Analytical frequency-dependent infinite elements for soil-structure interaction analysis in time domain

Abstract

This dissertation presents a time domain method for soil-structure interaction analysis in two dimensional medium using a direct approach incorporating finite element modeling for the structure and the near field soil region and infinite element modeling for the far soil region. Analytical frequency-dependent infinite elements are developed to model the far field soil region. The dynamic stiffness matrix for the far field region is obtained in terms of analytical functions of frequency and constant matrices. Hence it is easy to examine the contribution of the key parameters. The performance of the proposed infinite elements is examined for vertical, horizontal, and rocking compliances of rigid strip foundations on a homogeneous half-space, a layered half-space, and a layer with a rigid bedrock in the frequency domain. The results are found to be in excellent agreements with those using the conventional infinite elements obtained numerically at every frequency and those by other methods such as hybrid modeling and transmitting boundary methods. Then, a direct method for time domain soil-structure interaction analysis is developed, which is based on transformation of the dynamic stiffness matrix of the analytical frequency-dependent infinite element. The equation of motion in the time domain is obtained through analytical transformation without using numerical transformation techniques required for the conventional infinite elements. An efficient procedure is also devised for the convolution integrals to evaluate the lingering response effect on the interface between the near field and the far field soil regions, which depends on the response on the interface at past time points as well as the present instance. Verification of the present formulation is carried out by comparing the compliances for a strip foundation on a homogeneous and a layered half-spaces with those obtained by the frequency domain method. Numerical analyses are also carried out for the tran...