Permeability Characteristics of Porous Rock with Conduits under Stokes–Brinkman–Darcy Coupling Model

Abstract

Conduits, the main channels within a rock mass, can significantly affect the permeability characteristics of rock masses. This paper presents a Stokes–Brinkman–Darcy coupling model to study the permeability characteristics of porous rock masses with conduits. In this model, the Navier–Stokes equation and the Brinkman-extended Darcy equation are adopted to describe the fluid motions in the conduit and porous rock matrix, respectively. The analytical solutions of both the velocity distribution and the equivalent permeability coefficient, which is the average permeability for the complete rock volume, are derived under the stress jump boundary condition for a rock mass with a conduit. The results of the sensitivity analysis show that the equivalent permeability coefficient of the rock mass with a conduit is positively correlated with the permeability of the rock mass, the relative aperture of the conduit, and the porosity and is negatively correlated with the stress jump coefficient; the aperture of the conduit plays a dominant role in the equivalent permeability coefficient. In addition, the analytical solution of the equivalent permeability coefficient is verified by a seepage test.