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

Abstract

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.

In situ free‐vibration tests on unrestrained and restrained rocking masonry walls

“…Several studies were performed to understand to what extent ground motion features and system geometry affect the response. [15][16][17][18][19][20][21] One of the main issues under debate when facing rocking is energy dissipation. The well-known coefficient of restitution, ratio of velocity just after impact by velocity right before it, is used to damp oscillations, and it is computed as n the conservation of angular momentum.…”

Seismic behavior and assessment of masonry heritage structures. Needs in engineering judgement and education

“…As an advanced technique, the monolithic out-of-plane response to earthquakes, of masonry structural parts, is explained by means of rocking dynamics. The process requires complex analytical or numerical calculations of an incremental kinematic analysis, under an acceleration-time history [23].…”

Parametric analysis on external dissipative link system for seismic protection of low rise r.c. buildings

“…T Also, in the context of historical masonry buildings the improvement of seismic behaviour can be evaluated by different techniques, especially related to the fact that connections between vertical elements and between vertical and horizontal diaphragms are weak. For these issues, new approaches have recently been proposed, related to energy dissipation [10] and to rocking analysis of walls with horizontal restraints [11,12]. Indeed, steel tie-rods are generally the simplest and most effective tools to impede out-of-plane modes for both masonry and precast concrete structures [13,14] or to reduce relative displacements in case of flexible diaphragms [15].…”

“…In practice, the section of the elements Ak was determined by attempts using Eqn. (12) (attempt values of the sections) and then enforcing Eqn. (9).…”