Analysis of the Values of Ground Displacements, Shear Strains, Velocities, Accelerations, and Response Spectra of a Strong Earthquake Based on Synthetic Accelerograms

Abstract

In his early works, the author developed a mechanical–mathematical method for modeling synthetic seismograms and accelerograms of strong earthquakes for a given site with certain ground conditions, whereby an earthquake is viewed as an effect of instantaneous rupturing of Earth’s crust. This study examines ground displacements, velocities, accelerations, and relative shear strains, as well as earthquake response spectra based on synthetic accelerograms. All ground categories are reviewed, from the hardest rocks to the most unconsolidated soils. The maximum values for ground displacements, velocities, and accelerations are obtained as a function of the attenuation coefficient of rocks and the number of oscillation modes of the considered foundation bedding, as well as peak ground accelerations as a function of distance from the expected earthquake’s rupture. It is shown that higher oscillation modes increase ground acceleration 1.66 times if calculated using only the first oscillation mode; they also increase ground displacements 1.1 times, while decreasing shear strain 1.1 times. The maximum positive attenuation effect in hard ground compared to its absence reaches 37%. Shear strain values increase proportionally to an increase in soil category number. At a level of 15 m from Earth’s surface in rocky soils, at a magnitude of М = 7.0, the shear strain values exceed the critical thresholds, which implies a high probability of surface rupturing. Response spectra obtained by synthetic accelerograms are compared to similar spectra based on a large number of actual earthquakes, showing that they are quite similar both qualitatively and quantitatively. Based on the results, it is recommended to use them for assessing seismic hazard levels in various areas, monitoring for earthquake prediction, ensuring seismic safety of facilities and underground structures, and enhancing analysis methods of seismic impact on buildings and structures.