竖向分布荷载作用在半无限体内部任意区域的黏弹性解研究

Viscoelastic solutions of half space subjected to arbitrary distributed loads

在软土地基基础的沉降过程中,施加于半无限土体内部的荷载并不是单纯的集中荷载,受荷区域也不完全是形状规则的矩形或圆形,为此本文考虑半无限土体的黏弹性,基于Mindlin理论解,利用解析解辅以数值的近似积分法,对矩形或圆形受荷区域作关于子域的等积变换,得到了竖向分布荷载作用于半无限土体时应力与位移的封闭积分解,运用弹性-黏弹性相应原理,通过对弹性解进行Laplace变换与逆变换,给出了分布荷载作用于半无限体内部任意区域的应力与位移分量的黏弹性解答。

In order to solve the settlement process of soft soil foundation,the load applied to the space soil is not a simple concentrated load,and the loading region is not a rectangular or circular problem of the shape rule.In this paper,the viscoelasticity of the foundation soil is considered,based on the classical solution of Mindlin,the analytical solution is utilized to assist the approximate integral method of numerical value.The rectangular or circular loaded region is the equal product transformation of the subdomain,and the concentrated product decomposition of the stress and displacement is obtained when the vertical and horizontal distribution loads act on the half space.Then the corresponding elastic viscoelastic principle is used to carry out the Laplace transformation and inverse transformation of the elastic solution,and the distributed load is given in the half space of the body.The viscoelastic solutions of the stress and displacement components of the point are given.