硬岩介质中洞室渗水的随机数值模拟

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。

A Stochastic Numerical Simulation of Seepage around Cavity in the Hard Rock

A 2-D stochastic model of seepage around circular cavity in hard rock was given based on scenarios that the log-transformed intrinsic permeability of porous media is treated as normally distributed stochastic variables with a separable exponential covariance.The stochastic partial differential equations are solved by Karhunen-Loeve expansion and perturbation method.The results were compared with those derived from Monte Carlo simulations,and good agreement was obtained.Simulation results show that:(1) the standard deviation of saturation on left upper and right upper of cavity are most sensitive to heterogeneous of porous media;(2) the mean permeability is inversely correlated with mean saturation and standard deviation of saturation;the standard deviation of log-transformed permeability is positively correlated with standard deviation of saturation,and is not correlated with mean saturation.