An earthquake-source-based metric for seismic fragility analysis

Abstract

The seismic fragility of a system is the probability that the system enters a damage state under seismic ground motions with specified characteristics. Plots of the seismic fragilities with respect to scalar ground motion intensity measures are called fragility curves. Recent studies show that fragility curves may not be satisfactory measures for structural seismic performance, since scalar intensity measures cannot comprehensively characterize site seismicity. The limitations of traditional seismic intensity measures, e.g., peak ground acceleration or pseudo-spectral acceleration, are shown and discussed in detail. A bivariate vector with coordinates moment magnitude m and source-to-site distance r is proposed as an alternative seismic intensity measure. Implicitly, fragility surfaces in the (m, r)-space could be used as graphical representations of seismic fragility. Unlike fragility curves, which are functions of scalar intensity measures, fragility surfaces are characterized by two earthquake-hazard parameters, (m, r). The calculation of fragility surfaces may be computationally expensive for complex systems. Thus, as solutions to this issue, a bi-variate log-normal parametric model and an efficient calculation method, based on stochastic-reduced-order models, for fragility surfaces are proposed.

Performance‐based seismic design of tuned inerter dampers

“…The ( m , r ) distribution of the seismic hazard is essential in the seismic design of structures because the frequency content of the ground motions depends on ( m , r ), among other characteristics, such as local site conditions or seismic regime. ()…”

“…The (m, r) distribution of the seismic hazard is essential in the seismic design of structures because the frequency content of the ground motions depends on (m, r), among other characteristics, such as local site conditions or seismic regime. 29,64 The distribution of earthquakes by (m, r) is obtained from the UHT 65 from the United States Geological Survey. This online tool provides the contribution of the seismic sources characterized by (m, r) for a specified level of the seismic intensity (e.g., the spectral acceleration) at each site in the United States.…”

“…This method may yield unsatisfactory results for some nonlinear systems. () The limitations of scaling ground motions may be resolved by simulating synthetic ground motions, an approach that has already been adopted in the performance‐based seismic analysis of structures. ()…”

“…28,29 The limitations of scaling ground motions 30 may be resolved by simulating synthetic ground motions, an approach that has already been adopted in the performance-based seismic analysis of structures. 29,31 The issue of calculating the response of dynamic systems in the general nonlinear systems subjected to nonstationary, non-Gaussian input, because the framework of the random-vibration theory can not be used in complex realistic applications. The general random-vibration theory is insufficient to perform this task, 32 because it can only provide solutions for second-moment properties of the states of arbitrary linear systems subjected to Gaussian random input.…”

Stochastic reduced-order models for stable nonlinear ordinary differential equations

“…This is a significant limitation since realistic dynamic systems behave nonlinearly under strong random vibrations and the distribution of the response is non-Gaussian. For example, the distribution of the pressure field acting on a spacecraft during atmospheric re-entry is highly non-Gaussian [2]; the assumption that the responses of structures under extreme wind [3] or seismic [4] excitations are linear may be inadequate; the aircraft main landing-gears are nonlinear complex systems, which require time-consuming dynamic simulations to calculate steady-state solutions [5]. Thus, the reliability of such structures cannot be obtained within the framework of the random vibration theory.…”