PSI - Issue 37

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ICSI 2021 The 4th International Conference on Structural Integrity Editorial Pedro Moreira*, Paulo J. Tavares INEGI – Institute of Science and Innovation in Mechanical and Industrial Engineering, Porto, Portugal ICSI 2021 The 4th International Conference on Structural Integrity Editorial Pedro Moreira*, Paulo J. Tavares INEGI – Institute of Science and Innovation in Mechanical and Industrial Engineering, Porto, Portugal

© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira Keywords: Type your keywords here, separated by semicolons ; 1. Main text ICSI focuses on all aspects and scales of research on Structural Integrity. This ranges from basics to future trends, with special emphasis on multi-scale and multi-physics approaches, and applications to new materials and challenging environments. Current research topics in the realm of Structural Integrity targeted by ICSI include Fracture and Fatigue, Stress Analysis, Damage Tolerance, Durability, Crack Closure, Joining Technologies, Nanomechanics and Nanomaterials, Ageing, Coatings Technology, Environmental Effects, Structural Health Monitoring, New materials, Surface Engineering, Structural Integrity in Biomechanics and many other relevant research topics. In 2021, in spite of the pandemic which affected the entire R&D community and forced ICSI to go online, an effort was made to keep the momentum generated in the previous editions, increasing the visibility to the conference and its scientific impact. ICSI invited a number of prominent researchers which accepted to lecture on their own fields, such as Prof. Sabrina Vantadori from the University of Parma, Prof. Fabrice Pierron from Southampton University, Prof. Milos Djukic from the University of Belgrade, Profs. Nima Shamsaei and Shuai Shao from Auburn University, Prof. Youshi Hong from the Chinese Academy of Sciences and our dear friend Prof. Jesus Toribio from the University of Salamanca. ICSI has been organized into a general track and thematic symposia, as in previous editions. The response to the organization efforts has been outstanding: Fourteen symposia were proposed and accepted; the number of submissions was kept at a similar level to 2019, with 206 approved oral communications out of 224 2022 The Authors. Published by ELSEVIER B.V. T is is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) P r-review under responsibility of Pedro Mig el Guimaraes Pi s Moreira Keywords: Type your keywords here, separated by semicolons ; 1. Main text ICSI focuses on all aspects and scales of research on Structural Integrity. This ranges from basics to future trends, with special emphasis on multi-scale and multi-physics approaches, and applications to new materials and challenging environments. Current research topics in the realm of Structural Integrity targeted by ICSI include Fracture and Fatigue, Stress Analysis, Damage Tolerance, Durability, Crack Closure, Joining Technologies, Nanomechanics and Nanomaterials, Ageing, Coatings Technology, Environmental Effects, Structural Health Monitoring, New materials, Surface Engineering, Structural Integrity in Biomechanics and many other relevant research topics. In 2021, in spite of the pandemic which affected the entire R&D community and forced ICSI to go online, an effort was made to keep the momentum generated in the previous editions, increasing the visibility to the conference and its scientific impact. ICSI invited a number of prominent researchers which accepted to lecture on their own fields, such as Prof. Sabrina Vantadori from the University of Parma, Prof. Fabrice Pierron from Southampton University, Prof. Milos Djukic from the University of Belgrade, Profs. Nima Shamsaei and Shuai Shao from Auburn University, Prof. Youshi Hong from the Chinese Academy of Sciences and our dear friend Prof. Jesus Toribio from the University of Salamanca. ICSI has been organized into a general track and thematic symposia, as in previous editions. The response to the organization efforts has been outstanding: Fourteen symposia were proposed and accepted; the number of submissions was kept at a similar level to 2019, with 206 approved oral communications out of 224

* Corresponding author. Tel.: +351 225 082 151; fax: +351 229 537 352. E-mail address: pmoreira@inegi.up.pt * Corresponding author. Tel.: +351 225 082 151; fax: +351 229 537 352. E-mail address: pmoreira@inegi.up.pt

2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira 2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira

2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira 10.1016/j.prostr.2022.01.053

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submissions, from 38 countries; approximately 25% of the approved communications were submitted by students, an important landmark for the organizers, who strived to create favorable conditions for greater student involvement. The biennial ICSI conferences, at the end of summer, were planned to be a reference source of inspiration for the researchers in the field that want to keep abreast current R&D results and the outstanding response of the delegates in times of turmoil didn’t let us down. Above all, the organizers believe the ICSI conferences disseminate excellent research and share important knowledge for the enhancement of science and the prosperity of our society, and therefore actively contribute to the preservation and sustainability of our world.

Conference Chairs,

Pedro M. G. P. Moreira Paulo J. S. Tavares INEGI – Institute of Science and Innovation in Mechanical and Industrial Engineering

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Committees Chairmen

Pedro Moreira, INEGI, Portugal Paulo Tavares, INEGI, Portugal Organizing Committee Virginia Infante, IST, Portugal Luís Reis, IST, Portugal Paulo Lobo, UMA, Portugal Luís Borrego, IPC, Portugal Local Organizing Committee Behzad Farahani, INEGI, Portugal Carmen Sguazzo, INEGI Daniel Braga, INEGI, Portugal Nuno Viriato, INEGI, Portugal Shayan Eslami, INEGI, Portugal International Advisory Board

Aleksandar Sedmak, University of Belgrade, Serbia Alexopoulos Nikolaus, University of Aagen, Greece Alfonso Fernandez Canteli, University of Oviedo, Spain Constantinos Soutis, The University of Manchester, UK Daniel Kujawski, Western Michigan University, USA Francesco Iacoviello, Università di Cassino e del Lazio Meridionale, Italy Filippo Berto, Norwegian University of Science and Technology (NTNU), Norway Grzegorz Lesiuk, Wroclaw University of Technology and Science, Poland Jesus Toribio, University of Salamanca, Spain Jidong Kang, CanmetMATERIALS, Canada John Dear, Imperial College London John W. Hutchinson, Harvard University, USA José Correia, INEGI, Portugal José Xavier , Universidade NOVA de Lisboa Portugal Luis Borrego, Instituto Superior de Engenharia de Coimbra, Portugal Luis Reis, Instituto Superior Técnico , Portugal Manuel Freitas, Instituto Superior Técnico, Portugal Marcos Pereira, PUC, Brasil Mário Vaz, University of Porto, Portugal Mihaela Iordachescu, Polytechnic University of Madrid, Spain Miloslav Kepka, University of West Bohemia, Pilsen, Czech Republic

Nikolai Kashaev, Helmholtz-Zentrum Geesthacht, Germany Oleg Plekhov, Russian Academy of Sciences, Moscow, Russia Paulo Morais , LNEC, Portugal

Pedro Camanho, University of Porto, Portugal Sabrina Vantadori, University of Parma, Italy

Stefan Pastrama, University Politehnica of Bucharest, Romania Stéphane Sire, Université de Bretagne Occidentale, France Thierry Grosdidier, CNRS UMR, France Virginia Infante, Instituto Superior Técnico, Portugal

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International Scientific Committee Abilio de Jesus, University of Porto, Portugal

Aleksandar Sedmak, University of Belgrade, Serbia Alexopoulos Nikolaus, University of Aagen, Greece Alfonso Fernandez Canteli, University of Oviedo, Spain Bamber Blackman, Imperial College London Behzad Farahani , INEGI, Portugal Claudia Barile, Politecnico di Bari, Italy Constantinos Soutis, The University of Manchester, UK Dan Constantinescu, University Politehnica of Bucharest, Romania Daniel Braga, IST, Lisbon Daniel Kujawski, Western Michigan University, USA Dariusz Rozumek, Opole University of Technology, Poland Florian Schäfer, Universität des Saarlandes, Germany Filippo Berto, Norwegian University of Science and Technology (NTNU), Norway Francesco Iacoviello, Università di Cassino e del Lazio Meridionale, Italy Giuseppe Cata lanotti, Queen’s University Belfast Grzegorz Lesiuk, Wroclaw University of Technology and Science, Poland Hernani Lopes, Instituto Superior de Engenharia do Porto, Portugal José Xavier , Universidade NOVA de Lisboa Portugal Jürgen Bär, Universität der Bundeswehr München Liviu Marsavina, University of Timisoara Luis Borrego, Instituto Superior de Engenharia de Coimbra, Portugal Luis Reis, Instituto Superior Técnico , Portugal Malgorzata Kujawinska, Warsaw University of Technology, Poland Manuel Freitas, Instituto Superior Técnico, Portugal Marcos Pereira, PUC, Brasil Mário Vaz, University of Porto, Portugal Martins Ferreira, University of Coimbra, Portugal Mauro Madia, BAM, Germany Mihaela Iordachescu, Polytechnic University of Madrid, Spain Miloslav Kepka, University of West Bohemia, Pilsen, Czech Republic Natalia Kosheleva, Perm National Research Polytechnic University, Russia Oleg Plekhov, Russian Academy of Sciences, Moscow, Russia Paulo Lobo, University of Madeira, Portugal Paulo Morais , LNEC, Portugal Pedro Camanho, University of Porto, Portugal Peter Trampus , University of Dunaújváros, Hungary Roberto Lacalle, University of Cantabria, Spain Sabrina Vantadori, University of Parma, Italy Satish kumar Velaga, Indira Gandhi Centre for Atomic Research, India Stefan Pastrama, University Politehnica of Bucharest, Romania Stéphane Sire, Université de Bretagne Occidentale, France Thierry Grosdidier, CNRS UMR, France Virginia Infante, Instituto Superior Técnico, Portugal Vladimír Chmelko, Slovak University of Technology, Slovak republic Igor Varfolomeev, Fraunhofer IWM, Germany Jesus Toribio, University of Salamanca, Spain Jidong Kang, CanmetMATERIALS, Canada João Custódio, LNEC, Portugal John Dear, Imperial College London John W. Hutchinson, Harvard University, USA José Correia, INEGI, Portugal

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Weidong Zhu, University of Maryland, USA Zbigniew Marciniak, Opole University of Technology, Poland

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© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira Abstract Structural vulnerability assessment of heritage structures is a pivotal part of a risk mitigation strategy for preserving these valuable assets for the nations. For this purpose, developing digital twins has gained much attention lately to provide an accurate digital model for performing finite element (FE) analyses. Three-dimensional (3D) geometric documentation is the first step in developing the digital twin, and various equipment and methodologies have been developed to facilitate the procedure. Both aerial and terrestrial close-range photogrammetry can be combined with 3D laser scanning and geodetic methods for the accurate 3D geometric documentation. The data processing procedure in these cases mostly focuses on developing detailed, accurate 3D models that can be used for the FE modeling. The final 3D surface or volumes are produced mainly by combining the 3D point clouds obtained from the laser scanner and the photogrammetric methods. 3D FE models can be developed based on the geometries derived from the 3D models using FE software packages. As an alternative, developed 3D volumes provided in the previous step can be directly imported to some FE software packages. In this study, the challenges and strategies of each step are investigated by providing examples of surveyed heritage structures. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira Keywords: 3D geometric documentation; cultural heritage; digital twins; 3D laser scanner; photogrammetry; finite element model ICSI 2021 The 4th International Conference on Structural Integrity 3D simulation models for developing digital twins of heritage structures: challenges and strategies Amirhosein Shabani a, *, Margarita Skamantzari b , Sevasti Tapinaki b , Andreas Georgopoulos b , Vagelis Plevris c , Mahdi Kioumarsi a a Department of Civil Engineering and Energy Technology, Oslo Metropolitan University, Pilestredet 35, 0166 Oslo, Norway b Laboratory of Photogrammetry, School of Rural and Surveying Engineering, National Technical University of Athens, Greece c Department of Civil and Architectural Engineering, Qatar University, Doha, Qatar

* Corresponding author. Tel.: +47- 67237972. E-mail address: amirhose@oslomet.no

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2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira 10.1016/j.prostr.2022.01.090

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1. Introduction Heritage structures are important evidence of our civilizations that should be preserved with the most advanced available tools as stated by Shabani et al. (2020). The possibility of developing accurate enough digital simulation models where damage could be predicted would indeed help the restoration process of historic structures, as stated by Angjeliu et al. (2020), and Shabani, Hosamo, et al. (2021). Geometrical survey and providing more refined 3D numerical models of cultural heritage (CH) assets are the pivotal steps of developing digital twins’ procedure , as pointed out by Korumaz et al. (2017) and Shabani, Kioumarsi, et al. (2021). The interest in the documentation and enhancement of CH has been rising rapidly over the last decades, especially due to the significant technological advances that can contribute to its protection and promotion. Nowadays, many researchers explore different methods for documentation, management, and sustainability of CH, which have become an interdisciplinary approach to the development of the culture, as presented by Tobiasz et al. (2019). Digitization of CH assets and sites is a broad term that includes quantitative as well as qualitative data acquisition, as stated by Georgopoulos & Stathopoulou (2017). Within the photogrammetric, computer vision, and robotics communities, various techniques for 2D, 3D, even 4D data acquisition and digitization have been developed during the past years. CH assets are still a challenging object due to the complexity of their shape, the variety of their types, the high accuracy requirements, and the heterogeneity of the end-users. After performing the geometrical survey and providing the documentation, developing 3D simulation models is the next step for obtaining the more refined digital twins. Traditionally 3D FE models can be developed in FE analysis software packages based on the geometric documentation as employed by Bartoli et al. (2016), but recently automatically or semi-automatically conversion methodologies of the geometric documentation such as point clouds to 3D FE models are gaining attention, as stated by Panah & Kioumarsi (2021) and utilized by Castellazzi et al. (2015), Castellazzi et al. (2017), and Bartoli et al. (2020). Obtaining 3D models in computer-aided (CAD) software packages based on point clouds and importing them to 3D FE models in some of the FE analysis software packages (i.e., DIANA (2020), MIDAS (2021)) is a conventional method that is used by Pepi et al. (2021) and Kassotakis & Sarhosis (2021). This study presents a holistic methodology for 3D documentation of cultural heritage assets through geodetic, photogrammetric, and laser scanning data acquisition and post-processing methods. The 3D textured models, light 3D models, and cross-sections are the products of the workflow, and their applications are investigated. Furthermore, two methodologies for developing the 3D FE models were applied to two CH assets. Firstly, the FE model of the Roman bridge in Rhodes island in Greece was developed using the dimensions derived from the 3D documentation in FE software. Afterward, the developing procedure of the 3D FEM of the Slottsfjel tower (Slottsfjelltårnet) in Tønsberg, in Norway, is discussed. For making the 3D FE model of the tower, instead of modeling the structure in FE software, the 3D model was developed in 3D modeling software based on the point clouds and then imported to FE software and refined for meshing and performing the FE analysis. Furthermore, challenges and strategies through the presented This study focuses on the 3D geometric documentation of CH buildings of different historic areas and places around Europe, in order to provide the necessary products for the vulnerability assessment of the structures, the holistic approach of CH, and the development of digital twins. For the initial 3D modeling and representation of the CH buildings, the combination of geodetic, photogrammetric, and laser scanning data acquisition and processing methods have been applied, as discussed by Kolokoussis et al. (2021). Digital images were acquired in different ways according to the size, complexity, level of detail, and restrictions of each monument using both high-resolution full-frame cameras and Unmanned Aircraft Systems (UAS) with low resolution multispectral cameras. The data acquisition process using the UAS can be challenging or even impossible to achieve due to several restrictions. The weather conditions may not make it possible to plan and execute a flight, the vegetation and terrain may also pose restrictions since the aircraft is not able to fly near any obstacles and high trees may cover the CH buildings leading to a lack of information. Other parameters that should be taken into consideration are the flight time limitation of the UAS and mostly the flight restrictions applied by each country, and the no-fly zones. In order to overcome these restrictions, other methods were applied, such as acquiring the digital procedures have been discussed. 2. 3D geometric documentation

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images with either hand-held cameras or with cameras mounted to a 9-meter-high photographic pole. Moreover, terrestrial laser scanning has been conducted to accurately determine the surface of the structures and provide completeness to the point clouds. A local reference coordinate system was set up at each area to conduct the necessary measurements with the minimum constraints in order to avoid the deformations of the shape or size of each monument due to the projection. The standard workflow was followed to process the acquired data as in every documentation process. First, the digital images were processed using an Image Based Modeling (IBM) software package, where the dense point clouds were generated and further processed. Then the scanned point clouds were registered, georeferenced, and further processed to reduce inevitable scanner errors in order to lead to a smoother and more accurate 3D model. Finally, the dense point clouds from the IBM software were used to fill eventual gaps in the scans and generate the final point cloud for each CH building. Each point object was converted to a polygon object using the triangulated irregular network (TIN) method for the representation. The whole procedure of developing the 3D model is presented in Fig. 1.

Fig. 1. Workflow of the holistic methodology for developing 3D models of the CH assets.

The development of the integrated and accurate 3D models was imperative because these models were used for the production of all other necessary products, such as 3D textured models, light 3D models, vertical and horizontal cross sections etc. The 3D textured models (see Fig. 2. (a)) were primarily used to identify and map the various materials at each CH building, while they were also combined with Hyperspectral images in order to detect the material loss and pathology. The light 3D models, as illustrated in Fig. 2. (b) were developed for visualization purposes and were decimated for this reason. Finally, the cross-sections (see Fig. 2. (c)) were necessary for the 3D finite element modeling as well as the production of 2D vector drawings.

(a) (c) Fig. 2. (a) 3D textured models; (b) Light 3D model of the Nailac tower in Rhodes, Greece; (c) Cross section of the Roman bridge in Rhodes, Greece. 3. 3D finite element modeling Masonry is composed of units and joints. The micro modeling approach is considered as the most detailed modeling strategy in which masonry units and mortar joints are simulated and connected via the interface elements. In the (b)

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simplified micro modeling approach, the units are expanded modeled (unit and half of the thickness of the mortar) and connected with interface elements by neglecting to model the mortar element independently. The macro modeling approach is considered as the third strategy that all the components are modeled as a homogenized and composite material. FE modeling of complex, full-scale structures considering homogenized material for masonry is widely used for structural vulnerability assessment of architectural heritage assets as highlighted by D’Altri et al. (2020) , which is also utilized for 3D modeling of the case studies in this paper. Lower computational effort and lower input data are the two main advantages of this modeling strategy compared to micro modeling methods. However, micro modeling approaches provide more accurate results that can be more representative of the actual behavior of masonry, as stated by Ferreira et al. (2019). As a traditional way, geometrical documentation of a structure is provided, and the FEM is developed for the Roman bridge case study in Rhodes, Greece as illustrated in Fig. 3. (a). The 3D FE model of the stone masonry bridge is composed of backfill soil, spandrel walls, arches, and parapets as depicted in Fig. 3. (b) and presented by Sarhosis et al. (2016).

(a)

(b)

Fig. 3. (a) The Roman bridge in Rhodes, Greece; (b) Different parts of the 3D FE model of the bridge.

Two plane interface element types are utilized in the model. Firstly, for the boundary conditions, a plane interface element is utilized with high stiffness in normal and lateral directions and zero stiffness in tension, as stated by Gönen & Soyöz (2021). Another interface contact element is employed to simulate the connectivity of the backfill soil and the masonry sections (spandrel walls and arches). This interface element is modeled with a tension cut-off strategy to simulate the zero stiffness in tension, and high stiffness values are considered for normal and lateral directions as employed by Gönen & Soyöz (2021). A high normal stiffness value should be implemented to avoid overlapping of the backfill soil and the masonry structural media (interpenetration of interface element nodes). If a connection is defined for a particular shape part, DIANA (2020) interprets that shape part to be disconnected from all other shape parts unless explicitly defined. It should be noted that by modeling interface elements if three elements are connected, as illustrated in Fig. 2. (a), three sets of nodes exist at the connection location. Two sets are connected with the interface elements and another node set is disconnected. Therefore, as illustrated in Fig.4. (a), the disconnected faces must be tied together by means of unite connections. Unite connections are utilized to connect the arch and spandrel sections where three sets of coincident nodes exist due to modeling the interface elements to connect

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backfill soil and the masonry parts. Adaptive mesh size of 0.5 m is considered, and FE mesh of the bridge is illustrated in Fig. 4. (b).

Fig. 4. (a) An example of the assembly of the interface elements and unite connection; (b) 3D mesh of the Roman bridge.

Developing 3D models in a CAD software package is more accurate than the previous method employed for 3D FE modeling of the Slottsfjell tower in Tønsberg, Norway, as shown in Fig. 5. (a). To perform the geometrical survey, a Topcon 2000 3D laser scanner was utilized. Twenty scans were performed inside and outside of the tower to provide the 3D point clouds. Point clouds were imported to the ReCap (2021) software and were merged to provide the 3D dense point clouds, as illustrated in Fig. 5. (b). Afterward, the 3D dense point cloud file was imported to Revit (2021) software package as depicted in Fig. 5. (c) and a 3D model of the tower was developed in the versatile environment of Revit software as shown in Fig.5. (d). Note that for this case study, the digital images were not provided, and the 3D model was developed based on the 3D point clouds from the laser scanners.

(a) (d) Fig. 5. (a) The Slottsfjel tower in Tønsberg, Norway; (b) 3D dense point clouds in Recap software; (c) Imported 3D point cloud to Revit software; (d) Developed 3D model of the tower in Revit software. To develop the 3D FEM of the tower, the industry foundation classes (IFC) format of the 3D model was exported, and by means of the CAD exchanger software, the IFC format file was converted to the standard for the exchange of product model data (STEP) format which is suitable for importing 3D models with solid elements in DIANA (2020) software. Imported CAD files may need to be repaired before generating mesh as discussed by Ademi (2020). There are (unintended) small entities, small edges, duplicate curves, and surfaces, for example, in a model that makes generating high-quality mesh difficult or even impossible. Three tools are available to remove small entities, clean and optimize the geometric model in DIANA (2020). The cleaning tool was utilized to find and repair the shapes, including self-intersecting surfaces, small edges, discontinuities, etc. The geometry was simplified by means of the optimization tool. Edge inaccuracies were healed, duplicate curves and surfaces, and redundant edges and vertices (b) (c)

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were removed. Furthermore, small entities such as small faces, silver faces (a face with a high aspect ratio and a small area), gashes (a gash is a set of connected laminar edges where each edge is within the tolerance of the other edges in the set) etc. were removed using the removal of small entities tool. Fig.6. (a) and (b) show the imported STEP file to the DIANA (2020) software before and after healing, and Fig. 6. (c) depicts the FEM mesh of the tower with a maximum mesh size of 0.2 m. Furthermore, the procedure of converting the point clouds derived from the 3D laser scanners to the 3D FEM is illustrated in Fig. 7.

(a) (c) Fig. 6. (a) Imported 3D model in DIANA software; (b) Modified 3D FE model of the Tower; (c) 3D mesh of the tower model. (b)

Fig. 7. The workflow utilized for converting the point clouds derived from the 3D laser scanners to the 3D mesh of the FE model.

4. Conclusion A holistic methodology is presented in this paper for providing 3D documentation of CH assets. Digital images composing aerial and ground images are imported to IBM software to be processed, and laser scanners are utilized to provide the point clouds. Georeferencing of data is carried out to avoid the deformations of the shape or size of each monument due to the projection for both sets of data. Afterward, 3D dense point clouds from the digital images are processed with the point clouds from the scanners to fill the possible gaps and developing the final 3D point clouds. 3D models are then provided by means of the TIN method. 3D textured models, light 3D models, vertical and horizontal cross-sections are the production of the 3D models in the previous step. FE modeling of two CH assets is investigated so that for the Roman bridge, 3D FE models were made in FE software utilizing the dimensions derived from the light 3D models or the cross-sections. However, in a more efficient way, the 3D model of the Slottsfjel tower was developed in CAD software based on the point clouds and then imported to the DIANA software. Various tools exist in the DIANA software to clean, simplify, and modify the imported STEP format files used to prepare the 3D FE model of the tower. The procedure utilized for making the 3D FE model of the tower is more efficient and accurate compared to the traditional procure utilized for the bridge. Moreover, the methodology is recommended for developing the digital twin of CH assets with complex architecture.

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Acknowledgements This work is a part of the HYPERION project. HYPERION has received funding from the European U nion’s Framework Programme for Research and Innovation (Horizon 2020) under grant agreement No 821054. The contents of this publication are the sole responsibility of OsloMet and NTUA and do not necessarily reflect the opinion of the European Union. References Ademi, A. (2020). Finite element model updating of a stone masonry tower using 3D laser scanner and accelerometers. (Master of Science Thesis). Oslo Metropolitan University, Oslo, Norway. Angjeliu, G., Coronelli, D., & Cardani, G., 2020. Development of the simulation model for Digital Twin applications in historical masonry buildings: The integration between numerical and experimental reality. Computers & Structures , 238, 106282. doi:https://doi.org/10.1016/j.compstruc.2020.106282 Bartoli, G., Betti, M., Bonora, V., Conti, A., Fiorini, L., Kovacevic, V. C., Tesi, V., & Tucci, G., 2020. From TLS data to FE model: a workflow for studying the dynamic behavior of the Pulpit by Giovanni Pisano in Pistoia (Italy). Procedia Structural Integrity , 29, 55-62. doi:https://doi.org/10.1016/j.prostr.2020.11.139 Bartoli, G., Betti, M., &Vignoli, A., 2016. A numerical study on seismic risk assessment of historic masonry towers: a case study in San Gimignano. Bulletin of Earthquake Engineering , 14(6), 1475-1518. doi:10.1007/s10518-016-9892-9 Castellazzi, G., Altri, A. M., Bitelli, G., Selvaggi, I., & Lambertini, A., 2015. From Laser Scanning to Finite Element Analysis of Complex Buildings by Using a Semi-Automatic Procedure. Sensors , 15(8). doi:https://doi.org/10.3390/s150818360 Castellazzi, G., D’Altri, A. M., de Miranda, S., & Ubertini, F., 2017. An innovative numerical modeling strategy for the structural analysis of historical monumental buildings. Engineering Structures , 132, 229-248. doi:https://doi.org/10.1016/j.engstruct.2016.11.032 D’Altri, A. M., Sarhosis, V., Milani, G., Rots, J., Cattari, S., Lagomarsino, S., Sacco, E., Tralli, A., Castellazzi, G., & d e Miranda, S., 2020. Modeling Strategies for the Computational Analysis of Unreinforced Masonry Structures: Review and Classification. Archives of Computational Methods in Engineering , 27(4), 1153-1185. doi:10.1007/s11831-019-09351-x DIANA. 2020. DIANA FEA, Diana User’s Manual, Release 10.4. In DIANA FEA BV, Delft University of Technology, Netherland. Ferreira, T. M., Mendes, N., & Silva, R., 2019. Multiscale Seismic Vulnerability Assessment and Retrofit of Existing Masonry Buildings. Buildings , 9(4), 91. Retrieved from https://www.mdpi.com/2075-5309/9/4/91 Georgopoulos, A., & Stathopoulou, E. K., 2017. Data acquisition for 3D geometric recording: state of the art and recent innovations. Heritage and archaeology in the digital age, 1-26. Gönen, S., & Soyöz, S., 2021. Seismic analysis of a masonry arch bridge using multiple methodologies. Engineering Structures , 226, 111354. doi:https://doi.org/10.1016/j.engstruct.2020.111354 Kassotakis, N., & Sarhosis, V., 2021. Employing non-contact sensing techniques for improving efficiency and automation in numerical modelling of existing masonry structures: A critical literature review. Structures , 32, 1777-1797. doi:https://doi.org/10.1016/j.istruc.2021.03.111 Kolokoussis, P., Skamantzari, M., Tapinaki, S., Karathanassi, V., & Georgopoulos, A., 2021. D and Hyperspectral Data Integrat ion for Assessing Material Degradation in Medieval Masonry Heritage Buildings. ISPRS-International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences , 43, 583-590. Korumaz, M., Betti, M., Conti, A., Tucci, G., Bartoli, G., Bonora, V., Korumaz, A. G., & Fiorini, L., 2017. An integrated Terrestrial Laser Scanner (TLS), Deviation Analysis (DA) and Finite Element (FE) approach for health assessment of historical structures. A minaret case study. Engineering Structures , 153, 224-238. doi:https://doi.org/10.1016/j.engstruct.2017.10.026 MIDAS. 2021. MIDASoft, Inc. New York, United States. In. Panah, R. S., & Kioumarsi, M., 2021. Application of Building Information Modelling (BIM) in the Health Monitoring and Maintenance Process: A Systematic Review. Sensors , 21(3), 837. Retrieved from https://www.mdpi.com/1424-8220/21/3/837 Pepi, C., Cavalagli, N., Gusella, V., & Gioffrè, M., 2021. An integrated approach for the numerical modeling of severely damaged historic structures: Application to a masonry bridge. Advances in Engineering Software , 151, 102935. doi:https://doi.org/10.1016/j.advengsoft.2020.102935 ReCap. 2021. Autodesk, ReCap Pro, California, U.S. In. Revit. 2021. Autodesk, Revit BIM (Building Information Modeling), California, U.S. In. Sarhosis, V., De Santis, S., & de Felice, G., 2016. A review of experimental investigations and assessment methods for masonry arch bridges. Structure and Infrastructure Engineering , 12(11), 1439-1464. Shabani, A., Hosamo, H., Plevris, V., & Kioumarsi, M., 2021. A Preliminary Structural Survey of Heritage Timber Log Houses in Tønsberg, Norway. Paper presented at the 12th International Conference on Structural Analysis of Historical Constructions (SAHC 2021), Spain. Shabani, A., Kioumarsi, M., Plevris, V., & Stamatopoulos, H., 2020. Structural Vulnerability Assessment of Heritage Timber Buildings: A Methodological Proposal. Forests , 11(8), 881. doi:https://doi.org/10.3390/f11080881 Shabani, A., Kioumarsi, M., & Zucconi, M., 2021. State of the art of simplified analytical methods for seismic vulnerability assessment of unreinforced masonry buildings. Engineering Structures , 239, 112280. doi:https://doi.org/10.1016/j.engstruct.2021.112280 Tobiasz, A., Markiewicz, J., Łapiński, S., Nikel, J., Kot, P., & Muradov, M., 2019. Review of Methods for Documentation, Mana gement, and Sus tainability of Cultural Heritage. Case Study: Museum of King Jan III’s Palace at Wilanów. Sustainability , 11(24), 7046.

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Procedia Structural Integrity 37 (2022) 788–795 Structural Integrity Procedia 00 (2022) 000–000 Structural Integrity Procedia 00 (2022) 000–000

www.elsevier.com / locate / procedia www.elsevier.com / locate / procedia

© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira Abstract Confinement of concrete columns with fiber reinforced polymers results in an increase of strength and ductility. For this reason, the use of aramid, carbon and glass-based composites for confinement of reinforced concrete columns has significantly increased over the last decades. Nevertheless, few models adequately predict the failure strain of the fiber reinforced polymer, which has a determinant influence on the computed results. In this paper the accuracy of existing models of confined concrete using di ff erent proposals for the prediction of the failure strain of the confining composite is assessed. This is based on the comparison of analytical results with experimental test results of concrete columns with circular cross-section reported in the literature. The comparison focusses on di ff erent parameters such as strength, maximum strain and strain energy density. 2022 The Authors. Published by Elsevier B.V. is is an open access article under the CC BY-NC-ND license (http: // creativec mmons.org / licenses / by-nc-nd / 4.0 / ) er-review under responsibility of Pedro Mig el Guimaraes Pi s Moreira. Keywords: Fiber Reinforced Polymers ; Failure Strain ; Concrete Confinement ICSI 2021 The 4th International Conference on Structural Integrity Accuracy of models of concrete in circular columns using di ff erent proposals for the prediction of failure of the confining FRP Paulo Silva Lobo a,b , Mariana Jesus a,c, ∗ a CERIS, Instituto Superior Te´cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal b Departamento de Engenharia Civil e Geologia, Faculdade de Cieˆncias Exatas e da Engenharia, Universidade da Madeira, Campus Universita´rio da Penteada, 9020-105 Funchal, Portugal c DEC, NOVA School of Science and Technology, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal Abstract Confinement of concrete columns with fiber reinforced polymers results in an increase of strength and ductility. For this reason, the use of aramid, carbon and glass-based composites for confinement of reinforced concrete columns has significantly increased over the last decades. Nevertheless, few models adequately predict the failure strain of the fiber reinforced polymer, which has a determinant influence on the computed results. In this paper the accuracy of existing models of confined concrete using di ff erent proposals for the prediction of the failure strain of the confining composite is assessed. This is based on the comparison of analytical results with experimental test results of concrete columns with circular cross-section reported in the literature. The comparison focusses on di ff erent parameters such as strength, maximum strain and strain energy density. © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira. Keywords: Fiber Reinforced Polymers ; Failure Strain ; Concrete Confinement ICSI 2021 The 4th International Conference on Structural Integrity Accuracy of models of concrete in circular columns using di ff erent proposals for the prediction of failure of the confining FRP Paulo Silva Lobo a,b , Mariana Jesus a,c, ∗ a CERIS, Instituto Superior Te´cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal b Departamento de Engenharia Civil e Geologia, Faculdade de Cieˆncias Exatas e da Engenharia, Universidade da Madeira, Campus Universita´rio da Penteada, 9020-105 Funchal, Portugal c DEC, NOVA School of Science and Technology, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

1. Introduction 1. Introduction

The confinement with externally applied fiber reinforced polymers (FRP) results in notorious improvement of ductility and strength. For this reason, the use of FRP-based composites for the confinement of reinforced concrete columns has significantly increased over the last decades. Confinement has been studied with great emphasis in recent years, particularly regarding the behaviour of reinforced concrete columns confined with aramid fiber reinforced polymers (AFRP), carbon fiber reinforced polymers (CFRP) and glass fiber reinforced polymers (GFRP) sheets. The first studies regarding confinement of columns were presented by Richard and Abbott (1975) and Mander et al. (1988), who proposed the first equations to compute the maximum strength, the axial strain and the behaviour of FRP confined columns. In the following studies FRP models were categorized in two main groups, namely theoretical The confinement with externally applied fiber reinforced polymers (FRP) results in notorious improvement of ductility and strength. For this reason, the use of FRP-based composites for the confinement of reinforced concrete columns has significantly increased over the last decades. Confinement has been studied with great emphasis in recent years, particularly regarding the behaviour of reinforced concrete columns confined with aramid fiber reinforced polymers (AFRP), carbon fiber reinforced polymers (CFRP) and glass fiber reinforced polymers (GFRP) sheets. The first studies regarding confinement of columns were presented by Richard and Abbott (1975) and Mander et al. (1988), who proposed the first equations to compute the maximum strength, the axial strain and the behaviour of FRP confined columns. In the following studies FRP models were categorized in two main groups, namely theoretical

∗ Corresponding author. E-mail address: mc.jesus@campus.fct.unl.pt ∗ Corresponding author. E-mail address: mc.jesus@campus.fct.unl.pt

2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira 10.1016/j.prostr.2022.02.010 2210-7843 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under re ponsibility of Pedro Miguel Guimaraes Pires Morei a. 2210-7843 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira.

Paulo Silva Lobo et al. / Procedia Structural Integrity 37 (2022) 788–795 Silva Lobo and Jesus / Structural Integrity Procedia 00 (2022) 000–000

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models, based on physical concepts, that use an incremental numeric procedure to obtain stress-strain curves, and, design-oriented models, obtained through calibration of the parameters that influence the stress-strain curve, using experimental results. Numerical implementation of theoretical models is usually more complex, making it possible to determine the stress-strain curve until failure of the FRP, while design-oriented models are easier to implement, resulting in adequate predictions of strength and ultimate strain of confined concrete columns. The theoretical model proposed by Spoelstra and Monti (1999) for monotonic loading of concrete columns confined with FRP describes the stress-strain relationship based on the equation by Popovics (1973), which considers the increase of the lateral confining pressure with the increase of the axial load, being the maximum confining stress obtained through an equation proposed by Mander et al. (1988). The design-oriented models by Chastre and Silva (2010) for CFRP, by Jesus et al. (2018) for GFRP and by Silva Lobo et al. (2018) for AFRP are based on a constitutive model for circular columns based on the stress-strain re lationship by Richard and Abbott (1975). For each of these models, the authors calibrated the required parameters mainly based on experimental results found in the literature. Also, the peak strength is obtained through the equation proposed by Mander et al. (1988). Regarding the design-oriented models by Lam and Teng (2003a) and by Wei and Wu (2012) for FRP, only the stress-axial strain relationship was proposed, and in both models the peak stress is based on the equation proposed by Mander et al. (1988). The stress-axial strain relationship of the model by Lam and Teng (2003a) was obtained through calibration of the parameters of the model by Spoelstra and Monti (1999), and the stress-axial strain relationship of the model by Wei and Wu (2012) was obtained through calibration of the parameters of the models by Lam and Teng (2003a,b, 2004). In the present work, the accuracy of both theoretical and design-oriented models were assessed with di ff erent proposals for the prediction of failure of the FRP.

2. Experimental tests from the literature

The experimental results of circular columns confined with AFRP chosen for comparison with results obtained with the mentioned numerical models are from Dai et al. (2011) (AT2, a set of three equal specimens with the same char acteristics), Wu et al. (2008) (AF2) , Silva Lobo et al. (2018) (AC) and Vincent and Ozbakkaloglu (2013) (NWE90, a set of three equal specimens with the same characteristics). For CFRP, the experimental results considered are from Toutanji (1999) (C1 and C5) and Berthet et al. (2005). Regarding GFRP, the experimental tests considered are those by Toutanji (1999) (GE), Lam and Teng (2004) (G1 and G2, a set of two equal specimens with the same characteristics) and Silva and Chastre (2006) (EE75C). The main properties of the specimens considered can be found in Table 1.

Table 1. Experimental results Author

Specimen Geometry

FRP Properties

Concrete Properties

E j [GPa]

f co [MPa]

f cc [MPa]

D [mm]

t j [mm]

ε ju [%]

ε lu [%]

ε co [%]

ε cc [%]

type no. layers

Wu et al. (2008) Dai et al. (2011)

AF2 AT2

150 150 150 200 160 160 152 152 250 76 76 76

AFRP AFRP AFRP AFRP CFRP CFRP CFRP CFRP GFRP GFRP GFRP GFRP

1 2 3 1 2 2 1 2 2 1 2 2

0.29 115 2.0 2.5 23.1 0.27 50.7 3.03 0.17 115 3.2 3.0 39.2 0.33 88.9 3.45 0.20 116 2.5 2.2 49.4 0.24 106.2 3.02 0.20 120 2.3 2.3 18.9 0.49 36.9 2.73 0.11 231 1.5 1.3 30.9 0.19 95.0 2.45 0.17 373 0.8 0.6 30.9 0.19 94.0 1.55 0.17 230 1.4 1.0 25.0 0.23 42.8 1.63 0.17 230 1.4 0.9 25.0 0.23 55.2 1.73

Vincent and Ozbakkaloglu (2013)

NWE90

Silva Lobo et al. (2018)

AC C1 C5

Toutanji (1999) Toutanji (1999)

Berthet et al. (2005) Berthet et al. (2005)

C20C1 C20C2

Toutanji (1999)

GE G1 G2

0.12 1.27 1.27 1.27

73 22 22 21

2.1 1.6 29.9 0.19 60.8 1.53 1.6 1.5 38.5 0.20 55.1 1.39 1.6 1.6 38.5 0.20 76.5 2.33 2.2 0.6 26.5 0.19 55.8 1.10

Lam and Teng (2004) Lam and Teng (2004) Silva and Chastre (2006)

EE75C

D is the diameter of the cross-section, no . layers is a reference to the number of layers of FRP used, t j is the design thickness of one FRP sheet, E j is the Young’s modulus of the FRP, ε ju is the ultimate strain provided by the manufacturer, ε lu is the observed experimental failure strain, f co is the unconfined concrete strength, ε co is the strain corresponding to f co , f cc is the peak strength and ε cc is the strain corresponding to f cc .

Paulo Silva Lobo et al. / Procedia Structural Integrity 37 (2022) 788–795 Silva Lobo and Jesus / Structural Integrity Procedia 00 (2022) 000–000

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3. Comparison of numerical and experimental results

The accuracy of models of confined concrete using di ff erent proposals for the prediction of the failure strain of the confining composite is assessed herein. The comparison between numerical results and experimental tests focus on the analysis of di ff erent parameters such as f cc , ε cc and strain energy density ( W ) for all three FRP. Each model was combined with the equations for the prediction of the FRP lateral failure strain found in literature, presented in Table 2.

Table 2. Equations of ε lu / ε ju for columns with circular cross-section. Author ε lu /ε ju Note: Arabshahi et al. (2020) 0 . 83 − 2 × f co E j (1) for AFRP Benzaid et al. (2010) 0.73 (2) for CFRP Ilky et al. (2004) 0.79 (3) for CFRP Lam and Teng (2003a) (4)

0.586 0.788 0.851 0.624 0.632 0.685

for CFRP for HM CFRP

for AFRP for GFRP for FRP for FRP

Manfredi and Realfonzo (2001)

(5) (6) (7) (8) (9)

Matthys et al. (2005)

0.60

for CFRP and GFRP

0 . 9 − 0 . 75 × E j

2 . 3 × f co 10 3

for FRP

Ozbakkaloglu and Lim (2013)

10 6 −

Silva Lobo et al. (2018) Toutanji et al. (2010)

0.85 0.43

for AFRP for FRP

Vincent and Ozbakkaloglu (2013)

0.737 0.656 0.548

(10)

for NSC and CFRP for HSC and CFRP for UHSC and CFRP

The error of each numerical models compared to the experimental results, regarding f cc and ε cc , for columns with circular cross-section confined with AFRP is presented in Table 3. The error, in general, can be obtained by

t v − n v

100

(1)

error (%) =

t v ×

were t v is the value of the experimental test and n V is the value of the numerical model.

Table 3. Error of model predictions compared to experimental results for columns confined with AFRP. Equation (1) Equation (4) Equation (5) Equation (7)

Equation (8)

Equation (9)

f cc

f cc

f cc

f cc

f cc

Specimen Model

f cc

ε cc

ε cc

ε cc

ε cc

ε cc

ε cc

AC Spoelstra and Monti (1999) -9.89 -170.70 -11.13 -182.42 -3.03 -112.09 -12.74 -198.17 -11.09 -182.05 11.81 -16.12 Lam and Teng (2003a) 4.54 -38.83 3.09 -43.96 12.00 -13.55 1.18 -50.55 3.14 -43.59 25.67 26.74 Wei and Wu (2012) 16.79 -35.90 15.81 -38.46 21.88 -22.34 14.51 -41.76 15.85 -38.46 31.40 4.40 Silva Lobo et al. (2018) -3.20 -3.30 -4.20 -6.59 2.14 13.92 -5.51 -10.99 -4.17 -6.59 12.84 45.42 AF2 Spoelstra and Monti (1999) -2.05 -74.92 -3.32 -83.50 3.97 -38.28 -4.68 -93.07 -3.27 -83.17 17.56 23.43 Lam and Teng (2003a) -3.35 -17.82 -5.49 -23.43 6.20 5.61 -7.96 -30.03 -5.41 -23.43 24.16 44.22 Wei and Wu (2012) 21.05 32.01 19.89 30.69 26.27 38.61 18.56 29.04 19.93 30.69 36.25 52.15 Silva Lobo et al. (2018) -5.78 -11.22 -7.05 -15.51 -0.02 6.93 -8.51 -20.13 -7.01 -15.18 11.33 41.25 AT2 Spoelstra and Monti (1999) -1.16 -138.03 -3.10 -156.56 4.02 -93.73 -4.34 -169.02 -3.07 -156.27 17.62 -6.56 Lam and Teng (2003a) 17.27 14.58 14.98 8.78 22.96 28.76 13.48 4.73 15.03 8.78 35.23 55.69 Wei and Wu (2012) 20.26 39.48 18.28 37.74 25.22 44.40 16.98 36.29 18.33 37.74 36.10 55.98 Silva Lobo et al. (2018) 7.90 18.05 6.35 13.42 11.86 29.92 5.35 10.23 6.38 13.42 21.10 55.41 NWE90 Spoelstra and Monti (1999) -9.40 -59.20 -12.01 -75.12 -4.70 -33.67 -13.19 -82.75 -12.01 -75.12 9.76 24.71 Lam and Teng (2003a) -3.30 -5.14 -7.85 -15.75 4.11 11.77 -9.94 -20.73 -7.78 -15.75 22.49 48.26 Wei and Wu (2012) 13.29 52.90 10.28 50.91 18.26 56.22 8.92 49.92 10.33 50.91 30.74 64.84 Silva Lobo et al. (2018) -7.13 -7.79 -9.84 -16.42 -2.68 5.80 -11.05 -20.40 -9.81 -16.42 8.90 39.97 The stress-strain curves for columns confined with AFRP were analysed for the models with lower error values of f cc and ε cc (see Fig. 1). The comparison of the W of the models with the W of the experimental test, for the smaller error value of f cc and ε cc , are presented in Table 4. Regarding the specimen AC, the stress-axial strain curve and the stress-lateral strain curve of the model by Silva Lobo et al. (2018) coupled with equations (1) and (7) presents a similar behaviour and almost coincident with the