Distribution of Earthquake Peak Ground Accelerations for a Construction Site

Abstract

To solve the problem of antiseismic strengthening, the integer macroseismic intensity of a building is insufficient, because this intensity cannot describe the seismic hazard of a territory. For this, it is necessary to establish the peak ground accelerations and estimate their statistical parameters. The paper constructs the probability density function of the peak ground acceleration for a building site. The basic data for such construction are the shaking of the territory, the peak ground acceleration values on a seismic scale, and the hypothesis on the distribution of peak ground accelerations according to Weibull’s law for the conditions under which the earthquake has occurred. The peak ground acceleration values are taken in accordance with the new seismic scale developed by F.F. Aptikaev. Shaking of the territory was taken in accordance with the traditional linear dependence of the recurrence macroseismic intensity logarithm. Limiting oneself to integer intensity values leads to a polyextremal distribution of peak ground accelerations with peaks at integer intensity values, since it is assumed that there are no earthquakes with intermediate intensities. A peculiarity of the research is construction of the probability density function of peak ground accelerations without using the discrete macroseismic earthquake intensity, but its continuous calculated value, replacing summation over discrete intensity values with the corresponding integration. As a result, a monotonically decreasing distribution density function is obtained, which, in a first approximation, can be described as exponential distribution.