## 1 Introduction  
It is widely recognized that the occurrence of tunnel water inrush or mudslide has consistently posed significant challenges to tunnel excavation, and a comprehensive analysis of its generation mechanism remains imperative [1; 2; 3]. In comparison to tunnel water inrush, research on tunnel mud inrush commenced relatively late, necessitating targeted and systematic investigation into this issue. Tunnel water or mud inrush can be conceptualized as a complex fluid-particle coupling process, presenting considerable challenges for the development of an effective numerical modeling framework due to its inherent complexity. The evolution of water and mud inrush disasters in mountain tunnels is a strongly coupled process of seepage erosion, essentially constituting fluid-particle coupling dynamics. Currently, numerical simulation is an important method for studying such phenomena. During the past half-century, a considerable amount of effort has been expended on developing diverse numerical techniques for simulating the interactions between fluids and particles, and there has also been remarkable progress in the efficient computational solvers of the Navier-Stokes equations [4; 5; 6; 7; 8]. In recent years, particle transport within fluid flows hasfound widespread applications in science and engineering domains [9]. Simulation methods involving fluid-particle coupling include lattice Boltzmann method (LBM)/discrete element method (DEM), discontinuous deformation analysis (DDA)/smoothed particle hydrodynamics (SPH), particle flow code (PFC)/computational fluid dynamics (CFD), DEM-CFD, and others [3; 10; 11; 12]. Among these approaches, the DEM-CFD approach holds particular appeal owing to its computational convenience [13; 14; 15; 16]. However, the weakness of this method lies in that it depends on the semi-empirical equations to handle the complex coupling between the fluid and the particles. Therefore, the coupled LBM-DEM has been demonstrated to be a potent method for resolving the problem of particle-fluid and particle-particle interactions [9; 17; 18]. The developed LBM-DEM serves as a robust tool for fundamental research, enabling the exploration of hydromechanical physics in flows through porous media [19]. The coupled LBM-DEM excels in providing a detailed depiction of the flow field surrounding each particle while maintaining a clear physical understanding of solid particle behaviors such as friction, collision, migration, and more. Furthermore, its implementation readily lends itself to parallel computing, significantly enhancing the speed and efficiency of simulations. The coupled LBM-DEM can effectively overcome the limitations of the CFD-DEM and is better suited for simulating complex fluid-particle systems at the pore scale. When solid particles in motion are partially or entirely submerged within the fluid, the particles will alter the velocity and pressure distribution in the surrounding flow field. On the contrary, fluids exert resistances on solid particles, like resistance, lift, and torque, thus influencing the mechanical behavior of solid particles. In the coupling process, to accurately capture the LBM-DEM coupling mechanism, pressure and velocity boundary conditions, no-slip conditions, and bounce-back boundaries are typically utilized for boundary treatment [20; 21]. The mixing behaviors of particles in a sheared particle flow were investigated [22]. The particle flow method was used to study the particle transport mechanism in a basic soil-filter system [23]. A numerical study was presented on soil fluidization induced by local leakage of a buried pipe using the coupled LBM-DEM [5]. A collision model for phase-resolved direct numerical simulation of sediment transport, coupling fluid-particle via the immersed moving boundary method [24; 25], was presented [26]. Four variants of boundary conditions were analyzed and compared in terms of their accuracy in the free-surface lattice Boltzmann method [27].