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.     

PREDICTION OF DAMAGE IN R/C SHEAR PANELS SUBJECTED TO REVERSED CYCLIC LOADING

In this paper, the damage prediction of shear-dominated reinforced concrete (RC) elements subjected to reversed cyclic shear is presented using an existing damage model. The damage model is primarily based on the monotonic energy dissipating capacity of structural elements before and after the application of reversed cyclic loading. Therefore, it could be universally applicable to different types of structural members, includeing shear-dominated RC members. The applicability of the damage model to shear-dominated RC members is assessed using the results from reversed cyclic shear load tests conducted earlier on eleven RC panels. First, the monotonic energy dissipating capacities of the panels before and after the application of reversed cyclic loading are estimated and employed in the damage model. Next, a detailed comparison between the analytically predicted damage and the observed damage from the experimental tests of the panels is performed throughout the loading history. Subsequently, the effects of two important parameters, the orientation and the percentage of reinforcement, on the damage of such shear-dominated panels are studied. The research results demonstrated that the analytically predicted damage is in reasonably good agreement with the observed damage throughout the entire loading history. Furthermore, the orientation and percentage of reinforcement is found to have considerable effect on the extent of damage.     

Sonic Tomography for Masonry Walls Characterization

ABSTRACT

Nowadays, Sonic Pulse Velocity tests (SPV tests) are widely applied for detecting the morphology, hidden defects, and voids within structural elements. This technique, largely applied because non invasive and easy to perform, reveals particularly adapt in the case of ancient buildings, where usually any damage is not tolerated due to the historical preservation requirements. Moreover, recently the SPV tests have been also applied with tomography technology to obtain images of sonic speeds from which it is possible to rapidly reconstruct the internal elements morphology.

In this article, the results of some SPV tomographies regarding masonry elements are presented. The tests are carried out with the aim of establishing consistency and accuracy of this technique in determining the morphology of the investigated elements. The influence of investigation points number and noise smoothing is taken into account, too. At first, the results of a tomography derived from synthetic data of an ideal section are shown. Then, the SPV tomographies of some masonry specimens and of elements sections of a real case study are illustrated and compared among them.     

SIMULATION OF THE CYCLIC BEHAVIOUR OF R/C RECTANGULAR HOLLOW SECTION BRIDGE PIERS VIA A DETAILED NUMERICAL MODEL

In the search for robust constitutive models suitable for reproducing the performance of bridge piers during a seismic event, this paper details the simulation of the cyclic responses of four rectangular hollow section R/C bridge piers. These four R/C bridge piers were built at scale 1/2.5 and tested experimentally. Both tall and short piers are considered, covering situations where bending or shear are of relevance. Furthermore, the four piers were reinforced according to rather different design strategies: (I) the first is a 30-year-old bridge designed without allowance to the seismic action, and (ii) the second is a bridge fulfilling the EC8 provisions. The detailed constitutive model that provides the numerical predictions includes two submodels: one with two scalar damage variables, reproducing the tensile and compressive degradations of concrete, and the other is based on the Giuffre-Menegotto-Pinto formulation, simulating the cyclic behaviour of the re-inforcement. The Damage Mechanics submodel is implemented at the Gauss points of the finite elements that discretize the concrete, whereas the steel submodel is implemented on the 2-noded truss elements adopted for the rebars. A comparison between the numerical and the experimental results is discussed in detail in this paper.     

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.     

SIGNIFICANT GROUND MOTION PARAMETERS FOR EVALUATION OF THE SEISMIC PERFORMANCE OF SLENDER MASONRY TOWERS

The evaluation of seismic risk of masonry monuments requires to study the combination of vulnerability and hazard. In the present work, the global seismic response of slender masonry towers has been studied by means of a specific 3-D fibre model. Accounting for the particular behaviour of such structures, the hazard should also be described by a suitable measure of intensity of the seismic action. A variety of different parameters relating with the ground acceleration recordings have been investigated for what regards their correlation with the damage indicators of the model. The combination of the peak ground velocity of the horizontal component and of the significant duration is an effective measure of intensity. This measure can be improved by considering the accord of the frequency content of the ground motion with the dynamical characteristics of the tower. Since in some cases the effect of the vertical component proved to be important, a further improvement can be obtained by taking into account also the vertical ground motion intensity.     

NUMERICAL ANALYSIS OF EMBANKMENT FOUNDATION LIQUEFACTION COUNTERMEASURES

Computational simulations are presented for a unique series of centrifuge tests conducted to assess the performance of liquefaction countermeasure techniques. In these centrifuge tests, the dynamic response of an embankment supported on a liquefiable foundation (medium sand) is investigated. The experimental series included: (i) a benchmark test without a liquefaction countermeasure, (ii) foundation densiflcation below the embankment toe, and (iii) use of a sheet-pile containment enclosure below the embankment. This series of experiments documents a wide range of practical liquefaction response mechanisms (including countermeasure implementation). In order to numerically simulate the above centrifuge tests, a new calibrated soil stress-strain constitutive model is incorporated into a two-phase (solid-fluid) fully coupled Finite Element formulation. Comparison of the computational and experimental results demonstrates: (i) importance of post-liquefaction dilative soil behavior in dictating the dynamic response and deformation characteristics of the embankment-foundation system, and (ii) capabilities and limitations of the numerical modeling procedure.     

SEISMIC BEHAVIOUR OF A R/C WALL: NUMERICAL SIMULATION AND EXPERIMENTAL VALIDATION

This paper describes the numerical simulation of the seismic behaviour of a mock-up of a six-floor building, constituted by two parallel R/C walls and experimentally tested on a shaking table. Within the scope of an international benchmark the mock-up was submitted to three earthquakes with intensities up to 0.71 g, which induced nonlinear behaviour in the concrete and reinforcement. For the numerical simulations concrete is discretised with 2D finite elements, and its behaviour reproduced via a constitutive model with two scalar damage variables. Steel rebars are discretised with 2-noded truss elements, and their constitutive behaviour under cyclic conditions reproduced by the Menegottb-Pinto model. Specific attention is devoted to Rayleigh damping, focusing on two different strategies: (i) disregarding the damping contribution, or (ii) adopting a damping matrix that takes into account the stiffness changes during the nonlinear analyses. Main results and strategies for simulating the benchmark axe presented, with emphasis on the comparison between the numerical and the experimental results, which show good agreement when the damping contribution is neglected.     

Force-Based Beam Finite Element (FE) for the Pushover Analysis of Masonry Buildings

A simplified approach for analyzing the nonlinear response of masonry buildings, based on the equivalent frame modeling procedure and on the nonlinear equivalent static analyses, is presented. A nonlinear beam finite element (FE) is formulated in the framework of a force-based approach, where the stress fields are expanded along the beam local axis, and introduced in a global displacement-based FE code. In order to model the nonlinear constitutive response of the masonry material, the lumped hinge approach is adopted and both flexural and shear plastic hinges are located at the two end nodes of the beam. A classical elastic-plastic constitutive relationship describes the nonlinear response of the hinges, the evolution of the plastic variables being governed by the Kuhn-Tucker and consistency conditions. An efficient element state determination procedure is implemented, which condenses the local deformation residual into the global residual vector, thus avoiding the need to perform the inner loops for computing the element nonlinear response. The comparison with some relevant experimental and real full-scale masonry walls is presented, obtaining a very good agreement with the available results, both in terms of global pushover curves and damage distributions.     

Experimental Out-Of-Plane Behavior of Brick Masonry Infilled Frames

ABSTRACT

The vulnerability of masonry infills within reinforced concrete (rc) frames under out-of-plane loading induced by earthquakes has been observed in several past earthquakes through severe damage and often total collapse. Although the infill panels are assumed as non-structural elements, their damage or collapse is not desirable, given the possible consequences in terms of human life losses and repair or reconstruction costs.

Therefore, it is important to gather better insight on the out-of-plane behavior of existing infills so that strengthening guidelines can be derived. In this scope, the main objective of this study is to analyze the out-of-plane experimental behavior of masonry infilled frames that are characteristic of Portuguese buildings and can be seen in other south European countries. In the experimental study carried out, different parameters affecting the out-of-plane response of infilled frames were considered, namely, workmanship, existence of openings and prior in-plane damage. The experimental program was designed to test six half-scale specimens. The out-of-plane loading was applied uniformly to the brick infills by means of an airbag to simulate the effect of earthquakes.     

Simplified Macro-Model for Infill Masonry Panels

In structural analyses, masonry infill walls are commonly considered to be non structural elements. However, the response of reinforced concrete buildings to earthquake loads can be substantially affected by the influence of infill walls. In this article, an improved numerical model for the simulation of the behavior of masonry infill walls subjected to earthquake loads is proposed and analyzed. First, the proposed model is presented. This is an upgrading of the equivalent bi-diagonal compression strut model, commonly used for the nonlinear behavior of infill masonry panels subjected to cyclic loads. Second, the main results of the calibration analyses obtained with two series of experimental tests are presented and discussed: one on a single frame with one story and one bay tested at the LNEC Laboratory; and the second, on a full-scale four story and three-bay frame tested at the ELSA laboratory.     

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.     

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.     

NONLINEAR ANALYSIS OF REINFORCED CONCRETE SHEAR WALL UNDER EARTHQUAKE LOADING

A constitutive model for predicting the cyclic response of reinforced concrete structures is proposed. The model adopts the concept of a smeared crack approach with orthogonal fixed cracks and assumes a plane stress condition. Predictions of the model are compared firstly with existing experimental data on shear walls which were tested under monotonic and cyclic loading. The same model is then used in the finite element analysis of a complete shear wall structure which was tested under a large number of cyclic load reversals due to earthquake loading at NUPEC's Tadotsu Engineering Laboratory. Two different finite element approaches were used, namely a two-dimensional and a three-dimensional representation of the test specimen. The ability of the concrete model to -reproduce the most important characteristics of the dynamic behaviour of this type of structural element was evaluated by comparison with available experimental data. The numerical results showed good correlation between the predicted and the actual response, global as well as local response being reasonable close to the experimental one.     

Determination of Shear Strength of Masonry Panels Through Different Tests

This study addresses the problem of evaluation of strength of masonry walls. In-plane behavior of masonry panels has been studied under monotonic diagonal-compression and shear-compression loading in quasi-static test facility. The results of 35 laboratory and in situ tests are analyzed to show that in the case of the diagonal compression test results are lower than the strength of masonry walls evaluated trough the shear-compression test, highlighting the problem of choosing the test which best simulates to the real behavior of the masonry when stressed by lateral loads. A presentation is also given of the results of a F.E. investigation for shear strength evaluation of masonry walls. F.E. modeling non-linear procedure was used for the representation of masonry panels. The numerical simulations are compared with experimental results and the reliability of the different finite element models is discussed, thus confirming the different shear strength values measured in the experimental campaign.     

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.     

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.     

Masonry Italian Code-Conforming Buildings. Part 2: Nonlinear Modelling and Time-History Analysis

ABSTRACT

The unreinforced masonry (URM) buildings designed to be conforming with the Italian building code, as illustrated in the companion paper, were analyzed by performing time-history analyses on models realized using an equivalent frame approach and by adopting two different constitutive laws. Both the effect of record-to-record variability and of epistemic and aleatory uncertainties in modelling were explored. The achieved results constitute the basis for the evaluation of the risk level implicit in Italian code-conforming buildings. Two main performance conditions are considered, namely usability-preventing damage and global collapse limit states.     

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.     

Minimum Thrust of Rounded Cross Vaults

This study analyzes the static behavior of the rounded cross vaults based on the limit analysis approach developed for masonry structures and adopts a rigid no-tension constitutive model with no sliding. The kinematic theorem of the limit analysis with a compatible tridimensional mechanism is applied on these structures with the aim of evaluating the minimum thrust. In this way it was possible to build some abaci in which the ratio between the minimum thrust and the weight is plotted versus the geometrical characteristics of the vaults. Finally, the proposed abaci are used to calculate the thrust of the main vault of the Diocletian Baths in Rome.