## 4 Case Study
### Risk Coupling of DFP Construction in Adjacent Existing Underpass Tunnels  
In this study, 86 risk events from 51 similar engineering projects that the Survey and Design Institute Group Ltd. was involved in over the period from 2015 to 2021 were compiled and counted, as shown in Table 5. Moreover, the coupling degree between various risk factors was calculated. In order to calculate the mutual information T, the probabilities of occurrence of different coupling cases were calculated, and the results are shown in Table 6. Additionally, the coupling degree of two-factor and multi-risk coupling were calculated according to Equations (11) and (12), respectively. For two-factor risk coupling and multi-factor risk coupling, the coupling values are as shown in Table 7. Therefore, the coupling values were arranged as follows: T4 \(>\) T33 \(>\) T32 \(>\) T21 \(>\) T23 \(>\) T34 \(>\) T31 \(>\) T22 \(>\) T26 \(>\) T24 \(>\) T25. The results show that multi-factor coupling usually has a higher coupling degree than two-factor coupling, but there are also cases where the multi-factor coupling degree is lower than the two-factor coupling degree such as T23 \(>\) T34. Moreover, the larger the coupling degree value, the greater the interaction of risk factors; hence great attention must be paid to this point. This study combined the expert recommendations and summaries of historical accidents, attached great significance to coupling cases with a coupling degree greater than or equal to 0.1, and introduced nodes T4, T33, T32, T21, and T23 in the Bayesian network. Therefore, the overall risk is not only influenced by SFPI (A1), SET (A2), SSE (A3), and HF (A4) but is also affected by multi-factor coupling. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Left Side of Association Rules** & **Right Side of Association Rules** & **Lift** & **Support** & **Confidence** \\ \hline \{UEU-Y, DSTS-Y, EE-Y} & \(\xrightarrow{}\) & \(\xrightarrow{}\) & 1.3327 & 0.581 & 0.983 \\ \{PWI-M, ETF-L, ECTS-Y} & \(\xrightarrow{}\) & \(\xrightarrow{}\) & 1.3319 & 0.560 & 0.982 \\ \{SS-Y, HL-M, RSS-Y, SFPI-M} & \(\xrightarrow{}\) & \(\xrightarrow{}\) & 1.3218 & 0.552 & 0.982 \\ \{IRS-Y, HC-Y, BP-Y, LOSC-Y} & \(\xrightarrow{}\) & \(\xrightarrow{}\) & \(\xrightarrow{}\) & 1.3201 & 0.561 & 0.966 \\ \{PWI-M, ETF-L, ECTS-Y} & \(\xrightarrow{}\) & \(\xrightarrow{}\) & \(\xrightarrow{}\) & 1.3105 & 0.540 & 0.931 \\ \{HL-M, RSS-Y, SS-Y, EWS-L} & \(\xrightarrow{}\) & \(\xrightarrow{}\) & \(\xrightarrow{}\) & 1.3098 & 0.551 & 0.932 \\ \{DRSS-M, HC-Y, IRS-Y} & \(\xrightarrow{}\) & \(\xrightarrow{}\) & 1.3051 & 0.511 & 0.879 \\ \(\dots\) & & \(\dots\) & \(\dots\) & \(\dots\) & \(\dots\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Schematic of the association rules. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Two Frequent Item Sets** & **Support** & **Three Frequent Item Sets** & **Support** & **Four Frequent Item Sets** & **Support** \\ \hline \{SLO-Y, SI-Y\} & 0.511 & \{ISR-Y, SLO-Y, SI-Y\} & 0.452 & \{SS-Y, HL-M, RSS-Y, SFPI-M\} & 0.405 \\ \{RSS-Y, SS-Y\} & 0.498 & \{RSS-Y, EWS-M, SS-Y\} & 0.471 & \{HL-M, RSS-Y, SS-Y, EWS-L\} & 0.409 \\ \{UGS-Y, CFS-L\} & 0.492 & \{BP-Y, DRSS-L, IRS-Y\} & 0.422 & \{SET-M, UEU-Y, USLU-Y, DSTS-M\} & 0.401 \\ \{HF-Y, FOP-Y\} & 0.507 & [DRSS-M, HC-Y, IRS-Y] & 0.455 & \{SSE-M, BID-Y, UGS-Y, UWS-M\} & 0.411 \\ \{BH-Y, ISS-N\} & 0.514 & \{UEU-Y, DSTS-Y, EE-Y\} & 0.436 & \{SS-Y, SI-Y, BH-Y, SFPI-M\} & 0.413 \\ \{HF-Y, HE-Y\} & 0.489 & \{PWI-M, ETF-L, ECTS-Y\} & 0.408 & \{IRS-Y, HC-Y, BP-Y, SFPI-Y\} & 0.414 \\ \{IRS-Y, DRSS-L\} & 0.496 & \{UWS-M, CFS-M, UGS-Y\} & 0.434 & \{FPI-Y, SFPI-M, SPF-Y, HGL-Y\} & 0.408 \\ \(\dots\) & & \(\dots\) & \(\dots\) & \(\dots\) & \(\dots\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Frequent item set of construction risks of DFPs in adjacent existing underpass tunnels.