Error estimation of closed‐form solution for annual rate of structural collapse

Abstract

With the increasing emphasis of performance-based earthquake engineering (PBEE) in the engineering community, several investigations have been presented outlining simplified approaches suitable for performance-based seismic design (PBSD). Central to most of these PBSD approaches is the use of closed-form analytical solutions to the probabilistic integral equations representing the rate of exceedance of key performance measures. Situations where such closed-form solutions are not appropriate primarily relate to the problem of extrapolation outside of the region in which parameters of the closed-form solution are fit. This study presents a critical review of the closed form solution for the annual rate of structural collapse.The closed form solution requires the assumptions of lognormality of the collapse fragility and power model form of the ground motion hazard, of which the latter is more significant regarding the error of the closed-form solution. Via a parametric study, the key variables contributing to the error between the closed-form solution and solution via numerical integration are illustrated. As these key variables can not be easily measured it casts doubt on the use of such closed-form solutions in future PBSD, especially considering the simple and efficient nature of using direct numerical integration to obtain the solution. KEYWORDSPerformance-based seismic design (PBSD), performance-based earthquake engineering (PBEE), ground motion hazard, annual rate of collapse, deaggregation.2

Seismic Hazard Epistemic Uncertainty in the San Francisco Bay Area and Its Role in Performance-Based Assessment

“…Again the different methods provide similar results (the second moment and Monte Carlo methods are similar, and thus only one is shown), but more importantly it can be seen that the uncertainty in the collapse probability has been significantly increased when collapse fragility uncertainty is considered. This is in agreement with analytical solutions, which show that the uncertainty in the collapse capacity are the epistemic uncertainty in the collapse capacity and hazard respectively, and k is the log-log slope of the seismic hazard curve (which increases with reducing exceedance probability) (Bradley and Dhakal 2008).…”

A closed form solution for seismic risk assessment incorporating intensity bounds

“…(3)). Several authors [14,15,18] have argued that this assumption can lead to inaccurate results. This error can be partly eliminated if the hazard curve is approximated by a second-order polynomial in log-log coordinates, as suggested by Vamvatsikos [15]:…”

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