Effect of stochastic soil stiffness variability on the response of shield tunnels subjected to fault displacement

Shield tunnels crossing active faults could experience excessive deformations; yet existing deterministic analyses often neglect the influence of stochastic soil stiffness variability. This study proposes a probabilistic framework integrating an analytical solution with Lasso regression, calibrated against published model test and numerical data. The framework quantifies the effects of stochastic soil elastic modulus (Es) on tunnel deformation and failure probability under normal faulting. Results show that Es has limited influence on settlement-profile shape but strongly affects the settlement magnitude and dispersion. Increasing Es amplifies the variability of joint shear displacement and the probability of exceeding its allowable limit. The coefficient of variation of Es governs the dispersion of both settlement and joint shear displacement. Probabilistic results indicate that joint shear failure is more sensitive to soil stiffness variability than settlement-induced failure. The framework provides an efficient approach for fragility assessment of shield tunnels in fault-prone areas with spatially variable soils.