求解饱和半空间上弹性圆板固结沉降的积分方程

Integral Equations for Solving the Consolidation Settlement of an Elastic Circular Plate Resting on a Poroelastic Half Space

本文采用解析方法分析了弹性圆板在饱和半空间上的固结沉降。考虑弹性圆板与饱和半空间的接触面上无摩擦力,且饱和半空间表面为全部透水的。运用Biot固结理论和积分方程技术,在Laplace变换域上建立了弹性圆板固结沉降的对偶积分方程,并化此对偶积分方程为第二类Fredholm积分方程。通过对其核函数的有效数值积分得到第二类Fredholm积分方程的解,再利用Laplace反演技术获得弹性板在时间域中的固结沉降值。文末给出弹性板中心点固结沉降的固结度的数值算例。

The paper analytically examined the consolidation settlement of an elastic cirular plate resting on a poroelas-tic half space that is saturated with fluid. The contact between the elastic circular plate and the poroelastic half space is assumed to be smooth. The drainage condition at the surface of the poroelastic half space is considered as completely drained. By using Biot' s theory for soil consolidation and the technique of integral transform, the paper develops a governing dual integral equation. This governing integral equation is further reduced to a standard Fredholm integral equation of the second kind in the Laplace transform domain, whose solution is then computed via efficient algorithm for the evalution of the associated kernel function. The consolidation displacement of the elastic circular plate in time domain is obtained by a numerical method for the inversion of Laplace transform. The numerical results for the degree of consolidation displacement at center of the elastic circular plate are given in the end of the paper.