The most popular method in dynamic soil-structure interaction analysis is the finite element method. The versatility in problems involving different materials and complex geometries is its main advantage, yet FEM can not simulate unbounded domains completely. A hybrid method is proposed in this research, which models the near field (structure and surrounding soil) by finite elements and the far field by a continuum approach. The system is excited by monochromatic body waves (P and SV) propagating with oblique incidence and harmonic time dependence. The far field problem is solved using Thomson-Haskell formulation associated with the delta matrix technique. The soil profile does not contain any soft layer and the layers are assumed to be linearly elastic, isotropic, homogeneous and perfectly bonded at the interfaces. Two-dimensional (in-plane) formulation is considered and the analysis is performed on both k- and o-planes through time and spatial Fourier transforms of the field equations and boundary conditions. (Abstract shortened with permission of author.)

The most popular method for dynamic soil-structure interaction analysis is the finite element method. The versatility in problems involving different materials and complex geometries is its main advantage, yet the FEM can not simulate unbounded domains completely. Several schemes have been proposed to overcome this shortcoming, such as the use of either imperfect or perfect transmitting boundaries, infinite elements and hybrid techniques. However, most of them were derived on the assumption that the soil mass can be represented as a homogeneous material despite the fact that stratified soil deposits are a common occurrence in nature. A hybrid method is proposed in this research for soil-structure interaction analysis in the frequency domain involving a multilayered linear elastic half-space. The near field region (structure and a portion of soil surrounding it) is modeled by finite elements while the far field formulation is obtained through the classical wave propagation theory based on the assumption that the actual scattered wave fields can be represented by a set of line sources. Traction reciprocity between the two regions is satisfied exactly, while the displacement continuity across the common interface is enforced in a least-squares sense. The two-dimensional system is excited by harmonic body waves (P and SV) propagating with oblique incidence. The structure can be considered either on the surface or deeply embedded in the multilayered half-space. Analytic solutions for the far field domain is obtained through the combined response of four simple problems that take into account the overall effects of the incident, reflected and scattered wave fields. The delta matrix technique is employed in order to eliminate the loss of precision problem associated with the Thomson-Haskell matrix method in its original form. Special numerical schemes are used to transform the solution from the κ- into the ω-plane due to the presence of poles on the path of integration. The few numerical examples studied in this research validate the proposed hybrid technique, but the relatively high computational cost required for evaluation of the Green's functions is still a serious drawback. Some suggestions are made to minimize the problem as well as to extend this technique to cases involving material attenuation and forced vibrations.

The general principles of continuum mechanics such as conservation of mass, conservation of momenta, first and second law of thermodynamics are applicable to all materials irrespective of their internal constitutions. These principles alone do not provide sufficient equations to obtain solutions for any boundary value problems. The additional equations are provided by the constitutive laws. There are many groups of constitutive theories. Of them, the theory of plasticity describes rate independent nonlinear and inelastic behavior of materials. A plasticity-based constitutive law is proposed herein for geological materials. The model, however, may also be used for other frictional materials. A generalized approach is followed in formulating the proposed constitutive model. The technique can be used to construct plasticity-based constitutive models for any other materials. A series of laboratory tests are performed on cubical soil specimens using a truly triaxial testing device. The testing device is such that the samples can be subjected to a general three-dimensional state of stress. The test data is used to determine the material constants associated with the proposed constitutive model. The model is then verified by back-predicting the stress-strain curves obtained from the laboratory. As a final step, the proposed constitutive model is implemented into a three-dimensional finite element procedure. A number of boundary value problems are analyzed using the proposed model. The results are compared with the observation. It is found that the proposed model can effectively characterize the nonlinear and inelastic response of frictional materials. Although the proposed model is investigated with respect to soils, it can also be applied for concrete, rocks, etc.

This thesis presents the development of a reliable and efficient technique for the numerical simulation of dynamic soil-structure interaction problems in anisotropic and nonhomogeneous unbounded soils of arbitrary geometry. Such a technique is indispensable in the seismic analysis of large-scale engineering constructions and, to my best knowledge, does not exist at present. The theoretical framework of the research is based on the scaled boundary finite-element method. The following advances are achieved: The scaled boundary finite-element method is extended to simulate the dynamic response of non-homogeneous unbounded domains. The scaled boundary finite element equations in the frequency and time domains are derived for power-type non-homogeneity frequently employed in geotechnical engineering. A high-frequency asymptotic expansion of the dynamic-stiffness matrix is developed. The frequency domain analysis is performed by integrating the scaled boundary finite-element equation in dynamic stiffness. In the time domain, the scaled boundary finite-element equation including convolution integrals is solved for the unit-impulse response at discrete time stations. A Pad?? series solution for the scaled boundary finite-element equation in dynamic stiffness is developed. It converges over the whole frequency range as the order of the approximation increases. The computationally expensive task of numerically integrating the scaled boundary finite-element equation is circumvented. Exploiting the sparsity of the coefficientmatrices in the scaled boundary finite-element equation leads to a significant reduction in computer time and memory requirements for solving large-scale problems. Furthermore, lumped coefficient matrices are obtained by adopting the auss-Lobatto-Legendre shape functions with nodal quadrature, which avoids the eigenvalue problem in determining the asymptotic expansion. A high-order local transmitting boundary constructed from a continued-fraction solution of the dynamic-stiffness matrix is developed. An equation of motion as occurring in standard structural dynamics with symmetric and frequency-independent coefficient matrices is obtained. This transmitting boundary condition can be coupled seamlessly with standard finite elements. Transient responses are evaluated by using a standard timeintegration scheme. The expensive task of evaluating convolution integrals is circumvented. The advances developed in this thesis are applicable in other disciplines of engineering and science to the analysis of scalar and vector waves in unbounded media.

This thesis presents the development of a reliable and efficient technique for the numerical simulation of dynamic soil-structure interaction problems in anisotropic and nonhomogeneous unbounded soils of arbitrary geometry. Such a technique is indispensable in the seismic analysis of large-scale engineering constructions and, to my best knowledge, does not exist at present. The theoretical framework of the research is based on the scaled boundary finite-element method. The following advances are achieved: The scaled boundary finite-element method is extended to simulate the dynamic response of non-homogeneous unbounded domains. The scaled boundary finite element equations in the frequency and time domains are derived for power-type non-homogeneity frequently employed in geotechnical engineering. A high-frequency asymptotic expansion of the dynamic-stiffness matrix is developed. The frequency domain analysis is performed by integrating the scaled boundary finite-element equation in dynamic stiffness. In the time domain, the scaled boundary finite-element equation including convolution integrals is solved for the unit-impulse response at discrete time stations. A Pad?? series solution for the scaled boundary finite-element equation in dynamic stiffness is developed. It converges over the whole frequency range as the order of the approximation increases. The computationally expensive task of numerically integrating the scaled boundary finite-element equation is circumvented. Exploiting the sparsity of the coefficientmatrices in the scaled boundary finite-element equation leads to a significant reduction in computer time and memory requirements for solving large-scale problems. Furthermore, lumped coefficient matrices are obtained by adopting the auss-Lobatto-Legendre shape functions with nodal quadrature, which avoids the eigenvalue problem in determining the asymptotic expansion. A high-order local transmitting boundary constructed from a continued-fraction solution of the dynamic-stiffness matrix is developed. An equation of motion as occurring in standard structural dynamics with symmetric and frequency-independent coefficient matrices is obtained. This transmitting boundary condition can be coupled seamlessly with standard finite elements. Transient responses are evaluated by using a standard timeintegration scheme. The expensive task of evaluating convolution integrals is circumvented. The advances developed in this thesis are applicable in other disciplines of engineering and science to the analysis of scalar and vector waves in unbounded media.

A finite element procedure is developed for stress-deformation analysis of three-dimensional solid bodies including geometric and material nonlinearities. The formulation also includes the soil-structure interaction effect by using an interface element. A scheme is formulated to allow consistent definitions of stress, stress and strain rates, and constitutive laws. The analysis adopts the original Newton-Raphson technique coupled with incremental approach. Different elasto-plastic laws based on Von-Mises, Drucker-Prager, critical state, and cap criteria are incorporated in the formulation and computer code, and they can be used depending on the geological material involved. A special cap model is also incorporated to predict the behavior of the artificial soil used in current research. Examples are given to verify the formulation and the finite element code. Examples of the problems of soil-moving tool are also shown to compare to the experimental solutions observed in a prototype soilbin test facility. / Ph. D.