Transcript Academic-Practitioner Forum 16th ICSMGE Osaka

Critical-State Soil Mechanics
Paul W. Mayne, PhD, P.E.
Civil & Environmental Engineering
Georgia Institute of Technology
PROLOGUE
 Critical-state soil mechanics is an effective stress
framework describing mechanical soil response
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In its simplest form here, we consider only shearinduced loading.
We merely tie together two well-known concepts:
(1) one-dimensional consolidation behavior,
represented by e-logsv’ curves; and (2) shear
stress-vs. normal stress (t-sv’) 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)
 Experimental evidence provided by Hvorslev (1936; 1960,
ASCE); Henkel (1960, ASCE Boulder) Henkel & Sowa (1961,
ASTM STP 361)
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Mathematics presented elsewhere, including: Schofield &
Wroth (1968); Burland (1968); Wood (1990).
In basic form: 3 material constants (f', Cc, Cs)
state (e0, svo', OCR)
plus initial
Constitutive Models, include: Original Cam-Clay, Modified Cam
Clay, NorSand, Bounding Surface, MIT-E3 (Whittle, 1993) &
MIT-S1 (Pestana) and others (Adachi, Oka, Ohta, Dafalias)
"Undrained" is just one specific stress path
Yet !!! CSSM is missing from most textbooks and undergrad &
grad curricula in the USA.
One-Dimensional Consolidation
Sandy Clay (CL), Surry, VA: Depth = 27 m
svo'=300 kPa
1.0
Cr = 0.04
0.9
Void Ratio, e
sp'=900
kPa
Overconsolidation Ratio, OCR = 3
0.8
Cs = swelling index (= Cr)
cv = coef. of consolidation
D' = constrained modulus
Cae = coef. secondary compression
k ≈ hydraulic conductivity
0.7
0.6
Cc = 0.38
0.5
1
10
100
1000
Effective Vertical Stress, s
svo'
v’ (kPa)
10000
Direct Shear Test Results
Slow Direct Shear Tests on Triassic Clay,NC
(kPa)
sn'
120
(kPa)=
214.5
Peak
Strength Parameters:
c' = 0; f ' = 26.1 o
120
100
t
100
80
Shear Stress,
Shear Stress, t (kPa)
140
Slow Direct Shear Tests on Triassic Clay, Raleigh, NC
140
Peak
135.0
60
40
Peak
20
45.1
0
80
60
0.491 = tan f '
40
20
0
0
1
2
3
4
5
Displacement,
t t
sv’
6
d
7
8
9
10
50
0
(mm)
d
100
Effective Normal Stress,
t
t
200
150
sn'
(kPa)
sv’
gs
Direct Shear Box (DSB)
Direct Simple Shear (DSS)
250
Void Ratio, e
CC
NC
CSL
Void Ratio, e
CSSM
line (CSL)”
Shear stress t
on the critical state
CSL
Effective stress sv'
Log sv'
CSSM Premise:
“All stress paths fail
NC
c=0
CSL
tanf'
f
Effective stress sv'
CC
e0
De
NC
ef
Void Ratio, e
Void Ratio, e
CSSM
NC
CSL
CSL
STRESS PATH No.1
NC Drained Soil
Given: e0, svo’, NC (OCR=1)
Drained Path: Du = 0
Volume Change is Contractive:
evol = De/(1+e0) < 0
Effective stress sv'
Shear stress t
Log sv'
svo
c’=0
tmax = c + s tanf
CSL
tanf'
svo
Effective stress sv'
CC
e0
NC
Void Ratio, e
Void Ratio, e
CSSM
NC
CSL
CSL
svf
svo
Effective stress sv'
Log sv'
Given: e0, svo’, NC (OCR=1)
Undrained Path: DV/V0 = 0
+Du = Positive Excess
Porewater Pressures
Shear stress t
STRESS PATH No.2
NC Undrained Soil
CSL
tanf'
Du
tmax = cu=su
svf
svo
Effective stress sv'
CSSM
NC
Void Ratio, e
Void Ratio, e
CC
NC
CSL
CSL
Effective stress sv'
Note: All NC undrained
stress paths are parallel
to each other, thus:
su/svo’ = constant
DSS: su/svo’NC = ½sinf’
Shear stress t
Log sv'
CSL
tanf'
Effective stress sv'
CS
NC
Void Ratio, e
CC
OC
NC
CSL
CSL
Log sv'
Effective stress sv'
s p'
Overconsolidated States:
e0, svo’, and OCR = sp’/svo’
where sp’ = svmax’ = Pc’ =
preconsolidation stress;
OCR = overconsolidation ratio
CSL
Shear stress t
Void Ratio, e
CSSM
tanf'
Effective stress sv'
s p'
CSSM
e0
CS
NC
Void Ratio, e
Void Ratio, e
CC
OC
NC
CSL
CSL
Effective stress sv'
Log sv'
Stress Path No. 3
Undrained OC Soil:
e0, svo’, and OCR
Stress Path: DV/V0 = 0
Negative Excess Du
Shear stress t
svo' svf'
CSL
tanf'
Du
svo'
Effective stress sv'
CSSM
e0
CS
NC
Void Ratio, e
Void Ratio, e
CC
OC
NC
CSL
CSL
Effective stress sv'
Log sv'
Stress Path No. 4
Drained OC Soil:
e0, svo’, and OCR
Stress Path: Du = 0
Dilatancy: DV/V0 > 0
CSL
Shear stress t
svo'
tanf'
svo'
Effective stress sv'
Critical 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):
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Undrained (evol = 0): +Du and tmax = su = cu
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Drained (Du = 0) and contractive (decrease evol)
• For OC soil:
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Undrained (evol = 0): -Du and tmax = su = cu
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Drained (Du = 0) and dilative (Increase evol)
There’s more !
Semi-drained, Partly undrained, Cyclic…..
Equivalent Stress Concept
NC
e0
De
ep
CS
sp'
Void Ratio, e
Void Ratio, e
CC
NC
OC
CSL
CSL
2. Project OC state to NC
line for equivalent stress, se’
De = Cs log(sp’/svo’)
De = Cc log(se’/sp’)
3. se’ = svo’ OCR[1-Cs/Cc]
Shear stress t
svo' svf' se' Log sv'
1. OC State (eo, svo’, sp’)
sp'
Effective stress sv'
CSL
tanf'
su
at se’
suOC = suNC
svo'
s e'
Stress sv'
Critical 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: se’ = svo’ OCR[1-Cs/Cc]
Normalized Undrained Shear Strength:
su/svo’ = ½ sinf’ OCRL
where L = (1-Cs/Cc)
Undrained Shear Strength from CSSM
su/svo' NC (DSS)
0.4
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)
0.3
0.2
0.1
su/svo'NC (DSS) =½sinf'
0.0
0.0
0.1
0.2
0.3
0.4
sinf'
0.5
0.6
0.7
0.8
Undrained Shear Strength from CSSM
DSS Undrained Strength, su/svo'
10
Amherst CVVC
Atchafalaya
Bangkok
Bootlegger Cove
o
f' = 40
Boston Blue
Cowden
o
30
20o
Intact
Clays
Drammen
Hackensack
Haga
1
Lower Chek Lok
Maine
McManus
su/svo' = ½ sinf' OCR
Paria
L
Portland
Portsmouth
Note: L = 1 - Cs/Cc  0.8
Silty Holocene
Upper Chek Lok
0.1
1
10
Overconsolidation Ratio, OCR
100
20
30
40
Porewater Pressure Response from CSSM
1
Amherst CVVC
Atchafalaya
Bangkok
0
Bootlegger Cove
Boston Blue
-1
Cowden
Drammen
Hackensack
-2
Du/svo'
Normalized Porewater Pressure,
Dus/svo' = 1 - ½cosf'OCRL
Haga
Lower Chek Lok
-3
Maine
McManus
Intact
Paria
-4
f' = 20 30
o
o
40
Portland
o
Portsmouth
-5
Silty Holocene
L = 0.9
0.8
Upper Chek Lok
0.7
20
-6
1
10
Overconsolidation Ratio, OCR
100
30
40
Yield Surfaces
NC
NC
Void Ratio, e
Void Ratio, e
CSL
OC
OC
sp'
CSL
sp'
Yield surface represents
3-d preconsolidation
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Quasi-elastic behavior
within the yield surface
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Normal stress sv'
CSL
Shear stress t
Log sv'
Normal stress sv'
Port of Anchorage, Alaska
10
Critical State Soil Mechanics
(Modified Cam Clay)
f ' = 27.7o
L = 0.75
0.7
Bootlegger
0.6
Cove Clay
Strength Ratio, su/s vo'
Deviatoric Stress = q* = (s 1-s 3)/s p'
0.8
0.5
0.4
M c = (q/p')f = 1.10
0.3
M c = 6sinf '/(3-sinf ')
0.2
f ' = 27.7o
1
DSS Data
CIUC Data
MCC Pred CIUC
0.1
MCC Pred DSS
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Effective Stress, p'* = (s 1'+s 2'+s 3')/(3s p')
0.8
0.1
1
10
Overconsolidation Ratio, OCR
100
Cavity Expansion – Critical State Model for Evaluating
OCR in Clays from Piezocone Tests

 qT - ub  
1


OCR = 2 
. M  1  s vo '  
 195
where M = 6 sinf’/(3-sinf’)
L = 1 – Cs/Cc 
Overconsolidation Ratio, OCR
0
0.8
1
2
3
4
5
0
2
4
Depth (meters)
and
1/ L
fs
ub
6
8
10
12
CPTU
CRS
14
16
qc  qT
Bothkennar, UK
18
20
IL Oed
RF
6
Critical state soil mechanics
• Initial state: e0, svo’, and OCR = sp’/svo’
• Soil constants: f’, Cc, and Cs (L = 1-Cs/Cc)
• Using effective stresses, CSSM addresses:

NC and OC behavior
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Undrained vs. Drained (and other paths)
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Positive vs. negative porewater pressures
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Volume changes (contractive vs. dilative)
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su/svo’ = ½ sinf’ OCRL where L = 1-Cs/Cc
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Yield surface represents 3-d preconsolidation