Study On The Modified Equation Of Single Fracture Seepage With Roughness Angle

Study on the problem of rock fracture seepage has important scientific significance and engineering practical value. The influence of roughness in the fractures on seepage characteristics cannot be ignored. Aiming at some deficiencies of study on the rough fracture seepage, this paper proposes a fracture seepage equation modified with roughness angle. Then the equation is compared by numerical simulation and verified by previous seepage test. Finally, the equation is applied to the seepage model of fractured rock, and the influence of roughness on seepage is revised. The main research contents are as follows.The roughness parameters of 10 typical JRC profile curves are analyzed, and the effective inclination angle namely roughness angle α is proposed as the key parameter to study the hydraulic characteristics of rough fracture. The software Fluent based on Navier-Stokes equation is used to simulate two dimensional seepage field of fracture with jagged and JRC profile shapes. After analyzing about 300 calculating cases with different roughness, aperture and pressure gradient, it is found that the flow coefficient of 2D fracture seepage and the roughness angle have a relationship as C=cos4α when the Reynolds number is less than 10 in the laminar flow regime. When the Reynolds number is more than 10 in the transition flow regime, the flow coefficient is related to α, deflection angle β and Re. The laminar seepage equation of 2D rough fractured can also be deduced by using local cubic law(LCL).A laminar seepage equation of fracture with 3D roughness surface is derived based on fracture microelement by local cubic law. The equation can consider the influence on seepage by the roughness angles in both two directions on the fracture surface, and shows the anisotropy effect of roughness angles on seepage. According to the relationship between roughness angle and other roughness parameters, seepage equations containing various kinds of rough variables are obtained, which expands the application range.More than 100 kinds of 3D numerical models of roughness fractures are established, including four shapes of triangular sawtooth, sine curve, JRC profile and fractal random fractal surface. The calculated result of numerical simulation is compared with Cubic Law, the seepage equation modified by only one roughness angle, and the seepage equation modified by two roughness angles in the two directions on 3D rough surface. It turns out that the equation with two roughness angles is closest to the simulated result, with an average error of only 0.79%, and the accuracy of the equation is proved.The equation is validated by using the fracture seepage experimental data by Geng Keqin. In the tensile fracture seepage test, the equation predicts the relationship between the seepage flow and the aperture in two kinds of artificial and natural rough fracture. In the compressed fracture seepage test, the results verify the new seepage equation, the theory of fracture deformation, and the new coupling relation between seepage and stress, which indicates that the equation can also be suitable for the coupling of seepage and stress.Finally, the seepage equation with roughness angles is applied to the analysis of flow in crossing fractures, the calculation of fracture network seepage model and the seepage and stress coupling model. All the calculated results are changed obviously when the roughness is taken into account. Therefore the impact of fracture roughness cannot be ignored. Furthermore, the application examples indicate that the seepage equation of rough fracture has significant practicality.