Stochastic analysis of steady seepage underneath a water-retaining wall through highly anisotropic porous media

Steady seepage is determined by a head drop upstream/downstream of a water retaining wall. Due to its erratic variations, hydraulic log-conductivity Y = ln K is modelled as a stationary random space function (RSF). We deal with a highly anisotropic porous formation, i.e. an axisymmetric medium where the horizontal correlation integral scale of Y is much larger than the vertical one. The goal of computing the resulting flow field within a stochastic framework is complicated by non-uniformity of the mean flow. Simple (closed-form) expressions for the correlation functions of the flow variables as well as the mean head are derived. We use these results to quantify the impact of spatial variability of Y upon the probability that the exit volumetric flow rate downstream of the wall is greater than that obtained by regarding the formation as homogeneous (with constant hydraulic conductivity). In particular, we show that the spatial variability of Y may lead to predictions (and consequently to design choices) which significantly differ from those achieved by regarding the porous formation as homogeneous.