Materials and Structures

, 52:11 | Cite as

Century-long expansion of hydrating cement counteracting concrete shrinkage due to humidity drop from selfdesiccation or external drying

  • Saeed Rahimi-Aghdam
  • Enrico Masoero
  • Mohammad Rasoolinejad
  • Zdeněk P. BažantEmail author
50 years of Materials and Structures
Part of the following topical collections:
  1. 50 years of Materials and Structures


A physically based model for auotgenous shrinkage and swelling of portland cement paste is necessary for computation of long-time hydgrothermal effects in concrete structures. The goal is to propose such a model. As known since 1887, the volume of cement hydration products is slightly smaller than the original volume of cement and water (chemical shrinkage). Nevertheless, this does not imply that the hydration reaction results in contraction of the concrete and cement paste. According to the authors’ recently proposed paradigm, the opposite is true for the entire lifetime of porous cement paste as a whole. The hydration process causes permanent volume expansion of the porous cement paste as a whole, due to the growth of C–S–H shells around anhydrous cement grains which pushes the neighbors apart, while the volume reduction of hydration products contributes to porosity. Additional expansion can happen due to the growth of ettringite and portlandite crystals. On the material scale, the expansion always dominates over the contraction, i.e., the hydration per se is, in the bulk, always and permanently expansive, while the source of all of the observed shrinkage, both autogenous and drying, is the compressive elastic or viscoelastic strain in the solid skeleton caused by a decrease of chemical potential of pore water, along with the associated decrease in pore relative humidity. As a result, the selfdesiccation, shrinkage and swelling can all be predicted from one and the same unified model, in which, furthermore, the low-density and high-density C–S–H are distinguished. A new thermodynamic formulation of unsaturated poromechanics with capillarity and adsorption is presented. The recently formulated local continuum model for calculating the evolution of hydration degree and a new formulation of nonlinear desorption isotherm are important for realistic and efficient finite element analysis of shrinkage and swelling. Comparisons with the existing relevant experimental evidence validate the proposed model.


Autogenous shrinkage Swelling Hydration Swelling Drying Biot coefficient Pore water Thermodynamics Unsaturated poromechanics Capillarity and adsorption 



Partial financial support of poromechanics studies from DoE through Los Alamos National Lab grant to Northwestern University is gratefully acknowledged. Preliminary research was supported by the U.S. Department of Transportation through Grant 20778 from the Infrastructure Technology Institute of Northwestern University, and from the NSF under Grant CMMI-1129449.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Bažant ZP, Yu Q, Li G-H (2012) Excessive long-time deflections of prestressed box girders. II: numerical analysis and lessons learned. J Struct Eng 138(6):687–696Google Scholar
  2. 2.
    Bažant ZP, Hubler MH, Yu Q (2011) Pervasiveness of excessive segmental bridge deflections: wake-up call for creep. ACI Struct J 108(6):766Google Scholar
  3. 3.
    Bažant ZP, Yu Q, Li G-H (2012) Excessive long-time deflections of prestressed box girders. I: record-span bridge in palau and other paradigms. J Struct Eng 138(6):676–686Google Scholar
  4. 4.
    Bažant Z, Donmez A, Masoero E, Aghdam SR (2015) Interaction of concrete creep, shrinkage and swelling with water, hydration, and damage: nano-macro-chemo. In: CONCREEP 10, 10th international conference on mechanics and physics of creep, shrinkage, and durability of concrete and concrete structures, held in Vienna, Austria, Sept, ASCE, Washington, D.C, pp 1–10Google Scholar
  5. 5.
    Bažant ZP, Rahimi-Aghdam S (2018) Century-long durability of concrete structures: expansiveness of hydration and chemo-mechanics of autogenous shrinkage and swelling. In: Computational modelling of concrete structures: proceedings of the conference on computational modelling of concrete and concrete structures (EURO-C 2018), February 26–March 1, 2018, Bad Hofgastein, Austria, CRC PressGoogle Scholar
  6. 6.
    Abuhaikal M, Ioannidou K, Petersen T, Pellenq RJ-M, Ulm F-J (2018) Le châteliers conjecture: measurement of colloidal eigenstresses in chemically reactive materials. J Mech Phys Sol 112:334–344Google Scholar
  7. 7.
    Rahimi-Aghdam S, Bažant ZP, Cusatis G (2018) Extended microprestress-solidification theory for long-term creep with diffusion size effect in concrete at variable environment. J Eng Mech 145(2):04018131Google Scholar
  8. 8.
    Rahimi-Aghdam S, Bažant ZP, Qomi MA (2017) Cement hydration from hours to centuries controlled by diffusion through barrier shells of CSH. J Mech Phys Sol 99:211–224Google Scholar
  9. 9.
    Rahimi-Aghdam S, Rasoolinejad M, Bažant Z (2018) Moisture diffusion in unsaturated selfdesiccating concrete with humidity dependent permeability and nonlinear sorption isotherm. J Eng Mech. Google Scholar
  10. 10.
    Brooks J, Wainwright P (1983) Properties of ultra-high-strength concrete containing a superplasticizer. Mag Concr Res 35(125):205–213Google Scholar
  11. 11.
    Persson B (2002) Eight-year exploration of shrinkage in high-performance concrete. Cement Concr Res 32(8):1229–1237Google Scholar
  12. 12.
    Bažant ZP, Jirásek M, Hubler M, Carol I (2015) RILEM draft recommendation: Tc-242-mdc multi-decade creep and shrinkage of concrete: material model and structural analysis. model B4 for creep, drying shrinkage and autogenous shrinkage of normal and high-strength concretes with multi-decade applicability. Mater Struct 48(4):753–770Google Scholar
  13. 13.
    Kovler K, Jensen O (2007) Report 41: Internal curing of concrete-state-of-the-art report of RILEM technical committee 196-ICC, vol 41. RILEM Publications S.A.R.L. France, BagneuxGoogle Scholar
  14. 14.
    Lura P, Couch J, Jensen OM, Weiss J (2009) Early-age acoustic emission measurements in hydrating cement paste: evidence for cavitation during solidification due to self-desiccation. Cement Concr Res 39(10):861–867Google Scholar
  15. 15.
    Jensen OM, Hansen PF (1999) Influence of temperature on autogenous deformation and relative humidity change in hardening cement paste. Cement Concr Res 29(4):567–575Google Scholar
  16. 16.
    Patel R, Killoh D, Parrott L, Gutteridge W (1988) Influence of curing at different relative humidities upon compound reactions and porosity in portland cement paste. Mater Struct 21(3):192–197Google Scholar
  17. 17.
    Powers T, Brownyard T (1947) The thermodynamics of adsorption of water on hardened cement paste. J Am Concr Inst 18:549–602Google Scholar
  18. 18.
    Wyrzykowski M, Lura P (2016) Effect of relative humidity decrease due to self-desiccation on the hydration kinetics of cement. Cement Concr Res 85:75–81Google Scholar
  19. 19.
    Bažant ZP, Jirásek M (2017) Creep and hygrothermal effects in concrete structures. Springer, BerlinGoogle Scholar
  20. 20.
    Diamond S (1996) Delayed ettringite formation. processes and problems. Cement Concr Compos 18(3):205–215Google Scholar
  21. 21.
    Taylor H, Famy C, Scrivener K (2001) Delayed ettringite formation. Cement Concr Res 31(5):683–693Google Scholar
  22. 22.
    Bažant ZP, Rahimi-Aghdam S (2016) Diffusion-controlled and creep-mitigated ASR damage via microplane model. I: mass concrete. J Eng Mech 143(2):04016108Google Scholar
  23. 23.
    Rahimi-Aghdam S, Bažant ZP, Caner FC (2016) Diffusion-controlled and creep-mitigated ASR damage via microplane model. II: material degradation, drying, and verification. J Eng Mech 143(2):04016109Google Scholar
  24. 24.
    Detournay E, Cheng AH-D (1993) Fundamentals of poroelasticity. In: Analysis and design methods, Elsevier, Amsterdam, pp 113–171Google Scholar
  25. 25.
    Biot M, Willis D (1957) The elastic coefficients of the theory of consolidation. J Appl Mech 24:594–601MathSciNetGoogle Scholar
  26. 26.
    Nielsen LF (1991) A research note on sorption, pore size distribution, and shrinkage of porous materials. Danmarks Tekniske Højskole, Laboratoriet for BygningsmaterialerGoogle Scholar
  27. 27.
    Coussy O, Dangla P, Lassabatère T, Baroghel-Bouny V (2004) The equivalent pore pressure and the swelling and shrinkage of cement-based materials. Mater Struct 37(1):15–20Google Scholar
  28. 28.
    Brunauer S (1943) The adsorption of gases and vapors. Vol. I. Physical adsorption. Princeton University Press, Princeton, NJGoogle Scholar
  29. 29.
    Brunauer S, Emmett PH, Teller E (1938) Adsorption of gases in multimolecular layers. J Am Chem Soc 60(2):309–319Google Scholar
  30. 30.
    Xi Y, Bažant ZP, Jennings HM (1994) Moisture diffusion in cementitious materials adsorption isotherms. Adv Cement Based Mater 1(6):248–257Google Scholar
  31. 31.
    Bazant ZP, Nguyen HT (2018) Direct multilayer adsorption of vapor in solids with multiscale porosity and hindered adsorbed layers in nanopores. arXiv preprint arXiv:1812.11235
  32. 32.
    Chau VT, Bažant ZP, Su Y (2016) Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale. Phil Trans R Soc A 374(2078):20150418Google Scholar
  33. 33.
    Baroghel-Bouny V, Mounanga P, Khelidj A, Loukili A, Rafaï N (2006) Autogenous deformations of cement pastes: part II. w/c effects, micro–macro correlations, and threshold values. Cement Concr Res 36(1):123–136Google Scholar
  34. 34.
    Jiang Z, Sun Z, Wang P (2006) Internal relative humidity distribution in high-performance cement paste due to moisture diffusion and self-desiccation. Cement Concr Res 36(2):320–325Google Scholar
  35. 35.
    Qomi MA, Krakowiak K, Bauchy M, Stewart K, Shahsavari R, Jagannathan D, Brommer D, Baronnet A, Buehler M, Yip S et al (2014) Combinatorial molecular optimization of cement hydrates. Nat Commun 5:4960Google Scholar
  36. 36.
    Taplin J (1959) A method for following the hydration reaction in portland cement paste. Aust J Appl Sci 10:329–345Google Scholar
  37. 37.
    Constantinides G, Ulm F-J, Van Vliet K (2003) On the use of nanoindentation for cementitious materials. Mater Struct 36(3):191–196Google Scholar
  38. 38.
    Jennings HM (2000) A model for the microstructure of calcium silicate hydrate in cement paste. Cement Concr Res 30(1):101–116Google Scholar
  39. 39.
    Tennis PD, Jennings HM (2000) A model for two types of calcium silicate hydrate in the microstructure of Portland cement pastes. Cement Concr Res 30(6):855–863Google Scholar
  40. 40.
    Kim J-K, Lee C-S (1999) Moisture diffusion of concrete considering self-desiccation at early ages. Cement Concr Res 29(12):1921–1927Google Scholar
  41. 41.
    Gajewicz A, Gartner E, Kang K, McDonald P, Yermakou V (2016) A 1h nmr relaxometry investigation of gel-pore drying shrinkage in cement pastes. Cement Concr Res 86:12–19Google Scholar
  42. 42.
    Muller A, Scrivener K, Gajewicz A, McDonald P (2013) Use of bench-top nmr to measure the density, composition and desorption isotherm of c-s-h in cement paste. Microporous Mesoporous Mater 178:99–103Google Scholar
  43. 43.
    Wyrzykowski M, McDonald PJ, Scrivener KL, Lura P (2017) Water redistribution within the microstructure of cementitious materials due to temperature changes studied with 1h nmr. J Phys Chem C 121(50):27950–27962Google Scholar
  44. 44.
    Muller AC, Scrivener KL, Gajewicz AM, McDonald PJ (2012) Densification of c-s-h measured by 1h nmr relaxometry. J Phys Chem C 117(1):403–412Google Scholar
  45. 45.
    Masoero E, Di Luzio G, Cusatis G et al. (2018) The impact of CSH nanostructure on autogenous shrinkage and sorption isotherms. In: SynerCrete18: interdisciplinary approaches for cement-based materials and structural concrete: synergizing expertise and bridging scales of space and time, vol 2, pp 791–796. RILEM Publications SARLGoogle Scholar
  46. 46.
    Persson B (1996) Hydration and strength of high performance concrete. Adv Cement Based Mater 3(3):107–123Google Scholar
  47. 47.
    Persson B (1997) Self-desiccation and its importance in concrete technology. Mater Struct 30(5):293–305Google Scholar
  48. 48.
    Pathirage M, Bentz DP, Di Luzio G, Masoero E, Cusatis G (2017) A multiscale framework for the prediction of concrete self-desiccation. In: Proceedings of the EURO-C 2018 conference - computational modelling of concrete and concrete, Austria (2018)Google Scholar
  49. 49.
    Chen H, Wyrzykowski M, Scrivener K, Lura P (2013) Prediction of self-desiccation in low water-to-cement ratio pastes based on pore structure evolution. Cement Concr Res 49:38–47Google Scholar
  50. 50.
    Miyazawa S, Monteiro PJM (1996) Volume change of high-strength concrete in moist conditions. Cement Concr Res 26(4):567–572Google Scholar
  51. 51.
    Bentz DP (1997) Three-dimensional computer simulation of portland cement hydration and microstructure development. J Am Ceram Soc 80(1):3–21Google Scholar
  52. 52.
    Bažant Z, Najjar L (1972) Nonlinear water diffusion in nonsaturated concrete. Mater Struct 5(1):3–20Google Scholar
  53. 53.
    Di Luzio G, Cusatis G (2009) Hygro-thermo-chemical modeling of high performance concrete. I: theory. Cement Concr Compos 31(5):301–308Google Scholar
  54. 54.
    Di Luzio G, Cusatis G (2009) Hygro-thermo-chemical modeling of high-performance concrete. II: numerical implementation, calibration, and validation. Cement Concr Compos 31(5):309–324Google Scholar

Copyright information

© RILEM 2019

Authors and Affiliations

  • Saeed Rahimi-Aghdam
    • 1
  • Enrico Masoero
    • 2
  • Mohammad Rasoolinejad
    • 1
  • Zdeněk P. Bažant
    • 1
    Email author
  1. 1.Northwestern UniversityEvanstonUSA
  2. 2.Newcastle UniversityNewcastle upon TyneUK

Personalised recommendations