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.

In-plane strength of masonry walls is affected by the resistant mechanisms activated in the walls, i.e., related to flexural or shear behavior. The latter one can occur in the walls according to different failure modes depending on both mortar and unit strengths and on the type of assembling, i.e., ‘regular’ or ‘irregular’ texture. In this paper, a critical review of the existing design formulations for the in-plane strength of masonry walls is firstly presented, with important information on the achievable failure modes depending on the geometrical and mechanical features of the masonry fabric. Then, experimental tests are collected from the literature and a comparison between theoretical and experimental results is carried out. The presented analyses are aimed to highlight the differences between the existing formulations and to identify the most suitable ones.