## 5 Numerical Simulation Results Analysis
### Response Characteristics of Roadway Surrounding Rock  
The distribution of elastic strain energy before and after the application of vibrational waves is analyzed using the impact instability energy assessment methodology. Figure 21 illustrates the distribution of elastic strain energy that has accumulated around the roadway at various time intervals. As depicted in Figure 21a, prior to the application of vibrational waves, the elastic energy is primarily concentrated within the coal seams adjacent to the roadway. Notably, the accumulation of energy in the upper section of the left side of the roadway is approximately \(5\times 10^{5}\) J, which signifies a greater concentration in comparison to the right side. Additionally, the volume of the area demonstrating this concentration is relatively larger, leading to an increased energy density. This is consistent with previous research [26], which indicates that the elastic energy of coal and rock masses primarily accumulates on both sides of the roadway. At 0.12 s, the distribution of elastic energy in the vicinity of the roadway is largely comparable to that observed in the absence of the vibrational wave. This observation indicates that the P-wave has not yet exerted a significant influence on the surrounding roadway, which remains in a stable condition. At 0.23 s, the elastic energy on the left side of the roadway increased by approximately \(1.5\times 10^{4}\) J, accompanied by a minimal overall growth rate. Simultaneously, there was no notable increase in the area of elastic energy available for release around the roadway. As illustrated in Figure 21d, following the application of low-frequency, high-energy S-waves, there is a notable enhancement in both the range and amplitude of elastic energy on the left side of the roadway. Additionally, a significant accumulation of energy is observed in the upper region of the left side of the roadway, as well as at the bottom angle of the right side of the roadway. Due to the placement of the seismic source on the left side of the roadway, the area of concentrated high elastic performance extends over a larger region, approaching the boundary of the roadway. As a result, there is a substantial increase in the accumulation of elastic energy in the coal surrounding the roadway. As illustrated in Figure 22, the excavation process has led to the formation of a plastic zone around the roadway, which exhibits an approximately ellipsoidal shape. Notably, the severity of the plastic zone is more pronounced in the upper regions on both the left and right sides. When a vibrational wave is applied for a duration of 0.12 s, the P-wave, which primarily induces tensile and compressive failure, has not yet produced a corresponding plastic failure zone in the vicinity of the source. During the interval from 0.12 to 0.23 s, a slight degree of plastic deformation was observed to commence in the vicinity of the source, attributable to the influence of S-wave shear. During the time interval from 0.23 to 0.7 s, the impact of two low-frequency, high-energy S-waves led to a significant incidence of shear failure in the vicinity of the source. This observation suggests that low-frequency, high-energy S-waves play a crucial role in inducing shear failure within the roadway. Importantly, when the energy levels are sufficiently high, the shear effects result in a widespread area of plastic failure. failure threshold of the surrounding rock mass. This finding indicates an increased risk of instability in the lower left corner of the roadway. According to Figure 23(a), at 0.7 s, the upper half of both sides of the roadway exhibited significant displacement. The direction indicated by the arrow represents the displacement direction of the surrounding rock. The maximum net displacement on the upper side of the left side was 21.2 mm, while the maximum net displacement of the right side as a whole was 10.1 mm. As illustrated in Figure 23(b), the application of the vibration wave results in a general downward displacement of the roadway roof.