## 6 Conclusions  
The purpose of the current study was to investigate the effect of spatial variable MCC model parameters on the ground surface settlement reliability of a braced excavation during the entire draining, bracing, and excavating process. Employed an MCS-FORM hybrid approach, the uncertainties of the ground surface settlement and the location with the maximum settlement were analyzed, and the effect of the controlled standard threshold of surface settlement and COV of the parameters on the results were also investigated. The following conclusions can be drawn from the study:  
1. The deformation parameters of the MCC models can be obtained from the laboratory oedometer test and corresponding empirical relation. Based on the sensitivity analysis, the surface settlement has a positive relationship with the parameters associated with compression and rebound deformation (\(\lambda\) and \(\kappa\)) of the MCC model, of which \(\kappa\) has a greater effect than \(\lambda\).
2. The observed maximum settlement and the location with the maximum settlement of the probabilistic analysis follow a log-normal distribution. An increasing COV of parameters leads to an enhanced surface settlement, expansion of the significant influence region of settlement, and decreased reliability.
3. A comparison of the settlement between the deterministic and probabilistic results reveals that adopting the deterministic analysis for excavation surface settlement evaluation is capable of underestimating the risk due to the settlement and the significant influence region remarkably.
4. The reliability index is enhanced dramatically with the delimited controlled standard value of the surface settlement, \(H_{\text{con}}\). It decreases significantly at the preliminary stage and then decreases progressively until stable during further excavating. Hence it is recommended to strengthen the settlement monitoring, particularly in the first two stages during construction.  
To obtain more sophisticated observations, the further study enables to introduce more refined excavation analytical model with complex stratigraphic sequence and varied hydraulic boundary conditions, and considering more random variables and the correlation between variables. Meanwhile, the framework can be extended to perform the unsaturated hydro-mechanical coupling analysis by introducing perform the unsaturated hydro-mechanical coupling analysis.  
Conceptualization, S.Z. and H.C. ([PERSON]); methodology, H.C. ([PERSON]); software, H.C. ([PERSON]) and H.J.; validation, S.Z. and X.L.; formal analysis, S.Z.; investigation, H.C. ([PERSON]) and H.J.; resources, H.C. ([PERSON]); data curation, H.C. ([PERSON]); writing--original draft preparation, H.C. ([PERSON]) and H.J.; writing--review and editing, S.Z.; visualization, H.C. ([PERSON]); supervision, S.Z. and X.L.; project administration, H.C.; funding acquisition, H.C. ([PERSON]) and S.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Research Project of China Railway Siyuan Survey and Design Group Co., Ltd. (No. 2020k158), National Natural Science Foundation of China (No. 42090055), Open Fund of Badong National Observation and Research Station of Geohazards (BNORSG202213), National Natural Science Foundation of China (Nos. 42072314, 41807271).  
Not applicable.