Multi-Scale Digital-Image-Based Modelling of Cement-Based Materials


Computer modelling of the properties and performance of cement-based materials is complicated by the large range of relevant size scales. Processes occurring in the nanometersized pores ultimately affect the performance of these materials at the structural level of meters and larger. One approach to alleviating this complication is the development of a suite of models, consisting of individual digital-image-based structural models for the calcium silicate hydrate gel at the nanometer level, the hydrated cement paste at the micrometer level, and a mortar or concrete at the millimeter level. Computations performed at one level provide input properties to be used in simulations of performance at the next higher level. This methodology is demonstrated for the property of ionic diffusivity in saturated concrete. The more complicated problem of drying shrinkage is also addressed.

This is a preview of subscription content, access via your institution.



degree of hydration


liquid surface tension







c, d:

constants in equation to estimate mortar relative diffusivity




heaviside function = (1: x ≥0; 0 otherwise)




pore radius


universal gas constant


absolute temperature


volume fraction


water to cement ratio




bulk solution


interfacial zone cement paste






bulk cement paste


  1. [1]

    Scrivener, K.L., in Materials Science of Concrete I, edited by Skalny, J.P. (American Ceramic Society, Westerville, OH, 1989), p. 127.

  2. [2]

    Bentz, D.P., Schlangen, E., and Garboczi, E.J., in Materials Science of Concrete IV, edited by Skalny, J.P. and Mindess, S. (American Ceramic Society, Westerville, OH, 1994).

    Google Scholar 

  3. [3]

    Garboczi, E.J., Schwartz, L.M., and Bentz, D.P., “Modelling the Influence of the Interfacial Zone on the Conductivity and Diffusivity of Mortar,” submitted to J. of Advanced Cement-Based Mat.

  4. [4]

    Garboczi, E.J., Schwartz, L.M., and Bentz, D.P., “Modelling the D.C. Electrical Conductivity of Mortar,” these proceedings.

  5. [5]

    Schwartz, L.M., Garboczi, E.J., and Bentz, D.P., “Interfacial Transport in Porous Media: Application to D.C. Electrical Conductivity of Mortars,” submitted to Phys. Rev. B.

  6. [6]

    Neubauer, C.M., Jennings, H.M., and Garboczi, E.J., “Modelling the Effect of Interfacial Zone Microstructure and Properties on the Elastic Drying Shrinkage of Mortar,” submitted to J. of Advanced Cement-Based Mat.

  7. [7]

    Bentz, D.P., Quenard, D.A., Baroghel-Bouny, V., Garboczi, E.J., and Jennings, H.M., “Modelling Drying Shrinkage of Cement Paste and Mortar: Part 1. Structural Models from Nanometers to Millimeters,” to appear in Mat. and Struc.

  8. [8]

    Jennings, H.M., and Xi, Y., in Creep and Shrinkage of Concrete, edited by Bazant, Z.P. and Carol, I. (E & F Spon, London, 1993), p. 85.

  9. [9]

    Huet, C., in Micromechanics of Concrete and Cementitious Composites, edited by Huet, C. (Presses Polytechniques et Universitaires Romandes, Lausanne, 1993), p. 117.

  10. [10]

    Bentz, D.P., Martys, N.S., Stutzman, P.E., Levenson, M.S., Garboczi, E.J., Dunsmuir, J., and Schwartz, L.M., “X-Ray Microtomography of an ASTM C109 Mortar Exposed to Sulfate Attack,” these proceedings.

  11. [11]

    Stutzman, P.E., Ceramic Trans. 16, 237 (1991).

    CAS  Google Scholar 

  12. [12]

    Allen, A.J., Oberthur, R.C., Pearson, D., Schofield, P., and Wilding, C.R., Phil. Mag. B 56 (3), 263 (1987).

    CAS  Article  Google Scholar 

  13. [13]

    Baroghel-Bouny, V., PhD thesis, L’ecole Nationale des Ponts et Chaussees, Paris, France 1994.

    Google Scholar 

  14. [14]

    Bentz, D.P., Coveney, P.V., Garboczi, E.J., Kleyn, M.F., Stutzman, P.E., Modelling and Sim. in Mat. Sci. and Eng. 2 (4), 783 (1994).

    CAS  Article  Google Scholar 

  15. [15]

    Bentz, D.P., and Garboczi, E.J., “Guide to Using HYDRA3D: A Three-Dimensional Digital-Image-Based Cement Microstructure Model,” NISTIR 4746, U.S. Department of Commerce (1992).

    Google Scholar 

  16. [16]

    Bentz, D.P., and Garboczi, E.J., Cem. and Conc. Res. 21, 325 (1991).

    CAS  Article  Google Scholar 

  17. [17]

    Garboczi, E.J., and Bentz, D.P., J. of Mat. Sci. 27 2083 (1992).

    CAS  Article  Google Scholar 

  18. [18]

    Winslow, D.N., Cohen, M.D., Bentz, D.P., Snyder, K.A., and Garboczi, E.J., Cem. and Conc. Res. 24 (1), 25 (1994).

    CAS  Article  Google Scholar 

  19. [19]

    Bentz, D.P., Hwang, J.T.G., Hagwood, C., Garboczi, E.J., Snyder, K.A., Buenfeld, N., Scrivener, K.L., “Interfacial Zone Percolation in Concrete: Effects of Interfacial Zone Thickness and Aggregate Shape,” these proceedings.

  20. [20]

    Garboczi, E.J., and Day, A. R., “An Algorithm for Computing the Effective Linear Elastic Properties of Heterogeneous Materials: 3-D Results for Composites with Equal Phase Poisson Ratios,” submitted to J. of AppI. Phys.

  21. [21]

    Halamickova, P., Detwiler, R.J., Bentz, D.P., and Garboczi, E.J., “Water Permeability and Chloride Ion Diffusion in Portland Cement Mortars: Relationship to Sand Content and Critical Pore Diameter,” accepted by Cem. and Conc. Res.

  22. [22]

    Olson, R.A., Christensen, B.J., Coverdale, R.T., Ford, S.J., Moss, G.M., Jennings, H.M., Mason, T.O., and Garboczi, E.J., “Microstructural Analysis of Freezing Cement Paste Using Impedance Spectroscopy,” submitted to J. of Mat. Sci.

  23. [23]

    Bentur, A., Berger, R.L., Lawrence Jr., F.V., Milestone, N.B., Mindess, S., and Young, J.F., Cem. and Conc. Res. 9, 83 (1979).

    CAS  Article  Google Scholar 

  24. [24]

    Fu, Y., Gu, P., Xie, P., and Beaudoin, J.J., Cem. and Conc. Res. 24 (6), 1085 (1994).

    CAS  Article  Google Scholar 

  25. [25]

    Wittmann, F.H., in Creep and Shrinkage in Concrete Structures, edited by Bazant, Z.P. and Wittmann, F.H. (John H. Wiley & Sons, Ltd., New York, 1982) p. 129.

  26. [26]

    Quenard, D.A., Bentz, D.P., and Garboczi, E.J., in Drying ’92, edited by Mujumdar, A.S. (Elsevier Science, 1992) p. 253.

Download references

Author information



Corresponding author

Correspondence to D. P. Bentz.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bentz, D.P., Garboczi, E.J., Jennings, H.M. et al. Multi-Scale Digital-Image-Based Modelling of Cement-Based Materials. MRS Online Proceedings Library 370, 33–41 (1994).

Download citation