Prediction of fluid flow through rocks subjected to increasing non-hydrostatic stress is of fundamental importance in various fields of science and engineering such as hydraulic fracture control, the exploration and production of hydrocarbons, environmental and hydro-geological studies, the utilization of hydrothermal energy, underground storage and disposal of highlevel nuclear waste. Fluid migrates mainly through a flow network formed by (micro) cracks in brittle rocks, and this flow network is completely altered when both nucleation and growth of cracks (damage growth) occur along with accumulation of inelastic strain under increasing non-hydrostatic stress. In this paper, an analytical coupled fluid flow and solid deformation model is applied to simulate the transport process of fluid flow in brittle rocks and investigate the stress dependence of permeability. Specifically, the mathematical model incorporates the physics of fluid flow in brittle rock, the physics of rock deformation, and the cross-couplings between them. The causative flow processes and the effect of rock physical and filtration parameters such as intrinsic permeability and porosity on fluid flow in brittle porous rocks are also parameterized and investigated.
Rock permeability is important in civil and geohydraulic engineering, the mining and petroleum industries, and in environmental and engineering geology. Disastrous water in-rush and coal and gas outbursts into excavations pose a potential significant risk to mining and civil engineering projects. Fluid flow in rock strata also influences the regular construction and daily service of geoengineering projects. In the last several decades hydrologist and mining engineers have become increasingly involved in the study of the permeability evolution in underground rocks and reservoirs [1–19]. Brace et al. carried out experimental measurements of the permeability of granite under high pressure. They concluded that the permeability of granite decreases with increasing effective confining pressure. Somerton  studied the effect of stress on permeability of coal. Patsouls and Gripps  reached a similar conclusion regarding the permeability of Yorkshire chalk of UK. Gangi  derived phenomenological models to determine the variation in permeability with the confining pressure of whole and porous rocks. Walsh  studied the effect of both the pore pressure and confining pressure on fracture permeability and proposed the cube root of the fluid permeability. Durucan and Edwards studied the effects of stress and fracturing on permeability of coal. Li et al. [8, 9] investigated the permeability in Yinzhuang sandstone with respect to a complete stress–strain path, and found that the permeability of tested sandstone is a function of strain and stress. In addition, the ratio of pore pressure to confining pressure gives only an obvious influence on the value of highest permeability. Zhu [10, 11] investigated the relationship between permeability and pore structure in a wide range of geological materials, including sedimentary rocks and found that the connections between permeability and porosity can best be described by two different power law relationships.