## 7 Summary and Conclusions  
The duration of the pulse-type near-fault ground motions (NFGMs) has a significant effect on the nonlinear dynamic response and degree of damage in an hydraulic arched tunnel-water-surrounding rock dynamic interaction system. Firstly, the concept of the effective velocity duration (EVD) index, according to the specific energy density was explained, considering the duration of the low-frequency velocity impulse and the energy released from the velocity time-history. The dynamic interaction system was then subjected to a variety of time-history investigations to reveal the effect of the EVD on the structural response. Subsequently, the most efficient EVD of the limit value and the replaceable acceleration-type duration indicator was discussed. Finally, the feasibility of replacing the reduced ground motion records defined by the EVD duration index for the full-time ground motion records was established. The following conclusions could be drawn from the calculation results:  
(1) The correlation analysis results showed that the EVD positively correlates to the maximum relative displacement, which means that the longer the NF earthquake excitation time, the easier it is to cause more considerable deformation and instability to the tunnel. Furthermore, the impacts of the EVD on the cumulative damage pattern were investigated using the concrete damage plasticity model, which simulated the softening and strain hardening behaviors of concrete materials. According to the cracking profiles, it could be deduced that in the majority of instances, the concrete lining exhibited minor cumulative damage and cracks in the bottom and top sections, with a tendency to grow to the sidewall portion as the EVD rose;  
(2) The presented three fixed threshold values (5-75%, 15-85%, and 5-95%) of the EVD index could successfully capture the duration of the low-frequency velocity impulse and most of the energy released by strong NFGMs. The link between maximum relative displacement and damage indices was strongest between the 5-95% fixed threshold values evaluated. As a consequence, the fixed threshold value of EVD between 5-95% is proposed as the most appropriate duration measurement for characterizing the duration of the pulse-like NFGMs. Moreover, for the convenience of engineering applications, significant duration indicators can be considered as a backup option for near-fault effective duration indicators to identify the impact of the ground motion duration;  
(3) To undertake an efficient and fast analysis of the dynamic response, a simplified time-history technique was provided that covered the time-history range of EVD 5-95% of the original NFGMs. Subsequently, the reduced time history of the NFGMs was then applied to the inelastic dynamic analysis of the hydraulic arched tunnel, and the computational findings suggested that the reduced and original NFGM records were similar, indicating that the time-history of the original NFGMs can be replaced by the reduced time-history of the NFGMs and employed to predict the structural response with a high efficiency and high precision. Conceptualization and methodology, W.L. and B.S. ; software, B.S. ; validation, B.S., S.Z. and C.W. ; formal analysis, W.L. and B.S. ; investigation, W.C.; resources, X.Z. ; data curation, W.L. and B.S. ; writing--original draft preparation, B.S. ; writing--review and editing, W.L. and B.S. ; supervision, B.S and S.Z. ; project administration, B.S. All authors have read and agreed to the published version of the manuscript. National Natural Science Foundation of China (No. 52009126 & No. 52209169). Not applicable. The authors declare no conflict of interest. * _[PERSON] et al. (2009)_ [PERSON]; [PERSON]; [PERSON] Empirical Equations for the Prediction of the Significant, Bracketed, and Uniform Duration of Earthquake Ground Motion. _Bull. Seism. Soc. Am._**2009**, _99_, 3217-3233. [CrossRef]
* _[PERSON] et al.