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1、2006,Critical-State Soil MechanicsFor Dummies,Paul W.Mayne,PhD,P.E.Civil&Environmental EngineeringGeorgia Institute of TechnologyAtlanta,GA 30332-0355,PROLOGUE,Critical-state soil mechanics is an effective stress framework describing mechanical soil responseIn its simplest form here,we consider only
2、 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 de
3、scribe strength&compressibility response.,Critical State Soil Mechanics(CSSM),Experimental evidence provided by Hvorslev(1936;1960,ASCE);Henkel(1960,ASCE Boulder)Henkel Wood(1990).In basic form:3 material constants(f,Cc,Cs)plus initial state(e0,svo,OCR)Constitutive Models,include:Original Cam-Clay,M
4、odified 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,Overconsolidation Ratio,OCR=3,Cs
5、=swelling index(=Cr)cv=coef.of consolidationD=constrained modulusCae=coef.secondary compressionk hydraulic conductivity,sv,Direct Shear Test Results,sv,Direct Shear Box(DSB),CSSM for Dummies,Log sv,Effective stress sv,Shear stress t,Void Ratio,e,NC,CC,CSSM Premise:“All stress paths fail on the criti
6、cal state line(CSL)”,f,c=0,CSSM for Dummies,Log sv,Effective stress sv,Shear stress t,Void Ratio,e,Void Ratio,e,NC,NC,CC,tanf,CSL,CSL,STRESS PATH No.1NC Drained Soil,Given:e0,svo,NC(OCR=1),e0,svo,svo,Drained Path:Du=0,tmax=c+s tanf,Volume Change is Contractive:evol=De/(1+e0)0,Effective stress sv,c=0
7、,CSSM for Dummies,Log sv,Effective stress sv,Shear stress t,Void Ratio,e,Void Ratio,e,NC,NC,CC,tanf,CSL,CSL,STRESS PATH No.2NC Undrained Soil,Given:e0,svo,NC(OCR=1),Undrained Path:DV/V0=0,+Du=Positive Excess Porewater Pressures,Du,tmax=cu=su,Effective stress sv,CSSM for Dummies,Log sv,Effective stre
8、ss sv,Shear stress t,Void Ratio,e,NC,NC,CC,tanf,CSL,CSL,Note:All NC undrainedstress paths are parallelto each other,thus:su/svo=constant,Effective stress sv,DSS:su/svoNC=sinf,Void Ratio,e,CSSM for Dummies,Log sv,Effective stress sv,Effective stress sv,Shear stress t,Void Ratio,e,Void Ratio,e,NC,NC,C
9、C,tanf,CSL,CSL,CSL,CS,sp,sp,OC,Overconsolidated States:e0,svo,and OCR=sp/svowhere sp=svmax=Pc=preconsolidation stress;OCR=overconsolidation ratio,CSSM for Dummies,Log sv,Effective stress sv,Shear stress t,Void Ratio,e,NC,NC,CC,tanf,CSL,CSL,CSL,CS,OC,Stress Path No.3Undrained OC Soil:e0,svo,and OCR,s
10、vo,Stress Path:DV/V0=0,Negative Excess Du,Effective stress sv,Void Ratio,e,CSSM for Dummies,Log sv,Effective stress sv,Shear stress t,Void Ratio,e,Void Ratio,e,NC,NC,CC,tanf,CSL,CSL,CSL,CS,OC,Stress Path No.4Drained OC Soil:e0,svo,and OCR,Stress Path:Du=0,Dilatancy:DV/V0 0,Effective stress sv,Critic
11、al state soil mechanics,Initial 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
12、-drained,Partly undrained,Cyclic.,Equivalent Stress Concept,Log sv,Stress sv,Shear stress t,Void Ratio,e,NC,NC,CC,tanf,CSL,CSL,CSL,CS,OC,1.OC State(eo,svo,sp),svo,2.Project OC state to NC line for equivalent stress,se,3.se=svo OCR1-Cs/Cc,Effective stress sv,Void Ratio,e,sp,sp,se,su,De=Cs log(sp/svo)
13、De=Cc log(se/sp),at sesuOC=suNC,Critical state soil mechanics,Previously: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
14、 OCR1-Cs/Cc,Undrained Shear Strength from CSSM,Undrained Shear Strength from CSSM,Porewater Pressure Response from CSSM,Yield Surfaces,Log sv,Normal stress sv,Shear stress t,Void Ratio,e,NC,NC,CSL,CSL,CSL,OC,Normal stress sv,Void Ratio,e,sp,sp,OC,Yield surface represents 3-d preconsolidation Quasi-e
15、lastic behavior within the yield surface,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 0.8,Critical state soil mechanics,Initial state:e0,svo,and OCR=sp/svoSoil constants:f,Cc,and Cs(L=1-Cs/Cc)Using effective stresses,CSSM 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/CcYield surface represents 3-d preconsolidation,
