Direct Transient Response of Coupled Structures-Soil Systems Modelled by Matrix Methods and Green’s Functions Approach

Resumo

Even today it is still a big computational challenge to obtain the dynamic transient response of complex
systems constituted of a structure interacting with a foundation supported by the soil. The most common numerical
solution schemes for the two sub-systems, the structure and the soil-foundation support are distinct. Usually, the
foundation dynamics is modelled by the Finite Element Method (FEM) or related matrix methods. On the other
hand, the soil dynamics has been best solved using either the direct or indirect version of the Boundary Element

Method (BEM). A coupling of both numerical schemes is the most versatile scheme to solve Dynamic Soil-
Structure Interaction (DSSI) problems. The coupling of the methods to obtain transient solutions is still

computationally very demanding. I this work we propose an alternative approach. For subsystem 1, the structure,

modal quantities are obtained in coordinate relative to the structure base displacement. For sub-system 2, the soil-
foundation scheme, the BEM is applied to obtain frequency domain solution of foundations resting on soils or on

piles. A coupling of the structure with foundations in the frequency domain delivers modified Frequency Response
Functions (FRFs). New or modified modal quantities are now extracted from the FRFs that already include the
influence of the soil-foundation dynamics on the structure. These extracted modal quantities may be used to
integrate directly the equations of motion in the time domain. All degrees of freedom of the soil-foundation system
are incorporated in the modified modal quantities, which retain the number of degrees of freedom of the original
structure. The numerical examples will address the transient response of structures resting foundation scheme
composed of a homogeneous half-space and a pile embedded in the half-space.