Application of Similarity and Dimensional Theory for Seismic Treatment

Abstract

The paper considers the problem of seismic treatment in building codes. Some definitions used in earthquake engineering in Russia and abroad are analyzed. Inconsistencies between definitions and empirical data and similarity and dimensional theory are revealed. Seismic treatment is still based on different assumptions that were made during in the early days of engineering seismology and earthquake engineering despite advances in modern seismology in theoretical problems and a representative strong ground motion database. Many of these assumptions were made in violation of the rules of similarity and dimensional theory, and these errors migrated to modern building codes. For example, the definitions of magnitude, duration of vibrations, quality factor, ground accelerations, and some other quantities used in regulations in the engineering scope of seismic ground motion turned out to be incorrect. This is because many definitions valid for small deformations are incorrect for large ones. Confusion with terminology causes many problems: definitions of some quantities (e.g., the duration of vibrations or the vibration period) used in calculations depend on the posed problem. There are both identical definitions for different physical quantities and different definitions for the same quantity even in the glossaries of regulations. Physically incorrect definitions of some quantities that can lead to incorrect engineering calculation results are a significant source of calculation errors. The paper considers dimensionless quantities that describe seismic ground motion. Dimensionless quantities do not depend on the scale of the phenomenon according to similarity and dimensional theory. Therefore, the use of seismic treatment characteristics, such as the dynamic amplification factor, deformation, shape of the response spectrum, shape of the vibration envelope, and number of vibration cycles, greatly increases calculation accuracy.