In deep foundation pit engineering, the soil undergoes a complex stress path, encompassing both loading and unloading phases. The Shanghai model, an advanced constitutive model, effectively accounts for the soil’s deformation characteristics under these varied stress paths, which is essential for accurately predicting the horizontal displacement and surface settlement of the foundation pit’s enclosure structure. This model comprises eight material parameters, three initial state parameters, and one small-strain parameter. Despite its sophistication, there is a scarcity of numerical studies exploring the correlation between these parameters and the deformation patterns in foundation pit engineering. This paper initially establishes the superiority of the Shanghai model in ultra-deep circular vertical shaft foundation pit engineering by examining a case study of a nursery circular ultra-deep vertical shaft foundation pit, which is part of the Suzhou River section’s deep drainage and storage pipeline system pilot project in Shanghai. Subsequently, utilizing an idealized foundation pit engineering model, a comprehensive sensitivity analysis of the Shanghai model’s multi-parameter values across their full range was performed using orthogonal experiments. The findings revealed that the parameter most sensitive to the lateral displacement of the underground continuous wall was κ, with an increase in κ leading to a corresponding increase in displacement. Similarly, the parameter most sensitive to surface subsidence outside the pit was λ, with an increase in λ resulting in greater subsidence. Lastly, the parameter most sensitive to soil uplift at the bottom of the pit was also κ, with an increase in κ leading to more significant uplift.
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