Stochastic finite-element analysis of soil layers with random interface

This paper addresses the problem of a medium with two layers separated by an interface randomly fluctuating in space. The medium is subjected to an in-plane strain held simulating the effect of a surface foundation. The second-moments characteristics of the interface spatial fluctuations are used to formulate the problem. The Karhunen-Loeve and the polynomial chaos expansions are utilized to transform the problem into :a computationally tractable form, thus resulting in a system of linear algebraic equations to solve. The difficulty in this problem stems from the geometric nature of the randomness, resulting in a stiffness matrix that is nonlinear in the randomness. This leads to a nonlinear stochastic problem, the solution of which is accomplished by relying on the polynomial chaos representation of stochastic processes.