Artificial Boundary Condition Based On Continued Fraction Of Dynamic Stiffness Matrix Of Infinite Multi-layrted Media

The dynamic interaction between the major infrastructure projects such as large-scale underground structures and the rock or soil media subjected to the seismic or blast load is not able to ignore, which is called the dynamic soil-structure interaction problems. The analysis methods of dynamic soil-structure interaction include the direct method and the substructure method in the frequency or in time domain. The structure-soil system is divided into the finite and infinite domains by introducing an artificial boundary. The finite element method is applicable to analyze the finite domain that can contain structure, and the artificial boundary condition is used to simulate the truncated infinite domain. The dynamic stiffness relationship between force and displacement on the artificial boundary can be obtained based on the infinite domain. It and its formulation in time domain are a kind of effective artificial boundary conditions. The equation with respect to the dynamic stiffness matrix can be obtained by the spatially half-discretized method such as that used in the thin-layer method and the scaled boundary finite element method. Continued fraction is an effective approach to represent the dynamic stiffness matrix. The existing continued fractions cannot effectively represent the dynamic stiffness matrix of the multi-layered media resting the rigid bedrock. This model is usually used in engineering practice. In this thesis, a new continued fraction of dynamic stiffness matrix is proposed for the out-of-plane motion of multi-layered media. Based on the proposed continued fraction, the corresponding high-accuracy artificial boundary conditions and seismic motion input methods are developed. Their effectiveness is verified by the numerical examples. The works are as follows.1. A new continued fraction is proposed to model the dynamic stiffness matrix of the unbounded layered domain. An equation with respect to the dynamic stiffness is derived by the half discretization along the artificial boundary which is done in the thin layer method and the scaled boundary finite method. A new continued fraction of dynamic stiffness matrix is developed. The constants of the continued fraction are determined recursively. The proposed continued fraction is compared with the existing high-frequency continued fraction and doubly-asymptotic continued fraction. The high-frequency continued fraction has the much low accuracy. The doubly-asymptotic continued fraction can have the good accuracy if its parameter is chosen as an appropriate value. However, it is difficult to obtain the good parameter value in practice. The proposed continued fraction has the higher accuracy than the existing high-frequency and doubly-asymptotic continued fractions.2. High-accuracy artificial boundary condition is developed based on the proposed continued fraction of dynamic stiffness matrix. The dynamic-stiffness relationship between force and displacement represented by the proposed continued fraction is a high-accuracy artificial boundary condition. It can be applied to the frequency-domain direct analysis of the dynamic soil-structure interaction under the load acting directly on the structure-soil system. Introducing auxiliary variables, the dynamic-stiffness relationship between force and displacement represented by the proposed continued fraction can be transformed into a first-order ordinary differential equation system in time domain. It is a high-accuracy artificial boundary condition and can be applied to the time-domain direct analysis of the dynamic soil-structure interaction under the load acting directly on the structure-soil system. After the proposed continued fraction couples with the frequency-domain finite element equation of the finite soil, the dynamic stiffness matrix on the structure-soil interface can be obtained by condensing all soil degrees of freedom. It is a high-accuracy artificial boundary condition and can be applied to the frequency-domain substructure analysis of the structure under the load acting directly on the structure.3. Seismic motion input method is developed based on the proposed high-accuracy artificial boundary conditions. Based on the proposed high-accuracy artificial boundary conditions for the frequency- and time-domian direct analysis of the dynamic soil-structure interaction, the method is developed to input the seismic motion of the rigid bedrock. The formulations with respect to the absolut and relative displacements are given respectively. Theoretical derivation and numerical experiments indicate that the absolute and relative displacement formulations are equivalent.