As an important transportation facility, the safety and stability of mountain tunnels are of great concern when natural disasters such as earthquakes occur. Seismic wave reflection and coherence effect will occur in the mountain body, and the mountain body, seismic isolation layer, and tunnel as “scattering body” and “secondary source” can change the spatial distribution of ground shaking distribution and values of seismic ground motion. In order to study the influence of isolation measures on seismic wave scattering in double line tunnels within mountains, we uses high-precision indirect boundary element method （IBEM） to analyze the overall response of mountains, isolation layers, and tunnels under P-wave incidence. The isolation effect of flexible isolation layers on double line tunnels crossing Gaussian-shaped mountains.

Firstly, a comprehensive computational model was developed. A two-lane lined tunnel is traversed within the Gaussian-shaped mountain, and a seismic isolation layer is set between the tunnel and the mountain site. It is assumed that the mountain site, the tunnel and the seismic isolation layer are all linear isotropic media. In this article, there is not complete consolidation between the tunnel and the surrounding rock, but rather dislocation slip. Therefore, a series of virtual linear springs and dampers are used to connect the isolation layer and the surrounding rock, and a viscoelastic boundary is set to simulate this imperfect boundary.

Secondly, wave field analysis was conducted based on elastic wave theory. The formulas for the free field and scattering field are provided in the article, and an equilibrium equation is established based on the displacement and stress continuity conditions at the interface of each computational domain. Solving this equation can obtain the virtual wave source density. Multiplying the concentration of the virtual wave source by the corresponding Green’s function can obtain the scattering field of observation points in each domain. The superposition of scattering field and free field yields the full wave field.

Thirdly, the correctness of the results is also verified. Due to the lack of an accurate analytical solution for mountainous tunnels under P-wave incidence in current research, we degenerates the model into a half space tunnel model and compares it with published results, with the same setting of the calculation parameters. It can be found that the results of this paper are in good agreement with those of published paper, thus verifying the accuracy of this method.

Finally, the effects of the modulus of elasticity, thickness, and incident frequency of the seismic isolation layer on the seismic ground motion response of the tunnels were discussed in detail, and the displacements and stresses of the tunnel inside the mountain and the displacements on the mountain surface are obtained. The research results can provide some reference for seismic isolation design and construction of double-line tunnel in mountain site. The following main conclusions are obtained:

1） IBEM can accurately solve the seismic dynamic response of lined tunnels in mountain, including the amplification effect of seismic ground motion in mountain ranges and the stress concentration effect of the lining, etc. Setting up seismic isolation and damping measures can effectively change the distribution of the stress and give full play to the load-bearing capacity of the surrounding rock, thus playing a role in protecting the tunnel lining.

2） As the modulus of elasticity of the isolation layer material decreases, there is a significant reduction in the values of dynamic tunnel stresses. The structural response of the flexible seismic isolation layer for suppressing high-frequency waves is more obvious. When high-frequency waves are incident, an isolation layer with elastic modulus of 12 MPa can reduce the tunnel peak stress to 25.4% of which without an isolation layer. At the same time, when the modulus of elasticity is small, it can effectively reduce the area of its stress amplification zone, thus effectively avoiding lining cracks caused by seismic action.

3） The seismic isolation layer can make the lining circumferential stress distribution tend to be uniform, and with the increase of the thickness of the vibration isolation layer, the tunnel lining dynamic stress gets smaller, and the reduction can be about 50% or more.

4） Considering the efficiency of seismic isolation as well as the cost of the project, among the several sets of parameters studied in this paper, the combined effect of a seismic isolation layer with a modulus of elasticity of 12 MPa and a thickness of 20 cm is superior.

5） Considering the existence of broken soil between the tunnel and the surrounding rock, a staggered slip boundary is introduced on the boundary. The staggered slip boundary model proposed in this paper is still simplified and does not take into account the nonlinear effects such as elastic-plasticity and large deformation.