2006Critical-State Soil MechanicsFor DummiesPaul W. Mayne, PhD, P.E.Civil and (2) shear stress-vs. normal stress (t-sv) from direct shear box or simple shearing.q Herein, only the bare essence of CSSM concepts are presented, sufficient to describe strength 1960, ASCE); Henkel (1960, ASCE Boulder) Henkel Burland (1968); Wood (1990).q In basic form: 3 material constants (f, Cc, Cs) plus initial state (e 0, svo, OCR)q 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)q Undrained is just one specific stress pathq 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 0.5 0.6 0.7 0.8 0.9 1.0 1 10 100 1000 10000 Effective Vertical Stress, svo (kPa) Vo id R at io, e Cc = 0.38 Cr = 0.04 svo=300 kPasp=900 kPaOverconsolidation Ratio, OCR = 3Cs = swelling index (= Cr)cv = coef. of consolidationD = constrained modulusCae = coef. secondary compressionk hydraulic conductivity v Direct Shear Test Resultssvt Direct Shear Box (DSB) svtDirect Simple Shear (DSS)t d tgs CSSM for DummiesLog sv Effective stress svShear stress tVoid Ratio, e NCCC tanfCSLEffective stress svVoid Ratio, e NCCSLCSSM Premise:“All stress paths fail on the critical state line (CSL)” CSL fc=0 CSSM for DummiesLog sv Effective stress svShear stress tVoid Ratio, e Void Ratio, eNC NCCC tanfCSLCSLCSLSTRESS PATH No.1NC Drained Soil Given: e 0, svo, NC (OCR=1) e0 svo svoDrained Path: Du = 0 tmax = c + s tanfef DeVolume Change is Contractive: evol = De/(1+e0) 0 svo e0 s vo 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): q Undrained (evol = 0): +Du and tmax = su = cuq Drained (Du = 0) and contractive (decrease evol) For OC soil: q Undrained (evol = 0): -Du and tmax = su = cuq Drained (Du = 0) and dilative (Increase evol) Theres more ! Semi-drained, Partly undrained, Cyclic. Equivalent Stress ConceptLog sv Stress svShear stress tVoid Rat io, e NC NCCC tanf CSLCSLCSLCS OC1. OC State (eo, svo, sp) s vo2. Project OC state to NC line for equivalent stress, se3. se = svo OCR1-Cs/Ccsvo e0 Effective stress svVoid Ratio, esp spse s esusvf epDe = Cs log(sp/svo)De = C c log(se/sp) De at sesuOC = suNC 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 = sin f Equivalent stress: Normalized Undrained Shear Strength:s u/svo = sinf OCRL where L = (1-Cs/Cc)se = svo OCR1-Cs/Cc Undrained Shear Strength from CSSM Undrained Shear Strength from CSSM Porewater Pressure Response from CSSM Yield SurfacesLog sv Normal stress svShear stress tVoid Rat io, e NC NC CSLCSLCSL OC Normal stress svVoid Ratio, esp spOCq Yield surface represents 3-d preconsolidation q Quasi-elastic behavior within the yield surface Port of Anchorage, Alaska Cavity Expansion Critical State Model for Evaluating OCR in Clays from Piezocone Tests OCR M q uT bvo= - 2 1195 1 1. /s Lwhere M = 6 sinf/(3-sinf) and L = 1 C s/Cc 0.8qcfsub 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: q NC and OC behaviorq Undrained vs. Drained (and other paths) q Positive vs. negative porewater pressuresq Volume changes (contractive vs. dilative)q su/svo = sinf OCRL where L = 1-Cs/Ccq Yield surface represents 3-d preconsolidation