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

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 first-order 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.