Acta Mechanica Solida Sinica

, Volume 31, Issue 2, pp 161–173 | Cite as

Experimental and Theoretical Analyses on the Density and Modulus Development of Concrete Under Continued Hydration

  • Lanzhen Yu
  • Jiankang Chen
  • Hui Song


In this paper, new models of the density and modulus development of concrete under continued hydration were studied. Experimental study was performed for different mixes of concrete. To avoid considering the effect of variation of Poisson’s ratio, the one-dimensional ultrasonic technique was adopted to detect the modulus development of concrete under continued hydration. The experimental results indicate the nonlinear characteristics of density and modulus evolution. At the initial stage of continued hydration, the density and modulus increase quickly, and then the increases slow down and finally tend to be constant. The mechanism of modulus enhancement is that the newly produced C–S–H gel in the continued hydration process not only leads to the decrease in porosity, but also repairs the initial defects of concrete. Based on this mechanism, simple differential equations for the density and modulus development of concrete were established by considering the chemical reactions of continued hydration, and new simple models for density and modulus development were proposed.


Concrete Continued hydration Density development Modulus development Ultrasonic 



The authors would like to acknowledge the financial support by the National Natural Science Foundation of China (NSFC #11772164, #11272165, #11572163), the National Basic Research Program of China (973 Program, 2009CB623203), the Key Research Program of Society Development of Ningbo (2013C51007), and the K.C. Wong Magna Fund in Ningbo University. The authors were also supported by the Research Project Foundation of Zhejiang Educational Department (Y201636745).


  1. 1.
    Al-Amoudi OSB. Attack on plain and blended cements exposed to aggressive sulfate environments. Cement Concrete Compos. 2002;24(3–4):305–16.CrossRefGoogle Scholar
  2. 2.
    Lee ST, Moon HY, Swamy RN. Sulfate attack and role of silica fume in resisting strength loss. Cement Concrete Compos. 2005;27(1):65–76.CrossRefGoogle Scholar
  3. 3.
    Bakharev T, Sanjayan JG, Cheng YB. Sulfate attack on alkali-activated slag concrete. Cement Concrete Res. 2002;32(2):211–6.CrossRefGoogle Scholar
  4. 4.
    Chen JK, Qian C, Song H. A new chemo-mechanical model of damage in concrete under sulfate attack. Constr Build Mater. 2016;115:536–43.CrossRefGoogle Scholar
  5. 5.
    Ouyang WY, Chen JK, Jiang MQ. Evolution of surface hardness of concrete under sulfate attack. Constr Build Mater. 2014;53(2):419–24.CrossRefGoogle Scholar
  6. 6.
    Chen JK, Jiang MQ, Zhu J. Damage evolution in cement mortar due to erosion of sulphate. Corros Sci. 2008;50(9):2478–83.CrossRefGoogle Scholar
  7. 7.
    Wilby CB. Concrete materials and structures. Cambridge: Cambridge University Press; 1991.Google Scholar
  8. 8.
    Bai J, Chaipanich A, Kinuthia JM, Farrell MO, Sabir BB, Wild S, et al. Compressive strength and hydration of wastepaper sludge ash-ground granulated blastfurnace slag blended pastes. Cement Concrete Res. 2003;33(8):1189–202.CrossRefGoogle Scholar
  9. 9.
    Calvo JLG, Alonso MC, Hidalgo A, Luco F, Flor-Laguna V. Development of low-pH cementitious materials based on CAC for HLW repositories: long-term hydration and resistance against groundwater aggression. Cement Concrete Res. 2013;51(9):67–77.CrossRefGoogle Scholar
  10. 10.
    Tittelboom KV, Gruyaert E, Rahier H, Belie ND. Influence of mix composition on the extent of autogenous crack healing by continued hydration or calcium carbonate formation. Constr Build Mater. 2012;37(37):349–59.CrossRefGoogle Scholar
  11. 11.
    Grant SA, Boitnott GE, Korhonen CJ, Sletten RS. Effect of temperature on hydration kinetics and polymerization of tricalcium silicate in stirred suspensions of CaO-saturated solutions. Cement Concrete Res. 2006;36(4):671–7.CrossRefGoogle Scholar
  12. 12.
    Bullard JW, Jennings HM, Livingston RA, Nonat A, Scherer GW, Schweitzer JS, et al. Mechanisms of cement hydration. Cement Concrete Res. 2011;41(12):1208–23.CrossRefGoogle Scholar
  13. 13.
    Xi Y, Siemer DD, Scheetz BE. Strength development, hydration reaction and pore structure of autoclaved slag cement with added silica fume. Cement Concrete Res. 1997;27(1):75–82.CrossRefGoogle Scholar
  14. 14.
    Bernard O, Ulm FJ, Lemarchand E. A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials. Cement Concrete Res. 2003;33(9):1293–309.CrossRefGoogle Scholar
  15. 15.
    Freidin C. Hydration and strength development of binder based on high-calcium oil shale fly ash. Part 2: influence of curing conditions on long-term stability. Cement Concrete Res. 1999;29(11):1713–9.CrossRefGoogle Scholar
  16. 16.
    Mak SL, Torii K. Strength development of high strength concretes with and without silica fume under the influence of high hydration temperatures. Cement Concrete Res. 1995;25(8):1791–802.CrossRefGoogle Scholar
  17. 17.
    Livingston RA. Fractal nucleation and growth model for the hydration of tricalcium silicate. Cement Concrete Res. 2000;30(12):1853–60.CrossRefGoogle Scholar
  18. 18.
    Ohtsu M. Elastic wave methods for NDE in concrete based on generalized theory of acoustic emission. Constr Build Mater. 2016;122:845–54.CrossRefGoogle Scholar
  19. 19.
    Chu HY, Chen JK. Evolution of viscosity of concrete under sulfate attack. Constr Build Mater. 2013;39:46–50.CrossRefGoogle Scholar
  20. 20.
    Song H, Chen JK. Effect of damage evolution on Poisson’s ratio of concrete under sulfate attack. Acta Mech Solida Sin. 2011;24(3):209–15.CrossRefGoogle Scholar
  21. 21.
    Meyers MA. Dynamic behavior of materials. Chichester: Wiley; 1994.CrossRefzbMATHGoogle Scholar
  22. 22.
    Stephan D, Dikoundou SN, Raudaschl-Sieber G. Hydration characteristics and hydration products of tricalcium silicate doped with a combination of MgO, \(\text{ Al }_{2}\text{ O }_{3}\), and \(\text{ Fe }_{2}\text{ O }_{3}\). Thermochim Acta. 2008;472(1–2):64–73.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2018

Authors and Affiliations

  1. 1.The Faculty of Mechanical Engineering and MechanicsNingbo UniversityNingboChina
  2. 2.State Key Laboratory of Turbulence and Complex SystemsPeking UniversityBeijingChina
  3. 3.Department of Architectural EngineeringNingbo PolytechnicNingboChina

Personalised recommendations