Random Responses of Shield Tunnel to New Tunnel Undercrossing Considering Spatial Variability of Soil Elastic Modulus

Abstract

This paper investigates the effect of spatial variability of soil elastic modulus on the longitudinal responses of the existing shield tunnel to the new tunnel undercrossing using a random two-stage analysis method (RTSAM). The Timoshenko–Winkler-based deterministic method considering longitudinal variation in the subgrade reaction coefficient and the random field of the soil elastic modulus discretized by the Karhunen–Loeve expansion method are combined to establish the RTSAM. Then, the proposed RTSAM is applied to carry out a random analysis based on an actual engineering case. Results show that the increases in the scale of fluctuation and the coefficient of variation of the soil elastic modulus lead to higher variabilities of tunnel responses. A decreasing pillar depth and mean value of the soil elastic modulus and an increasing skew angle strengthen the effect of the spatial variability of the soil elastic modulus on tunnel responses. The variabilities of tunnel responses under the random field of the soil elastic modulus are overestimated by the Euler–Bernoulli beam model. The results of this study provide references for the uncertainty analysis of the new tunneling-induced responses of the existing tunnel under the random field of soil properties.