# Study on Water Inrush Characteristics of Hard Rock Tunnel Crossing Heterogeneous Faults
## 1 Introduction  
In recent years, driven by China's economic and technological development, the construction of tunnels has been shifting from shallow-buried soft rock tunnels to deeply-buried hard brittle rock tunnels [1; 2]. Hard brittle rocks can provide high strength and overall stability for deep engineering projects [3]. However, under the influence of tectonic stress, they are also prone to generating numerous brittle fracture zones [4]. These geological formations serve as crucial pathways for fluid flow in the upper crust [5; 6; 7]. Once tunnel excavation exposes these formations, groundwater trapped within them flows into the tunnel, leading to severe water inflow disasters [8]. Statistics reveal that nearly all hard rock tunnels have been affected by fault water inflow, resulting in direct economic losses amounting to billions of yuan. Therefore, revealing the characteristics of water inflow caused by traversing water-rich fault zones in hard and brittle rock tunnels holds significant importance for the current stage of tunnel engineering development in China. Researchers have conducted extensive research on the evolution mechanisms of water gushing and mud gushing during tunnel excavation in hard-brittle fault breccia belts. These efforts have yielded valuable insights. [PERSON], et al. [9] conducted a comprehensive analysis of 23 cases of water surges in hard and brittle rock tunnel faults in the Alps, revealing a correlation between the rate of water surges and rock properties. [PERSON], et al. [10] reviewed three significant tunnel projects in the Himalayan region, analyzing the adverse effects of continuous surface water supply and tectonics on construction. [PERSON] summarized the construction experience of nearly 50 typical hard rock subsea tunnels in Norway, and found the main characteristics of fault water gushing and significant deformation of hard rock tunnels [11; 12; 13]. At the laboratory scale, similar physical simulation experiments can more intuitively observe the disaster process and evolution mode of fault water inflow in deep tunnel scenarios [14; 15]. [PERSON], et al. [16] developed a model experimental system to simulate tunnel excavation and water injection for inrush, utilizing Acoustic Emission (AE) for positioning and monitoring the evolution of inrush channels in the surrounding rock during the water supply process. In recent years, with the advancement of computer technology, more and more researchers use numerical simulation methods to study the phenomenon of fault water gushing. Using FEM to discretize faults is the most common method for studying water inrush disasters [17; 18; 19; 20]. [PERSON], et al. [21] elucidated the process of water inrush in deep tunnels by establishing a finite element model. [PERSON], et al. [22] conducted a study on the fluid-structure interaction effect of water inrush from water-rich faults using COMSOL Multiphysics software. In recent years, with the advancement of numerical calculation methods, the Discrete Element Method (DEM) and Smoothed Particle Hydrodynamics (SPH) have been applied to tackle water inrush issues in fractured rock tunnels [23; 24]. [PERSON], et al. [25] coupled SPH with the Discontinuous Deformation Analysis (DDA) method to simulate the fluid motion state in fault water inrush disasters. The above research is of great significance for advancing the research on the mechanism of cement gushing flow in tunnels. In these studies, fault zones are generally assumed to be homogeneous and isotropic. However, fault breccia zones in hard-brittle rock formations exhibit a heterogeneous structure [26; 27; 28]. Extensive field observations have shown that the brittle fracture zone consists of a high-strain core region and an outer low-strain fracture network region, called the damage zone (Figure 1) [29; 30]. This structural change results in complex hydraulic behavior within the fault zone [31; 32].