Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (VI): Discrete Element Approach

ABSTRACT

Although many experimental tests and numerical models are available in the literature, the numerical simulation of the seismic response of existing masonry buildings is still a challenging problem. While the nonlinear behavior of masonry structures is reasonably predictable when the out-of-plane behavior can be considered inhibited, when the in-plane and out-of-plane responses coexist and interact, simplified models seem unable to provide reliable numerical predictions. In this article, taking advantage of the experimental tests carried out in a shaking table on two masonry prototypes at LNEC, a macro-element approach is applied for the numerical simulations of their nonlinear response. The adopted approach allows simulating the nonlinear behavior of masonry structures considering the in-plane and out-of-plane responses. Since it is based on a simple mechanical scheme, explicitly oriented to representing the main failure mechanisms of masonry, its computational cost is greatly reduced with respect to rigorous solutions, namely nonlinear FEM approaches. Two modeling strategies are adopted, namely a regular mesh independent from the real texture of the prototypes and a detailed one coherent with the units disposal. The numerical results are discussed and the correlation between the nonlinear static analyses and the dynamic response is provided.     

Methods and Approaches for Blind Test Predictions of Out-of-Plane Behavior of Masonry Walls: A Numerical Comparative Study

ABSTRACT

Earthquakes cause severe damage to masonry structures due to inertial forces acting in the normal direction to the plane of the walls. The out-of-plane behavior of masonry walls is complex and depends on several parameters, such as material and geometric properties of walls, connections between structural elements, the characteristics of the input motions, among others. Different analytical methods and advanced numerical modeling are usually used for evaluating the out-of-plane behavior of masonry structures. Furthermore, different types of structural analysis can be adopted for this complex behavior, such as limit analysis, pushover, or nonlinear dynamic analysis.

Aiming to evaluate the capabilities of different approaches to similar problems, blind predictions were made using different approaches. For this purpose, two idealized structures were tested on a shaking table and several experts on masonry structures were invited to present blind predictions on the response of the structures, aiming at evaluating the available tools for the out-of-plane assessment of masonry structures. This article presents the results of the blind test predictions and the comparison with the experimental results, namely in terms of formed collapsed mechanisms and control outputs (PGA or maximum displacements), taking into account the selected tools to perform the analysis.     

Earthquake Protection of Colonial Bell Towers in Colima,Mexico with Externally Prestressed FRPs

A methodology for the seismic vulnerability reduction of old masonry towers with external prestressing is presented. It is applied at the Colonial bell-towers of the Cathedral of Colima, Mexico, characterized for being a high seismic area (M>7.5). The 3D FE models are calibrated with experimental data and assessed through nonlinear static approaches including the seismic demand and an accurate validated masonry model. Based on an extensive parametric study on different configurations of old masonry towers, it is selected an optimal prestressing force and device. The Colonial towers are retrofitted with four prestressing devices of FRPs to convert them into a high energy-dissipative reinforced masonry. The external vertical prestressing is included at key points identified in the seismic vulnerability assessment. This technique is in compliance with the demand for architectural conservation and may be located without drilling and unbounded in order to be fully removable. The seismic performance is enhanced by increasing force, displacement, and internal confinement. It is observed an upgrading of 35% and 20% of displacement capacity. With these results it is corroborated that external vertical prestressing allows a substantial increment of ductility for seismic energy dissipation purposes.     

Effect on the Structure in Elevation of Wood Deterioration on Small-Pile Foundation: Numerical Analyses

Wooden pile foundations are quite common in Venice historical building. Very short, small-diameter piles are embedded into the soft shallowest soil layer under the groundwater level, but wood degradation is not prevented as anaerobic bacteria can flourish even in anoxic condition. This study couples the behavior of the masonry structure and the foundation as result of pile degradation. The numerical analyses, relative to the ancient piling, consider wood decay and secondary settlement of soil. The effect of deterioration as a function of the pile spacing and the possible presence of a stiff layer under pile tips are also investigated. The geotechnical results are then used as input for the structural model. The behavior of the masonry as result of different states of wood conservation along the wall is studied numerically.     

Rodrigo Gil de Hontañón and 16th-Century Building Techniques: The Cimborio Vault of Archbishop Fonseca College Chapel in Salamanca (Spain)

Rodrigo Gil is one of the greatest masters of Spanish architecture. His brilliant career is partially explained by the efficiency of his design methods and his building techniques, especially evident in his ribbed vaults. If we examine the latter as a whole, the first aspect to be noted is undoubtedly their great formal complexity. However, the detailed study discloses that rather limited geometric and building techniques are hidden behind those elaborated patterns, aimed at simplifying and making the execution more economical. In order to bring some of these devices to light, one of his best-known vaults was selected for an in-depth study. The construction of a large-scale model of it also revealed some interesting features regarding the placing of the centerings and shorings during the erection.     

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 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.     

ON THE SEISMIC VULNERABILITY OF EXISTING UNREINFORCED MASONRY BUILDINGS

A large part of the building population in Switzerland is made of unreinforced masonry. For the assessment of the seismic risk the evaluation of the seismic vulnerability of existing unreinforced masonry buildings is therefore crucial. In this paper a method to evaluate existing buildings, which was developed for the earthquake scenario project for Switzerland, is briefly introduced and discussed in more detail for unreinforced masonry buildings. The method is based on a non-linear static approach where the seismic demand on the building is compared with the capacity of the building. In-plane and out-of-plane behaviour are considered. Comparisons with test results from model buildings show that the proposed method suitably forecasts the capacity of a building. Finally, a numerical example of the application of the method to a building in the city of Basel is given.     

ANALYTICAL MODELS FOR BRICK MASONRY INFILLED R/C FRAMES UNDER LATERAL LOADING

Proposed in this paper are two analytical models for predicting the inelastic response of unreinforced brick masonry infills in reinforced concrete frames subjected to mono-tonic and reversed cyclic loading. The first model is based on the traditional diagonal strut concept, while the second one is a simple isoparametric element with shear deformation only. All the essential characteristics of the hysteretic behaviour of the panel, including strength and stiffness degradation, pinching and slippage, are explicitly taken into account. The models are implemented in a general-purpose program for the inelastic time-history analysis of structures, and are used for studying the seismic behaviour of typical multistorey frames with various arrangements of infill panels, including structures with an open ground storey. The results of the analysis are in agreement with both experimentally observed behaviour and with experience regarding seismically damaged buildings.     

SEISMIC FRAGILITY OF LRC FRAMES WITH AND WITHOUT MASONRY INFILL WALLS

This paper summarises the first phase of the fragility analyses of generic (representative) buildings in the area of Memphis, Tennessee, USA. The study was conducted at Cornell University as a part of the project Loss Assessment of Memphis Buildings (LAMB) for the National Center for Earthquake Engineering Research (NCEER). In this study, the fragility analyses focus on low-rise Lightly Reinforced Concrete (LRC) frame buildings with and without infill walls. The obtained fragility curves are compared with those of ATC-13 for different facility classes. Based on the obtained fragility curves, it is concluded that adding masonry infill wails to low-rise LRC frame buildings significantly reduces the likelihood of seismic damage.