## 1 Introduction  
With a large-scale construction project that is part of China's transportation infrastructure, the corresponding tunnel construction projects are increasing. Drilling and blasting are still the primary methods of tunnel excavation due to their economic and efficiency characteristics. However, blasting vibrations may damage the tunnel's support structure and cause a collapse of the adjacent surrounding rock. The blasting seismic wave will attenuate as it propagates [1, 2]. Due to variable and uncertain geological conditions in the tunnel, this attenuation is complex. Many scholars have studied vibration attenuation inside tunnels to improve structural safety and stability [3, 4, 5]. Clarifying which segment blasting has the strongest impact on vibration and what the influencing factors are important to tunnel blasting design, real vibration reduction, and disaster prevention. More importantly, the response mechanism of different engineering structures to blasting vibration is different. The blast centre conditions and the properties of the measured structure will affect the dynamic response characteristics of the structure. [PERSON] [6] and [PERSON] [7] used the superposition method and reciprocity theorem to calculate the response of columnar and slender chambers under finite long-term dynamic loads, respectively. [PERSON] [8] studied the impact response of subway tunnels under blast loading by numerical simulation, which provided a reference for blast-resistant protection and emergency plan for subway tunnels. [PERSON] et al. [9] studied the effect of tunnel blasting vibration on the excavated part of the lining of different ages through model tests. [PERSON] et al. [10] analysed the damage characteristics of tunnel lining structures based on numerical simulation and the energy principle. [PERSON] et al. [11] found that the response spectrum analysis method can be used to investigate the dynamic response of tunnel structures under blasting vibration. Various structures respond differently to blast seismic waves; thus, it is necessary to quantify the effects of the inherent properties of the vibrated structure's response to blasting vibration. Chinese safety regulations for blasting vibration [12] stipulate that the PPV and the dominant frequency are used as the comprehensive criterion for the tunnel structure. However, the tunnel structure is sometimes damaged when the PPV is much lower than the safe allowable PPV, which indicates that the current safety criteria are imperfect. [PERSON] et al. [13] proposed that the integral value of the response spectrum curve be used as the evaluation standard for the damage effect of blasting vibration. [PERSON] [14] proposed the equivalent velocity under the maximum instantaneous input energy as the blasting vibration safety criterion based on the HHT (Hilbert-Huang Transform) method. [PERSON] [15] proposed the evaluation index of EPE (Equivalent Peak Energy) and preliminarily discussed the possibility of establishing the EPE evaluation index. [PERSON] [16] established the integral value of the TEDI (Integral of the Time-Energy Density) based on the wavelet time-energy density method as a unified safety criterion for blasting vibration damage and determined the damage threshold of TEDI > 15 through a neural network. That research provides a basis for blasting vibration safety criterion and highlights the direction for follow-up safety criterion research. However, the energy response of the tunnel structure under the action of blasting vibration is affected by the blasting seismic wave characteristics and the inherent properties of the structure itself. Based on the above analysis, the safety criterion based solely on the characteristics of blasting seismic waves or the inherent properties of the structure markedly cannot fully describe the real hazards of engineering structures under the action of blasting seismic waves.