中文摘要：

基于van Genuchten-Mualem非饱和水分特征模型，建立了非饱和流运动的随机数值模型。将饱和水力传导度和孔隙大小分布参数视为服从对数正态分布的随机场，用Karhunen-Loeve展开分解，水头表示为混沌多项式展开。通过摄动方法得到一系列关于水头展开的偏微分方程，并用有限差分法进行求解。应用本文的模型分析了两随机场在统计不相关和完全相关模式下对水流随机分析的影响，结果表明两种模式下的水头均值相同，完全相关模式下的水头标准差较不相关模式下的明显偏小。

英文摘要：

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 differential equations in which the dependent variables are the deterministic coefficients of the head expansion and then solve these equations with the method of finite 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 uneorrelated case.