Soil thermal conductivity model by de Vries: Re‐examination and validation analysis
Authors: Tarnawski Vlodek R. , Wagner Bernhard , Leong Wey H. , McCombie Marlon , Coppa Paolo , Bovesecchi Gianluigi 
Published: April 2021

AbstractThe thermal conductivity (λ) of soils is an important property in a variety of science and engineering applications. One of the most widely used λ models in soil science was proposed by de Vries (deV‐0). This model is complicated and difficult to use as it is based on several controversial assumptions. The deV‐0 assumes that a soil system is composed of non‐contacting solid particles (rotated uniform ellipsoids) that are dispersed in a continuous homogeneous medium (air or water). Furthermore, deV‐0 assumes that soil solids consist of quartz and consolidated bulk minerals. These assumptions do not reflect the true nature of soils that are composed of several compacted minerals, diverse in shape and notably different in size. A critical analysis of this model concluded that its most controversial feature was inherited from an electrical conductivity model for a two‐phase dispersion system; specifically, from weighting shape factors of non‐contacting rotated oblate ellipsoids. Furthermore, deV‐0 has not yet been fully examined and verified with respect to a comprehensive and complete soil λ database. Also, there is a lack of comparable models to deV‐0 that would contain a complete set of clearly described and linked expressions. Consequently, two slightly adjusted versions of deV‐0 were developed; namely, deV‐1 with soil bulk mineralogy (quartz plus integrated residual minerals) and deV‐2 with complete soil mineralogy (i.e., including individual contributions from all soil minerals). Both models underwent successful calibration and verification against λ data of 39 Canadian field soils and three Standard sands. Markedly improved estimates (λest) were obtained when, instead of dry air thermal conductivity (λa), an apparent air thermal conductivity (λa‐app = λa + λv) was applied (λv represents thermal effects caused by migration of water vapour and evaporation/condensation processes). For deV‐1, the following reduction of standard deviation (SD) data was obtained: 53.5% for 17 coarse soils, 34% for 22 fine soils, and 44.5% for all 39 soils. Then, the same calibration factors of deV‐1 were applied to the deV‐2 model and a similar reduction of SD data was obtained (52.7, 24.1 and 40.1%, respectively). Generally, for 39 Canadian field soils, both models (deV‐1 and deV‐2), with quartz thermal conductivity (λqtz) of 7.6 W·m−1·K−1, produced very close λ estimates (SD ≈ 0.099 and 0.094 W·m−1·K−1, respectively). Taking into account the simplicity of mineral composition and fewer calibration coefficients, deV‐1 was a preferable choice. For that reason, soil bulk mineralogy appears to be a good equivalent to complete soil mineralogy. Also, for Standard sands (100% sand: C‐109, C‐190, NS‐04), improved λest were obtained by replacing λa with λa‐app. Finally, the deV‐1 model was successfully applied to 10 Chinese soils and the following average SD values were obtained: for four coarse soils 0.135 W·m−1·K−1, whereas for six fine soils 0.127 W·m−1·K−1.Highlights
The original λ model by de Vries (deV‐0) underestimates experimental λ data.
Two modified deV‐0 versions were developed: deV‐1, quartz + bulk minerals; deV‐2, all soil minerals.
Improved estimates were obtained when, instead of dry air λ, an apparent air λ was applied.
The deV‐1 model was successfully applied to 10 Chinese soils.