## 5 Conclusions  
Based on the braced excavation project in Hangzhou, this study proposes an step-by-step inverse method for identifying the proportional relationships among the important constitutive parameters and then the values of key constitutive parameters. An empirical relationship between the inversion parameter and the SPT blow counts was established. The following conclusions can be drawn:  
1. Through sensitivity and correlation analysis of the important parameters in the constitutive models, \(E_{50}^{ref}\) and \(\gamma_{0.7}\) are identified as the key parameters in the HS and HSS constitutive models. Given the relatively small strain associated with foundation pit excavation, the sensitivity of small strain parameters is significantly higher than that of large strain parameters. 2. The step-by-step inverse method not only reduces the number of parameters, but also improves the predicting accuracy. The maximum horizontal displacement of the retaining wall predicted by the proposed method is within \(\pm 15\%\) of the measured value. 3. For the soil layer composed of sandy silt mixed with silty sand, the goodness of fit \(R^{2}\) between the key parameter \(E_{50}^{ref}\) of the HS model and the SPT blow counts was found to be 0.93, indicating a good linear correlation between them. 4. The proposed SPT-based step-by-step inverse method can effectively predict the horizontal displacement of the retaining wall and the ground settlement at multiple excavation stages, demonstrating that it is an accurate, practical, and efficient method for parameter determination. The proposed method has proven to be effective and provides insights for the selection of the constitutive model parameters. The empirical relationship established in this study can be applied to the parameter selection of a similar soil layer around the construction site. Future work is suggested to investigate the influence of multiple soil layers, supporting system, and excavation method. Consequently, it is necessary to collect more foundation pit case studies and conduct parameter analysis to further enhance the current findings. Figure 10: Measured ground surface settlement and simulated value based on the proposed method. **Author Contributions:** Conceptualization, H.Z., M.S. and X.Z. ; methodology, M.S. and W.Z. ; software, W.Z. ; validation, H.Z. and X.Z. ; formal analysis, M.S. ; investigation, W.Z. ; resources, X.Z. and H.Z. ; data curation, W.Z. ; writing--original draft preparation, W.Z. ; writing--review and editing, M.S. ; visualization, W.Z. ; supervision, X.Z. and H.Z. ; project administration, H.Z. ; funding acquisition, M.S. All authors have read and agreed to the published version of the manuscript. **Funding:** This study is supported by the Zhejiang Provincial Natural Science Foundation (Grant No. LY24D020001) and the Engineering Research Center of the Ministry of Education of Renewable Energy Infrastructure Construction Technology. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by corresponding author on request. **Conflicts of Interest:** Authors [PERSON], [PERSON] and [PERSON] were employed by the Zhejiang University of Technology Engineering Design Group Co., Ltd. The remaining authors declare that the re-search was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. * _[PERSON] and [PERSON] (2016)_ _[PERSON]; [PERSON] Small Strain Based Method for Predicting Three-Dimensional Soil Displacements Induced by Braced Excavation._ _Tunn. Undergr. Space Technol._ **2016**_, 52, 12-22. [CrossRef]_
* _[PERSON] and [PERSON] (2019)_ _[PERSON]; [PERSON] Inverse Analysis of a Supported Excavation in Chicago._ _J. Geotech. Geoenviron. Eng._ **2019**_, 145, 04019050.