Closed-Form Solution for Seismic Response of Tunnels in Loess with Damping Joints in Alternating Soil–Rock Strata

When tunnels in loess traverse sections of alternating soil and rock layers, variations in soil properties can induce an arching effect, potentially leading to the shear failure of the tunnel’s structural components. Therefore, seismic design in these areas is particularly crucial. To address these challenges, this paper analyzes the mechanical behavior of damping joints under dynamic earthquake loads using a pseudo-static approach. Based on Bernoulli–Euler beam theory and Pasternak’s dual-parameter elastic foundation beam theory, a closed-form solution is derived for the longitudinal response of tunnels in loess with damping joints under seismic loading. The solution is further validated through numerical modeling. Additionally, the study investigates the effects of filling materials (used in damping joints) and design schemes on the effectiveness of damping joints, supported by practical engineering cases. The findings indicate that installing damping joints can reduce the restraining forces on the tunnel lining, allowing the structure to better accommodate the deformation of the surrounding rock. Among the tested materials, rubber was identified as the optimal material for damping joints due to its excellent elasticity and energy absorption capacity. However, the exclusive use of damping joints may result in excessive localized deformation, potentially compromising the tunnel’s normal operation. Therefore, careful design of these joints is essential. This research provides theoretical support for the seismic design of tunnels in loess in alternating soil–rock strata.