Analysis of tangential contact boundary value problems using potential functions

This paper presents an analysis technique of high-order contact potential problems and its application to an elastic settlement analysis of a shallow foundation system subjected to a combined traction boundary condition. Closed-form solutions of potential functions are derived for an elastic half-space subjected to bilinear tangential traction boundary conditions over rectangular surface regions. Using the principle of superposition, the present solutions provide a means to form an approximate and continuous solution of elastic contact problems with higher-order tangential boundary conditions. As an application example, an elastic settlement analysis of a rigid footing founded on a dense granular soil is performed under a tangential traction boundary condition prescribed in an analogy with the stress equilibrium states of static sandpiles. A generalized solution approach to combined normal and tangential traction boundary value problems is discussed in the context of foundation engineering.