The paper deals with the behavior of restrained rocking blocks under seismic actions. Structural or non-structural masonry or r.c. elements, such as building façades or pre-cast panels subjected to out-of-plane modes, may be assimilated to rocking blocks restrained by horizontal springs. Horizontal restraints can represent flexible floors or steel anchorages or any anti-seismic device designed to impede overturning probability. Their effect could improve, in most cases, the dynamic response of blocks in terms of reduction of rotation amplitude. Nevertheless, this effectiveness could vanish or, surprisingly, affect the response in negative way, resulting in overturning when low values of stiffness or one-sided motion in particular conditions are assumed. Two cases of horizontal restraints are analyzed: (i) concentrated restraint as single spring and (ii) smeared restraint as spring bed with constant or linearly variable stiffness. The single stabilizing or destabilizing terms of the formulation are here analyzed and commented, providing practical evaluations to obtain enhancement of response in static and dynamic perspective. A numerical example of a masonry façade with non-linear boundary conditions has been provided highlighting how the choice of stiffness values affects the oscillatory motion and rebound effects. Finally, unit stiffness for masonry/concrete walls and retrofitting techniques, such as steel tie-rods, has been calculated

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.

This paper investigates the out-of-plane behavior of masonry walls interacting with roofs. Often, collapses of masonry portions supporting roofs may occur due to the roof thrust, which generates a destabilizing effect over motion. Nevertheless, the roof weight can produce a positive stabilizing effect for rotation amplitudes smaller than the critical value. The dynamics of a rocking masonry block interacting with roofs is discussed, by properly modifying the Housner equation of motion of the free-standing single degree-of-freedom block. The dependence of the restoring moment on the rotation angle is investigated and the minimum horizontal stiffness is calculated so that the same ultimate displacement as the system without roof thrust is obtained. Two case studies are presented as applicative examples of the proposed method: an unreinforced masonry structure tested on shaking table and a spandrel beam subjected to roof thrust that survived the Emilia Romagna earthquake. Inertia moments and radius vectors of different failure mechanisms are also provided to solve the equation of motion for different block shapes. Finally, a parametric analysis of a trapezoidal rocking block has been carried out by changing its geometrical shape. This analysis shows that the influence of the shape is relevant for the calculation of the failure load, although is not possible to determine an a priori most critical shape

Summary In the out‐of‐plane assessment of rocking walls, a relevant and yet uncertain aspect is the influence of energy dissipated during motion due to impacts and restraints, such as a floor or tie rods. Therefore, in situ rocking tests on unrestrained and restrained unreinforced masonry walls, made of composite (rubble + blockwork) masonry, were performed and analyzed. The restraint is given by steel springs of assigned stiffness, simulating a floor connected to full‐scale (4 × 1 × 0.6 m3) specimens from a dismantling building. The specimens are displaced from a static equilibrium position and released, allowing to evaluate energy dissipation. The coefficient of restitution is estimated as the square root of consecutive peak velocities of the same sign, to take into account nonhomogeneities in walls. For unrestrained walls, experimental coefficients of restitution vary between 81 and 88% of analytical ones, confirming the latter as conservative. For restrained configurations, experimental coefficients of restitution are between 74% and 83% of analytical values of unrestrained walls. Hence, an additional energy damping can be ascribed to the springs. Equivalent viscous damping ratios of a nonlinear rocking system are calculated by considering a velocity logarithmic decrement, resulting between 6% and 8% (unrestrained condition) and between 8% and 10% (restrained condition). An analytical formula is proposed for estimating the coefficient of restitution for restrained walls if the dynamic properties of the unrestrained wall and the horizontal restraint are known. Finally, the relevance of a refined estimation of energy dissipation is discussed by means of numerical time history analyses.

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Probabilistic models for two soil erosion parameters needed to model the erodibility of water-retaining structures are developed. The models predict the values of the critical shear stress and the coefficient of erosion starting from other measurable soil properties.\ud The models include both noncohesive and cohesive contributions to the erosion behavior. An importance sampling simulation method is parallelized to be implemented in parallel computing resources to calibrate the models and estimate the unknown parameters using laboratory data. The probabilistic models are then used to develop fragility curves that capture the vulnerability of a typical earth dam to internal\ud erosion

Abstract:The paper deals with the use of vibro-compressed units with bio-natural components on construction. The proposed mix design of vibrated blocks consist of cork granules and/or hemp shives, with the aim to substitute polymeric elements or expanded clay, together with the use of natural hydraulic lime (NHL) as binder. An experimental campaign is presented, with mechanical tests to evaluate the influence of each component on flexural and compression behavior. The proposal is also investigated from a productive point of view, considering how it can be harmonized in the productive process of lightweight aggregate concrete units without modifications in the productive process. The tested elements could perform a certain reduction of the carbon impact, maintaining interesting mechanical properties. The application of the proposed units in several contexts, as separating elements joined with structural components, is considered to improve rehabilitation or to obtain higher performances in buildings.