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![Page 1: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/1.jpg)
SimplifiedCritical-State Soil Mechanics
SimplifiedCritical-State Soil Mechanics
Paul W. MayneGeorgia Institute of Technology
Paul W. MayneGeorgia Institute of Technology
![Page 2: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/2.jpg)
PROLOGUEPROLOGUE Critical-state soil mechanics is an
effective stress framework describing mechanical soil response
In its simple form here, we consider only shear loading and compression-swelling.
We merely tie together two well-known concepts: (1) one-dimensional consolidation behavior (via e-logsv’
curves); and (2) shear stress-vs. normal stress ( -t sv’) plots from direct
shear (alias Mohr’s circles).
![Page 3: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/3.jpg)
Critical State Soil Mechanics (CSSM)
Critical State Soil Mechanics (CSSM)
Experimental evidence 1936 by Hvorslev (1960, ASCE) Henkel (1960, ASCE Boulder) Parry (1961) Kulhawy & Mayne (1990): Summary of
200+ soils Mathematics presented elsewhere
Schofield & Wroth (1968) Roscoe & Burland (1968) Wood (1990) Jefferies & Been (2006)
Basic form: 3 material constants (f', Cc, Cs) plus initial state parameter (e0, svo', OCR)
![Page 4: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/4.jpg)
Critical State Soil Mechanics (CSSM)
Critical State Soil Mechanics (CSSM)
Constitutive Models in FEM packages: Original Cam-Clay (1968) Modified Cam Clay (1969) NorSand (Jefferies 1993) Bounding Surface (Dafalias) MIT-E3 (Whittle, 1993) MIT-S1 (Pestana, 1999; 2001) Cap Model “Ber-Klay” (Univ. California) others (Adachi, Oka, Ohta, Dafalias, Nova, Wood, Huerkel)
"Undrained" is just one specific stress path Yet !!! CSSM is missing from most textbooks and
undergrad & grad curricula.
![Page 5: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/5.jpg)
One-Dimensional Consolidation 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 10000
Eff ective Vertical Stress, svo' (kPa)
Void
Rati
o,
e
Cc = 0.38
Cr = 0.04
svo'=300 kPa
sp'=900
kPa
Overconsolidation Ratio, OCR = 3
Cs = swelling index (= Cr)
cv = coef. of consolidation
D' = constrained modulus
Cae = coef. secondary compression
k ≈ hydraulic conductivity
sv’
![Page 6: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/6.jpg)
Direct Shear Test ResultsDirect Shear Test Results
sv’t
Direct Shear Box (DSB)
sv’t
Direct Simple Shear (DSS)
t d t
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)
She
ar S
tres
s, t
(k
Pa) sn'
(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
Eff ective Normal Stress, sn' (kPa)
She
ar S
tres
s, t
(k
Pa)
0.491 = tanf '
Strength Parameters:
c' = 0; f ' = 26.1 oPeak
Peak
Peak
![Page 7: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/7.jpg)
CSSM for DummiesCSSM for Dummies
sCSL’ sNC’
Effective stress sv'
She
ar s
tres
s t
Voi
d R
atio
, e
NC
CC
tanf'CSL
Effective stress sv'
Voi
d R
atio
, e
NC
CSL
CSSM Premise:
“All stress paths
fail on the critical
state line (CSL)”
CSL
fc=0
e0e0
sCSL’ ½sNC’
Log sv'
![Page 8: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/8.jpg)
CSSM for DummiesCSSM for Dummies
Log sv'
Effective stress sv'
Sh
ear
str
ess
t
Vo
id R
ati
o, e
Vo
id R
ati
o, e
NCNC
CC
tanf'CSL
CSLCSL
STRESS PATH No.1
NC Drained Soil
Given: e0, svo’, NC
(OCR=1)
e0
svo
svo
Drained Path: Du = 0
tmax = c + s tanf
ef
De
Volume Change is
Contractive: evol =
De/(1+e0) < 0
Effective stress sv'
c’=0
![Page 9: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/9.jpg)
CSSM for DummiesCSSM for Dummies
Log sv'
Effective stress sv'
Sh
ear
str
ess
t
Vo
id R
ati
o, e
Vo
id R
ati
o, e
NCNC
CC
tanf'CSL
CSLCSL
STRESS PATH No.2
NC Undrained Soil
Given: e0, svo’, NC
(OCR=1)
e0
svo
svo
Undrained Path: DV/V0 = 0
+Du = Positive Excess Porewater Pressures
svf
svf
Dutmax = cu=su
Effective stress sv'
![Page 10: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/10.jpg)
CSSM for DummiesCSSM for Dummies
Log sv'
Effective stress sv'
She
ar s
tres
s t
Voi
d R
atio
, e
NC NC
CC
tanf'
CSL
CSLCSL
Note: All NC
undrained
stress paths are
parallel
to each other, thus:
su/svo’ = constant
Effective stress sv'
DSS: su/svo’NC =
½sinf’
Voi
d R
atio
, e
![Page 11: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/11.jpg)
CSSM for DummiesCSSM for Dummies
Log sv'Effective stress sv'
Effective stress sv'
Sh
ear
stre
ss t
Voi
d R
atio
, e
Vo
id R
atio
, e
NC NC
CC
tanf'
CSL
CSLCSL
CS
sp'
sp'
OC
Overconsolidated States:
e0, svo’, and OCR = sp’/svo’
where sp’ = svmax’ = Pc’ =
preconsolidation stress;
OCR = overconsolidation ratio
![Page 12: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/12.jpg)
CSSM for DummiesCSSM for Dummies
Log sv'
Effective stress sv'
Sh
ear
str
ess
t
Vo
id R
ati
o, e
NC NC
CC
tanf'
CSL
CSLCSL
CS
OC
Stress Path No. 3
Undrained OC Soil:
e0, svo’, and OCR
svo'
e0
svo'
Stress Path: DV/V0 = 0
Negative Excess Du
Effective stress sv'svf'
Vo
id R
ati
o, e
Du
![Page 13: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/13.jpg)
CSSM for DummiesCSSM for Dummies
Log sv'
Effective stress sv'
Sh
ear
str
ess
t
Vo
id R
ati
o, e
Vo
id R
ati
o, e
NC NC
CC
tanf'
CSL
CSLCSL
CS
OC
Stress Path No. 4
Drained OC Soil:
e0, svo’, and OCR
Stress Path: Du =
0 Dilatancy: DV/V0 > 0
svo'
e0
svo'
Effective stress sv'
![Page 14: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/14.jpg)
Critical state soil mechanicsCritical state soil mechanics
• Initial state: e0, svo’, and OCR = sp’/svo’
• Soil constants: f’, Cc, and Cs (L = 1-Cs/Cc)
• For NC soil (OCR =1): Undrained (evol = 0): +Du and tmax = su = cu
Drained (Du = 0) and contractive (decrease evol)
• For OC soil: Undrained (evol = 0): -Du and tmax = su = cu
Drained (Du = 0) and dilative (Increase evol)
There’s more ! There’s more ! Semi-drained, Partly undrained, Cyclic response….. Semi-drained, Partly undrained, Cyclic response…..
![Page 15: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/15.jpg)
Equivalent Stress ConceptEquivalent Stress Concept
Log sv'
Stress sv'
Sh
ear
stre
ss t
Vo
id R
atio
, e NC
NC
CC
tanf'
CSL
CSLCSL
CS
OC
1. OC State (eo, svo’, sp’)
svo'
2. Project OC state to NC
line for equivalent stress,
se’
3. se’ = svo’ OCR[1-Cs/Cc]
svo'
e0
Effective stress sv'
Vo
id R
atio
, e
sp' sp'
se'
se'
su
svf'
ep
De = Cs log(sp’/svo’)
De = Cc log(se’/sp’)
De
at se’suOC = suNC
![Page 16: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/16.jpg)
Critical state soil mechanicsCritical state soil mechanics
• Previously: su/svo’ = constant for NC soil
• On the virgin compression line: svo’ = se’
• Thus: su/se’ = constant for all soil (NC &
OC)
• For simple shear: su/se’ = ½sin f’
• Equivalent stress: Normalized Undrained Shear
Strength:
su/svo’ = ½ sinf’ OCR L
where L = (1-Cs/Cc)
se’ = svo’ OCR[1-Cs/Cc]
![Page 17: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/17.jpg)
Undrained Shear Strength from CSSMUndrained Shear Strength from CSSM
0.0
0.1
0.2
0.3
0.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
sinf'
s u/s
vo' N
C
(DS
S)
AGS Plastic
Amherst
Ariake
Bootlegger
Bothkennar
Boston Blue
Cowden
Hackensack
James Bay
Mexico City
Onsoy
Porto Tolle
Portsmouth
Rissa
San Francisco
Silty Holocene
Wroth (1984)
su/svo'NC (DSS) =½sinf'
plasticity index, PI (%)
s u/s
vo' N
C
(DS
S)
AGS Plastic AmherstAriake Bootlegger
Bothkennar Boston BlueCowden Hackensack
James Bay Mexico CityOnsoy Porto Tolle
Portsmouth RissaSan Francisco Silty Holocene
![Page 18: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/18.jpg)
Undrained Shear Strength from CSSMUndrained Shear Strength from CSSM
0.1
1
10
1 10 100Overconsolidation Ratio, OCR
DS
S U
ndra
ined
Str
engt
h , s
u/s v
o' Amherst CVVC
Atchafalaya
Bangkok
Bootlegger Cove
Boston Blue
Cowden
Drammen
Hackensack
Haga
Lower Chek Lok
Maine
McManus
Paria
Portland
Portsmouth
Silty Holocene
Upper Chek Lok
40
30
20
f' = 40o
20o 30o
su/svo' = ½ sinf' OCRL
Note: L = 1 - Cs/Cc 0.8
IntactClays
L
![Page 19: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/19.jpg)
Porewater Pressure Response from CSSMPorewater Pressure Response from CSSM
-6
-5
-4
-3
-2
-1
0
1
1 10 100Overconsolidation Ratio, OCR
Nor
mal
ized
Por
ewat
er, D u
/svo'
Amherst CVVC
Atchafalaya
Bangkok
Bootlegger Cove
Boston Blue
Cowden
Drammen
Hackensack
Haga
Lower Chek Lok
Maine
McManus
Paria
Portland
Portsmouth
Silty Holocene
Upper Chek Lok
20
30
40
L = 0.9 0.8 0.7
IntactClays
f' = 20o 30o 40o
Dus/svo' = 1 - ½cosf'OCRL
![Page 20: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/20.jpg)
Yield SurfacesYield Surfaces
Log sv'
Normal stress sv'
Sh
ear
stre
ss t
Vo
id R
atio
, eNC NC
CSL
CSL
CSL
OC
Normal stress sv'
Vo
id R
atio
, e
sp'
sp'
OC
Yield surface represents 3-d preconsolidation
Quasi-elastic behavior within the yield surface
![Page 21: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/21.jpg)
Critical state soil mechanicsCritical state soil mechanics• This powerpoint: geosystems.ce.gatech.edu
• Classic book: Critical -State Soil Mechanics by Schofield & Wroth (1968): http://www.geotechnique.info
• Schofield (2005) Disturbed Soil Properties and Geotechnical Design Thomas Telford
• Wood (1990): Soil Behaviour and CSSM
• Jefferies & Been (2006): Soil liquefaction: a critical-state approach www.informaworld.com
![Page 22: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/22.jpg)
ESA versus TSA• Effective stress analysis (ESA) rules:
c' = effective cohesion intercept (c' = 0 for OCR < 2 and c' ≈ 0.02 sp' for short term loading)
f' = effective stress friction angle t = c' + s' tan f' = Mohr-Coulomb strength
criterion sv' = sv - u0 - Du = effective stress
• Total stress analysis (TSA) is (overly) simplistic for clay with strength represented by a single parameter, i.e. "f = 0" and tmax = c = cu = su = undrained shear strength (implying "Du = 0")
![Page 23: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/23.jpg)
Explaining the myth that "f = 0"
The effective friction angle (f') is usually between 20 to 45 degrees for most soils. However, for clays, we here of "f = 0" analysis which applies to total stress analysis (TSA). In TSA, there is no knowledge of porewater pressures (PWP). Thus, by ignoring PWP (i.e., Du = 0), there is an illusional effect that can be explained by CSSM. See the following slides.
![Page 24: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/24.jpg)
5.1688665.7431846.3813157.09035
7.8781678.7535199.72613210.8068112.0075713.3417514.8241616.4712918.3014320.3349322.5943625.10485
0.5
0.6
0.7
0.8
10 100 1000
Vo
id R
atio
, e
Log Effective stress, sv'
0.5
0.6
0.7
0.8
0 100 200 300 400 500
Vo
id R
ati
o, e
sv' (kPa)
0
100
200
300
0 100 200 300 400 500
t=
Sh
ear
Str
ess
(kP
a)
sv' (kPa)
f' = 30 °Cc = 0.50Cr = Cs = 0.05
(Undrained) Total Stress Analysis - ConsolidatedUndrained Triaxial Tests
Three specimens initially consolidated to svc' = 100, 200, and 400 kPa
![Page 25: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/25.jpg)
(Undrained) Total Stress Analysis
0 100 200 300 400 5000
100
200
300
Effective stress, sv' (kPa)
=
(
)t
Shear
Str
ess
kPa
su100
su200
su400
In TSA, however, Du not known, so plot stress paths for "Du = 0"
Obtains the illusion that " f ≈ 0° "
![Page 26: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/26.jpg)
5.1688665.7431846.3813157.09035
7.8781678.7535199.72613210.8068112.0075713.3417514.8241616.4712918.3014320.3349322.5943625.10485
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600
Vo
id R
ati
o, e
sv' (kPa)
0
100
200
300
0 100 200 300 400 500 600
t=
Sh
ear
Str
ess
(kP
a)
sv' (kPa)
0.5
0.6
0.7
0.8
10 1000
Vo
id R
ati
o, e
sv' (kPa)
VCL
CSL
Cs from Pc' = 400 kPa
Cs from Pc' = 500 kPa
Cs from Pc' = 600 kPa
Another set of undrained Total Stress Analyses (TSA) for UU tests on clays:
UU = Unconsolidated Undrained
![Page 27: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/27.jpg)
(Undrained) Total Stress Analysis
0 100 200 300 400 5000
100
200
300
Effective stress, sv' (kPa)
=
(
)t
Shear
Str
ess
kPa
su
Again, Du not known in TSA, so plot for stress paths for "Du = 0"
Obtains the illusion that " f = 0° "
![Page 28: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/28.jpg)
Explaining the myth that "f = 0"
Effective Stress Analyses (ESA)• Drained Loading (Du = 0)• Undrained Loading (DV/V0 = 0)
Total Stress Analyses (TSA) Drained Loading (Du = 0) Undrained Loading with " f = 0"
analysis: DV/V0 = 0 and "Du = 0"
![Page 29: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/29.jpg)
Cambridge University q-p' spaceCambridge University q-p' space
P' = (s1' + s2' + s3')/3
q =
(s 1
- s
3) TriaxialCompression
CSL
'sin3
'sin6
ff
cMs2' = s3'
s1'
Undrained NCStress Path
Undrained OCStress Path
svo' = P0'
DrainedStress Path3V : 1H
L
22
)'/( 0
OCRMps c
TCu
![Page 30: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/30.jpg)
Port of Anchorage, AlaskaPort of Anchorage, Alaska
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Effective Stress, p'* = (s1'+s2'+s3')/(3sp')
Dev
iato
ric
Str
ess
= q
* =
(s1-s
3)/s
p'
Bootlegger
Cove Clay
Mc = (q/p')f = 1.10
Mc = 6sinf '/(3-sinf ')f' = 27.7o
0.1
1
10
1 10 100
Overconsolidation Ratio, OCR
Str
en
gth
Ra
tio
, su/s
vo'
DSS Data
CIUC Data
MCC Pred CIUC
MCC Pred DSS
Critical State Soil Mechanics(Modified Cam Clay)
f ' = 27.7o
L = 0.75
![Page 31: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/31.jpg)
Cavity Expansion – Critical State Model for Evaluating OCR in Clays from Piezocone Tests
OCRM
q uT b
vo
2
1
1 95 1
1
. '
/
s
L
where M = 6 sinf’/(3-sinf’)
and L = 1 – Cs/Cc 0.8
qc
fs
ub
qT
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6
Overconsolidation Ratio, OCR
Dep
th (
met
ers)
CPTU
CRS
IL Oed
RF
Bothkennar, UK
![Page 32: Simplified Critical-State Soil Mechanics Paul W. Mayne Georgia Institute of Technology Paul W. Mayne Georgia Institute of Technology.](https://reader033.fdocuments.us/reader033/viewer/2022061615/551c5576550346b1458b4f64/html5/thumbnails/32.jpg)
Cambridge University q-p' spaceCambridge University q-p' space
P' = (s1' + s2' + s3')/3
q =
(s 1
- s
3)
CSL'sin3
'sin6
ff
cM
Yield SurfaceOriginal Cam Clay
Modified Cam Clay
Pc'
Bounding Surface
Cap ModelCap Model
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Anisotropic Yield SurfaceAnisotropic Yield Surface
P’ = (s1’ + s2’ + s3’)/3
q =
(s 1
- s
3)Mc = 6sinf’/(3-sinf’)
fctn(K0NC)
Y3 = Limit State
Yield Surface
e0
svo’
K0
G0
Y2
CSL
sp’
Y1
OCOCNCNC
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Cambridge University q-p' spaceCambridge University q-p' space
P' = (s1' + s2' + s3')/3
q =
(s 1
- s
3) fctn(K0NC)
Y3 = Limit State
Yield SurfaceCSL
sp’
'sin3
'sin6
ff
cM
Apparent
Mc
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MIT q-p' spaceMIT q-p' space
P' = ½(s1' + s3')
q =
½(s
1 - s 3
)
fctn(K0NC)
Yield Surface
sp’
'sintan f c
OCOCDiaz-Rodriguez, Leroueil, and Aleman (1992, JGE)
Diaz-Rodriguez, Leroueil, and Aleman (1992, JGE)
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Diaz-Rodriguez, Leroueil, & Aleman
(ASCE Journal Geotechnical
Engineering July 1992)
Yield Surfaces of Natural ClaysYield Surfaces
of Natural Clays
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Friction Angle of Clean Quartz Sands
Friction Angle of Clean Quartz Sands
(Bolton, 1986 Geotechnique) (Bolton, 1986 Geotechnique)
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State Parameter for Sands, y(Been & Jefferies, 1985; Jefferies & Been 2006)
log p'
voidratio
e
p' = ⅓ (s1'+s2'+s3')
VCLCSL
l10
l10
p0'
y = e0 - ecsl
Dry of Critical (Dilative)
Wet of Critical (Contractive)
e0
ecsl
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State Parameter for Sands, y(Simplified Critical State Soil Mechanics)
log p'
voidratio
e
p' = ⅓ (s1'+s2'+s3')
VCLCSL
l10
l10
p0'
y = e0 - ecsl
y = (Cs - Cc )∙log[ ½ cos f' OCR ]
Du = (1 - ½ cos f' OCRL ]∙svo'
e0
ecsl
then CSL = OCR = 2/cosf'
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Georgia Tech
State Parameter for Sands, y(Been, Crooks, & Jefferies, 1988)
log OCRp = log2L + Y/( -k l)where OCRp = R = overconsolidation ratio in Cambridge q-p' space, = 1- /L k l, l = Cc/ln(10) = compression index, and k Cs/ln(10) = swelling index
log OCRp = log2L + Y/( -k l)where OCRp = R = overconsolidation ratio in Cambridge q-p' space, = 1- /L k l, l = Cc/ln(10) = compression index, and k Cs/ln(10) = swelling index
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MIT Constitutive Models Whittle et al. 1994: JGE Vol. 120 (1)
"Model prediction of anisotropic behavior of Boston Blue Clay"
MIT-E3: 15 parameters for clay Pestana & Whittle (1999) "Formulation of
unified constitutive model for clays and sands" Intl. J. for Analytical & Numerical Methods in Geomechanics, Vol. 23
MIT S1: 13 parameters for clay MIT S1: 14 parameters for sand
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MIT E-3 Constitutive Model
Whittle (2005)
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MIT S-1 Constitutive ModelPestana and Whittle (1999)
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MIT S-1 Constitutive Model
Predictions forBerlin Sands
(Whittle, 2005)
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Critical state soil mechanicsCritical state soil mechanics• Initial state: e0, svo’, and OCR = sp’/svo’
• Soil constants: f’, Cc, and Cs
• Link between Consolidation and Shear Tests• CSSM addresses:
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• State parameter: y = e0 - ecsl
• Yield surface represents 3-d preconsolidation• State parameter: y = e0 - ecsl
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Simplified Critical State Soil Mechanics
Log sv' Effective stress sv'
Effective stress sv'
Sh
ear
str
ess
t
Vo
id R
ati
o, e
Vo
id R
ati
o, eNC
NCCC
CSL
CSLCSL
CS
sp'
sp'
OC
Four Basic Stress
Paths:
1. Drained NC (decrease
DV/Vo)
2. Undrained NC (positive Du)
3. Undrained OC (negative
Du)
4. Drained OC (increase
DV/Vo)
f'
eNC
consolidationswellingeOC
12
3
4
YieldSurface
dilative
contractive
+Du
-Du
sCS½sp
tmax = su NC
tmax = stanf
su OC
tmax = c+stanf c'
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