Vertical stress under vertical pressure by extended Mindlin's equation

Abstract

Analytical elasticity solutions provide an efficient means of performing a first approximate analysis in foundation engineering. One of the well-known basic solutions is Mindlin's solution to the stress and displacement induced by a point load at an embedment depth in a half-space. This solution is more superior but less widely used than Boussinesq's solution for a point load at only the boundary of half-space. To promote the applications of Mindlin's solution, its vertical stress equation is integrated to obtain an explicit formula for calculating vertical stresses at any arbitrary point. The stresses are induced by uniformly and triangularly distributed vertical pressure, which is exerted over a rectangular area in the interior of a homogeneous, isotropic, elastic half-space. It shows that the vertical stress decreases as the embedment depth of loaded area increases.