Analytical Pseudo-static Solution To Seismic Response Of Rectangular Underground Structures

Since the Daikai subway station experienced significant damage in the1995Kobe, Japan earthquake, along with the development and construction of various types of underground space, aseismic research of underground structure increasingly prosperously develops and gets attention. Due to the rapid increasemcnt of computing technology in recent years, various types of numerical methods represented by finite element method and finite difference method are widely used in the study. At present, plenty of complex and difficult practical problem can be solved. Nevertheless, numerical method has its restrictions and limitations, such as the main factors influencing the structural response cannot be expressed in explicit formulation. With numerous secondary factors mixed together, structural engineers and researchers hardly understand and grasp how the main factors influence the structural distortion, which is bad for the structural conceptual design. In the numerical method is popular today, analytical solution is still an appealing method, because it can seize the main influencing factors and explicitly reflect the change rule and trend. The work of this paper is to carry out research on seismic design and calculation of rectangular underground structures using analytical methods.Underground structures with rectangular cross section are mainly adopted in water conservancy and traffic engineering, typically, such as subway station, large reinforced concrete pipes, etc. At present, analytical solutions of seismic design and calculation aiming at this kind of underground structures arc less, while which of underground structures with circular, oval cross section in the infinite domain based on different methods are given more and relatively mature. It is because the design variables at the junction of cross-sectional right angles are continuous but not derivable cause the mathematical difficulties. Current research status is as follows, the closed-form analytical pseudo-static solutions of seismic-induced internal forces and deformations for rectangular underground structures subjected to far field shear stresses from vertically incident SV wave had been presented by Huo et al. But solution procedures arc not detailed, comprehensive and accurate enough. On the other hand, in recent years, worldwide near fault strong earthquake records show that the vertical component produced by seismic p-wave is significant and should not be ignored, but the related analytical solutions of anti-seismic calculation in the case of rectangular structure subjected to far field compressive stresses from P wave haven’t yet been reported.In this paper, deep-buried square and rectangular underground structures are the main study objects. Basing on pseudo-static assumption, adopting plane elasticity complex variable theory, considering the interaction between soil and structure, analytical solutions of underground structural displacement and internal force subjected to far-field horizontal shear stresses from SV wave and compression stresses from P wave arc derived respectively. The effectiveness of the method and the correctness of the results are verified by examples, and compared with the numerical solutions. Example results indicate that the proposed method has higher precision and reliability, and the form of internal force is simple and convenient to be used for the estimation of seismic response in elementary seismic design. Finally, the research contents arc summarized, and the problems which need to be further discussed arc prospected.