## 1 Introduction
[22] employed a shear failure model combined with a contact algorithm to simulate the cutting process and interactions between tools and both non-cohesive and cohesive soils. During the discretization of the continuum, [PERSON] and [PERSON] [23] formulated an efficient interaction among immediate neighbors by incorporating a spring-like connection between discrete particles. The degradation of these spring forces  
Figure 1: Planetary composition process diagram. is governed by a material damage evolution law. When the impact velocity increases, a similar sequence of failures is observed: tensile tearing at the support occurs at 40 m/s, and shear failure is evident at the impact site at 60 m/s (Figure 2). [PERSON] et al. [24] argued that SPH, with its Lagrangian framework and meshless nature, is becoming a prominent method in tunneling and underground engineering applications. [PERSON] and [PERSON], [PERSON] et al. [25; 26; 27; 28] suggested that SPH excels in handling complex phenomena such as free-surface and multiphase flows, making it particularly useful for simulations involving soil excavation and ground deformation in recent studies. [PERSON] et al. [29] validated the stability and accuracy of the SPH method in analyzing water-soil coupling interactions during dam seepage processes and underwater landslides through experiments utilizing a novel water-soil coupling wall boundary model. As illustrated in Figure 3, several key moments (t = 0 s, t = 125 s, t = 500 s, and t = 1156 s) were chosen for analysis. Initially, the seepage velocity is high due to the dam's low water content. By approximately 125 s, the water front has advanced to a position near x = 0.8 m. As the process continues and soil saturation increases, the seepage velocity decreases gradually. By around 500 s, the water front reaches approximately x = 1.2 m. At about 1156 s, the seepage process concludes, stabilizing at a steady state. These findings are consistent with the actual seepage process and provide preliminary evidence supporting the SPH method's effectiveness in simulating seepage behavior. Despite these advancements, significant limitations remain in simulating large-deformation problems in tunnels and underground engineering, particularly regarding computational efficiency and model accuracy. To address these issues, researchers have proposed combining meshless methods with computational fluid dynamics (CFD) to enhance simulation accuracy and efficiency in complex tunnel environments [30; 31; 32; 33]. This approach integrates SPH with CFD to refine smoothing length calculations, thereby improving model stability and convergence in large-deformation and multiphase flow scenarios [34; 35]. To investigate fluid-solid interactions related to water and mud intrusion during tunnel construction, [PERSON] et al. [36] developed a coupled discontinuous SPH method. Numerical simulations and case studies have validated the effectiveness of this method in tunnel excavation and related ground-deformation issues, offering valuable theoretical insights for future engineering applications [37; 38; 39]. Figure 2: Deformed configuration with (**a**) initial velocity of 60 m/s and (**b**) initial velocity of 40 m/s; (**c**) enlarged view at fracture point. Although the smoothed particle hydrodynamics (SPH) method is well suited for the numerical simulation of large deformations in soft rock and mechanical cutting in hard rock within tunnel and underground engineering, several challenges limit its broader application. These challenges stem from the complexity of constitutive models for surrounding rock materials, the rheological characteristics of tunnel structures, and the spatiotemporal effects inherent in the tunnel excavation process. Notably, the current derivation of the fundamental theory behind the SPH method remains significantly underdeveloped, particularly under multi-field coupling conditions.