A Theoretical Model for Nonlinear Flow in a Single Marble Fracture under High-Stress Conditions

Abstract

This study focuses on the nonlinear flow characteristics of a single rough-walled fracture in a marble sample subject to various confining pressures (5.0–50.0 MPa) and deviatoric stresses (0–60.0 MPa). First, a series of seepage tests were conducted to investigate the impacts of fracture dilation and inertial effect on the nonlinear flow behaviors. Then, the competitive effects of fracture dilation and inertial effect on the transition of the nonlinear flow regime were theoretically evaluated. Finally, a novel seepage model incorporating fracture dilation was proposed based on the Goodman hyperbolic closure deformation relationship. This model was further validated through a comparison with both experimental observations and classical theory. The investigation reveals that variations in confining pressures and deviatoric stresses induce a substantial reduction in flow rate by factors of 5 and 2 magnitudes, correspondingly. Notably, the influence of the inertial effect diminishes as the fracture dilation effect becomes more pronounced, particularly evident under conditions of lower confining pressures. The proposed model considering the fracture dilation effect accurately predicts the relationship between flow rate and pressure conditions. Moreover, it demonstrates superior performance compared with the Forchheimer equation. This study can provide guidance for underground engineering practices when encountering high confining pressure, high deviatoric stress, and high water pressure.