{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:05:11Z","timestamp":1760058311402,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Foundation for Science and Technology","award":["UIDB\/04625\/2020"],"award-info":[{"award-number":["UIDB\/04625\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Buildings"],"abstract":"<jats:p>Traditional stone masonry walls are structural elements in most historic buildings. To preserve them and improve their ability to withstand extreme events, such as earthquakes, it is necessary to implement effective reinforcement solutions. This paper presents the modeling of traditional Portuguese rubble stone masonry walls, reinforced with external steel mesh, sprayed micro-concrete layers and transverse confinement by steel connectors, which were developed and tested experimentally in uniaxial compression. The modeling is carried out using micro-modeling through a 2D particle model (PM). The process of calibrating the properties of both micro-concrete and concrete is presented, the methodology for generating the numerical models is described and the numerical response is compared with the experimental results. The numerical results show that the PM can adequately reproduce the experimentally observed behavior of this type of reinforcement solution.<\/jats:p>","DOI":"10.3390\/buildings15071058","type":"journal-article","created":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T12:18:52Z","timestamp":1742905132000},"page":"1058","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Modeling of Reinforcement Solutions in Traditional Stone Masonry Using a Particle Model"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8838-3760","authenticated-orcid":false,"given":"Nuno Monteiro","family":"Azevedo","sequence":"first","affiliation":[{"name":"Concrete Dams Department, Laborat\u00f3rio Nacional de Engenharia Civil (LNEC), 1700-066 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7662-1215","authenticated-orcid":false,"given":"Ildi","family":"Cisma\u015fiu","sequence":"additional","affiliation":[{"name":"CERIS and Department of Civil Engineering, NOVA School of Science and Technology|FCT-NOVA, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0344-1867","authenticated-orcid":false,"given":"Fernando F. S.","family":"Pinho","sequence":"additional","affiliation":[{"name":"CERIS and Department of Civil Engineering, NOVA School of Science and Technology|FCT-NOVA, 2829-516 Caparica, Portugal"}]},{"given":"Filipe","family":"Neves","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, NOVA School of Science and Technology|FCT-NOVA, 2829-516 Caparica, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Roca, P., Louren\u00e7o, P.B., and Gaetani, A. (2019). Historic Construction and Conservation: Materials, Systems and Damage, Routledge.","DOI":"10.1201\/9780429052767"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1492","DOI":"10.1080\/15583058.2019.1702738","article-title":"Influence of bond pattern on the in-plane behavior of URM piers","volume":"15","author":"Malomo","year":"2021","journal-title":"Int. J. Arch. Herit."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105269","DOI":"10.1016\/j.jobe.2022.105269","article-title":"Probabilistic approach to assess URM walls with openings using discrete rigid block analysis (D-RBA)","volume":"61","author":"Pulatsu","year":"2022","journal-title":"J. Build. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s10518-011-9280-4","article-title":"Rubble stone masonry walls in Portugal strengthened with reinforced micro-concrete layers","volume":"10","author":"Pinho","year":"2012","journal-title":"Bull. Earthq. Eng."},{"key":"ref_5","unstructured":"Coburn, A., and Spence, R. (1992). Earthquake Protection, John Wiley & Sons."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.conbuildmat.2018.11.246","article-title":"Destructive and minor destructive tests on masonry buildings: Experimental results and comparison be-tween shear failure criteria","volume":"199","author":"Ferretti","year":"2019","journal-title":"Constr. Build. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"108904","DOI":"10.1016\/j.soildyn.2024.108904","article-title":"Seismic performance of masonry structures after 06 February 2023 earthquakes; site survey and FE modelling approach","volume":"186","author":"Avcil","year":"2024","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3863","DOI":"10.1007\/s10518-020-00834-y","article-title":"Nepal earthquake: Seismic performance and post-earthquake reconstruction of stone in mud mortar masonry buildings","volume":"18","author":"Adhikari","year":"2020","journal-title":"Bull. Earthq. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1193\/010817eqs009m","article-title":"Damage reconnaissance of unreinforced masonry buildings after the 2015 Gorkha, Nepal, earthquake","volume":"33","author":"Brando","year":"2017","journal-title":"Earthq. Spectra"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5583","DOI":"10.1007\/s10518-018-0370-4","article-title":"Seismic behaviour of ordinary masonry buildings during the 2016 central Italy earthquakes","volume":"17","author":"Sorrentino","year":"2019","journal-title":"Bull. Earthq. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"104803","DOI":"10.1016\/j.engfailanal.2020.104803","article-title":"Learning from failure: Damage and failure of masonry structures, after the 2017 Lesvos earthquake (Greece)","volume":"11","author":"Vlachakis","year":"2020","journal-title":"Eng. Fail. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bilgin, H., Leti, M., Shehu, R., \u00d6zmen, H.B., Deringol, A.H., and Ormeni, R. (2023). Reflections from the 2019 Durr\u00ebs Earthquakes: An Earthquake Engineering Evaluation for Masonry Typologies. Buildings, 13.","DOI":"10.3390\/buildings13092227"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2306","DOI":"10.1177\/87552930241260263","article-title":"Damage to stone masonry buildings in historical centers due to the 2023 earthquake sequence in Turkey","volume":"40","author":"Vintzileou","year":"2024","journal-title":"Earthq. Spectra"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.3390\/heritage3040065","article-title":"The Failure of Masonry Walls by Disaggregation and the Masonry Quality Index","volume":"3","author":"Borri","year":"2020","journal-title":"Heritage"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s10518-010-9209-3","article-title":"Experimental testing, numerical modeling and seismic strengthening of traditional stone masonry: Comprehensive study of a real azorean pier","volume":"10","author":"Costa","year":"2012","journal-title":"Bull. Earthq. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"107428","DOI":"10.1016\/j.soildyn.2022.107428","article-title":"Seismic upgrading of existing masonry structures: A state-of-the-art review","volume":"161","author":"Gkournelos","year":"2022","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"137380","DOI":"10.1016\/j.conbuildmat.2024.137380","article-title":"Assessment, repair, and retrofitting of masonry structures: A comprehensive review","volume":"442","author":"Keshmiry","year":"2024","journal-title":"Constr. Build. Mater."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1617\/s11527-012-9832-3","article-title":"Strengthening of three-leaf stone masonry walls: An experimental research","volume":"45","author":"Oliveira","year":"2012","journal-title":"Mater. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Costa, A., Ar\u00eade, A., and Varum, H. (2018). Strengthening of Stone and Brick Masonry Buildings. Strengthening and Retrofitting of Existing Structures, Building Pathology and Rehabilitation; Springer.","DOI":"10.1007\/978-981-10-5858-5"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"114432","DOI":"10.1016\/j.engstruct.2022.114432","article-title":"Cyclic in-plane behavior of un-reinforced and confined masonry walls retrofitted by shotcrete: Experimental investigation","volume":"264","author":"Rezaee","year":"2022","journal-title":"Eng. Struct."},{"key":"ref_21","unstructured":"Pinho, F.F.S. (2007). Paredes de alvenaria ordin\u00e1ria\u2014Estudo experimental com modelos simples e refor\u00e7ados, Tese de doutoramento em Engenharia Civil\u2014Ci\u00eancias da Constru\u00e7\u00e3o. [Ph.D. Thesis, FCT NOVA]. (In Portuguese)."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1080\/15583058.2013.878413","article-title":"Rubble Stone Masonry Walls Strengthened By Three-dimensional Steel Ties and Textile Reinforced Mortar Render, under Compression and Shear Loads","volume":"9","author":"Pinho","year":"2015","journal-title":"Int. J. Archit. Herit."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1007\/s10518-014-9659-0","article-title":"Seismic assessment of existing and strengthened stone-masonry buildings: Critical issues and possible strategies","volume":"13","author":"Penna","year":"2015","journal-title":"Bull. Earthq. Eng."},{"key":"ref_24","first-page":"685","article-title":"Rubble stone masonry walls. Material properties, carbonation depth and mechanical characterization","volume":"11","author":"Pinho","year":"2017","journal-title":"Int. J. Archit. Herit."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1002\/pse.120","article-title":"Computations of historical masonry constructions","volume":"4","year":"2002","journal-title":"Prog. Struct. Eng. Mater."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1007\/s11831-019-09351-x","article-title":"Modeling Strategies for the Computational Analysis of Unreinforced Masonry Structures: Review and Classification","volume":"27","author":"Sarhosis","year":"2020","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ibrahim, Y., Nagy, B., and Benedek, C. (2020). Deep Learning-Based Masonry Wall Image Analysis. Remote Sens., 12.","DOI":"10.3390\/rs12233918"},{"key":"ref_28","unstructured":"Endo, Y., and Hanazato, T. (2024). Micro Modeling of Irregular Stone Masonry Walls Using Mathematical Programming. Structural Analysis of Historical Constructions, Springer."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.ijsolstr.2017.02.014","article-title":"Micro-mechanical finite element modeling of diagonal compression test for historical stone masonry structure","volume":"112","author":"Zhang","year":"2017","journal-title":"Int. J. Solids Struct."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.conbuildmat.2018.06.085","article-title":"A 2D typology generator for historical masonry elements","volume":"184","author":"Zhang","year":"2018","journal-title":"Construct. Build. Mater."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s11831-010-9046-1","article-title":"Structural analysis of masonry historical constructions. Classical and advanced approaches","volume":"17","author":"Roca","year":"2010","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_32","first-page":"660","article-title":"Multisurface Interface Model for Analysis of Masonry Structures","volume":"123","author":"Rots","year":"1997","journal-title":"J. Eng. Mech."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Pande, G., Middleton, J., and Kralj, B. (1998). Discrete element modelling of the seismic behaviour of stone masonry arches. Computer Methods in Structural Masonry\u20144 Fourth International Symposium, CRC Press. [1st ed.].","DOI":"10.4324\/9780203223147"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Azevedo, N.M., Lemos, J.V., and Rocha, J.d.A. (2016). Discrete Element Particle Modelling of Stone Masonry. Computational Modeling of Masonry Structures Using the Discrete Element Method, IGI Global.","DOI":"10.4018\/978-1-5225-0231-9.ch007"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.compstruc.2018.06.003","article-title":"A detailed micro-modelling approach for the structural analysis of masonry assemblages","volume":"206","author":"Sarhosis","year":"2018","journal-title":"Comput. Struct."},{"key":"ref_36","first-page":"730","article-title":"Seismic Vulnerability Assessment of a Stone Arch Using Discrete Elements","volume":"17","author":"Silva","year":"2021","journal-title":"Int. J. Archit. Herit."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.engstruct.2013.02.010","article-title":"A combined finite-discrete element analysis of dry stone masonry structures","volume":"52","year":"2013","journal-title":"Eng. Struct."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1007\/s40571-019-00286-5","article-title":"Structural applications of the combined finite\u2013discrete element method","volume":"7","author":"Munjiza","year":"2020","journal-title":"Comput. Part. Mech."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"608","DOI":"10.3390\/applmech3020036","article-title":"A Hybrid Particle\/Finite Element Model with Surface Roughness for Stone Masonry Analysis","volume":"3","author":"Azevedo","year":"2022","journal-title":"Appl. Mech."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1007\/s11803-023-2198-4","article-title":"Numerical simulation on the seismic performance of retrofitted masonry walls based on the combined finite-discrete element method","volume":"22","author":"Wu","year":"2023","journal-title":"Earthq. Eng. Eng. Vib."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2839","DOI":"10.1007\/s40571-024-00757-4","article-title":"Simulating the damage of rubble stone masonry walls using FDEM with a detailed micro-modelling approach","volume":"11","author":"Chen","year":"2024","journal-title":"Comput. Part. Mech."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"411","DOI":"10.12989\/sem.2006.24.4.411","article-title":"Aggregate shape influence in the fracture be-haviour of concrete","volume":"24","author":"Azevedo","year":"2006","journal-title":"Struct. Eng. Mech."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"343","DOI":"10.12989\/sem.2010.36.3.343","article-title":"A discrete particle model for reinforced concrete fracture analysis","volume":"36","author":"Azevedo","year":"2010","journal-title":"Struct. Eng. Mech."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1680\/geot.1979.29.1.47","article-title":"Discrete numerical model for granular assemblies","volume":"29","author":"Cundall","year":"1979","journal-title":"G\u00e9otechnique"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Azevedo, N.M., Fernando, F.F.S., Cismasiu, I., and Souza, M. (2022). Prediction of Rubble-Stone Masonry Walls Response under Axial Compression Using 2D Particle Modelling. Buildings, 12.","DOI":"10.3390\/buildings12081283"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Cisma\u015fiu, I., Azevedo, N.M., and Fernando, F.F.S. (2023). Numerical Evaluation of Transverse Steel Connector Strengthening Effect on the Behavior of Rubble Stone Masonry Walls under Compression Using a Particle Model. Buildings, 13.","DOI":"10.3390\/buildings13040987"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Milani, G., and Ghiassi, B. (2025). Particle-Based DEM to Assess Masonry Behaviour Under Compression. 18th International Brick and Block Masonry Conference, IB2MaC 2024. Lecture Notes in Civil Engineering; Springer.","DOI":"10.1007\/978-3-031-73310-9"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3337","DOI":"10.1016\/j.conbuildmat.2009.06.045","article-title":"Experimental characterization of stone masonry in shear and compression","volume":"23","author":"Vasconcelos","year":"2009","journal-title":"Constr. Build. Mater."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1617\/s11527-023-02126-8","article-title":"In-plane cyclic tests of strengthened rubble stone masonry","volume":"56","author":"Ponte","year":"2023","journal-title":"Mater. Struct."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/s41597-023-02417-3","article-title":"Geometrical digital twins of the as-built microstructure of three-leaf stone masonry walls with laser scanning","volume":"10","author":"Saloustros","year":"2023","journal-title":"Sci. Data"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"123626","DOI":"10.1016\/j.conbuildmat.2021.123626","article-title":"Updating mechanical properties of two-leaf stone masonry walls through experimental data and Bayesian inference","volume":"298","author":"Murano","year":"2021","journal-title":"Constr. Build. Mater."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"04021008","DOI":"10.1061\/AJRUA6.0001110","article-title":"Bayesian Methodology for Probabilistic Description of Mechanical Parameters of Masonry Walls","volume":"7","author":"Croce","year":"2021","journal-title":"ASCE-ASME J. Risk Uncertain. Eng. Syst. Part A Civ. Eng."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"107401","DOI":"10.1016\/j.compstruc.2024.107401","article-title":"Automatic calibration of a discrete element model of a masonry arch by swarm intelligence methods","volume":"299","author":"Kibriya","year":"2024","journal-title":"Comput. Struct."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1016\/j.compstruc.2004.03.041","article-title":"Implementation of a constitutive model for the cyclic behaviour of interface elements","volume":"82","author":"Oliveira","year":"2004","journal-title":"Comput. Struct."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1930","DOI":"10.1016\/j.engstruct.2009.02.046","article-title":"Finite element modelling of deformation characteristics of historical stone masonry shear wall","volume":"31","author":"Senthivel","year":"2009","journal-title":"Eng. Struct."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/0045-7949(94)90261-5","article-title":"Finite element prediction of masonry compressive strength","volume":"52","author":"Riddington","year":"1994","journal-title":"Comput. Struct."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s40571-018-0213-8","article-title":"Comparison between pure MPI and hybrid MPI-OpenMP parallelism for Discrete Element Method (DEM) of ellipsoidal and poly-ellipsoidal particles","volume":"6","author":"Yan","year":"2019","journal-title":"Comput. Part. Mech."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Dong, Y., Yan, D., and Cui, L. (2022). An Efficient Parallel Framework for the Discrete Element Method Using GPU. Appl. Sci., 12.","DOI":"10.3390\/app12063107"}],"container-title":["Buildings"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-5309\/15\/7\/1058\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:00:04Z","timestamp":1760029204000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-5309\/15\/7\/1058"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,25]]},"references-count":58,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["buildings15071058"],"URL":"https:\/\/doi.org\/10.3390\/buildings15071058","relation":{},"ISSN":["2075-5309"],"issn-type":[{"type":"electronic","value":"2075-5309"}],"subject":[],"published":{"date-parts":[[2025,3,25]]}}}