## 5 Case Study
### Analysis of Calculation Results  
#### 5.3.1 Analysis of Weight Results  
As shown in Table 4, the equipment risk (\(R_{3}\)) represents the highest risk. The experts participating in the evaluation believed that although the China Railway Group has been extensively involved in rail transit projects, it may not be familiar with the management of large-scale machinery and equipment in deep pit projects. Delays in providing and maintaining equipment and incorrect installation and positioning can occur in a tight construction period. The management personnel of the construction machinery and equipment and the construction safety management personnel of the unit are responsible for the use, maintenance, and safety inspection of machinery and equipment. Since there are hidden dangers when using large equipment, the operators, managers, and maintenance personnel must be educated on the equipment operation and safety to improve their professional and technical expertise and safety awareness. The index weight of the Method (\(R_{4}\)) ranks second, which is attributed to the characteristics of the construction process and high technology level of deep foundation pit projects. The excavation of a foundation pit follows the theory of the \"time-space effect\". The time when the foundation pit is unsupported should be minimized. Global positioning system (GPS) data can be used to accurately locate the position of the supporting piles and anchor cables to ensure the overall safety performance. When unique geological or hydrological conditions are encountered, the slurry mix ratio can be increased to ensure adequate grouting pressure and grouting time to prevent water inrush in overlapping water-stop curtains. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Index**} & **Third Partial** & \multirow{2}{*}{**Situation**} & **Fourth Partial** & \multirow{2}{*}{**Situation**} \\  & **Derivative** & & & \\ \hline \(R_{11}\) & \(0.526+0.511i_{\mu 1}\) & Same & 0.507 & Same \\ \(R_{12}\) & \(0.432+0.550i_{\mu 1}\) & Contrary & 0.440 & Contrary \\ \(R_{13}\) & \(0.418+0.526i_{\mu 1}\) & Contrary & 0.443 & Contrary \\ \(R_{14}\) & \(0.422+0.535i_{\mu 1}\) & Contrary & 0.441 & Contrary \\ \(R_{15}\) & \(0.465+0.495i_{\mu 1}\) & Contrary & 0.484 & Contrary \\ \(R_{1}\) & \(0.454+0.520i_{\mu 1}\) & Contrary & 0.466 & Contrary \\ \(R_{21}\) & \(0.574+0.356i_{\mu 1}\) & Same & 0.618 & Same \\ \(R_{22}\) & \(0.504+0.445i_{\mu 1}\) & Same & 0.531 & Same \\ \(R_{23}\) & \(0.451+0.511i_{\mu 1}\) & Contrary & 0.469 & Contrary \\ \(R_{24}\) & \(0.450+0.532i_{\mu 1}\) & Contrary & 0.458 & Contrary \\ \(R_{2}\) & \(0.501+0.451i_{\mu 1}\) & Same & 0.528 & Same \\ \(R_{31}\) & \(0.491+0.494i_{\mu 1}\) & Contrary & 0.499 & Contrary \\ \(R_{32}\) & \(0.537+0.423i_{\mu 1}\) & Same & 0.559 & Same \\ \(R_{33}\) & \(0.406+0.514i_{\mu 1}\) & Contrary & 0.441 & Contrary \\ \(R_{34}\) & \(0.452+0.457i_{\mu 1}\) & Contrary & 0.497 & Contrary \\ \(R_{35}\) & \(0.407+0.580i_{\mu 1}\) & Contrary & 0.412 & Contrary \\ \(R_{3}\) & \(0.458+0.494i_{\mu 1}\) & Contrary & 0.481 & Contrary \\ \(R_{41}\) & \(0.500+0.523i_{\mu 1}\) & Contrary & 0.489 & Contrary \\ \(R_{42}\) & \(0.550+0.425i_{\mu 1}\) & Same & 0.564 & Same \\ \(R_{43}\) & \(0.471+0.459i_{\mu 1}\) & Same & 0.506 & Same \\ \(R_{44}\) & \(0.479+0.515i_{\mu 1}\) & Contrary & 0.482 & Contrary \\ \(R_{4}\) & \(0.497+0.484i_{\mu 1}\) & Same & 0.507 & Same \\ \(R_{51}\) & \(0.501+0.512i_{\mu 1}\) & Contrary & 0.495 & Contrary \\ \(R_{52}\) & \(0.466+0.503i_{\mu 1}\) & Contrary & 0.481 & Contrary \\ \(R_{53}\) & \(0.521+0.481i_{\mu 1}\) & Same & 0.520 & Same \\ \(R_{54}\) & \(0.480+0.542i_{\mu 1}\) & Contrary & 0.470 & Contrary \\ \(R_{55}\) & \(0.515+0.555i_{\mu 1}\) & Contrary & 0.481 & Contrary \\ \(R_{5}\) & \(0.495+0.525i_{\mu 1}\) & Contrary & 0.485 & Contrary \\ \(R\) & \(0.480+0.495i_{\mu 1}\) & Contrary & 0.493 & Contrary \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Third and fourth partial derivatives.