Reliability-based critical earthquake load models. Part 1: linear structures

In this two-parts study the problem of determining stochastic critical earthquake excitations for linear and nonlinear structural systems is considered. In the first part of the study attention is focussed on linear structures. The earthquake load is modelled as a partially specified Gaussian random process. The known information on the excitation involves bounds on total average energy, zero crossing rate and the amount of expected disorder quantified in terms of average entropy rate. The unknown power spectral density function of the earthquake acceleration is computed with three alternative objectives: (a) maximization of probability of exceedance of extreme value of the response over a given duration across a specified permissible limit, (b) minimization of the Hasofer–Lind reliability index associated with the performance criterion considered above and (c) maximization of the steady-state response variance. The relative scope of these methods is discussed. The optimal input power spectral density functions are shown to be nearly identical in all the three cases. The paper discusses the implications of this result and illustrates the formulations with reference to a steel frame and a stack-like structure.