Chapter Six - Critical Envelope Function for Nonstationary Random Earthquake Input

Abstract

This chapter discusses a new probabilistic critical excitation method for identifying the critical envelope function of ground motions. It is well known that the envelope shape of ground motions depends on various factors. These factors include an arrival time and an order of various kinds of waves. The maximum structural responses of models with rather shorter natural periods are often induced by the intensive motions existing mostly in the first half portion of ground motions. It is therefore of practical interest to investigate the most critical envelope shape in ground motions. Time histories of four ground motions have been outlined here to show that a monotonically increasing function may be a candidate for the envelope function in the former half part of the total duration. The chapter assumes the nonstationary ground motion to be expressed as the product of a deterministic envelope function and another probabilistic function representing the frequency content. The former is determined such that the corresponding mean–square drift of a single–degree–of–freedom model attains its maximum under the constraint on mean total energy. The critical excitation method is expected to provide useful information for the design of important structures to which functional and structural damages must be absolutely avoided during severe earthquakes.