Abstract: To investigate seepage characteristics of a single rough fracture, based on lattice Boltzmann method, a numerical model is established to analyze the water flow in laminar under pressure. The D2Q9 model is applied to simulate the discrete velocity direction. On the macroscopic-scale, the upper and lower boundaries (ux =uy =0) are assumed to be impermeable, and the left and right boundaries are controlled by pressure (i.e., the pressure on the left side is larger than that on the right side). On the microscopic-scale, the non-equilibrium extrapolation scheme is set on the pressure boundary and smooth fracture surface boundary, and the standard bounce-back scheme is set on the rough fracture surface boundary. The corresponding program is compiled to verify the classical cubic law of smooth plate fracture flow. The rough fracture surface is generated by setting piecewise random length and random width, and seepage characteristics of different rough fracture surfaces are discussed in detail. The results show that fracture surface roughness greatly affects seepage characteristics. With the increase of relative roughness, the deviation from cubic law becomes more obvious. Therefore, by considering the effect of relative fracture surface roughness, the modified cubic law is proposed according to numerical results of different schemes of rough fracture surface. This study lays the foundation for further research on the complex hydraulic characteristics of rough fracture.

Key words: lattice Boltzmann method, single fracture, seepage characteristics, numerical simulation