Abstract
Basic creep plays an important role in assessing the risk of early-age cracking in massive structures. In recent decades, several models have been developed to characterize how the hydration process impacts the development of basic creep. This study investigates the basic creep of various concrete mixes across different ages at loading. The analysis focuses on the very early stages (less than 24 hours) and early stages (less than 28 days) of concrete development. It is shown that a logarithmic expression that contains two parameters describing the material can accurately model basic creep from a very early age. One parameter relates to the creep amplitude and depends solely on the composition of the concrete. The other relates to the kinetics of creep and depends on the age of the material at loading and the nature of the concrete mixture. The logarithmic expression corresponds to a rheological model consisting of a single dashpot wherein viscosity exhibits a linear evolution over time. The model offers the advantage of eliminating the need to store the entire stress history for computing the stress resulting from the restriction of the free deformation. This approach significantly reduces computation time. A power-law correlation is also observed between the material aging parameter and the degree of hydration. This relationship depends on the composition. At least two compressive creep tests performed at two different degrees of hydration are needed to calibrate the material parameters and consider the effect of aging on basic creep compliance.
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Atrushi, D.S.: Tensile and compressive creep of early age concrete: Testing and modelling Thesis. PhD Thesis, Norwegian University of Sciences and Technology (2003)
Azenha, M., Kanavaris, F., Schlicke, D., Jędrzejewska, A., Benboudjema, F., Honorio, T., Šmilauer, V., Serra, C., Forth, J., Riding, K., Khadka, B., Sousa, C., Briffaut, M., Lacarrière, L., Koenders, E., Kanstad, T., Klausen, A., Torrenti, J.-M., Fairbairn, E.M.R.: Recommendations of RILEM TC 287-CCS: thermo-chemo-mechanical modelling of massive concrete structures towards cracking risk assessment. Mater. Struct. 54(4), 135 (2021)
Banfill, P.F.G.: Rheology of fresh cement and concrete (1991)
Bazant, Z.P.: Creep and shrinkage prediction model for analysis and design of concrete structures - Model B-3. Mater. Struct. 28, 357–365 (1995)
Bažant, Z.P., Prasannan, S.: Solidification theory for concrete creep. II: Verification and application. J. Eng. Mech. 115(8), 1704–1725 (1989)
Bazant, Z.P., Hauggaard, A., Baweja, S., Ulm, F.-J.: Microprestress-solidification theory for concrete creep. I. Aging and drying effects. J. Eng. Mech. 123, 1188–1194 (1997)
Benboudjema, F., Torrenti, J.M.: Early age behaviour of concrete nuclear containments. Nucl. Eng. Des. 238, 2495–2506 (2008)
Benboudjema, F., Meftah, F., Torrenti, J.M.: Interaction between drying, shrinkage, creep and cracking phenomena in concrete. Eng. Struct. 27(2), 239–250 (2005)
Benboudjema, F., Briffaut, M., Hilaire, A., Torrenti, J.M., Nahas, G.: Early age behavior of massive concrete structures: from experiments to numerical simulations. In: CONCRACK 3-RILEM-JCI International Workshop on Crack Control Mass Concrete and Related Issues Concerning Early-Age of Concrete Structures, Paris, France, pp. 1–12 (2012)
Benboudjema, F., Carette, J., Delsaute, B., Honorio de Faria, T., Knoppik, A., Lacarrière, L., Neiry de Mendonça Lopes, A., Rossi, P., Staquet, S.: Mechanical properties. In: Fairbairn, E.M.R., Cham, M.A. (eds.) Thermal Cracking of Massive Concrete Structures: State of the Art Report of the RILEM Technical Committee 254-CMS, pp. 69–114. Springer, Berlin (2019)
Binder, E., Königsberger, M., Díaz Flores, R., Mang, H.A., Hellmich, C., Pichler, B.L.A.: Thermally activated viscoelasticity of cement paste: minute-long creep tests and micromechanical link to molecular properties. Cem. Concr. Res. 163, 107014 (2023)
Boulay, C., Staquet, S., Delsaute, B., Carette, J., Crespini, M., Yazoghli-Marzouk, O., Merliot, E., Ramanich, S.: How to monitor the modulus of elasticity of concrete, automatically since the early age? Mater. Struct. (2013)
Bourchy, A.: Relation chaleur d’hydratation du ciment: montée en température et contraintes générées au jeune âge du béton. These de l’Universite Paris-Est. (2018)
Briffaut, M., Benboudjema, F., Torrenti, J.M., Nahas, G.: Numerical analysis of the thermal active restrained shrinkage ring test to study the early age behavior of massive concrete structures. Eng. Struct. 33(4), 1390–1401 (2011)
Briffaut, M., Benboudjema, F., Torrenti, J.-M., Nahas, G.: Concrete early age basic creep: experiments and test of rheological modelling approaches. Constr. Build. Mater. 36, 373–380 (2012)
Briffaut, M., Benboudjema, F., Torrenti, J.M., Nahas, G.: Analysis of semi-adiabiatic tests for the prediction of early-age behavior of massive concrete structures. Cem. Concr. Compos. 34(5), 634–641 (2012)
CEN: prEN 1992-1-1:2023, Eurocode 2: Design of concrete structures — Part 1-1: General rules — Rules for buildings (2023). Bridges and civil engineering structures
Cervera, M., Oliver, J., Prato, T.: Thermo-chemo-mechanical model for concrete. II: Damage and creep. J. Eng. Mech. 125(9), 1028–1039 (1999)
Charpin, L., Niepceron, J., Corbin, M., Masson, B., Mathieu, J.-P., Haelewyn, J., Hamon, F., Åhs, M., Aparicio, S., Asali, M., Capra, B., Azenha, M., Bouhjiti, D.E.M., Calonius, K., Chu, M., Herrman, N., Huang, X., Jiménez, S., Mazars, J., Mosayan, M., Nahas, G., Stepan, J., Thenint, T., Torrenti, J.-M.: Ageing and air leakage assessment of a nuclear reactor containment mock-up: VERCORS 2nd benchmark. Nucl. Eng. Des. 377, 111136 (2021)
Chidiac, S.E., Mahmoodzadeh, F.: Plastic viscosity of fresh concrete – a critical review of predictions methods. Cem. Concr. Compos. 31(8), 535–544 (2009)
Dabarera, A., Li, L., Dao, V.: Experimental evaluation and modelling of early-age basic tensile creep in high-performance concrete. Mater. Struct. 54(3), 130 (2021)
De Schutter, G.: Degree of hydration based Kelvin model for the basic creep of early age concrete. Mater. Struct. 32, 260–265 (1999)
De Schutter, G., Taerwe, L.: Degree of hydration-based description of mechanical properties of early age concrete. Mater. Struct. 29(190), 335–344 (1996)
Delsaute, B., Staquet, S.: Decoupling thermal and autogenous strain of concretes with different water/cement ratios during the hardening process. Adv. Civ. Eng. Mater. 6(2), 1–22 (2017)
Delsaute, B., Staquet, S.: Development of strain-induced stresses in early age concrete composed of recycled gravel or sand. J. Adv. Concr. Technol. 17, 319–334 (2019)
Delsaute, B., Staquet, S.: Monitoring the viscoelastic behaviour of cement based materials by means of repeated minute-scale-duration loadings. In: Serdar, M., Gabrijel, I., Schlicke, D., Staquet, S., Azenha, M. (eds.) Advanced Techniques for Testing of Cement-Based Materials, pp. 99–134. Springer, Cham (2020a)
Delsaute, B., Staquet, S.: Testing concrete since setting time under free and restrained conditions. In: Serdar, M., Gabrijel, I., Schlicke, D., Staquet, S., Azenha, M. (eds.) Advanced Techniques for Testing of Cement-Based Materials, pp. 177–209. Springer, Cham (2020b)
Delsaute, B., Boulay, C., Staquet, S.: Creep testing of concrete since setting time by means of permanent and repeated minute-long loadings. Cem. Concr. Compos. 73, 75–88 (2016)
Delsaute, B., Torrenti, J.M., Staquet, S.: Monitoring and modeling of the early age properties of the vercors concrete. In: TINCE 2016, Paris, France, p. 12 (2016)
Delsaute, B., Torrenti, J.M., Staquet, S.: Modeling basic creep of concrete since setting time. Cem. Concr. Compos. 83(Supplement C), 239–250 (2017)
Fairbairn, E.M.R., Azenha, M.: Thermal Cracking of Massive Concrete Structures. Springer, Cham (2019)
Frech-Baronet, J., Sorelli, L., Charron, J.P.: New evidences on the effect of the internal relative humidity on the creep and relaxation behaviour of a cement paste by micro-indentation techniques. Cem. Concr. Res. 91, 39–51 (2017)
Frech-Baronet, J., Sorelli, L., Chen, Z.: A closer look at the temperature effect on basic creep of cement pastes by microindentation. Constr. Build. Mater. 258, 119455 (2020)
Gawin, D., Pesavento, F., Schrefler, B.A.: Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part II: shrinkage and creep of concrete. Int. J. Numer. Methods Eng. 67(3), 332–363 (2006)
Ghasabeh, M., Göktepe, S.: Phase-field modeling of thermal cracking in hardening mass concrete. Eng. Fract. Mech. 289, 109398 (2023)
Gutsch, A.W.: Stoffeigenschaften Jungen Betons – Versuche und Modelle (2000)
Han, B., Xie, H.-B., Zhu, L., Jiang, P.: Nonlinear model for early age creep of concrete under compression strains. Constr. Build. Mater. 147, 203–211 (2017)
Hanson, J.A.: A 10-year study of creep properties of concrete. Report SP-38, Design and Construction Division (1953)
Hauggaard, A., Damkilde, L., Hansen, P.F.: Transitional thermal creep of early age concrete. J. Mater. Civ. Eng. 125, 458–465 (1999)
Hermerschmidt, W., Budelmann, H.: Creep of Early Age Concrete Under Variable Stress. CONCREEP 10. American Society of Civil Engineers, Reston (2015)
Hilaire, A., Benboudjema, F., Darquennes, A., Berthaud, Y., Nahas, G.: Modeling basic creep in concrete at early-age under compressive and tensile loading. Nucl. Eng. Des. 269, 222–230 (2014)
Hubler, M.H., Wan-Wendner, R., Bazant, Z.P.: Comprehensive database for concrete creep and shrinkage: analysis and recommendations for testing and recording. ACI Mater. J. 112(4), 547–558 (2015)
Irfan-ul-Hassan, M., Pichler, B., Reihsner, R., Hellmich, C.: Elastic and creep properties of young cement paste, as determined from hourly repeated minute-long quasi-static tests. Cem. Concr. Res. 82, 36–49 (2016)
Irfan-ul-Hassan, M., Königsberger, M., Reihsner, R., Hellmich, C., Pichler, B.: How water-aggregate interactions affect concrete creep: multiscale analysis. J. Nanomech. Micromech. 7(4), 04017019 (2017)
Jiang, C., Yang, Y., Wang, Y., Zhou, Y., Ma, C.: Autogenous shrinkage of high performance concrete containing mineral admixtures under different curing temperatures. Constr. Build. Mater. 61, 260–269 (2014)
Khan, I., Castel, A., Gilbert, R.I.: Tensile creep and early-age concrete cracking due to restrained shrinkage. Constr. Build. Mater. 149, 705–715 (2017)
Klausen, A.E., Kanstad, T., Bjøntegaard, Ø., Sellevold, E.: Comparison of tensile and compressive creep of fly ash concretes in the hardening phase. Cem. Concr. Res. 95, 188–194 (2017)
Klemczak, B., Knoppik-Wróbel, A.: Reinforced concrete tank walls and bridge abutments: early-age behaviour, analytic approaches and numerical models. Eng. Struct. 84, 233–251 (2015)
Lacarriere, L., Sellier, A., Souyris, P., Kolani, B., Chhun, P.: Numerical prediction of cracking risk of reinforced concrete structures at early age. RILEM Tech. Lett. 5(0), 41–55 (2020)
Lackner, R., Mang, H.A.: Chemoplastic material model for the simulation of early-age cracking: from the constitutive law to numerical analyses of massive concrete structures. Cem. Concr. Compos. 26(5), 551–562 (2004)
Larson, M., Jonasson, J.E.: Linear logarithmic model for concrete creep I. Formulation and evaluation. J. Adv. Concr. Technol. 1(2), 172–187 (2003)
Leroy, R., Le Maou, F., Torrenti, J.M.: Long term basic creep behavior of high performance concrete. Data and modelling. Mater. Struct. 50, 85 (2017)
Liu, Y., Wei, Y., Ma, L., Wang, L.: Restrained shrinkage behavior of internally-cured UHPC using calcined bauxite aggregate in the ring test and UHPC-concrete composite slab. Cem. Concr. Compos. 134, 104805 (2022)
Mallick, S., Anoop, M.B., Rao, K.B.: Early age creep of cement paste-governing mechanisms and role of water-a microindentation study. Cem. Concr. Res. 116, 284–298 (2019)
Martin, R.P.: Analyse sur structures modèles des effets mécaniques de la réaction sulfatique interne du béton Thesis (2010). Thèse de l’Université de Paris-Est
Mazzotti, C., Savoia, M.: Nonlinear creep damage model for concrete under uniaxial compression. J. Eng. Mech. 129(9), 1065–1075 (2003)
Mohammad, R., Rahimi-Aghdam, S., Bažant, Z.P.: Statistical filtering of useful concrete creep data from imperfect laboratory tests. Mater. Struct. 51, 1–14 (2018)
Muller, H.S., Anders, I., Breiner, R., Vogel, M.: Concrete: treatment of types and properties in fib Model Code 2010. Struct. Concr. 14, 320–334 (2013)
Naqi, A., Delsaute, B., Königsberger, M., Staquet, S.: Monitoring early age elastic and viscoelastic properties of alkali-activated slag mortar by means of repeated minute-long loadings. Dev. Built Environ. 16, 100275 (2023)
Østergaard, L., Lange, D.A., Altoubat, S.A., Stang, H.: Tensile basic creep of early-age concrete under constant load. Cem. Concr. Res. 31(12), 1895–1899 (2001)
Ranaivomanana, N., Multon, S., Turatsinze, A.: Basic creep of concrete under compression, tension and bending. Constr. Build. Mater. 38(Supplement C), 173–180 (2013)
Rasoolinejad, M., Rahimi-Aghdam, S., Bažant, Z.P.: Statistical filtering of useful concrete creep data from imperfect laboratory tests. Mater. Struct. 51(6), 153 (2018)
Rossi, P., Tailhan, J.-L., Le Maou, F., Gaillet, L., Martin, E.: Basic creep behavior of concretes investigation of the physical mechanisms by using acoustic emission. Cem. Concr. Res. 42(1), 61–73 (2012)
Rossi, P., Tailhan, J.-L., Le Maou, F.: Comparison of concrete creep in tension and in compression: influence of concrete age at loading and drying conditions. Cem. Concr. Res. 51(Supplement C), 78–84 (2013)
Rossi, P., Charron, J.P., Bastien-Masse, M., Tailhan, J.-L., Le Maou, F., Ramanich, S.: Tensile basic creep versus compressive basic creep at early ages: comparison between normal strength concrete and a very high strength fibre reinforced concrete. Mater. Struct. 47(10), 1773–1785 (2014)
Saliba, J., Loukili, A., Grondin, F., Regoin, J.P.: Experimental study of creep-damage coupling in concrete by acoustic emission technique. Mater. Struct. 45(9), 1389–1401 (2012)
Sellier, A., Multon, S., Buffo-Lacarrière, L., Vidal, T., Bourbon, X., Camps, G.: Concrete creep modelling for structural applications: non-linearity, multi-axiality, hydration, temperature and drying effects. Cem. Concr. Res. 79, 301–315 (2016)
Su, X., Jia, M., Wu, Y., Yao, L., Xu, W.: A hierarchical creep model for cement paste: from decoding nano-microscopic CSH creep to considering microstructure evolution. J. Build. Eng. 78, 107606 (2023)
Suwanmaneechot, P., Aili, A., Maruyama, I.: Creep behavior of CSH under different drying relative humidities: interpretation of microindentation tests and sorption measurements by multi-scale analysis. Cem. Concr. Res. 132, 106036 (2020)
Switek-Rey, A., Denarié, E., Brühwiler, E.: Early age creep and relaxation of UHPFRC under low to high tensile stresses. Cem. Concr. Res. 83, 57–69 (2016)
Torrenti, J.M.: Basic creep of concrete-coupling between high stresses and elevated temperatures. Eur. J. Environ. Civ. Eng. 22(12), 1419–1428 (2018)
Torrenti, J.-M., Nedjar, B., Aili, A.: Dependence of basic creep on the relative humidity. In: Building for the Future: Durable, Sustainable, Resilient, Springer, Cham (2023)
Ulm, F.J., Le Maou, F., Boulay, C.: Creep and shrinkage coupling: new review of some evidence. Revue française de génie civil 3(7), 21–37 (1999)
Vandamme, M., Ulm, F.J.: Nanoindentation investigation of creep properties of calcium silicate hydrates. Cem. Concr. Res. 52, 38–52 (2013)
Walraven, J., Bigaj-van Vliet, A.: Fib, Model Code for Concrete Structures 2010. Ernst and Son (2013)
Wyrzykowski, M., Scrivener, K., Lura, P.: Basic creep of cement paste at early age-the role of cement hydration. Cem. Concr. Res. 116, 191–201 (2019)
Zhang, Q., Le Roy, R., Vandamme, M., Zuber, B.: Long-term creep properties of cementitious ma-terials: comparing microindentation testing with macroscopic uniaxial compressive testing. Cem. Concr. Res. 58, 89–98 (2014)
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B.D. and J.M.T. wrote the main manuscript text and B.D. prepared figures. B.N. contributed to the part concerning modelling. A.B. contributed to the part concerning her tests. M.B. contributed to the part concerning his tests. J.M.T and S.T. supervised B.D. work. J.M.T. supervised A.B and M.B. works. All authors reviewed the manuscript.
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Delsaute, B., Torrenti, J.M., Nedjar, B. et al. Modeling compressive basic creep of concrete at early age. Mech Time-Depend Mater 28, 143–162 (2024). https://doi.org/10.1007/s11043-024-09668-6
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DOI: https://doi.org/10.1007/s11043-024-09668-6