Analysis of Tunnel Deformation Using Elastoplastic Stillinger Weber (SW) Potential Embedded Discretized Virtual Brand (DVIB) Method +
Footnote †: This paper is an extended version of our paper published in Proceedings of the RoccScience International Conference (RIC 2023), Toronto, ON, Canada, 24–26 April 2023. [PERSON]  
1 Mining Engineering, China University of Mining and Technology, 1, Daxue Road, Xuzhou 221116, China 1,  
numerical modeling techniques [8; 9; 10], capturing the nonlinear and discontinuous behavior of rock masses under excavation-induced stresses remains challenging [11; 12; 13]. Empirical methods such as the Q-system [14; 15; 16], Rock Mass Index (RMi) [17; 18], Rock Mass Rating (RMR) [19; 20], and Geological Strength Index (GSI) [21; 22; 23; 24; 25; 26] have been extensively applied in preliminary tunnel design. These classification systems provide qualitative or semi-quantitative assessments based on geological features and observed performance. However, they lack the capacity to quantitatively evaluate stress redistribution, localized deformation, and failure mechanisms under complex boundary conditions, which limits their reliability in intricate geological environments. To address these shortcomings, continuum-based numerical approaches, such as the Finite Element Method (FEM), Extended Finite Element Method (XFEM) [27; 28; 29], and Finite Difference Method (FDM) [30], have been extensively applied. These methods discretize rock formations as continuous entities and employ elastoplastic constitutive laws (e.g., Mohr-Coulomb, Drucker-Prager, Hoek-Brown) to simulate stress-strain responses [31]. Although effective in representing plastic flow and yielding, these models inherently assume material continuity, thereby restricting their ability to capture discrete crack initiation, propagation, and coalescence in brittle and quasi-brittle rock masses. Beyond continuum models, lattice-based numerical approaches represent materials as networks of interacting mechanical elements such as springs or bars, where fractures evolve through progressive element failure [32; 33; 34; 35; 36]. Although lattice-based models provide valuable insights into brittle fracture mechanics and microstructural effects [37], they impose fixed Poisson's ratios, rely on external failure criteria, and exhibit sensitivity to lattice topology, which affects numerical consistency and adaptability. Efforts to mitigate these limitations have included the introduction of beam and angular spring elements [38; 39; 40]. Despite advances in numerical modeling for tunnel stability assessments, accurately capturing plastic deformation, fracture evolution, and anisotropic failure mechanisms remains challenging. Traditional continuum-based approaches such as FEM, (XFEM), and FDM impose material continuity constraints, limiting their ability to simulate discontinuous cracking and stress redistribution. Lattice models, which are effective for brittle fracture representation, often suffer from fixed Poisson's ratios and mesh sensitivity issues that affect the numerical consistency. Compared to conventional continuum-based techniques, such as the Finite Element Method (FEM) and Finite Difference Method (FDM), the elastoplastic Stillinger-Weber (SW) potential-based Discretized Virtual Internal Bond (DVIB) framework eliminates the need for external fracture criteria and remeshes by modeling fractures through intrinsic bond failure mechanisms. This enables the direct simulation of crack initiation and propagation under large deformation conditions. Furthermore, unlike classical lattice models, which typically impose fixed Poisson's ratios and rely on external failure conditions, the SW-DVIB approach incorporates plasticity at the bond level and utilizes both two-body and three-body interactions. This allows simultaneous control over the irreversible deformation and lateral stiffness, resulting in a physically consistent and topology-independent simulation framework.