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 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.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (IV): Macro and Micro FEM Based Approaches

ABSTRACT

This article presents a study on the out-of-plane response of two masonry structures without box behavior tested in a shaking table. Two numerical approaches were defined for the evaluation, namely macro-modeling and simplified micro-modeling. As a first step of this study, static nonlinear analyses were performed for the macro models in order to assess the out-of-plane response of masonry structures due to incremental loading. For these analyses, mesh size and material model dependency was discussed. Subsequently, dynamic nonlinear analyses with time integration were carried out, aiming at evaluating the collapse mechanism and at comparing it to the experimental response. Finally, nonlinear static and dynamic analyses were also performed for the simplified micro models. It was observed that these numerical techniques correctly simulate the in-plane response. The collapse mechanism of the stone masonry model is in good agreement with the experimental response. However, there are some inconsistencies regarding the out-of-plane behavior of the brick masonry model, which required further validation.     

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.     

Masonry Italian Code-Conforming Buildings. Part 1: Case Studies and Design Methods

ABSTRACT

Several architectural configurations of unreinforced masonry residential buildings are designed according to the different methods proposed in the Italian code: rules for the so-called simple masonry buildings, linear and nonlinear static analyses. Always complying with code requirements, for each building-site combination, the design was made, as much as possible, without an excessive margin of safety. The different design methods provided buildings with very different levels of safety, being linear static analysis largely overconservative with respect to the nonlinear static approach. These buildings were then analyzed in the companion paper.     

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.     

Protecting a Cemetery in Saqqara: Site Works 1975–2009

Abstract

This article considers the varied threats to Ancient Egyptian architectural remains that have been exposed by modern excavation. A number of possible measures that counter such threats are outlined, together with the practical difficulties facing the architectural conservator working in this context. The approach taken at the New Kingdom Necropolis in Saqqara — a group of elite tombs constructed c. 1350–1250 BC — during the post-excavation phase is detailed, with an emphasis on the works carried out by the author from 2004 to 2009. This encompasses the conservation of surviving limestone relief decoration in situ, the reconstruction of missing masonry elements, and the final presentation of the site to visitors.     

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.     

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

ABSTRACT

The analysis of the shaking table test of a 3-wall stone masonry structure performed with a discrete element model is presented. The numerical model, created with the code 3DEC, employed a rigid block representation and a Mohr-Coulomb joint model. Joint stiffness calibration to match the experimental natural frequencies is discussed, as well as the boundary conditions to simulate the shake table. Comparisons are made with the measured displacements at key locations, and the modes of deformation and fracture of the walls. The DEM model was able to reproduce important features of the shaking table tests. The experimental deformation and near collapse patterns were clearly identifiable in the numerical simulations, which produced displacements within the observed orders of magnitude, for the various levels of excitation.     

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 Vulnerability of Historical Masonry Aggregate Buildings in Oriental Sicily

ABSTRACT

The seismic vulnerability assessment of historical UnReinforced Masonry (URM) buildings is a very complex task since it is strongly related to a great variety both of geometrical layouts and of masonry mechanical characteristics. In this article, some results of a Catania University research project, denomined “FIR 2014”, focused on the seismic vulnerability estimation of historical buildings, built in Catania after the 1963 earthquake, are presented. First, a detailed typological analysis of the considered urban fabric, characterized by typical residential masonry buildings, has been performed. Such analysis allowed recognizing an elementary structural modulus, which has been studied according to different geometrical layouts representative of isolated or aggregate buildings. The results of nonlinear static analyses, performed by applying an innovative macro-element approach, allowed for the assessment the seismic vulnerability of typical URM buildings coherently to the Italian seismic code. The adopted macro-element strategy for the seismic assessment of aggregate masonry buildings, although related to a specific historical center, may be applied to similar urban fabrics and can also be used for the calibration and validation of fast seismic assessment strategies, particularly useful for the evaluation of the seismic risk at urban scale.     

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.     

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.     

Seismic vulnerability assessment methodology for slender masonry structures

ABSTRACT

Slender masonry structures such as towers, minarets, chimneys, and Pagoda temples can be characterized by their distinguished architectural characteristics, age of construction, and original function, but their comparable geometric and structural ratios yield to the definition of an autonomous structural type. These structures constitute a part of the architectural and cultural heritage. Their protection against earthquakes is of great importance. This concern arises from the strong damage or complete loss suffered by these structures during past earthquakes. Seismic vulnerability assessment is an issue of most importance at present time and is a concept widely used in works related to the protection of buildings. However, there is few research works carried out on developing the seismic vulnerability assessment tools for such structures.

This article presents a new method for assessing the seismic vulnerability of slender masonry structures based on vulnerability index evaluation method. The calculated vulnerability index can then be used to estimate structural damage after a specified intensity of a seismic event. Here, 12 parameters are defined to evaluate the vulnerability index for slender masonry structures. Implementation of this methodology is carried out in different types of slender masonry structures to develop vulnerability curves for these structure types.     

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.     

The use of ‘statbilized earth’ in the conservation of megalithic monuments

Abstract

The main features of the megalithic monuments in Sardinia, Italy, dated to the Middle-Late Bronze Age, are described. These constructions are in a poor state of preservation, especially those built with stones particularly vulnerable to weathering. To impede water ingress into the masonry structure of these archaeological ruins, it is proposed to use a stabilized earth-based mortar that acts as an effective substrate for a water-repellent polymer.     

Numerical Modeling of a Church Nave Wall Subjected to Differential Settlements: Soil-Structure Interaction,Time-Dependence and Sensitivity Analysis

ABSTRACT

Historic masonry structures are particularly sensitive to differential soil settlements. These settlements may be caused by deformable soil, shallow or inadequate foundation, structural additions in the building and changes in the underground water table due to the large-scale land use change in urban areas.

This paper deals with the numerical modeling of a church nave wall subjected to differential settlement caused by a combination of the above factors. The building in question, the church of Saint Jacob in Leuven, has suffered extensive damage caused by centuries-long settlement. A numerical simulation campaign is carried out in order to reproduce and interpret the cracking damage observed in the building.

The numerical analyses are based on material and soil property determination, the monitoring of settlement in the church over an extended period of time and soil-structure interaction. A sensitivity study is carried out, focused on the effect of material parameters on the response in terms of settlement magnitude and crack width and extent. Soil consolidation over time is considered through an analytical approach. The numerical results are compared with the in-situ observed damage and with an analytical damage prediction model.     

Long-term performance evaluation of an earthen grouting mortar: the Nuraghic complex of Genna Maria,Sardinia

Abstract

This paper presents a critical assessment of the long-term performance of an earth-based material employed nine years ago in conservation work on a building of massive, Cyclopean-style construction at the Genna Maria Nuraghic complex in central-southern Sardinia (Italy). The material was used for filling the large gaps between stones in the masonry walls to create a barrier to ingress of water into the masonry walls. In situ observations and laboratory analyses were conducted on samples of the grouting material to assess its condition after nine years.     

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.     

RESPONSE OF UNREINFORCED MASONRY BUILDINGS

Abstract

A summary of dynamic measurements are presented that illustrate relations between linear seismic demand and true nonlinear response of unreinforced masonry buildings with flexible diaphragms and rocking piers subjected to a series of simulated earthquake motions.