Fragility of Built Urban Objects to Vicious Attacks: Assessment by Means of Limited Data on Abnormal Violent Actions

An assessment of fragility of objects built (constructed) in urban environment to deliberately imposed abnormal actions (loads) is considered. The actions under analysis are explosions, vehicular impacts and fires that can be imposed by acts of terrorism and sabotage as well as such highly random events as car crashes into structures due to unintentional roadway departures. The fragility is assessed by means of mathematical models known as fragility functions and developed for vulnerable building and transportation structures, protective barriers, and energy supply facilities. The result of fragility assessment is the probability of the damage that can be foreseen and modelled by means of mathematical models used for structural analysis. The case is studied where information on an abnormal action can be expressed in the form of a small-size statistical sample with components acquired in post-mortem investigations of attacks or unintentional accidents. The basic idea is an application of the statistical (bootstrap) resampling for the estimation the damage probability. The resampling procedure is applied to values of the fragility function that can be developed for the damage caused by the abnormal action in question. The values of the fragility function are estimated for components of the small-size sample of abnormal action values. The resampling of the fragility function values yields a conservative estimate of the damage probability expressed by the limit of a one-sided confidence interval. The estimate of the damage probability can be applied to making decisions concerning the level of resilience of vulnerable urban objects.