Abstract: The site investigation on earthquake damage shows that tunnels in the active fault zone suffer the most serious disasters. To investigate the longitudinal response of tunnels crossing the active fault under the dislocation, this paper proposed and verified an analytical solution of longitudinal mechanical behavior for tunnels. The active fault zone has worse mechanical properties and is the place where the main dislocation occurs. Therefore, the tunnel is divided into three parts in the longitudinal direction, including dislocation affected zone, transient zone and non-influence zone. Assuming that these three zones have different model parameters and calculation modes, an analytical mechanical model of the tunnel is formulated based on the double-parameter Pasternak elastic foundation beam. The proposed model satisfies the continuity of deformation and stress along the longitude direction. Analytical solutions agree well with the numerical simulation results and the laboratory mock-up test observations, demonstrating its good capacity. Analytical results reveal that the tunnel internal force and deformation show a significant increase in the active fault zone under the dislocation. The longitudinal deflection of the tunnel is similar to the dislocation while it has a reverse deflection at the junction zone between the fault zone and the foot or hanging wall. For the dislocation of normal fault, the longitude moment reaches its maximum value at the junction zone between the fault zone and the foot or hanging wall, and a tensile and compressive zone appear in the crown of tunnel on the side of the foot and hanging wall respectively. Shear force in the active fault zone is also bigger than that in the foot and hanging wall. All above responses result in the serious disasters in the fault zone, which is consistent with the site investigation results. Therefore, the proposed analytical solution could be used for the tunnel longitude response analysis under the dislocation. Finally, sensitivity analyses of the ground coefficient and the fault width are performed and useful results are summarized, which can provide technical supports for the tunnel design and construction in the active fault zone.

Key words: active fault, dislocation, analytical solution, elastic foundation beam, longitudinal response