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.     

Seismic Behavior of Reinforced Concrete Interior Wide-Beam Column Joints

In this article, experimental and finite element (FE) numerical investigations on interior wide-beam column joints are presented. The experimental research consisting of three full-scale interior wide-beam column specimens was carried out at Nanyang Technological University, Singapore to study the seismic behavior. Details of the test results are discussed to understand the specimens' seismic performance in terms of general behavior, hysteresis loops response, and strain profiles of longitudinal reinforcement. In the FE numerical study, the three-dimensional (3D) model developed is validated by comparing the analysis results with the experimental test results, which has shown a good agreement. A parametric study is performed to elucidate more information and to understand the influence of critical parameters affecting the joint behavior such as column axial load, beam anchorage ratio, and wide beam participation.     

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.     

A Novel Procedure for Simplified Nonlinear Numerical Modeling of Structural Units in Masonry Aggregates

ABSTRACT

Historical centers are always composed of masonry building aggregates often designed without respecting seismic design criteria. The current seismic Italian code does not foresee a clear calculation method to predict their static nonlinear behavior. For this reason, in this article the seismic response of structural units into masonry aggregates has been predicted through a simplified modeling approach. The implemented procedure has been calibrated on the results of a numerical model performed by using the Equivalent Frame Method (EFM), implemented within a Finite Element Method (FEM) calculation program, used to investigate a basic building compound representative of the constructive techniques developed in the past decades in the Southern Italy.

First, the whole aggregate has been modeled and analyzed in the nonlinear static field in order to evaluate the seismic behavior of both intermediate and head structural units.

Later on, the seismic response of these structural units, considered as isolated structures, has been assessed by considering in simplified way their position in the aggregate, as well as the influence of other constructions.

Finally, the achieved results on the above single analysis cases have been compared with those deriving from the investigation of the whole building compound, allowing to confirm the effectiveness of the proposed novel analysis procedure.     

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.     

A Static Nonlinear Procedure for the Evaluation of the Elastic Buckling of Anchored Steel Tanks Due to Earthquakes

Ground-supported steel tanks experienced extensive damage in past earthquakes. The failure of tanks in earthquakes may cause severe environmental damage and economic losses. This study deals with the evaluation of the elastic buckling of above-ground steel tanks anchored to the foundation due to seismic shaking. The proposed nonlinear static procedure is based on the capacity spectrum method (CSM) utilized for the seismic evaluation of buildings. Different from the standard CSM, the results are not the base shear and the maximum displacement of a characteristic point of the structure but the minimum value of the horizontal peak ground acceleration (PGA) that produces buckling in the tank shell. Three detailed finite element models of tank-liquid systems with height to diameter ratios H/D of 0.40, 0.63, and 0.95 are used to verify the methodology. The 1997 UBC design spectrum and response spectra of records of the 1986 El Salvador and 1966 Parkfield earthquakes are used as seismic demand. The estimates of the PGA for the occurrence of first elastic buckling obtained with the proposed nonlinear static procedure were quite accurate compared with those calculated with more elaborate dynamic buckling studies. For all the cases considered, the proposed methodology yielded slightly smaller values of the critical PGA for the first elastic buckling compared to the dynamic buckling results.     

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 Fully Graphical Approach for Limit State Analysis of Existing Structures: Application to Plane Elastic-Plastic Bended Structures and to Plane Masonry Arches

ABSTRACT

When classical elastic analysis fails to model correctly the structural behavior of historical masonry structures because of the brittle, rigid, anisotropic, and inhomogeneous characteristics of their building material, equilibrium-based limit state analysis constitutes an efficient alternative for their structural assessment. The lack of knowledge about the history of loading makes the actual state of stresses impossible to determine for these statically indeterminate structures. However, Plastic Theory provides a powerful theoretical framework that defines in a rather simple way the structural safety level. The lower-bound theorem of plasticity can be applied using graphic statics because it ensures that equilibrium and yield conditions are respected when applying specific constraints to the nodes of the reciprocal diagrams.

This article focuses on limit stat analysis of statically indeterminate structures by means of geometrical considerations using graphic statics reciprocal diagrams. For linear-bended structures, we show that: (1) the conditions of stability can be defined graphically by constructing safety domains; (2) collapse modes can be identified and related to specific reciprocal polygons; and (3) the exact value of the collapse load factor can be deduced graphically from the diagrams. Finally, we extend these results to plane masonry arches in relation with the classical thrust line approach.     

Effect of the joint type on the bearing capacity of a multi–drum column under static load

The results of an experimental study on the effect of the joints between the blocks on the ultimate bearing capacity of a multi-drum column loaded to centric vertical force and horizontal force in the middle of its height are shown. The column is approximately 2.5 m high, with one hinge at the top and another hinge at the bottom. Four types of joints between the blocks were considered: a dry joint (column C-DJ) and joints with stone powder (column C-SPJ), lead (column C-PBJ), and epoxy (column C-EPJ). The applied vertical and horizontal forces, horizontal displacement, vertical strains, and horizontal circumferential strains in the middle of the column height, as well as shortening of the column, were measured. Under axial compression, ratios between the ultimate load bearing capacities of tested columns were C-EPJ: C-DJ: C-SPJ: C-PBJ = 1: 0.68: 0.59: 0.51. The bearing capacity of the tested columns with regard to the horizontal force depended on the level of the applied centric compression force. Columns with soft joints (C-PBJ, C-SPJ) had the largest shortening and the largest horizontal displacements for the equal forces.     

Contact Dynamics of Masonry Block Structures Using Mathematical Programming

A simple variational formulation for contact dynamics is adopted to investigate the dynamic behavior of planar masonry block structures subjected to seismic events. The numerical model is a two-dimensional assemblage of rigid blocks interacting at potential contact points located at the vertices of the interfaces. A no-tension and associative frictional behavior with infinite compressive strength is considered for joints. The dynamic contact problem is formulated as a quadratic programming problem (QP) and an iterative procedure is implemented for time integration. Applications to analytical and numerical case studies are presented for validation. Comparisons with the experimental results of a masonry wall under free rocking motion and of a small scale panel with opening subjected to in-plane loads are also carried out to evaluate the accuracy and the computational efficiency of the formulation adopted.     

Seismic Load Capacity of Historical Masonry Mosques by Rigid Body Kinetics

ABSTRACT

Kinetic analysis methods based on linear and nonlinear rigid body dynamics are used to evaluate earthquake safety of masonry structures. In this study, the formulas used to calculate the in-plane and out-of-plane load capacities of masonry load-bearing walls were evaluated and a procedure based on rigid body mechanism was proposed to calculate the out-of-plane load capacities of the walls of Ottoman period masonry mosques. New aspects of the method with respect to existing formulations is the inclusion of dynamic axial load and definition of the collapse limit spectral acceleration on the overturning wall. The calculated capacities of the mosque and individual walls were compared with the results of nonlinear pushover analysis and time history analyses performed under 1.0 and 0.5 scaled forms of nine different 3-component ground motion records. It was displayed that the seismic load capacity estimated by the proposed method is very close to the values calculated by pushover and time history analyses. The method was developed on Lala Pasha Mosque, and the reliability and applicability of the proposed methodology is verified on a different historical masonry mosque in comparison to finite element analyses results.     

Simple Homogenization-Topology Optimization Approach for the Pushover Analysis of Masonry Walls

ABSTRACT

A topology optimized rigid triangular FE macro-model with non-linear homogenized interfaces for the pushover analysis of in plane loaded masonry is presented. The shape of the mesh and the position of the interfaces is evaluated through a topology optimization approach that detects the main compressive stress fluxes in the structure. Different values of the horizontal action are considered to derive an adaptive mesh or an optimal discretization that is suitable for multiple loads. Masonry properties are calibrated by means of a homogenization approach in the nonlinear range. To tackle elastic and inelastic deformations, interfaces are assumed to behave as elasto-plastic with softening in both tension and compression, with orthotropic behavior. The two-step procedure competes favorably with classic equivalent frame approaches because it does not require a-priori assumptions on the mesh and on the length of the rigid offsets. An example of technical relevance is discussed, relying into a multi-story masonry wall loaded up to failure.     

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.     

Stiffness Behavior and Shear Effect in Partially Infilled Reinforced Concrete Frames

The captive column effect is regarded as one of the deficiencies in concrete buildings. During earthquakes, partially infilled frames often get damaged due to large shear force within columns. Past studies indicate that the column failure is due to the high shear force occurrence; however, exact quantification of the shear force is still a topic of interest. A particular analytical expression for strut width has been adopted in this article and it is concluded that the masonry walls do enhance stiffness of frames but due to the shear force, the walls play adverse role in damaging the columns.     

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.     

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.     

Effectiveness of FRCM Reinforcement Applied to Masonry Walls Subject to Axial Force and Out-Of-Plane Loads Evaluated by Experimental and Numerical Studies

ABSTRACT

An experimental campaign and a numerical analysis devoted to the investigation of the out-of-plane behavior of masonry walls reinforced with Fiber Reinforced Cementitious Matrix (FRCM) are presented here. The main goal of this study is to analyze and evaluate the effectiveness of the strengthening system, by discussing failure modes and capacity of strengthened masonry walls, in order to assess their behavior under out-of-plane horizontal actions, such as, for example, seismic actions. A purposely designed experimental set-up, able to separately and independently apply an axial force and out-of-plane horizontal actions on masonry walls, was used. Experimental results are discussed and compared with the outcomes of nonlinear analyses performed on simplified finite element models of the walls. A proper evaluation of the flexural capacity of FRCM strengthened walls is the first step of the ongoing process of drawing reliable code guidelines leading to a safe design of strengthened masonry structures.     

Theoretical and Numerical Seismic Analysis of Masonry Building Aggregates: Case Studies in San Pio Delle Camere (L’Aquila,Italy)

Masonry building aggregates are large parts of the Italian building heritage often designed without respecting seismic criteria. The current seismic Italian code does not foresee a clear calculation method to predict their static nonlinear behavior. For this reason, in this article a simple methodology to forecast the masonry aggregate seismic response has been set up. The implemented procedure has been calibrated on the results of two FEM structural analysis programs used to investigate three masonry building compounds. As a result, a design chart used to correctly predict the base shear of aggregate masonry units starting from code provisions has been set up.     

中国古代砖砌体力学性能研究综述

古代砖砌体建筑由于材料劣化、环境影响,材料特性及力学性能均受到不同程度的影响和损伤,为了保护历史文化的载体,结合古建筑材料获取原始且必要的数据,系统总结了古砖、传统灰浆的制备工艺和材料性能,简要归纳了古砖、传统灰浆和古砖砌体基本力学性能及其测试方法,对比分析了单砖和砌体抗压强度的差异以及古建筑砌体材料力学性能研究现状。并对今后古砌体如弹性模量等力学性能、古砌体材料及结构的损伤机理等的研究提出了展望或建议,可为砖石古建筑的修缮保护提供参考依据。