## 4 Conclusions  
The innovation of this paper was that from the perspective of vibration control of urban shallow-buried tunnels, an identification method of new-free-surface formation time was given. At present, there is no unified definition of the formation standard of a free surface in practice, so the formation time of a new free surface cannot be accurately identified. In the past, even if high-precision detonators and hole-by-hole initiation were used, researchers could only ignore the new free surface and calculate all possible vibration waves caused by multihole cut blasting by using the traversal method. Such calculations are  
Figure 14: Vibration wave curves.  
Figure 13: Blasting excavation design of CD method.  
conservative and time-consuming. Our method provides a basis for further improvements in vibration-control technology.  
1. A vibration-prediction method that considered the action of the newly created free surface during blasting was proposed. The crucial step was to determine the formation time of the new free surface by comparing the vibration energy. The specific process combined the detonator sample test of each delay with the VMD method so the exact initiation time sequence of each delay could be determined in the observed blast vibration wave. The predicted wave with the same initiation time sequence was constructed using the linear superposition method. The Hilbert transform then found the accumulated energy curves of the observed and predicted the vibration waves. The new-free-surface formation time was found by comparing the linear correlation of the two curves.
2. The formation time of the new free surface was determined to be 64.5 ms through the case study, while the change in rock conditions around the blast hole caused by its action could last up to 91.375 ms. For this reason, the applicable range of the linear superposition model for predicting the superposed vibration velocity was determined to be the first three blast holes. The maximum vibration peaks that could be achieved by using 1.0 kg and 1.2 kg in a single-hole charge were 0.775 cm-s\({}^{-1}\) and 0.868 cm-s\({}^{-1}\), respectively, under a vibration velocity threshold of 1.0 cm-s\({}^{-1}\). Considering that the actual range of the detonator's delay error may have been larger and due to the superposed effect of vibration caused by subsequent holes, a single-hole charge of 1.0 kg was finally used to ensure blasting safety.
3. There is great potential for solving complex blast calculation problems through the rapid development of computer technology. Since NONEL detonators have a wide range of delay errors, using their nominal initiation times to calculate superposed waves is simple but can result in significant errors. If the enumeration method traverses all possible initiation time groups, it will consume a lot of time. This paper used the Monte Carlo method to simulate the randomness of detonations, which saved computing time and accurately obtained the maximum superposed vibration velocity value. The blasting results in the field showed that the selected charge could meet the requirements for low-vibration velocity control.  
Conceptualization, H.W. and M.G.; methodology, H.W. and X.L.; software, Q.Z.; validation, H.W. and X.L.; formal analysis, H.W.; investigation, H.W., M.G., and X.W.; resources, M.G.; data curation, H.W.; writing--original draft preparation, H.W.; writing--review and editing, H.W., M.G., and Q.Z.; visualization, H.W., M.G., and Q.Z.; supervision, H.W. and X.W.; project administration, M.G.; funding acquisition, M.G. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Fundamental Research Funds for the Central Universities (No. FRF-AT-19-005).  
Not applicable.  
The authors sincerely thank all the editors and reviewers for their support and help.  
The authors declare no conflict of interest.