粘性土的弹粘塑性模型及其固结分析应用（讲稿）一种可考虑排水板、多层土和多级荷载的软黏土固結沉降的通用簡單計算方法 A General Simple Method for Calculating Consolidation Settlements of Layered Clayey Soils with Vertical Drains under Staged Loadings

武汉理工大学土木工程与建筑学院：5天课程课程题目：ElasticVisco-PlasticModelsforClayeySoilsandApplicationsinConsolidationAnalysis粘性土的弹粘塑性模型及其固结分析应用Lecture4:from9:55amto12:55pmon1June2021AGeneral Simple Method forCalculatingConsolidation Settlements ofLayered Clayey Soilswith Vertical Drains under Staged Loadings一种可考虑排水板、多层土和多级荷载的软黏土固结沉降的通用簡罩計算方法Jian-HuaYIN（殷建华）ChairProfessorofSoilMechanicsDepartment of Civil and Environmental Engineering (CEE)TheHong Kong Polytechnic University (PolyU),Hong Kong, ChinaDEPARTMENTOFTHEHONGKONGCIVILANDENVIRONMENTALENGINEERINGPOLYTECHNICUNIVERSITY土木及環境工程學系香港理工大學

1 Jian-Hua YIN (殷建华) Chair Professor of Soil Mechanics Department of Civil and Environmental Engineering (CEE) The Hong Kong Polytechnic University (PolyU), Hong Kong, China A General Simple Method for Calculating Consolidation Settlements of Layered Clayey Soils with Vertical Drains under Staged Loadings 一种可考虑排水板、多层土和多级荷载的软黏土固結 沉降的通用簡單計算方法 武汉理工大学土木工程与建筑学院: 5 天课程 课程题目：Elastic Visco-Plastic Models for Clayey Soils and Applications in Consolidation Analysis 粘性土的弹粘塑性模型及其固结分析应用 Lecture 4: from 9:55 am to 12:55 pm on 1 June 2021

Contents1.Introduction2.Formulation ofa General SimpleMethod for CalculatingConsolidation Settlements ofMulti-layered Soils ExhibitingCreep under Staged Loading3. Verifications with Fully Coupled Finite Element Method andMeasured dataCaseI:Consolidation Settlements of a ClayLayerwith OCR-lor1.5Case Il:Consolidation Settlements of Layered Soils with Vertical Drains underStagedLoading-Unloading-ReloadingCase Ill:Consolidation Settlements of TestEmbankment onLayered Soils withVertical Drains under Staged Loading4.Conclusions and Remarks

2 Contents 1. Introduction 2. Formulation of a General Simple Method for Calculating Consolidation Settlements of Multi-layered Soils Exhibiting Creep under Staged Loading 3. Verifications with Fully Coupled Finite Element Method and Measured data 4. Conclusions and Remarks Case I: Consolidation Settlements of a Clay Layer with OCR=1 or 1.5 Case II: Consolidation Settlements of Layered Soils with Vertical Drains under Staged Loading-Unloading-Reloading Case III: Consolidation Settlements of Test Embankment on Layered Soils with Vertical Drains under Staged Loading

l.IntroductionManyreal projects:Multi-layersof soils,Vertical drains areused for someor all soil layers,andVertical surcharge is applied in multi-staged ramp loading,includingun-loadingandreal loading

3 1. Introduction Many real projects: • Multi-layers of soils, • Vertical drains are used for some or all soil layers, and • Vertical surcharge is applied in multi-staged ramp loading, including un-loading and real loading

SecondRunwaySettlement (updated)98.1299.1200.1201.1202.1209.1204.1205.1206.1208.1209.1210.12*11.1212.12'07.126: The second runway opened on 2 August 2007, but2withthe originally planned terminal portionpostponed. A new terminal building opened in late 2012610Post-construction settlement1214The second airport island (KIX 2)ThefrstaiportistandKiX116aDto18maverogHolocene Clay LayerMa12Sand laveMa1tTreated sandcompactionpilesMa11LMa10cand180mUpper PleistoceneMasavenaverageDoc5NogroundimprovementMas0omaweragMa7LDwBcPleeneClay layerMa4-3Sand layer

Second Runway Settlement (updated) Treated sand compaction piles No ground improvement • The second runway opened on 2 August 2007, but with the originally planned terminal portion postponed • A new terminal building opened in late 2012 Post-construction settlement 9

2.Formulation of a General Simple Method forCalculating Consolidation Settlements ofMulti-layeredSoils ExhibitingCreepunder StagedLoading2.1 Formulation of a general simplified Hypothesis B method2.2CalculationofS2.3 Calculations of U,and U2.4 Calculations of Sereep , Sepf , Secre.dj and Sereepj10

10 2. Formulation of a General Simple Method for Calculating Consolidation Settlements of Multi￾layered Soils Exhibiting Creep under Staged Loading 2.1 Formulation of a general simplified Hypothesis B method 2.2 Calculation of Sf 2.3 Calculations of Uj and U 2.4 Calculations of Screep , Screep,fj , Screep,dj and Screepj

2.1 Formulation of a general simplified Hypothesis B methodFor layered soft soils with or without vertical drains underuniform surcharge g(t):Smry:the“primary consolidation settlements,Zus,+Zs.U,; the average degree of consolidationStotalB=S+Scm=of j-layer,j=lJ=lS, : the total final settlements ofj-layer,E[aus..LIre,f+(1-αUp)Sere.a]j=lS:thetotalcreepsettlementsofj-layerfor all tztEop,lab (t2teoP,Jeua for Sorep,a)Soap/ : the total final creep settlementsTop boundaryg(t)ofj-layer,Sowpg:thetotal“delayedcreepsettlementsHilofj-layer,H20≤α,β≤1:empiricalparametersdg=2rgwithk,forvertical drainHα=O:Hypothesis A Methodd, =2r, withk,for smear zoneHd,=2r, withi, for equivalent cyinder α=1:OldSimplifiedHypothesisBMethod(Yin2011)α=0.8,β=0:NewSimplifiedHypothesisBHu!n(Yin and Feng 2017; Feng and Yin 2017)Hn-:Bottom boundary11

2.1 Formulation of a general simplified Hypothesis B method 11 1 1 , , 1 1 , , [ (1 ) ] ( ) jn jn totalB primary creep j fj creepj j j jn jn fj j creep fj j creep dj j j EOP lab EOP field creep dj S S S US S U S US U S for all t t t t for S                         For layered soft soils with or without vertical drains under uniform surcharge q(t): primary S Uj fj S creepj S creep ji , S creep dj , S : the “primary consolidation settlements, : the average degree of consolidation of j-layer, : the total final settlements of j-layer, : the total creep settlements of j-layer, : the total final creep settlements of j-layer, : the total “delayed creep” settlements of j-layer, 0 : 1: ( 2011) 0.8, 0 : ( 2017; 2017) Hypothesis A Method Old Simplified Hypothesis B Method Yin New Simplified Hypothesis B Yin and Feng Feng and Yin         0, 1     : empirical parameters

S, =m,Ao.H2.2 Calculation of S, for the j-layerS,/H=m,Ao,=8Ifcoefficientofvolumecompressibilitym,isknown as constant:m,=6. /A0.In most cases, m, is unknown and should not be considered as constant.S, should be calculated using the &,-logo,' curve, as shown in the figure.C, if o,≤op,e.g.point 1 to26-01+e。Logarithmic stressa6.=functionCa, if o, >op, e.g. point I to 48og1+e。1+e00C32logo.(Om.E): compression index for normalI+e.261(0a.eg)consolidation line (NCL)C3(0g.6g):compressionindexofunloadingolidation2I+e。 / reloading line (OCL)lineC,/(I+e,)(.2..a)Assimed instantloadingpaths(i)framPointItoPoint2and(il)fromPointI toPoint4(.,c.):Pre-consolidationpressureandthecorrespondingstraine。:initial voidratio(0.....)4(04.6.4)S15The above parameters are determined fromThioding/roding ineC,/+)(.)standard oedometertest withduration of24Normal consolidaffon line C, /(1 +e,) (at t)07hours.12

2.2 Calculation of Sfj for the j-layer 12 If coefficient of volume compressibility mv is known as constant: ' ' ' / / f vz f vz z vz z Sm H SHm m            In most cases, mv is unknown and should not be considered as constant. Sf should be calculated using the εz-logσz' curve, as shown in the figure. 1 c o C e : compression index for normal consolidation line (NCL), : compression index of unloading / reloading line (OCL) 1 r o C e ' (,) zp zp  : Pre-consolidation pressure and the corresponding strain oe : initial void ratio The above parameters are determined from standard oedometer test with duration of 24 hours. ' ' ' ' ' ' ' ' ' ' log( ) , if , e.g. point 1 to 2 1 log( ) log( ) , if , e.g. point 1 to 4 1 1 r z zo z zp o zo z r z zp c zo z zp o zo o zp C e C C e e                         Logarithmic stress function

2.2 Calculation of S, for the j-layerProblem of traditional logarithmic stress function:logo.2Stresscannotbezero!(.0.E.)61(0Ea)lim log(-e.g.=-803(0eg)solidafion0,→04200limec,/(+e,)(..8,2)Assumedinstant loadingpaths() from Point Ito Point2and(i)fromPoint ItoPoint4However,initial stressatsurfaceornear surface of seabed soilsorsoilground could be zero.6(0..E.s)4(0..:4)6.5Unlding/reloading limeC,/(1+) (g.es)Toovercomethisproblem,YinproposedaNormal consolidaion line C, /(1+e) (at t)nonlinearlogarithmic stressfunctionby?introducing a unit stressSOunitcan be 0.001~1 kPa.0 umin1 for elastic compression (along the OCL)O unit2 for elastic-plastic compression (along the NCL)13

2.2 Calculation of Sfj for the j-layer 13 Problem of traditional logarithmic stress function: ' ' ' 0 lim log( ) z z zo       To overcome this problem, Yin proposed a nonlinear logarithmic stress function by introducing a unit stress . '  unit ' can be 0.001 1 kPa.  unit  Stress cannot be zero! e.g. However, initial stress at surface or near surface of seabed soils or soil ground could be zero. '  unit1 for elastic compression (along the OCL) '  unit 2 for elastic-plastic compression (along the NCL)

2.2 Calculation of S, for the j-layerlogoG......61(oaea)(i)Loadingfrompoint1topoint23(og.Eg)ontolidation+2Iine C, /(I+e,)(02.6,Assumed instantloadingpaths02+0mitl:)HSf,1-2 =61-2H :10g(i)fromPointItoPoint2and1+e。+0O-1(ii)fromPoint ItoPoint 4mitl(u) Loading from point 1topoint 4b(O.s.E.s)C.foumitl$4(0.4.64)6.HSf.-4 = 8.J-4H15Uhloading/reloading hineC,/(+e)(s.E)1+e。+0-1tmitC0.4 +0m2)HNormal consolidatfion line C, /(1+e,) (at ta)1+eO+umit2(ii) Loading from point 3 to point 4(v)Reloadingfrompoint6topoint5CO+omit2)Hf 3-4 = 8. 3-umitl)HSf.6-5 = 8:,6-sH :1+e.=3+0Omi21+e+Oitl(iv)Unloadingfrompoint4topoint6(vi)Reloading from point 6 to point7+00-7+0mitl)Hmi)H1.4-6=6:.4-6HSf.6-7 = 6:.6-7H :0010g1+e。1+e。0.6+0+umitumitl14

2.2 Calculation of Sfj for the j-layer 14 (i) Loading from point 1 to point 2 ' ' 2 1 ,1 2 ,1 2 ' ' 1 1 log( ) 1 r z unit f z o z unit C SH H e             (ii) Loading from point 1 to point 4 ' ' 1 ,1 4 ,1 4 ' ' 1 1 ' ' 4 2 ' ' 2 log( ) 1 log( ) 1 zp unit r f z o z unit c z unit o zp unit C SH H e C H e                     (iii) Loading from point 3 to point 4 ' ' 4 2 ,3 4 ,3 4 ' ' 3 2 log( ) 1 c z unit f z o z unit C SH H e             (iv) Unloading from point 4 to point 6 ' ' 6 1 ,4 6 ,4 6 ' ' 4 1 log( ) 1 r z unit f z o z unit C SH H e             (v) Reloading from point 6 to point 5 ' ' 5 1 ,6 5 ,6 5 ' ' 6 1 log( ) 1 r z unit f z o z unit C SH H e             (vi) Reloading from point 6 to point 7 ' ' 7 1 ,6 7 ,6 7 ' ' 6 1 log( ) 1 c z unit f z o z unit C SH H e            

2.2Calculationof S,forthej-layerAnother problem:the initial stresses and stress increments in a clayey soillayerarenotuniform0:1.0hMethod1:atz=ha=Z,Dividingthesoil layerinto sub-layersSuggestedsub-layerthickness:<0.5m0-.0hMethod 2:Integrationofstrainwithdepthforalayerz-h11=0100p.0Assumptions:h2logo,C.,C。 are constant(GE0)61(..e)-o,-p are linearly changed with z3(0.cg)latoExample+ineC,/(+e,)(0...5)Asstmed inistanr loading pathsLoadingfrompoint"1"topoint“4"(i)fromPoint I toPoint2and(i) fron Point I to Point 4Z16000-1,0)-1.0HZ6#0O0O(o......)p.0p.HT=p,0H6.$4(0.4.8.)15tloading/reloadnglineC,/a+e)(os.e)Z1a0=4,0)a0-=4.04.HNormal consolidafion line C, / (1 +e,) (at g)H15

2.2 Calculation of Sfj for the j-layer 15 Another problem: the initial stresses and stress increments in a clayey soil layer are not uniform. Method 1: Dividing the soil layer into sub-layers Suggested sub-layer thickness: <0.5m Method 2: Integration of strain with depth for a layer Assumptions: are constant are linearly changed with z , C Cc c ' ' 0 ,  z zp  Example: Loading from point “1” to point “4” ,0 , ,0 ( ) '' ' ' z1 z1 z1 H z1 z σσ σ σ H   ,0 , ,0 ( ) '' ' ' zp zp zp H zp z σσ σ σ H   4,0 4, 4,0 ( ) '' ' ' z z zH z z σσ σ σ H  