Earthquakes cause damages to structures and result in great human casualties and economic loss. A fraction of the kinetic energy released from earthquakes is transferred into buildings through soils. The investigation on the mechanism of the energy transferring from soils to buildings during earthquakes is critical for the design of earthquake resistant structures and for upgrading existing structures. In order to understand this phenomena well, a wave-soil-structure interaction analysis is presented. The earthquake wave-soil-structure interaction analysis of tall buildings is the main focus of this research. There are two methods available for modeling the soil-structure interaction (SSI): the direct method and substructure method. The direct method is used for modeling the soil and a tall building together. However, the substructure method is adopted to treat the unbounded soil and the tall building separately. The unbounded soil is modeled by using the Scaled Boundary Finite-Element Method (SBFEM), an infinitesimal finite-element cell method, which naturally satisfies the radiation condition for the wave propagation problem. The tall building is modeled using the standard Finite Element Method (FEM). The SBFEM results in fewer degrees of freedom of the soil than the direct method by only modeling the interface between the soil and building. The SBFEM is implemented into a 3-Dimensional Dynamic Soil-Structure Interaction Analysis program (DSSIA-3D) in this study and is used for investigating the response of tall buildings in both the time domain and frequency domain. Three different parametric studies are carried out for buildings subjected to external harmonic loadings and earthquake loadings. The peak displacement along the height of the building is obtained in the time domain analysis. The coupling between the building’s height, hysteretic damping ratio, soil dynamics and soil-structure interaction effect is investigated. Further, the coupling between the structure configuration and the asymmetrical loadings are studied. The findings suggest that the symmetrical building has a higher earthquake resistance capacity than the asymmetrical buildings. The results are compared with building codes, field measurements and other numerical methods. These numerical techniques can be applied to study other structures, such as TV towers, nuclear power plants and dams.

[Truncated abstract] The scaled boundary finite element method is a novel computational method developed by Wolf and Song which reduces partial differential equations to a set of ordinary linear differential equations. The method, which is semi-analytical, is suitable for solving linear elliptic, parabolic and hyperbolic partial differential equations. The method has proved to be very efficient in solving various types of problems, including problems of potential flow and diffusion. The method out performs the finite element method when solving unbounded domain problems and problems involving stress singularities and discontinuities. The scaled boundary finite element method involves solution of a quadratic eigenproblem, the computational expense of which increases rapidly as the number of degrees of freedom increases. Consequently, to a greater extent than the finite element method, it is desirable to obtain solutions at a specified level of accuracy while using the minimum number of degrees of freedom necessary. In previous work, no systematic study had been performed so far into the use of elements of higher order, and no consideration made of p adaptivity. . . The primal problem is solved normally using the basic scaled boundary finite element method. The dual problem is solved by the new technique using the fundamental solution. A guaranteed upper error bound based on the Cauchy-Schwarz inequality is derived. A iv goal-oriented p-hierarchical adaptive procedure is proposed and implemented efficiently in the scaled boundary finite element method.

[Truncated abstract] The study reported in this thesis extends the scaled boundary finite-element method to firstorder and second-order wave diffraction problems. The scaled boundary finite-element method is a newly developed semi-analytical technique to solve systems of partial differential equations. It works by employing a special local coordinate system, called scaled boundary coordinate system, to define the computational field, and then weakening the partial differential equation in the circumferential direction with the standard finite elements whilst keeping the equation strong in the radial direction, finally analytically solving the resulting system of equations, termed the scaled boundary finite-element equation. This unique feature of the scaled boundary finite-element method enables it to combine many of advantages of the finite-element method and the boundaryelement method with the features of its own. ... In this thesis, both first-order and second-order solutions of wave diffraction problems are presented in the context of scaled boundary finite-element analysis. In the first-order wave diffraction analysis, the boundary-value problems governed by the Laplace equation or by the Helmholtz equation are considered. The solution methods for bounded domains and unbounded domains are described in detail. The solution process is implemented and validated by practical numerical examples. The numerical examples examined include well benchmarked problems such as wave reflection and transmission by a single horizontal structure and by two structures with a small gap, wave radiation induced by oscillating bodies in heave, sway and roll motions, wave diffraction by vertical structures with circular, elliptical, rectangular cross sections and harbour oscillation problems. The numerical results are compared with the available analytical solutions, numerical solutions with other conventional numerical methods and experimental results to demonstrate the accuracy and efficiency of the scaled boundary finite-element method. The computed results show that the scaled boundary finite-element method is able to accurately model the singularity of velocity field near sharp corners and to satisfy the radiation condition with ease. It is worth nothing that the scaled boundary finite-element method is completely free of irregular frequency problem that the Green's function methods often suffer from. For the second-order wave diffraction problem, this thesis develops solution schemes for both monochromatic wave and bichromatic wave cases, based on the analytical expression of first-order solution in the radial direction. It is found that the scaled boundary finiteelement method can produce accurate results of second-order wave loads, due to its high accuracy in calculating the first-order velocity field.