Probabilistic analysis of the longitudinal performance of shield tunnels based on a simplified finite element procedure and its surrogate model considering spatial soil variability

Abstract

This paper presents a probabilistic analysis framework for the longitudinal performance of a shield tunnel considering spatial soil variability. Within this framework, a finite element procedure of a Timoshenko beam-based soil-shield tunnel interaction model is developed as the deterministic model to capture tunnel responses. Winkler elastic supports with varying stiffnesses configured in the analytical model are utilized to account for the spatial variation in the subgrade stiffness along the longitudinal direction of the tunnel. The random field discretized by the Karhunen-Loève expansion technique is introduced to simulate the spatial variation in the subgrade stiffness. The Kriging metamodel-based Monte Carlo simulation method is employed to perform probabilistic analysis to improve the computational efficiency. Based on this framework, the probabilistic analysis for surcharge load-induced longitudinal responses of a shield tunnel is performed considering the variability of the ground stiffness under the tunnel. The probabilistic analysis results show that the spatial soil variability leads to a nonnegligible impact on the longitudinal performance of the shield tunnel. As the variability of the subgrade stiffness increases, the failure probability of the shield tunnel rises significantly. The coefficient of variation of the subgrade stiffness has a remarkable influence on the probabilistic characteristics of the tunnel longitudinal performance, while the influence of the autocorrelation distance is slight. The maximal settlement and minimum curvature radius of the tunnel can provide a more conservative evaluation of the tunnel performance than the joint deformations.