Horizontally restrained rocking blocks: evaluation of the role of boundary conditions with static and dynamic approaches

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: (1) concentrated restraint as single spring and (2) 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

Economic vs environmental isocost and isoperformance curves for the seismic and energy improvement of buildings considering Life Cycle Assessment

A methodology to quantitatively assess the improvement of seismic and energy performance of masonry buildings through retrofitting interventions is here proposed. The approach is developed at mesoscale level, considering entire façades with openings and taking into account Life Cycle Assessment (LCA). The costs of retrofitting interventions that couple effects of seismic and thermal improvement (called integrated interventions/approaches) are different whether only the construction phase or the entire life cycle of the building is considered. Therefore, it is necessary to estimate at what extent it is correct to neglect LCA in the analysis of integrated approaches. In this paper, the analysis of three masonry façades is performed with and without LCA. Traditional (insulating panels, diatons, ferro-cement) and more innovative interventions (carbon and glass fiber reinforced polymer composites) are considered. For the comparison, isocost and isoperformance curves, which determine both the economic (Euros) and environmental costs (kg CO2eq) for each intervention, are discussed. The comparison shows the necessity of always considering LCA for a reliable assessment: some retrofitting interventions are the most expensive in the construction phase but they result the most convenient in economic terms and in the amount of CO2eq emissions

A new seismic isolation device based on tribological smooth rocking (TROCKSISD)

In the field of seismic risk mitigation of art objects, an innovative isolation device is here illus-trated. The device, called TROCKSISD (Tribological ROCKing Seismic ISolation Device), couples multiple components to dissipate energy and control smooth rocking: spherical con-tact surfaces with frictional layers, elastic springs ensuring re-centering and viscous elastic dampers. The conceptual idea is described and the equations of motions of the two degrees of freedom system presented, discussing the performance-based structural behaviour and the mechanical/geometric parameters involved. Moreover, dynamic analyses are performed to understand the role of the frictional layers with respect to the peripheral dampers in the miti-gation of motion under spectrum compatible seismic records. The results in terms of rocking spectra are presented and comparisons with the equivalent single degree of freedom system without the isolation device are made

The corner failure in a masonry building damaged by the 2016-2017 Central Italy earthquake sequence

Although still poorly investigated, the failure of corners is a frequent event in masonry buildings and clearly recognizable in the aftermath of a seismic event. It is characterized by the formation of a masonry wedge, mainly due to the thrust of roof elements in addition to inertial forces, and it generally involves rocking-sliding motion along the cracks on the interlocked orthogonal walls. In this paper, the case study of the corner failure in a masonry building located in Visso (Italy) is analyzed. The building was seriously damaged by the seismic events of August 24th, 2016 and October 26th and 30th, 2016. In particular, one of the free corners at the first storey completely collapsed. The seismic capacity with respect to the onset of this failure mode is analyzed by means of a refined macro-block model and by adopting the linear kinematic approach of limit analysis, accounting for frictional resistances and the thrust of roof elements. The key aspect of the proposed approach is the introduction of a criterion to evaluate the contribution of the actual frictional resistances depending on the inclination angles of the crack lines. Moreover, the loads transmitted from the roof to the walls are defined by assuming simplified static conditions according to the typology of the hipped roof. Lastly, the achieved results are compared to the seismic demand obtained by adopting the Italian Technical Standards for Constructions, both the earlier version (2008) and the current one (2018), together with that obtained using in situ recorded floor accelerations

Environmental and economic impact of retrofitting techniques to prevent out‐of‐plane failure modes of unreinforced masonry buildings

This paper presents an innovative methodology to assess the economic and environmental impact of integrated interventions, namely solutions that improve both structural and energy performance of existing masonry buildings, preventing out‐of‐plane modes and increasing their energy efficiency. The procedure allows the assessment of the environmental and the economic normalized costs of each integrated intervention, considering seismic and energy‐saving indicators. In addition, the work introduces in relative or absolute terms two original indicators, associated with seismic displacement and thermal transmittance. The iso‐cost curves so derived are thus a powerful tool to compare alternative solutions, aiming to identify the most advantageous one. In fact, iso‐cost curves can be used with a twofold objective: to determine the optimal integrated intervention associated with a given economic/environmental impact, or, as an alternative, to derive the pairs of seismic and energy performance indicators associated with a given budget. The analysis of a somehow relevant case study reveals that small energy savings could imply excessive environmental impacts, disproportionally increasing the carbon footprint characterizing each intervention. Iso‐cost curves in terms of absolute indicators are more suitable for assessing the effects of varying acceleration demands on a given building, while iso‐cost curves in terms of relative indicators are more readable to consider a plurality of cases, located in different sites. The promising results confirm the effec-tiveness of the proposed method, stimulating further studies

Stochastic assessment of rocking masonry façades under real seismic records

This contribution assesses in stochastic terms the safety level of masonry façades potentially subjected to out-of-plane loading and the beneficial effect offered by horizontal restraints – such as steel tie rods - under earthquakes. A parametric analysis is performed on façades of different slenderness and size to state their influence on the response in probabilistic terms, showing that velocity and energy based Intensity Measures are optimal since they usually re-spect the efficiency and practicality criteria. In case of retrofitting interventions, the univariate FCs can be plotted in the two configurations (with and without steel tie rods). In order to ef-fectively present the results, the graph of the difference of conditional probability is elaborat-ed, which directly gives the information on the earthquake intensity for which the level of im-provement is more relevant. Univariate and bivariate curves are also compared and the for-mer may be not in favor of safety, especially for stronger seismic records. This probabilistic procedure is ideal for applications in earthquake engineering, assessing in stochastic sense the level of improvement obtained with traditional retrofitting solutions

Experimental tests on a dowel-type timber connection and validation of numerical models

This paper examines the dynamic behaviour of timber framed buildings under wind and dynamic loads, focusing on the role of connections being experimentally tested. The main aim of this manuscript is to analyze the in-service dynamic behaviour of a semi-rigid moment-resisting dowel-type connection between timber beam and column. For this purpose, two laboratory tests have been performed, the first on a connection and another one on a portal frame. The results are used to validate a numerical model of the simple portal frame, analyzed in OpenSees. The obtained relationships are also discussed and compared with Eurocode rules. The main result is that the joint stiffness is calculated through the Eurocode (EC) formulation underestimates the experimental one. A mutual agreement is obtained between the numerical model, validated from the experimental stiffness value for the connections, and the experimental results on the portal frame

Graphical methods, kinematic and finite element analysis of the premilcuore masonry bridge

This paper presents the results of static and seismic vulnerability analyses performed on a single-span masonry bridge located in Northern Italy. The structure, dated back to the 17th century, is a bridge with single-span of about 16 meters and height of 8 meters, built with rubble and irregular masonry. A preliminary static analysis was performed on the bridge through traditional graphic approaches such as the Méry's rule and the Durand-Claye's method. Afterwards, a kinematic non-linear analysis was executed once the collapse mechanism under horizontal earthquake-type actions was identified. Finally, a static finite element analysis with brick elements was performed to state the seismic vulnerability of the bridge, by changing its mechanical properties to evaluate their influence on the structural response. Collapse load factors have been also computed considering non-uniform gravitational loads and horizontal settlements at the bridge foundations

Out-of-plane seismic response of masonry façades using discrete macro-element and rigid block models

This paper investigates the out-of-plane response of masonry façades under earthquakes by means of two different approaches. A discrete macro-element approach, based on modelling the structure by means of spatial deformable macro-elements interacting through nonlinear zero-thickness interfaces, and the classical approach in which the masonry façade is assumed as a rigid block subjected to earthquake loading. The latter method neglects the elasticity of the masonry element and contemplates the energy dissipation only at each impact by means of a coefficient of restitution. The results of dynamic non-linear analyses, performed with the two methods on a real case of a church façade, provide a first comparison between the two ap-proaches highlighting some limits of application of the simplified rigid block model

Rocking and kinematic analysis of two masonry church façades

The paper deals with the application of two methods of local analysis on masonry structures. Rocking and kinematic analysis are applied to two cases study: a gable of the Ica Cathedral that survived the 2007 Pisco earthquake and a church façade connected to transverse walls, which collapsed in the 2012 Emilia Romagna earthquake. The critical aspects of both analysis are discussed and the differences in the outputs commented. Being the two rigid blocks at height different from zero, an amplification factor of the seismic record was calculated for performing the rocking analysis. The gable is treated as free-standing block whereas the upper part of the church façade is analyzed in the rocking analysis by accounting for the rebound effect caused by the transverse walls, through the stiffness of a bed spring.The authors wish to thank Ing. Luciano Bellesia for his helpful cooperation. The activity is cosponsored by Consortium RELUIS – Masonry 2014