Fragility curves, damage matrices, and wind induced loss estimation

This note presents a conceptual framework for the definition of basic damage states and of the corresponding fragility curves and conditional probabilities, and its use for the estimation of damage matrices. The framework is designed with two considerations in mind. First, losses due to multiple types of damage are calculated so that no type of damage is counted more than once, no type of possible damage is omitted from the calculations, and all interactions between various types of damage are accounted for. Damage is included that may vary continuously as a function of wind speed but is discretized for computational purposes. Second, the losses are calculated by correctly accounting for the dependence between various damage states (e.g., window breakage and roof uplift). The note also discusses the use of damage matrices for the estimation of expected losses due to a windstorm event, of expected annual losses, and of measures of uncertainty pertaining to expected losses, both at a specified location and over a larger geographical area. The framework developed in the paper is illustrated for the conceptually simple case of two basic damage states. Work is in progress on the application of the framework to various types of structures involving larger numbers of basic damage states with various mutual dependence and damage sequence scenarios. Work is also in progress for the estimation of uncertainties in loss calculations, based on uncertainties in the estimation of fragility curves, associated conditional probabilities, and hurricane wind speeds. One of the applications of our work is the development of vulnerability curves and associated uncertainty measures for cases where comprehensive loss data from which such curves may be developed are not available.