Analytical Solutions To Internal Forces Of Tunnel Lining Under Rayleigh Wave

With the rapid development of underground structures that widely used in civil engineering, water conservancy engineering and other various fields, they have played a very important role in the economy and society. Compared with the above ground structures, underground structures don’t undertake strong inertia motions, therefore, it was widely believed that the underground structures had good seismic performances. However, since the earthquake of Kobe, Japan in 1995, many underground structures experienced significant damages in the previous several large earthquakes, which change people’s wrong view that the underground structures do not need seismic designs. Now aseismic researches of underground structures are then drawn more and more attention.In recent years, the numerical methods represented by the finite element method have been widely used in researches due to the development of computing technology. However, the numerical analysis method has its own limitations. For example, it cannot be expressed in explicit form to reflect main factors affecting the seismic responses of the structures. So it is difficult for structural engineers to understand and grasp the influence factors how to affect the stresses and deformations, and it is not conducive to the concept design of the underground structures. Therefore, the study on finding the analytical solutions for underground structures still has a special meaning.In cases of S wave and P wave incident into the ground, many researchers have presented some closed analytical solutions to seismic internal forces for tunnels of circular and rectangular cross section. But so far, few researches have been carried out for the case that the tunnel is excited by Rayleigh wave considering the soil structure interaction. In this paper, based on underground structure mechanics and elastic wave theory, considering the interaction between soil and structure, in the case of incident Rayleigh wave at any angle, the analytical expressions are derived for the longitudinal and lateral deformations and internal forces of shallow buried tunnels, respectively. Then, through the engineering examples, the effectiveness of the proposed methods is verified and discussed.The example results show that the proposed methods have reliable accuracy and reliability. In addition, the internal forces resulted from Rayleigh-wave are much higher than those from SV wave, especially the lateral axial force. If Rayleigh wave travels parallel along the tunnel axis, the maximum normal stress of the cross section is obtained, which is mainly caused by compressional wave component and the contribution of the shear wave component is negligible. If the incident direction of Rayleigh wave is perpendicular to the tunnel axis, the internal forces of the tunnel lining cross section reach the maximum values and the internal force differences between two contact conditions are minor. In aseismic design of shallow tunnel linings, internal forces caused by Rayleigh wave should be paid adequate attentions.In the final, the main conclusions in this paper are summarized and future work to be conducted is pointed out.