中文摘要：

用二维座逾渗模型描述裂隙岩体的渗透问题,将岩体划分为众多单元网格,每个单元赋与一定的渗透概率,提出一种解析方法计算裂隙岩体的渗透概率。建立多单元网格渗透概率递推矩阵的概念,并根据相邻列单元渗透递推关系,推导出3×n及4×n型单元网格的渗透概率递推矩阵;应用渗透概率递推矩阵可以计算任意列数单元网格的渗透概率。基于渗透概率递推矩阵,推导出3×3及4×4型单元网格的渗透概率解析表达式,并应用重整化群方法分别计算出基于2×2,3×3及4×4型基元的临界渗透概率,并与Monte Carlo法结果进行比较,分析重整化群化误差产生的原因。

英文摘要：

　The 2D site percolation model is used for characterizing the permeability problem of fractured rock,in which the rock mass is divided into a network of many elements,each element assigned a definite permeable probability.An analytical method is proposed for calculating the permeable probability of fractured rock mass.The concept of recurrence matrix of permeable probability is introduced;and the recurrence matrices of permeable probability are derived for the networks of 3×n and 4×n elements,with which the permeable probabilities of arbitrary columns of elements can be determined.Based on the recurrence matrix of permeable probability,the analytical formulas of permeable probability are derived for networks of 3×3 and 4×4 elements.By using the renormalization group method,the critical permeable probabilities are calculated for networks of 2×2,3×3 and 4× 4 elements respectively in comparison with the results obtained by the Monte Carlo method.Finally,the errors inherently in the renormalization group method are investigated.