## 4 Numerical Simulation Analysis
### Effective Stress Analysis of Specific Element
The distances from the selected four elements to the explosion source are almost the same, and the explosion stress wave reaches these elements at almost the same time. Therefore, the time-history curves of the effective stress for all four elements change significantly at almost the same moment (around 12.2 ms) and reach a second peak at around 12.4 ms. The peak effective stresses are as follows: element C (26.2 MPa) > element D (16.6 MPa) > element B (9.45 MPa) > element A (7.79 MPa). At this point, the peak effective stresses of elements C and D exceed the dynamic tensile strength of the rock, causing damage to these elements. Subsequently, the effective stress decreases and levels off. At 24 ms, the leftmost blast hole detonates. Since elements C and D are now closer to the explosion source, the stress intensity of the explosion stress wave reaching them is greater, resulting in significant changes in their effective stress, with a third peak appearing at around 24.6 ms. Elements A and B, being farther from the explosion source at this time, experience smaller changes in the effective stress, with less pronounced peaks. In pre-splitting blasting with sequential detonation, even when the inter-hole delay times are varied, the time-history curves of the effective stress for the selected characteristic elements exhibit similar overall patterns, with differences primarily being present in the magnitude of the stress peaks. To avoid repetition, only models with delay times of 0 ms and 12 ms are analyzed in detail, while models with delay times of 18 ms and 24 ms are presented in figure form without further elaboration. The specific data regarding the peak effective stresses of the selected characteristic elements for the four delay times are summarized in Table 10.  
The variation curves of the maximum effective stress peaks for elements A, B, C, and D under different inter-hole delay settings are plotted, as shown in Figure 14. Under different inter-hole delay time settings, when the delay times are set to 0 ms, 12 ms, and 18 ms, the maximum effective stress peaks of elements A, B, C, and D are all greater than the dynamic tensile strength of the rock, indicating that these four elements can all be destroyed. When the inter-hole delay time is set to 24 ms, the maximum effective stress peaks of elements A and B are greater than the dynamic tensile strength of the rock, while those of elements C and D are less than the dynamic tensile strength, indicating that elements A and B can be destroyed, but elements C and D cannot. When the inter-hole delay time is set to 0 ms, which corresponds to simultaneous initiation, the maximum effective stress peaks of elements A, B, C, and D are all greater than those at other delay times due to the optimal stress superposition effect. For sequential initiation, the magnitude of the inter-hole delay time is not inversely proportional to the peak effective stress experienced by the elements. When the inter-hole delay time is set to 18 ms, the peak effective stress of the selected characteristic elements is greater than that at delay times of 12 ms and 24 ms. It is therefore crucial to appropriately set the inter-hole delay time in order to ensure the rock fragmentation effect.