## 1 Introduction  
Recent advancements in numerical simulation technologies have significantly impacted tunneling and underground engineering. As a mesh-free technique, smoothed particle hydrodynamics (SPH) offers significant advantages in addressing issues with mobile boundaries, especially those involving extensive deformations and intricate free-surface interactions. Based on current research findings, both domestically and internationally, SPH is predominantly applied in the following fields: celestial mechanics, explosive phenomena, high-velocity impact science, mining engineering, and fluid dynamics. The method's broad application is largely due to its ability to incorporate constitutive equations that align with the properties of various materials. Furthermore, the existing literature strongly suggests that SPH has immense potential for future developments in tunnel and underground engineering. [PERSON], X and [PERSON] et al. [1; 2; 3] have highlighted the growing importance of meshless methods and computational fluid dynamics (CFD) in tackling intricate engineering problems. [PERSON] et al. [4] underscored that meshless methods, which do not rely on grid structures, offer remarkable adaptability when managing complex boundary conditions and significant deformations, particularly in tunnel excavation and associated large-scale ground deformations. In contrast, [PERSON], [PERSON], and [PERSON] et al. [5; 6; 7; 8] have pointed out that traditional finite element methods (FEM) and finite difference methods (FDM), which depend on predefined mesh structures, often face challenges such as mesh distortion and diminished computational accuracy during large-deformation simulations. [PERSON] et al. [9] provided an extensive technical review of CFD applications in high-rise buildings and structures, while [PERSON] et al. [10] utilized CFD models to analyze flow fields around bridge peers and study bridge scour. [PERSON], [PERSON], and [PERSON] et al. [11; 12; 13; 14] argued that advancements in computational resources have facilitated the integration of CFD and meshless methods, enhancing the accuracy and stability of numerical simulations under complex conditions. Furthermore, [PERSON] et al. [15] emphasized that alternative meshless methods, such as the meshless Galerkin method (EFG) and the discrete element method (DEM), have the potential to model complex stress-strain relationships and nonlinear boundary conditions, though they still encounter issues related to computational efficiency and precise parameter determination in practical engineering applications. [PERSON] et al. [16] proposed a CFD-based simulation approach that employs dynamic grid updating techniques and explores the effects of pier-type bridges on scour behavior. These advancements are anticipated to further advance the use of meshless methods and CFD in tunneling and underground engineering, thereby enhancing their practical value across various fields [17; 18; 19]. SPH was initially conceived to address astrophysical challenges within three-dimensional open space, with a particular focus on variability problems. Given that the movement of these particles mimics that of liquids or gases, they can be accurately described using the governing equations of classical Newtonian fluid dynamics. Related research on this topic was first seen in the relevant literature of [PERSON] [1]. Figure 1 shows a planetary synthesis process simulated by SPH. Ongoing problems such as galaxy and star formation, binary interactions, comet and asteroid impacts, and the dynamics of self-gravitational disks can be addressed. [PERSON] et al. [20] addressed the challenge of simulating the coupling of large deformations and failure in porous materials using the smoothed particle hydrodynamics (SPH) method. [PERSON] et al. [21] introduced a numerical approach that integrates discontinuous deformation analysis (DDA) with SPH to model interactions between rock structures and soil particles. [PERSON] et al.