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1、2006 Critical-State Soil Mechanics For Dummies Paul W. Mayne, PhD, P.E. Civil 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 1960, ASCE); Henkel (1960, ASCE Boulder)
2、 Henkel 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) f = 26. 1 o P ea k P ea k P ea k CSSM for Dummies Log sv Effect
3、ive stress sv Sh ear str ess t Void Ra tio, e NC CC tanf CSL Effective stress sv Void Ra tio, e NC CSL CSSM Premise: “All stress paths fail on the critical state line (CSL)” CSL f c=0 CSSM for Dummies Log sv Effective stress sv Shear stre ss t Void Ratio, e Void Ratio, e NC NC CC tanf CSL CSL CSL ST
4、RESS PATH No.1 NC Drained Soil Given: e0, svo, NC (OCR=1) e0 svo svo Drained Path: Du = 0 tmax = c + s tanf ef De Volume Change is Contractive: evol = De/(1+e0) 0 svo e0 svo Effective stress sv Critical state soil mechanics Initial state: e0, svo, and OCR = sp/svo Soil constants: f, Cc, and Cs (L =
5、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. Equivalent Stress
6、 Concept Log sv Stress sv Shear stre ss 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 svo e0 Effective stress sv Void Ratio, e sp sp se se su svf ep De = Cs log(sp/svo) De = Cc log(se/sp)
7、De at se suOC = 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: su/svo = sinf OCRL where L = (1-
8、Cs/Cc) se = svo OCR1-Cs/Cc Undrained Shear Strength from CSSM 0 .0 0 .1 0 .2 0 .3 0 .4 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 sin f s u / s vo NC (D SS) AG S P las t ic Am h er st Ari ak e Bo o t legg er Bo t h ke n n ar Bo sto n Blue Co w d en Hack ensac k Ja mes Bay M ex ico Cit y O n soy P
9、o r t o To lle P o r t smo u t h Riss a S an F r ancisc o S ilty Ho locene W r o t h ( 19 84 ) s u / s vo N C ( DS S ) = sin f 0 .0 0 .1 0 .2 0 .3 0 .4 0 10 20 30 40 50 60 70 80 90 100 Undrained Shear Strength from CSSM 0 .1 1 10 1 10 100 O verconso lid atio n Ra tio , OC R DSS Undraine d Stre ng th
10、 , s u / s vo A mh er st CVV C A t chaf ala y a Bang kok Bo o t legg er Co v e Bo sto n Blue Co w d en Dra mm en Hack ensac k Haga L o w er Ch ek Lo k M aine M cM anu s P ar ia P o r t land P o r t smo u t h S ilty Ho locene Up p er Ch ek Lo k 20 30 40 f = 40 o 20 o 30 o s u / s vo = sin f OC R L No
11、t e : L = 1 - C s /C c 0 .8 Intac t Cla y s Porewater Pressure Response from CSSM -6 -5 -4 -3 -2 -1 0 1 1 10 100 O verconso lid atio n Ra tio , OC R Normali zed Po rewate r Pre ssure, D u / s vo A mh er st CVV C A t chaf ala y a Bang kok Bo o t legg er Co v e Bo sto n Blue Co w d en Dra mm en Hack e
12、nsac k Haga L o w er Ch ek Lo k M aine M cM anu s P ar ia P o r t land P o r t smo u t h S ilty Ho locene Up p er Ch ek Lo k 20 30 40 L = 0. 9 0. 8 0. 7 Intac t f = 20 o 30 o 40 o D u s / s vo = 1 - cos f O C R L Yield Surfaces Log sv Normal stress sv Shear stre ss t Void Ratio, e NC NC CSL CSL CSL
13、OC Normal stress sv Void Ratio, e sp sp OC Yield surface represents 3-d preconsolidation Quasi-elastic behavior within the yield surface Port of Anchorage, Alaska 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 E f f e c t i v e S t r e s s
14、 , p * = ( s 1 + s 2 + s 3 ) / ( 3 s p ) D e v i a t o r i c S t r e s s = q * = ( s 1 - s 3 )/ s p Bo ot le g g e r C ov e C la y M c = ( q / p ) f = 1 . 1 0 M c = 6 s i n f / ( 3 - s i n f ) f = 2 7 . 7 o 0 . 1 1 10 1 10 100 O v e r c o n s o l i d a ti o n R a ti o , O C R Str e n g th R a ti o ,
15、 s u / s vo D S S D a t a C I U C D a t a M C C P r e d C I U C M C C P r e d D S S C r i t i c a l S t a t e S o i l M e c h a n i c s ( M o d i f i e d C a m C l a y ) f = 2 7 . 7 o L = 0 . 7 5 Cavity Expansion Critical State Model for Evaluating OCR in Clays from Piezocone Tests O C R M q uT b vo
16、 = - 2 1 1 95 1 1 . / s L where M = 6 sinf/(3-sinf) and L = 1 Cs/Cc 0.8 qc fs ub qT 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 O v e r c o n s o l i d a t i o n R a t i o , O C R D e p t h ( m e t e r s ) C P T U C R S I L O e d RF Bo t h k e n n ar, U K Critical state soil mechanics Initial state: e
17、0, 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 = sinf OCRL where L = 1-Cs/Cc Yield surface represents 3-d preconsolidation