# Research on the Laws of Overlying Rock Fracture and Energy Release under Different Mining Speeds
## 4 Numerical Simulation of Influence of Mining Speed on Energy Release in Mining Field
### The Time Sequence Law of Different Energy Release at the Same Excavation Amount  
Using a single excavation amount of 5 m and 600 time steps as an example, Figure 13 shows the relationship between the total energy and frequency with the equilibrium time step. The energy released by the overlying rock of the working face is greatest at the initial stage of the simulated excavation during a single equilibrium period. As excavation continues, this energy release first sharply increases and then gradually decreases. Similarly, the frequency of mine earthquakes initially rises and then falls, peaking around the 360 time step mark post-excavation. This pattern indicates the necessity for time adjustment to maintain the stability of the overlying rock of the working face. Energy is first monitored at the moment the overlying rock breaks, followed by continuous mine earthquake monitoring during the rock's stable period. Figure 14 illustrates the time series curves of the total energy and the total frequency of mine earthquakes during the process of continuous mining-balance-mining-balance with a single recovery of 5 m. The total energy and frequency released by the overlying strata of the working face exhibit a pattern of periodic fluctuations. In correlation with Figure 13, it is observable that for single time steps of 300 and 600, the total energy peak ascends in  
Figure 13: The figure shows the changes in total energy and frequency with equilibrium time step. tandem with an increase in the recovery amount. Conversely, with a single time step of 900, the total energy peak diminishes as the recovery amount augments. Moreover, with a constant single recovery, a reduction in the single time step corresponds to a heightened total energy peak released by the stop. Figure 15 depicts the distribution of the total energy and maximum energy released by the surrounding rock of the mining field, given a constant single time step. The curve representing the total energy of the model varies in response to different mining speeds. Specifically, the total energy peak value for a single excavation amount of 20 m is recorded at 9.8 \(\times\) 10\({}^{7}\) J. This value exceeds the energy releases measured at lower single excavation amounts: 9.6 \(\times\) 10\({}^{7}\) J for 15 m, 9.1 \(\times\) 10\({}^{7}\) J for 10 m, and 8.4 \(\times\) 10\({}^{7}\) J for 5 m. These observations indicate that, with a consistent time step, an increase in the single excavation amount results in a proportional augmentation of the total energy released per unit time step, with a particular emphasis on the peak value. Figure 14: The figure shows the variation in total energy peak during continuous excavation. Figure 15: The figure shows the time series distributions of total energy under different excavation quantities. Figure 16 shows that the curve delineating the maximum energy of the model unit fluctuates in accordance with variations in mining speed. Under a constant single time step, the maximum elastic energy peak for a single excavation amount of 20 m is calculated to be 0.94 \(\times\) 10\({}^{6}\) J. This value surpasses the energy peaks associated with smaller excavation amounts: 0.7 \(\times\) 10\({}^{6}\) J at 15 m, 0.56 \(\times\) 10\({}^{6}\) J at 10 m, and 0.31 \(\times\) 10\({}^{6}\) J at 5 m. These data signify that curtailing the excavation amount per unit of time moderates the discharge of elastic energy from the surrounding rock, thereby mitigating the potential for impact disasters. Figure 17 illustrates the evolution of elastic energy during the energy adjustment and balance process under various combinations of single excavation quantities and single time steps. Every five time steps, the figure records the maximum unit elastic energy event released post-energy adjustment, offering a representative view. The purple source ball indicates the highest energy level. Initially, the energy source is concentrated around the roof and floor of the mining area.