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

2.3 Calculation of U, for j-layer and UCalculation of m,m,:valume compressibilityIn many consolidation analyses, m, is neededC, =k, /(m,yw)e.g.c, =k, / (yum,)AS., which can be calculated by S, in 2.2.mAgS.1-e.g.Loading:m,,I-4H(o.4-0.)Unloading: m,4-6 =H(o,-0.6)m, is always positive.21

2.3 Calculation of Uj for j-layer and U 21 Calculation of mvj   ,1 4 ,1 4 1 f v ' ' z4 z S m H σ σ     In many consolidation analyses, mv is needed. mv : valume compressibility ' z v z m      e.g. Loading: Unloading:   ,4 6 ,4 6 6 f v ' ' z4 z S m H σ σ     mv is always positive. /( ) v v vw e.g. ckm   /( ) r r wv ck m   , which can be calculated by Sf in 2.2

2.3 Calculation of U, for j-layer and UCalculationof u.,U,and Ua) Terzaghi's solution for 1-D consolidation of a single layer under instantaneous loading4TForU,<0.6:T,="u3,UA元T,+0.0850.933ForU,≥0.6:T,=-0.944log(1-U,)-0.085,U,=1-101.50d2T,d?We assumed that t = teopfela when U,=98%. = t eop.feldC,c,b) Spectral Method for general cases with multiple layers, vertical drains and ramploading byWalkerand Indraratna (2009), Walker et al. (2009)auaam.ououkm.ndT1azm,atm,atnnk2mcNwheredTH2Hymyum,run = k, / (r?μ) is related to radial permeability k,, equivalent radius r of cylinder cell, and μu is a dimensionless drain geometry/smear zoneparameter.22

2.3 Calculation of Uj for j-layer and U 22 Calculation of , and ej u U j U a) Terzaghi’s solution for 1-D consolidation of a single layer under instantaneous loading 2 0.085 0.933 4 0.6 : , 4 0.6 : 0.944log(1 ) 0.085, 1 10 v v v v vv T vv v v T For U T U U For U T U U               We assumed that t = tEOP,field when Uv=98%. 2 2 , v 1.50 EOP field v v T d d t c c   b) Spectral Method for general cases with multiple layers, vertical drains and ramp loading by Walker and Indraratna (2009), Walker et al. (2009). 2 2 v vv v rv r v vv v m kk m u uu dT u dT dT w m t Zk Z k Z m t                                        2 2 2 ,d ,d , = , r v v vrv e wv wv k z c k TT cZ r H m mH     where    2 /( ) r e   k r  is related to radial permeability , equivalent radius kr re of cylinder cell, and   is a dimensionless drain geometry/smear zone parameter

2.3Calculation of U,for j-layerand UCalculation of u,,U,and Ub) Spectral Method for general cases with multiple layers, vertical drains and ramploading by Walker and Indraratna (2009),Walker et al. (2009).Hansbo(1981)considered smearzoneand wellresistance:n?52s2k.1s4-1(lnn_3k,ins52 + 1) + 元≥(21 - 2)un?44n4nkkn-12sqwWalker and Indraratna (2006) considered parabolic smear zone permeability:x(s-1)ss(s-1) /x(x-1),(Vx+Vx-13nh4s(s2-2ks+x)(Vx-yx-V2(s2-2ks+x)WalkerandIndraratna(2009)providedanExcel spreadsheetcalculationprogramimplemented with VBA program named SPECCON to enable convenient adoption ofthis methodSoil parametersAo.(t),wH,k,ks,ra,r,rorspacingam...Inputs:Vertical drainsue,(t)Output:23

2.3 Calculation of Uj for j-layer and U 23 Calculation of , and ej u U j U b) Spectral Method for general cases with multiple layers, vertical drains and ramp loading by Walker and Indraratna (2009), Walker et al. (2009). Walker and Indraratna (2009) provided an Excel spreadsheet calculation program implemented with VBA program named SPECCON to enable convenient adoption of this method. 2 22 4 2 2 2 2 22 2 3 11 1 (ln ln ) (1 ) ( 1) (2 ) (1 ) 1 4 1 4 14 rr r ss w nn s s s kk k s s zlz n s k n n kn n q n                 Hansbo (1981) considered smear zone and well resistance: Walker and Indraratna (2006) considered parabolic smear zone permeability:          2 2 2 3 1 1 1 1 =ln ln ln 4 2 22 1 n s s s s s ss ss                              Inputs: Output: u t ej   ' ( ), , , , , , , , , or spacing z vj j v r s d s e  t tm H k k k r r r a Soil parameters Vertical drains