A study of the permeability of fractures with variable attitude in rock mass subjected to natural crustal stresses

In order to investigate the influence of fracture attitude variation on the permeability of fractures in deep rock mass under natural crustal stresses, based on the permeability law of a single fracture obeying the law of negative exponential change, the theoretical formula of coefficient of permeability of fractures with variable attitude subjected to 3D stresses is proposed. The Lagrange multiplier method is applied to analyze the change of variable attitude on fracture permeability, and influence factors and sensibility of fracture permeability with or without infillings are also analyzed. Statistic law of crustal stress in Chinese mainland is taken as an example, and the variable laws of the permeability of fractures in rock mass with depth and fracture attitude are analyzed. The results show that (1) the permeability of fractures in rock mass is obviously influenced by the attitude of fractures. For shallow rock mass, under the condition of the maximum principle stress distribution in the horizontal direction, the permeability of fractures gradually decreases with the increasing dip angle of fractures; but with the increasing depth, when the depth is more than 200 m and the strike of fracture is roughly consistent with the direction of large or medium principal stress, the permeability of fractures can increase with the increasing dip angle of fractures, especially the strike of fractures perpendicular to the direction of the minimum principle stress. For deep rock mass, the permeability of fracture is very weak, and the impact of fracture attitude change on its permeability is very slight. (2) For fractures with infillings, the change of elastic modulus ratio of rock block to infillings and Poisson’s ratio of infillings have little effect on fracture permeability. The conclusions can be used for reference for further investigating the variation of deep rock permeability characteristics.