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The fluid flow in fractured rock was determined by the aperture of fractures, which is influenced by the complex variation and wide distribution of in situ stress conditions. While extensive studies focused on qualitative analysis of the experimental phenomena, much less was the quantitative mechanism of permeability under confining pressure in theory, which is frequently required in rock engineering projects. In this work, we proposed a new negative exponential model to quantitatively describe the flow rate Q, seepage pressure Ps, hydraulic aperture eh, and permeability k under different confining pressures Pc at a low flow rate. Hydromechanical tests with two experimental modes (constant Q test mode and constant Ps test mode) were conducted on cutting shale samples, and test data were collected. Furthermore, regression analyses were performed on the test data, based on the proposed model. Results suggest that the negative exponential model quantitatively predicts the seepage properties (Q, Ps, eh, and k) under the changeable in situ stress conditions in the application of low flow velocities in natural fractures, such as the development of oil/gas reservoirs and controlling of solute transport in the main aquifer. The proposed model assists in understanding and applying the behavior of the fluid flow in fractured rock under in situ stress conditions at low flow velocity.

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