Uncertainty of One-Dimensional Ground-Water Flow in Strongly Heterogeneous Formations

Abstract

The writers have formulated quasi-analytical nonlinear solutions to investigate the uncertainty of one-dimensional ground water flow in heterogeneous formulations in which the standard deviation of the log hydraulic conductivity σ\Dln(\iK)\N > 1. The writers have studied three cases for fixed boundary conditions: a semibounded domain, a free domain, and a both-side-bounded domain. The writers have also studied the random boundary conditions for the bounded domain. The writers have obtained variances and covariances of head for semibounded and free domains, and have calculated variances of head for the both-side-bounded domain. Monte Carlo simulations are generated to obtain the head variances and are used to verify the quasi-analytical solutions. The ergodicity assumption is proven to be rigorously correct in a semibounded or a free domain but not correct in a both-side-bounded domain by using a linear autocorrelation function.