Seismic Response and Predictive Modeling of Large-Diameter Shield Tunnels with Voids Behind Lining

Voids behind the lining that develop during long-term operation can seriously compromise the seismic safety performance of metro shield tunnels. To investigate the influence of such void defects on large-diameter shield tunnels, this study systematically analyzed the causes and distribution patterns of voids. A three-dimensional discontinuous finite element model was developed to simulate the interaction among lining segments, connecting bolts, and surrounding rock. The seismic responses, including circumferential stress, interface slip, interface opening, and bolt tensile stress, were analyzed considering coupled factors such as the void circumferential angle, radial depth, distribution location, and geological conditions. Single-factor and multi-factor sensitivity analyses were conducted to evaluate the significance of the above coupled factors on the overall seismic response. The results show that lining circumferential stress, displacement, interface opening, and bolt stress increase with void enlargement, a shift in void location from the crown to the haunch, and deterioration of geological conditions. A void located at the right haunch leads to a peak circumferential stress of 3.27 MPa, causing local segment damage. Sensitivity analysis reveals that void location is the most influential factor affecting the seismic response, while geological conditions exhibit lower sensitivity. A predictive model for the peak circumferential stress around the void was established using multiple linear regression, incorporating void position, circumferential angle, and radial depth. Within the parameter range considered in this study, this model provides a theoretical basis and practical reference for rapid seismic risk assessment and safety management of shield tunnels with void defects.