Abstract：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.
