Homogenization of cohesive fracture in masonry structures

We derive a homogenized mechanical model of a masonry-type structure constituted by a periodic assemblage of blocks with interposed mortar joints. The energy functionals in the model under investigation consist in (i) a linear elastic contribution within the blocks, (ii) a Barenblatt's cohesive contribution at contact surfaces between blocks and (iii) a suitable unilateral condition on the strain across contact surfaces, and are governed by a small parameter representing the typical ratio between the length of the blocks and the dimension of the structure. Using the terminology of Gamma-convergence and within the functional setting supplied by the functions of bounded deformation, we analyze the asymptotic behavior of such energy functionals when the parameter tends to zero, and derive a simple homogenization formula for the limit energy. Furthermore, we highlight the main mathematical and mechanical properties of the homogenized energy, including its non-standard growth conditions under tension or compression. The key point in the limit process is the definition of macroscopic tensile and compressive stresses, which are determined by the unilateral conditions on contact surfaces and the geometry of the blocks

Structural Assessment of the Historical Yozgat Clock Tower

Many methods and tools have been used to measure time throughout history. People started using mechanical watches instead of sundials and hourglasses because of technological advances. After that, they built clock towers, which have become a symbol of cities. Although clock towers were first constructed in Europe, they soon spread to the Ottoman Empire. Now these structures are considered an important component of a country’s cultural heritage, and therefore must be preserved for future generations. The clock tower in Yozgat, Turkey is one such structure. For this study, a three-dimensional model of the Yozgat clock tower was constructed in a digital environment and subjected to static and dynamic analyses. The static analyses demonstrated that the structure is safe in terms of stress and displacement. However, the dynamic analyses demonstrated that damage would be formed in the lower regions of the tower base and extend all the way to the balcony in the event of an earthquake. Both the linear and nonlinear analyses yielded similar results in terms of where the damage would occur. This study could be used as a guide for future restoration studies or endeavors

Structural Assessment of the Historical Yozgat Clock Tower

Many methods and tools have been used to measure time throughout history. People started using mechanical watches instead of sundials and hourglasses because of technological advances. After that, they built clock towers, which have become a symbol of cities. Although clock towers were first constructed in Europe, they soon spread to the Ottoman Empire. Now these structures are considered an important component of a country’s cultural heritage, and therefore must be preserved for future generations. The clock tower in Yozgat, Turkey is one such structure. For this study, a three-dimensional model of the Yozgat clock tower was constructed in a digital environment and subjected to static and dynamic analyses. The static analyses demonstrated that the structure is safe in terms of stress and displacement. However, the dynamic analyses demonstrated that damage would be formed in the lower regions of the tower base and extend all the way to the balcony in the event of an earthquake. Both the linear and nonlinear analyses yielded similar results in terms of where the damage would occur. This study could be used as a guide for future restoration studies or endeavors

A new OMA method to perform structural dynamic identification: numerical and experimental investigation

Operational modal analysis (OMA) methods are nowadays common in civil, mechanical and aerospace engineering to identify and monitor structural systems without any knowledge on the structural excitation provided that the latter is due to ambient vibrations. For this reason, OMA methods are embedded with stochastic concepts and then it is difficult for users that have no-knowledge in signal analysis and stochastic dynamics. In this paper an innovative method useful for structural health monitoring (SHM) is proposed. It is based on the signal filtering and on the Hilbert transform of the correlation function matrix. Specifically, the modal shapes are estimated from the correlation functions matrix of the filtered output process and then the frequencies and the damping ratios are estimated from the analytical signals of the mono-component correlation functions: a complex signals in which the real part represents the correlation function and the imaginary part is its Hilbert transform. This method is very simple to use since requires only few interactions with the users and thus it can be used also from users that are not experts in the aforementioned areas. In order to prove the reliability of the proposed method, numerical simulations and experimental tests are reported also considering comparisons with the most popular OMA methods

Dynamic characterization of progressively damaged segmental masonry arches with one settled support: experimental and numerical analyses

This paper aims to explore the dynamic behavior of a segmental masonry arch subjected to increasing horizontal displacements of one support. To this end, output-only dynamic identification techniques are first used to track the evolution of the dynamic features of the system under progressive damage scenarios and evaluate their sensitivity to settlement-induced cracks. Considerations on the structural response of the segmental arch up to failure are also included. Then, a numerical procedure coupling linear perturbation and modal analysis is applied to simulate the dynamic behavior of the arch over consecutive scenarios, taking into account the influence of the damage on the structure's dynamic properties in an automatic way. The combination of experimental and numerical analyses allows to fully investigate the dynamics of the cracked masonry arch and to shed light on relevant aspects about the effects of settlement-induced cracks on the modal blueprints of masonry arches

Performance of rammed earth subjected to in-plane cyclic displacement

Rammed earth structures are worldwide spread, both as architectural heritage and new constructions. Yet, rammed earth buildings present, in general, high seismic vulnerability. Despite the several studies conducted on the mechanical characterisation of rammed earth and on the numerical modelling of structural elements built with this material, further in-plane cyclic tests on rammed earth sub-assemblies are required to characterise their hysteretic behaviour. In this framework, an experimental program was conducted where cyclic in-plane tests were performed on a large-scale rammed earth wall. The geometry of the wall was defined to represent a sub-assembly commonly found in rammed earth dwellings from Alentejo (Southern Portugal). The wall was subjected to cyclic shear displacements with increasing amplitude, imposed in both positive and negative directions. To detect the dynamic properties of the wall and to assess the development of the structural damage, dynamic identification tests were conducted along the experimental programme. The results are analysed in terms of crack pattern, dynamic properties, displacement capacity, base shear performance and stiffness degradation. Further discussion is led on the dissipated energy, while a bi-linear and linear equivalent systems are proposed as simplified modelling approach. In conclusion, degradation of structural capacity was observed due to cyclic loads, while adequate energy dissipation and base shear coefficient were obtained.This work was partly financed by FEDER funds through the Operational Programme Competitiveness Factors (COMPETE 2020) and by national funds through the Foundation for Science and Technology (FCT) within the scope of project SafEarth-PTDC/ECM-EST/2777/2014 (POCI-01-0145-FEDER-016737). The support from grants SFRH/BD/131006/2017 and SFRH/BPD/97082/2013 is also acknowledged. Acknowledgments are addressed to the Laboratory of Structures (LEST) of the University of Minho, Joao Bernardino, Lda, and TERRACRUA-Construcoes Ecologicas Unipessoal, Lda for building the rammed earth model

Discrete and Continuous Models for Static and Modal Analysis of Out of Plane Loaded Masonry

A critical review of analytical and numerical models for studying masonry out of plane behaviour is presented. One leaf historical masonry, composed by rigid blocks arranged regularly with dry or mortar joints, is considered. Discrete model with rigid blocks, Love-Kirchhoff and Reissner-Mindlin plate models and 3D heterogeneous FEM are adopted. An existing simple and effective discrete model is adopted and improved by applying matrix structural analysis techniques for static and modal analysis of masonry walls in the elastic field, but the formulation allows to account also for material nonlinearity. Elastic parameters of both plate models are based on an existing compatible identification between 3D discrete model and 2D plate models. Static and modal analysis of masonry walls with several boundary conditions are carried on, numerical tests account for in plane size of heterogeneity and structure thickness by means of in and out of plane scale factors. Results show that discrete model is simple and effective for representing masonry behaviour, especially when size of heterogeneity is smaller than overall panel size. Decreasing in plane scale factor, plate models converge to the discrete one, but the Reissner-Mindlin one shows a better convergence and also allows adopting a simple FE for performing numerical analysis

Influence of Temperature on the Structural Behaviour of Masonry Buildings

This paper investigates the mechanical behaviour of heritage structures subjected to seasonal temperature variations. To this end, the constitutive equation of masonry-like materials, which has been embedded in the finite element code NOSA-ITACA (www.nosaitaca.it), is used to model the static and dynamic behaviour of simple arched masonry structures subjected to thermal load

DISCRETE AND CONTINUOUS MODELS FOR THE IN PLANE MODAL ANALYSIS OF MASONRY STRUCTURES

A modal analysis, developed in plane dynamics and linear elasticity, for periodic masonry structure is presented and validated both by means of a continuum modelling within the frame of the micropolar continuum theory and of a discrete model (DEM) within the frame of a molecular dynamic algorithm. For running-bond masonry brickwork numerical micropolar models already exist [1,2] in static frameworks [2] and in dynamic frameworks [3,4]. Here the aim is twofold: i) a multi-scale modal analysis both at Representative Elementary Volume (REV) level -micro-scale- and at masonry panel level -macro-scale-; ii) a multimodel analysis both with continuum micro-structured and discrete models such as to evaluate sensitivity to masonry local microstructure and sensitivity to characteristic length of REV by reference to masonry panel size. Two models are presented and compared. A discrete element model and a continuous micropolar model based on analytical homogenization procedures. Both models are based on the following assumptions: i) the structure is composed of rigid blocks; ii) the mortar joints are modelled as interfaces. The rigid block hypothesis is particularly suitable for historical masonry, in which stone blocks may be assumed as rigid bodies. Continuum homogenized model provides, in an analytical form, constitutive equivalent elastic functions, mass and inertia; discrete model describes masonry as a rigid skeleton such as to evaluate both its global and local behaviour. A parametric analysis is carried out to investigate the effect of i) masonry texture (running versus header bond); ii) size of heterogeneity (block dimensions) respect panel dimensions. Modal analysis is hence carried on for a REV and different panels. Focus is on the sensitivity to heterogeneity size such as to verify models reliability and applicability field