Ninth International Conference on Permafrost ... - IARC Research

Ni n t h In t e r n at i o n a l Co n f e r e n c e o n Pe r m a f r o s ta little delay is maintained in the frozen part of the curve,progressively increasing with depth. As the same thermalparameters (conductivity and capacity) are given bothto the analytical solution and to the model, it seems thatthe uncertainty relies on the choice of the Van Genuchtenparameters, upon which depends the unfrozen water contentand the apparent heat capacity. Further investigations arebeing taken at present to evaluate the influence of theseparameters through a sensitivity analysis.Figure 1. Soil freezing characteristic curve (SFCC) and paths forfreezing and thawing calculations.Figure 2. A comparison between the model and the analyticalsolution at various depths.the unknown is the temperature T eqat the equilibrium. Whenthe equilibrium curve is reached, the model follows thecurve with linearized paths using the apparent heat capacityformulation.ApplicationThe model has been tested against the Neumann problem,a simple case of a moving boundary. Nakano and Brown(1971), following the approach described by Carslawand Jaeger (1959) for a homogeneous substance, give theanalytical solution of an initially frozen soil bound to aconstant Dirichlet boundary condition at the top. We appliedthe same formulation to a saturated soil initially thawed atan initial temperature T i=2°C, and later forced to a freezingboundary condition T s=-5°C at the surface.The results in Figure 2 show that the model followsthe analytical solution at the surface, whereas at depths,ConclusionsThis work describes a new freezing soil paradigm basedon the soil freezing characteristic curves. The model, testedagainst the analytical solution of the Neumann problemwith a moving boundary, seems to be very sensitive to theVan Genucthen parameters and therefore to the shape of theSFCC.ReferencesCarslaw, H.S. & Jaeger, J.C. 1959. Conduction of Heat inSolids. Oxford: Clarendon Press.Christoffersen, P. & Tulaczyk, S. 2003. Response ofsubglacial sediments to basal freeze-on: 1. Theory andcomparison to observations from beneath the WestAntarctica Ice Sheet. J. Geophys. Res. 108: 2222.Farouki, O.T. 1981. The thermal properties of soils in coldregions. Cold Regions Sci. and Tech. 5: 67-75.Fowler, A.C. & Krantz W.B. 1994. A generalized secondaryfrost heave model. SIAM Journal on AppliedMathematics 54(6): 1650-1675Fuchs, M., Campbell, G.S. & Papendick, R.I. 1978. Ananalysis of sensible and latent heat flow in a partiallyfrozen unsaturated soil. Soil Sci. Soc. Am. J. 42(3):379-385.Hansson, K. et al 2004. Water flow and heat transport infrozen soil: Numerical solution and freeze-thawapplications. Vadose Zone Journal 3(2): 693-704.Johansen, O. 1975. Thermal Conductivity of Soils. Ph.D.dissertation. Trondheim: Norwegian Technical Univ.Nakano, Y. & Brown, J. 1971. Effect of a freezing zone offinite width on the thermal regime of soils. WaterResources Research 5: 1226-1233.Van Genuchten, M.Th. 1980. A closed-form equation forpredicting the hydraulic conductivity of unsaturatedsoils. Soil Sci. Soc. Am. J. 44: 892-898.Williams, P.J. & Smith, M.W. 1989. The Frozen Earth:Fundamentals of Geocryology. Cambridge:Cambridge University Press.70