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

Abstract

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.

Progressive Collapse Fragility Models of Rc Framed Buildings Based on Pushdown Analysis

“…Although such concepts currently pertain to a well-established approach for disaster mitigation in earthquake engineering (see e.g. [45][46][47][48][49][50]), only a few applications have been recently presented for disproportionate collapse under blast loads and/or sudden column loss scenarios [36][37][38][39][40][41].…”

“…Analytical fragility curves were derived in case of gravity-load designed [42] and earthquake resistant [43] RC framed buildings. As discussed in the following, concepts of methodologies developed for earthquake engineering applications [45][46][47][48][49][50] and recently applied in this field [39,40] were integrated with specific analysis techniques for progressive collapse simulation. A flowchart presenting the proposed routine and their prevailing components is shown in Fig.…”

“…mean (µ), standard deviation (σ) and coefficient of determination (R 2 ) -of each lognormal fragility function, fitting discrete points from damage probability matrices through the least squares technique. To evaluate progressive collapse fragility, several thousands of structural prototypes for each building class were randomly generated on the basis of statistics and probability distributions for each RV, as specified in Section 3, and their capacity was estimated by means of classical fiber force-based [51] FE approaches commonly adopted in earthquake [46,48,50,52] and progressive collapse analysis [11, 12, 17, 19, 25, 29-32, 35, 40]. To this aim, pushdown simulation techniques [11,17,18,23,24,31] rather than IDA procedures [19,26,40] were implemented and the downward load on beams (Q b ) was assumed as reference IM.…”

“…A similar criterion was applied in past studies for random sampling associated with seismic vulnerability analysis of RC structures (see e.g. [45,46,48,50]). The center-to-center plan dimensions were equal at any floor, but varied in length (x-direction) and width (y-direction) according to different random combinations of column spacing in the two directions.…”

Seismic fragility assessment of existing sub-standard low strength reinforced concrete structures

“…A Displacement Based Earthquake Loss Assessment (DBELA) framework was developed by Pinho et al (2002) and Crowley et al (2004)for the analytical vulnerability assessment of Reinforced Concrete (RC) structures using the methodology of Calvi (1999). In contrast, the detailed analytical methods deÞ ne capacity through analysis of the structural model, the sophistication of which varies based on the required accuracy.…”