{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:46:26Z","timestamp":1760132786739,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T00:00:00Z","timestamp":1697068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PIDDAC","award":["FCT\/MCTES"],"award-info":[{"award-number":["FCT\/MCTES"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Buildings"],"abstract":"<jats:p>Concrete structures that experience internal swelling reactions are often affected by other deleterious mechanisms, such as creep and shrinkage. In Brazil and many other countries around the world, numerous cases of building foundations and concrete dams were investigated due to the damage associated with internal expansions. Macroscopic models for the numerical representation of these expansions must take into account the influence of key environmental parameters such as temperature, degree of saturation, and the rate of development of the chemical reaction. To be relevant in structural applications, concrete creep models must consider several important phenomena, such as non-linearity, multi-axiality, and thermal and drying effects. In order to prevent these pathologies, to plan rehabilitation work, and to develop new design procedures, numerical simulation using the finite element method (FEM) is a very useful tool. This work aimed to implement a chemical model to simulate the advancement of the internal expansion reactions and a mechanical model to simulate creep and shrinkage phenomena in COMSOL Multiphysics\u00ae to reassess concrete structures suffering from these mechanisms. Both models were implemented separately to evaluate their responses and compare them with the theoretical results and experimental benchmarks proposed by the developers of these models. The numerical results obtained presented an excellent agreement with the experimental results, with a deviation of less than 10%, which showed that the implementation of the developed numerical models was very efficient. Moreover, this research holds significant importance as the mathematical models used to simulate internal expansions in concrete are currently only available in limited-use FEM software\u2019s. Therefore, demonstrating the successful implementation of these models in widely used finite element programs and their ability to produce reliable results would be a valuable contribution.<\/jats:p>","DOI":"10.3390\/buildings13102575","type":"journal-article","created":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T07:28:44Z","timestamp":1697095724000},"page":"2575","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Chemical and Creep Models Applied to Concrete Damaged by Alkali\u2013Silica Reactions"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0791-2438","authenticated-orcid":false,"given":"Rodrigo F.","family":"Roma","sequence":"first","affiliation":[{"name":"Civil Engineering Department, Pernambuco Catholic University, Recife 50050-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4471-4294","authenticated-orcid":false,"given":"Fernando A. N.","family":"Silva","sequence":"additional","affiliation":[{"name":"Civil Engineering Department, Pernambuco Catholic University, Recife 50050-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3829-4406","authenticated-orcid":false,"given":"Mohamed K.","family":"Bourbatache","sequence":"additional","affiliation":[{"name":"Institut National des Sciences Appliqu\u00e9es de Rennes, 35700 Rennes, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8835-1758","authenticated-orcid":false,"given":"Mahfoud","family":"Tahlaiti","sequence":"additional","affiliation":[{"name":"Research Institute in Civil Engineering and Mechanics, Centrale Nantes, 44321 Nantes, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1026-4523","authenticated-orcid":false,"given":"Jo\u00e3o M. P. Q.","family":"Delgado","sequence":"additional","affiliation":[{"name":"CONSTRUCT-LFC, Department of Civil Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4530-9880","authenticated-orcid":false,"given":"Ant\u00f3nio C.","family":"Azevedo","sequence":"additional","affiliation":[{"name":"Instituto Federal de Ci\u00eancias de Educa\u00e7\u00e3o e Tecnologia de Pernambuco (IFPE), Recife 50670-430, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1177\/1056789510386857","article-title":"Anisotropic damage model for concrete affected by alkali-aggregate reaction","volume":"20","author":"Comi","year":"2011","journal-title":"Int. J. Damage Mech."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Silva, F.A.N., Delgado, J.M.P.Q., Azevedo, A.C., Mahfoud, T., Khelidj, A., Nascimento, N., and Lima, A.G.B. (2021). Diagnosis and assessment of deep pile cap foundation of a tall building affected by internal expansion reactions. Buildings, 11.","DOI":"10.3390\/buildings11030104"},{"key":"ref_3","first-page":"1059","article-title":"Diagnostic of Concrete Samples of Pile Caps Affected by Internal Swelling Reactions","volume":"45","author":"Delgado","year":"2021","journal-title":"Iran. J. Sci. Technol. Trans. Civ. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s40996-021-00615-w","article-title":"Numerical analysis of bottle-shaped isolated struts concrete deteriorated by delayed ettringite formation","volume":"46","author":"Silva","year":"2021","journal-title":"Iran. J. Sci. Technol. -Trans. Civ. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Silva, K.K.S., Silva, F.A.N., Mahfoud, T., Khelidj, A., Brientin, A., Azevedo, A.C., Delgado, J.M.P.Q., and De Lima, A.G.B. (2021). On the use of embedded fiber optic sensors for measuring early-age strains in concrete. Sensors, 21.","DOI":"10.3390\/s21124171"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"128239","DOI":"10.1016\/j.conbuildmat.2022.128239","article-title":"Alkali-reactivity of Pernambuco east shear zone coarse concrete aggregates: An experimental discussion","volume":"344","author":"Matos","year":"2022","journal-title":"Constr. Build. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.cemconres.2015.05.024","article-title":"Alkali-silica reaction: Current understanding of the reaction mechanisms and the knowledge gaps","volume":"76","author":"Rajabipour","year":"2015","journal-title":"Cem. Concr. Res."},{"key":"ref_8","first-page":"227","article-title":"Creep, shrinkage, and anisotropic damage in alkali-aggregate reaction swelling mechanism\u2014Part I: A constitutive model","volume":"105","author":"Grimal","year":"2007","journal-title":"ACI Mater. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11709-012-0141-2","article-title":"Modeling of alkali-silica reaction in concrete: A review","volume":"6","author":"Pan","year":"2012","journal-title":"Struct. Civ. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1016\/j.cemconres.2008.01.003","article-title":"Diagnosing delayed ettringite formation in concrete structure","volume":"38","author":"Thomas","year":"2008","journal-title":"Cem. Concr. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.cemconres.2010.01.006","article-title":"Guest editorial","volume":"40","author":"Broekmans","year":"2010","journal-title":"Cem. Concr. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.matchar.2004.09.006","article-title":"Alkali-silica reaction damage to Elgeseter Bridge, Trondheim, Norway: A review of construction, research and repair up to 2003","volume":"53","author":"Jensen","year":"2004","journal-title":"Mater. Charact."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"51","DOI":"10.3221\/IGF-ESIS.64.04","article-title":"A review of the application of the simulated annealing algorithm in structural health monitoring (1995\u20132021)","volume":"17","author":"Ghannadi","year":"2023","journal-title":"Frat. Ed. Integrit\u00e0 Strutt."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Thomas, M.D.A., Fournier, B., and Folliard, K.J. (2013). Alkali-Aggregate Reactivity (AAR) Facts Book, Report No. FHWA-HIF-13-019.","DOI":"10.1007\/978-94-007-6567-2_2"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.cemconres.2005.12.022","article-title":"Different manifestations of the alkali-silica reaction in concrete according to the reaction kinetics of the reactive aggregate","volume":"36","author":"Ponce","year":"2006","journal-title":"Cem. Concr. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1016\/S0008-8846(01)00522-1","article-title":"A discussion of the paper \u201cMathematical model for kinetics of alkali-silica reaction in concrete\u201d by Z.P. Baz\u0103nt and A. Steffens","volume":"31","author":"Idorn","year":"2001","journal-title":"Cem. Concr. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.cemconres.2005.06.003","article-title":"Mechanism of damage for the alkali\u2013silica reaction","volume":"36","author":"Riche","year":"2006","journal-title":"Cem. Concr. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1016\/j.cemconres.2007.06.008","article-title":"Modified model of alkali-silica reaction","volume":"37","author":"Ichikawa","year":"2007","journal-title":"Cem. Concr. Res."},{"key":"ref_19","unstructured":"Pourbehi, M.S. (2018). Numerical Modelling of Alkali Silica Reaction in Concrete Dams. [Ph.D. Thesis, Stellenbosch University]."},{"key":"ref_20","unstructured":"Morenon, P. (2017). Mod\u00e9lisation des Reactions de Gonflement Interne des B\u00e9tons Avec Prise en Compte des Couplages Poro-M\u00e9caniques et Chimiques. [Ph.D. Thesis, Universit\u00e9 Toulouse 3 Paul Sabatier]."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.cemconres.2012.10.015","article-title":"Alkali-silica reaction (ASR) expansion: Pessimum effect versus scale effect","volume":"44","author":"Gao","year":"2013","journal-title":"Cem. Concr. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.cemconres.2007.09.013","article-title":"Effects of aggregate size and alkali content on ASR expansion","volume":"38","author":"Multon","year":"2010","journal-title":"Cem. Concr. Res."},{"key":"ref_23","unstructured":"Larive, C. (1997). Apports Combin\u00e9s de L\u2019exp\u00e9rimentation et de la Mod\u00e9lisation \u00e0 la Compr\u00e9hension de L\u2019alcali-R\u00e9action et de Ses effects M\u00e9caniques. [Ph.D. Thesis, Ecole Nationale des Ponts et Chauss\u00e9es]."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1061\/(ASCE)0733-9399(2000)126:3(233)","article-title":"Thermo-chemo-mechanics of ASR expansion in concrete structures","volume":"126","author":"Ulm","year":"2000","journal-title":"J. Eng. Mech."},{"key":"ref_25","unstructured":"Multon, S. (2003). \u00c9valuation Exp\u00e9rimentale et Th\u00e9orique des Effects M\u00e9caniques de L\u2019alcali-R\u00e9action sur des Structures Mod\u00e8les. [Ph.D. Thesis, Universit\u00e9 de Marne-la-Vall\u00e9e]."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1016\/j.cemconres.2005.11.012","article-title":"Effect of applied stresses on alkali-silica reaction induced expansions","volume":"36","author":"Multon","year":"2006","journal-title":"Cem. Concr. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.cemconres.2011.12.004","article-title":"Effects of uniaxial stress on alkali-silica reaction induced expansion of concrete","volume":"42","author":"Dunant","year":"2012","journal-title":"Cem. Concr. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3495","DOI":"10.1617\/s11527-015-0734-z","article-title":"A new method of applying long-term multiaxial stresses in concrete specimens undergoing ASR, and their triaxial expansions","volume":"49","author":"Gautam","year":"2016","journal-title":"Mater. Struct."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.cemconres.2015.10.001","article-title":"Concrete creep modelling for structural applications: Non-linearity, multi-axiality, hydration, temperature and drying effects","volume":"79","author":"Sellier","year":"2016","journal-title":"Cem. Concr. Res."},{"key":"ref_30","unstructured":"(2023, February 18). COMSOL Muliohysics\u00ae v. 5.5. COMSOL AB, Stockholm, Sweden. Available online: www.comsol.com."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1680\/macr.2005.57.10.623","article-title":"Experimental studies on creep of sealed concrete under multiaxial stresses","volume":"57","author":"Kim","year":"2005","journal-title":"Mag. Concr. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1617\/s11527-012-9879-1","article-title":"Analysis of interactions between damage and basic creep of HPC and HPFRC heated between 20 and 80 \u00b0C","volume":"46","author":"Ladaoui","year":"2013","journal-title":"Mater. Struct."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.engfracmech.2012.10.012","article-title":"Orthotropic damage coupled with localized crack reclosure processing\u2014Part I: Constitutive laws","volume":"971","author":"Sellier","year":"2013","journal-title":"Eng. Fract. Mech."}],"container-title":["Buildings"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-5309\/13\/10\/2575\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:05:39Z","timestamp":1760130339000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-5309\/13\/10\/2575"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,12]]},"references-count":33,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["buildings13102575"],"URL":"https:\/\/doi.org\/10.3390\/buildings13102575","relation":{},"ISSN":["2075-5309"],"issn-type":[{"type":"electronic","value":"2075-5309"}],"subject":[],"published":{"date-parts":[[2023,10,12]]}}}