Modeling of three-dimensional single rough rock fissures: A study on flow rate and fractal parameters using the Weierstrass-Mandelbrot function

Abstract

The irregular asperities of rock fissures crucially affect the fluid flow through rock masses. In this paper, the Weierstrass-Mandelbrot (W-M) function was employed to model the irregular fissure surfaces. Based on the above fissure model, we numerically analyzed the effects of the fractal parameters on fluid flow by solving the Reynolds equation with the local Cubic Law approach. The classical Cubic Law was then modified in regard to two fitted correction functions of D and G, which indicated the actual fracture aperture and the actual hydraulic gradient of W-M surfaces and were both found to be S-shaped. The outcomes reveal a high correlation between the flow rate and the fractal parameters. Then, the similarity of W-M surfaces to real fissure surfaces was discussed in terms of absolute roughness, ensure the modified cubic law is applicable to real rock fractures. To verify the accuracy of correction functions, dynamic water grouting test device based on single fracture were innovatively developed and the corresponding injection tests were carried out.