Analytical Solutions For Dynamic Response Of Underground Tunnels Under SH Waves

This paper presents an analytical solution of dynamic rigid tunnel-soil-rigid tunnel interaction in axial direction in half-space, and verifies its precision of the solution by the convergence analysis of surface displacement residuals. This paper studies the effects of tunnel depth, tunnel mass, tunnel interval, incident wave frequency and incident angle on the dynamic response of tunnels in axial direction. It is shown that, when the tunnel depth is shallow the dynamic response of tunnels is large; when the tunnel mass is heavy the dynamic response of tunnels is large; when the tunnel interval is small the dynamic response of tunnels is large, but its effect is not monotone, significantly influenced by incident frequency, and the dynamic response of tunnels can be up to 2.7 times of that of single tunnel. It is suggested that tunnel-soil-tunnel interaction should be considered in seismic design of underground tunnels, when tunnel interval is small.And then this paper presents an analytical solution of dynamic flexible tunnel-soil-flexible tunnel interaction in axial direction in half-space. This paper studies the effects of shear-wave velocity ratio, incident angle, incident wave frequency and tunnel interval on the dynamic response of tunnels in axial direction. It is shown that, when the shear-wave velocity ratio is large the dynamic response of flexible tunnels is small, is close to the responses of rigid tunnels. The peak of tunnel displacement mainly shows in the direction of incident wave and the vertical one. When the frequency of incident waves is large the peak point of tunnel displacement is more; when the tunnel interval is small the dynamic response of tunnels is large.