Critical State Soil Mechanics (CSSM)

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Steven F. Bartlett, 2010

2006

Critical-State Soil MechanicsFor Dummies

Paul W. Mayne, PhD, P.E.

Civil & Environmental Engineering

Georgia Institute of TechnologyAtlanta, GA 30332-0355

www.ce.gatech.eduEmail: [email protected]

Critical-state soil mechanics is an effective stress framework

describing mechanical soil response.

•

In its simplest form here, we consider only shear-induced loading.•

We tie together two well-known concepts: (1) one-dimensional

consolidation behavior, represented by (e-log v ’) curves; and

(2) shear stress-vs. normal stress ( v ’) from direct shear box

or simple shearing.

•

Herein, only the bare essence of CSSM concepts are presented,sufficient to describe strength & compressibility response.

•

Critical State Soil Mechanics (CSSM)Thursday, March 11, 2010

11:43 AM

CSSM for Dummies



In an attempt to advance soil testing techniques, Kenneth Harry

Roscoe of Cambridge University, in the late forties and early fifties,

developed a simple shear apparatus in which his successive students

attempted to study the changes in conditions in the shear zone bothin sand and in clay soils. In 1958 a study of the yielding of soil based

on some Cambridge data of the simple shear apparatus tests, and on

much more extensive data of triaxial tests at Imperial College,

London, led to the publication of the critical state concept (Roscoe,

Schofield & Wroth 1958). Subsequent to this 1958 paper, concepts of

plasticity were introduced by Schofield and published later in a classic

text book (Schofield & Wroth 1968).

Pasted from <http://en.wikipedia.org/wiki/Critical_state_soil_mechanics >


BackgroundThursday, March 11, 2010

11:43 AM

CSSM for Dummies

http://en.wikipedia.org/wiki/Cambridge_University

http://en.wikipedia.org/wiki/Critical_state_soil_mechanics#CITEREFRoscoeSchofieldWroth1958


http://en.wikipedia.org/wiki/Critical_state_soil_mechanics#CITEREFSchofieldWroth1968

http://en.wikipedia.org/wiki/Critical_state_soil_mechanics


http://en.wikipedia.org/wiki/Critical_state_soil_mechanics#CITEREFSchofieldWroth1968



http://en.wikipedia.org/wiki/Cambridge_University




Direct Shear Test Results

v’

Direct Shear Box (DSB)

v’

Direct Simple Shear (DSS)

d

gs

Slow Direct Shear Tests on Triassic Clay,NC

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7 8 9 10

Displacement, d (mm)

S h e a r

S t r e s s ,

( k P

a )

n'

(kPa)= 214.5

135.0

45.1

Slow Direct Shear Tests on Triassic Clay, Raleigh, NC

0

20

40

60

80

100

120

140

0 50 100 150 200 250

Effective Normal Stress, n' (kPa)

S h e a r

S t r e s s ,

( k P

a )

0.491 = tan '

Strength Parameters:

c' = 0; ' = 26.1 o

Peak

Peak

Peak

Shear Strength TheoryThursday, March 11, 2010

11:43 AM

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The critical Ssate concept states that soils and other granular

materials, if continuously distorted (sheared) until they flow as a

frictional fluid, will come into a well-defined critical state. At the onset

of the critical state, shear distortions occur without any furtherchanges in mean effective stress or deviatoric stress or void ratio. The

void ratio at the critical state is called the critical state void ratio.

Pasted from <http://en.wikipedia.org/wiki/Critical_state_soil_mechanics >

Shear Strength TheoryThursday, March 11, 2010

11:43 AM

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One-Dimensional Consolidation

Sandy Clay (CL), Surry, VA: Depth = 27 m

0.5

0.6

0.7

0.8

0.9

1.0

1 10 100 1000

Effective Vertical Stress, svo' (kPa)

V o i d

R a t i o , Cc = 0.38

Cr = 0.04

vo'=300 kPap'=900 kPa

Overconsolidation Ratio, OCR = 3

Cs = swelling index (= Cr)cv = coef. of consolidationD' = constrained modulus

Cae = coef. secondary compressionk ≈ hydraulic conductivity

v ’

In some textbooks the effective vertical stress is replaced with

the mean effective stress, which is:

m' = V'1 + V

'2 + V

'3)/3

1D Consolidation TheoryThursday, March 11, 2010

11:43 AM

CSSM for Dummies




CSSM for Dummies

Log v'

Effective stress v'

S h e a r s t r e s s

V o i d R a t i o , e

NC

CC

tanf'

CSLEffective stress v'


NC

CSL

CSSM Premise:

“All stress paths fail

on the critical state

line (CSL)”

CSL

fc=0

The above statement means that the critical state line forms an

envelope that defines the failure state of soil. This failure or critical

state is a function of the state of stress (vertical or mean effective

stress and shear stress) and the void ratio.

Comparison of Critical State Line with Normally ConsolidatedThursday, March 11, 2010

11:43 AM

CSSM for Dummies




CSSM for Dummies

Log v'

Effective stress v'




NC NC

CC

tanf'

CSL

CSLCSL

STRESS PATH No.1NC Drained Soil

Given: e0, vo’, NC (OCR=1)

e0

vo

vo

max

= c + tanf

ef

De

Volume Change is Contractive:

evol = De/(1+e0) < 0

Effective stress v'

c’=0

The above stress path is

straight because there is no

excess pore pressure

generated during shear

because the test is drained

and the applied vertical

stress is not changing during

the direct shear mode of failure.

Stress Path for Normally Consolidated Drained Soil in DSSThursday, March 11, 2010

11:43 AM

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CSSM for Dummies

Log v'

Effective stress v'



V o i d R a t i o ,

e

NC NC

CC

tanf'

CSL

CSLCSL

STRESS PATH No.2NC Undrained Soil

Given: e0, vo’, NC (OCR=1)

e0

vo

vo

+Du = Positive ExcessPorewater Pressures

vf

vf

Dumax = cu=su

Effective stress v'

Note that there is no change in void ratio in the above consolidation

plots because the test is undrained .

Stress Path for Normally Consolidated Undrained Soil (DSS)Thursday, March 11, 2010

11:43 AM

CSSM for Dummies




CSSM for Dummies

Log v'

Effective stress v'



NC NC

CC

tanf'CSL

CSLCSL

Note: All NC undrained

stress paths are parallel

to each other, thus:

su/vo’ = constant

Eff ective stress v'

DSS: su/vo’NC = ½sinf’


Effect of Increasing effective vertical stress on undrained strength

Stress Path for Normally Consolidated Undrained Soil (DSS)Thursday, March 11, 2010

11:43 AM

CSSM for Dummies




CSSM for Dummies

Log v'Effective stress v'

Effective stress v'




NC NC

CC

tanf'

CSL

CSLCSL

CS

p'

p'

OC

Overconsolidated States:

e0, vo’, and OCR = p’/vo’

where p’ = vmax’ = Pc’ =

preconsolidation stress;

OCR = overconsolidation ratio

Critical State Line and Overconsolidated SoilsThursday, March 11, 2010

11:43 AM

CSSM for Dummies




CSSM for Dummies

Log v '

Effective stress v'



NC NC

CC

tanf'

CSL

CSLCSL

CS

OC

Stress Path No. 3

Undrained OC Soil:

e0, vo’, and OCR

vo'

e0

vo'

Stress Path: DV/V0 = 0

Negative Excess Du

Effective stress v'vf '


Du

Stress Path for Undrained Over-consolidated Soil (DSS)Thursday, March 11, 2010

11:43 AM

CSSM for Dummies




Yield Surfaces

Log v '

Normal stress v'



NC NC

CSL

CSL

CSL

OC

Normal stress v'


p'

p'

OC

Yield surface represents3-d preconsolidation

Quasi-elastic behaviorwithin the yield surface

The behavior of the soil is elastic until the state of stress on the soil

reaches the yield surface. After that, the soil behaves in a plastic

manner and undergoes both elastic and plastic strains. The yield

surface will expand as the soil dilates or strain hardens: it will contract

as the soil contracts or strain softens until the critical state is reached.

At this point, this yield surface no longer changes and is known as the

yield surface at critical state.

Yield Surfaces and Stress Paths for Undrained TestsThursday, March 11, 2010

11:43 AM

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Initial state: e0, svo’, and OCR = sp’/svo’•

Soil constants: f ’, Cc, and Cs (L = 1-Cs/Cc)•

NC and OC behavior•

Undrained vs. Drained (and other paths)•

Positive vs. negative porewater pressures•

Volume changes (contractive vs. dilative)•

su/svo’ = ½ sinf’ OCRL where L = 1-Cs/Cc•

Yield surface represents 3-d preconsolidation•

Using effective stresses, CSSM addresses:•

Summary of CSSMThursday, March 11, 2010

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CSSM for Dummies




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11:43 AM

Critical State Soil Mechanics (CSSM)

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