Stresses Induced by Surficial and Deep Loading in Elastic Medium

Closed solutions are obtained for the vertical normal stress at any point within an elastic half-space for two loading conditions. In the first case, the stress is caused by a linearly distributed load acting on a superficial polygon. In the second, the stress is produced by uniform distributed load acting on a polygon in the interior of the half-space. The expressions are obtained by integration over a triangle of well-known solutions for stresses induced by concentrated loads: the Boussinesq and Mindlin formulas in the first and second cases respectively. Since any polygonal area can be broken into several triangles, these integrations readily lead to solutions valid for polygonal surfaces with the same type of loading. These expressions can be included in stress estimation computer programs commonly used in soil mechanics to evaluate settlement of superficial and deep foundations instead of approximate numerical methods. Notwithstanding the performance of modern computers, the expressions are considered to be useful from both research and practice point of view, since they lead to important computer-time savings and improved accuracy.