饱和土体瞬态响应有限元分析

Finite Element Analysis of the Transient Response of Saturated Soils

给出基于Biot多孔介质理论分析饱和土体在动载荷作用下瞬态响应的有限元公式,数值计算部分采用本文有限元法分别计算一维饱和土柱在两种不同类型动载荷作用下的瞬态响应,并将数值计算结果与文献中的解析解进行比较,二者结果十分吻合,从而验证本文方法的可行性。

An investigation of the dynamic response of saturated soil plays an important role in classical application fields such as soil mechanics,hydrology,ocean engineering and so on.Furthermore,it is essential to the development of emerging sciences and technologies,such as the mechanical characteristic of skin and soft tissue in biology.Therefore,it is important to provide appropriate theoretical analyses and numerical simulation methods.In addition,the transient response of saturated soil is also essential to the understanding of deformation and the pore water pressures generated by ground motion.This response is a key factor in the dynamic analysis of building foundations,offshore structures,and wave propagation in geological medium during blasts or earthquakes.Saturated soil is one that exhibits a solid faction and a porous space filled with a viscous fluid on a microscopic scale.Two approaches are possible for addressing the description of such a soil.The first approach is at the microscopic scale.Here,the＂solid elastic＂and＂viscous fluid＂phases each constitute distinct geometric domains.A geometric point is found at a given instant in one of these two clearly identifiable phases.The second approach considers the problem from the macroscopic level.The elementary volume is considered to be the superposition of two material particles with different kinematics occupying the same geometric points at the same instant.Thus,the saturated soil is considered as a two-phase continuum;the skeleton particle is constituted by the solid matrix and connected porous space,and the fluid particle is formed from the fluid saturating this connected porous space.There are many theories describing the characteristics of saturated soils,e.g.,Biot Theory,porous media theory,hybrid mixture theory,and so on.Most of the transient response studies for saturated soils are solved by numerical methods such as the finite element method（FEM）and finite difference method（FDM）.Compared to the FDM,the most attractive feature of the FEM is its ability to handle nonlinear material and complicated geometries（and boundaries）with relative ease.In this investigation,based on Biot Theory,a mathematical model of a two-dimensional saturated elastic soil is established,and a time-domain FEM for analyzing the transient dynamic response of saturated soil under cyclic loading is presented.To verify the efficiency and accuracy of the proposed method,a one-dimensional saturated soil column subject to two different surface loadings was simulated.The first numerical example models the transient response of the saturated soil column due to sine wave loading.The second case is for the dynamic response of the soil column subject to step loading.For both numerical examples,the solid displacement history and pore pressure history are presented and compared with analytical solutions.Good agreement between the computed results and analytical solutions show the efficiency and accuracy of the proposed method.