A 2.5D Finite Element Method Combined with Zigzag-Paraxial Boundary for Long Tunnel under Obliquely Incident Seismic Wave

Abstract

Seismic waves propagation with an oblique angle to the tunnel axis will cause asynchronous tunnel motions and have a significant effect on the axial response. A high-precision 2.5D finite element method is established in the frequency domain to simulate the 3D seismic response of the tunnel. This method avoids the disturbance caused by the truncation of the tunnel in the longitudinal direction. Meanwhile, a 2.5D zigzag-paraxial boundary is derived to further improve the calculation efficiency of the 2.5D finite element model. Moreover, by combining the 2.5D finite element method, 2.5D zigzag boundary condition and seismic motion input methods, an obliquely incident substructure method for plane seismic waves is built by converting the plane seismic wave into equivalent nodal forces. The proposed 2.5D finite element method is verified by comparing with a reference solution. Finally, the 2.5D finite element method is applied to study the seismic response of the long lined tunnel. Parameter analyses illustrate that the wave propagation effect to the tunnel axis has a non-negligible influence on the axil deformation of long tunnels.