsolidation, #7* "7#572 in filler design* $!1validity for other soils* $ tvni(al val%es* 12

%at%. -1ane* 55&== , Effe(tive stress, 1!'aytona 4ea(h* lorida, 1 !"* 16"r $ Q r ,dennea* L. Ielfe(t of gro%nd water loweringQ raisiog*

in oedo.eter, 2$, *, , o ,,,K ,e

5D -hysi(al .eaning* $1251"nrin(iole of* $1 * "61

, J -rofiles* $!5 ! 2'egree of sat %ration* definition, 1#5 - Q - - tion

'ensit y9(*11e(t1ve sir=3== , ,JPl 5*1

:%oyant or s%:.erged* definition* 1 delinition* #7-5 :

(o.-r(ssion in oedo.eter, 2$des(ri-tors* " .aterials* $7#8I. s((ant .od %l%s* 6$

definition* 1 E-:..1 V?' 1 settle.ent* $7

field* 12$stressoistrio%ti%n, ,;..-.-Dtangent .od%l%s, 6$

***K*,*,,,* *,, $ $

n %(lear* IJJ 3, *

relative9 55 Elasti(ity9

????' '?''????'' -ty-i(al val%es* 12

linear elasti( .aterial, "6!theory, #22 55 555

sat%rated* definition, 1 Elasti( .aterial955 . . 5

solids* definition, 12 -ore -ress%re 99 l'--9Jtv,

s%:.erged* ty -i(al val%es, 1 stress5strain5ti.e r(lationshi-s, $7#5

total* wefJ^lenni1i%11, ,** . . ,5t3 --

t y -i(al va1%(s* 1 , 1 s-e(ifi(ationsB

! rirnn $$'en·s-i-ty· in.d Je@,,* $$ Relative densityB Erosion, liF%efa(tion (a%se, $1

'esi((ation9 E+(ess hydrostati( -ress%re, $76, $61, #!!57*(a%sing -re(onsolidation* $6 #7$, "7!

dry (r%st* 1 #"* 1 7" E@,,*((ss -ore water -r(ss%re, #!!

ZZ .j

35 3553

5 5D- - , D 5D5 D55D5 H,erial

1.

-

. ,***ty-i(al val%es* 1"

(hange in, "61

'efor .

ty-es of* $7#. . distortion, $7#

in (Konsolidation tes ing,

(h % n <*

inde@,,*, 1#, 12$

- -

- .



555 5 5



4

E+(hanga :le (ations, 7#, 6#562valen(e of* 62

E+it gradient, $" :y rnethod of fragrnents* $"#

$A A ( s$$ oil (lassifi(ation syste.sBa :ri( (s$$ as oil fa:ri(@ oil str%(t%re@

li %**t %1eBa:ri(s as filters* $!$ail%re (riter;a9

rna+i rn % rn shear stress,22 Goh r, 226Gohr5Co%lo. : (riterion, 22657Goh r fail%re hy-ot hesis* 22

aih.9 -laAe, aAgle gf iA(li AatigA gf* "J

ield density tests (s$$ Co.-a(tion testsBield* identifi(ation -ro(ed %res, iganewtons, "!1ilt(rs9

(1 i te1 ia* $!15!$ fa:ri(s, $!$

-rote(tive, $!5 !$%sed to (ontrol see -age, $!5 !$

(riteria, $!$i ne grained soils, $95$", 26, "i nes, 26

low slides (s$$ LiF %efa(tionBlow slides, $2or. fa(tor (s$$ rag.ents, .ethod oo%ndation engineering, definition, $rag.ents* .ethod of* $#, $75!

detailed e+arn -le* $"1 5"7e+it gradient (al(%lation , $"1 , $"2fr. fa(tgr, $6, $"$ $"2 $"!fragrnent ty-es, $65"

ree swell test, 177576ree water s% rfa(e, 1"6ri(tion angle (s$$ a/s hear strength@ Angle

of interna fri(tionBrost a(tion, 1656

defined* 16

effe(t of -ore si&e, 16$frost s%s(e-ti :le soils, identifi(ation of, 16$5

6i(e lenses* 1656$nece&&ar cond!t!on& 1 91 092sol%tions to, 16#56

rost heave (s$$ rost a(tionBro&en soils (s$$ rost a(tionB

,a-5or s<1-5graded s.l, $65#en %s :ovinas .as(%linas sona . :%lot%.,

4erno%lli energy eF%ation, $$5#(hannels, $15$(onfined, $1

dis(harge velo(ity, $2head loss, $1heads* ill %stration, $$7inde+, 2"La-la(e3s eF%ation, $1 , "7157$

-ie&o.etri( head, $$1, $2"52! -otential -ositionB head, $$* $$!- ress11(e :ead $$ $$!see-age velo(ity, $2tort %osity, $total, e+a.-le (al(%lat1ons, $27526total head -ie&o.etri(B, $$, $$!ty-es, aefineEI* *00 *0%n(onfined, $#velo(ity head, $$, $$!

low lines (s$$ low netsBlow nets (s$$ rag.ents, .ethod ofB3low nets9

defined, $26dra wi ng rnles $1 5$eF %ation of* $1eF %i -otential dro-s, $$eF %1-otent1al flowB hnes, $2651e+it gradients, $5!'l5D ehannels, $B 1 B$flow lines, $2651flow g %antity (al(%lation, $$5#% -lift (al(%lations, $#5

eote(hni(al engineering, definition, i::site (s$$ Clay .ineralsBla(iation, (a%sing -re(onsolidation, $6

radation (s$$ a/s rain si&e distri:%tionB

-oorly5graded, s< i-5or ga-5graded well5graded,

rai n si&e, effe(tive %se in (a-illarity, 1!2rain sha-e*

effe(t on ^QJ, 1"ty-esD

ang%la r, ## :%l<y, ##fla <ey, ##ro%nded, ##s%:ang%lar, ##s%:ro%nded, ##

rain si&e distri:%tion, $"5#$

effe(t on shear strength, 12, 1!ga-5graded, $6gradation test, *8hydro.eter analysis, $7roe(:a ni(al a nalysis *8

-oorly graded, $6sieve analysis, $7s<1- graded, $6%nifor.ly graded, $65#=ell graEleEI, $6 #1

rave, ", $!, , "(hara(teristi(s, $"%sed in (lassifi(ation, * "



lndD

ro% nd water ta :le* 1 ""ro% - i nde3l* "5"", "7

Hallovsi(e ( s$$ Cln .ineralslHa&e Ds eF%ation, D$1 1Heads (.D$$ lowBHead los* $1

e+a . -les of* $2"527Hea ve (.$$ wel li ngBHen < le -ore -ress%re (oeffi(ien ts* "6"5!H yd ra %l i( gradient* $

(riti(a9defined* $#25#ty-i(al val %es* $#

defined* $1in -er.ea :ilit y tests* $"

H yd ro.eter analysis, $7Hydrostati( (onsohda%on (s$$ a/s hear

strength tests@ (y(li( tria+ial@ Tria+ialtests9 (onfining -ress%reB

H a rva rd . inat % re (o.-a(tor* 1 1"

M7

/ Fcontinut]d:

t y-i(al ,aloe* * $$", 27

sands* 16

La.inar flow, $1La-la(e3s eF%ations, $1

deri vation* "71 57$Lateral ea rt h -ress%re at rest* (oeffi(ient of*

K * $$5$"

Leda (lay9(o.-ression i nde+* !"*(onsolidation :ehavior* ## -rofile* ##6val%es of C,*QC( 2756

Lif ts ( s$$ Co.-a(tionBLine of o-ti.%.3s s$$ Co.-a(tion (%rveB

LiF%efa(tion9defined* $2* $1differen(es :et ween (y(i( .o:ility* T 1 1 5,

#2 *

flow slides* $2

D sifi(ation $#

* I(e lenses s$$ rost a(tion l

lllite ( D$$ Cla y roio(ralsBl . .ediate sett le.ent* $7l . -a(t theory* Co-rogeni(* !1 1l nfl %en(e (ha rts (J$$ tress dist ri :%t ionBl ntergran %lar stress (s$$ Effe(tive stressBl nter.ediate -ri n(i -a l stress* effe(t on shear

strengt h, 12

l . .ediaiely a fter (onstr%(tion (s$$ hear strength* (laysBlowa :orehole shear test* !$5!#* 7lso:ars* #!6lso(hrones* #!6* #72* 2$lso.or-ho%s s%:stit %tion, !6* 7, 6#lso-a(hs* #!6sal r n-i( (onsolidation (s$$ hear strength

tests* t ria+ial test BIR G* 6IG E* 6

/aolinite ( s$$ C1ay .ineralsB/ao-e(tate* 7$/ 1* 2!6, "#!

Goh r5Co%lo. :, relationshi - with* 27$ -ara.eters Pf F 27$

/ $$5$"* 2!6(lays* "51 O

effe(t of 8CR* "751effe(t of stress -ath* "!r(lation te t,3. "YBrelation to PI* "!

defined, $$eff((t on (y(li( .o:ility* #t heoreti(al relationshi -9

nor.ally (onsolidated sands* 16over(onsolid ated sands* $

how to avoid* ##relation to F% i(<*sand* $2$* $2steady state h ne* #$5##%se of Pea(o(< diagra.* $!

L;F % id li . it* LL (.$$ Atter:erg l;.itsBLiF % idit y ind(+* #6* 7"57!* 6Li near .a teria ls* $7#L 1R ( s$$ Load in(r(.ent ratioB

L L %e A tter:erg li.itsBdeh ned* #$"effe(t on (v* #6

Load in(re.ent ratio* #6defined, #$"effe(t on (v, #6

Loess* #"5!

Gaterials9anisot ro-i(* # :ritt le* 22!527density* ty -i(al val %es* 1 elasti(, $7#* 22"heterogeno%s*

:oroog(n(o%s #isot ro-i(* #

linear* $7#* 22"52!non(onservat1ve, #* $7#nonlinear* #* $7#* 22"52! -lasti(* 22!527 Dvis(o5(lasti(* $7#* 22"wor< hardeni ng and softening* 22!5

27 Genis(%s9 :elow gro%nd water ta:le* 1!!5!7defin(d, 1 "!5"7geo.et ry* 1 "!5!ia(o.o, 1 "!ha-e, 1!

.j



728

Get hod s-e(ifi(ations (s$$ Corn -a(tion

s-e(ifi(ationsBGet ri( systern* """5"6Get ri( % n its, ""57Ge+i(o City (lay9

Ca QCe, val %es of* 2756(oeffi(ient of (onsolidation, 22(orn -ression i nde+, #2$(onsolidation :eha vior, ##52

Gi(a, 7G0ala* 1Go, 1God i fied (orn -ression i nde+, #12

a--ro+i rnations, #21se(onda ry, 2"

God i fied Pro(tor test (s$$ Corn -a(tion testsBGod i fied re(o. -ression inde+, #$

God %l %s (s$$ a/s Elasti(B(onstrained, #1 $oedo.etri(, #1 $se(a n t, B6$t angent* 6$% nd rai ned, 6$5

6 Got% i n99le9fail%re -lane, a1, 21o:li F % i ty, .a +,. %., 2"!, 2o:liF %ity relationshi-s, 2!

-ole .et hod, 2#"origi n of -la nes -ole .ethodB9

definition* 2#"e+a. -les of* 2#"* 2#7* 22, 22$* 222 -ro-erty of, 2#"* 2

Goh r5Colo. : strengt h (riteria, 2#57Goh r5Colo. : strengt h -ara.eters, 2#Gohr fa i l %re en velo-es, 22651 (s$$ a/s hear

strengt hB(%rved, 1"effe(t of -re(onsolidation -ress%re, 2#, 1nor.ally (onsohdated (lays, 21 5over(onsol idated (lays, 2152$* 1

sensitive (lay, 2Gohr fail %re hy-othesis9

defin ition, 21Gohr fail % re t heory, differen(e :etween,21%se in dire(t shear, 2"

Gonotoni( loading, $1, (s$$ a/s

LiF %efa(tionB

Gont.orillonite (s$$ Clay .ineralsB

N*C* ( s$$ Nor.ally (onsolidated soilsB Ne%tral stress (s$$ Pore water -ress%reB New.a r<3s (harts, $756 Non(onservative .aterials, $7# Nor .al stress, 2#

o(tahedral, "6!56 Nor.ally (onsolidated soils, defined, $62 N%(lear density .eters (s$$ Co.-a(tion testsB

lndex

R@ ( s$$ 8ver(onsolidated soilsB8(ta hed ral al %.inaB sheet, !7578(tahed ral9

nor.al stress, "6!566shear stress, "6!566

8edo.eter (s$$ Consolido.eterB8edo.et ri( .od %l %s (s$$ Constrained

.od %l %sB8ne5di .ensional9

(o. -ressi :ility, $757"(onsol i dation theory* #757, "7#57"loadi ng* #2$

8-ti . % . water (ontent* 1 1 #8rga ni( soi ls, 8rigi n of -la nes (s$$ Gohr (i r(leB8ver:%rden -ress%re, $77 (s$$ a/s tressB

8ver(onsolidated soils9defined, 1 7", $62reasons for, $6256settle.ent (al(%lations, #$5$"

8ver(onsolidation9(a%ses, $6effe(t on -ore -ress% re -ara .eters, "5"#effeet 11 shear streflgt h, 1 2, 2 1 2#, $,

6#568ver(onsolidation ratio, 8C R9

defined, $62effe(t on (y(li( rno:ility* #effe(t on / $* "751effe(t on %nd rained shear strength, 6#56effe(t on % nd rained .od %l %s, 656!

- s$$ tress -ath BParti(le sha-e (s$$ a/s rain sha-eBParti(le sha-e* effe(t on shear strengt h, 1251! Parti(le si&e, effe(t on shear strength, 12Parti(le s%rfa(e ro%ghness* effe(t on shear

strength, 12, 1 !Pa vernent9

rigid, 12Pea(o(< diagra., #52Peat, ", 265

(o. -ression inde+, #2$(onsolidation :ehavior, #756val %es of C D QC , 2756

Pedology, 1 n5 e

Peds (s$$ oil fa:ri(BPenetro.eter, "

'%t(h (one, 2!#, !$5!2, !6571 -o(<et,!$5!2

tandard -enetration test, 2!#, !$5!2, !7Per.ea:ility9

(oeffi(ient of, $2, #7$Casagra nde3s :en(h .ar< val %es, $6e.-iri(al for. %las, $651$fa(tors affe(ting, $, $6.eas%re.ent of* $"57



lndex 727

$relation to -ore si&e, $1 1 51$relation wi t h effe(t i ve grai n si&e, $11ty -i(al val%e(* (hart* $1%nits* 2l ,

d(ter .i nation :y oedo.eter test, 2$5#

Pore ress% re -ara.eters9 (c%i%C$d)

derivation, "6156#theoreti(al 4 val %es, "%se . eng.eer.g -ra( i(e,

Pore si&e* effe(tive, 1 !25!

-er.ea :ility* $1 151$

w er ress%re9

(onstant head, $"5 !fattors a ffe(ti ng,$6 falling (a * K la :oratory .eas% re.ents* $"56

Phase diagra. defined* 1 151$%tion of 1"5$

:a(< -ress%re, 27, "(al(%lation of* $1#

Porosit y9 1$Phase relat ions* 1 1 5$ ty-i(al val%es* 12,¡, / &ero analysis* "#, 7"577

Pre(onsolidated soils ( s$$ 8ver(onsolidated

PI (.$$ a s Alter erg 1.1ts9 as t(t y in e+Pie&o.eter* $$!, $#

(riti(a lo(ation* $defined $1 1 * $

Plain strain, 2"756, 1!, "1* "#!Plasti(ity (hart (s$$ Atter:erg li. itsB

astt(1ty ( art* D

Plasti(ity inde+* #2* #6 (s$$ a/s Atter:erg

Plasti( li.it, PL (s$$ Atte r:erg li.itsB

(orrelation with / , "!(orrelation with ,p , 2#52(orrelation with %nd rai ned .od %l %s,

(orrelation with % nd rained shear strength,

Po(<et -enet ro.eter* !$5!2Poisson3s ratio* #"$Pole (.$$ Goh r (i r(leBPoorl y5graded soil* $65#

soilsBPre(onsolidation, (a%ses, $6256re(onso I a 1n -ress%re,Casagrnd (onstr%(tion, $6"

effe(t of sa.-le dist%r:an(e, $6!567fa(tors affe(ti n d(ter.ination of, #$"5$7gra-hi(al -ro(ed %re for, $6".ethods to eval%ate, $6"56!

Press% re.eter test, !$5!#, 7$

Pri.ary (onsolidation, #!" (s$$ a/sConsolidationB

Prin(i -al -lanes (s$$ tressBPrin(i-al stress (s$$ tressBPrin(i -al stress9

at fail%re, 2"5!

-a ra.ettersBD % r) ara.eters, 665", "615!

A -a ra.eter, "6#

rotation of, 2"1* 2!1 , "$, "6#

Pro(tor test (s$$ Co.-a(tion testsBdefined* "$* "6# Profiles s$$ oil rofiles

Proof rolli ng* 1$6* 122

4 -a ra.eter, 665"$, "6$56#d(fined* 66PH test , "2

defined :y -rin(i -al stress in(re.ents* "2,"6#56"

for ditTerent stress -aths* "2, "$* "6256effe(t of sat%ration on 4* "5"1Hen<el3s -ara.eters (oeffi(ientsB* "25

derivation* "6"5!wit h rotation of -rin(i -al stresses "$,

"6#562<e.-ton3s -ara.eters (oeffi(ientsB* 665

"

( s$$ tress 0ath< test, * (s$$ a/s U U testsB%art&* density of, 1%i(< (lays, #6%i(< (ondition, $##5#2, $#"

e+a. -les of* $2$52 :low %-, $22

%i(< tests (s$$ U U testsB%i(<sand, 1#, $##

drowning in, $2$%i(<sand tan<, $252#

._



728 lndex

! test see 3l3 testsB

R a n < i ne* 7Rea(tion to sha < i ng ( s$$ oil (hara(teristi(s*

dilata n(,BRe(o. -ress1onD . de+* J$

-ro(ed % re for deter. i n i ng* #$#5$2Re(onsolidat ion (% rve* $62Referen(e elevat ion* **Relative (o.-a(tion* 1 2$

relat ion to rel, iive densi t y* 12$Relat i ve densit y* !7* 1 #5!

effe(t on (y(li( .o:i li ty* #relat ion to rel at i ve (o. -a(tion* 1 2$

Ro(< engi n(eri ng* defi n it ion* #Ro(< Ro% r* !!Ro(< .e(ha n i(s* $Rollers (s$$ Co. -a(%on eF %i -.entB

R % ::er t i re rol lers ( s$$ Co. -a(tioneF %i -.ent B

a.-le -re-aration, effe(t on (D(h( .o:lhty*)!0

a. -l i ng* effe(t on (onsol idation test, $6!567a nd* "* $!* * "

%sed i n (lassifi(at i on* * "and :oi l ( s$$ % i(< (ondit ionBands ( s$$ hear st rengt h B

(hara(teristi (s* 1"frost s%s(e-ti :i l i ty, 1 6

S n Ar! nc! &co )1 8 m11d

(oeffi(ien t of (onsolidat ion* 22(o. -ression i n de+* #2$(onsohda %on :eha v1 or* +15+*

val%e of C=3 QCe, 27eaflfl iflg eleetrefl . iereseefe ( s$$ a.!% Clay

. inerals9 EG B(h .ert .a n n -ro(ed%re9

for n or.al h (onsolidated soils* #$75#$for over(onol idated soi ls* #$6* ##$5##

&c1 a0e1 (.\ee Co1t10actio11 eNui0nient<

(rew -late (o. -resso.eter* !$5!#, 7#572r(a n t . ad11l11s ee last i( t heory e(on da ry (o. -ression * #!", #7, 2

eval %ation of* 251 #.de+* 2"rat io* 2"

i n deri vation of t heory (onsolidation, #7,"7#

e(on da ry (o.-ression ratio ( s$$Consolidat ion -a ra .etersB

eeon d,t ry settle.eflt* $7f * 2 6 *1tt al.rnConsol idat ion -a ra.eters* eval%ation3

ee-age ( s$$ lowBee-age* 1 ""

(ontrol of* $!5 !$;low F %a nt i ty (al(%lat ions9

3

ee-age ( c%i%C$d)with .et hod of frag.ents* $"1 5"#

ee-age an alyses ( s$$ low Bflow nets* $2"57.et hod o f rag.en ts* 175 JA

ee-age for(esDdefi ned, $#$eva l %ation of* $#"52i n filters* $!1

-er %n i t vol % .e* j. $#!ee-age velo(i ty, $2ensit i ve (lays* #6* 2* "#ensit i vit v9

defi ne(q* 757"e+a . -le of* #6relat ion v* it h LI. 7!

t y -1(a l va l %es ot*7"ettle.ent9

(a l(%lat ions* #65$"(o. -onen ts of* $7257"(o.-rehensi ve e+a . -le* 2125$#(onsol i dat ion* $7, 511 !d istort ion i . .ediateB* $7* 6$as a f% n(t i on of t i .e* #61* 21 7of . % l ti -le layers* #$over(onsolidated soils* #$5$" -red i(tion a((% ra(y* 21 7rate of, #7eco11dd1 < co11101 eio11. 37$

tota l* $72* #7!:ra( :o+ F see ajo :(a ( st ((ngt : testsD 'i(r(t

shearBhear strength9angle oi interna f n(t1on, >/8, 2$, 261(lays9

(ri t i(a CHl8it i II for statii lity*"J6 d ra i ned strengt h -ara.eters*2#52 effe(t ive st ress a--roa(h,#!effe(t of t i .e* 7!fa(tors a ffe(ti ng, 6!567i111111(d iately afte r eonst r%et io11, )8sat % rated, #"567total stress a--roa(h #!%n(onfined (o.-ression* ""%se of C' strengt h, 2%se o CU strength, "5!

%se of U U strength, 7"577

defin i t i on, 226en velo-e* Gohr fai l %re* 226

sta:le (ondition, 2fa(tor of safet v, 22fail%re angle, a5 ,

22fail% re (riteria, 22", 227526, 2#52, 2!, 262,

#, 25"(o.-ressive strengt h, 262.a +i . %. -ri n(i -al effe(tive stress ratio,

2EJ2* #, 22.a+i . % . -ri n(i -al stress differen(e, 262,

,K



5555555555555555DDD5D5D5D - --- - -------



lndex

hear st rengt hF conrinued: at a -res(ri :ed st rain* 262fa i l % re definitions* 2," .a Bi . %. shear st ress*22 .o:ili &ed* 22 -ara.eters* (* >/8. 2#* " -ri n(i -al stress differen(e* definition* 2" -ro:le. soils* 6567resid %al* 2"7* 6!sands9

:ehavior d%ri ng shear, 26"(avitat ion* 2C' tri aBial test* e*a. -le* !drained shear* 26#5#effe(ts of (onfini ng -ress% re* 26"fa(tors t hat affe(t* 12Gohr (ir(le* % ndrai ned shear*

negati ve -ore water* 2d ained shear 2512

%lti.ate* 2"7he,H strengt h :ehavior9

(lays9

hear strengt h test F continued:s(rew -la te (o. -resso.eter test* 2!#* !$,7#572

torsional or ring shear, 2"7t r%e t ria9,Zial or (% :oidal test* 2"7tandard Penet ration Test, 2!#, !$5!2, !7test (onditions, d rainage* 2"t riaBial test* 2"#5"7, 262* #6, 2"52!

advantages and disadva ntages, 2"#anisot ro -i( non5hydrostati(B

(onsolidation, #7(v(li(* $!5#isot ro-i( hydrostati(B (onsolidation, #7 -ri n(i -ies of* 2"2, 2"6, 262

%n(onfined (o. -ression, why it wor<s*""5 !

ass%. -tions* "" #7U U* defined* 2"

hear stress* o(t ahedral* "6!566hee-sfoot rollers F.ee o.-a(t1on

eF%i -.entBC'* (onsolidated5d rained, test, #75#6 (a %si ng over(onsolidation* 17"

la s 1$1 1$2

2* 2! ! !57 en gi neeri ng signifi(an(e, 17"56t % :( analogy* 1 !757, 17

si .ila rit v to sands* #"#7U U* %n)onsolidated5% ndrai ned, tests*

"(o. -a(ted (lays, 1$2

effe(l of sensitivity, "1art iall sal%rat(d (lavs* PH test, "#5"2

hear strength testing9area (orre(tion wit h strain* "7

C'* 2"* 26#562* #75#6 25

(y(li( stress* definition* #5#1(y(li( t ria+ial, $!5#

dire(t shear, 275"#advanta es and disadvanta es, 2"1Gohr (ir(le* 2"$Goh r diagra., 26

-r.(1-a stress rotat1on,t -i(al es%lts, 26

'%t(h (one -enetro.eter, 2!#, !$5!2*

hrin<age 1 .ll ( s$$ a s tter defined, 1 7

of sensit ive (lZys* 1 7$ 2l. 1 7572

I %nits* 6* ""57 :asi( %nits* ""!(onvers1on a( ors*density and %nit weight* "!"5!6

figanewtons* "!1for(e, "!5 !#geostati( stress* "!657%sed in geote(hni(al (ngine(ring* ""757

stress and -ress%re* "!#5!"ti.e* "!

ieve analysis ( s$$ rain s1&e 1stn %t1onieve si &es, U* * tandard si&es, $7

ilts, "* $5$!* !!

(hara(teristi(s* $"(oeffi(i(nt of (onsolidation, 22(o. -ress1on . 1(1(s,(onsolidation :(havior, #"56

hollow (ylin-er test* 2"7

-lai n strain test, 2"75"6

7 %s(d in (lassifi(ation, , "

<e.-ton3s -ore -ress%re eF%ation,

ress%re.eter test* 2!#, !$* 7$ d(rivation of, "6156#

.j



Í '1

73, lndex

<e.-ton3s -ore -ress%re -ara.eters,

665", "615!L (s$$ hrin <age li .itBla<ing9

defined, 17t% :e analogy, 1 7

low test (s$$ C' testsB.e(tite (s$$ Clay .ineralsBoil :eha vior*

stress h istory, 1!

oil str%(t%re, 6"dense, $5#ef fe(t on (y(li( .o:ility, #loose, 1$5#.a(rostr%(t%re, 6!.i(rostr%(t%re, 6!51$at sa.e relative density, 1"si ngle grained, $

-eeiRe s191rfaee, EleRneEI, 76 61-ring =:rea< %-,= 16

1 1se of -lasli(ily (:a rt 1 ta:ility (riti(a (onditions, "#6oil (hara(teristi(s9

(o.-ressi:ility, Idilatan(y, dry strenglh, 1 , -er.ea:ility, *0"

role of vol% .e (hange, 1

ta:ili&ation9(he.i(al, 16dewatering, 6.e(hani(al, 09

-reloading, 16

tand3ard Penetration test, 2!#, !$5!#, !7li1g:oess !! tandard Pro(tor test (s$$ Co.-a(tion testsBnear PL, 1

oil (lassifi(ation9field ident1fi(atJon -ro(ed %res, UC and A AHT8 (o. -a red, !5!$ i,rnal deseri-tien, "1

oil (lassifi(ation syste.s, 2!A AHT8, 27, "25!$(o.-arison of, !$A A, 27526

-%r-ose, 2!527U nified soil (lassifi(at ion syste., 275"2

-ro(ed %res, !5"1%se of A tter:erg li.its, 26

oil de-osits, "5!, 6651$, $15$#, 7", 656"( s$$ a/s oil -rofilesB

/ola Pen;ns%la, !1 1oil for.ation , "5!

/ola Pen; ns%la, !1 1oil fa:ri(9

(ohesionless soils, 1$5!(ohesi ve soils, 6"5$(l%sters, 6!567

o.ain ,gran %la r, $5!

tand-i-e (s$$ Pie&o.eterBteady state li ne (s$$ LiF %efa(tionBtress9

:ody, $1 #d ne to s.fa(e loads #2=5"!effe(ti ve, $1#

-hysi(al .eaning, $1251"Goh r (ir(le, derivation, 2#2ne%tral -ore waterB, -ress%re defined, $1#over:%rden, $62 -la ne two di .ensionalB, 2#"

-re(onsolidation, $61 , $6256! -rin(i -al -lanes, 2#25#"

-rin(i -al stresses, 2#25#"inter.ediate, 2#5#", 2!

01iuci0al.inter.ediate, 2#".a0or, 2#".inor, 2#"

i n soil .asses9efte(t ol dens1ty (hanges, $$5$1effe(t of gro%nd water (hanges, $1!517,

e+a . -le (al(%lations, $1 "5$:ooey(oro :ed , 0* relation :etween hori&ontal and verti(al, -eds, 6!567, I8I

$$5$"

sin gle grained, 1$ tress distri:%tion9oil .e(hani(s9

dP5finition* *fathe, of, 7, $1 histori(al develo-.ent, !56

4o%ss.esF t heory, #2527, #"$, #"25"!

(ir(%lar load, #$52inft%ense d1arts9

New.ar<3s #75"1 oil -rn"les t y-i(al ##52 Westergaard, #" , #"$

gla(ial (lays, #2.arine (lays, ##", ##7F % i(< (lays, ##6wedish (lays, ##!

line load, #2"527long e.:an< .ent, #25

-o.t load, #252", #"5""re(tang%lar load, #27, #"$5"#

oils* <5$ !5& G62& G64& G66resid %al, "trans-orted, "

stri- load, #"theory of elasti(ity, #22



lndex 131

tress distri:%tion F continued:t riang%lar load, #"57$ to 1 $9 1 B rnet hod, #2$522Westergaard t heory, #2!, #"#5"!

tress -at hs>9 3for A E and LC tests, "$!a --li(ations9

engi neeri ng -ra(ti(e* "#25#6o%ndat ion e+(avation , "#75#6fo%ndat ion loadi ng* "#5#!

"* "1, "#"(lays, over(onsolidated9

A E and LC tests, "#1d % riKng % nd rai ned loadi ng, 27#572,"#5#1

di fferen(es :etween AC5LE, "$di fferen(es :el weffe(ti ve EPB* 27#, "12, "1!517, "$1 5$$*

"$25$"* "#, "#$, "#!5#7e+arn - e (orn -%tat1ons* 55 12* "#15#2 fail%re line K Z5lineB9

-ara.eters* /, /*, l,, 27

hyd rostati(, 2!"

over(onsol i dated (lay , 27# -5F diagra .* 2!25!" -lane st rai n (ondition* "1 8

tress strain (c%"d+ li near elasti(* 22"non linear* 22"

rigid5-lasti(* 227vis(o5elast;(, 22"

tress5st rain relat;onshi-s9elasti(* $7#* 22"

non5linear* $7#* 22" -lasti(, 227vis(o5elasti(* $6#* 22"wor< hardening* 227

tr%(t %re9(orn a(ted

(orn -ar;son of -ro-erties* 1$#%-erfi(ial velo(;ty, *0"

(oeffi(ient of (onsolidation, "0"(orn -ression inde+, #2$ -ro es,

wedish fall (one test* !$5!#, !

(la ys, $72, #"(orn a(ted (lavs* 1 17, 1 $2(orrelation wit h Atter:erg li.its, 1 7!(orrelati on wit h (olloidal (ontent, 17!

lahoratory tests, 1 77576h sio5(hern i(al as

how to -redi(t* 17!56 -ress% res develo-ed* 17!

-ore -ress% re -ara .eters, for. %la for* "625 Ta.-ing foot rollers ( s$$ Co.-a(tioneF.-.entB

-ore water* effe(t of, 27#st ress -oi nt re-resena tion* 2!#5!2total TPB, 27#, "1251 * "1!517* "$1 5$$*

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holtz& kovacs - an introduction to geotechnical engineering.docx

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