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2006 Critical-State Soil Mechanics For Dummies Paul W. Mayne, PhD, P.E. Civil & Environmental Engineering Georgia Institute of Technology Atlanta, GA 30332-0355.

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Presentation on theme: "2006 Critical-State Soil Mechanics For Dummies Paul W. Mayne, PhD, P.E. Civil & Environmental Engineering Georgia Institute of Technology Atlanta, GA 30332-0355."— Presentation transcript:

1 2006 Critical-State Soil Mechanics For Dummies Paul W. Mayne, PhD, P.E. Civil & Environmental Engineering Georgia Institute of Technology Atlanta, GA 30332-0355 www.ce.gatech.edu Email: paul.mayne@ce.gatech.edu

2 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-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.

3 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 (  ', C c, C s ) plus initial state (e 0,  vo ', 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.

4 One-Dimensional Consolidation C c = 0.38 C r = 0.04  vo ' =300 kPa  p ' =900 kPa Overconsolidation Ratio, OCR = 3 C s = swelling index (= C r ) c v = coef. of consolidation D' = constrained modulus C  e = coef. secondary compression k ≈ hydraulic conductivity v’v’

5 Direct Shear Test Results v’v’  Direct Shear Box (DSB) v’v’  Direct Simple Shear (DSS)    ss

6 CSSM for Dummies Log  v ' Effective stress  v ' Shear stress  Void Ratio, e NC C tan  ' CSL Effective stress  v ' Void Ratio, e NC CSL CSSM Premise: “All stress paths fail on the critical state line (CSL)” CSL  c =0

7 CSSM for Dummies Log  v ' Effective stress  v ' Shear stress  Void Ratio, e NC C tan  ' CSL STRESS PATH No.1 NC Drained Soil Given: e 0,  vo ’, NC (OCR=1) e0e0  vo Drained Path:  u = 0  max = c +  tan  efef ee Volume Change is Contractive:  vol =  e/(1+e 0 ) < 0 Effective stress  v ' c’=0

8 CSSM for Dummies Log  v ' Effective stress  v ' Shear stress  Void Ratio, e NC C tan  ' CSL STRESS PATH No.2 NC Undrained Soil Given: e 0,  vo ’, NC (OCR=1) e0e0  vo Undrained Path:  V/V 0 = 0 +  u = Positive Excess Porewater Pressures  vf uu  max  c u =s u Effective stress  v '

9 CSSM for Dummies Log  v ' Effective stress  v ' Shear stress  Void Ratio, e NC C tan  ' CSL Note: All NC undrained stress paths are parallel to each other, thus: s u /  vo ’ = constant Effective stress  v ' DSS: s u /  vo ’ NC = ½sin  ’ Void Ratio, e

10 CSSM for Dummies Log  v ' Effective stress  v ' Shear stress  Void Ratio, e NC C tan  ' CSL CSCS p'p' p'p' OC Overconsolidated States: e 0,  vo ’, and OCR =  p ’/  vo ’ where  p ’ =  vmax ’ = P c ’ = preconsolidation stress; OCR = overconsolidation ratio

11 CSSM for Dummies Log  v ' Effective stress  v ' Shear stress  Void Ratio, e NC C tan  ' CSL CSCS OC Stress Path No. 3 Undrained OC Soil: e 0,  vo ’, and OCR  vo ' e0e0 Stress Path:  V/V 0 = 0 Negative Excess  u Effective stress  v '  vf ' Void Ratio, e uu

12 CSSM for Dummies Log  v ' Effective stress  v ' Shear stress  Void Ratio, e NC C tan  ' CSL CSCS OC Stress Path No. 4 Drained OC Soil: e 0,  vo ’, and OCR Stress Path:  u = 0 Dilatancy:  V/V 0 > 0  vo ' e0e0 Effective stress  v '

13 Critical state soil mechanics Initial state: e 0,  vo ’, and OCR =  p ’/  vo ’ Soil constants:  ’, C c, and C s (  = 1-C s /C c ) For NC soil (OCR =1):  Undrained (  vol = 0): +  u and  max = s u = c u  Drained (  u = 0) and contractive ( decrease  vol ) For OC soil:  Undrained (  vol = 0): -  u and  max = s u = c u  Drained (  u = 0) and dilative ( Increase  vol ) There’s more ! Semi-drained, Partly undrained, Cyclic…..

14 Equivalent Stress Concept Log  v ' Stress  v ' Shear stress  Void Ratio, e NC C tan  ' CSL CSCS OC 1. OC State (e o,  vo ’,  p ’)  vo ' 2. Project OC state to NC line for equivalent stress,  e ’ 3.  e ’ =  vo ’ OCR [1-Cs/Cc]  vo ' e0e0 Effective stress  v ' Void Ratio, e p'p' p'p' e'e' e'e' susu  vf ' epep  e = C s log(  p ’/  vo ’)  e = C c log(  e ’/  p ’) ee at  e ’ s uOC = s uNC

15 Critical state soil mechanics Previously: s u /  vo ’ = constant for NC soil On the virgin compression line:  vo ’ =  e ’ Thus: s u /  e ’ = constant for all soil (NC & OC) For simple shear: s u /  e ’ = ½sin  ’ Equivalent stress: Normalized Undrained Shear Strength: s u /  vo ’ = ½ sin  ’ OCR  where  = (1-C s /C c )  e ’ =  vo ’ OCR [1-Cs/Cc]

16 Undrained Shear Strength from CSSM

17

18 Porewater Pressure Response from CSSM

19 Yield Surfaces Log  v ' Normal stress  v ' Shear stress  Void Ratio, e NC CSL OC Normal stress  v ' Void Ratio, e p'p' p'p' OC  Yield surface represents 3-d preconsolidation  Quasi-elastic behavior within the yield surface

20 Port of Anchorage, Alaska

21 Cavity Expansion – Critical State Model for Evaluating OCR in Clays from Piezocone Tests where M = 6 sin  ’/(3-sin  ’) and  = 1 – C s /C c  0.8 qcqc fsfs ubub  qT qT qT qT

22 Critical state soil mechanics Initial state: e 0,  vo ’, and OCR =  p ’/  vo ’ Soil constants:  ’, C c, and C s (  = 1-C s /C c ) 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)  s u /  vo ’ = ½ sin  ’ OCR  where  = 1-C s /C c  Yield surface represents 3-d preconsolidation


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