Cross Vault Research Articles

DEM Analysis of Masonry Open Vaults with Square Bays

ABSTRACT Masonry vaults are usually considered as shell structures, whose geometry strongly determines the mechanical behaviour. In this article, the discrete element method is applied as a tool to perform virtual experiments to study three different types of open vaults (sail vault, fan vault, and cross vault). The three vaults have the same ground plan, but the sail vault is an elliptical shell, the fan vault is hyperbolic, and the cross vault is parabolic. All vaults are first gradually equilibrated under their self-weight, and then submitted to gradually increasing downwards forces at different positions, or to quasi-statically increasing outwards support displacements. The ultimate loads and the failure mechanisms of the vaults are compared. The orientation of the reactions is measured. The main results of the investigations are that (1) under concentrated loads, while the elliptic shell (the sail vault) fails locally, the hyperbolic vault (i.e. the fan vault) show either global failure or local failure but global cracking, depending on the position of the load; (2) under gradually increasing outwards support displacements, the orientation of the reactions is most favourable for the fan vault and worst is for the cross vault.

Comparison of Continuous and Discrete Modeling Strategies for the Structural Assessment of a Masonry Vault Under Dynamic Seismic Loading

ABSTRACT To begin, the paper introduces methodologies employing both homogeneous continuous Finite Element Method (FEM) and block-by-block Discrete Element Method (DEM) to model masonry behaviors. In the continuous approach, the masonry is modeled as an anisotropic damageable material (homogeneous or not). In contrast, the block-based approach represents rigid blocks interacting through contact joints governed by frictional cohesive behaviors. The DEM framework allows for significant displacements, rotations, and complete detachments of blocks, aspects often overlooked in traditional FEM models. The primary application of this research involves the seismic assessment of a masonry cross vault. Notably, the numerical results exhibit the approach’s capability to provide realistic predictions of failure mechanisms, crucial for retrofitting efforts. This includes an accurate representation of the actual cracking pattern, accounting for significant displacements. The numerical implementation is accessible through the open-source LMGC90 software. Comparative analyses are then carried out, focusing on the strengths and weaknesses of FEM macro-modeling (continuous homogeneous description) and DEM utilizing rigid blocks.

Dynamic changes on a masonry cross vault after a forced damage

Dynamic changes on a masonry cross vault after a forced damage

Modelling of the Dynamic Response of a Full-Scale Masonry Groin Vault: Unstrengthened and Strengthened with Textile-Reinforced Mortar (TRM)

ABSTRACT This article presents the results of the numerical simulations of a dynamic experimental campaign on the shaking table. The specimen is a full-scale masonry cross vault without and with the textile-reinforced mortar used as a strengthening solution. The specimen was tested in the scope of the European project SERA.ta 07 “Seismic Response of Masonry Cross Vaults: Shaking table tests and numerical validations”. The specimen replicates a generic cross-section of a central bay located in the lateral nave of a three-nave church, where the recurrent in-plane shear mechanism is induced. Finite element model (FEM) and discrete element model (DEM) were built and calibrated based on the experimental frequencies and mode shapes. Then, a unidirectional seismic action was applied to the numerical model in order to develop shear damage in the shell of the vault. A detailed description of the two simulations and their main outcomes are presented. The response was evaluated based on the displacements, damage, collapse mechanisms and hysteretic behaviour.

Combined Finite-Discrete Element Model Simulations of Shake-Table Tests on a Full-Scale Masonry Cross Vault

ABSTRACT This work presents the numerical simulations of shaking table tests of a full-scale masonry cross vault. The boundary conditions simulate the presence of a continuous lateral wall and of a colonnade-between-naves condition. The seismic action is applied along the longitudinal direction of the specimen, with increasing amplitude. The model used for the simulations allows for the elastic finite element modelling of masonry units and the discrete element modelling of the interfaces between them. A tension cut-off governs the interface: no tensile stress can be transmitted once this strength is exceeded. The shear response is defined by cohesion and friction: once the former is exceeded the interface reacts according to Coulomb’s behaviour. The simulations are related to the blind predictions, according to the scheduled tests, and the post-dictions, according to the actual testing sequence. The prediction model overestimates displacements and does not catch the actual crack distribution. Therefore, a post-simulation model was implemented, revising the masonry elastic modulus as well as the stiffness and boundary conditions of the supporting piers. Simulations are improved both in terms of displacement predictions and damage mechanism. Finally, the sensitivity to finite-element size, damping ratio and block discretisation was explored.

Shaking Table Testing of an Unstrengthened and Strengthened with Textile Reinforced Mortar (TRM) Full-Scale Masonry Cross Vault

ABSTRACT This article presents the results of the LNEC-3D shaking table tests on a full-scale masonry cross vault without and with the textile reinforced mortar used as strengthening solution. The specimen has been tested in the scope of the European project SERA. TA 07 “Seismic Response of Masonry Cross Vaults: Shaking table tests and numerical validations”. The specimen replicates a generic cross-section of a central bay located in a lateral nave of a three-nave church, derived from the intersection of two semi-circular barrel vaults with low rise. It is representative of a generic monumental church in Central Italy, generated by a squared base groin vault with a net span of 3.13 m and 1.13 m rise at full scale. A unidirectional seismic action is applied to develop shear damage in the shell of the vault. A detailed description of the two tests and the conclusions are presented. The response is evaluated based on the displacements, damage, and collapse mechanisms developed as a function of an increasing intensity earthquake testing protocol, in which a pre-processed strong ground motion component of the L’Aquila (Italy) earthquake (April 6, 2009) was used.

Diaphragm effect of unreinforced historical masonry vaults

In historical masonry structures, and particularly in churches, vaults have a fundamental role in bearing the vertical loads of floors and roofs. However, in past earthquakes they have proved vulnerable, representing a source of fragility under horizontal loading. In addition, the global seismic behavior of masonry structures is strongly affected by the stiffness of flooring elements (diaphragm effect), which, when sufficient, allows for transfer of horizontal actions to stiffer wall working in-plane.In this paper, the diaphragm effect of historical masonry vaults under horizontal loads is investigated numerically. A parametric nonlinear Finite Element model of a cross vault is subjected to in-plane shear actions on two supports to evaluate the response and damage during an earthquake. This work is preparatory for future physical testing activities on scaled prototypes to be performed within a broader research project, aimed at the enhancement and exploitation of artistic and cultural heritage.

Simplified Analysis of a Masonry Cross Vault Under Dynamic Actions

ABSTRACTDynamic tests performed on masonry cross vaults provide important information to improve the knowledge under seismic actions of these particular structural elements. Under seismic actions, curved masonry elements show a behaviour strongly influenced by several parameters (both physical and mechanical). Their structural behaviour is hard to predict due to the significant variability of the input parameters and the strong heterogeneity of these elements. Refined nonlinear models often require specific numerical calibrations of nonlinear parameters in order to assess the structural capacity of tested element. Conversely, simplified Finite Element models represent useful tools to develop a basic knowledge on the expected structural behaviour. Initial knowledge level in SERA TA blind competition favoured simple assumptions. Therefore, the main goal was to evaluate key information of a masonry vault under dynamic action: triggering and the type of damage, the most stressed areas and the threshold at which evident damage is expected. The results obtained by these preliminary analyses have been compared with the experimental tests.

Numerical Simulation of the Response of an Unreinforced Brick-Masonry Cross Vault Subjected to Seismic Loading

ABSTRACTThis paper presents the numerical evaluation of the seismic response of a masonry cross vault using the Discrete Macro-Element Method (DMEM). The case study corresponded to a full-scale unstrengthened cross vault that was experimentally investigated within the scope of the SERA Project — Seismic Response of Masonry Cross Vaults: Shaking table tests and numerical validations. The cross vault was subjected to repeated shaking table and dynamic identification tests until reaching significant damage. The numerical simulations involved the calibration of the Young’s modulus of the masonry material aiming at reproducing the cross vault’s experimental natural frequencies and mode shapes. The comparison of frequencies was carried out by estimating the difference between experimental and numerical results, whereas the correspondence between mode shapes was studied using the Modal Assurance Criterion. Subsequently, a sensitivity analysis was performed to identify the influence of nonlinear properties on the seismic response of the cross vault (displacement and acceleration time histories and failure mechanism). The accuracy of the numerical time histories was evaluated by estimating magnitude and phase discrepancies. The results aimed at demonstrating the applicability of the DMEM for assessing the seismic response of masonry cross vaults with an acceptable degree of accuracy and low computational cost.

3D Rigid Block Limit Analysis of a Masonry Cross Vault Subjected to Shaking Table Tests

ABSTRACT This paper presents the results of a numerical study on a brick masonry cross vault that was tested on a shaking table, on a scale of 1:1. The study was part of the blind prediction competition organized within the activities of the SERA-AIMS project “Seismic Response of Masonry Cross Vaults: Shaking table tests and numerical validations”. The main objective of the blind prediction competition was to compare various numerical techniques. Among others, the one presented in this paper is based on 3D rigid block limit analysis. In the numerical model, the masonry units of the cross vault are modeled with rigid blocks interacting at no tension-frictional interfaces. A simple iterative procedure is used to take into account the non-associative behavior in sliding failure. Preliminary analyses carried out at the blind prediction competition stage as well as post-diction studies, after the experimental tests, are presented. The paper emphasizes the differences between the pre-diction and post-diction phases to highlight the improvements made during the numerical investigation. The study shows the influence of support and action modeling as well as of friction coefficient on the failure mechanisms and force capacity.

Finite-Element Seismic Assessment of a Masonry Cross Vault Through Blind Predictions and Numerical Simulations

ABSTRACT In this paper, a continuum 3D finite-element model is presented to determine the seismic behaviour of masonry cross vaults under seismic motions. The work regards the investigation of a regular cross vault made of clay bricks and hydraulic mortar, accounting for two distinct configurations: an un-strengthened design and one strengthened through the application of a fibre-based reinforcement. The research adopts parts of the blind prediction simulation developed during the SERA project. For both configurations, the manuscript follows two main steps: a prediction simulation, based on laboratory tests executed on specimens made with the same materials of the cross vault, and a post-diction calibration, based on the outcomes of the experimental tests on the full-scale model. The final FE models, realized through the commercial software ABAQUS CAE, have allowed a satisfactory simulation of the experiment, providing insights for the modelling of these structural systems through continuum approaches.

Generalized Thrust Network Analysis of Triangular Masonry Cross Vaults Inspired by Musmeci

A triangular parabolic cross vault, that was designed by Musmeci in the 1950s as a reinforced concrete structure but remained unbuilt, is revisited from the original perspective of its reinvention as a masonry structure. In the framework of static limit analysis under classical Heyman’s assumptions, a generalized thrust network analysis is adopted for a structural safety assessment. The performances of the vault, subject to its self-weight, are investigated through minimum-thrust and minimum-thickness analyses by conforming to the original geometry and assuming the vault thickness as the only design parameter. Further insight is achieved by exploring a more general class of triangular parabolic masonry cross vaults, whose rise-to-span ratio is an additional design parameter. The static efficiency of the smart and unconventional geometry proposed by Musmeci is thus proven, motivating the possibility of bringing it to new life in the form of a masonry structure.

Pre- and Post-Diction Simulation of the Seismic Response of a Masonry Cross Vault Tested on a Shaking Table

ABSTRACT Masonry vaults are widely employed in ancient constructions and play a crucial role in their static and dynamic behaviour. In the last decades, the scientific community has carried out, on the one hand, several experimental campaigns aimed at characterising the response of masonry vaults to horizontal actions; on the other, it has developed sophisticated numerical models able to capture the crucial features of their structural response. Within the framework of the SERA.TA project (Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe), pre- and post-diction contests have been organised to assess the capability of numerical methods to predict the seismic response of a 1:1 scale model of a masonry cross vault, realised and tested at LNEC laboratory (Portugal). This paper outlines the numerical analyses performed on two vault models within the pre- and post-diction phases of the project. The numerical models have been created and analysed with NOSA-ITACA, a finite element software developed by ISTI−CNR and devoted to the structural analysis of ancient masonry constructions. Pros and cons of the numerical simulations have been analysed, comparing the prediction and post-diction results with the experimental data in terms of accelerations, displacements, and crack patterns. Numerical results fit the experimental outcomes, and betterment is evident in the post-diction phase.

A Cross-Vault System’s Relative Periodisation Based on Geometric Analysis •

The cross-vault system of the Inner City Parish Church of Budapest was the subject of numerous scientific works so far. In our present article, we aimed to supplement the information known about the vaults by providing exact geometric data gathered via laser scanning. Based on this data, we attempted to filter out common characteristics of the individual vaults, regarding the geometry of their ribs, their webs and the positions of their keystones. As a result, we proved that the cross vaults composing the system cannot be hallmarked as the remains of a given building period, and even within a given cross vault, more building periods can appear. Combining the results of the different geometric analyses, we concluded six distinct scenarios concerning the relative periodisation of the elements composing the cross-vault system, complemented by the evaluation of these. Thus, in the present article, we give an example of how to use point cloud-based building survey techniques to approach the questions of a given building’s relative periodisations.

Seismic assessment of masonry vaults by means of an advanced hybrid FEM-DEM modeling strategy

The current work presents a hybrid Finite Element Method and Discrete Element Method (FEM-DEM) strategy, which combines classical finite and discrete element methods in a common tool, and illustrates its capabilities in reproducing the real behavior of masonry during experimental quasi-static tests and seismic actions. The numerical implementation is available in the open-source LMGC90 code. In this hybrid approach, anisotropic damageable deformable blocks interact each other through contact joints governed by frictional cohesive behaviors. The DEM framework permits large displacements, rotations, and complete detachments of the blocks, which is usually neglected with FEM models. A comparative work is developed with a focus on the advantages and disadvantages of the hybrid model with respect to FEM micro- and macro-modeling (aka block based description or continuous homogeneous description), and DEM using rigid blocks. In this regard, validations through experimental benchmarks are achieved and the results of a diagonal compression test are discussed. Then, the main application performed in this work concerns the seismic assessment of a masonry cross vault. The key aspect of the numerical results concerns the ability of this approach in providing realistic prediction of failure mechanisms, which are relevant for retrofitting works, according to the real cracking pattern, considering the real stereotomy of the masonry and large deformations.

Shake-Table Testing of a Cross Vault

Domes, vaults and arches are structural components of high vulnerability, due to the horizontal component of the thrust they impose to the supporting vertical elements (piers or walls), accentuated by the asymmetry of loading due to seismic actions. In order to explore the possibilities of reducing this vulnerability, a cross vault made of brickwork and supported by two stone masonry walls was tested on the earthquake simulator. A series of seismic tests was performed to the specimen at its as-built state, as well as after strengthening using techniques adequate for monuments, namely, grouting of piers, arrangement of struts/ties at the base of the cross vault and vertical prestressing of the masonry piers. The tests have confirmed the vulnerability of the original specimen, as well as the improvement of its behavior after strengthening, in terms of sustained maximum base acceleration, deformations and observed damage.

Seismic Assessment of Roman Concrete Groin Vaults through UAV, NDT and 3D Analyses

In Roman Baths, the Romans employed barrel and groin vaults of great dimensions, with maximum span more than 20 m; simple tools of structural analysis of ancient wide span vaulted halls are still lacking, due to geometrical and material complexity. In this paper, we study the collapse behavior, under horizontal static action, of a corner cross vault of the Baths of Diocletian in Rome (Hall I). Two methods of analysis are here used: non-linear incremental finite element and limit analysis. In both cases, 3D models have been developed by means of UAV inspection, NDT measures, and AVT monitoring. The construction of the overall 3D geometry has been here afforded with a specific pre-processing approach. Midas commercial software has been employed for FEM analysis, assuming a constitutive law specifically developed for Roman concrete. In limit analysis, masonry is discretized as a system of interacting rigid bodies in no-tension and frictional contact. The computational code consists in a linear approach, which makes use of a series of optimization packages via lower and upper bound techniques. Finally, a strategy based on FEM analysis including discontinuities was implemented, and the results were compared with the two previous approaches.

АНАЛИЗ РАБОТОСПОСОБНОСТИ ОПОРНЫХ УЧАСТКОВ КАМЕННЫХ СВОДОВ

The article substantiates that in cylindrical vaults with stripping and cross vaults of historical buildings, the most stressed areas are the areas where the vaults rest on the supporting structures (walls and pillars) and the zones of interface between strippings and vaults. In particular, in cross vaults, the most loaded are the diagonal ribs, in which the compressive forces act at an angle of 45° (it is in this direction that the masonry has the least resistance to compression), and the flow of compressive forces within the diagonals of the vault accumulates, reaching maximum values in its supporting heels. From which it is concluded that it is the supporting consoles that most often determine the bearing capacity of the cross vault as a whole. The article gives approximate calculated dependences for assessing the bearing capacity of the supporting consoles of the cross vaults and concludes that the most accurate picture of the stress state of the supporting consoles can be established by numerical modeling, and to assess the bearing capacity, it is necessary to use particular strength criteria.

Сalculation methodology and determination of efforts in vault

Abstract. Problem. In this article we offer the meth-odology of calculation, based on the idea of dismem-berment of vault on the separate archs of single width. It is recommended for the estimation of efforts in the designed and damaged vaults. Also offered a methods of calculation effort in serried vaults. As spatial inflexibility of cross vault below than inflexi-bility of serried vault, then it is necessary to execute the calculation of the cheek arch abstracted from the tray of cross vault also. If the outline of tray is exe-cuted on a circular curve, then it is possible to take methodology of calculation of archs with the outline of axis a curve as catenoid. Goal. The proposed methodology for calculating closed and cross vaults is also based on the idea of dividing the arch into separate arches of unit width. The results of studies of efforts and rational forms of arches of V.A. Kiselev [1]. Methodology. Calculation based on the idea of dismemberment of vault on the separate archs of single width. Recommended for the estimation of efforts in the designed and damaged vaults. A method over of calculation of dome is brought for determina-tion of effort in serried vaults. Results. At the choice of outline of axis of arch it is necessary aspires to that an axis, on possibility, coincided with the curve of pressure. Such outline of axis is rational, as there are only central forces of N in an arch. Flexion mo-ments M and transversal forces of Q are equal to the zero. The coincidence of axis of arch with the curve of pressure can be got for the three-hinged arch. For the statically undetermined arch of complete coinci-dence of axis with the curve of pressure attaining is impossible, so that the origin of flexion moments at any her outline is inevitable. Originality. The tech-nique based on the separation of flat elements from the spatial structure does not show the reserves of strength of the structure. Experience of long-term operation of vaulted structures designed or verified by calculation using similar methods [2], [9] shows caution and reliability. Practical value. The tech-nique is also suitable for assessing the strength of damaged vaults with collapsed corners or walms.

The Nativity Chapel in the Church of Santa Maria dei Martiri in Maranola: Court Patronage in Southern Latium

In Maranola there is the Church of Santa Maria dei Martiri, famous for the Nativity Chapel. Despite the fact that the sacellum was realized in modern age, it is very difficult to obtain sure information, because of the lack of documentation. The sacellum has a rectangular plan, at about half of its height it is divided horizontally by a barrel vault that simulates a cave; the two floors are connected by stairs on the left. In the cross vault of the upper level there are painted the four Evangelists with their symbols. In the lower level of the chapel are recognizable two pictorial layers in which the fragmentary Nativity is visible. It is possible to date these paintings to the beginning of the 16th century because they are stylistically close to the manner of Cristoforo Scacco, a painter well known in Southern Latium at that time. The decoration of the chapel is completed by a Nativity scene with twenty-seven terracotta sculptures. In the lower floor of the chapel there are: Baby Jesus, The Holy Virgin, St. Joseph, the ox and the donkey and two Prophets: king David and Malachi. In the upper floor there are the Three Magi, the Annunciating Angel, two shepherds and many animals. The crèche is stylistically close to the Neapolitan sculpture of the end of the 15th — beginning of the 16th century. Even if there are no documents, it seems possible to connect the patronage of the Nativity Chapel to Caterina Pignatelli, the wife of the count of Fondi Onorato II Caetani. With this patronage, she wanted to underline her power over the feud of Maranola.