bearing capacity shear wave (1)

8/12/2019 Bearing Capacity Shear Wave (1)

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Allowable Bearing Capacity of Shallow Foundations Semih S. Tezcan, Ali Keceli, and Zuhal OzdemirBased on Shear Wave Velocity

Revised 23 !" 2!!#

ALLOWABLE BEARING CAPACITY

OF SHALLOW FOUNDATIONSBASED ON SHEAR WAVE VELOCITY

Semih S. Tezcan1, Ali Keceli 2, Zuhal Ozdemir3

ABSTRACT

Firstly$ the historical bac%ground is presented for the deter&ination of ulti&atebearing capacity of shallow foundations' (he principles of plastic e)uilibriu& used in the

classical for&ulation of the ulti&ate bearing capacity are reviewed$ followed by a discussionabout the sources of appro*i&ations inherent in the classical theory'

Secondly$ based on a variety of case histories of site investigations$ includinge*tensive bore hole data$ laboratory testing and geophysical prospecting$ an e&piricalfor&ulation is proposed for the deter&ination of allowable bearing capacity of shallowfoundations' (he proposed e*pression corroborates consistently with the results of theclassical theory and is proven to be reliable and safe$ also fro& the view point of &a*i&u&allowable settle&ents' +t consists of only two soil para&eters$ na&ely$ the insitu &easuredshear wave velocity$ and the unit weight' (he unit weight &ay be also deter&ined withsufficient accuracy$ by &eans of another e&pirical e*pression$ using the ,-wave velocity' +tis indicated that once the shear and ,-wave velocities are &easured insitu by an appropriategeophysical survey$ the allowable bearing capacity is deter&ined reliably through a singlestep operation' Such an approach$ is considerably cost and ti&e-saving$ in practice'

Key words : bearing capacity, shear wae, !"undati"n design, shall"w !""tings,all"wable bearing pressure

1. Introduction

The ultimate bearing capacity of a particular soil, under a shallow footing, wasinvestigated theoretically by Prandtl (1921) #$%and Reissner (192) #&%using the concept of

plastic e!uilibrium as early as in 1921" The formulation however is slightly modified,generalised, and updated later by Ter#aghi (192$) #12%, %eyerhof (19$&) #'%, 'ansen (19&)#3%, e *eer (19+) #2%, and -ieffert et al" (2) #(%"

The historical bearing capacity formulation, as will be discussed briefly in the ne.t-ection, is still widely used in geotechnical engineering practice" 'owever, there are variousuncertainities in representing the real insitu soil conditions by means of a few laboratory1,rofessor of Civil .ngineering$ Boga/ici 0niversity$ Bebe%$ +stanbul$ (ur%ey

,hone1 !' 242' 352 "5 56 Fa*1 !' 242' 352 "5 576 8obile1 !' 532' 92! 27 47: tezokan @ superonline. com ;

2,rofessor of #24524794'doc !3!32!!#

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tested shear strength parameters" The basic soil parameters are cu0 cohesion, undrained shearstrength and )0 angle of internal friction, which can only be determined by laboratory testingof undisturbed soil samples" t is sometimes impossible to tae undisturbed soil samplesespecially in sandy and gravelly soils"

The insitu measured shear wave velocity, s

, however as a single field inde. representsthe real soil conditions, much more effectively and reliably than the laboratory tested shearstrength parameters" n addition to geophysical refraction seismic survey, there are severalother techni!ues of measuring the shear wave velocity at the site as discussed by -tooe et al"(19+2) #11%, Te#can et al" (19+$) #1'%. *ecause, the insitu measured shear wave velocity, s ,reflects the true photograph of the soil, containing the contributions of the void ratio,effective confining stresses, stress history, shear and compressive strengths, geologic age etc"3s will be seen later in this study, the shear wave velocity, s, enables the practicing engineerto determine the allowable bearing capacity, *a , in a most convenient, reliable and straightforward manner"

. C!"##ic"! $or%u!"tion

4sing the principles of plastic e!uilibrium, the ultimate bearing capacity, *! , of ashallow strip footing, with a depth of+, from the surface and with a width of and length-,/igure 10, is given by Ter#aghi (19&+) #13%as,

qf= c Ncsc + D Nq + 0.5 B N s (1)

where,

a) earing capacity !act"rs

* e4p tan )0 tan2'$56 ) 720

c * 8 10 c"t ) 1.9 * 810 tan ) by =ansen ?4"7@ #3%or * 8 10 tan 1.' )0 "by 8eyerhof ?45"@ [4]

b) Shape !act"rs:

sc 1 6 5.25 7- 55555555555"55555" ) 0 conditions)sc [1 6 5.25 7-][1 6 5.3 +705.2$]5"" ) =5 c"nditi"ns, saturated clays0

s 1 8 5.2 7-0 555555555" 7- !""ting width t" length rati"0s 5.& 555555555555555555555 circular !""ting0

t is customary to tae7- 5 for a strip footing, and7- 1 for a s!uare footing"The formulation is applicable to;shall"w


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&. Sourc'# o$ "((ro)i%"tion# in c!"##ic"! "((ro"c*

The appro.imations involved in the derivation and use of the ultimate bearing capacity,*!, given by=*.1, may be summari#ed as follows:

a@ (he soil &ass is assu&ed to be purely ho&ogeneous and isotropic$ while the soil in nature ise*tre&ely heteregenous and ti*otropic$ further the classical theory is developed only for aplanar case$ while all footings are 3- di&ensional in real behaviour'

b@ (he first ter& of Eq.1represents the shear strength$ the second ter& is the contribution ofthe surcharge pressure due to the depth of foundation$ and the third ter& represents thecontribution of the self-weight' +t is only an appro*i&ation to superi&pose the contributions ofvarious load cases in an entirely nonlinear plastic stress-strain environ&ent'

c@ (he contribution of self-weight can be deter&ined only appro*i&ately$ by nu&erical orgraphical &eans$ for which no e*act for&ulation is available'

d@ (he shear strength of soil within a depth D$ fro& the surface is neglected'

e@ epending on the degree of$ co&pressibility of the soil$ there &ay be three types of failure&odes6 (i)general shear$ (ii) local shear$ and (iii)unching shear$ as shown in !igure 1'(he theoretical considerations behind Eq.1$ correspond only to the general shear mode$ whichis typical for soils of low co&pressibility$ such as dense sands and stiff clays' +n the localshear "ailure$ only a partial state of plastic e)uilibriu& is developed with significantco&pression under the footing' +n the unching shear mode, however$ direct planar shearfailures occur only along the vertical directions around the edges of the footing' (herefore$Eq.1is no longer applicable for soils of high co&pressibility$ such as loose sand and soft clay$which &ay undergo$ either (ii) #he local shear or (iii) #he unching shear failures'Conse)uently$ the results of Eq.1 will only be appro*i&ate for such soils' +n reality$ thee*cessive settle&ent and not the shear failure is nor&ally the li&iting criterion in highco&pressibility soils'

f) (he ulti&ate bearing capacity calculations are very sensitive to the values of shear strengthpara&eters c$ and $ which are deter&ined in the laboratory using undisturbed soil sa&ples$

which &ay not necessarily represent the true conditions prevailing at the site' 0nrealistically$

high bearing capacity is calculated especially$ if the shear strength para&eter$ $ is

inappropriately deter&ined to be on the high side in the laboratory' All soil para&etersincluding the real values of internal angle of friction$ water content$ void ratio$ confiningpressure$ presence of boulders or cavities$ etc are not necessarily the sa&e in the soilsa&ples'

g@ Custo&arily$ after a due geotechnical survey$ a single value of allowable bearing capacity qa$is assigned in practice$ to a particular construction site' =owever$ &inor variations in si/es$

shapes and depths of different foundations at a particular site are overloo%ed$ and the sa&eqavalue is used in foundation design$ through- out the construction site'

h@ A factor of safety of 3 is used nor&ally$ in order to obtain the allowable bearing capacity$ qa$which contains a significant a&ount of reserve strength in it$ accounting for all theinaccuracies and appro*i&ations cited herein' (his significantly large factor of safetyrepresents the degree of uncertainties and our ignorance in deter&ining the real soilconditions'

i@ Dast$ but not the least$ although so&e )uantitative guidance is available as contained inSec#ion $$ there is )uite a bit of intuition in deter&ining whether the soil is on the %s#rong&or the%'ea(& side$ for the purpose of using reduced )#'o #hirds* shear strength para&eters$ inaccordance with Eq $'

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+. Pr"ctic"! r'co%%'nd"tion#

*ased on the practical e.periences of the writers, the ranges of allowable bearingcapacities for different categories of cohesive and granular soils are summari#ed in Table 1";or comparisons as well as for !uic reference purposes, the values of -PT counts &5 , shearstrength parameters cu , and , relative density+r , and also the shear wave velocity s , foreach soil category are also given in Table 1" The ranges of allowable bearing pressures *a, aretested to be in conformity with the empirical recommendations of the >?8@( 1@@(0 #1&%,the Turish


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qa= 0.024 vs sv ( 35.& ()

sv= ! *!0 ", vs" 500 ) !., ($)

The variation of allowable bearing capacity *a , with shear wave velocity s , isillustrated in /igure 2, where the reduction factor s , sets an asymptotic upper limit of*a0 35.& for shear wave velocities s C 2 555 m7sec.

c0 For calc&lat$n% &n$t we$%-ts

There is a direct relationship between the average unit weight , and the P>wavevelocity of a soil layer" *ased on e.tensive case histories of laboratory testing, a convenientempirical relationship in this regard, is proposed by the writers as follows:

' = o + 0.002 v' (&)

where, p0 the unit weight in 7m3based on P>wave velocity, p0 P>wave velocity in m7sec,and "0 the reference unit weight values given as follows:

o+ 1 "or loose sand-, sil#- and cla-e- soils

o + 1 "or dense sand and gra/el

o+ 10 "or muds#one, limes#one, cla-s#one, conglomera#e, e#c.

o+ $ "or sands#one, #u"", gra-'ac(e, schis#, e#c.

3s seen in/igure 3, the unit weights calculated by the empirical e.pression given in=*.&, are in e.cellent agreement with those determined in the laboratory" n the absence ofany bore hole sampling and laboratory testing of soil samples, the above empirical e.pression

provides a reliable first appro.imation for the unit weights of various soils, once the insitumeasured P>wave velocities are available" n fact, the speedy evaluation of unit weights, priorto any soil sampling, enables the practicing engineer to calculate the allowable bearingcapacity *a, readily from=*. 3"

. C"#' *i#tori'#

a ) F$eld $nvest$%at$ons

n order to establish a sound and reliable relationship between the allowable bearingcapacity *a , and the shear wave velocity s, a series of case histories have been studied assummari#ed in Table 2" ;or each case, in>depth geotechnical and geophysical siteinvestigations have been conducted and a comprehensive set of insitu and laboratory testedsoil parameters have been determined" %ost of the basic soil parameters, for each typical soillayer, are shown in/igures 'through/igure &. f however, for any particular soil parameterin any typical soil layer, multiple values were available, from various bore hole and seismicsurvey measurements, only the average of these multiple values have been indicated"

# ) llowa#le #ear$n% ca'ac$t$es #y t-e class$cal t-eory


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The first column in these ;igures contain the insitu measured -PT data, 35, thelaboratory tested values of cu0 undrained shear strength Ba0 , #24524794'doc !3!32!!#

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density, void ratio, nonuniformity, discontinuity, nonhomogeneity, shear and compressivestrength, etc" The complications and misrepresentations associated with soil sampling, sampledisturbance, accurate simulations in the laboratory testing, etc" are all avoided" -hear wavevelocity measurement at a site however, calls for additional cost and e.pert geophysical

personnel"

c) The depth, width and length of a foundation plays a significant role especially in granularsoils, in the derivation of mathematical formulation when following the classical approach" ncohesive soils, the geometry of foundation does not play a significant role anyhow"

@evertheless in classical theory, the soil is ideali#ed into an isotropic, homogeneous anduniform elasto>plastic planar geometrical medium" n the shear wave velocity approachhowever, there is absolutely no need to consider the foundation si#e and depth, even ingranular soils, since the influence of all these parameters are inherently incorporated in theinsitu measured sA values" The classical approach is further handicapped by the layeredconditions" n shear wave velocity approach however, the bearing capacity of a single layer,immediately under the foundation, is directly determined, as a one step operation"

d) The empirical formulations proposed for calculating both the allowable bearing capacity *a ,and the unit weight , are proven to be safe and reliable as verified consistently by 1 differentlaboratory tested case histories" The validity and reliability of the proposed scheme will be

better established however, as the proposed empirical method is constantly calibrated byconventional method at more and more sites"

3. Ac4no-!'d5%'nt#

The authors gratefully acnowledge the assistance and cooperation e.tended by %r"Tufan urgunoglu, and %r" 3bdullah =alisir of the Beotechnics =o", stanbul, who conductedthe geotechnical and geophysical soil investigations of all the case studies discussed herein"

-incere thans are also due to Professor Csman 4yani, of -uleyman emirel 4niversity,sparta, for his invaluable criticisms and corrections of the manuscript"

6. R'$'r'nc'#

718. *ritish -tandard (19&)" ?"de "! Bractice !"r /"undati"ns, *ritish -tandardsnstitution, Dondon"

78. e*eer, 11"

7&8. 'ansen, H"*" (19&)" EA reised e4tended !"rmula !"r bearing capacityF, anishBeotechnical nstitute *ulletin, @o" 2"

7+8. %eyerhof, B"B" (19$&)" E Benetrati"n tests and bearing capacity "! c"hesi"nlesss"ilsF, Proceedings 3-=2"


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78. Reissner, '" (192)" EZum =rddrucpr"blemG ?"ncerning the earth8pressurepr"blem0, Proc" 1st nt" =ongress of 3pplied %echanics, elft, pp" 29$>/11"

728. -ieffert, H"B", and =h" *ay>Bress (2)" E?"mparis"n "! the =ur"pean bearingcapacity calculati"n meth"ds !"r shall"w !"undati"nsF, Beotechnical &"

718. Ter#aghi, K" (192$)" EStructure and "lume "! "ids "! s"ilsF, Pages 1, 11, 12, andpart of 1/ of =rdbaumechani au! "denphysialisher Drundlage, translated by 3"=asagrande in/r"m the"ry t" practice in s"il mechanics, @ew Lor, Hohn Jiley and-ons, 19&, pp" 1&>1"

71&8. Ter#aghi, K", and Pec, R" *" (19&+)" ES"il Lechanics in =ngineering BracticeF, 2ndedn, Hohn Jiley and -ons, @ew Lor"

71+8. Te#can, -" -",


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/igure 1. F"i!ur' %'c*"ni#%# und'r " #tri( $ootin5



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/igure 2. A!!o-":!' :'"rin5 c"("cit/ o$ #oi!# :"#'d on vs


4!

--


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/igure 3. Unit -'i5*t# :"#'d on (; '!ociti'#


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/igure '.8 A!!o-":!' :'"rin5 c"("citi'# $or c"#' *i#tori'# No.1 t*rou5* No.+(4nits areO g 0 @m/, c 0 @m2, !a0 @m2, vs , vp0 msec)


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/igure $.8 A!!o-":!' :'"rin5 c"("citi'# $or c"#' *i#tori'# No.,< < 2< "nd 6

(4nits areO g 0 @m/, c 0 @m2, !a0 @m2, vs , vp0 msec)


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/igure &.8 A!!o-":!' :'"rin5 c"("citi'# $or c"#' *i#tori'# No.19 t*rou5* No.1+(4nits areO g 0 @m/, c 0 @m2, !a0 @m2, vs , vp0 msec)


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/igure (. Co%("ri#on# o$ "!!o-":!' :'"rin5 c"("citi'#

(@umerals beside the data points are the case study numbers)


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Table 1.8 R'co%%'nd'd r"n5'# o$ "!!o-":!' :'"rin5 c"("citi'# =4P"0


4"


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Table 2.8 Loc"tion# "nd t*' #co(' o$ in'#ti5"tion# $or '"c* c"#' #tud/

No Bui!din5 Id'ntit/

Nu%:'r

O$

#ur'/#

umber m m a b c0 d0

1 3tatr Primary -chool *uilding*abaesi KQrlareli Jestern Ture

2 1$"/ " 2 2 21 32

2 Residential 3partmentsLeilSay =ooperative, ay, 3fyon

9"$ 2"$ / / 11 1+2

/ Iei Urne, 'ousing comple.,BVtr Gillage, "in Ba

No

bearing capacity shear wave (1)

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