## 4 Results
### The Probabilistic Analysis
#### 4.3.2 Reliability of Ground Surface Settlement of the Excavation
\begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Reference** & **Depth of Excavation (m)** & **Monitored \(H_{m}\) (mm)** \\ \hline
1 & [PERSON] [66] & 24 & 85.65 \\  & & 16.6 & 61.3 \\
2 & [PERSON] [67] & 14.8 & 88.0 \\  & & 16.2 & 55.9 \\  & & 16.5 & 71 \\  & & 17\(\sim\)18.5 & 37.26 \\
3 & [PERSON] [68] & 16\(\sim\)18.5 & 79.68 \\  & & 18\(\sim\)20 & 44.43 \\  & & 16\(\sim\)17.2 & 69.41 \\
4 & [PERSON] et al. [69] & 33 & 67\(\sim\)88.61 \\ \hline \end{tabular}
\end{table} 
Table 6: Surface settlement values for similar excavation projects in the Hangzhou area. Figure 15: Effect of \(H_{\text{com}}\) on settlement control guarantee rate (\(R_{g}\)) and reliability index (\(\beta\)). Figure 18 presents the variable response of the PDF curves of the \(H_{\text{m}}\) and \(D^{\prime}{}_{m}\) with the COV of MCC model parameters. With regard to the \(H_{\text{m}}\), as shown in Figure 18a, it followed a log-normal distribution for all the investigated \(\text{COV}_{\lambda,x}\). The \(\mu_{\text{Hm}}\) and \(\sigma_{\text{Hm}}\) increased with the increasing \(\text{COV}_{\lambda,x}\), and the peak of the PDF curve shifted to the right, indicating that the variation range became larger; thus, the \(\text{COV}_{H\text{m}}\) increased accordingly, which corresponded to the results reflected in Figure 17. A closer inspection of the data shows the equivalence of the values of \(\text{COV}_{H\text{m}}\) and \(\text{COV}_{\lambda,x}\). This observation was compatible with related studies [70], and the subtle discrepancy may be explained by the distinction between the single random variable approach and the random field variable approach. With regard to \(D^{\prime}{}_{m}\), as shown in Figure 18b, it also followed a log-normal distribution for all the investigated \(\text{COV}_{\lambda,x}\). The mean and standard deviation (\(\mu_{\text{D}\text{m}}\) and \(\sigma_{\text{D}\text{m}}\)) generally increased with the increasing \(\text{COV}_{\lambda,x}\), and the COV of \(D^{\prime}{}_{m}\) increased from 0.45 to 0.72, indicating a remarkable increase in dispersion. Besides, it is noticeable that the statistical characteristics were insignificantly different when the \(\text{COV}_{\lambda,x}\) were taken as 0.2 and 0.25, and their PDF curves were practically overlapped. The relationship between the reliability index, \(\beta\), and the \(\text{COV}_{\lambda,x}\) have also been investigated, as shown in Figure 19. With the increase of \(\text{COV}_{\lambda,x}\), the \(\beta\) reduced significantly from 2.7 to merely 0.1, which is virtually a linear decline. It can be learned that the variability of the deformation parameters of the MCC model has a considerable influence  
Figure 16: Time-varying reliability of ground surface settlement of the excavation. Figure 17: Effect of \(\text{COV}_{\lambda,x}\) on the ground surface settlement at various construction stages: (**a**) mean of \(H_{\text{m}}\); (**b**) COV of \(H_{\text{m}}\). on the reliability of the foundation settlement. It requires a thorough investigation to avoid underestimating COV, resulting in an overestimated reliability.