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（u

x

=u

y

=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 pr

ogram 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.