## 4 Structural Energy Response Spectrum of the Tunnel Blasting Vibration
### Influence of blasting Vibration Characteristics on the Hysteretic Energy Consumption Spectrum
Thus, when the input energy is constant, the greater the damping ratio is, the greater the damping energy is, and the corresponding hysteretic energy will decrease. Evidently, setting obstacles on the propagation path of the blasting seismic wave can reduce the probability of cumulative damage or failure of the engineering structure. Figure 19: Influence of the duration on the hysteretic energy consumption. Figure 18: Influence of the dominant frequency on the hysteretic energy consumption. The influence of the natural period of the structure on the hysteretic energy dissipation is analysed using the same method. The natural periods are set as 0.02 s, 0.04 s, and 0.08 s, respectively. Figure 21 shows that the better the coupling between the vibration predominant period of the blasting seismic wave and the natural period of the structure, the greater the hysteretic energy consumption. Considering the resonance when the two are completely coupled, this is the case where the hysteretic energy consumption will have an extreme value, that is, the greatest threat to the related engineering structure. The influence of the yield strength coefficient and stiffness reduction coefficient on hysteretic energy consumption is analysed by the same method. The stiffness reduction factor of the bilinear restoring force model after yielding is 0.02, the yield strength coefficients are 0.15, 0.25, and 0.3, and the hysteretic energy spectrum is shown in Figure 22. The yield strength coefficient of the bilinear restoring force model is 0.3, the stiffness reduction coefficients are 0, 0.02, and 0.05, and the hysteretic energy spectrum is shown in Figure 23. Figures 22 and 23 show that the increase or decrease in the yield strength coefficient and the stiffness reduction coefficient does not affect the shape of the hysteretic energy consumption spectrum, nor does it cause a drastic change in the hysteretic energy consumption value. The two curves nearly coincide, and the smoothness of the curve does not change. Therefore, the parameters of the restoring force model are not the influencing factors that change the shape of the hysteretic energy dissipation spectrum. Figure 21: Influence of the natural period on the hysteretic energy consumption. Figure 20: Influence of the damping ratio on the hysteretic energy consumption. Influence of Blasting Seismic Waves on the Hysteretic Energy Consumption Spectrum under Different Blasting Conditions  
Excluding the influence of distances from the blasting centre, delay time, and site factors, the influence of charge weight on the hysteretic energy spectrum is analysed. The charge weights of the cut hole are 38 kg, 30 kg, 24 kg, and 20 kg. The damping ratio of the structure is 0.05. The yield strength coefficient of the bilinear restoring force model is 0.3, and the stiffness reduction coefficient after yielding is 0.02. Figure 24 shows that the peak energy of the hysteretic energy spectrum increases markedly with increasing segment charge. The segment charge is an important factor that affects the hysteretic energy consumption and provides theoretical support for the generally accepted measure of controlling the segment charge to achieve safe production in real blasting. The influence of the distance from the blasting centre on the hysteretic energy spectrum is analysed in the same way. The charge weight of the cut hole is 30 kg, and the distances from the blasting centre are 38 m, 48 m, 68 m, and 98 m, respectively. Figure 25 shows that the change in distance from the blasting centre has no effect on the shape of hysteretic energy consumption, which is reflected in the smoothness of the hysteretic energy spectrum curve. It can be explained that the distance from the blasting centre is not the influencing factor of the shape change of the hysteretic energy spectrum. The increase in the distance from the blasting centre will lead to a decrease in the peak hysteretic energy dissipation, PPV, and dominant frequency, while the duration of the vibration will be prolonged.