Energy-based method for identifying vulnerable macro-elements in historic masonry churches

Seismic vulnerability of historic churches is a well known issue in earthquake engineering. The need of preserving these buildings encourages the development of reliable numerical methods to assess their seismic behavior. In this paper a new approach is presented, based on evaluating damage pattern obtained by non-linear dynamic analysis and the energy dissipated by each macro-element during earthquakes. A “hierarchy of dissipated energy” concept emerges to give a scale of vulnerability of the parts that compose the church. By modifying masonry mechanical parameters or geometric characteristics, the crack pattern and amount of energy dissipation density of each element is varied and calibrated to achieve the desired hierarchy. The structural designer can therefore state the effectiveness of strengthening devices by checking reduction and possibly migration of dissipated energy density from weaker structural elements to more resistant ones, together with a preferable damage pattern. The proposed strategy is applied to a single nave church, hit by the Emilia Romagna earthquake (Italy, 2012), first defining a scale of vulnerability of the macro-elements and then proposing a rehabilitation strategy, which improves the seismic response in terms of damages and dissipated energy. In the case study the strong vulnerability of the main dome vault was shown, due to the combination of its high dissipated energy density with its intrinsic weakness. Strengthening techniques have been aimed to reduce the amount of dissipated energy of vulnerable macro-elements and to attenuate out-of-plane mechanisms

Design strategy for the rocking stability of horizontally restrained masonry walls

This paper investigates the pure rocking of a rigid block with horizontal restraints. The model simulates the behavior of a masonry wall connected to transverse walls and/or steel tie-rods, very frequently adopted as safety measures against seismic actions. From the system rotational stiffness, found for a Winkler-type model and for a single restraint, the resonance conditions of the horizontally restrained blocks are defined. The role of the horizontal restraint can be unilat-eral (acting only one direction of rotation) and/or bilateral (restraint with similar stiffness in both directions). Real earthquakes or Ricker’s wavelets, representing near-fault ground mo-tions, are assumed as input parameters. It is found that in the bilateral case the response is more predictable, as response spectra are monotonic curves whit a reduction of normalized rotation obtained for higher values of restraint stiffness. Moreover, the effect of horizontal re-straints is beneficial for the range of frequency parameters valid for typical masonry walls. These considerations allow to define a design strategy to ensure the rocking stability of re-strained masonry walls, through a self-centered rocking behavior

Reduction of Housner’s coefficient of restitution for masonry walls under one-sided rocking

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

Traditional and Innovative Approaches in Seismic Design

This special issue collects selected papers about a wide range of innovative applications in earthquake engineering. These studies were presented during the 2nd Edition of the International Workshop “Traditional and Innovative Approaches in Seismic Engineering”, held in Pisa in March 2017. The topics refer to the investigation of traditional and innovative materials for earthquake engineering applications: masonry, reinforced concrete, steel, structural glass and timber. In particular, advanced analytical and numerical analyses are described for considering effects of strength and material irregularities and rocking behavior under seismic excitations on historic buildings and industrial facilities. Experimental tests are also illustrated with the purpose of investigating the strengthening on masonry arches due to lime-based mortar composites and of obtaining reliable values of stiffness for moment resisting steel-timber connections. Among the innovative approaches, studies on original pavilions made of long-spanned TVT-portals braced with hybrid glass-steel panels are illustrate

Modelling Techniques and Rocking Analysis for Historic Structures: Influence of Vaulted Systems in the Seismic Response of Churches

The thesis deals with modelling techniques and rocking analysis suitable to assess the churches seismic vulnerability. Both local and global approaches are considered, discussing the role of masonry vaults in these historic buildings during earthquakes. A new method based on the dissipated energy during the ground motion is presented, together with the subdivision of the church in macro-elements and the evaluation of failure modes

Fragility curves and seismic demand hazard analysis of rocking walls restrained with elasto-plastic ties

AbstractThe dynamic stability of out‐of‐plane masonry walls can be assessed through non‐linear dynamic analysis (rocking analysis), accounting for transverse walls, horizontal diaphragms and tie‐rods. Steel tie‐rods are widely spread in historical constructions to prevent dangerous overturning mechanisms and can be simulated by proper elasto‐plastic models. Conventionally, design guidelines suggest intensity‐based assessment methods, where the seismic demand distribution directly depends upon the selected intensity measure level. Fragility analysis could also be employed as a more advanced procedure able to assess the seismic vulnerability in a probabilistic manner. The boundedness of this approach is herein overcome by applying a robust stochastic seismic performance assessment to obtain seismic demand hazard curves. A sensitivity study is carried out to account for the influence of wall geometry, the minimum number of seismic inputs, and the mechanical parameters of tie‐rods. Fragility analysis, prior to seismic demand hazard analysis is applied on over 6000 analyses, revealing that intensity measures are poorly correlated both for 1‐D and 2‐D correlation, hardly leading to the selection of the optimal intensity measure. The tie‐rod ductility, followed by its axial strength and wall size, is the mechanical parameter mostly influencing the results, whereas the wall slenderness does not play a significant role in the probabilistic response

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

Influence of the elasto-plastic behavior of tie-rods in the response of rocking masonry walls through seismic demand hazard curves

Rocking analysis is a powerful tool to assess the seismic vulnerability assessment of masonry walls subjected to out-of-plane modes, especially when in view of checking the efficiency of traditional retrofitting solutions, such as steel tie-rods restraining rocking blocks. The study focuses on a probabilistic approach for the seismic assessment of the out-of-plane behavior of masonry walls, mainly aiming to reliably predict fragility and seismic demand hazard curves in case steel tie rods are used as anti-seismic device. To identify the most appropriate steel tie-rod device, more than thousand multistripe analyses have been performed considering the Italian site with highest seismic hazard (Carlentini, Sicily), duly modifying ductility and strength of the tie rods themselves. The resulting fragility curves and seismic demand hazard curves are critically discussed, so allowing the definition of the most efficient and proficient intensity measures referring to five relevant limit states. As expected, remarkable changes in the response are recorded by passing from a brittle to a ductile tie-rod, but when the ultimate strain is bigger than 2%, an increased tie-rod ductility does not sensitively improve the response even for high-intensity earthquakes. The probabilistic approaches show that even low-ductility tie-rods can sensibly reduce the probability of exceedance of limited and moderate rocking limit states, up to an order of magnitude. As for the influence of the tie-rod strength, even low-medium values produce a remarkable reduction of annual exceedance rate. For instance, a severe rocking limit state occurs for the unrestrained monumental wall every 450 years and every 2000 years for the wall restrained by a tie rod of strength just fitting the minimum required design value

Rocking analysis of masonry walls interacting with roofs

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

Mitigation of amplified response of restrained rocking walls through horizontal dampers

Failure mechanisms in masonry walls are commonly due to the low tensile strength of masonry that could cause overturning or pounding due to the interaction with transverse walls. In this paper, the influence of dissipative devices easing the dynamic stability of rocking blocks is studied considering the main parameters affecting the response. Normalized rotation time- histories are obtained for six geometrical configurations under several acceleration records in order to analyse possible resonant effects and beneficial reductions due to the presence of a damper, accounted for in the equation of motion of the one-sided restrained rocking block. Rocking response spectra obtained for undamped systems show that possible beat phenomena may arise for certain geometrical configurations and restraint stiffness values. A design equation for the damping coefficient is proposed for the anti-seismic device and its influence on restrained facade walls under real strong motions is analysed.(undefined