Fragility curves for free and restrained rocking masonry façades in one-sided motion

Abstract

This paper deals with the need of extending results of deterministic rocking analyses to stochastic analyses on restrained masonry façades in one-sided motion. The purpose is to define the level of improvement achieved with any anti-seismic device of a given stiffness and strength, in terms of reduction of probability of exceedance of a certain limit state. The most efficient intensity measures (IMs) are identified for three masonry façades of churches in free and restrained conditions. A reliability analysis is carried out by considering over 70 earthquakes, of which 50 recorded during the recent 2016-2017 Central Italy Earthquake. Four limit states are taken into account: rocking initiation, limited rocking, moderate rocking and near-collapse condition. The yielding limit state is considered for the analysis with anti-seismic devices. Univariate and bivariate fragility curves (FCs) are compared in free and restrained configurations, to discuss the reduction of probability of exceedance depending on 15 intensity measures. The results show that the best IMs are velocity-based parameters, in particular the Fajfar Index and Peak Ground Velocity, together with Peak Ground Acceleration. In one-sided motion without restraints, the higher the compression stiffness of the sidewalls, the more unstable the wall is in probabilistic terms. Practical curves show, for each IM, the reduction of probability of exceedance obtained thanks to assumed horizontal restraints. These help to understand, in a stochastic perspective, to what extent the anti-seismic device can be beneficial or detrimental (in case of amplifications of motion) for given earthquake intensities. The comparison of univariate and bivariate FCs confirms the superiority of bivariate FCs. Indeed, often the univariate curves sensitively underestimate the probability of exceedance, especially for low-medium intensity earthquakes, and are not able to offer any information regarding the influence of other IMs.

Modelling rocking response via equivalent viscous damping

“…[9][10][11][12][13] The CR was largely adopted for the study of the dynamic behaviour of rigid blocks under trigonometric pulses [14][15][16] and earthquake excitations. 22 Moreover, recent studies concerning the derivation of overturning fragility curves of historical masonry façades 23,24 and rocking elements 25,26 also adopted a CR. 22 Moreover, recent studies concerning the derivation of overturning fragility curves of historical masonry façades 23,24 and rocking elements 25,26 also adopted a CR.…”

“…[17][18][19] The CR was also employed for simulating the energy dissipation characterising the dynamic response of walls under one-way (vertical) bending, 20 portal frames, 21 and multi block systems representing potential masonry collapse mechanisms. 22 Moreover, recent studies concerning the derivation of overturning fragility curves of historical masonry façades 23,24 and rocking elements 25,26 also adopted a CR.…”

Nonlinear Static and Dynamic Analysis of Rocking Masonry Corners Using Rigid Macro-Block Modeling

“…In particular, the capacity thresholds are herein referred to three limit states, i.e. LS0, LS1 and LS2, according to the threshold values proposed by Giresini et al 37 The¯rst one corresponds to the rocking initiation, which conventionally occurs when the PGA or PFA is greater than or equal to the minimum acceleration that causes rocking. The second one, LS1, is assumed to be a limit state for which the maximum displacement of the control point attains a value of 40% of d à 0 , being d à 0 the instability displacement under quasi-static loading, also called static instability displacement.…”

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].…”