Seismic analysis of a long tunnel based on multi-scale method

Seismic analysis of long tunnels is difficult due to the lack of available computing power. In this paper, a multi-scale method is used to simulate dynamic responses of a long tunnel, which involves the concurrent discretization of the entire domain with both coarse- and fine-scale finite element meshes. The method can not only capture seismic responses along the full tunnel length, but also the detail structural responses of the segment linings and joints. Both material and contact nonlinearities are considered in the multi-scale model. Effects of buried depths, spectrum characteristics of input seismic waves, non-uniform seismic excitation and flexible joints, are thoroughly investigated on seismic responses of the tunnel. Results show: (1) the seismically induced stress of the tunnel is strongly correlated with the depth and is significantly amplified when the depth is one quarter of the incident wavelength; (2) the spectrum characteristics of the given seismic input waves do affect the amplitude and distribution of tunnel ovaling deformations as well as stresses; (3) the non-uniform seismic excitation will greatly aggravate the tunnel responses compared to the uniform excitation, and the effect of spatial distribution of earthquake excitation should be considered in the design of long tunnels; and (4) it is proved that the flexible joints can slightly mitigate the stress concentration, however, especial attention should be paid to the water proof capability of the flexible joints due to the expected additional deformation. Furthermore, stress and deformation response in lining segments and their connecting bolts are investigated and analyzed within the fine-scale model, and the capacity of critical structural components such as bolts and joints is evaluated.