## 5 Numerical Simulation Results Analysis
### Response Characteristics of Roadway-Anchored Surrounding Rock
#### 5.2.1 Response Characteristics of Rock at the Anchorage End  
(1) Anchorage end of left-side anchor bolt  
Stage I (0-0.12 s): During the initial phase of P-wave propagation, the variations in vibration velocity at the measurement point are minimal, the stress values remain constant, and the displacement approaches zero. This observation indicates that the surrounding rock is not significantly affected by the dynamic load and is in a state of static compression. When the amplitude of the P-wave vibration hits its initial peak, it results in significant vibrations in the surrounding rock of the anchorage area. The maximum velocity in the horizontal direction is measured at 0.16 m/s, whereas in the vertical direction, it is recorded at 0.02 m/s. The tension and compression experienced in the horizontal direction, as a consequence of the P-wave, resulted in periodic fluctuations in stress within a limited range. The horizontal displacement demonstrates a pattern of periodic migration, whereas the range of vertical displacement is not clearly discernible. This shows that the anchored surrounding rock is in the elastic response stage at this time; no plastic deformation occurs, and the surrounding rock can be restored to the initial state. Stage II (0.12-0.23 s): The simultaneous propagation of P-waves and S-waves leads to a significant increase in both the frequency and amplitude of vibrational velocity in horizontal and vertical directions. Between 0.12 s and 0.19 s, the horizontal vibrations primarily induced by the P-wave remain elevated. After 0.19 s, the horizontal vibration velocity associated with the P-wave begins to progressively diminish, while the horizontal displacement approaches a state of stability. During this period, the energy of the P-wave gradually decays. At this time, the energy of the S-wave is low, and the monitored amplitude is primarily generated by the P-wave. After 0.19 s, the vertical velocity caused by the S-wave began to exhibit high-frequency vibrations, and the vertical displacement showed an increasing trend during this phase. Stage III (0.23-0.7 s): The low-frequency, high-energy S-wave peak nodes occur at 0.29 s and 0.46 s. During these intervals, the horizontal vibration velocity of the surrounding rock experiences two substantial increases, while the vibration frequency of the vertical velocity exhibits a significant rise. The shear failure caused by low-frequency, high-energy S-waves within the rock mass leads to an increase in horizontal stress from 3 MPa to 11.5 MPa, a displacement increase of 5.5 mm, and a trend towards stabilization after 0.62 s. Due to the direct floor located beneath the measuring point of the side bolt, the range of vertical stress fluctuations caused by the low-frequency, high-energy S-wave is minimal, resulting in a vertical displacement increase of 2.2 mm. (2)a tendency to decrease. However, the vibration frequency associated with the S-wave is significantly higher than that associated with the P-wave, as illustrated in Figure 18.  
Stage III (0.23\(\sim\)0.7 s): At the low-frequency and high-energy vibration nodes occurring at 0.29 s and 0.46 s, two S-waves are detected. The vibration frequency of the surrounding rock of the roof induced by these S-waves is significantly higher than that observed during the initial two stages. Simultaneously, the horizontal stress demonstrated a rapid increase from 3.8 MPa to 5.1 MPa. The horizontal displacement exhibits an initial trend of rapid increase, followed by a subsequent rapid decrease. This phenomenon occurs when the surface of the roadway is influenced by vibrational waves, resulting in a net horizontal displacement away from the originating source. Subsequently, due to tectonic stress, this horizontal displacement undergoes a rebound effect. The vertical stress exhibits a periodic upward trend, and the vibration amplitude is linearly correlated with the vertical particle vibration velocity.