{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T08:48:43Z","timestamp":1774169323158,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,21]],"date-time":"2022-08-21T00:00:00Z","timestamp":1661040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Buildings"],"abstract":"<jats:p>To predict the structural behaviour of ancient stone masonry walls is still a challenging task due to their strong heterogeneity. A rubble-stone masonry modeling methodology using a 2D particle model (2D-PM), based on the discrete element method is proposed given its ability to predict crack propagation by taking directly into account the material structure at the grain scale. Rubble-stone (ancient) masonry walls tested experimentally under uniaxial compression loading conditions are numerically evaluated. The stone masonry numerical models are generated from a close mapping process of the stone units and of the mortar surfaces. A calibration procedure for the stone-stone and mortar-mortar contacts based on experimental data is presented. The numerical studies show that the 2D-PM wall models can predict the formation and propagation of cracks, the initial stiffness and the maximum load obtained experimentally in traditional stone masonry walls. To reduce the simulation times, it is shown that the wall lateral numerical model adopting a coarser mortar discretization is a viable option for these walls. The mortar behaviour under compression with lateral confinement is identified as an important micro-parameter, that influences the peak strength and the ductility of rubble-masonry walls under uniaxial loading.<\/jats:p>","DOI":"10.3390\/buildings12081283","type":"journal-article","created":{"date-parts":[[2022,8,21]],"date-time":"2022-08-21T21:05:51Z","timestamp":1661115951000},"page":"1283","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Prediction of Rubble-Stone Masonry Walls Response under Axial Compression Using 2D Particle Modelling"],"prefix":"10.3390","volume":"12","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\/0000-0003-0344-1867","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"}]},{"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"}]},{"given":"Murilo","family":"Souza","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":[[2022,8,21]]},"reference":[{"key":"ref_1","unstructured":"Pinho, F.F.S. (2007). Ordinary Masonry Walls\u2013Experimental Study with Unstrengthened and Strengthened Specimens. [Ph.D. Thesis, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa]. (In Portuguese)."},{"key":"ref_2","first-page":"685","article-title":"Rubble Stone Masonry Walls in Portugal: Material Properties, Carbonation Depth and Mechanical Characterization","volume":"11","author":"Pinho","year":"2017","journal-title":"Int. J. Archit. Herit."},{"key":"ref_3","first-page":"49","article-title":"Numerical simulation of cracking in structural masonry","volume":"36","author":"Rots","year":"1991","journal-title":"Heron"},{"key":"ref_4","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_5","doi-asserted-by":"crossref","unstructured":"Pande, G., Middleton, J., and Kralj, B. (1998). Discrete element modelling of the seismic behaviour of stone masonry arches. Proceedings of the Computer Methods in Structural Masonry\u20144 Fourth International Symposium, CRC Press. [1st ed.].","DOI":"10.4324\/9780203223147"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Azevedo, N.M., Lemos, J.V., and de Almeida, J.R. (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_7","doi-asserted-by":"crossref","first-page":"101850","DOI":"10.1016\/j.jobe.2020.101850","article-title":"Statistical analysis of mesoscopic concrete with random elastic modulus","volume":"33","author":"Luo","year":"2021","journal-title":"J. Build. Eng."},{"key":"ref_8","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_9","first-page":"150","article-title":"Numerical analysis of 3D dry-stone masonry structures by combined finite-discrete element method","volume":"136","author":"Munjiza","year":"2018","journal-title":"Int. J. Solids Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1080\/08905459708945496","article-title":"Limit Analysis for No-Tension and Frictional Three-Dimensional Discrete Systems","volume":"26","author":"Baggio","year":"1998","journal-title":"Mech. Struct. Mach."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1821","DOI":"10.1016\/S0045-7949(01)00102-X","article-title":"Computational framework for discontinuous modelling of masonry arch bridges","volume":"79","author":"Thavalingam","year":"2001","journal-title":"Comput. Struct."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1177\/1056789506064943","article-title":"Structural Damage Analysis of Masonry Walls using Computational Homogenization","volume":"16","author":"Massart","year":"2007","journal-title":"Int. J. Damage Mech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1007\/s00603-014-0601-1","article-title":"A Rigid Particle Model for Rock Fracture Following the Voronoi Tessellation of the Grain Structure: Formulation and Validation","volume":"48","author":"Azevedo","year":"2014","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"102558","DOI":"10.1016\/j.jobe.2021.102558","article-title":"Simulating the failure of masonry walls subjected to support settlement with the combined finite-discrete element method","volume":"43","author":"Chen","year":"2021","journal-title":"J. Build. Eng."},{"key":"ref_15","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_16","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 walls","volume":"31","author":"Senthivel","year":"2009","journal-title":"Eng. Struct."},{"key":"ref_17","unstructured":"Bergonse de Souza, M. (2019). Numerical Modeling of Ordinary Masonry Walls Using a Particle Model. [Master\u2019s Thesis, FCT UNL]. (In Portuguese)."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1016\/j.compstruc.2004.03.041","article-title":"Implementation and validation of a constitutive model for the cyclic behaviour of interface elements","volume":"82","author":"Oliveira","year":"2004","journal-title":"Comput. Struct."},{"key":"ref_19","unstructured":"Pinho, F.F.S. (2021). Structural Rehabilitation of Traditional Stone Masonry Walls, FCT Editorial. (In Portuguese)."},{"key":"ref_20","unstructured":"(1968). Aggregates Volumetric Ratio Determination (Standard No. E223:1968). (In Portuguese)."},{"key":"ref_21","unstructured":"(2008). Natural Stone Test Methods. Determination of Real Density and Apparent Density, and of Total and Open Porosity (Standard No. NP EN 1936:2008). (In Portuguese)."},{"key":"ref_22","unstructured":"(2000). Test Methods for Natural Stone. Determination of Compression Resistance (Standard No. NP EN 1926:2000). (In Portuguese)."},{"key":"ref_23","unstructured":"Veiga, M., Aguiar, J., Silva, A., and Carvalho, F. (2004). Conservation and Renovation of Ancient Building Walls Coverings, LNEC. (In Portuguese)."},{"key":"ref_24","unstructured":"(1999). Methods of Test for Mortar for Masonry\u2014Part 11: Determination of Flexural and Compressive Strength of Hardened Mortar (Standard No. EN1015-11:1999)."},{"key":"ref_25","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_26","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1080\/15583058.2012.727062","article-title":"Rubble Stone Masonry Walls Strengthened by Three-Dimensional Steel Ties and Textile Reinforced Mortar Render, Under Compression","volume":"8","author":"Pinho","year":"2014","journal-title":"Int. J. Archit. Herit."},{"key":"ref_27","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_28","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1080\/15583058.2017.1377314","article-title":"Experimental analysis of rubble stone masonry walls strengthened by transverse confinement under compression and compression-shear loadings","volume":"12","author":"Pinho","year":"2018","journal-title":"Int. J. Archit. Herit."},{"key":"ref_29","unstructured":"Correia, J. (2011). Experimental Analysis of a Large Rubble Stone Masonry Specimen. [Master\u2019s Thesis, FCT UNL]. (In Portuguese)."},{"key":"ref_30","unstructured":"Morais, H. (2010). Experimental Analysis of a Small Rubble Stone Masonry Specimen. [Master\u2019s Thesis, FCT UNL]. (In Portuguese)."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1061\/(ASCE)0733-9399(2003)129:12(1439)","article-title":"Confinement-shear lattice model for concrete damage in tension and compression: I. Theory","volume":"129","author":"Cusatis","year":"2003","journal-title":"J. Eng. Mech."}],"container-title":["Buildings"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-5309\/12\/8\/1283\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:13:16Z","timestamp":1760141596000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-5309\/12\/8\/1283"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,21]]},"references-count":31,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["buildings12081283"],"URL":"https:\/\/doi.org\/10.3390\/buildings12081283","relation":{},"ISSN":["2075-5309"],"issn-type":[{"value":"2075-5309","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,21]]}}}