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以岩石的绝对渗透率符合对数正态分布,及其协方差函数为离散指数型的假设为基础,建立了硬岩介质中圆形洞室渗水的二维随机模型。采用Karhunen-Loeve展开、随机摄动法对随机偏微分方程进行求解,并用蒙特卡罗法对计算结果进行了验证,进一步说明该方法的正确性及高效性。计算结果说明:(1)岩石非均质性对洞室壁左上方与右上方两点的水饱和度标准差影响最大;(2)渗透率均值与水饱和度均值及标准差反相关;渗透率对数标准差与水饱和度标准差正相关,与水饱和度均值不相关。
Based on the assumption that the rock’s absolute permeability complies with the logarithmic normal distribution and the covariance function is discrete exponential type, a two-dimensional stochastic model of water seepage in circular cavern in hard rock is established. Using Karhunen-Loeve expansion method, the stochastic perturbation method is used to solve the stochastic partial differential equation. The Monte Carlo method is used to verify the calculation results, further illustrating the correctness and high efficiency of the method. The calculation results show that: (1) Rock heterogeneity has the strongest influence on standard deviation of water saturation at the upper left and upper right of two points on the wall of the cave; (2) Mean of permeability is inversely related to mean and standard deviation of water saturation; The log-log standard deviation is positively correlated with the standard deviation of water saturation and not correlated with the water-saturation mean.