Experimental Investigation of Nonlinear Flow Characteristics of Real Rock Joints under Different Contact Conditions

Laboratory experiments were conducted on three artificial rock joints with natural characteristics to study the nonlinear fluid flow characteristics in a single joint under different contact conditions. A noncontact, three-dimensional stereotopometric measurement instrument was used to measure the three-dimensional surface morphology of rock joints before they were tested. Subsequently, the composite morphology parameters of rock joints under different contact conditions were calculated by using self-programmed software. The experimental results showed that both the Forchheimer’s equation (emphatically discussed) and Izbash’s equation could provide an excellent description for the nonlinear fluid flow in a single joint. The linear coefficient a and nonlinear coefficient b of the Forchheimer’s law both generally decreased, and such rate of decrease was gradually reduced along with increasing offset distance. The value of linear coefficient a approached zero and the value of coefficient n was close to 2 with increment of offset distance to a certain extent. A factor E was used for quantitatively estimating the nonlinear characteristics of fluid flow in single rock joint. In this work, a critical value E=0.9 was defined to classify the regime of fluid flow, which indicated that the inertial terms were more important than the viscous terms. These findings indicated that a non-Darcian turbulent flow in the single joint occurred with the Reynolds number ranging between 1,408.2 and 5,674.4 under high water pressure. For the first time, an empirical mathematical equation was proposed to describe the apparent transmissivity by a single joint by using the Reynolds number, the root-mean square height of the joint composite morphology, and the mean aperture under different contact conditions based on laboratory observations. These findings may be useful for the computational studies of coupled shear-flow properties flow in jointed rocks.