Analysis of axis dynamic response of rock tunnels through fault fracture zone under P waves of earthquake

On the basis of the time-domain wave method coupling the explicit finite element method with the viscous-spring artificial boundary condition, the input seismic motion was converted into the equivalent nodal force acted on the viscous-spring artificial boundary condition. For the three-dimensional (3D) fault site, the free-field response of the 3D field model was obtained by solving the seismic response of the equivalent two-dimensional field model, and the free-field response was converted into the equivalent node force of the 3D model. Subsequently, the oblique-incidence input method of P waves was proposed for the 3D fault site in the study. The precision of the present approach was verified by half-space numerical examples. Finally, the proposed method was applied to investigate the influence of fault on the seismic response of a long lined tunnel through fault subjected to P waves. The numerical results indicate that the seismic response of tunnel lining near the fault is amplified greatly. The tunnel is in the complex stress state of tensile, compression and shear under P waves. The seismic response increases with the weakening of the mechanical properties of the fault, and the depth of fault also influences the seismic response of the tunnel. With increasing the incident angle of earthquake waves, the axial force and bending moment of the tunnel lining near the fault increase first and then decrease. However, the shear force gradually decreases with increasing the incident angle.