Seismic Reliability Analysis of Structures

“…Once the CDF of the demand and the capacity have been found, the calculation of the probability of exceedance of a specified limit state can be obtained using the standard time-invariant reliability formulation (e.g. Pinto et al, 2004). The probability of being in a particular damage band may then be found from the difference between the bordering limit state exceedance probabilities.…”

Section: Proposed Methodologymentioning

confidence: 99%

“…The reader is referred for example to Pinto et al, (2004) for a description of the theory of FORM, as well as Restrepo-Velez (2004) for a detailed description of the application of FORM to the displacement capacity equations for un-reinforced masonry structures. Essentially, FORM can be used to compute the approximate CDF of a non-linear function of correlated parameters, such as the limit state displacement capacity function and limit state period function.…”

Section: Probabilistic Treatment Of the Capacitymentioning

confidence: 99%

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A Probabilistic Displacement-based Vulnerability Assessment Procedure for Earthquake Loss Estimation

Crowley

Pinho

Bommer

2004

Bull Earthquake Eng

198

128

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Earthquake loss estimation studies require predictions to be made of the proportion of a building class falling within discrete damage bands from a specified earthquake demand. These predictions should be made using methods that incorporate both computational efficiency and accuracy such that studies on regional or national levels can be effectively carried out, even when the triggering of multiple earthquake scenarios, as opposed to the use of probabilistic hazard maps and uniform hazard spectra, is employed to realistically assess seismic demand and its consequences on the built environment. Earthquake actions should be represented by a parameter that shows good correlation to damage and that accounts for the relationship between the frequency content of the ground motion and the fundamental period of the building; hence recent proposals to use displacement response spectra. A rational method is proposed herein that defines the capacity of a building class by relating its deformation potential to its fundamental period of vibration at different limit states and comparing this with a displacement response spectrum. The uncertainty in the geometrical, material and limit state properties of a building class is considered and the firstorder reliability method, FORM, is used to produce an approximate joint probability density function (JPDF) of displacement capacity and period. The JPDF of capacity may be used in conjunction with the lognormal cumulative distribution function of demand in the classical reliability formula to calculate the probability of failing a given limit state. Vulnerability curves may be produced which, although not directly used in the methodology, serve to illustrate the conceptual soundness of the method and make comparisons with other methods.

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“…However, vulnerability curves are not explicitly derived in DBELA, but the failure probability is calculated through the integration of the variability in the displacement capacity and in the displacement demand in the classical reliability formula (e.g. Pinto et al, 2004). Figure 2 shows how the probability of exceeding a limit state is influenced by aleatory variability (sigma) at different levels of spectral displacement, wherein it can be observed that the incorporation of sigma does not always lead to higher probabilities of exceedance: the influence of sigma depends on the level of spectral displacement.…”

Section: Calculating Losses From Single Earthquake Scenariosmentioning

confidence: 99%

The Influence of Ground-Motion Variability in Earthquake Loss Modelling

Bommer

Crowley²

2006

Bull Earthquake Eng

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Earthquake loss models are subject to many large uncertainties associated with the input parameters that define the seismicity, the ground motion, the exposure and the vulnerability characteristics of the building stock. In order to obtain useful results from a loss model, it is necessary to correctly identify and characterise these uncertainties, incorporate them into the calculations, and then interpret the results taking account of the influence of the uncertainties. An important element of the uncertainty will always be the aleatory variability in the ground-motion prediction. Options for handling this variability include following the traditional approach used in site-specific probabilistic seismic hazard assessment or embedding the variability within the vulnerability calculations at each location. The physical interpretation of both of these approaches, when applied to many sites throughout an urban area to assess the overall effects of single or multiple earthquake events, casts doubts on their validity. The only approach that is consistent with the real nature of ground-motion variability is to model the shaking component of the loss model by triggering large numbers of earthquake scenarios that sample the magnitude and spatial distributions of the seismicity, and also the distribution of ground motions for each event as defined by the aleatory variability.

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Seismic Reliability Analysis of Structures

Cited by 42 publications

References 0 publications

Probabilistic fragility analysis parameterized by fundamental response quantities

Probabilistic fragility analysis parameterized by fundamental response quantities

A Probabilistic Displacement-based Vulnerability Assessment Procedure for Earthquake Loss Estimation

The Influence of Ground-Motion Variability in Earthquake Loss Modelling

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