Probabilistic Analysis of Shield Tunnel Responses to Surface Surcharge Considering Subgrade Nonlinearity and Variability

Accidental surface surcharge will generate additional load in the stratum, which then leads to unfavorable impacts on the underlying shield tunnel. This paper proposes a probabilistic analysis method to address this problem. In this framework, an improved soil–tunnel interaction model considering the nonlinearity of the subgrade is established at first, and the Newton–Raphson iterative solution algorithm is employed to acquire tunnel responses. Then, the random field models of the initial stiffness and the ultimate reaction of the subgrade are constructed to realize the spatial variability of soil properties. Finally, with the aid of the Monte Carlo Simulation method, the probabilistic analyses on tunnel responses are performed by combining the improved soil–tunnel interaction model and the random field model of subgrade parameters. The applicability and the superiority of the improved soil–tunnel interaction model are validated by a historical case from Shanghai Metro Line 9. The results prove that the traditional linear foundation model will overestimate the bearing capacity of the subgrade, thereby leading to overly optimistic assessments of surcharge-induced tunnel responses. This shortcoming could be addressed by the improved nonlinear soil–tunnel interaction model. The influences of spatial variability of soil properties on tunnel responses are nonnegligible. The stronger the uncertainties of subgrade parameters, in terms of the initial stiffness and the ultimate reaction concerned in this work, the higher the failure risk of the shield tunnel subjected to the surcharge. The failure modes of the tunnel subjected to the surcharge are controlled by the longitudinal curvature radius of the tunnel within the current assessment criteria, which means if this evaluation indicator can be restricted within the allowable value, then the opening of the circumferential joint and the longitudinal settlement can also meet the requirements. Compared with the influences of the uncertainty of the subgrade ultimate reaction, the spatial variability of the subgrade initial stiffness has greater influences on tunnel failure risk under the same conditions. An increase in the range of surcharge will raise the risk of tunnel failure, while the influence of tunnel burial depth is just the opposite.