A Simple Thermal Conductivity Model for Unsaturated Geomaterials Accounting for Degree of Saturation and Dry Density
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(2020) 6:46
TECHNICAL NOTE
A Simple Thermal Conductivity Model for Unsaturated Geomaterials Accounting for Degree of Saturation and Dry Density Agostino Walter Bruno1 · Doaa Alamoudi1 Received: 14 August 2020 / Accepted: 27 September 2020 © The Author(s) 2020
Abstract This paper proposes a simple thermal conductivity model for geomaterials accounting for the combined effect of both degrees of saturation and dry density. The model only requires the determination of the thermal conductivity under dry conditions (i.e., at a degree of saturation equal to zero) and as little as two additional measurements of thermal conductivity performed at different levels of degree of saturation and dry density. The model is a function of only two fitting parameters, namely the moisture factor mf and the density factor md . Despite its simplicity, the model can correctly predict the thermal conductivity of geomaterials and this has been validated against five sets of experimental data obtained on a very broad range of materials ranging from fine (e.g., bentonite) to coarser soils (e.g., a mix of gravel, coarse sand and silt) tested at different levels of degree of saturation and dry density. The paper also shows that the model can be applied to different engineering contexts such as (a) the thermal behaviour of earth materials used for building construction, (b) the thermal performance of bentonites employed for the storage of nuclear waste and (c) the estimation of the heat exchange in shallow geothermal reservoirs. Finally, the proposed model can be easily implemented in a finite element code to perform numerical simulations to study the heat transfer in unsaturated geomaterials. Keywords Thermal conductivity · Geomaterials · Partial saturation · Dry density · Heat transfer
Introduction The thermal conductivity of unsaturated geomaterials plays a fundamental role in a broad range of engineering, geophysical and geoenvironmental applications such as (a) the storage and recovery of heat from shallow geothermal reservoirs [1–4]; (b) the thermal performance of bentonitic clay used for the storage of highly radioactive nuclear waste [5–7]; (c) the indoor thermal comfort inside earth dwellings [8, 9]; (d) management of crops and cultivations in agricultural applications [10, 11]. Over the past few decades, the experimental measurement of the thermal conductivity of unsaturated porous geomaterials has enjoyed a significant progress and it can be obtained by means of various techniques involving either steady-state or transient methods [12]. The former group of * Agostino Walter Bruno [email protected] 1
School of Engineering, Geotechnics and Structures, Newcastle University, Devonshire Terrace, Drummond Building, Room 2.19, Newcastle upon Tyne NE1 7RU, UK
methods encompasses various laboratory techniques, such as the absolute technique for which a sample is heated by a heat source with a known steady-state power and the resulting temperature gradient across the thickness of the material is monitored. Other steady-
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