Academic-Practitioner Forum 16th ICSMGE Osaka

SimplifiedCritical-State Soil Mechanics Paul W. MayneGeorgia Institute of Technology08 July 2014PROLOGUE Critical-state soil mechanics is an effective stress framework describing mechanical soil responseIn 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 Mohrs circles). Critical State Soil Mechanics (CSSM) Experimental evidence 1936 by Hvorslev (1960, ASCE) Henkel (1960, ASCE Boulder) Parry (1961) Kulhawy & Mayne (1990): Summary of 200+ soilsMathematics 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)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 ModelBer-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.One-Dimensional Consolidation

Cc = 0.38Cr = 0.04svo'=300 kPasp'=900 kPaOverconsolidation Ratio, OCR = 3Cs = swelling index (= Cr)cv = coef. of consolidationD' = constrained modulusCae = coef. secondary compressionk hydraulic conductivitysvDirect Shear Test ResultssvtDirect Shear Box (DSB)svtDirect Simple Shear (DSS)tdtgs

CSSM for DummiessCSL sNC Effective stress sv'Shear stress tVoid Ratio, eNCCCtanf'CSLEffective stress sv'Void Ratio, eNCCSLCSSM Premise:All stress paths fail on the critical state line (CSL)CSLfc=0e0sCSL sNCLog sv'CSSM for DummiesLog sv'Effective stress sv'Shear stress tVoid Ratio, eVoid Ratio, eNCNCCCtanf'CSLCSLCSLSTRESS PATH No.1NC Drained Soil Given: e0, svo, NC (OCR=1)e0svosvoDrained Path: Du = 0tmax = c + s tanfefDeVolume Change is Contractive: evol = De/(1+e0) < 0Effective stress sv'c=0CSSM for DummiesLog sv'Effective stress sv'Shear stress tVoid Ratio, eVoid Ratio, eNCNCCCtanf'CSLCSLCSLSTRESS PATH No.2NC Undrained Soil Given: e0, svo, NC (OCR=1)e0svosvoUndrained Path: DV/V0 = 0+Du = Positive Excess Porewater Pressures svfsvfDutmax = cu=suEffective stress sv'CSSM for DummiesLog sv'Effective stress sv'Shear stress tVoid Ratio, eNCNCCCtanf'CSLCSLCSLNote: All NC undrainedstress paths are parallelto each other, thus:su/svo = constantEffective stress sv'DSS: su/svoNC = sinfVoid Ratio, eCSSM for DummiesLog sv'Effective stress sv'Effective stress sv'Shear stress tVoid Ratio, eVoid Ratio, eNCNCCCtanf'CSLCSLCSLCSsp'sp'OCOverconsolidated States: e0, svo, and OCR = sp/svowhere sp = svmax = Pc = preconsolidation stress;OCR = overconsolidation ratioCSSM for DummiesLog sv'Effective stress sv'Shear stress tVoid Ratio, eNCNCCCtanf'CSLCSLCSLCSOCStress Path No. 3Undrained OC Soil: e0, svo, and OCRsvo'e0svo'Stress Path: DV/V0 = 0 Negative Excess Du Effective stress sv'svf'Void Ratio, eDuCSSM for DummiesLog sv'Effective stress sv'Shear stress tVoid Ratio, eVoid Ratio, eNCNCCCtanf'CSLCSLCSLCSOCStress Path No. 4Drained OC Soil: e0, svo, and OCRStress Path: Du = 0 Dilatancy: DV/V0 > 0 svo'e0svo'Effective stress sv'Critical state soil mechanicsInitial state: e0, svo, and OCR = sp/svoSoil constants: f, Cc, and Cs (L = 1-Cs/Cc)For NC soil (OCR =1): Undrained (evol = 0): +Du and tmax = su = cuDrained (Du = 0) and contractive (decrease evol) For OC soil: Undrained (evol = 0): -Du and tmax = su = cuDrained (Du = 0) and dilative (Increase evol)

Theres more ! Semi-drained, Partly undrained, Cyclic response.. Equivalent Stress ConceptLog sv'Stress sv'Shear stress tVoid Ratio, eNCNCCCtanf'CSLCSLCSLCSOC1. OC State (eo, svo, sp)svo'2. Project OC state to NC line for equivalent stress, se3. se = svo OCR[1-Cs/Cc]svo'e0Effective stress sv'Void Ratio, esp'sp'se'se'susvf'epDe = Cs log(sp/svo)De = Cc log(se/sp)Deat sesuOC = suNCCritical state soil mechanicsPreviously: su/svo = constant for NC soilOn the virgin compression line: svo = seThus: su/se = constant for all soil (NC & OC)For simple shear: su/se = sin fEquivalent stress: Normalized Undrained Shear Strength:su/svo = sinf OCRL where L = (1-Cs/Cc)se = svo OCR[1-Cs/Cc]Undrained Shear Strength from CSSM

Undrained Shear Strength from CSSM

Porewater Pressure Response from CSSM

Yield SurfacesLog sv'Normal stress sv'Shear stress tVoid Ratio, eNCNCCSLCSLCSLOCNormal stress sv'Void Ratio, esp'sp'OC Yield surface represents 3-d preconsolidation

Quasi-elastic behavior within the yield surfaceYield SurfaceCritical state soil mechanicsThis powerpoint: geosystems.ce.gatech.eduClassic book: Critical -State Soil Mechanics by Schofield & Wroth (1968): http://www.geotechnique.infoSchofield (2005) Disturbed Soil Properties and Geotechnical Design Thomas TelfordWood (1990): Soil Behaviour and CSSMJefferies & Been (2006): Soil liquefaction: a critical-state approach www.informaworld.comESA versus TSAEffective 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 stressTotal 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")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.

(Undrained) Total Stress Analysis - ConsolidatedUndrained Triaxial TestsThree specimens initially consolidated to svc' = 100, 200, and 400 kPa(Undrained) Total Stress Analysissu100su200su400In TSA, however, Du not known, so plot stress paths for "Du = 0"Obtains the illusion that " f 0 "

Another set of undrained Total Stress Analyses (TSA) for UU tests on clays:

UU = Unconsolidated Undrained

(Undrained) Total Stress AnalysissuAgain, Du not known in TSA, so plot for stress paths for "Du = 0"Obtains the illusion that " f = 0 "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"Cambridge University q-p' spaceP' = (s1' + s2' + s3')/3q = (s1 - s3)TriaxialCompressionCSL

s2' = s3's1'Undrained NCStress PathUndrained OCStress Pathsvo' = P0'DrainedStress Path3V : 1H

Port of Anchorage, Alaska

Cavity Expansion Critical State Model for Evaluating OCR in Clays from Piezocone Tests

where M = 6 sinf/(3-sinf) and L = 1 Cs/Cc 0.8qcfsub qT

Cambridge University q-p' spaceP' = (s1' + s2' + s3')/3q = (s1 - s3)CSL

Yield SurfaceOriginal Cam ClayModified Cam ClayPc'Bounding SurfaceCap ModelAnisotropic Yield SurfaceP = (s1 + s2 + s3)/3q = (s1 - s3)Mc = 6sinf/(3-sinf)fctn(K0NC)Y3 = Limit StateYield Surfacee0svoK0G0Y2CSLsp Y1OCNCCambridge University q-p' spaceP' = (s1' + s2' + s3')/3q = (s1 - s3)fctn(K0NC)Y3 = Limit StateYield SurfaceCSLsp

Ko UnloadingApparentMcMIT q-p' spaceP' = (s1' + s3')q = (s1 - s3)fctn(K0NC)Yield Surfacesp

OCNatural ClaysDiaz-Rodriguez, Leroueil, and Aleman (1992, JGE)Diaz-Rodriguez, Leroueil, & Aleman (ASCE Journal Geotechnical Engineering July 1992)

Yield Surfaces of Natural ClaysFriction Angle of Clean Quartz Sands

(Bolton, 1986 Geotechnique)State Parameter for Sands, y(Been & Jefferies, 1985; Jefferies & Been 2006) log p'voidratioep' = (s1'+s2'+s3')VCLCSLl10l10p0'y = e0 - ecslDry of Critical (Dilative)Wet of Critical (Contractive)e0ecslState Parameter for Sands, y(Simplified Critical State Soil Mechanics) log p'voidratioep' = (s1'+s2'+s3')VCLCSLl10l10p0'y = e0 - ecsly = (Cs - Cc )log[ cos f' OCR ] Du = (1 - cos f' OCRL ]svo' e0 ecslthen CSL = OCR = 2/cosf'Georgia TechState Parameter for Sands, y(Been, Crooks, & Jefferies, 1988) log OCRp = log2L + Y/(k-l)where OCRp = R = overconsolidation ratio in Cambridge q-p' space, L = 1-k/l, l = Cc/ln(10) = compression index, and k Cs/ln(10) = swelling index

MIT Constitutive ModelsWhittle et al. 1994: JGE Vol. 120 (1) "Model prediction of anisotropic behavior of Boston Blue Clay"MIT-E3: 15 parameters for clayPestana & Whittle (1999) "Formulation of unified constitutive model for clays and sands" Intl. J. for Analytical & Numerical Methods in Geomechanics, Vol. 23MIT S1: 13 parameters for clayMIT S1: 14 parameters for sand

MIT E-3 Constitutive ModelWhittle (2005)MIT S-1 Constitutive Model

Pestana and Whittle (1999)MIT S-1 Constitutive Model

Predictions forBerlin Sands(Whittle, 2005)Critical state soil mechanicsInitial state: e0, svo, and OCR = sp/svoSoil constants: f, Cc, and Cs Link between Consolidation and Shear TestsCSSM addresses: NC and OC behaviorUndrained vs. Drained (and other paths)Positive vs. negative porewater pressuresVolume changes (contractive vs. dilative)su/svo = sinf OCRL where L = 1-Cs/Cc

Yield surface represents 3-d preconsolidation State parameter: y = e0 - ecslSimplified Critical State Soil MechanicsLog sv'Effective stress sv'Effective stress sv'Shear stress tVoid Ratio, eVoid Ratio, eNCNCCCCSLCSLCSLCSsp'sp'OCFour 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'eNCconsolidationswellingeOC1234YieldSurfacedilative contractive+Du-DusCSsptmax = su NCtmax = stanfsu OCtmax = c+stanfc'

q-p' Stress Space 11.6 CRITICAL STATE SOIL MECHANICS (Generalized Case) NC Specimen OC Specimen CRITICAL STATE SOIL MECHANICS 25 Feb 2013 Total Stress Analysis for UU Tests svO' =80 f ' =30 OCR =1 OCR =010001000 eo =1 sin f' =0.50 svO' =700 sISO' =0 Cc =0.5 Mc =1.20 su/svo' =0.25 su/svo' =0 Cs =0.1 L =0.80500 Du/svo' =0.57 Du kPa =0 r = 2.3 tanf ' =0.58288.6494243845 su (kPa)=174.99 su (kPa)=0 sp' =400 cos f' =0.87 Du (kPa)=396.88

VCL sv' eo VCL eo Cs sv' CSL t t gs2.74694705621.730.871.411.59003.05216339581.710.861.571.76100.33.3912926621.690.861.741.96200.73.76810295781.660.851.942.18301.14.18678106421.640.852.152.42401.54.65197896021.620.842.392.69502.25.16886551141.590.842.652.98602.85.74318390151.570.832.953.32703.56.38131544611.550.833.283.68804.27.09035049571.530.833.644.09854.87.87816721751.500.824.054.55905.58.75351913051.480.824.505.059569.72613236721.460.815.005.61100710.80681374141.430.815.556.241057.812.00757082381.410.806.176.93110.7913.34174535971.390.806.857.701081014.82416151081.370.797.618.5616.47129056761.340.798.469.5118.3014339641.320.789.4010.5720.33492662661.300.7810.4411.7422.59436291851.270.7811.6013.0425.10484768721.250.7712.8914.4927.8942752081.230.7714.3316.1027.890.7027.8942752080.7330.993639121.210.7615.9217.8930.990.6930.993639120.7234.43737681.180.7617.6919.8834.440.6934.43737680.7238.2637521.160.7519.6522.0938.260.6838.2637520.710142.515281.140.7521.8424.5442.520.6842.515280.711000147.23921.110.7424.2627.2747.240.6747.23920.7052.4881.090.7426.9630.3052.490.6752.4880.7058.321.070.7329.9533.6758.320.6658.320.7064.81.050.7333.2837.4164.800.6664.80.69721.020.7236.9841.5772.000.65720.69801.000.7241.0946.1880.000.65800.6882.35645283790.990.7242.3047.54123.530.63102.94556604730.67 CRITICAL STATE SOIL MECHANICS (Generalized Case)91.50716981980.970.7147.0052.83137.260.63114.38396227480.67 NC Specimen0101.67463313320.950.7152.2258.70152.510.62127.09329141640.66 svO' =80 f ' =30 OCR =1112.97181459240.930.7158.0265.22169.460.62141.21476824050.66 eo =1 sin f' =0.4999666003 svO' =700125.5242384360.900.7064.4772.46188.290.61156.9052980450.65 Cc =0.5 Mc =1.1999038103 su/svo' =0.2499833002139.471376040.880.7071.6380.52209.210.61174.339220050.65 Cs =0.1 L =0.8 Du/svo' =0.5669776569154.96819560.860.6979.5989.46232.450.60193.71024450.64 r = 2.3 tanf ' =0.5772988488 su (kPa)=174.9883101196172.1868840.830.6988.4399.40258.280.60215.2336050.64 sp' =400 cos f' =0.8660446862 Du (kPa)=396.8843598204191.318760.810.6898.26110.45286.980.59239.148450.63212.57640.790.68109.18122.72318.860.59265.72050.63236.1960.760.67121.31136.36354.290.59295.2450.62262.440.740.67134.79151.51393.660.58328.050.620.55291.60.720.66149.76168.34437.400.58364.50.6228.993240.700.66166.40187.04486.000.574050.613600.670.66184.89207.83540.000.574500.614000.650.65205.44230.92600.000.565000.604500.62231.12259.785000.60256.80288.65Void ratio e = 1.405500.58282.48317.51 Speciific GravityGs=2.656000.56308.15346.38 Sat Unit Wt g/cc =1.696500.55333.83375.24 Gamma Sat kN/m3=16.887000.53359.51404.11 Depth below ML m =14.607500.51385.19432.97 zeroed at Total sv kPa =246.388000.50410.87461.84 Mudline Hydrostatic uo kPa146.008500.49436.55490.70 Effective svo' kPa =100.389000.47462.23519.579500.46487.91548.4312000.41616.31692.76

References

REFERENCES

Dafalias, Y.F., Herrmann, L.R. and DeNatale, J.S. (1980). Description of natural clay behavior by a simple bounding surface plasticity formulation. Limit Equilibrium, Plasticity, and Generalized Stress-Strain in Geotechnical Engineering, Proceedings NSF-NSERC Workshop at McGill University Ed. By R.K. Yong and H-Y. Ko, published by ASCE New York (Reston, VA), pp. 711-745.

Wood, D. M. (1990). Soil Behavior and Critical State Soil Mechanics, Cambridge University Press, UK, 462 pages.

Wroth, C.P. (1984). The interpretation of in-situ soil tests. Rankine Lecture. Geotechnique 34 (4), pp. 449-489.

Wroth, C.P and Houlsby, G.T. (1985). Soil mechanics: property characterization & analysis procedures. Proceedings, 11th International Conference on Soil Mechanics & Foundation Engineering ICSMFE, Vol. 1, San Francisco, pp. 1-56.

ANSWERS 4406 Hmk 1 - CSSM - Spring 2013 STUDENT NAME PROBLEMANSWER

1.11.21.31.41.51.61.71.81.922.12.22.32.42.5