Seismic response of deep rectangular tunnels considering nonlinear ground and excess pore pressures accumulation

The seismic response of rectangular tunnels under undrained loading is not well understood. Two-dimensional dynamic numerical analyses are performed to evaluate the undrained seismic response of deep rectangular tunnels. For comparison purposes, drained analyses and circular tunnels are also included. To simulate the nonlinearity of the ground and excess pore pressures, a cyclic nonlinear constitutive model is used, while the liner is assumed to remain in its elastic regime. The flexibility ratio $F$ is the main factor controlling the distortions of the cross section and loading on the liner. For drained loading and stiff, or low-flexibility, structures with initial $F$ $\le$ 2.5, the tunnel shape has almost negligible effect on its distortions. As the tunnels become more flexible, the differences in distortions among the different cross sections increase, with the smallest values for circular structures, followed by square, and rectangular tunnels having the largest distortions. For undrained loading, except for the stiffest structure with initial $F$ = 0.10, there is a clear effect of the tunnel shape on the distortions. In this case, the smallest distortions are for the square tunnels, followed by the rectangular and then the circular tunnels, which produce the largest deformations. The liner loading follows the expected trend of larger axial thrusts and lower bending moments for the tunnel with a circular cross section than for the square and rectangular tunnels. The loads on the structures do not change much once the structure becomes flexible. The changes are negligible from $F$ $>$ 2.5 for axial forces and from $F$ $>$ 10 for bending moments. For flexible structures, the drained loading produces larger loading than the undrained loading, with smaller differences for bending moments and larger differences for axial forces, which increase as the tunnel becomes stiffer ($F$ $\le$ 2.5).