New Developments in the Theory of Dynamics for Seismic Analysis of Buildings

Abstract

One of the most vexing problems in seismic engineering is the dynamic coupling of a structure and the soil beneath it. However, the soil itself is also resting on a bedrock (a half space) that is the one that actually transmits the seismic signal to the soil-structure interface. In this paper a semidefinite model will be introduced that allows us to perform accurate dynamic analyses that in turn will shed light upon many important aspects of the, up to now, simply termed the “Soil-structure interaction problem” that does not mention how and what would be the role of a moving bedrock (the half-space) transmitting seismic induced motion. It will also be shown that the “Soil-Structure-Half space model” is worked out as a single semidefinite structure with the half space, the soil and the structure dynamically coupled. Once this model is set up, then the analysis of the modes and frequencies of the complete model can be analyzed and discussed in relation to the frequency density^{[1 and 2]} of the rigidly fixed building and the frequency changes that occur when the soil and the half space are included in the analysis. With regard to the seismic excitation it is common practice to use seismic records like those of the SCT accelerogram which is assigned to each and every one of the building’s masses. In this work the authors propose to adopt as input loading, a seismic signal SCT-CAL calibrated in such a way that when it is applied to the half space, we recover, at the top of the soil deposits, the accelerogram and the spectrum recorded during the earthquake of September 19, 1985 at the SCT accelerograph.