复杂加载条件下饱和砂土的应力应变关系及数值模拟

The laboratory tests and disaster site survey are showed that it is hard to predict the deformation and strength characteristics of sands under complex loading conditions. Compared with clay, the influence of density and pressure dependence for sands on stress-strain relationship is more obviously than that of clay. Sands can be regarded as a state-related material. The state parameter χ is constructed by distance relationship among the normal compression line the current state point located and the densest compression line, loosest compression line in e-(p/pa)ξ space. The dilatancy equation is revised by χ and the density and pressure dependence are reflected. The change law between the plastic deviatoric strain, plastic volume strain and yielding surface is researched by investigating the test results of cyclic loading condition and a variety of different stress path testing. The evolutionary relationship of stress-induced anisotropy is obtained and the stress-induced anisotropy parameter ζ is introduced into the yielding surface equation to reflect the cyclic loading behavior. The characteristic state stress ratio and the failure state stress ratio are expressed as the exponential functions of the state parameter χ and are introduced into the UH parameter to reflect the positive and negative dilatancy, strain hardening and softening behaviors. A practical critical state constitutive model is established to reflect the stress-strain relationship under static and dynamic loading conditions for sands. The Transformed Stress method is adopted to generalize the model. The generalized model is embedded into a commercial FEM software and to serve the engineering practice.

室内试验及灾害现场调查表明：砂土在复杂加载条件下会表现出难以预估的变形与强度特性。与黏土相比，砂土的密度与压力依存性对于应力应变关系的影响更为显著，即砂土可视为一种状态相关材料。通过当前状态点在e-(p/pa)ξ空间中正常压缩线与最密压缩线、最松压缩线之间的距离关系来构造状态参量χ，并用之来修正砂土的剪胀方程，反映密度与压力依存性。通过循环加载路径及多种不同应力路径试验，研究塑性偏应变、塑性体应变与砂土屈服面之间的变化规律，得出能反映应力诱导各向异性的演化关系式，将应力诱导各向异性参数ζ引入到屈服面方程中，使其能反映循环加载特性。将特征状态应力比、破坏应力比表示为状态量的指数函数，并引入到统一硬化参数中用来反映剪缩、剪胀、应变硬化、软化等力学特性，建立能反映静、动荷载下砂土应力应变关系的实用临界状态本构模型，并采用变换应力方法实现三维化。将三维模型嵌入到商用有限元软件中，使其服务工程实际。

饱和砂土在复杂加载条件下同样表现出了复杂的应力应变关系特点，岩土材料的变形以及强度最终会直接决定工程结构的工作状态，因而得到明确的影响饱和砂土在复杂加载作用下的剪缩、剪胀特性以及强度规律，对于预测以及定量评估工程结构的服役工作状态，都具有直接的参考价值以及理论意义。主要在以下内容取得了相应成果，(1)岩土材料具有摩擦性，摩擦性决定了砂土等岩土材料是一种应力比确定的破坏材料，然而，各种不同岩土介质之间的摩擦性与粘聚性多少会存在一些差异，如何表述这种差异性，成为度量岩土材料破坏形态以及破坏规律是否准确合理的核心关键点，采用了扣除有效粘聚力，使用有效摩擦角的概念，将具有一定粘聚力的岩土材料的破坏规律分别表述，在偏平面上，所建议的a准则能够有效的描述从SMP准则到广义Mises准则之间所有的强度曲线，在子午面上采用幂函数能够考虑岩土材料强度准则的静水压力效应，压剪耦合屈服特性也可以描述，并建议了基于a准则的变换应力公式。(2)将e-p空间中当前状态点距离CSL线的距离作为状态参量，在循环加载中将应力比参量R作为状态参量，使所建议模型既能够考虑单调加载下的压力与密度依存性，也能有效的描述循环加载下剪切模量的衰减特性、刚度衰化性质、强度减小特性，在不排水约束作用下，则会产生往返活动性现象。(3)针对纯主应力轴旋转作用下导致的变形规律，采用威布尔函数建立了剪应力与正应力之比和剪应变的双曲线关系，通过与Rowe剪胀方程联立，得到二维应力条件下的增量模型，利用砂土单元的三维受力特性，将上述二维特性扩展为三维增量本构模型，WB模型。并分析了物理空间中主应力轴旋转的过程，建立了纯主应力轴旋转角与摩尔圆中剪正应力比反正切值的关系，利用WB模型模拟了主应力轴循环旋转作用下的岩土材料的变形。以上所取得的成果可望用于对饱和砂土材料的复杂加载模拟中。

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