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Analytical solution for circular tunnel under obliquely incident shear waves
Abstract The incident direction plays an important role in the seismic response of long lined tunnels. A simplified analytical solution is developed for estimating the seismic response of the circular tunnel under obliquely incident shear waves, including the principle stress and the internal forces and deformations on the cross section and longitudinal of the tunnel. Based on the elastic wave theory, the oblique incident shear wave can be decomposed into an axially propagating shear wave and a shear wave propagating transversely to the tunnel axis. A modified elastic foundation beam model is used to calculate the tunnel longitudinal response, which is based on Timoshenko beams resting on Winkler foundations with considering different tangential contact conditions. Furthermore, by adopting wave theory and Fourier transform, longitudinal response of tunnels under arbitrary seismic load can be obtained. Moreover, the flattening effect and out-plane response of tunnel cross-section caused by longitudinal bending are considered. The proposed analytical solution is verified by comparing with the dynamic numerical results. The effect of the incident angle, ground condition and contact condition on the seismic response of long lined tunnel is investigated by the simplified analytical solution. It is demonstrated that the proposed solution can be adopted to predict internal forces and deformations of circular tunnels under obliquely incident shear wave in preliminary design.
Highlights A simplified analytical solution is developed for estimating the seismic response of the circular tunnel under obliquely incident shear waves. A modified foundation beam model is used for the tunnel longitudinal response, with considering different tangential contact conditions. By adopting wave theory and Fourier transform, longitudinal response of tunnels under arbitrary seismic load can be obtained. Moreover, the flattening effect and out-plane response of tunnel cross-section caused by longitudinal bending are considered. Parameter studies are conducted to investigate the effects of incident angle, ground condition and contact condition.
Analytical solution for circular tunnel under obliquely incident shear waves
Abstract The incident direction plays an important role in the seismic response of long lined tunnels. A simplified analytical solution is developed for estimating the seismic response of the circular tunnel under obliquely incident shear waves, including the principle stress and the internal forces and deformations on the cross section and longitudinal of the tunnel. Based on the elastic wave theory, the oblique incident shear wave can be decomposed into an axially propagating shear wave and a shear wave propagating transversely to the tunnel axis. A modified elastic foundation beam model is used to calculate the tunnel longitudinal response, which is based on Timoshenko beams resting on Winkler foundations with considering different tangential contact conditions. Furthermore, by adopting wave theory and Fourier transform, longitudinal response of tunnels under arbitrary seismic load can be obtained. Moreover, the flattening effect and out-plane response of tunnel cross-section caused by longitudinal bending are considered. The proposed analytical solution is verified by comparing with the dynamic numerical results. The effect of the incident angle, ground condition and contact condition on the seismic response of long lined tunnel is investigated by the simplified analytical solution. It is demonstrated that the proposed solution can be adopted to predict internal forces and deformations of circular tunnels under obliquely incident shear wave in preliminary design.
Highlights A simplified analytical solution is developed for estimating the seismic response of the circular tunnel under obliquely incident shear waves. A modified foundation beam model is used for the tunnel longitudinal response, with considering different tangential contact conditions. By adopting wave theory and Fourier transform, longitudinal response of tunnels under arbitrary seismic load can be obtained. Moreover, the flattening effect and out-plane response of tunnel cross-section caused by longitudinal bending are considered. Parameter studies are conducted to investigate the effects of incident angle, ground condition and contact condition.
Analytical solution for circular tunnel under obliquely incident shear waves
Li, Huifang (author) / Zhao, Mi (author) / Huang, Jingqi (author) / Liao, Weizhang (author) / Ma, Chao (author) / Zhao, Xu (author)
2023-04-03
Article (Journal)
Electronic Resource
English
Swash Dynamics Under Obliquely Incident Waves
| British Library Conference Proceedings | 1995