## 4 Case Study
### Model Validation Stage  
In this study, a coupled dynamic Bayesian network was established for the risk of DFPs adjacent to existing underpass tunnels, and 20 additional sets of data collected previously  
\begin{table}
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were input into the model. The risk states obtained from the Bayesian inference were compared with the actual risk states to validate the model, and the validation results are shown in Table 8. Of the 20 test samples, only the third group's results did not agree with the actual measurements, which means that the model's accuracy was 95%. In addition, the proposed coupled dynamic Bayesian network model was partially validated for the risk of DFPs adjacent to existing underpass tunnels. For example, when the probability of the low safety of foundation pits, existing tunnels, surrounding environment, and human factors is set to 100%, the probability of low safety of the overall risk increases from 9.96% to 13.1%, 14.0%, 14.7%, and 15.6%, respectively. In contrast, when the high probability of the safety degree for these parent nodes is set to 100%, the low safety degree probability of the overall risk decreases from 9.96% to 9.09%, 8.73%, 8.42%, and 7.83%, confirming the three axioms. In summary, the accuracy of the constructed coupled dynamic Bayesian network model for the risk of DFPs adjacent to existing underpass tunnels was verified, and the model can be used for risk assessment in similar projects.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(T_{21}\) & \(T_{22}\) & \(T_{23}\) & \(T_{24}\) & \(T_{25}\) & \(T_{26}\) & \(T_{31}\) & \(T_{32}\) & \(T_{33}\) & \(T_{34}\) & \(T_{4}\) \\ \hline
0.183 & 0.115 & 0.178 & 4 \(\times\) 10\({}^{-4}\) & 2 \(\times\) 10\({}^{-4}\) & 0.091 & 0.174 & 0.238 & 0.343 & 0.176 & 0.463 \\ \hline \hline \end{tabular}
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Table 7: Coupling values of each risk factor for construction accidents in the DFPs of adjacent existing underpass tunnels.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Test Samples**} & \multicolumn{6}{c}{**Safety of DFPs Adjacent to Existing**} & \multirow{2}{*}{**Expectation**} & \multirow{2}{*}{**Actuality**} \\ \cline{3-3} \cline{5-8}  & & & \multicolumn{2}{c}{**Undergass Tunnels**} & & & \\ \cline{3-3} \cline{5-8}  & & & **High** & **Medium** & **Low** & & \\ \hline
1 & C1 = No; C3 = Yes; C13 = Low; C14 = No; B5 = Yes & 64.8\% & 24.8\% & 10.5\% & High & High \\
2 & A1 = Medium; A2 = Low; B7 = No; B7, B11 = Yes & 43.3\% & 43.6\% & 13.1\% & Medium & Medium \\
3 & A2 = Medium; B5, C11, C3 = Yes; B6 = No; C18 = High & 60.5\% & 28.6\% & 10.9\% & High & High \\
4 & C1, C3 = Yes; B2, C12 = No; C13, C22 = High & 67.0\% & 23.0\% & 10.0\% & High & High \\
5 & A4, A1 = Low; B6, B7, B8, B9 = Yes & 42.3\% & 42.4\% & 15.2\% & Medium & High \\
6 & B5 = No; C2 = Yes; C18 = High; A1 = Medium & 49.8\% & 38.0\% & 12.2\% & High & High \\
7 & A4 = Medium, B2, B7 = Yes, & 62.0 & 26.9\% & 11.1\% & High & High \\
8 & B8, B6, C11, C12 = No; B2 = Yes; C17 = High & 64.3\% & 25.1\% & 10.6\% & High & High \\
20 & B2, B3, B8, B9, C11, C12 = No; C13, C21, C16 = High & 59.6\% & 29\% & 11.4\% & High & High \\ \hline \hline \end{tabular}
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Table 8: Model validation (comparison of predicted and actual results).  
Figure 11: Risk factors for the construction of DFPs adjacent to existing underpass tunnels.