Governing equation has significant effects on the results of fluid flow through rough joint. In order to investigate flow through a rough joint

Navier-Stokes equation

Stokes equation

Reynolds equation and cubic law

which are commonly used in analyses of flow through a rough joint

are firstly introduced and their applicability are evaluated. And Reynolds equation is chosen as the governing equation

a void model is established to analyze fluid flow through a rough joint. Then taking artificial rock joints as objects

laboratory flow tests are first performed and the flow rates through joint derived from void model under the same boundary conditions are also predicted after obtaining the joint aperture distributions. Three other models including void model taking cubic law as governing equation

Cubic law referred to the whole joint surface and Su B.Y. empirical modified cubic law are also applied to predict the volumetric flow rates through joint samples. The predictions of four models are compared with experimental observations. It is found from the comparisons that flow rates derived from void model based on Reynolds equation agree well with experimental observations; while the predictions of other three models have large discrepancy from experimental observations. According to the comparison

Reynolds equation is able to predict flow rates through rough joint exactly. In addition

tortuosity phenomenon of flow through joints can also be derived from the distributions of volumetric flow rates vectors

which provides a theoretical basis for investigating the influences of tortuosity on flow rates in a rough joint.