# Effects of Vibration on Adjacent Pipelines under Blasting Excavation
## 6 Conclusions  
In this study, by utilizing a water diversion tunnel project in Zhejiang, the response characteristics of a buried pipe under blasting construction conditions were explored, pipeline safety was analyzed, and the following conclusions were drawn:  
1. A three-dimensional numerical model considering in situ stress was established. The triangular equivalent load method was used to reflect the explosion effect. The reasonableness of the model was verified based on a comparative analysis of the field-monitoring results and a solution using the empirical equation of stress wave theory. The results show the error of the _PPV_ is within a reasonable range (\(\leq\)7.69%) with high simulation accuracy. 2. The _PPV_ results for each construction condition show the _PPV_ decays exponentially with increasing horizontal and axial distances. The maximum _PPV_ appeared at the horizontal distance of 0 m from the explosion source when the axial distance was 0 m with a value of 2.6 cm/s. The minimum _PPV_ appeared at the horizontal distance of 60 m from the explosion source when the axial distance was 40 m with a value of 0.7 cm/s. In addition, the axial vibration velocity distribution results indicate a  
Figure 13: Statistical relationship: (a) _PPV_ prediction model; (b) PES safety criterion. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Horizontal Distance** & **PES of Simulation (MPa)** & **PPV of Simulation (cm/s)** & **PPV Predicted by Equation (11)** & **Error Rate of _PPV_** \\ \hline
0 & 1.87 & 2.60 & 2.58 & 0.77 \\
8 & 1.48 & 2.29 & 2.31 & 0.87 \\
16 & 1.20 & 2.02 & 2.03 & 0.50 \\
24 & 1.05 & 1.77 & 1.69 & 4.52 \\
32 & 0.84 & 1.50 & 1.48 & 1.33 \\
40 & 0.65 & 1.26 & 1.22 & 3.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Simulation data and predicted results. significant cavity amplification effect above the excavation area, which should be seriously considered in future research. 3. The _PPV_ distribution results at the pipe cross-section indicate the _PPV_ on the blast side was more significant than that behind the blast side when the blast vibration was transmitted to the pipeline. The maximum _PPV_ value appeared nearest to the source of the explosion, and the minimum value appeared farthest from the blast source. 4. The PES occurring had exponential decay on both sides of the blast source with increasing horizontal distance from the blast source. The PES results of the pipe sections under different construction conditions show the PES of the lower part of the pipe section was significantly lower than that of the upper part due to the interaction between the soil and the pipe. In addition, the maximum PES value at the cross-section (1.53 MPa) when in a hazardous situation (pipe directly above the blast source) was less than the safe threshold (\(\leq\)4.6 MPa). This indicates the blast vibration will not affect the normal service of the buried pipeline. 5. This paper effectively reflects blast vibration propagation law by proposing an effective _PPV_ prediction model for pipelines which applies a dimension and composition analysis combined with numerical simulation and field-monitoring results. This prediction model may guide the subsequent development of a reasonable blasting scheme. In addition, this study proposes an empirical safety criteria formula for the scientific implementation of safety assessments for subsequent construction. Conceptualization, T.Q. and M.W. ; methodology, T.Q. and L.J. ; software, T.Q. and M.W. ; validation, T.Q., L.X. and L.J. ; formal analysis, T.Q. and M.W. ; investigation, T.Q. and L.J. ; resources, L.W. ; data curation, T.Q. ; writing--original draft preparation, T.Q. ; writing--review and editing, T.Q. ; visualization, M.W. ; supervision, L.W. ; project administration, L.J. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.