Abstract
A computational framework for extracting effective diffusivities from microtomographic images is presented. As an example of the capabilities of this framework, the effective diffusivity of a cement paste whose microstructure has been digitized to a resolution of 1 μm is derived. Besides presenting a consistent homogenization procedure, the importance of statistical testing is also highlighted. Indeed, for the problem at hand, it appears that statistical testing and subsequent interpretation of the results in terms of statistical quantities is a necessity for obtaining quantitative information on the property of interest.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Tang and L. O. Nilsson. Rapid determination of the chloride diffusivity in concrete by applying an electric field. Cement and Concrete Research, 89: 49–53, 1992.
C. Andrade. Calculation of chloride diffusion coefficients in concrete from ionic migration measurements. Cement and Concrete Research, 23: 724–742, 1993.
H. Friedmann, O. Amiri, A. Ait-Mokhtar, and P. Dumargue. A direct method for determining chloride diffusion coefficient by using migration test. Cement and Concrete Research, 34: 1967–1973, 2004.
S. Goto and D. M. Roy. Diffusion of ions through hardened cement pastes. Cement and Concrete Research, 11: 751–757, 1981.
S. W. Yu and C. L. Page. Diffusion in cementitious materials: 1. Comparative study of chloride and oxygen diffusion in hydrated cement pastes. Cement and Concrete Research, 21: 581–588, 1991.
V. T. Ngala et al. Diffusion in cementitious materials: II. Further investigations of chloride and oxygen diffusion in well-cured OPC and OPC/30% PFA pastes. Cement and Concrete Research, 25: 819–826, 1995.
J. Z. Zhang and N. Buenfeld. Presence and possible implications of a membrane potential in concrete exposed to chloride solution. Cement and Concrete Research, 27: 853–859, 1997.
S. Chatterji. Colloid electrochemistry of saturated cement paste and some properties of cement based materials. Advances in Cement Based Materials, 7: 102–108, 1998.
D. P. Bentz et al. Microstructure and transport properties of porous building materials. II: Three-dimensional X-ray tomographic studies. Materials and Structures, 33: 147–153, 2000.
C. Manwart et al. Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media. Physical Review E, 66 (016702), 2002.
M. Koster, J. Hannawald, and W. Brameshuber. Simulation of water permeability and water vapor diffusion through hardened cement paste. Computational Mechanics, 37: 164–172, 2006.
D. P. Bentz et al. The Visible Cement Data Set. Journal of Research of the National Institute of Standards and Technology, 107: 137–148, 2002. URL http://visiblecement.nist.gov.
W. B. Lindquist et al. Pore and throat size distributions measured from sychrotron x-ray tomographic images of fontainebleau sandstones. Journal of Geophysical Research, 105B: 21508–21528, 2000.
P. Lehman et al. Tomographical imaging and mathematical description of porous media used for the prediction of fluid distribution. Vadose Zone Journal, 5: 80–97, 2006.
P. Weiss et al. Synchrotron and non synchrotron x-ray microtomography three dimensional representation of bone ingrowth in calcium phosphate biomaterials. European Cells and Materials, 9: 48–49, 2005.
E. Maire et al. Characterization of the morphology of cellular ceramics by 3D image processing of X-ray tomography. Journal of the European Ceramic Society, 27: 1973–1981, 2007.
T. J. Chotard et al. Characterisation of early stage calcium aluminate cement hydration by combination of non-destructive techniques: acoustic emission and X-ray tomography. Journal of the European Ceramic Society, 23: 2211–2223, 2003.
M. A. Knackstedt et al. Elastic and transport properties of cellular solids derived from three-dimensional tomographic images. Proceedings of the Royal Society A, 462: 2833–2862, 2006.
E. Maire et al. On the application of X-ray microtomography in the field of materials science. Advanced Engineering Materials, 3: 539–546, 2001.
M. Hain and P. Wriggers. On the numerical homogenization of hardened cement paste. Compational Mechanics, 2007. Submitted.
M. Ostoja-Starzewski and J. Schulte. Bounding of effective thermal conductivities of multiscale materials by essential and natural boundary conditions. Physical Review B, 54: 278–285, 1996.
FEAP. A Finite Element Analysis Program (R. L. Taylor). URL http://www.ce.berkeley.edu/rlt/feap.
D. Stauffer and A. Aharony. Introduction to Percolation Theory. Taylor and Francis, London 1992.
W. Voigt. Lehrbuch der Kristallphysik. Teubner, Leipzig, 1928.
A. Reuss. Berechnung der fleissgrense von Mischkristallen auf Grund der Plastizitätsbedingung für einkristalle. Zeitschrift für Angewandte Mathematik und Mechanik, 9: 49–58, 1929.
J. C. Maxwell. A Treatise on Electricity and Magnetism. Dover, New York 1954.
Z. Hashin and S. Shtrikman. A variational approach to the theory of the effective magnetic permeability of multiphase materials. Journal of Applied Physics, 33 (10): 3125–3131, 1962.
P. Sen, C. Scala, and M. Cohen. A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. Geophysics, 46: 781–795, 1981.
J. P. Chiles and P. Delfiner. Geostatistics, Modeling Spatial Uncertainty. Wiley, New York 1999.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science + Business Media B.V
About this chapter
Cite this chapter
Krabbenhoft, K., Hain, M., Wriggers, P. (2008). Computation of Effective Cement Paste Diffusivities from Microtomographic Images. In: Composites with Micro- and Nano-Structure. Computational Methods in Applied Sciences, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6975-8_15
Download citation
DOI: https://doi.org/10.1007/978-1-4020-6975-8_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-6974-1
Online ISBN: 978-1-4020-6975-8
eBook Packages: EngineeringEngineering (R0)