Probabilistic approach in Rocking Analysis of Masonry Elements: influence of the restitution coefficient on the response

Abstract

Rocking phenomenon is a dynamic behavior exhibited by rigid bodies subjected to transient actions such as seismic excitations. With rocking analysis it is possible to assess the seismic response - in terms of survival or collapse - of masonry façades or masonry elements that can be assimilated to rigid blocks. The formulation is that first introduced by Housner (Housner 1963) and the dissipation properties are represented by a restitution coefficient, which reduces the velocity of the block after each impact. The present paper investigates the influence of geometrical dimensions and restitution coefficient of several blocks under acceleration time-histories. The dynamic behavior of the case study is shown to be markedly dependent on the slenderness ratio and the value of restitution coefficient. Gaussian distributions of the restitution coefficient are adopted, by fixing different mean and standard deviation values. The analysis result is that it does not exist an upper limit value of restitution coefficient for which the block is always stable and a lower limit value for which the block does overturn, and therefore it should be recommended to assume stochastic distribution for it in the vulnerability assessment process.