Analytical solution for longitudinal seismic response of tunnel liners with sharp stiffness transition

Sharp transitions in structure stiffness and/or ground properties have a significant influence on the seismic response of tunnels. These issues are not well understood yet, or at least not well considered during design. An analytical solution is derived to investigate the seismic response of long tunnels, built in non-homogeneous ground, subjected to sinusoidal shear motions. It is assumed that the tunnel is excavated in two different soil deposits that have a sharp contact, and there is a transition zone through the contact. It is also assumed that the tunnels can be represented as beams on an elastic medium. Continuity at the contact between the different contact sections of the tunnel is imposed to solve the governing equations of equilibrium. In addition, wave passage effects along the tunnel are considered by including a phase angle in the far-field displacements. Explicit formulations are obtained for tunnel deflection, bending moments and shear forces. The solution is verified by providing comparisons between its results and those from the Finite Element program ABAQUS. A parametric analysis is presented where the effects of the stiffness of the structure, the shear velocity of the soil and the length of the transition zone are investigated.