High-pressure hydraulic fractures are often reported in real engineering applications, which occur due to the existence of discontinuities such as cracks, faults, or shear bands. In this paper, a hybrid finite volume and extended finite element method (FVM-XFEM) is developed for simulating hydro-fracture propagation in quasi-brittle materials, in which the coupling between fluids and deformation is considered. Flow within the fracture is modelled using lubrication theory for a one-dimensional laminar flow that obeys the cubic law. The solid deformation is governed by the linear momentum balance equation under quasi-static conditions. The cohesive crack model is used to analyze the non-linear fracture process zone ahead of the crack tip. The discretization of the pressure field is implemented by employing the FVM, while the discretization of the displacement field is accomplished through the use of the XFEM. The final governing equations of a fully coupled hydro-mechanical problem is solved using the Picard iteration method. Finally, the validity of the proposed method is demonstrated through three examples. Moreover, the fluid pressure distribution along the fracture, the fracture mouth width, and the pattern of the fracture are investigated. It is shown that the numerical results correlated well with the theoretical solutions and experimental results.

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To better understand the seepage field in tailings dam with a drainage structure that combines drainage mat, drainage tube, and geotextile, an equivalent seepage analysis method for the drainage structure is presented. In the method, an equivalent drainage structure is suggested to replace the original drainage. It has enough size to be easily presented in the three-dimensional (3d) model of a tailings dam. According to a back analysis procedure using the quasi-3d models of a tailings dam with original and equivalent drainage structures, the material properties of the equivalent drainage structure can be obtained under the principle of drainage capacity equivalence. It is demonstrated that the suggested method is accurate enough to capture the seepage field in a tailings dam based on comparing the calculated and measured phreatic lines in a tailings dam for verification. Then, the method is employed to investigate the seepage field in a tailings dam in China for a case study. The rise of water level, damage of drainage structure, or increase of tailings discharge speed and time will lift up phreatic line. After terminating tailings discharge, phreatic line will first rise and then fall. The effect of tailings discharge on phreatic line will almost disappear after terminating tailings discharge for 24 h.

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