## 4 Results
### The Probabilistic Analysis
#### 4.3.2 Reliability of Ground Surface Settlement of the Excavation  
As observed from Equation (10), the value of \(H_{\text{{con}}}\) contributed directly to the performance function G. As shown in Figure 14, the solid black line indicates the cumulative probability density curve of \(H_{\text{{m}}}\) from 1000 realizations. The red dashed line indicated that it has different guarantees within the control criteria under selected four individual values of \(H_{\text{{con}}}\), i.e., 40 mm, 45 mm, 50 mm, and 60 mm. The \(H_{\text{{m}}}\) of the deterministic analysis was at the 0.32 quantiles of the cumulative probability density curve of \(H_{\text{{m}}}\) of the probabilistic analysis. It suggests that the risk of the excavation surface settlement assessed by deterministic analysis tends to be underestimated remarkably. As displayed in Figure 15, the comparison of the settlement control guarantee rate, \(R_{g}\), and reliability index, \(\beta\), increased significantly with \(H_{\text{{con}}}\) values. According to the related international standard [64], the reliability index for structures with irreversible deformation for a regular service limit state is 1.5. Given that the excavation is a temporary construction and the surface settlement is characterized by extendable deformation, the target \(\beta\) for surface settlement was delimited as 2.0 by referring to the prior studies combined with  
Figure 14: CDF of surface settlement with various control standard values. economic guidelines. This reliability indicator was also recognized by excavation construction research [65]. Meanwhile, with the monitoring data of analogous excavations in the Hangzhou area (Table 6) and the actual excavating depth, \(H_{\text{com}}\) herein was delimited as 60 mm, thereby the \(R_{g}\) was 98.5%, and \(\beta\) was 2.7, meeting the requirements of engineering and construction. Based on the above regulations, Figure 16 provides the temporal variation of reliability during the entire draining-bracing-excavating construction process. It demonstrates that no settlement was observed at the beginning of construction (\(t=0\)). During Stage I and Stage II, the \(\beta\) decreases rapidly from 42.5 to 23.6 and then levels off during Stage II and Stage III. There are two possible explanations for this result. Firstly, due to the noticeable dropping of water level in the preliminary draining stage, the effect of ground consolidation and settlement was significant, and the reliability of surface settlement reduced rapidly. Secondly, with the step-by-step construction of the brace, the capability of resisting the deformation effect from draining and excavating was gradually enhanced. In particular, the pit tends to be stable as the entire formation of the third level of bracing structure. 3.3 Effect of \(\text{COV}_{\lambda,\kappa}\) on Surface Settlement and Reliability of the Excavation  
Figure 17 presents the correlation between the mean and COV of \(H_{\text{m}}\) at different construction stages with \(\text{COV}_{\lambda,\kappa}\). As shown in Figure 15a, \(\mu_{H\text{m}}\) increases with the increase of \(\text{COV}_{\lambda,\kappa}\) at each stage of construction. In terms of the incremental magnitude, Stage I was the least, followed by Stage II, and Stage III was the largest. An observation that \(\text{COV}_{Hm}\) increases with increasing \(\text{COV}_{\lambda,\kappa}\) was also depicted in Figure 15b. It is also quite revealing that with the same \(\text{COV}_{\lambda,\kappa}\), both \(\mu_{H\text{m}}\) and \(\text{COV}_{Hm}\) increased gradually with the construction of the excavation.