Boundary element formulations for stochastic flow in semi-confined aquifers with random boundary conditions

A boundary element technique is developed to solve steady state flow in a shallow aquifer with random boundary conditions. The aquifer is bounded by a leaky aquifer above, and an impervious layer below. The flow problem is formulated in terms of a stochastic boundary value problem involving a Helmholtz equation. The moment of unknown random hydraulic head is obtained by application of an expectation operation to the boundary element formulations. The influence of the spatial structure of the boundary conditions on the hydraulic head statistics is discussed. The significance of the presence of the leaky layer on the hydraulic head statistics is also investigated.