# Numerical models for the analysis of soil, structure and their interaction

• Numerische Modelle zur Analyse von Boden, Bauwerk und deren Interaktion

Aachen : Rheinisch-Westfälische Technische Hochschule Aachen, Fakultät für Bauingenieurwesen, Lehrstuhl für Baustatik und Baudynamik (2015, 2016)
Book, Dissertation / PhD Thesis

In: Schriftenreihe des Lehrstuhls für Baustatik und Baudynamik der RWTH Aachen 06 (2016)
Page(s)/Article-Nr.: X, 177 Seiten : Illustrationen, Diagramme

Dissertation, RWTH Aachen, 2015

Abstract

The thesis is concerned with the analysis of soil-structure interaction (SSI). In the SSI problem, three linked systems should be considered: the structure, the foundation, and the soil underlying and surrounding the foundation. In order to gain insight into the phenomena associated with this subject, the thesis splits the original field of interest into four parts of research: the soil, the foundation, the structure and the final soil-structure interaction analysis. For the analysis of soil medium the Fourier-Bessel and Fourier transforms as well as precise integration method (PIM) are employed. The former are used to convert the wave motion equation from spatial domain to wavenumber domain, which results in a second order ordinary differential equation (ODE). Then, the dual vector representation of wave motion equation is introduced to reduce the second ODE to first order, which is solved by the PIM. Finally, the dynamic response (Green's function) of soil medium in the wavenumber domain is obtained. To approach the solutions in the spatial domain, the inverse transform over wavenumber is performed. In investigating the forced vibration of surface foundations, the contact area between the foundation and ground is divided into a number of sub-regions. Here, the force-displacement relation of each sub-region is expressed as the newly obtained Green's function. Then, considering the displacement boundary conditions and force equilibrium of foundations, the desired dynamic impedance functions are obtained. The accuracy of the proposed method is validated by comparing with the solutions in the literature. For the analysis of structure, a boundary oriented formulation is proposed. It is derived within two dimensional (2D) in-plane and three dimensional (3D) frame. In the analysis, the isogeometric approach is adopted to exactly describe the boundary. Then, the boundary scaling technique is employed to represent the solid. To solve the ODE for displacement in the radial scaling direction, the NURBS based collocation method is applied. Numerical examples relative to 2D and 3D problems are presented, all validating the proposed approach. Finally, for the soil-structure interaction analysis, the proposed boundary oriented formulation is employed to model the structure. The geometry of structure is exactly represented. It will allow to handle the structure with an arbitrary number of contour boundaries. For the modeling of soil medium, the boundary element method is applied with the newly derived fundamental solution (Green's function). These formulations provided in the thesis are applicable for engineering practice.

Institutions

• Chair and Institute of Structural Analysis and Dynamics