CriticalState Soil Mechanics

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• Critical-State Soil Mechanics

Paul W. Mayne, PhD, P.E.Civil Environmental
EngineeringGeorgia Institute of Technology
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PROLOGUE

• 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 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.

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Critical State Soil Mechanics (CSSM)

• Experimental evidence provided by Hvorslev
  (1936 1960, ASCE) Henkel (1960, ASCE Boulder)
  Henkel Sowa (1961, ASTM STP 361)
• Mathematics presented elsewhere, including
  Schofield Wroth (1968) Burland (1968) Wood
  (1990).
• In basic form 3 material constants (f', Cc, Cs)
  plus initial state (e0, svo', OCR)
• 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.

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One-Dimensional Consolidation
Overconsolidation Ratio, OCR 3
Cs swelling index ( Cr) cv coef. of
consolidation D' constrained modulus Cae
coef. secondary compression k hydraulic
conductivity
sv
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Direct Shear Test Results
sv
Direct Shear Box (DSB)
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CSSM
CC
Void Ratio, e
NC
Log sv'
CSSM Premise All stress paths fail on the
critical state line (CSL)
Shear stress t
f?
c?0
Effective stress sv'
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CSSM
CC
Void Ratio, e
Void Ratio, e
e0
NC
NC
CSL
CSL
svo?
Effective stress sv'
Log sv'
tmax c? s? tanf?
tanf'
STRESS PATH No.1 NC Drained Soil
Shear stress t
Given e0, svo, NC (OCR1)
Drained Path Du 0
Volume Change is Contractive evol De/(1e0) lt 0
c0
svo?
Effective stress sv'
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CSSM
CC
Void Ratio, e
Void Ratio, e
NC
NC
CSL
CSL
Effective stress sv'
Log sv'
tanf'
STRESS PATH No.2 NC Undrained Soil
Du
tmax cusu
Shear stress t
Given e0, svo, NC (OCR1)
Undrained Path DV/V0 0
Du Positive Excess Porewater Pressures
Effective stress sv'
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CSSM
CC
Void Ratio, e
Void Ratio, e
NC
NC
CSL
CSL
Effective stress sv'
Log sv'
tanf'
Note All NC undrained stress paths are
parallel to each other, thus su/svo constant
Shear stress t
DSS su/svoNC ½sinf
Effective stress sv'
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CSSM
CC
Void Ratio, e
OC
Void Ratio, e
CS
NC
NC
CSL
CSL
Effective stress sv'
sp'
Log sv'
CSL
Overconsolidated States e0, svo, and OCR
sp/svo where sp svmax Pc
preconsolidation stress OCR overconsolidation
ratio
tanf'
Shear stress t
sp'
Effective stress sv'
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CSSM
CC
Void Ratio, e
Void Ratio, e
OC
CS
NC
NC
CSL
CSL
Effective stress sv'
Log sv'
CSL
Stress Path No. 3 Undrained OC Soil e0, svo,
and OCR
tanf'
Shear stress t
Stress Path DV/V0 0
Negative Excess Du
svo'
Effective stress sv'
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CSSM
CC
Void Ratio, e
Void Ratio, e
OC
CS
NC
NC
CSL
CSL
Effective stress sv'
Log sv'
CSL
Stress Path No. 4 Drained OC Soil e0, svo, and
OCR
tanf'
Shear stress t
Stress Path Du 0
Dilatancy DV/V0 gt 0
Effective stress sv'
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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)
• 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)

Theres more !
Semi-drained, Partly undrained, Cyclic..
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Equivalent Stress Concept
CC
NC
Void Ratio, e
Void Ratio, e
NC
OC
CS
sp'
sp'
CSL
CSL
Log sv'
Effective stress sv'
CSL
1. OC State (eo, svo, sp)
tanf'
2. Project OC state to NC line for equivalent
stress, se
Shear stress t
su
at se suOC suNC
De Cs log(sp/svo) De Cc log(se/sp)
3. se svo OCR1-Cs/Cc
svo'
se'
Stress sv'
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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 OCR1-Cs/Cc
Normalized Undrained Shear Strength su/svo ½
sinf OCRL where L (1-Cs/Cc)
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Undrained Shear Strength from CSSM
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Undrained Shear Strength from CSSM
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Porewater Pressure Response from CSSM
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Yield Surfaces
NC
NC
CSL
OC
OC
Void Ratio, e
Void Ratio, e
sp'
CSL
sp'
Normal stress sv'
Log sv'
CSL

• Yield surface represents 3-d preconsolidation
• Quasi-elastic behavior within the yield surface

Shear stress t
Normal stress sv'
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Port of Anchorage, Alaska
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Cavity Expansion Critical State Model for
Evaluating OCR in Clays from Piezocone Tests
where M 6 sinf/(3-sinf) and L 1 Cs/Cc
? 0.8
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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
• 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