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An elastoplastic damage constitutive model of concrete considering the effects of dehydration and pore pressure at high temperatures

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Pore pressure and thermal dehydration of concrete are two major factors which affect the spalling of concrete at high temperatures. Thermal dehydration can cause deterioration of concrete properties and promote the development of micro cracks in the skeleton of concrete. Pore pressure will also be influenced by dehydration when the hydrated water enters the micro pores. In the current study, a framework of elastoplastic damage constitutive model is developed to described the mechanical behaviour of concrete and pore pressure at high temperatures. Both load induced damage and thermal dehydrated damage are considered. The thermal dehydrated damage is temperature related, which reflects the impact of temperature on concrete properties. A model of pore pressure is developed by considering the influence of thermal dehydration and damage related permeability. The pore pressure field associated with vapor, liquid water and dry air is predicted and compared with experimental results.

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  1. 1.

    Bažant ZP (1997) Analysis of pore pressure, thermal stress and fracture in rapidly heated concrete. In: International workshop on fire performance of high-strength concrete, Gaithersburg, USA

  2. 2.

    Ulm FJ, Coussy O, Bažant ZP (1999) The “Chunnel” fire. I: chemoplastic softening in rapidly heated concrete. J Eng Mech 125(3):272–282

  3. 3.

    Gawin D, Pesavento F, Schrefler B (2002) Simulation of damage–permeability coupling in hygro-thermo-mechanical analysis of concrete at high temperature. Commun Numer Methods Eng 18(2):113–119

  4. 4.

    Gawin D, Schrefler BA, Galindo M (1996) Thermo-hydro-mechanical analysis of partially saturated porous materials. Eng Comput 13(7):113–143

  5. 5.

    Gawin D, Pesavento F, Schrefler B (2004) Modelling of deformations of high strength concrete at elevated temperatures. Mater Struct 37(4):218

  6. 6.

    Gawin D, Pesavento F, Schrefler BA (2006) Towards prediction of the thermal spalling risk through a multi-phase porous media model of concrete. Comput Methods Appl Mech Eng 195(41–43):5707–5729.

  7. 7.

    Gawin D, Pesavento F, Schrefler B (2003) Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation. Comput Methods Appl Mech Eng 192(13–14):1731–1771

  8. 8.

    Tenchev RT, Li L, Purkiss J (2001) Finite element analysis of coupled heat and moisture transfer in concrete subjected to fire. Numer Heat Transf Part A Appl 39(7):685–710

  9. 9.

    Tenchev R, Purnell P (2005) An application of a damage constitutive model to concrete at high temperature and prediction of spalling. Int J Solids Struct 42(26):6550–6565

  10. 10.

    Ichikawa Y, England GL (2004) Prediction of moisture migration and pore pressure build-up in concrete at high temperatures. Nucl Eng Des 228(1–3):245–259

  11. 11.

    Davie CT, Pearce CJ, Bićanić N (2006) Coupled heat and moisture transport in concrete at elevated temperatures—effects of capillary pressure and adsorbed water. Numer Heat Transf Part A Appl 49(8):733–763

  12. 12.

    Chung JH, Consolazio GR, McVay MC (2006) Finite element stress analysis of a reinforced high-strength concrete column in severe fires. Comput Struct 84(21):1338–1352

  13. 13.

    Dwaikat MB, Kodur V (2009) Hydrothermal model for predicting fire-induced spalling in concrete structural systems. Fire Saf J 44(3):425–434

  14. 14.

    Millard R, Pimienta P (2019) Modelling of concrete behaviour at high temperature, state-of-the-art report of the RILEM Technical Committee 227-HPB, RILEM State-of-the-Art Reports, Springer

  15. 15.

    Meftah F, Dal Pont S, Schrefler BA (2012) A three-dimensional staggered finite element approach for random parametric modeling of thermo-hygral coupled phenomena in porous media. Int J Numer Anal Methods Geomech 36(5):574–596

  16. 16.

    Meftah F, Dal Pont S (2010) Staggered finite volume modeling of transport phenomena in porous materials with convective boundary conditions. Transp Porous Media 82(2):275–298

  17. 17.

    Schrefler BA, Khoury GA, Gawin D, Majorana CE (2002) Thermo-hydro-mechanical modelling of high performance concrete at high temperatures. Eng Comput 19(7–8):787–819

  18. 18.

    Kodur VKR (2000) Spalling in high strength concrete exposed to fire—concerns, causes, critical parameters and cures. In: Proceedings of the ASCE structures congress: advanced technology in structural engineering, pp 1–9

  19. 19.

    Liu JC, Tan KH, Yao Y (2018) A new perspective on nature of fire-induced spalling in concrete. Constr Build Mater 184:581–590

  20. 20.

    Fu YF, Wong YL, Tang CA, Poon CS (2004) Thermal induced stress and associated cracking in cement-based composite at elevated temperatures—part I: thermal cracking around single inclusion. Cem Concr Compos 26(2):99–111.

  21. 21.

    Fu YF, Wong YL, Tang CA, Poon CS (2004) Thermal induced stress and associated crackin in cement-based composite at elevated temperatures—part II: thermal cracking around multiple inclusions. Cem Concr Compos 26(2):113–126.

  22. 22.

    Yao Y, Wang KM (2017) Elastic–plastic damage model to predict pore-pressure effect on concrete behavior at elevated temperatures. J Eng Mech 143(10):9.

  23. 23.

    Yao Y, Wang KM, Hu XX (2017) Thermodynamic-based elastoplasticity multiaxial constitutive model for concrete at elevated temperatures. J Eng Mech 143(7):04017039.

  24. 24.

    Connolly R (1995) The spalling of concrete in fires. The University of Aston, Birmingham

  25. 25.

    Kalifa P, Chene G, Galle C (2001) High-temperature behaviour of HPC with polypropylene fibres—from spalling to microstructure. Cem Concr Res 31(10):1487–1499.

  26. 26.

    Kalifa P, Menneteau FD, Quenard D (2000) Spalling and pore pressure in HPC at high temperatures. Cem Concr Res 30(12):1915–1927.

  27. 27.

    Dal Pont S, Colina H, Dupas A, Ehrlacher A (2005) An experimental relationship between complete liquid saturation and violent damage in concrete submitted to high temperature. Mag Concr Res 57(8):455–461

  28. 28.

    Phan LT (2002) High-strength concrete at high temperature—an overview. In: Proceedings of 6th international symposiumon utilization of high strength/high performance concrete, Leipzig, Germany, pp 501–518

  29. 29.

    Hertz KD, Sørensen LS (2005) Test method for spalling of fire exposed concrete. Fire Saf J 40(5):466–476

  30. 30.

    Dauti D, Dal Pont S, Briffaut M, Weber B (2019) Modeling of 3D moisture distribution in heated concrete: from continuum towards mesoscopic approach. Int J Heat Mass Transf 134:1137–1152

  31. 31.

    Dauti D, Dal Pont S, Weber B, Briffaut M, Toropovs N, Wyrzykowski M, Sciumé G (2018) Modeling concrete exposed to high temperature: impact of dehydration and retention curves on moisture migration. Int J Numer Anal Methods Geomech 42(13):1516–1530.

  32. 32.

    Dauti D, Tengattini A, Dal Pont S, Toropovs N, Briffaut M, Weber B (2018) Analysis of moisture migration in concrete at high temperature through in situ neutron tomography. Cem Concr Res 111:41–55

  33. 33.

    Zhang C, Liu J, Han S, Hua Y (2018) Pore pressure and spalling in fire-exposed high-strength self-consolidating concrete reinforced with hybrid fibres. Eur J Environ Civ Eng 22:1–31

  34. 34.

    Bangi MR, Horiguchi T (2011) Pore pressure development in hybrid fibre-reinforced high strength concrete at elevated temperatures. Cem Concr Res 41(11):1150–1156

  35. 35.

    Sabeur H, Meftah F (2008) Dehydration creep of concrete at high temperatures. Mater Struct 41(1):17–30.

  36. 36.

    Meschke G, Lackner R, Mang HA (1998) An anisotropic elastoplastic-damage model for plain concrete. Int J Numer Methods Eng 42(4):703–727

  37. 37.

    Cicekli U, Voyiadjis GZ, Al-Rub RKA (2007) A plasticity and anisotropic damage model for plain concrete. Int J Plast 23(10–11):1874–1900

  38. 38.

    Voyiadjis GZ, Taqieddin ZN, Kattan PI (2008) Anisotropic damage–plasticity model for concrete. Int J Plast 24(10):1946–1965

  39. 39.

    Voyiadjis GZ, Taqieddin ZN, Kattan PI (2009) Theoretical formulation of a coupled elastic—plastic anisotropic damage model for concrete using the strain energy equivalence concept. Int J Damage Mech 18(7):603–638

  40. 40.

    Baker G, Borst Rd (2005) An anisotropic thermomechanical damage model for concrete at transient elevated temperatures. Philos Trans R Soc A Math Phys Eng Sci 363(1836):2603–2628

  41. 41.

    Nechnech W, Meftah F, Reynouard J (2002) An elasto-plastic damage model for plain concrete subjected to high temperatures. Eng Struct 24(5):597–611

  42. 42.

    Gernay T, Millard A, Franssen J-M (2013) A multiaxial constitutive model for concrete in the fire situation: theoretical formulation. Int J Solids Struct 50(22–23):3659–3673

  43. 43.

    Hassen S, Colina H (2006) Transient thermal creep of concrete in accidental conditions at temperatures up to 400 °C. Mag Concr Res 58(4):201–208

  44. 44.

    Sabeur H, Meftah F, Colina H, Platret G (2008) Correlation between transient creep of concrete and its dehydration. Mag Concr Res 60(3):157–163

  45. 45.

    Wu JY, Li J, Faria R (2006) An energy release rate-based plastic–damage model for concrete. Int J Solids Struct 43(3–4):583–612

  46. 46.

    Grassl P, Jirásek M (2006) Damage–plastic model for concrete failure. Int J Solids Struct 43(22–23):7166–7196

  47. 47.

    Matallah M, La Borderie C (2009) Inelasticity–damage-based model for numerical modeling of concrete cracking. Eng Fract Mech 76(8):1087–1108

  48. 48.

    Karsan ID, Jirsa JO (1969) Behavior of concrete under compressive loadings. J Struct Div ASCE 95(12):2543–2563

  49. 49.

    Ehm C, Schneider U (1985) The high temperature behaviour of concrete under biaxial conditions. Cem Concr Res 15(1):27–34

  50. 50.

    Lie T, Erwin R (1993) Method to calculate the fire resistance of reinforced concrete columns with rectangular cross section. ACI Struct J 90(1):52–60

  51. 51.

    Chang YF, Chen YH, Sheu MS, Yao GC (2006) Residual stress–strain relationship for concrete after exposure to high temperatures. Cem Concr Res 36(10):1999–2005

  52. 52.

    Kodur V, Wang T, Cheng F (2004) Predicting the fire resistance behaviour of high strength concrete columns. Cem Concr Compos 26(2):141–153

  53. 53.

    Standardization ECf (2004) Eurocode 2. Design of concrete structures. Part 1.2: general rules—structural fire design. Commission of European Communities, Brussels

  54. 54.

    Aslani F, Bastami M (2011) Constitutive relationships for normal-and high-strength concrete at elevated temperatures. ACI Mater J 108(4):355

  55. 55.

    Anderberg Y, Thelandersson S (1976) Stress and deformation characteristics of concrete at high temperatures. 2. Experimental investigation and material behaviour model. Bulletin of Division of Structural Mechanics and Concrete Construction, Bulletin 54

  56. 56.

    Schneider U (1986) Modelling of concrete behaviour at high temperatures. In: Anchor RD et al (eds) Design of structures against fire. Elsevier, London, pp 53–70

  57. 57.

    Khoury GA (1995) Strain components of nuclear-reactor-type concretes during first heat cycle. Nucl Eng Des 156(1–2):313–321

  58. 58.

    Terro MJ (1998) Numerical modeling of the behavior of concrete structures in fire. ACI Struct J 95:183–193

  59. 59.

    Bazant ZP, Chern J (1985) Concrete creep at variable humidity: constitutive law and mechanism. Mater Struct 18(1):1

  60. 60.

    Benboudjema F, Meftah F, Torrenti JM (2005) Interaction between drying, shrinkage, creep and cracking phenomena in concrete. Eng Struct 27(2):239–250

  61. 61.

    Dal Pont S, Ehrlacher A (2004) Numerical and experimental analysis of chemical dehydration, heat and mass transfers in a concrete hollow cylinder submitted to high temperatures. Int J Heat Mass Transf 47(1):135–147

  62. 62.

    Hassen S (2011) On the modeling of the dehydration induced transient creep during a heating–cooling cycle of concrete. Mater Struct 44(9):1609

  63. 63.

    Guo F, He B, Niu X (2015) Analysis of vapor pressure and void volume fraction evolution in porous polymers: a micromechanics approach. Int J Solids Struct 66:133–139

  64. 64.

    Thomson GW (1946) The Antoine equation for vapor-pressure data. Chem Rev 38(1):1–39

  65. 65.

    Hervé E, Stolz C, Zaoui A (1991) A propos de l’assemblage de sphères composites de Hashin. Comptes Rendus de l’Academie des Sciences Serie II 313:857–862

  66. 66.

    Zhang W, Xu Z, Wang TJ, Chen X (2009) Effect of inner gas pressure on the elastoplastic behavior of porous materials: a second-order moment micromechanics model. Int J Plast 25(7):1231–1252

  67. 67.

    Bazant Z, Kaplan M (1996) Concrete at high temperature: material properties and mathematical modeling. Longman Group Limited, Harlow

  68. 68.

    Bary B, Bournazel JP, Bourdarot E (2000) Poro-damage approach applied to hydro-fracture analysis of concrete. J Eng Mech 126(9):937–943

  69. 69.

    Dal Pont S, Schrefler B, Ehrlacher A (2005) Intrinsic permeability evolution in high temperature concrete: an experimental and numerical analysis. Transp Porous Media 60(1):43–74

  70. 70.

    Hager I (2004) Comportement à haute température des bétons à haute performance: évolution des principales propriétés mécaniques. ENPC, Paris

  71. 71.

    Kupfer H, Hilsdorf HK, Rusch H (1969) Behavior of concrete under biaxial stresses. J Proc 8:656–666

  72. 72.

    Gopalaratnam V, Shah SP (1985) Softening response of plain concrete in direct tension. J Proc 3:310–323

  73. 73.

    Vonk RA (1992) Softening of concrete loaded in compression. Eindhoven University of Technology, Eindhoven

  74. 74.

    Lie TT (1992) Structural fire protection. American Society of Civil Engineers, Reston.

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This study was funded by the National Natural Science Foundation of China (No. 11772257); Fundamental Research Funds for the Central Universities (No. G2019KY05212) and the Alexander von Humboldt Foundation (Fellowship for Experienced Researchers).

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Correspondence to Yao Yao.

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Yao, Y., Guo, H. & Tan, K. An elastoplastic damage constitutive model of concrete considering the effects of dehydration and pore pressure at high temperatures. Mater Struct 53, 19 (2020).

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  • Concrete
  • Plastic damage model
  • Dehydration
  • Pore pressure
  • High temperature