×

Modelling of cement hydration in concrete structures with hybrid finite elements. (English) Zbl 1297.80010

Summary: A hybrid finite element formulation is used to model temperature evolutions in concrete structures at early ages, taking into account the thermo-chemical process of cement hydration. The most relevant fields in the application problem, namely the temperature and the hydration degree fields, are selected for direct and independent approximation. The Galerkin formulation used qualifies as hybrid because the heat flux is also approximated on the boundary of the element. The temperature and hydration degree bases are used to enforce the thermal equilibrium condition and the hydration law, respectively, and the heat flux basis is used to enforce the thermal continuity conditions. The resulting nonlinear transient hybrid formulation leads to high-degree, naturally hierarchical elements. They can be implemented on coarse meshes, eventually unstructured and involving high aspect-ratio elements to reduce the dimension of the solving system, while preserving adequate levels of accuracy. The system is symmetric, sparse and well-suited to adaptive refinement and parallelization. Modelling of boundary conditions and thermo-chemical properties of concrete is designed to accommodate experimentally defined properties and code of practice recommendations, as well as other research results reported in the literature. The quality of the model is assessed using a set of testing problems supported by experimental data and results obtained with conventional (conform) finite elements.

MSC:

80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
80A32 Chemically reacting flows
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Cervera, M.; Faria, R.; Oliver, J.; Prato, T., Numerical modelling of concrete curing, regarding hydration and temperature phenomena, Computers and Structures, 80, 18-19, 1511-1521, (2002)
[2] Faria, R.; Azenha, M.; Figueiras, J. A., Modelling of concrete at early age: application to an externally restrained slab, Cement & Concrete Composites, 28, 6, 572-585, (2006)
[3] Briffaut, M.; Benboudjema, F.; Torrenti, J.-M.; Nahas, G., Effects of early-age thermal behaviour on damage risks in massive concrete structures, European Journal of Environmental and Civil Engineering, 16, 5, 589-605, (2012)
[4] A.W. Gutsch, Crack control for the massive concrete structures of the new central railway station in Berlin, Germany. In: International Workshop on Control of Cracking in Early Age Concrete, 2002, pp. 351-358.
[5] De Schutter, G., Finite element simulation of thermal cracking in massive hardening concrete elements using degree of hydration based material laws, Computers and Structures, 80, 2035-2042, (2002)
[6] Bertagnoli, G.; Mancini, G.; Tondolo, F., Early age cracking of massive concrete piers, Magazine of Concrete Research, 63, 10, 723-736, (2011)
[7] Lawrence, A. M.; Tia, M.; Ferraro, C. C.; Bergin, M., Effect of early age strength on cracking in mass concrete containing different supplementary cementitious materials: experimental and finite-element investigation, Journal of Materials in Civil Engineering, 24, 4, 362-372, (2012)
[8] Gawin, D.; Pesavento, F.; Schrefler, B. A., Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. part I: hydration and hygro-thermal phenomena, International Journal for Numerical Methods in Engineering, 67, 299-331, (2006) · Zbl 1110.74821
[9] Buffo-Lacarrière, L.; Sellier, A.; Escadeillas, G.; Turatsinze, A., Multiphase finite element modelling of concrete hydration, Cement and Concrete Research, 37, 131-138, (2007)
[10] Di Luzio, G.; Cusatis, G., Hygro-thermo-chemical modeling of high performance concrete. I: theory. II: numerical implementation, calibration, and validation, Cement & Concrete Composites, 31, 301-324, (2009)
[11] Choi, S.; Cha, S. W.; Oh, B. H.; Kim, I. H., Thermo-hygro-mechanical behavior of early-age concrete deck in composite bridge under environmental loadings. part 1: temperature and relative humidity, Materials and Structures/Materiaux et Constructions, 44, 7, 1325-1346, (2011)
[12] Fraeijs de Veubeke, B. M.; Hogge, M. A., Dual analysis for heat conduction problems by finite elements, International Journal for Numerical Methods in Engineering, 5, 65-82, (1972) · Zbl 0251.65061
[13] Jirousek, J.; Qin, Q. H., Application of hybrid-Trefftz element approach to transient heat conduction analysis, Computers and Structures, 58, 1, 195-201, (1996) · Zbl 0900.73802
[14] Chen, W.-H.; Ting, K., Hybrid finite element analysis of transient thermoelastic fracture problems subjected to general heat transfer conditions, Computational Mechanics, 4, 1-10, (1989) · Zbl 0711.73197
[15] Chen, H. T.; Chang, S. M., Application of the hybrid method to inverse heat conduction problems, International Journal of Heat and Mass Transfer, 33, 4, 621-628, (1990)
[16] Farhloul, M.; Mounim, A. S., A mixed-hybrid finite element method for convection-diffusion problems, Applied Mathematics and Computation, 171, 2, 1037-1047, (2005) · Zbl 1090.65130
[17] J.A.T. Freitas, P.T. Cuong, R. Faria, Modelling of Cement Hydration in High Performance Concrete Structures with Hybrid Finite Elements. Internal Report, ICIST, IST-id, 2012. · Zbl 1352.74117
[18] J.A.T. Freitas, J.V.M. Marques, Hybrid-Trefftz Finite Elements for Thermo-Mechanics. Internal Report, ICIST, IST-id, 2013.
[19] Freitas, J. A.T.; Almeida, J. P.M., Pereira EBR. non-conventional formulations for the finite element method, Computational Mechanics, 23, 5-6, 488-501, (1999) · Zbl 0946.74068
[20] M. Azenha, Numerical Simulation of the Structural Behaviour of Concrete Since its Early Ages. Ph.D. Thesis, University of Porto, 2009.
[21] H.W. Reinhardt, J. Blaauwendraad, J. Jongedijk. Temperature development in concrete structures taking account of state dependent properties. In: International Conference on Concrete at Early Ages, 1982.
[22] Ulm, F. J.; Coussy, O., Modeling of thermochemomechanical couplings of concrete at early ages, Journal of Engineering Mechanics, 121, 7, 785-794, (1995)
[23] Lackner, R.; Mang, H. A., Chemoplastic material model for the simulation of early-age cracking: from constitutive law to numerical analyses of massive concrete structures, Cement & Concrete Composites, 26, 551-562, (2004)
[24] Cervera, M.; Oliver, J.; Prato, T., Thermo-chemo-mechanical model for concrete. I: hydration and aging, Journal of Engineering Mechanics, 125, 9, 1018-1027, (1999)
[25] Freitas, J. A.T.; Moldovan, I. D.; Toma, M., Mixed and hybrid stress elements for biphasic media, Computers and Structures, 88, 23-24, 1286-1299, (2010)
[26] Briffaut, M.; Benboudjema, F.; Torrenti, J.-M.; Nahas, G., Effects of early-age thermal behaviour on damage risks in massive concrete structures, European Journal of Environmental and Civil, 16, 5, 589-605, (2012)
[27] McAdams, W. H., Heat transmission, (1954), McGraw-Hill Series in Chemical Engineering
[28] Palyvos, J. A., A survey of wind convection coefficient correlations for buildings envelope energy systems’ modeling, Applied Thermal Engineering, 28, 801-808, (2008)
[29] Tamma, K. K.; Zhou, X.; Sha, D., The time dimension: a theory towards the evolution, classification, characterization and design of computational algorithms for transient and dynamic applications, Archives Computational Methods in Engineering, 7, 67-290, (2000) · Zbl 0987.74004
[30] Freitas, J. A.T., Mixed finite element solution of time-dependent problems, Computer Methods in Applied Mechanics and Engineering, 197, 45-48, 3657-3678, (2008) · Zbl 1194.74495
[31] M. Azenha. Behaviour of Concrete at Early ages. Phenomenology and Thermo-Mechanical Analysis, M.Sc. Thesis, University of Porto, 2004 (in Portuguese).
[32] TNO-DIANA-BV. Release 9.2. Delft, 2007.
[33] Azenha, M.; Faria, R., Temperatures and stresses due to cement hydration on the R/C foundation of a wind tower - a case study, Engineering Structures, 30, 2392-2400, (2008)
[34] Bentz, D. P.; Waller, V.; de Larrard, F., Prediction of adiabatic temperature rise in conventional and high-performance concretes using a 3-D microstructural model, Cement & Concrete Research, 28, 2, 285-297, (1998)
[35] Lee, Y.; Kim, J.-K., Numerical analysis of the early age behaviour of concrete structures with a hydration based microplane model, Computers and Structures, 87, 1085-1101, (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.