Stochastic Analysis of Ground‐Water Flow in Semiconfined Aquifer

Abstract

A stochastic analysis for two‐dimensional steady‐state ground‐water flow through a homogeneous random shallow semiconfined aquifer is presented. The flow problems through a semiconfined aquifer with a random leakage factor but subject to deterministic boundary conditions and domain recharge are investigated by perturbation techniques associated with the boundary element method. The leakage factor is related to the physical properties of both the main aquifer and the leaky layer. The hierarchical equations based on the expansion of the potential into the perturbation series are derived and the boundary element method is applied for obtaining the solutions of these equations. The results from the present study are compared with those obtained using the Monte Carlo simulation method as well as the analytical solutions. The perturbation‐based boundary element method does not require the specification of the probability density function of the leakage factor, but only its mean, variance (or standard deviation), and/or higher‐order moments. Therefore, the perturbation‐based boundary element method is particularly useful when the statistical information is incomplete. The results of the present study are quite comparable with those of Monte Carlo simulations, but perturbation‐based boundary element method needs much less computational effort.