## 1 Introduction  
Rock blasting fragmentation is a crucial indicator for evaluating the blasting effect, directly impacting excavation efficiency. After blasting, the rock forms fragments of various sizes. Oversized fragments require secondary crushing, while undersized fragments lead to over-crushing [1, 2, 3]. However, predicting the results of rock blasting fragmentation is challenging due to the brief detonation time and the complex physical and chemical reactions involved. Therefore, it is essential to develop simulation and analysis methods to predict rock blasting fragmentation more accurately. The most common methods for predicting and researching rock blasting fragmentation include empirical formulas, such as the widely used Kuz-Ram model [4], modified Kuz-Ram [5], and Rosin-Rammler models [6]. For example, [PERSON] [5] applied these models to estimate average fragment sizes and validated their feasibility through onsite experiments. However, because the Kuz-Ram model assumes rock mass integrity, its practical applicability in engineering contexts is limited. To address this limitation, scholarsmodified the Kuz-Ram theoretical model and proposed the KCO model [7] and \(x_{p}\)-frag model [6]. Nevertheless, significant prediction errors persist, primarily due to two factors: the spatial variability of rock mass distributions and the inherent variability in the physical parameters of rock masses encountered in real-world engineering scenarios. As a result, predictions based on deterministic parameters may lack the required accuracy. Another method involves the use of artificial intelligence to predict rock blasting fragmentation. This approach uses rock parameters and data from multiple blasting results to train models for forecasting fragmentation results. For instance, [PERSON] et al. [8] employed a deep learning approach for rock fragmentation recognition. Similarly, 9. [PERSON] et al. [9] applied deep learning to analyze rock fragmentation, evaluating the accuracy of a deep neural network (DNN) model as an automated tool for rapid analysis. Their findings showed that the DNN model outperformed manual image labeling in prediction accuracy. Additionally, [PERSON] et al. [10] used DNN to identify fragment boundaries before watershed segmentation. By comparing DNN results with screening data, they confirmed that neural networks are viable for rock blasting fragmentation analysis. Other researchers have also used neural network methods to study rock blasting fragmentation [11]. However, the use of neural networks requires large datasets for effective analysis. Additionally, during training, the artificial statistics of rock fragmentation must be compared with DNN results to adjust model parameters, a process that is time-consuming. The lack of sufficient test data also presents challenges in training the model effectively. The third method involves numerical simulation techniques to predict and analyze rock fragmentation. [PERSON] et al. [12] investigated the impact of in situ stress on blasting-induced fracture patterns. They found that high in situ stress inhibited far-field crack development, resulting in smaller fragments as stress increased. Similarly, [PERSON] et al. [13;14] developed a two-dimensional numerical model to examine crack propagation and damage evolution during deep-buried tunnel excavation. Their studies showed that in situ stress resisted radial blasting pressure near boreholes, thereby reducing the damage zone area. [PERSON] et al. [15] combined theoretical analysis and numerical simulation to study the effects of in situ stress on rock response to blasting. Their findings revealed that in situ stress enhanced dynamic pressure by altering the loading path of the blast while suppressing fractures through circumferential compression. This suppression was most pronounced along the minor principal stress direction, with fractures concentrating along the principal stress as its disparity increased. In a subsequent work, [PERSON] et al.