饱和砂土局部变形带模拟的有限元数值实现

Finite element numerical implementation for simulation of deformation band in saturated sand

基于有限变形理论,推导了Newton-Raphson迭代算法在k+1步增量表达的矩阵形式,实现了饱和砂土变形局部化的有限元数值计算,得到了饱和砂土发生局部化变形的准则。基于Galerkin方法,得到了位移场和应力场的空间离散化矩阵方程;由土体局部变形带的连续性条件,引入第1切线算子,推导出了砂土等颗粒状媒介发生局部化变形的必要条件。基于此核心算法,编制了有限元计算程序,模拟了饱和砂土在不排水条件下平面压缩过程中剪切带的形成与发展;通过比较分析,研究了有限元网格粗细对于土体局部变形带的影响,结果表明,网格粗细的病态依赖只是微小的,它只与变形条带的宽度有关,对于土体所表现出来的其他力学特性没有影响。

The matrix form of Newton-Raphson incremental solution at the k＋1 iteration is updated based on the finite deformation theory, leading the finite element implementation to the simulation of the deformation band in the fluid-saturated sand, and the criteria for localized deformation under drained and undrained conditions are derived and utilized to detect instabilities. The spatial discretization of the displacements and the pressure fields are furnished by the classical Galerkin method; according to the continuity of tractions across the deformation band, the necessary condition for localization is obtained by introducing the first tangent operator. Based on the algebraic manipulation above, a finite element numerical computational program is coded by FORTRAN; and then numerical simulations on saturated sand under undrained condition is performed to study the onset and development of the shear band. Also, the mesh sensitivity is studied; and the results show that the pathological mesh dependence is mild, which is related to the apparent width of the shear band, while the different meshes display the same overall mechanical behavior.