## 1 Introduction  
Understanding the hydro-mechanical coupled behavior of a fractured rock mass is crucial for investigation of the rock mass properties encountered in underground engineering, such as in tunnel excavation [1, 2, 3], reservoir storage [4, 5, 6, 7], and geothermal energy development [8, 9, 10, 11, 12, 13, 14], as well as the safety assessment of high-level radioactive waste repositories [15, 16]. The interconnection of the fracture network in the rock mass provides a convenient path for fluid flow and gradually increases the flow capacity of the fractured rock mass. Therefore, fluid flow in fracture networks is important for understanding stability during the construction of rock engineering projects in fractured rock masses. A fractured rock mass is a complex geometric system. The geometric distribution of fractures can be obtained by field surveying and mapping outcrops in a limited area, as well as logging in a well with a limited borehole and depth [17, 18, 19, 20]. To represent the underground fracture system more realistically, the usual method is to assume the statistical distribution of the geometric parameters of the fractures and use that information in discrete -fracture networks (DFNs) modelling [21; 22; 23]. In recent years, many scholars have studied the influence of fracture networks on the stability of underground engineering [24; 25]. Notably, each generation of DFNs must strictly follow the statistical distribution law of each geometric parameter in the case study. Generally, porous media can be divided into various types by their application scope [26; 27; 28; 29]. It makes sense to investigate the effect of mechanical characteristics on other characteristics and performance, and the improvement of a numerical method for fractured porous media is especially significant in geoscience applications [30; 31]. When the flow rate is small or the flow velocity is slow in a rock mass, a fracture can be simplified into a parallel plate model with a smooth surface, and the regularity of fluid flow obeys the cubic law. The permeability of the fractured rock mass is closely related to the aperture, roughness, and stress boundary conditions. Experimental and numerical studies carried out by [PERSON] and [PERSON] et al. showed that the larger the aperture, and the smaller the roughness, the greater the permeability of the fracture will be [32; 33]. Extensive works related the influence of interface contact and Gouge production and plastic deformation of asperities on the permeability evolution were published in the literature [34; 35]. Permeability alterations due to a stress-induced closure of mated fractures were also studied. [PERSON] et al. indicated that the closure of a fracture reduced the fracture conductivity [36]. However, [PERSON] showed that the permeability of rock in a failure state under the action of stress was significantly improved through tests [37]. Permeability evolution during the shear process was investigated through theoretical models, laboratory experiments, and numerical simulations. These works studied the relationship between fracture geometric evolution and the change in flow behavior during shear. The results showed that the fracture expansion, in the early shearing stages, significantly increased the permeability of a fracture [38; 39]. However, some studies also show that the fracture was filled with the formatted gouge, due to asperity damage while the shear displacement was large, resulting in a gradual decrease of permeability [40]. In recent decades, many studies have focused on modifying the cubic law, for example, by determining mathematical expressions that calculate the hydraulic aperture while considering factors such as the fracture surface roughness, contact ratio, and curvature [41; 42; 43; 44]. However, in the case of high velocities, the relationship between hydraulic and flow become nonlinear; the cubic law would be no longer suitable, and the hydraulic characteristics predicted by cubic law would be quite different from the experimental results.