OUT-OF-PLANE SEISMIC RESISTANCE OF MASONRY WALLS

Seismic vulnerability of unreinforced masonry buildings is studied by means of simplified out-of-plane collapse mechanisms that take into account connections with transversal walls. According to experimental evidence, the analysis assumes that failure is reached with a rigid body motion of a part of the facade that falls down. Two classes of mechanism are examined: the overturning of the facade due either to a vertical crack at the connection or a diagonal crack on the transversal wall, both defined resorting to a simple model of masonry fabric, viewed as a regular assembly of rigid blocks and elastic plastic joints with friction but no cohesion. The use of simplified mechanisms give rise to an explicit evaluation of the seismic resistance to changes in the geometry and in the masonry fabrics, that could be used by practising engineers. This formulation is developed for both static horizontal actions and ground velocity peak, in the belief that the latter probably gives a better approximation of seismic action, while also providing, by comparison with the results of static forces, an estimate of the behaviour factor for unreinforced masonry. Eventually, the analytical forecasts are compared with numerical results obtained by means of the distinct element method.     

A Procedure to Investigate the Collapse Behavior of Masonry Domes: Some Meaningful Cases

Masonry domes represent an important part of the architectural heritage. However, the literature about domes analysis seems less consistent than that referred to other masonry structures. The collapses that have happened in recent years as a consequence of seismic actions or lack of maintenance show the need for detailed studies. Here a limit analysis to evaluate the masonry domes behavior is presented. An algorithm based on the kinematic approach has been developed to evaluate the geometric position of the hinges that determine the minimum collapse load multiplier. The proposed procedure is validated by a comparison with some meaningful cases—the collapse of Anime Sante Church in L’Aquila, the collapse of San Nicolò Cathedral in Noto, the crack pattern of San Carlo Alle Quattro Fontane Church in Rome, and the analysis developed on Hagia Sofia in Istanbul. The comparison with real cases shows a good agreement between the model results and the phenomenological crack patterns.     

Discrete Element Modeling of Groin Vault Displacement Capacity

Displacements experienced by many historic masonry structures concentrate at masonry joints and can be large before collapse is a concern, making modeling of stability using discrete element modeling (DEM) particularly suitable. In this study, masonry groin vault and arch models with several geometries were subjected to horizontal and vertical support displacements using DEM. Support movements were applied in a quasi-static manner to simulate the support settlement process. Displacements at collapse and at the point when the first block fell from the vault were recorded. Block separation and mechanisms were also noted during the simulations. A two-dimensional (2D) analytical model using thrust line analysis was developed to help evaluate the DEM results. In general, the displacements at first block fall were relatively large but significantly less than those at collapse. The groin vaults and arches exhibited significantly higher capacity to sustain vertical support displacement compared to horizontal displacements. For many geometries, the DEM collapse displacements of the groin vaults compared reasonably well to similar arches, indicating that the displacement capacity of groin vaults can be reasonably estimated using 2D simplifications. However, for certain geometries, three-dimensional effects were found to significantly affect displacement capacity.     

Nonlinear Structural Performance of a Historical Brick Masonry Inverted Dome

ABSTRACT

Traditional domes are obtained by double curvature shells, which can be rotationally formed by any curved geometrical plane figure rotating about a central vertical axis. They are self-supported and stabilized by the force of gravity acting on their weight to hold them in compression. However, the behavior of inverted domes is different since the dome is downward and masonry inverted domes and their structural behaviors in the literature received limited attention. This article presents a nonlinear finite element analysis of historical brick masonry inverted domes under static and seismic loads. The brick masonry inverted dome in the tomb of scholar Ahmed-El Cezeri, town of Cizre, Turkey, constructed in 1508 is selected as an application. First, a detailed literature review on the masonry domes is given and the selected inverted dome is described briefly. 3D solid and continuum finite element models of the inverted masonry dome are obtained from the surveys. An isotropic Concrete Damage Plasticity (CDP) material model adjusted to masonry structures with the same tensile strength assumed along the parallel and meridian directions of the inverted dome is considered. The nonlinear static analyses and a parametric study by changing the mechanical properties of the brick unit of the inverted masonry dome are performed under gravity loads. The acceleration records of vertical and horizontal components of May 1, 2003 Bingöl earthquake (Mw = 6.4), Turkey, occurred near the region, are chosen for the nonlinear seismic analyses. Nonlinear step by step seismic analyses of the inverted dome are implemented under the vertical and horizontal components of the earthquake, separately. Static modal and seismic responses of the inverted masonry dome are evaluated using mode shapes, minimum and maximum principal strains and stresses, and damage propagations.     

Dynamic One-Sided Out-Of-Plane Behavior of Unreinforced-Masonry Wall Restrained by Elasto-Plastic Tie-Rods

Past earthquakes have shown the high vulnerability of existing masonry buildings, particularly to out-of-plane local collapse mechanisms. Such mechanisms can be prevented if façades are restrained by tie rods improving the connections to perpendiculars walls. Whereas in the past only static models have been proposed, herein the nonlinear equation of motion of a monolithic wall restrained by a tie rod is presented. The façade, resting on a foundation and adjacent to transverse walls, rotates only around one base pivot and has one degree of freedom. Its thickness is explicitly accounted for and the tie rod is modeled as a linear elastic—perfectly plastic spring, with limited displacement capacity. The model is used to investigate the response to variations of wall geometry (height/thickness ratio, thickness), tie rod features (vertical position, length, prestress level), and material characteristics (elastic modulus, ultimate elongation, yield strength) typical of historical iron. The most relevant parameter is the steel strength, whereas other characteristics play minor roles allowing to recommend reduced values for pre-tensioning forces. The force-based procedure customary in Italy for tie design is reasonably safe and involves protection also against collapse, although probably not enough as desirable.     

Experimental and Analytical Investigation on the Corner Failure in Masonry Buildings: Interaction between Rocking-Sliding and Horizontal Flexure

ABSTRACT

The failure mechanism of corners in masonry buildings has frequently been observed in seismic scenarios, but only a few works and no experimental investigations devoted to it are available in the literature. In this aritcle, the experimental behavior of a simple masonry corner is first analyzed, by simulating the seismic horizontal actions through a progressive tilting of the supporting base. Then, the conditions of the onset of two possible failure modes are analytically formulated: they are the rocking-sliding and the horizontal flexure mechanism. A three-dimensional macro-block model with frictional joints is used to analyze these mechanisms, while the crack patterns and the load factors are derived through the kinematic approach of the limit analysis. The evaluation of the in-plane frictional resistances involved by the rocking-sliding mechanism is performed by applying a reliable criterion previously proposed, while for the torsion strength involved in the horizontal flexure mechanism, simplified yield conditions are adopted and a possible criterion is also introduced to take into account the actual reduction of the contact surfaces. Last, the experimental findings are compared and critically interpreted in light of the analytical results and the influence of the main parameters on the prevailing mechanism is highlighted.     

Rubble Stone Masonry Walls Strengthened by Three-Dimensional Steel Ties and Textile-Reinforced Mortar Render,Under Compression and Shear Loads

This article addresses the results of a structural strengthening solution for rubble stone masonry walls. The strengthening includes inserting three-dimensional steel ties across the thickness of the walls and a 30-mm layer of air-lime and cement mortar render reinforced with glass fiber mesh (textile-reinforced mortar), on both sides of the wall. The strengthening solution was found to be efficient for rehabilitating ancient rubble stone masonry walls due to the “three-dimensional” confinement, provided by the steel wires, by offsetting the low cohesive capacity of the mortar used in the walls and thus improving the mechanical resistance and delaying the collapse mechanisms. This study is part of an experimental research program carried out in Universidade Nova de Lisboa, to evaluate structural strengthening solutions for ancient rubble stone masonry buildings. To this end, three specimens of rubble stone masonry walls without strengthening (unreinforced masonry) and other three, with the mentioned strengthening solution, were subjected to compression and shear load tests. Building materials were also tested in order to characterize physical, chemical and mechanical properties.     

Numerical Assessment of Frictional Heating in Sliding Bearings for Seismic Isolation

This article proposes a numerical investigation of the frictional heating developed in sliding bearings under high velocities and the influence of the relevant temperature rise on the mechanical characteristics of the device. A three-dimensional finite element model of the bearing is created and frictional heat generation is modelled through a thermal source inserted at the sliding surface of the bearing, with intensity dependent on the coefficient of friction, the contact pressure and the velocity. The friction value is adjusted step-by-step on surface temperature and velocity and used to update the thermal flux and the resisting force developed by the bearing. The numerical predictions of temperature histories and force–displacement loops are compared with the results of laboratory tests to validate the numerical approach. The procedure can help in preliminary studies for the selection of bearing materials accounting for their thermal stability and for the estimation of change of design properties of sliding isolation bearings due to frictional heating.     

Seismic Analysis of Masonry Gravity Dams Using the Discrete Element Method: Implementation and Application

Much research in recent years has focused on the seismic analysis of concrete and earthfill dams, and few works have addressed the case of masonry dams. The structural behavior of masonry dams is controlled essentially by its discontinuous nature, which may induce significant nonlinear response during an intense earthquake. In this article, a numerical tool based on the Discrete Element Method is presented, aimed at the static, dynamic, and hydromechanical analysis of masonry gravity dams. The use of discontinuous models is mandatory for the study of failure mechanisms involving the masonry discontinuities, the dam-rock interface or the rock mass joints. The Discrete Element Method is able to assemble continuous and discontinuous meshes simultaneously in the same model, providing a versatile tool to consider various assumptions and levels of analysis, ranging from simplified to detailed structural representations. A comprehensive study of the seismic behavior of Lagoa Comprida Dam, located in Portugal, is presented. Both continuous and discontinuous models were developed to assess the main failure mechanisms, including overstress, partial and global sliding, and overturning.     

Simulation Of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (II): Combined Finite-Discrete Elements

ABSTRACT

Out-of-plane response of unreinforced masonry elements is frequently the most critical aspect of the seismic performance of existing masonry buildings. The response of such elements is usually governed by equilibrium rather than strength. Hence, it is customary to resort to rigid-body models, accounting for possible rotations, and/or sliding. However, the results of such analyses depend on the initial choice of the mechanism. In this article, the shaking-table experiments on a brick-masonry specimen, and on a stone-masonry specimen have been modeled by resorting to a combined finite-discrete element strategy. Despite the coarse discretization of both discrete and finite elements, the three-dimensional models are able to capture the experimentally observed multi-degree-of-freedom mechanisms, without any a priori assumption on the mechanism. A sensitivity analysis is carried out, addressing eight different parameters. The identification of the mechanism is sufficiently robust, but the assessment of its activation and failure is best done by combining the finite-discrete element model with a simplified model of the recognised mechanism.     

Performance of Wall to Diaphragm Anchors for Use in Seismic Upgrade of Heritage Masonry Buildings

Performance of wall to diaphragm (WD) anchors in heritage unreinforced masonry (URM) buildings during the recent New Zealand earthquake series is commented on, detailing typical failure modes. Current building code provisions for the design of masonry anchors are discussed and overview of an associated experimental program investigating the effectiveness of a relatively new type of retrofit WD anchors is presented. A total of 40 anchors were tested for pull out capacity (POC), of which 30 were installed in salvaged heritage material assemblages and 10 were tested in-situ at a heritage URM building. The POC of anchors ranged from 13.01 kN to 23.12 kN when installed in a heritage URM wall and between 9.54 kN and 12.16 kN when driven from side into two consecutive floor joists of a heritage timber diaphragm. Investigated also were the effects of embedment length, installation quality, anchor location, condition of masonry, and condition of substrate materials on anchor performance.     

Interaction Curves for In-Plane and Out-of-Plane Behaviors of Unreinforced Masonry Walls

Different types of macro-elements have been proposed to simulate the behavior of unreinforced masonry (URM) structures under seismic loads. In many of these, macro-elements URM walls are replaced with beam elements with different hysteretic behaviors. The effect of out-of-plane loading or change of gravity load due to the overturning moment is usually not considered in the behavior of these macro-elements. This article presents interaction curves for bidirectional loadings of unreinforced masonry walls to investigate the importance of these factors. Two parameters are systematically changed to derive the interaction curves for a wall with specific dimensions, including compressive traction atop the wall to represent gravity loading, and loading angle that represents a combination of in-plane and out-of-plane earthquake loadings. Interaction curves are developed considering various possible failure modes for bricks and mortar, including tension, crushing and a combination of shear and compression/tension failures. The proposed interaction curves show the initiation of failure of URM walls as a function of compressive traction and loading angle. Several examples are presented for URM walls with different aspect ratios to aid in understanding the effects of various parameters on the derived interaction curves. Finally, for a specific case, the derived interaction curve is compared with nonlinear finite element results and ASCE41. The results show that, as a simplified method, the derived interaction curves can be used for the preliminary evaluation of URM walls under bidirectional loadings.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (I): Displacement-based Approach Using Simple Failure Mechanisms

ABSTRACT

A displacement-based (DB) assessment procedure was used to predict the results of shake table testing of two unreinforced masonry buildings, one made of clay bricks and the other of stone masonry. The simple buildings were subject to an acceleration history, with the maximum acceleration incrementally increased until a collapse mechanism formed. Using the test data, the accuracy and limitations of a displacement-based procedure to predict the maximum building displacements are studied. In particular, the displacement demand was calculated using the displacement response spectrum corresponding to the actual shake table earthquake motion that caused wall collapse (or near collapse). This approach was found to give displacements in reasonable agreement with the wall’s displacement capacity.     

A MICROMECHANICAL INELASTIC MODEL FOR HISTORICAL MASONRY

A micromechanical damage model for the Snite element modelling of historical masonry structures is presented in this article. Masonry is considered as a composite medium made up of a periodic assembly of blocks connected by orthogonal bed and head mortar joints. The constitutive equations, in plane stress, are based on the homogenisation theory and they consider the non linear stress-strain relationship in terms of mean stress and mean strain. Different in-plane damage mechanisms, involving both mortar and blocks, are considered and the damage process is governed by evolution laws based on an energetic approach derived from Fracture Mechanics and on a non-associated Coulomb friction law. The failure domain of the model is analysed both in the equivalent stress and in the principal stress space considering different orientations of the bed joints relative to the loading direction. A comparison with experimental results is provided. A numerical simulation of masonry walls subjected to horizontal forces proportional to their own weight is shown in order to discuss the model's capability of describing the influence of the masonry microstructure on its mechanical behaviour.     

A DAMAGE MODEL FOR THE ANALYSIS OF THE SEISMIC RESPONSE OF MONUMENTAL BUILDINGS

In this paper the Author proposes a damage model for the analysis of masonry plates and shells, which is based on an improvement of a previous constitutive model. The modifications introduced, connected to the head joint damage, allow us to study the influence of masonry texture on the damage modes once the mechanical characteristics of the elements constituting the masonry and the results of tests on simple assemblages are known. Having a nonlinear constitutive model is certainly one of the basic elements for understanding the damage mechanisms in masonry buildings. If, in fact, an elastic-linear constitutive model may be used under normal loading conditions, in critical situations it is necessary to model the damage and the dissipation mechanisms that occur between the elements, stone (brick) and mortar, in correlation with their characteristics and kind of masonry. To validate the model a comparison is made between the numerical and experimental results, in the case of tests available in the literature in masonry panels subjected to out-of plane loading and in a real structure through the observation of the damage in Umbria (Italy) surveyed after the 1997 earthquake.     

Numerical Study on the Peak Strength of Masonry Spandrels with Arches

This article presents a numerical study on the force-deformation behavior of masonry spandrels supported on arches which are analyzed using simplified micro models. The model is validated against results from quasi-static cyclic tests on masonry spandrels. A large range of spandrels with different arch geometries, material properties, and axial load ratios are studied. The numerical results are compared to peak strength values predicted with an existing mechanical model. Finally, estimates for the initial stiffness and the spandrel rotation associated with the onset of strength degradation are derived.     

Restoration Techniques Applied to Tile Dome Conservation in the Western Mediterranean. Valencia,Spain

The domes studied, widespread in a large area of the Mediterranean, constitute an architectural heritage of great value to the history of architecture and construction. They were all built using brick masonry and ceramic tile roofs. Restoration work has made it possible to define their geometry, including the construction layouts of the buildings. In addition, on inspection it can be seen that common construction problems tend to be located at specific critical points. The restoration process of different cases sharing the same methodology, construction criteria, and solutions is accurately described. Following international charters, there is minimal intervention and maximum respect for the original solutions, but also a carefully considered incorporation of new materials and technologies to improve the critical points.     

Effect of stereotomy on the lower bound value of minimum thickness of semi-circular masonry arches

Constructing structural systems with the minimal required cross section of its members was a strong motivation for progress whole along the history of building. This article investigates the effect of stereotomy on the minimum thickness value of a semi-circular arch made of masonry: a material with negligible tensile strength. The arch is modeled with its center line to which the loading is assigned according to arch length. Here, instead of some scalar parameters such as the rupture angle and the location of the middle hinge on the intrados, the geometry of the stereotomy is associated with a continuous function. Stereotomy-related constraints are introduced to keep the results feasible from an engineering point of view, and it is also demonstrated that they are essential for a well-posed constrained optimization problem. The necessary condition for a non-vanishing lower bound of minimum thickness values is derived analytically considering the assumptions of limit state analysis, infinite friction, and a no-tension material model. The lower bound thickness to radius ratio (t/R) is found to be t/R = 0.0819. A numerical method is introduced to demonstrate the existence of a valid stereotomy at the lower bound. Multiple admissible stereotomy patterns are presented at various minimum thickness values (higher than the lower bound) to demonstrate that suitable stereotomy for a fixed (t/R) ratio is far not unique—in general even the location of the middle hinge and the rupture angle might vary.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (III): Two-Step FEM Approach

ABSTRACT

This article presents numerical simulations of two full-scale masonry structures which were tested on the shaking table within the scope of the workshop “Methods and challenges on the out-of-plane assessment of existing masonry buildings”. The numerical models have been developed on the basis of the blind-prediction models which have been improved after the publication of the test results. The solution procedure is divided into two steps with separate numerical simulations for each one. In the first step the collapse mechanism of the structure is determined by means of pushover analysis using a continuum, plasticity-based model. In the second step the dynamic response of the structure is simulated using a multibody model approach and frictional contacts. Results of the tests show reasonable, yet far from perfect predictive capabilities of the used numerical methods.