Incorporating intensity bounds for assessing the seismic safety of structures: Does it matter?

Abstract

SUMMARY The closed‐form solution for assessing the proportion of the mean annual frequency of limit‐state exceedance as a function of integration limits is introduced, in order to study whether or not the mean annual frequency of limit‐state exceedance is overestimated if the lower and(or) upper integration limit of the risk equation are(is) not selected in a physically consistent manner. Simple formulas for assessing the threshold value of the lower and upper integration limits are also derived. These formulas can be used to quickly assess the significant range of ground motion intensity that affects the mean annual frequency of limit‐state exceedance. It is shown that the threshold values of the integration limits depend on the median intensity causing a limit‐state, the corresponding dispersion and the slope of the hazard curve in the log domain. For several reinforced concrete buildings located in a region with moderate seismicity, it is demonstrated that the mean annual frequency of collapse can be significantly overestimated when assessed by integrating the risk equation over the entire range of ground motion intensity. Copyright © 2013 John Wiley & Sons, Ltd.

A closed form solution for seismic risk assessment incorporating intensity bounds

“…However, the correction factor C 1 has a different meaning than the proportion of the limit-state risk Dk LS,im1 , which was defined and presented in Fig. 4 of the previous study [11]. By comparing these two parameters it can be concluded that the effect of the lower bound of intensity is slightly reduced in the case of the correction factor C 1 since this factor is based on the truncated limit-state fragility function (Eq.…”

“…This assumption is the main difference between the formulae introduced in this paper and those published before [11]. The truncated fragility function is therefore expressed as follows:…”

“…The impact of the intensity bounds on the assessment of collapse risk is then demonstrated for a 4-storey and a 15-storey frame building by utilising the peak ground acceleration and the spectral acceleration at the first vibration period as intensity measures. It should be emphasised that the closed form solution of the risk equation is different to that previously published before [11]. In this case the solution is based on the truncated limit-state fragility function, which takes into account the fact that the probability of exceeding a designated limit state is zero if the ground-motion intensity is lower than the minimum ground-motion intensity which causes a designated limit state (e.g.…”

“…However, it has recently been argued that the integration of the risk equation over the entire range of ground-motion intensity, e.g. from zero to infinity, is unphysical, since lower and upper bounds of intensity exist [11], respectively, due to the nature of a structure and the ground motions, and the seismicity in the area close to the site of the structure. Similarly, the risk equation is integrated from zero to an infinite intensity in the process of computing the risk-targeting hazard maps [1,2,12].…”

Risk-Based Design Check for Collapse Safety Using Few Ground Motions

“…Commonly lognormal distribution of collapse fragility function is used. Lazar and Dolšek [15] showed that standard deviation of natural logarithms of collapse intensities in terms of spectral acceleration at fundamental period in the case of reinforced concrete frames is within the interval from 0.3 to 0.5. To minimize the influence of error in assumed standard deviation of natural logarithms of collapse intensities β t on the value of S a,ct Dolšek and Brozovič [13] showed that the target collapse intensity should be associated with a low percentile, so-called characteristic percentile, of collapse intensities.…”