## 1 Introduction  
Tunnel excavation in steep rock areas presents significant geotechnical challenges due to the complex mechanical behavior of rock masses. The distinctive geomechanical properties of steep rock frequently cause deformation and stability issues within tunnel infrastructure, with tunnel inverts being particularly susceptible to high stress concentrations [1; 2]. These concentrations, resulting from the unstable equilibrium of the surrounding rock, can lead to substantial deformation, instability, and even structural damage. A thorough understanding of the mechanical properties of steep rock is crucial for the effective design, construction, and long-term stability of tunnels in such complex geological settings. To address these challenges, preliminary research by several scholars has been undertaken. Different geological compositions, such as soft soil, soft rock, and composite strata, exhibit varying lithologies and engineering properties, each affecting large deformation in tunnels differently [3; 4; 5; 6; 7]. The impact of stress conditions, including high ground stress and groundwater presence, is also critical [8; 9; 10; 11]. Addressing these issues, researchers have utilized model tests to analyze tunnel deformation mechanisms. For instance, [PERSON] et al. [12]studied deformation and failure patterns in deep-buried composite strata, finding that damage is influenced by stress levels and lithological characteristics. Numerical simulations have similarly been employed to investigate tunnel deformation [13], with [PERSON] et al. [14] simulating soil deformation under deformation lining control and analyzing stress states and soil arch development in loess tunnels. Further research has focused on countermeasures for tunnel deformation. [PERSON] et al. [15] proposed a radial yield support method with a compressible layer to mitigate deformation, while [PERSON] et al. [16] outlined principles for designing prestressed support systems, demonstrated through a case study of layered carbonaceous shale tunnels. Alongside specific optimization measures, numerous scholars have extensively re-searched tunnel repair materials and monitoring techniques [17; 18; 19; 20; 21]. [PERSON] et al. [22] explored the effect of soil strength on base bulge damage mechanisms, revealing that soil strength increases with depth and that the sliding surface extends downward. [PERSON] et al. [23] analyzed tunnel floor heavy impacts using on-site monitoring and numerical simulations, noting that deformation pressure transfers to the filling layer due to surrounding rock weakening. [PERSON] et al. [24] investigated tunnel floor heavy mechanisms in inclined coal bed highways, identifying horizontal stress as a primary cause. [PERSON] et al. [25] examined floor heavy causes, including ground stress and surrounding rock structure, through field investigations and simulations. Regarding finite element methods (FEMs), [PERSON] et al. [26] utilized a two-dimensional geotechnical model to capture critical sliding surfaces. [PERSON] et al. [27] investigated coal mine tunnel bottom drumming, finding that the destruction of weak units causes displacement. [PERSON] et al. [28] combined FEMs with discrete element methods to simulate deep roadway excavation, focusing on rock deformation and lining damage. [PERSON] et al. [29] simulated seepage experiments using FEMs to study spatial seepage and tunnel interaction. In fluid mechanics, the volume of fluid (VOF) method has seen advancements. [PERSON] et al. [30] introduced a new VOF approach for fluid-fluid interfaces, considering surface tension and force equilibrium. [PERSON] et al. [31] developed an algebraic VOF approach to address operational issues in fluid simulation. [PERSON] et al. [32] used VOF to study clogging mechanisms in porous media, considering parameters such as oil droplets. Although significant advancements have been made in understanding large deformation in tunnel surrounding rock, much of the existing research adopts a macro perspective.