Rocking and kinematic approaches for rigid block analysis of masonry walls: State of the art and recent developments

Abstract

The assessment of the rocking and overturning response of rigid blocks to earthquakes is a complex task , due to its high sensitivity to the input motion , variations in geometry and dissipation issues. This paper presents a literature review dealing with classical and advanced approaches on rocking motion with particular reference to masonry walls characterized by a monolithic behavior. Firstly , the pioneering work of Housner based on the concept of the inverted pendulum is discussed in terms of the most significant parameters , i.e. , the size and slenderness of the blocks , the coefficient of restitution and ground motion properties. Free and restrained rocking blocks are considered. Then , static force-based approaches and performance-based techniques , mostly based on limit analysis theory , are presented to highlight the importance of investigating the evolution of the rocking mechanisms by means of pushover curves characterized by negative stiffness. From a dynamic perspective , a review of probabilistic approaches is also presented , evaluating the cumulative probability of exceedance of any response level by considering different earthquake time histories. Some recent simplified approaches based on the critical rocking response and the worst-case scenario are illustrated , as well.