剑桥模型

nullCam-clay model (剑桥模型)Cam-clay model (剑桥模型)孙德安 2011.12.28null实际土 理想土 理想土与实际土 压硬性 剪胀性 摩擦性应力历史依存性 应力路径依存性 软化特性 各向异性 结构性 蠕变特性 颗粒破碎特性 温度特性 ……亚基本特性 基本特性 正常固结黏土，松砂 超固结粘土，密砂null压硬性 高岭土等向压缩试验结果(Roscoe et al., 1963)压硬性的数学描述： 最简单的--饱和正常固结--重塑粘土的等向压缩试验： 一维或等向压缩过程中所表现出的应力应变关系 土材料的体积模量： 正常固结粘土的剪切试验正常固结粘土的剪切试验剪胀性 应力剪胀方程null*性擦摩Weald 粘土的三轴剪切强度试验结果 (Roscoe et al., 1958)对正常固结土摩擦性的描述： 约束压力 剪切强度 重塑苏州软黏土的剪切特性Introduction to Cam-clay Model (剑桥模型)Introduction to Cam-clay Model (剑桥模型)Cam-clay model was developed by Roscoe et al at Cambridge University in the 1960s Being a conceptual elastoplastic model that can represent mechanical behavior of normally consolidated clay Original (1963)(原始) Modified (1968)(修正) Theory of plasticityTheory of plasticityPlastic potential(塑性势) Yield function (屈服函数) Hardening parameter(硬化参数) Strain hardening rule (硬化法则)Key pointsKey pointsRelation between stress ratio and strain increment ratio Determination of the volumetric strain in isotropic stress using a linear e-log p relation and its extension to general stress on the basis of Henkel’s water content contours. Original Cam-clay model (原始剑桥模型)Original Cam-clay model (原始剑桥模型)a)  Principal direction of the plastic strain increment Assumption that principal directions of stresses and plastic strain increments are coaxial b) Determinations of the plastic potential and yield function Plastic potential defines direction of plastic strain increment. Yield function specifies whether plastic strain increments occur when subjected to a new loading increment c) Determinations of hardening parameter and strain hardening rule The strain hardening rule affects magnitude of plastic strain incrementPrincipal directions of plastic strain increment and stressPrincipal directions of plastic strain increment and stressStress variables(应力变量) Stress variables(应力变量) 等效应力/应力强度Strain increment variables (应变增量不变量)Strain increment variables (应变增量不变量)等效塑性应变nullDetermining plastic potential(塑性势) 1 Normality condition(正交法则 )nullq, dεdpp, dεvp0g(p,q)＝0(dεvp,dεdp)　Plastic potential and strain increment vectornullDetermining plastic potential(塑性势) 2 Direction of plastic strain increment vectors(塑性应变方向)Relation between stress ratio and plastic strain increment ratio Stress-dilatancy equation(应力剪胀方程)nullDetermining plastic potential(塑性势)+ (C: an integral constant) nullnullAssociated flow rule f=g （关联流动法则） Letting p＝px when q=0 results in C＝Mlnpx nullMechanical meaning of yield loci （屈服线）nullHardening parameter and strain-hardening ruleVoid ratio or volumetric strain硬化参数nullStrain-hardening rule （应变硬化法则）nullnullDetermination of Strain nullElastic strainPoisson’s ratio is often assumed to be 0 or 0.3 or 1/3 nullPlastic strain; nullnullnullnullnullnullAn example for predicting stress-strain relation using Cam-clay modelCalculate stress-strain relation and the effective stress path (a) Drained triaxial compression test =196kPa (b) Undrained triaxial compression under =196kPa Model parameters : Cc/(1+e0)=11.7%, Cs/(1+e0)=1.6%, =34ﾟ , =0.3 nullnullnullnullPrediction of stress-strain relation and stress path under undrained condition 　nullnullnullnullModified Cam-clay model实线- 修正 虚线- 原始