Investigation of Nonlinear Flow in Discrete Fracture Networks Using an Improved Hydro-Mechanical Coupling Model

Fractures commonly exist in rock masses; the coalescence of fractures provides fluid flow pathways in a fractured rock mass and greatly increases the flow capacity of fractured rock. This work aims to study the characteristics of nonlinear flow in fractures. A series of tests were conducted and indicated that the Forchheimer law performed well when describing the nonlinear relationship between hydraulic gradient and flow. The test results also indicate that higher water pressure may induce stronger nonlinearity. Additionally, the linear and nonlinear coefficients of the Forchheimer law increase with a decrease in the particle size of the filling material in fractures. On the basis of the laboratory results, the classical Forchheimer law was modified by considering the influence of stress on the variation of fracture aperture. A hydro-mechanical coupling model for fractured rock masses was built and programmed with a subroutine through ABAQUS. Furthermore, a random discrete fracture network was generated and simulated to prove that a high flow velocity will result in a nonlinear flow, not only in a single fracture, but also in a fracture network. The numerical results from fractured rock masses show that a ratio of the flow to the hydraulc gradient will change the flow from linear to weak nonlinearity and, finally, to strong nonlinearity with an increase in the hydraulic gradient. It also shows that the linear and nonlinear coefficients increase with an increase in the confining pressure and that they decrease with an increase in the aperture. Due to the complexity of fracture channels, a nonlinear flow is likely to occur in a fractured rock mass. Finally, the developed model was applied to simulate the flow behavior of underground engineering; the results show that the smaller the hydraulic aperture is, the higher the water pressure is required to be in order to change the flow regime from linear to nonlinear.