Statistics of free surface flow through stochastic earth dam

Even though soil is a highly variable material, the analysis of flow through earth dams typically proceeds deterministically and results can sometimes be quite misleading. In fact it is well known that soil permeability varies randomly from point to point in space and an improved earth dam model should incorporate this variability. In this paper the soil permeability in an earth dam of variable geometry is viewed as a weakly stationary spatially random field following a lognormal distribution with prescribed mean, variance, and spatial correlation structure. The mean and variance of the total flow rate through the dam and free surface drawdown are estimated using Monte Carlo simulations. A simplified empirical approach to the prediction of the mean and variance of the flow rate is presented to allow these quantities to be approximated easily and without resorting to simulation.