## 2 Problem Description  
Various indicators, such as rock fragmentation, vibration, and dust, are used to evaluate the rock blasting effects. Among these, rock fragmentation directly impacts excavation efficiency, which is most essential for evaluating rock blasting effects. By analyzing the distribution of rock fragmentation, valuable insights can be gained to optimize blasting parameter designs. Selecting appropriate parameters can significantly improve both project progress and economic efficiency.  
Explosives undergo detonation reactions in an extremely short time, involving complex physical and chemical processes that are difficult to observe directly [21, 22]. However, with the rapid advancement of computational power and software technologies, the rock blasting process can be reproduced though numerical simulation. By simulating rock blasting results based on site-specific conditions, this method provides crucial feedback for optimizing blasting parameter designs. This approach not only saves significant time and cost but has also become a widely adopted tool for studying rock blasting effects [23, 24].  
The most commonly used numerical simulation methods in current research include the finite element method (FEM), which assumes medium continuity. The most widely used FEM software, including LS-DYNA and AUTODYN, can accurately simulate the relationship between volume and energy during explosive detonation by incorporating built-in detonation equations. These programs perform well in simulating stress waves, loads, vibrations, and explosion-induced damage [25]. However, due to the continuum assumption in their formulation, FEM have limitations in simulating large deformation failures, such as rock fragmentation and ejection. In contrast, the discrete element method (DEM), which assumes medium discontinuity, models the system as a collection of discrete elements. Software such as PFC and 3 DEC allows elements to separate, translate, and rotate during simulations [26]. DEM is widely employed to study rock fragmentation and ejection during blasting [27, 28].  
However, a significant limitation of DEM tools is the absence of built-in explosion equations. As a result, rock blasting is often simplified as a static load applied within the rock mass, which fails to capture dynamic gas-rock interactions. This leads to less accurate representations of failure mechanisms, particularly in the near-blast hole zone where pressure gradients are most severe [29, 30, 31].  
The continuous-discontinuous method, used in numerical simulation software such as GDEM and FDEM, offers better accuracy in simulating rock failure under detonation. However, this approach has several limitations. First, the failure process in this method is highly sensitive to mesh division. Second, the software requires complex parameter settings, demanding extensive calibration and resulting in lower computational efficiency. Additionally, GDEM and FDEM struggle to simulate complex jointed rock masses due to their simplified representations of discontinuities. A comprehensive comparison of the advantages and disadvantages of current numerical simulation methods for rock blasting is provided in Table 1.