Elastic Solutions for Arbitrarily Shaped Foundations

The response of an elastic foundation, such as settlement, can generally be obtained by integrating the product of the influence factor and the distributed load over the entire foundation. The exact evaluation of this double integral is usually very involved, especially for arbitrarily shaped foundations. In the paper, a very simple method is developed for obtaining the elastic responses of soils and rocks using the computer package MathCAD and Green's theorem in calculus. Initially, the double integral is transformed into a line integral by invoking Green's theorem. The line integral can then be evaluated very conveniently using the built-in procedure in MathCAD for numerical integration. The proposed method can be applied to an arbitrarily loaded area with an arbitrary stress distribution and can be programmed very easily using MathCAD. Examples will be given to illustrate the use and accuracy of the proposed method.