Influence of correlation structure of porous media random parameters on unsaturated flow

On the basis of the van Genuchten Mualem constitutive relationship,a stochastic numerical model for unsaturated flow is developed.The saturated hydraulic conductivity and the pore size distribution parameter are assumed to be the random space functions with the log normal distributions. We decompose them through the Karhunen Loeve expansion and express the pressure head as polynomial chaos expansion. We derive a series of partial different ial equations in which the dependent variables are the deterministic coefficients of the head expansion and then solve these equations with the method off inite differences.The effect of perfectly correlated and uncorrelated case between two random space functions on flow quantities is studied by the proposed stochastic model.It is shown that the mean heads of the two cases are the same,but the head standard deviations of the perfectly correlated case are smaller than those of the uncorrelated case.