Experimental study of flow characteristics in non-mated rock fractures considering 3D definition of fracture surfaces

Three-dimensional (3D) morphology of rock fracture has a great influence on its hydraulic behavior. To experimentally investigate the 3D roughness dependent non-linear flow characteristics in deformable rock fractures, water flow tests through non-mated fractures were conducted under normal stresses ranging from 1.0 MPa to 5.0 MPa. Three types of granite samples were selected to produce rock fracture with different roughness. A 3D morphology parameter was used in the experiments to better understand the influence of joint roughness on the flow characteristics. By incorporating the 3D roughness metric, we proposed a new formula to describe the non-linear flow in rock fracture. The non-linear flow characteristics including the critical Reynolds number, Forchheimer's linear coefficient and nonlinear coefficient are analyzed and discussed. In addition, comparison among the proposed equation, Lomize's equation, Forchheimer equation and Izbash's law are examined from the perspective of the rationality of the formula. The limitations of Lomize's equation, Forchheimer equation and Izbash's law are analyzed in detail. The results show that the proposed equation is easier in the structure and more meaningful from an engineering point of view.