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Transport in Porous Media

, Volume 112, Issue 1, pp 139–166 | Cite as

Simulation of Mass, Linear Momentum, and Energy Transport in Concrete with Varying Moisture Content during Cooling to Cryogenic Temperatures

  • Syeda Rahman
  • Zachary GrasleyEmail author
  • Eyad Masad
  • Dan Zollinger
  • Srinath Iyengar
  • Reginald Kogbara
Article

Abstract

A set of governing equations comprising linear momentum, mass, and heat transfer is presented for thermoelastic freezing of a porous material. The theory of unsaturated freezing porous media is introduced to model deformation of concrete, a traditional building material, whose pore network is pressurized by the wet air, frozen ice, and unfrozen water. A general solution scheme is provided for the appropriate boundary conditions pertaining to the primary concrete containment in a liquefied natural gas tank, and simulated results are analyzed for fully and partially saturated non-air-entrained concrete and fully saturated air-entrained concrete. Effect of cooling rate is also demonstrated. It is found that high cooling rate results in high expansion provoked by high hydraulic pore pressure and the corresponding suppression of pore liquid freezing temperature. It is also revealed that air-entrained concrete, by allowing quick dissipation of the displaced pore water and accommodating the ensuing ice formation, shows less contraction and subsequently less crack initiating stresses than the high-porosity, non-air-entrained concrete. Similar outcomes are observed near the concrete surfaces subjected to evaporation prior to cryogenic freezing. High hydraulic pressure, induced by the delayed dissipation of excess pore water, is likely to generate at the center of surface-dried concrete walls.

Keywords

Thermoelasticity Transport in porous media Cryogenic LNG Cooling rate 

Notes

Acknowledgments

This work was supported by Qatar National Research Fund (QNRF—a member of The Qatar Foundation) through NPRP 4 - 410 - 2 - 156. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the QNRF; QNRF has not approved or endorsed its content. The authors are particularly indebted to Kåre Hjorteset for providing valuable information about the concrete composite cryogenic tank structural design and insulation detail. Thanks to the reviewers and editor for their valuable comments and suggestions.

References

  1. Baroghel-Bouny, V., Mainguy, M., Lassabatere, T., Coussy, O.: Characterization and identification of equilibrium and transfer moisture properties for ordinary and high-performance cementitious materials. Cem. Concr. Res. 29(8), 1225–1238 (1999). doi: 10.1016/S0008-8846(99)00102-7 CrossRefGoogle Scholar
  2. Beaudoin, J.J., MacInnis, C.: The mechanism of frost damage in hardened cement paste. Cem. Concr. Res. 4(2), 139–147 (1974)CrossRefGoogle Scholar
  3. Berryman, J., Blair, S.: Kozeny–Carman relations and image processing methods for estimating Darcy’s constant. J. Appl. Phys. 62(6), 2221–2228 (1987)CrossRefGoogle Scholar
  4. Biot, M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. J. Acoust. Soc. Am. 28(2), 168–178 (1956). doi: 10.1121/1.1908239 CrossRefGoogle Scholar
  5. Brun, M., Lallemand, A., Quinson, J.-F., Eyraud, C.: A new method for the simultaneous determination of the size and shape of pores: the thermoporometry. Thermochim. Acta 21(1), 59–88 (1977). doi: 10.1016/0040-6031(77)85122-8 CrossRefGoogle Scholar
  6. Cahn, J.W., Dash, J.G., Haiying, F.: Theory of ice premelting in monosized powders. J. Cryst. Growth 123, 101–108 (1992)CrossRefGoogle Scholar
  7. Carman, P.C.: Fluid flow through granular beds. Trans. Inst. Chem. Eng. 15, 150–166 (1937). doi: 10.1016/S0263-8762(97)80003-2 Google Scholar
  8. Chiu, T.-F., Shackelford, C.: Unsaturated hydraulic conductivity of compacted sand-kaolin mixtures. J. Geotech. Geoenviron. Eng. 124(2), 160–170 (1998)CrossRefGoogle Scholar
  9. Corres, H., Elices, M., Planas, J.: Thermal deformation of loaded concrete at low temperatures. 3: lightweight concrete. Cem. Concr. Compos. 16, 845–852 (1986)CrossRefGoogle Scholar
  10. Coussy, O.: Poromechanics. Wiley, West Sussex (2004)Google Scholar
  11. Coussy, O.: Poromechanics of freezing materials. J. Mech. Phys. Solids 53(8), 1689–1718 (2005)CrossRefGoogle Scholar
  12. Coussy, O.: Deformation and stress from in-pore drying-induced crystallization of salt. J. Mech. Phys. Solids 54(8), 1517–1547 (2006). doi: 10.1016/j.jmps.2006.03.002 CrossRefGoogle Scholar
  13. Coussy, O.: Mechanics and Physics of Porous Solids. Wiley, West Sussex (2010)CrossRefGoogle Scholar
  14. Coussy, O., Monteiro, P.: Unsaturated poroelasticity for crystallization in pores. Comput. Geotech. 34(4), 279–290 (2007)CrossRefGoogle Scholar
  15. Coussy, O., Monteiro, P.J.M.: Poroelastic model for concrete exposed to freezing temperatures. Cem. Concr. Res. 38(1), 40–48 (2008). doi: 10.1016/j.cemconres.2007.06.006 CrossRefGoogle Scholar
  16. Couture, F., Jomaa, W., Puiggali, J.R.: Relative permeability relations: a key factor for a drying model. Transp. Porous Med. 23(3), 303–335 (1996). doi: 10.1007/BF00167101 Google Scholar
  17. Crank, J., Nicolson, P.: A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Adv. Comput. Math. 6(1), 207–226 (1996). doi: 10.1007/bf02127704 CrossRefGoogle Scholar
  18. Dash, J., Rempel, A., Wettlaufer, J.: The physics of premelted ice and its geophysical consequences. Rev. Mod. Phys. 78(3), 695–741 (2006). doi: 10.1103/RevModPhys.78.695 CrossRefGoogle Scholar
  19. Dormieux, L., Molinari, A., Kondo, D.: Micromechanical approach to the behavior of poroelastic materials. J. Mech. Phys. Solids 50(10), 2203–2231 (2002). doi: 10.1016/S0022-5096(02)00008-X CrossRefGoogle Scholar
  20. Elices, M., Planas, J., Corres, H.: Thermal deformation of loaded concrete at low temperatures, 2: transverse deformation. Cem. Concr. Res. 16, 741–748 (1986)CrossRefGoogle Scholar
  21. Fen-Chong, T., Fabbri, A., Thiery, M., Dangla, P.: Poroelastic analysis of partial freezing in cohesive porous materials. J. Appl. Mech. 80(2), 020910–020910 (2013). doi: 10.1115/1.4007908 CrossRefGoogle Scholar
  22. Hjorteset, K., Wernli, M., Lanier, M.W., Hoyle, K.A., Oliver, W.H.: Development of large-scale precast, prestressed concrete liquefied natural gas storage tanks. Precast Prestress. Concr. Inst. 58(4), 40–54 (2013)Google Scholar
  23. Hoyle, K., Oliver, S., Tsai, N., Hjorteset, K., LaNier, M., Wernli, M.: Composite concrete cryogenic tank (C3T): a precast concrete alternative for LNG storage. In: The 17th International Conference & Exhibition on Liquefied Natural Gas, Houston, TX, pp. 1–19 (2013)Google Scholar
  24. Ippisch, O., Vogel, H.J., Bastian, P.: Validity limits for the van Genuchten–Mualem model and implications for parameter estimation and numerical simulation. Adv. Water Resour. 29(12), 1780–1789 (2006). doi: 10.1016/j.advwatres.2005.12.011 CrossRefGoogle Scholar
  25. Johannesson, B.: Dimensional and ice content changes of hardened concrete at different freezing and thawing temperatures. Cem. Concr. Compos. 32(1), 73–83 (2010)CrossRefGoogle Scholar
  26. Kaneuji, M., Winslow, D.N., Dolch, W.L.: The relationship between an aggregate’s pore size distribution and its freeze thaw in concrete. Cem. Concr. Compos. 10, 433–441 (1980)CrossRefGoogle Scholar
  27. Kogbara, R.B., Iyengar, S.R., Grasley, Z.C., Masad, E.A., Zollinger, D.G.: A review of concrete properties at cryogenic temperatures: towards direct LNG containment. Constr. Build. Mater. 47, 760–770 (2013). doi: 10.1016/j.conbuildmat.2013.04.025
  28. Kogbara, R.B., Iyengar, S.R., Grasley, Z.C., Rahman, S., Masad, E.A., Zollinger, D.G.: Relating damage evolution of concrete cooled to cryogenic temperatures to permeability. Cryogenics 64, 21–28 (2014). doi: 10.1016/j.cryogenics.2014.09.001 CrossRefGoogle Scholar
  29. Korb, J.P., McDonald, P.J., Monteilhet, L., Kalinichev, A.G., Kirkpatrick, R.J.: Comparison of proton field-cycling relaxometry and molecular dynamics simulations for proton-water surface dynamics in cement-based materials. Cem. Concr. Res. 37(3), 348–350 (2007). doi: 10.1016/j.cemconres.2006.02.009 CrossRefGoogle Scholar
  30. Kralj, B., Pande, G.N.: A stochastic model for the permeability characteristics of saturated cemented porous media undergoing freezing. Transp. Porous Med. 22(3), 345–357 (1996). doi: 10.1007/BF00161631 CrossRefGoogle Scholar
  31. Krstulovic-Opara, N.: Liquefied natural gas storage: material behavior of concrete at cryogenic temperatures. ACI Mater. J. 104(3), 297–306 (2007)Google Scholar
  32. Litvan, G.G.: The mechanism of frost action in concrete-theory and practical implications. In: Proceedings of Workshop on Low Temperature Effects on Concrete, Sapporo, Hakkaido, Japan, pp. 115–134. National Research Council Canada (1988)Google Scholar
  33. Luckner, L., van Genuchten, M.T., Nielsen, D.R.: A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface. Water Resour. Res. 25(10), 2187–2193 (1989)CrossRefGoogle Scholar
  34. Marshall, A.L.: Cryogenic concrete. Cryogenics 22(11), 555–565 (1982)CrossRefGoogle Scholar
  35. Marshall, T.J.: A relation between permeability and size distribution of pores. J. Soil Sci. 9(1), 1–8 (1958)CrossRefGoogle Scholar
  36. McTigue, D.F.: Thermoelastic response of fluid-saturated porous rock. J. Geophys. Res. 91(B9), 9533–9542 (1986)CrossRefGoogle Scholar
  37. Miura, T.: Properties of concrete at very low temperatures. Mater. Struct. 22(130), 243–254 (1989)CrossRefGoogle Scholar
  38. Mualem, Y.: A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12(3), 513–522 (1976)CrossRefGoogle Scholar
  39. Pigeon, M., Marchand, J., Pleau, R.: Frost resistant concrete. Constr. Build. Mater. 10(5), 339–348 (1996). doi: 10.1016/0950-0618(95)00067-4 CrossRefGoogle Scholar
  40. Planas, J., Corres, H., Elices, M., Chueca, R.: Thermal deformation of loaded concrete during thermal cycles from \(20 \,^{\circ }\text{ C }\) to \(-165 \,^{\circ }\text{ C }\). Cem. Concr. Res. 14, 639–644 (1984)CrossRefGoogle Scholar
  41. Powers, T.C., Willis, T.F.: The Air Requirement of Frost-Resistant Concrete. Portland Cement Association, Chicago (1949)Google Scholar
  42. Powers, T.C., Helmuth, R.A.: Theory of Volume Changes in Hardened Portland Cement Paste During Freezing. Portland Cement Association, Skokie (1953)Google Scholar
  43. Rahman, S., Grasley, Z.: A poromechanical model of freezing concrete to elucidate damage mechanisms associated with substandard aggregates. Cem. Concr. Res. 55, 88–101 (2014). doi: 10.1016/j.cemconres.2013.10.001 CrossRefGoogle Scholar
  44. Rempel, A.W., Wettlaufer, J.S., Worster, M.G.: Premelting dynamics in a continuum model of frost heave. J. Fluid Mech. 498, 227–244 (2004). doi: 10.1017/S0022112003006761 CrossRefGoogle Scholar
  45. Rostásy, F.S., Pusch, U.: Strength and deformation of lightweight concrete of variable moisture content at very low temperatures. Int. J. Cem. Compos. Lightweight Concr. 9(1), 3–17 (1987). doi: 10.1016/0262-5075(87)90033-9 CrossRefGoogle Scholar
  46. Rostásy, F.S., Schneider, U., Wiedemann, G.: Behaviour of mortar and concrete at extremely low temperatures. Cem. Concr. Res. 9(3), 365–376 (1979). doi: 10.1016/0008-8846(79)90129-7 CrossRefGoogle Scholar
  47. Scherer, G.W.: Freezing gels. J. Non-Cryst. Solids 155(1), 1–25 (1993). doi: 10.1016/0022-3093(93)90467-c CrossRefGoogle Scholar
  48. Scherer, G.W.: Crystallization in Pores. Cem. Concr. Res. 29(8), 1347–1358 (1999). doi: 10.1016/S0008-8846(99)00002-2 CrossRefGoogle Scholar
  49. Scherer, G.W., Valenza, J.J.: Mechanisms of frost damage. Mater. Sci. Concr. 7, 209–246 (2005)Google Scholar
  50. Setzer, M.J.: Einfluss des Wassergehaltes auf die Eigenschaften des erharteten Betons. Deutscher Ausschuss fur Stahlbeton 280, 103–103 (1977)Google Scholar
  51. Sun, Z., Scherer, G.W.: Effect of air voids on salt scaling and internal freezing. Cem. Concr. Res. 40(2), 260–270 (2010). doi: 10.1016/j.cemconres.2009.09.027 CrossRefGoogle Scholar
  52. Tognon, G.: Behaviour of mortars and concrete in the temperature range from \(+20 \,^{\circ }\text{ C }\) to \(-196 \,^{\circ }\text{ C }\). Paper presented at the Fifth International Symposium on the Chemistry of Cement, Tokyo (1968)Google Scholar
  53. Ven der Veen, C.: Properties of concrete at very low temperatures: a survey of the literature. In: Delft University of Technology (1987)Google Scholar
  54. Ven der Veen, C.: Theoretical and experimental determination of the crack width in reinforced concrete at very low temperatures. In: Delft University of Technology (1990)Google Scholar
  55. Valdes-Parada, F.J., Ochoa-Tapia, J.A., Alvarez-Ramirez, J.: Validity of the permeability Carman–Kozeny equation: a volume averaging approach. Phys. A 388(6), 789–798 (2009). doi: 10.1016/j.physa.2008.11.024 CrossRefGoogle Scholar
  56. van Genuchten, M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44(5), 892–898 (1980). doi: 10.2136/sssaj1980.03615995004400050002x CrossRefGoogle Scholar
  57. Verbeck, G., Landgren, R.: Influence of physical characteristics of aggregates on frost resistance of concrete. In: Proceedings of American Society for Testing Materials, Conshohocken, Philadelphis, pp. 1063–1079. American Society for Testing and Materials (1960)Google Scholar
  58. Vogel, T., Cislerova, M.: On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transp. Porous Media 3(1), 1–15 (1988). doi: 10.1007/BF00222683 CrossRefGoogle Scholar
  59. Wettlaufer, J., Worster, M.: Dynamics of premelted films: frost heave in a capillary. Phys. Rev. E 51(5), 4679–4689 (1995). doi: 10.1103/PhysRevE.51.4679 CrossRefGoogle Scholar
  60. Wiedemann, G.: Zum Einfluss tiefer Temperaturen auf Festigkeit und Verformung von Beton. Institut für Baustoffe, Massivbau und Brandschutz der Technischen Universität, Braunschweig (1982)Google Scholar
  61. Xu, S., Simmons, G.C., Mahadevan, T.S., Scherer, G.W., Garofalini, S.H., Pacheco, C.: Transport of water in small pores. Langmuir 25(9), 5084–5090 (2009). doi: 10.1021/la804062e CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Syeda Rahman
    • 1
  • Zachary Grasley
    • 1
    Email author
  • Eyad Masad
    • 1
    • 2
  • Dan Zollinger
    • 1
  • Srinath Iyengar
    • 2
  • Reginald Kogbara
    • 2
  1. 1.Zachry Department of Civil EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Mechanical Engineering ProgramTexas A&M University at QatarEducation City, DohaQatar

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