cssm for dummies

7/25/2019 CSSM for Dummies

1/22

2006

Critical-State Soil MechanicsFor Dummies

Paul W. Mayne, PhD, P.E.

Civil & Environmental EngineeringGeorgia Institute o !echnology

"tlanta, G" #$##%-$#'''.ce.gatech.e(u

Email) *aul.mayne+ce.gatech.e(u


2/22

PG/E Critical-state soil mechanics is an eective stress rame'or0

(escri1ing mechanical soil res*onse

In its sim*lest orm here, 'e consi(er only shear-in(uce(loa(ing.

We merely tie together t'o 'ell-0no'n conce*ts) 234 one-

(imensional consoli(ation 1ehavior, re*resente( 1y e-logv5curves6 an( 2%4 shear stress-vs. normal stress 2 v54 rom(irect shear 1o7 or sim*le shearing.

8erein, only the 1are essence o CSSM conce*ts are *resente(,suicient to (escri1e strength & com*ressi1ility res*onse.


3/22

Critical State Soil Mechanics 2CSSM4 E7*erimental evi(ence *rovi(e( 1y 8vorslev 239#:6 39:$, "SCE46 8en0el

239:$, "SCE ;oul(er4 8en0el & So'a 239:3, "S!M S!P #:34

Mathematics *resente( else'here, inclu(ing) Schoiel( & Wroth 239:


4/22

ne-Dimensional Consoli(ationSandy Clay (CL), Surry, VA: Depth = 27 m

0.5

0.6

0.7

0.8

0.

!.0

! !0 !00 !000 !0000

Eective ertical Stress, svo= 20Pa4

Coi(

a

tio,

e

Cc $.#C un(raine(

stress *aths are *arallel

to each other, thus)

suvo5 constant

Effective stress "#

DSS) suvo5>C Lsin5

VoidRatio

,e


10/22

CSSM for Dummies

Log "#Effective stress

"#

Effective stress "#

Shearst

ress

VoidRatio,e

VoidRatio

,e

$C $C

CC

tan#

CSL

CSLCSL

CS

p!

p!

%C

verconsoli(ate( States)

e$, vo5, an(C *5vo5'here

*5 "ma&5 Pc5

*reconsoli(ation stress6

C overconsoli(ation ratio


11/22

CSSM for Dummies

Log v'

Effective stress "#

Shearst

ress

VoidRatio,e

$C $C

CC

tan

#

CSL

CSLCSL

CS

%C

Stress Path >o. #

/n(raine( C Soil)e$, vo5, an( C

vo!

e0

vo!

Stress Path)

$ $

>egative E7cess

u

Effective stress"#vf!

VoidRatio

,e

u


12/22

CSSM for Dummies

Log v'

Effective stress "#

Shearst

ress

VoidRatio,e

VoidRatio

,e

$C $C

CC

tan

#

CSL

CSLCSL

CS

%C

Stress Path >o.

Draine( C Soil)e$, vo5, an( C

Stress Path)

u $

Dilatancy)

$ $

vo!

e0

vo!

Effective stress"#


13/22

"ritical state soil mechaics

Initial state: e0, vo, and OCR = p/vo

Soil constants: , Cc, and Cs = !"Cs/Cc#

$or %C soil OCR =!#: &ndrained vol= 0#: 'u and ma(= su= cu

Drained u = 0# and contractive decreasevol#

$or OC soil:

&ndrained vol= 0#: "u and ma(= su= cu Drained u = 0# and dilative Increasevol#

#here$s more % Semi&draied, 'artl draied, "clic*


14/22

)*uivalent Stress Concept

Log v'

Stress "#

Shearst

ress

VoidRatio,e

$C

$C

CC

tan

#

CSL

CSLCSL

CS%C

3. C State 2eo, vo5, *54

vo!

%. Pro@ect C state to >C

line or eNuivalent stress, e5

#. e5 vo5 CO3-CsCc

vo!

e0

Effective stress"#

VoidRatio

,e

p! p!

e!

e!

su

vf!

ep

e = Cslo+p/vo#

e = Cclo+e/p#

e

at e5suC su>C


15/22

"ritical state soil mechaics

reviousl-: su/vo = constant for %C soil

On t.e vir+in compression line: vo = e

.us: su/e = constant for all soil %C OC#

$or simple s.ear: su/e = 1sin )*uivalent stress:

>ormaliQe( /n(raine( Shear Strength)

suvo5 L sin5 C

'here 23-CsCc4

e5 vo5 CO3-CsCc


16/22

draied Shear Stregth from "SS-


17/22

draied Shear Stregth from "SS-


18/22

'ore.ater 'ressre Respose from "SS-


19/22

2ield Surfaces

Log v'

/ormal stress "#

Shearstress

VoidRatio,e

$C $C

CSL

CSL

CSL

%C

/ormal stress"#

VoidRatio

,e

p!

p!

%C

2ield surface represents

3"d preconsolidation4uasi"elastic 5e.avior6it.in t.e -ield surface


20/22

ort of 7nc.ora+e, 7las8a


21/22

Cavity E7*ansion R Critical State Mo(el or Evaluating

C in Clays rom PieQocone !ests

O C RM

q uT b

v o

=+

2 1

1 9 5 1

1

. '

/

'here M : sin

52#-sin

54

an(

3 R CsCc $.

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