Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T23:14:26.176Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical modeling of cement paste microstructure by mosaic pattern: Part I. Formulation

Published online by Cambridge University Press:  31 January 2011

Yunping Xi ,
Paul D. Tennis  and
Hamlin M. Jennings
Yunping Xi
Affiliation:
Department of Civil and Architectural Engineering, Drexel University, Philadelphia, Pennsylvania 19104
Paul D. Tennis
Affiliation:
Department of Civil Engineering Northwestern University, Evanston, Illinois 60208
Hamlin M. Jennings
Affiliation:
Department of Civil Engineering, and Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208
Get access

Abstract

This paper develops a mathematical model using mosaic patterns to characterize structural features of complex, multiphase, and multidimensional microstructures, such as those for cement paste. A multiphase microstructure can be characterized by m independent parameters; the first m– 1 parameters are equivalent to the volume fractions of the phases, while the final parameter describes the grain size, and thus, the spatial arrangement of the microstructure. An evaluation procedure for the parameters is given; they can be evaluated based on a 2D image, and then the 3D microstructure can be simulated by the present model. The relationship among the model parameters and material parameters, such as water-to-cement ratio and particle size distribution, are also established.

Type
Articles
Information
Journal of Materials Research , Volume 11 , Issue 8 , August 1996 , pp. 1943 - 1952
Copyright
Copyright © Materials Research Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Jennings, H.M. and Johnson, S. K., J. Am. Ceram. Soc. 69, 790–795 (1986).CrossRefGoogle Scholar
2.Bentz, D. P. and Garboczi, E.J., Ceramic Transactions, Vol. 16, Advances in Cementitious Materials, edited by Mindess, S. (The American Ceramic Society, Inc., Westerville, OH, 1990), pp. 211–226.Google Scholar
3.Bentz, D. P., Garboczi, E.J., Gingold, D., Lobb, C. J., and Jennings, H. M., Ceramic Transactions, Vol. 16, Advances in Cementitious Materials, edited by Mindess, S. (The American Ceramic Society, Inc., Westerville, OH, 1990), pp. 227–235.Google Scholar
4.Bentz, D. P. and Garboczi, E. J., ACI Mater. J. 88 (5), September-October, 518–529 (1991).Google Scholar
5.Naganuma, T., Deodatis, G., Shinozuka, M., and Samaras, E., Proc. 4th Int. Conf. on Structural Safety and Reliability, I, 251–260 (1985).Google Scholar
6.Shinozuka, M., Engineering Mechanics Division, ASCE 98 (6), 1433–1451 (1972).Google Scholar
7.Yamazaki, F. and Shinozuka, M., Structural Eng./Earthquake Eng. 5 (2), Japan Society of Civil Engineers (Proc. of ASCE No. 398/I-10), 313s–323s (1988).Google Scholar
8.Bazant, Z. P. and Xi, Y., in Materials Research in Concrete (Vom Werkstoff Zur Konstruktion, Karlsruhe, 1990), pp. 249–267.Google Scholar
9.Bazant, Z. P. and Xi, Y., Eng, J.. Mechanics Division, ASCE 119 (1), 301–322 (1993).Google Scholar
10.Delhomme, J. P., Adv. Water Resources 1 (5), 251–266 (1978).CrossRefGoogle Scholar
11.de Marsily, G., in Fundamentals of Transport Phenomena in Porous Media, edited by Bear, J. and Corapcioglu, M. Y. (NATO ASI Series, Series E: Applied Sciences–No. 82, Martinus Nijhoff Publishers, New York, 1984), pp. 721–764.Google Scholar
12.Smith, L. and Freeze, R. A.Water Resources Research 15 (6) Dec. 1543–1559 (1979).CrossRefGoogle Scholar
13.Delhomme, J. P., Water Resources Research 15 (2), April 269–280 (1979).CrossRefGoogle Scholar
14.Legendre, P. and Fortin, M. J., Vegetatio (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989), pp. 107–138.Google Scholar
15.Dale, M.R.T. and MacISAAC, D.A., J. Ecology 77, 78–91 (1989).CrossRefGoogle Scholar
16.Bartlett, M. S., Adv. Appl. Prob. 6, 336–358 (1974).CrossRefGoogle Scholar
17.Pielou, E. C., Biometrics, March, 156–167 (1964).CrossRefGoogle Scholar
18.Pielou, E. C., Mathematical Ecology (John Wiley / Sons, New York, 1977).Google Scholar
19.Schon, M., J. Hirnforsch 27 (4), 401–408 (1986).Google Scholar
20.Cole, L. C., Ecology 30, 411–424 (1949).CrossRefGoogle Scholar
21.David, H. A., Order Statistics (Wiley, New York, 1970).Google Scholar
22.Kendall, M. G. and Moran, P. A. P., Geometrical Probability (Hafner Publishing Company, New York, 1963).Google Scholar
23.Coverdale, R. T., Garboczi, E.J., Jennings, H. M., Christensen, B. J., and Mason, T.O., J. Am. Ceram. Soc. (1993).Google Scholar
24.Kemeny, J. G. and Snell, J. L., Finite Markov Chain (van Nostrand, New York, 1960).Google Scholar
25.Saxl, I., Stereology of Objects with Internal Structure (Elsevier, Amsterdam, 1989).Google Scholar
26.Underwood, E. E., Quantitative Stereology (Addison-Wesley Publishing Company, London, 1970).Google Scholar
27.Serra, J., Image Analysis and Mathematical Morphology, Vol. 1 (Academic Press, London, 1982).Google Scholar
28.Serra, J., Image Analysis and Mathematical Morphology, Vol. 2: Theoretical Advances (Academic Press, Harcourt Brace Jovanovich, Publishers, London, 1988).Google Scholar
29.Attiogbe, E. K., ACI Mater. J. 90 (2), March–April, 174–181 (1993).Google Scholar
30.Solomon, H., CBMS-NSF, Regional Conf. Series in Applied Mathematics (Soc. for Industrial and Applied Math., Philadelphia, PA, 1978).Google Scholar
31.Kendall, M. G. and Stuart, A., The Advanced Theory of Statistics 2, 2nd ed. (Griffin, London, 1967).Google Scholar
32.Fellous, A., Granara, J., and Krickeberg, K., Lecture Notes in Biomathematics, 23, Managing Editor S. Levin, Geometrical Probability and Biological Structures: Buffon's 200th Anniversary, edited by Miles, R.E. and Serra, J. (Springer-Verlag, Berlin, 1978).Google Scholar
33.Underwood, E. E., Stereology and Quantitative Metallography (1972).Google Scholar
34.Goudsmit, S., Rev. Mod. Phys. 17, 321–322 (1945).CrossRefGoogle Scholar
35.Bezjak, A., Cement and Concrete Research 16, 260–264 (1986).CrossRefGoogle Scholar
36.Knudsen, T., Cement and Concrete Research 14, 622–630 (1984).CrossRefGoogle Scholar
37.Bentz, D. P., Coveney, P. V., Garboczi, E.J., Kleyn, M. F., and Stutzman, P.E., Modelling and Stimulation in Materials Science and Engineering 2, 783–808 (1994).CrossRefGoogle Scholar
38.Tennis, P. D., Jennings, H.M., and Xi, Y., J. Mater. Res. (1996, submitted).Google Scholar