Skip to main content
SpringerLink
Log in

Ice Formation in Porous Media

  • Conference paper
Advances in Extended and Multifield Theories for Continua

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 59))

Abstract

Ice formation in porous media results from coupled heat and mass transport and is accompanied by ice expansion. The volume increase in space and time corresponds to the moving freezing front inside the porous solid. In this contribution, a macroscopic model based on the Theory of Porous Media (TPM) is presented toward the description of freezing and thawing processes in saturated porous media. Therefore, a quadruple model consisting of the constituents solid, ice, liquid and gas is used. Attention is paid to the description of capillary suction, liquid- and gas pressure on the surrounding surfaces, volume deformations due to ice formation, temperature distribution as well as influence of heat of fusion under thermal loading. For detection of energetic effects regarding the control of phase transition of water and ice, a physically motivated evolution equation for the mass exchange based on the local divergence of the heat flux is used. Numerical examples are presented to the applications of the model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aquirre-Punte, J., Philippe, A.: Quelques recherches effectuées en france sur le problème de la congélation des sols. Revue Generale de Thermique 96, 1123–1141 (1969)

    Google Scholar 

  2. Ateshian, G., Ricken, T.: Multigenerational interstitial growth of biological tissues. In: Biomechanics and Modeling in Mechanobiology. Springer, Heidelberg (2010), doi:10.1007/s10237-010-0205-y

    Google Scholar 

  3. Biot, M.: General theory of three-dimensional consolidation. Journal of Applied Physics 12, 155–164 (1941)

    Article  MATH  Google Scholar 

  4. Blome, K.P.: Ein Mehrpahsenmodell-Stoffmodell für Böden mit Übergang auf Interface-Gesetze. PhD thesis, Universität Stuttgart, Report No.: II-10. Institut für Mechanik (Bauwesen), Lehrstuhl II (2003)

    Google Scholar 

  5. Bluhm, J., Ricken, T., Bloßfeld, M.: Energetische Aspekte zum Gefrierverhalten von Wasser in porösen Strukturen. Proceedings in Applied Mathematics and Mechanics 8(10), 483–484 (2008)

    Google Scholar 

  6. Bluhm, J., Ricken, T., Bloßfeld, W.M.: Dynamic phase transition border under freezing-thawing load in porous media – a multiphase description. Schröder, J. (ed.): Tech. rep., Report 47. Institute of Mechanics, University Duisburg-Essen, Germany (2009)

    Google Scholar 

  7. Bowen, R.: Incompressible porous media models by use of the theory of mixtures. International Journal of Engineering Science 18, 1129–1148 (1980)

    Article  MATH  Google Scholar 

  8. Bowen, R.: Compressible porous media models by use of the theory of mixtures. International Journal of Engineering Science 20, 697–735 (1982)

    Article  MATH  Google Scholar 

  9. Brooks, R., Corey, A.: Hydraulic propertiesof porous media. Tech. Rep. 3, Colorado State University, Fort Collins (1964)

    Google Scholar 

  10. Coussy, O.: Poromechanics. Wiley, New York (2004)

    Google Scholar 

  11. Coussy, O.: Poromechanics of freezing materials. Journal of the Mechanics and Physics of Solids 53, 1689–1718 (2005)

    Article  MATH  Google Scholar 

  12. de Boer, R.: Theory of Porous Media – highlights in the historical development and current state. Springer, Berlin (2000)

    Book  Google Scholar 

  13. Ehlers, W.: Poröse Medien – ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. In: Habilitation, Heft 47, Forschungsbericht aus dem Fachbereich Bauwesen. Universität-GH Essen, Essen (1989)

    Google Scholar 

  14. Ehlers, W.: Constitutive equations for granular materials in geomechanical context. In: Hutter, K. (ed.) Continuum Mechanics in Environmental Sciences and Geophysics. CISM Courses and Lectures, vol. 337, pp. 313–402. Springer, Wien (1993)

    Chapter  Google Scholar 

  15. Ehlers, W.: Foundations of multiphasic and porous materials. In: Ehlers, W., Bluhm, J. (eds.) Porous Media: Theory, Experiments and Numerical Applications, pp. 3–86. Springer, Berlin (2002)

    Chapter  Google Scholar 

  16. Ehlers, W., Bluhm, J. (eds.): Porous media: Theory, experiments and numerical applications. Springer, Heidelberg (2002)

    Google Scholar 

  17. Fagerlund, G.: Internal frost attack – state of the art. In: Auberg, R., Setzer, M. (eds.) Frost Resistance of Concrete, RILEM Proceedings, vol. 34, pp. 321–338. E & FN Spon, London (1997)

    Google Scholar 

  18. van Genuchten, M.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44, 892–898 (1980)

    Article  Google Scholar 

  19. Graf, T.: Multiphsic flow processes in deformable porous media uner consideration of fluid phas transition. PhD thesis, Universität Stuttgart, Report No.: II-17, Institut für Mechanik (Bauwesen), Lehrstuhl II (2008)

    Google Scholar 

  20. Guymon, G.L., Hromadka II, T.V., Berg, R.L.: A one dimensional frost heave model based upon simulation of simultaneous heat and water flux. Cold Regions Science and Technology 3, 253–262 (1980)

    Article  Google Scholar 

  21. Helmig, R.: Multiphase flow and transport processes in the subsurface: a contribution to the modeling of hydrosystems. Springer, Heidelberg (1997)

    Book  Google Scholar 

  22. Helmuth, R.: Investigations of the low temperature dynamic mechanical response of hardened cement paste. In: Tech. rep., Vol. 154. Dept. of Civil Engineering, Standfort University (1972)

    Google Scholar 

  23. Humphrey, J., Rajagopal, K.: A constrained mixture model for growth and remodelling of soft tissues. Mathematical Models and Methods in Applied Sciences 12, 407–430 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  24. Kasparek, S.: Wärme- und Feuchtetransport in zementgebundenen Baustoffen während der Frostprüfung mit besonderer Beachtung des CIF-Testes. PhD thesis, Universität Duisburg-Essen (2005)

    Google Scholar 

  25. Kowalski, S.J.: Thermomechanics of drying processes. Springer, Heidelberg (2003)

    Book  MATH  Google Scholar 

  26. Lewis, R., Strada, M., Comini, G.: Drying induced stresses in porous bodies. International Journal for Numerical Methods in Engineering 11, 1175–1184 (1977)

    Article  Google Scholar 

  27. Lewis, R., Morgan, K., Thomas, H., Strada, M.: Drying – induced stresses in porous bodies – an elastoviscoplastic model. Computer Methods in Applied Mechanics and Engineering 20, 291–301 (1979)

    Article  MATH  Google Scholar 

  28. Li, N., Chen, F., Xu, B., Swoboda, B.: Theoretical modeling framework for an unsaturated freezing soil. Cold Regions Science and Technology 54, 19–35 (2008)

    Article  Google Scholar 

  29. Mikkola, M., Hartikainen, J.: Mathematical model of soil freezing and its numerical implementation. International Journal for Numerical Methods in Engineering 52, 543–557 (2001)

    Article  MATH  Google Scholar 

  30. Miller, R.: Freezing phenomena in soils. In: Hillel, D. (ed.) Applications of Soil Physics, pp. 254–299 (1980)

    Google Scholar 

  31. O’Neill, K., Miller, R.: Exploration of a rigid ice model of frost heave. Water Resources Research 21, 281–296 (1985)

    Article  Google Scholar 

  32. Powers, T.: A working hypothesis for further studies of frost resistance of concrete. Journal of the American Concrete Institute 41, 245–272 (1945)

    Google Scholar 

  33. Powers, T., Brownyard, T.: Studies of the physical properties of hardened portland cement paste (4) – Part IV: The thermodynamics of adsorption of water on hardened paste. Journal of the American Concrete Institute 43, 549–602 (1946)

    Google Scholar 

  34. Richards, L.A.: Capillary conduction of liquids through porous mediums. Physics 1, 318–333 (1931)

    Article  MATH  Google Scholar 

  35. Ricken, T.: Kappilarität in porösen Medien – theoretische Untersuchung und numerische Simulation. PhD thesis, Universität Duisburg-Essen, Fachbereich Bauwesen, Shaker Verlag, Aachen (2002)

    Google Scholar 

  36. Ricken, T., Bluhm, J.: Modeling fluid saturated porous media under frost attack. In: GAMM-Mitteilungen, vol. 33, pp. 40–56. WILEY-VCH Verlag, GmbH & Co, KGaA, Weinheim (2010)

    Google Scholar 

  37. Ricken, T., de Boer, R.: Multiphase flow in a capillary porous medium. Computational Materials Science 28, 704–713 (2003)

    Article  Google Scholar 

  38. Rodriguez, E., Hoger, A., McCulloch, A.: Stress-dependent finite growth in soft elastic tissues. Journal of Biomechanics 27, 455–467 (1994)

    Article  Google Scholar 

  39. Setzer, M.: Micro-ice-lens formation in porous solid. Journal of Colloid Interface Science 243, 193–201 (2001)

    Article  Google Scholar 

  40. Setzer, M.: Development of the micro-ice-lens model. In: Auberg, R., Keck, H.J., Setzer, M. (eds.) Frost Resistance of Concrete, RILEM Proceedings, vol. 24, pp. 133–145. RILEM Publications, France (2002)

    Google Scholar 

  41. Setzer, M.: Modelling and testing the freeze-thaw attack by micro-ice-lens model and cdf/cif-test. In: Proceedings of the International Workshop on Microstructure and Durability to Predict Service Life of Concrete Structures, pp. 17–28. Hokkaido University, Sapporo (2004)

    Google Scholar 

  42. Setzer, M., Heine, P., Palecki, S., Auberg, R., Feldrappe, V., Siebel, E.: CIF-test – capillary suction, internal damage and freeze-thaw test: Reference method and alternative methods. Material and Structures 37, 743–753 (2004)

    Article  Google Scholar 

  43. Whitaker, S.: Simultaneous heat, mass, and momentum transfer in porous media: A theory of drying. Advances in Heat Transfer 13, 119–203 (1977)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Mechanics, Faculty of Engineering, Department of Civil Engineering, University of Duisburg-Essen, 45117, Essen, Germany

    Joachim Bluhm & Moritz Bloßfeld

  2. Computational Mechanics, Faculty of Engineering, Department of Civil Engineering, University of Duisburg-Essen, 45117, Essen, Germany

    Tim Ricken

Authors
  1. Joachim Bluhm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tim Ricken
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Moritz Bloßfeld
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Applied Mechanics (Civil Engineering) Chair of Continuum Mechanics, University of Stuttgart, Pfaffenwaldring 7, 70569, Stuttgart, Germany

    Bernd Markert

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bluhm, J., Ricken, T., Bloßfeld, M. (2011). Ice Formation in Porous Media. In: Markert, B. (eds) Advances in Extended and Multifield Theories for Continua. Lecture Notes in Applied and Computational Mechanics, vol 59. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22738-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22738-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22737-0

  • Online ISBN: 978-3-642-22738-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation