The Application Of SBFEM In The Earthquake Response Analysis Of Underground Structures

The evaluation of earthquake response of underground structures is essentially to solve the problem of dynamic interaction of underground structures with unbounded media. Recently, the Scale Boundary Finite Element Method (SBFEM) has been developed to capture the dynamic behavior of unbounded media in finite element sense. In modeling unbounded media, SBFEM possesses main advantages of the boundary element method: only the boundary is discretized and radiation condition at infinity is satisfied exactly. In numerical implementation, SBFEM retains the simplicity and convenience as the finite element method (FEM) hold: no fundamental solution is required and singular integration is avoided. As FEM is a powerful tool to analyze the complex and inhomogeneous structures, the main objective of this thesis is to develop a coupling procedure of FEM and SBFEM in frequency domain that can be applied to analyze the unbounded soil-structure interaction of practical engineering systems.This thesis is divided into six chapters. The first chapter introduces the background and significance of the research. In addition, the developing history of soil-structure interaction is also mentioned.The basic theory of soil-structure interaction is mainly introduced in the second chapter, at the same time, the fundamental concepts and equations of calculation is proposed in this chapter.In the third chapter, the basic theory and the characteristics of SBFEM is discussed, followed by the fundamental equations and the solutions in frequency and time domain are derived. Finally, the advantages and the limitations of the application of SBFEM are concluded. The SBFEM is not only used to analyze a unbounded medium, but also used to analyze a bounded medium and it can apply for the frequency domain and also apply for the time domain. The frequency analysis of the SBFEM is mainly introduced in this chapter.The accuracy of the SBFEM is verified. Comparisons are made between the analytical solutions of dynamic stresses and displacements around cylindrical cavity due to plane harmonic shear wave and the solutions calculated by the SBFEM. The Comparisons indicate two solutions are well suited.In the fifth chapter, examples are utilized to verify the program. The characteristics of the earthquake response of the underground structures, in particular, the earthquake response in complicated unhomogeneous medium are analyzed. Based on the research results, we obtained deeper insight in the characteristics of earthquake response of the underground structure in the unhomogeneous medium.At last, the conclusion and prospect are discussed.