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

•Analytical solution is derived for long tunnels with sharp stiffness transition.•The wave passage effect along the tunnel axis is considered in the solution.•The structure stiffness ratio EI1/EI2 and soil shear velocity ratio Vs1/Vs2 have dramatic effects on tunnel responses.•A transition tunnel may reduce adverse effects created by a sudden change of structure or ground stiffness.•An approach to minimize the loading on the critical tunnel section in the transition zone is discussed.