Refractive index model to determine the vulnerability curves for different building typologies

In this paper, with reference to an analysis of seismic vulnerability on a territorial scale, we propose a new model for determining the damage in terms of a mean damage grade of a probabilistic nature. The theoretical approach is based on a behavioural analogy between a building and a particle in a dielectric, subjected respectively to an earthquake and a sinusoidal electric field: both phenomena are characterised by a critical value, and both phenomena obey the same rule when the relevant parameters are close to the critical value. We develop, in fact, a new expression for the vulnerability curves, simpler with respect to the existing one, and confirmed by data given in literature. This paper contributes to the development of a methodological process for estimating the degree of average damage in order to achieve results that can be used for preventive purposes.