Abstract
The problem of extracting effective diffusivities of cement pastes on the basis of X-ray microtomography images is considered. A general computational homogenization framework is developed and applied to a variety of cement pastes whose microstructure has been digitized to a resolution of 1 μm. At this resolution, important submicron features are not resolved. Consequently, we propose a methodology whereby the pore space is ascribed a diffusivity less than the free diffusivity. For this purpose, a simple rule that incorporates microtomography data is proposed and shown to yield satisfactory results.
Similar content being viewed by others
References
Andrade C.: Calculation of chloride diffusion coefficients in concrete from ionic migration measurements. Cem. Concr. Res. 23, 724–742 (1993)
Barberon F., Korb J.P., Petit D., Morin V., Bermejo E.: Probing the surface area of a cement-based material by nuclear magnetic relaxation dispersion. Phys. Rev. Lett. 90, 116103 (2003)
Bentz D.P. et al.: Microstructure and transport properties of porous building materials. II: Three-dimensional X-ray tomographic studies. Mater. Struct. 33, 147–153 (2000)
Bentz, D.P. et al.: The Visible cement data set. J. Res. Natl. Inst. Stand. Technol. 107, 137–148 (2002) URL:http://visiblecement.nist.gov
Buenfeld, N.: Concrete Durability Group. Secondary Electron Imaging. http://www.concrete.cv.ic.ac.uk/durability (2007)
Chiles J.P., Delfiner P.: Geostatistics, Modeling Spatial Uncertainty. Wiley, New York (1999)
Friedmann H., Amiri O., Ait-Mokhtar A., Dumargue P.: A direct method for determining chloride diffusion coefficient by using migration test. Cem. Concr. Res. 34, 1967–1973 (2004)
Garboczi E.J., Bentz D.P.: Computer simulation of the diffusivity of cement-based materials. J. Mater. Sci. 27, 2083–2092 (1992)
Huet C.: Application of variational concepts to size effects in elastic heterogeneous bodies. J. Mech. Phys. Solids 38, 813–841 (1990)
Jiang M., Jasiuk I., Ostoja-Starzewski M.: Apparent thermal conductivity of periodic two-dimensional composites. Comput. Mater. Sci. 25, 329–338 (2002)
Kanit T., Forest S., Galliet I., Mounoury V., Jeulin D.: Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Solids Struct. 40, 3647–3679 (2003)
Khisaeva Z.F., Ostoja-Starzewski M.: On the size of RVE in finite elasticity of random composites. J. Elast. 85, 153–173 (2006)
Kincaid D.R., Respess J.R., Young D.M., Grimes R.G.: Algorithm 586: ITPACK 2C: a FORTRAN package for solving large sparse linear systems by adaptive accelerated iterative methods. ACM Trans. Math. Softw. 8, 302–322 (1982)
Knackstedt, M.A. et al.: Elastic and transport properties of cellular solids derived from three-dimensional tomographic images. Proc. R. Soc. A 462, 2833–2862 (2006)
Koster M., Hannawald J., Brameshuber W.: Simulation of water permeability and water vapor diffusion through hardened cement paste. Comput. Mech. 37, 164–172 (2006)
Krabbenhoft K., Hain M., Wriggers P.: Computation of effective cement paste diffusivities from microtomographic images. In: Kompis, V. (eds) Composites with Micro- and Nano-Structure, pp. 281–297. Spinger, Berlin (2008)
Krabbenhoft K., Krabbenhoft J.: Application of the Poisson–Nernst–Planck equations to the migration test. Cem. Concr. Res. 38, 77–88 (2008)
Ostoja-Starzewski M.: Material spatial randomness: From statistical to representative volume element. Probab. Eng. Mech. 21, 112–132 (2006)
Ostoja-Starzewski M.: Microstructural Randomness and Scaling in Mecanics of Materials. Chapman & Hall/CRC, London/Boca Raton (2008)
Ostoja-Starzewski M., Schulte J.: Bounding of effective thermal conductivities of multiscale materials by essential and natural boundary conditions. Phys. Rev. B 54, 278–285 (1996)
Pal N.R., Pal S.K.: A review on image segmentation techniques. Pattern Recognit. 26, 1277–1294 (1993)
Pecullan S., Gibiansky L.V., Torquato S.: Scale effects on the elastic behavior of periodic and hierarchical two-dimensional composites. J. Mech. Phys. Solids 47, 1509–1542 (1999)
Powers, G. : Physical properties of cement paste. In: Proceedings of the 4th international symposium on the chemistry of cement, pp. 577–613 (1962)
Promentilla M.A.B., Sugiyama T., Hitomi T., Takeda N.: Characterization of the 3D pore structure of hardened cement paste with syncrotron microtomography. J. Adv. Concr. Technol. 6, 273–286 (2008)
Promentilla M.A.B., Sugiyama T., Hitomi T., Takeda N.: Quantification of tortuosity in hardened cement pastes using synchrotron-based X-ray computed microtomography. Cem. Concr. Res. 39, 548–557 (2009)
Tang L., Nilsson L.O.: Rapid determination of the chloride diffusivity in concrete by applying an electric field. Cem. Concr. Res. 89, 49–53 (1992)
Thomas J.J., Jennings H.M., Allen A.J.: The surface area of hardened cement paste as measured by various techniques. Concr. Sci. Eng. 1, 45–64 (1999)
Torquato S.: Random Heterogeneous Materials. Springer, Berlin (2002)
Tritthart, J., Häußler, F.: Pore solution analysis of cement pastes and nanostructural investigations of hydrated C3S. Cem. Concr. Res. 33, 1063–1070 (2003)
Whitaker S.: Coupled transport in multiphase systems: a theory of drying. Adv. Heat Transf. 31, 1–102 (1998)
Yeong C.L.Y., Torquato S.: Reconstructing random media. Phys. Rev. E 57, 495 (1998)
Zohdi T.I., Wriggers P.: Aspects of the computational testing of the mechanical properties of microheterogeneous material samples. Int. J. Numer. Methods Eng. 50, 2573–2599 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Karim, M.R., Krabbenhoft, K. Extraction of Effective Cement Paste Diffusivities from X-ray Microtomography Scans. Transp Porous Med 84, 371–388 (2010). https://doi.org/10.1007/s11242-009-9506-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-009-9506-y