Recovery of microstructure properties: random variability of soil solid thermal conductivity

Open access

Abstract

In this work, the complex microstructure of the soil solid, at the microscale, is modeled by prescribing the spatial variability of thermal conductivity coefficient to distinct soil separates. We postulate that the variation of thermal conductivity coefficient of each soil separate can be characterized by some probability density functions: fCl(λ), fSi(λ), fSa(λ), for clay, silt and sand separates, respectively. The main goal of the work is to recover/identify these functions with the use of back analysis based on both computational micromechanics and simulated annealing approaches. In other words, the following inverse problem is solved: given the measured overall thermal conductivities of composite soil find the probability density function f(λ) for each soil separate. For that purpose, measured thermal conductivities of 32 soils (of various fabric compositions) at saturation are used. Recovered functions f(λ) are then applied to the computational micromechanics approach; predicted conductivities are in a good agreement with laboratory results.

[1] Bristow K.L., Thermal conductivity, [in:] Methods of Soil Analysis. Part 4. Physical methods, Soil Science Society of America Book Ser. 5, SSSA and ASA, Madison, WI, 2002, 1209–1226.

[2] Černý V., Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm, Journal of optimization theory and applications, 1985, 45(1), 41–51.

[3] Clauser C., Huenges E., Thermal conductivity of rocks and minerals, Rock physics Phase Relations: A handbook of physical constants, 1995, 105–126.

[4] Côté J., Konrad J.M., Thermal conductivity of base-course materials, Canadian Geotechnical Journal, 2005a, 42(1), 61–78.

[5] Côté J., Konrad J.M., A generalized thermal conductivity model for soils and construction materials, Canadian Geotechnical Journal, 2005b, 42(2), 443–458.

[6] Farouki O.T., Thermal properties of soils (CRREL Monogr. 81-1). United States Army Corps of Engineers, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, 1981.

[7] Feller W., An Introduction to Probability Theory and Its Applications, John Wiley & Sons, Vol. 2, 2008.

[8] Gemant A., How to compute thermal soil conductivities, Heating, Piping and Air Conditioning, 1952, 24(1), 122–123.

[9] Gusev A.A., Representative volume element size for elastic composites: a numerical study, Journal of the Mechanics and Physics of Solids, 1997, 45(9), 1449–1459.

[10] Johansen O., Thermal conductivity of soils, Ph.D. dissertation, Norwegian University of Science and Technology, Trondheim (CRREL draft translation 637, 1977), 1975.

[11] Kanit T., Forest S., Galliet I., Mounoury V., Jeulin D., Determination of the size of the representative volume element for random composites: statistical and numerical approach, International Journal of Solids and Structures, 2003, 40(13), 3647–3679.

[12] Kirkpatrick S., Gelatt C.D., Vecchi M.P., Optimization by simulated annealing, Science, 1983, 220(4598), 671–680.

[13] Lu S., Ren T., Gong Y., Horton R., An improved model for predicting soil thermal conductivity from water content at room temperature, Soil Science Society of America Journal, 2007, 71(1), 8–14.

[14] Lu S., Ren T., Yu Z., Horton R., A method to estimate water vapour enhancement factor in soil, European Journal of Soil Science, 2011, 62(4), 498–504.

[15] Lu Y., Lu S., Horton R., Ren T., An empirical model for estimating soil thermal conductivity from texture, water content, and bulk density, Soil Science Society of America Journal, 2014, 78(6), 1859–1868.

[16] Łydżba D., Różański A., Microstructure measures and the minimum size of a representative volume element: 2D numerical study, Acta Geophysica, 2014, 62(5), 1060–1086.

[17] Ochsner T.E., Horton R., Ren T., A new perspective on soil thermal properties, Soil Science Society of America Journal, 2001, 65(6), 1641–1647.

[18] Puła W., Chwała M., On spatial averaging along random slip lines in the reliability computations of shallow strip foundations, Computers and Geotechnics, 2015, 68, 128–136.

[19] Torquato S., Random heterogeneous materials: microstructure and macroscopic properties, Springer Science and Business Media, 2013, 16.

[20] Vanmarcke E.H., Probabilistic modeling of soil profiles, Journal of the Geotechnical Engineering Division, 1977, 103(11), 1227–1246.

Studia Geotechnica et Mechanica

The Journal of Wroclaw University of Technology

Journal Information

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 40 40 17
PDF Downloads 11 11 9