饱和土体固结3D比例边界有限元法分析

基于饱和土体Biot固结理论,考虑土体体力与表面作用力,结合饱和土体中土骨架动力平衡方程与孔隙流体的连续方程,在计算域内采用Galerkin加权余量法,推导了3D无限、有限域全耦合饱和土体固结的比例边界有限元方程.理论推导表明:与单相弹性土体不同的是,由于孔隙水的存在,饱和土体固结比例边界有限元法方程中不仅有位移、应力矩阵,而且还存在孔隙水压力的影响耦合矩阵;该方程不仅能够满足无限域无穷远边界辐射条件,而且在径向(与饱和土体-结构接触面垂直方向,指向无限远)上具有严格的精确性,环向上(与饱和土体-结构接触面平行方向)具有有限元单元无限收敛的准确性.

Modelling of Saturated Soil Dynamic Coupled Consolidation Problems Using Three-Dimensional Scaled Boundary Finite Element Method

Abstract： Based on the Biot’s dynamic coupled consolidation theory, the scaled boundary finite element method was developed to correctly model the dynamic unbounded far field boundary of three dimensional (3D) fully saturated soil in this paper. Body forces and surface tractions were considered in the derivation. The concept of similarity, the compatibility equation, Biot’s coupled consolidation equations, and the Galerkin’s weighted residual method were used to derive the formulation for the governing equations. The main difference from the single phase version was the presence of pore water pressures as additional parameters to be solved, in addition to the displacements, strain and stress which were incorporated into the static stiffness matrices by producing fully coupled matrices. Solving the resulting equations yielded a boundary condition satisfying the far field radiation condition exactly. The computed solutions were exact in a radial direction (perpendicular to the boundary and pointing towards infinity), while converging to the exact solution in the finite element sense in the circumferential direction parallel to the soil structure boundary interface