## 1 Introduction
On the other hand, the water flow characteristic could be changed from linear Darcy flow to a nonlinear flow state due to the continuous loss of fine particles [21; 22; 23; 24]. Given that the flow in the fracture zone is nonlinear, using linear Darcy flow for simulation is impractical. Furthermore, the continuous increase in fracture zone porosity and permeability due to ongoing fine particle loss makes simulating the inrush process with constant porosity and permeability inadequate, as it fails to capture the essence of flow pattern transformation. Therefore, it is crucial to develop an appropriate model for fully weathered fault fracture zones that considers flow-erosion coupling behavior. So far, the erosion behavior has achieved some attention in piping and sand production [25; 26; 27]. For example, [PERSON] (2003) established a fine particle erosion model by using an empirical relationship between the eroded particle mass and the hydraulic gradient. [PERSON] and [PERSON] (2005) developed an erosion model for sand production with a porosity diffusion law by assuming that the eroded particle discharge follows a gradient law. These studies improved the understanding of erosion behavior and provided important references for erosion-induced water and mud inrush disasters in fault zones. However, more improvement should be made because the water inflow is different from the sand production and piping due to the different stress and flow conditions (e.g., nonlinear flow behavior and high water pressure in tunnel water inrush). Addressing the gaps in previous studies that overlooked the impact of fine particle erosion on the evolution of fracture zone seepage, this paper introduces a seepage erosion theoretical model that uses solute transport and seepage mechanics theories, establishing a comprehensive theory for mud and water inrush evolution in fault seepage-erosion, including seepage equations and porosity evolution laws. Space and time were discretizedusing the implicit difference and Galerkin finite element schemes, while the Newton-Raphson iteration method was used to address the nonlinear characteristics of the equation. The theoretical model was subsequently developed, and numerical simulations were carried out with COMSOL multifield coupling software. Then, this model was applied to a representative case of mud and water inrush in tunnel fault fracture zones, revealing the evolution of such inrush disasters in the fault fracture zones. Theoretical Modeling of Water and Mud Inrush for Completely Weathered Rock in a Fault Fracture Zone  
Water and mud inflow in completely weathered rock is a seepage-erosion coupling process, as observed in many experimental investigations [6] ([PERSON] et al. 2018). For example, the flow behavior (e.g., permeability and water flow velocity) is affected by the eroded mass, and the erosion process is controlled by the water flow velocity. Thus, a coupling seepage-erosion water inrush model was developed based on the following assumptions [6] ([PERSON] et al. 2018). (1) The completely weathered rock in fault fracture zones is regarded as a tri-phase system comprising solid grains (s), fluid (f), and fluidized solids (fs), as shown in Figure 1. (2) The fluidized grains are found to be a special solute flowing with the fluid. The interstitial spaces are fully filled with fluidized grains and fluid. (3) The fluidized grain velocity is usually equivalent to the fluid velocity. (4) The fluid is impenetrable, while the solid grains are rigid. The governing equations for this coupling water and mud inrush model include a set of mass balance equations for describing the interaction of the different phases (e.g., mass change), a coupled seepage equation for the water flow, a porosity evolution equation for the description of the porosity change caused by the erosion of the fluidized grains, and a permeability evolution equation for the description of the permeability change due to porosity change. These governing equations are illustrated in the following section.