## 1 Introduction  
In recent years, with the rapid development in China, the national high-speed railway network extends to the northwest and southwest mountainous areas, which are high-intensity earthquake zones. These areas contain many problematic areas including complicated formations, severely tectomized and faulted zones, and so on. Therefore, tunnels, as a major part of civil infrastructures, are likely to pass through soft-hard strata. Many post-earthquake investigations have shown that the tunnel section at the junction of the soft and hard rock is severely damaged [1, 2, 3]. Therefore, tunnels through soft-hard strata should be paid much attention. There are an increasing number of studies on dynamic responses of tunnel structures passing through soft-hard strata. [PERSON] et al. [4] conducted a series of shaking table tests and numerical simulations to investigate the dynamic responses of a shield tunnel passing through a soft-hard stratum. The results showed that the strain of the tunnel around the soft-hard interface increased significantly. [PERSON] and [PERSON] [5] showed that a secondary lining had a significant impact on responses of the segments under longitudinal excitation rather than transverse excitation using shaking table tests. [PERSON] et al. [6] found that the acceleration responses for the soft-hard junction stratum exhibited double predominant frequency by model tests and numerical simulations. [PERSON] et al. [7] proved that the seismic damage of tunnel was mainly caused by the forced displacement under the condition of interface between soft and hard rock through shaking table tests. [PERSON] et al. [8] investigatedthe seismic responses of a utility tunnel, and the results showed that a sharp variation of response occurred at the interface between soft soil and hard soil, and that the variation under a far-field earthquake could be more significant. In terms of theoretical calculations, two kinds of approaches have been developed to study the longitudinal response of tunnel structures, namely the free field deformation approach and the soil-structure interaction approach [9; 10]. The first method involves the strains and deformations of tunnel structure being obtained by imposing free-field deformations on the structure [11]. However, the method always overestimates or underestimates the structure deformations due to neglect of interaction between the tunnel and surrounding ground [12; 13; 14]. For the soil-structure interaction approach, the beam-on-elastic foundation approach is used to model soil-structure interaction effects [15]. [PERSON] et al. [16] proposed a mathematical model for analyzing the effect of submergence on the dynamic response of submerged floating tunnel due to moving load. [PERSON] et al. presented an analytical solution for the responses of tunnel liners crossing through soil-rock stratum based on the Euler-Bernoulli beam on elastic foundation approach [17; 18; 19]. The present approach mainly relies on the assumption that the surrounding rock is homogeneous, that is to say no sharp change of properties in surrounding rock along the tunnel. The transition of stiffness of the liner, e.g., over-excavation, lining thickening, or both, is often performed, and flexible connections between the transition segments and adjacent segments are also suggested in practice to mitigate effects of a sharp change when tunnels run through soft-hard junction stratum. However, little research can be found in literature on this problem. In this paper, seismic performances of a tunnel passing through soft-hard stratum equipped with a transition tunnel and flexible joints under earthquake motion were investigated by a new proposed simplified analytical solution and a series of scaled shaking table tests. First, a mechanical model of a tunnel passing through soft-hard stratum with flexible joints was proposed and the longitudinal seismic responses of the tunnel was derived by the Green's function method.