Rocking and Kinematic Approaches for Rigid Block Analysis of Masonry Walls: State of the Art and Recent Developments

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.