## 1 Introduction  
In the study of rock movement during blasting, throwing techniques are primarily applied in high-bench blasting in open-pit mining. This technique involves directly throwing part of the rock to a more ideal area or goat through blasting. The earliest application of high-bench blasting and throwing techniques dates back to the 1960s, when [PERSON] et al. [1] discovered that approximately 40% of the blasted rock was directly thrown into the goal, sparking interest and further research by scientists worldwide. Subsequent research and experimental results from various countries have demonstrated that this technique can significantly enhance the economic benefits of mining operations. However, the process of rock blasting and throwing can also lead to issues such as equipment damage, scattering of blasted rock piles, and increased costs. [PERSON] et al. [2] studied the application of cast blasting in Moroccan phosphate mines. [PERSON] et al. [3] determined the key factors influencing the effectiveness of casting blasting based on gray relational analysis theory, subsequently optimizing the blasting parameters for open-pit mining. Relevant studies indicate that the impact of shock waves on the borehole wall generates radial and circumferential cracks, and the explosive gases further propagate these cracks, leading to rock fragmentation. The residual energy of the explosive gases propels the fragmented rock in the direction of least resistance. [PERSON] et al. [4], through studying the impact of explosive charge ratio on high-bench casting blasting, found that the casting distance increases with the average explosive charge ratio. [PERSON] et al. [5] employed a locally weighted linear regression method to determine the formation of the muck pile resulting from casting blasting. [PERSON] et al. [6] established calculation methods for the projection velocity and rock-breaking projection energy under two blasting methods: spherical charges and cylindrical charges. By these methods, predicted velocity characteristics of fractured rocks can be obtained. Most researchers have focused on rock throwing in open-pit mines, aiming to improve the efficiency of shoveling, loading, and transportation by controlling the rock throwing distance to achieve the desired blast pile morphology. However, few have examined the impact of rock movement on fragmentation and blasting effects in underground settings, where such movement is rarely studied. In underground blasting, rock movement is constrained by tunnel layouts, making it difficult to disperse blast piles, which is often overlooked in the practical production stages. Nonetheless, in the confined spaces of underground operations, blast pile morphology can significantly affect the efficiency of mechanical shoveling, loading, and transportation. Therefore, this paper aims to investigate the influence of rock movement patterns on fragmentation and throwing in underground blasting. Given that the blasting process occurs instantaneously, existing technologies struggle to capture the complete process. International scholars were the first to conduct blasting research using numerical simulations. Early studies in this area were pioneered by these researchers. For continuous medium analysis methods, as early as the 1970s, [PERSON] and [PERSON] used the finite element method (FEM) to analyze crack propagation and stress wave transmission issues. This method has since been widely applied to numerical simulations of rock blasting. For instance, [PERSON] et al. [7] simulated the rock fragmentation process under different inter-hole delay conditions using the FEM. [PERSON] et al. [8] applied the FEM to study the explosive effects of coupling interactions in different charge structures. Additionally, the Finite Difference Method (FDM) has been used in blasting engineering, primarily to assess the impact of blasting activities on other targets [9]. However, continuous medium analysis methods are limited in simulating rock mass movement and the subsequent fragmentation process.