Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils
This paper proposes homogenization scheme for estimating the effective thermal conductivity of fully saturated soils. This approach is based on the random checkerboard-like microstructure. Two modeling scales and two modeling approaches are distinguished and used, i.e. microscale and mesoscale and 1...
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doaj-99221690672540b697a2cde4fc381e2c2020-11-24T21:40:49ZengElsevierJournal of Rock Mechanics and Geotechnical Engineering1674-77552017-02-0191182810.1016/j.jrmge.2016.06.010Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soilsDariusz ŁydżbaAdrian RóżańskiMagdalena RajczakowskaDamian StefaniukThis paper proposes homogenization scheme for estimating the effective thermal conductivity of fully saturated soils. This approach is based on the random checkerboard-like microstructure. Two modeling scales and two modeling approaches are distinguished and used, i.e. microscale and mesoscale and 1-step and 2-step homogenizations, respectively. The 2-step homogenization involves sequential averaging procedure, i.e. first, at microscale, a mineralogical composition of soil skeleton is considered and averaging process results in estimation of the skeleton effective thermal conductivity, and then, at mesoscale, a random spatial packing of solid skeleton and pores via random checkerboard microstructure is modeled and leads to evaluation of the soil overall thermal conductivity. The 1-step homogenization starts directly at the mesoscale and homogenization procedure yields evaluation of the overall soil thermal conductivity. At the mesoscale, the distinct nature of soil skeleton, as composed of soil separates, is considered and random variability of soil is modeled via enriched random checkerboard-like structure. Both approaches, i.e. 1-step and 2-step homogenizations, interrelate mineralogical composition with the soil texture characterized by the volume fractions of soil separates, i.e. sand, silt and clay. The probability density functions (PDFs) of thermal conductivity are assumed for each of the separates. The soil texture PDF of thermal conductivity is derived taking into consideration the aforementioned functions. Whenever the random checkerboard-like structure is used in averaging process, the Monte Carlo procedure is applied for estimation of homogenized thermal conductivity. Finally, the proposed methodology is tested against the laboratory data from our measurements as well as those available from literature.http://www.sciencedirect.com/science/article/pii/S1674775516302025Soil mechanicsMicromechanicsEffective thermal conductivity |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Dariusz Łydżba Adrian Różański Magdalena Rajczakowska Damian Stefaniuk |
spellingShingle |
Dariusz Łydżba Adrian Różański Magdalena Rajczakowska Damian Stefaniuk Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils Journal of Rock Mechanics and Geotechnical Engineering Soil mechanics Micromechanics Effective thermal conductivity |
author_facet |
Dariusz Łydżba Adrian Różański Magdalena Rajczakowska Damian Stefaniuk |
author_sort |
Dariusz Łydżba |
title |
Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils |
title_short |
Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils |
title_full |
Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils |
title_fullStr |
Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils |
title_full_unstemmed |
Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils |
title_sort |
random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils |
publisher |
Elsevier |
series |
Journal of Rock Mechanics and Geotechnical Engineering |
issn |
1674-7755 |
publishDate |
2017-02-01 |
description |
This paper proposes homogenization scheme for estimating the effective thermal conductivity of fully saturated soils. This approach is based on the random checkerboard-like microstructure. Two modeling scales and two modeling approaches are distinguished and used, i.e. microscale and mesoscale and 1-step and 2-step homogenizations, respectively. The 2-step homogenization involves sequential averaging procedure, i.e. first, at microscale, a mineralogical composition of soil skeleton is considered and averaging process results in estimation of the skeleton effective thermal conductivity, and then, at mesoscale, a random spatial packing of solid skeleton and pores via random checkerboard microstructure is modeled and leads to evaluation of the soil overall thermal conductivity. The 1-step homogenization starts directly at the mesoscale and homogenization procedure yields evaluation of the overall soil thermal conductivity. At the mesoscale, the distinct nature of soil skeleton, as composed of soil separates, is considered and random variability of soil is modeled via enriched random checkerboard-like structure. Both approaches, i.e. 1-step and 2-step homogenizations, interrelate mineralogical composition with the soil texture characterized by the volume fractions of soil separates, i.e. sand, silt and clay. The probability density functions (PDFs) of thermal conductivity are assumed for each of the separates. The soil texture PDF of thermal conductivity is derived taking into consideration the aforementioned functions. Whenever the random checkerboard-like structure is used in averaging process, the Monte Carlo procedure is applied for estimation of homogenized thermal conductivity. Finally, the proposed methodology is tested against the laboratory data from our measurements as well as those available from literature. |
topic |
Soil mechanics Micromechanics Effective thermal conductivity |
url |
http://www.sciencedirect.com/science/article/pii/S1674775516302025 |
work_keys_str_mv |
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