## 5 Conclusions  
In this study, we explored the global vibration impact assessment using several selected monitoring points on construction sites. By investigating the features of ground-borne vibration propagation due to vibratory pile driving work, we developed a time-based localization method to localize vibratory driving sources on construction sites. The localized vibratory driving sources and the site-specific empirical relationship derived from the field test data enable the estimation of vibration intensities over an extensive surrounding area rather than at a few monitoring points. The effects of pile toe depths, spatial relationships, and ground and construction conditions on localization performance were investigated through numerical parametric studies and field tests on a construction site with ongoing vibratory sheet pile driving work. The main findings are as follows:  
1. For vibratory sheet pile driving at a certain depth, surface waves dominate the ground surface vibrations, while cylindrical shear waves from the pile shaft dominate the underground vibrations within the range of the pile shaft, and spherical body waves from the pile toe dominate underground vibrations at depths below the pile toe.
2. The time-based localization method assuming the single surface wave content along the ground surface is proved to be effective in localizing a vibratory driving source (e.g., vibratory sheet pile diving) on construction sites under different ground and construction conditions.
3. The layout of monitoring points has a notable effect on the localization performance. Both numerical simulations and field tests of vibratory sheet pile driving show that using a layout of monitoring points deployed in both directions surrounding the driving location can achieve a better localization performance.
4. The localized driving location and the estimated vibration attenuation formula can jointly estimate vibration intensity in the entire surrounding area rather than at a few monitored points, and then realize a global vibration impact assessment.  
This study achieves an acceptable localization performance of unknown vibratory driving sources under the prerequisite that the ground is regarded as an infinite half-space domain with homogeneous soil properties. However, complex vibration propagations can be encountered due to soil stratification and geometric irregularity, which may result in the potential degradation of localization performance. Therefore, such complexity should be investigated in future studies.  
Data curation, methodology, software, investigation, validation, visualization, writing--original draft preparation, S.W.; conceptualization, supervision, funding acquisition, project administration, writing--review and editing, S.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China (grant no. 2019 YFB1600700) and the Hong Kong Polytechnic University (grant nos. ZE2L, BBWJ, ZVX6, ZJMV).  
Not applicable.  
The data generated or used during the study appear in the published article.  
The authors would like to thank the editor and the reviewers for their contributions.  
The authors declare no conflict of interest.