Soil Thermal Conductivity Models Research Articles

An effective medium theory-based unified model for estimating thermal conductivity of unfrozen and frozen soils

Soil thermal conductivity (STC) is a crucial parameter in modeling land surface processes. However, the current STC models are developed separately for unfrozen and frozen soils, leading to inconsistent understanding. In this study, we propose a unified model based on the work of Ghanbarian and Daigle (2016) originally developed for unfrozen soils. The unified model comprises three parameters: critical volume fraction (ϕc), scaling exponent (t), and a compensating factor (α), and considers dry soil as the low-conductivity component (weighted by air volume fraction) and saturated soil as the high-conductivity component (weighted by volumetric liquid content for unfrozen state and total water content for frozen state). Specifically, ϕc represents a critical point where high-conductivity component begins to govern the behavior of effective STC, characterized by t. α allows for accurate calibration of saturated STC. Using a dataset of 90 unfrozen samples (693 measurements) and 74 frozen samples (255 measurements), pedotransfer functions (PTFs) for the three parameters were trained. The unified model successfully reproduces the sharp rise in STC at low moisture conditions during wetting and the increase during freezing. Compared to an empirical model (Côté and Konrad, 2005a) and a theoretical model (Tian et al., 2016), the unified model demonstrates higher predictive skill for unfrozen and frozen soils, achieving Nash-Sutcliffe efficiency coefficients of 0.96 and 0.90, respectively. This work contributes to a more consistent and comprehensive understanding of STC in cold environments and has the potential to be integrated into land surface models.

Observing and modelling dynamic changes in temperature and volumetric fluxes within a riverbank aquifer under the influence of seasonal river stage fluctuations

AbstractSeasonal variation causes regular fluctuations in river water levels and water temperatures, which affects the distribution of temperature fields and seepage fields in riparian zones. In this paper, the monitoring device was used to continuously monitor Dongting Lake for a period of 1 year, and the temperature distribution characteristics of the riparian hyporheic zone under seasonal variation were analysed. Ten riparian hydrothermal coupling models based on different soil thermal conductivity models were verified, and the optimal model was used to simulate the influence of the flood process on the temperature field and seepage field of the riparian hyporheic zone. The results show that the changes in groundwater level and temperature in the riparian hyporheic zone had obvious lag and attenuation phenomena compared with the changes in river water level and ambient temperature. The temperature field of the riparian hyporheic zone changed obviously in the year. The vertical temperature gradient was large in summer and winter, the stratification phenomenon was obvious, and the temperature field fluctuation was small. The effect of the flood process on the temperature field and seepage velocity in the riparian hyporheic zone was obviously hysteretic. The effect of the flood‐withdrawing process on the temperature change of the shallow layer was greater than that of the flood‐rising process, while the response of the deep layer temperature change to flood‐rising and flood‐withdrawing processes was the opposite. The effect of floods on the variation in groundwater velocity was that the flood‐rising process was greater than the flood‐withdrawing process.

An improved model for predicting the thermal conductivity of sand based on a grain size distribution parameter

Soil thermal conductivity is a critical parameter in various fields related to soil heat transfer, mainly affected by porosity and saturation. In this research, the thermal conductivity of three types of sands with different properties was measured. Eight soil thermal conductivity models (including two semi-empirical models and six empirical models) were compared and evaluated. By analyzing the inadequacies of the existing models and microscopic mechanism of soil, a grain size distribution parameter was defined, and an improved model was proposed. The results showed that four empirical models from published literature provided relatively satisfactory performance but still required improvement. The improved model can accurately predict the thermal conductivity of different types of soils as the root mean square error for the three soils were 0.072, 0.073, and 0.056 W·m−1· k−1, respectively. Moreover, compared with the existing models, the improved model provided more scientific explanations for the limiting cases of porosity and saturation. In addition, this model revealed a close linear relationship between the thermal conductivity of soil and solid particles. The prominent nonlinear relationships between thermal conductivity and porosity or saturation were also depicted. Furthermore, the content of fine particles has a remarkable impact on the thermal conductivity of dry soil. It is suggested that the improved model can be used for predicting the complete thermal conductivity of soil in case there is no available field test data.

Validation of Soil Thermal Conductivity Models

This study describes the generation of a uniform data base of 2733 non-stationary thermal conductivity laboratory measurements of about 158 soil cores with varying texture, bulk density, soil organic matter, pH, and carbonate content. This data set has been used to validate ten well established pedo-transfer functions for predicting thermal conductivity by using easily available soil information such as soil texture, bulk density, and water content. Models were grouped into (i) physically based and (ii) empirical ones that need measured data for its calibration. The classical physical based transfer-function of deVries et al. has been finally chosen to set up a framework of standard values for the USDA soil classes. For planning purposes, these lambda estimates for selected pressure heads only need information on soil texture and bulk density and may be more valuable than single point values of thermal conductivity.

Research on water heat coupling model of riparian zone based on soil thermal conductivity model

In recent years, the research on the process of water and heat transfer in the riparian zone has become more and more extensive, a more accurate riparian water and heat coupling model is helpful for us to understand the law of water and heat transfer in the riparian zone. The hydro thermal coupling model of riparian zone is constructed based on different soil thermal conductivity models, the simulation effects of different models are verified and compared by using the experimental data, the parameter sensitivity analysis of the built model is carried out to determine the main parameters affecting the output of model temperature field, and the influence of revetment structure on the process of hydro thermal transport in riparian zone is simulated. The results show that: 1. the Hydrothermal Coupling Model of riparian zone based on Johansen thermal conductivity model has the best simulation effect and high reliability. 2. The permeability coefficient (ks ) and porosity (n) have the most significant influence on the temperature simulation results, and the parameter sensitivity is the highest. 3. The revetment structure hinders the infiltration of surface water into the riparian zone in the horizontal direction, reduces the infiltration water level and temperature fluctuation in the riparian zone.

An evaluation of soil thermal conductivity models based on the porosity and degree of saturation and a proposal of a new improved model

Soil thermal conductivity is a key factor for the soil heat transfer analysis, and is widely applied in many fields. However, it is difficult to measure the thermal conductivities of various soils with different porosities and degrees of saturation. Therefore, an accurate soil thermal conductivity model is essential for practical engineering. In this research, the comparisons and evaluations of eight soil thermal conductivity models (including seven from other scholars and a new improved model) are conducted based on the measured data from published literature. Additionally, these models are categorized into two groups: theoretical models and empirical models. The results show that the predictive capabilities of the empirical models are higher than those of the theoretical models because the first use fitted values of the empirical parameters better fit the experimental data. However, the theoretical models have definite physical meanings. The new proposed model shows better performance, and its Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values when the thermal conductivities of seven soils are calculated are less than 0.1 Wm−1K−1. This work provides references for the selection and application of soil thermal conductivity models

Response of soil thermal conductivity to various soil properties

Soil thermal conductivity is an important property of soil that has various applications in simulation of land-surface water and energy processes, and geothermal energy calculations. In this study we conduct laboratory experiments to evaluate the impacts of various soil properties on soil thermal conductivity. The experiments included three soil types (i.e., sand, sandy loam, silt loam), four soil salinity levels, and a wide range of soil water content. To find the most effective factors we utilized different statistical methods (i.e., linear regression, information theoretic sensitivity index, Pearson's correlation coefficient, and random forest). Moreover, we developed and tested three soil thermal conductivity models (i.e., linear regression, random forest and quadratic equations). The results show that soil water content has the highest level of influence on thermal conductivity. Also, the quadratic relationship between thermal conductivity and independent variables provide the most accurate predictions among the models evaluated in this study.

Evaluation of 14 frozen soil thermal conductivity models with observations and SHAW model simulations

Frozen soil thermal conductivity (FSTC, λeff) is a critical thermophysical property that is required for a variety of science and engineering applications. Measurements of λeff in frozen soils are prone to errors because the currently available thermal methods result in phase change (i.e., thawing and refreezing of ice) that affects the estimated λeff, especially near the freezing point of soil water (e.g., −4 to 0 °C) where rapid phase change occurs. In addition, measured λeff data are few compared to other physical properties. Therefore, many FSTC algorithms have been developed and a few of them have been incorporated in numerical simulation programs for calculating λeff. However, large discrepancies between simulated and observed soil thermal regimes have been reported. Previous studies either evaluated the performance of a few FSTC algorithms with limited λeff or simply compared the performance of the algorithms in numerical simulation programs. No study has been performed to systematically assess the performance of the FSTC algorithms included in numerical simulation programs with both observations and model simulations. In this study, 14 FSTC algorithms incorporated in various numerical simulation programs were evaluated with a compiled dataset consisting of 331 λeff measurements on 27 soils from seven studies made at temperatures on or below −4 °C. The Becker 1992 algorithm provided the best estimates of the λeff measurements, but the accuracy of the estimates was not good (i.e., RMSE = 0.46 W m−1 °C−1, Bias = -0.04 W m−1 °C−1 and NSE = 0.51). These FSTC algorithms were also incorporated in the Simultaneous Heat and Water (SHAW) model to compare their effects on the simulating soil temperature and water content at two field sites with contrasting soil textures in USA. The simulation results showed that the average bias of simulated and observed soil temperature for all depths ranged from −2.2 to 2.8 °C and the average differences of liquid water content ranged from −0.08 to 0.1 cm3 cm−3. Generally no FSTC algorithm combined with the SHAW model satisfactorily estimated the dynamic soil thermal regime. Perspectives on future studies are discussed.

Soil thermal conductivity model by de Vries: Re‐examination and validation analysis

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.

A review and evaluation of 39 thermal conductivity models for frozen soils

Frozen soil thermal conductivity (λeff) is a critical thermo-physical property that is required for environmental, earth science, geotechnical and geo-environmental applications and associated numerical modeling. Measurement of λeff in frozen soils is difficult and prone to errors, especially near the freezing/thawing point of soil water (e.g., −4 to 0 °C). Available steady-state or transient methods to measure λeff based on the soil temperature response to applied heat often result in melting of soil ice, violating the conduction-only assumptions of these methods and result in biased λeff measurements. Therefore, the choice of λeff models is often influence by their ease of implementation. A great number of such models have been developed during the last few decades since the latest comprehensive review of frozen soil thermal conductivity models in the early 1980s. There is a need to revisit this topic by comparing the models and evaluating their performance to provide information to the novice and expert alike, in order to guide them on their advantages, limitations and applications. A total of 39 models were categorized as: 1) linear and non-linear regression models (8 models); 2) physical models (6 models); 3) mixing models (6 models); 4) normalized models (17 models); and 5) models of other types based on their characteristics (2 models). These models were assessed with a large compiled dataset consisting of 331 λeff measurements taken at temperatures <−4 °C on 27 soils from seven studies, using steady-state or transient methods. Three performance indices including root mean square error (RMSE), average deviations (AD) and Nash-Sutcliff Efficiency (NSE) were used to evaluate performance of these models. The results showed that the models of Becker et al. (1992) (BB1992), Tian et al. (2016) (TZ2016), Zhang et al. (2018) (ZM2018) and Wang et al. (2017) (WL2017) were the best performing models in their affiliated category. However, none of the models performed satisfactorily, with NSE = 0.51, RMSE = 0.46 W m−1 °C−1 and AD = −0.04 W m−1 °C−1 for the best performing model among all the models investigated. Future studies that focus on conceptualization and development of new frozen soil thermal conductivity models for accurate and wide application is recommended.

A unified soil thermal conductivity model based on artificial neural network

An accurate prediction of thermal conductivity (k) of unsaturated soils is a challenging problem in geothermal applications because k is affected by various factors such as soil fabric, water content, dry density, soil mineralogy and type. This study proposes a unified soil thermal conductivity model to consider these influence factors based on a screened artificial neural network (ANN) approach. Two hundred and fifty-seven (257) thermal conductivity measurements of unsaturated soils were first collected from the literature to compile a database. The ANN approach constrained with model complexity optimization and monotonicity control was then utilized to overcome the potential sample insufficiency problem in order to establish reliable correlations between k (represented by an empirical coefficient) and its influence factors including dry density (ρd), porosity (n), saturation degree (Sr), quartz content (mq), sand content (ms) and clay content (mc). Using this approach, some easy-to-use ANN-based contours for predicting k were developed to guide engineering practice. Results revealed that ANN-based predictions of k by the developed model matched experimental data with enhanced accuracy as compared with some benchmarking thermal conductivity models. The model can rationally consider the effects of multiple influence factors and their coupling effects on k in a quantitative and systematical way.

Improving a thermal conductivity model of unsaturated soils based on multivariate distribution analysis

Soil thermal conductivity (k) is a key parameter for the design of energy geo-structures, and it depends on many soil properties such as saturation degree, porosity, mineralogical composition, soil type and others. Capturing these diversified influencing factors in a soil thermal conductivity model is a challenging task for engineers due to the nonlinear dependencies. In this study, a multivariate distribution approach was utilized to improve an existing soil thermal conductivity model, Cote and Konrad model, by quantitatively considering the impacts of dry density (ρd), porosity (n), saturation degree (Sr), quartz content (mq), sand content (ms) and clay content (mc) on thermal conductivity of unsaturated soils. A large database containing these seven soil parameters was compiled from the literature to support the multivariate analysis. Simplified bivariate and multivariate correlations for improving the Cote and Konrad model were derived analytically and numerically to consider different influencing factors. By incorporating these simplified correlations, the predicted k values were more concentrated around the measured values with the coefficient of determination (R2) increased from 0.83 to 0.95. It is concluded that the developed correlations with the information of different soil properties provide an efficient, rational and simple way to predict soil thermal conductivity more accurately. Moreover, the quartz content is a more important factor than the porosity that shall be considered in the establishment of thermal conductivity models for unsaturated soils with high quartz content.

Normalized concept for modelling effective soil thermal conductivity from dryness to saturation

AbstractEffective soil thermal conductivity (λ eff) is a critical parameter for environmental and earth science as well as engineering applications. Models to predict λ eff are required in diverse global and community land surface schemes as well as climate models to investigate coupled water and heat transport in soils and heat exchange at the earth surface. Among the many soil thermal conductivity models, models based on the normalized concept are most often developed and utilized for estimating λ eff. However, at present no systematic study has been performed to investigate the origin and evolution of the normalized thermal conductivity models, nor to evaluate their performance with large datasets. The objectives of this study were to: (a) review the development and evolution of the normalized thermal conductivity models, and (b) assess their performance with datasets consisting of soils with a full range of water saturation and a wide range of soil textures and bulk densities. A total of 38 normalized thermal conductivity models were critically reviewed and their relationships were clearly outlined. Their performance was evaluated by five categories according to model characteristics with a compiled dataset consisting of 71 soils and 669 tests collected from nine studies. Our analysis demonstrated key roles of the quartz content, solid thermal conductivity and choice of the Kersten functions in the model applicability and accuracy of estimating λ eff. The results showed that the Y2018, CK2005, CK2006, J1975, L2007 and T2009 models have the best performance among the models without fitting parameters, but further improvements are required to apply them universally. Although the models of H2017, LD2015, M2006 and K2007 are the best performing models with fitting parameters, approaches to calculate these parameters are required so they can be easily applied. Future studies on parametrization of currently well‐performing models for wider and more accurate application, development of a soil thermal conductivity database for model evaluation and calibration purposes, and connecting soil thermal conductivity models to hydraulic properties are recommended.Highlights The history and evolution of normalized thermal conductivity models and the potential Kersten (K e) functions are collated and synthesized. A total of 38 models were reviewed and their performance was evaluated with a total of 71 soils and 669 tests from nine studies. The Y2018, CK2005, CK2006, J1975, L2007 and T2009 are the best ranked models without fitting parameters. The models of H2017, LD2015, M2006 and K2007 are the best ranked models with fitting parameter.

A comparison of numerical and Lu modeling of water flow and heat transport with laboratory experiments

Reservoirs are considered to result in significant changes to river water temperature. Discharge of deep water has a large impact on aquatic ecosystems downstream of dam and on both river banks. A laboratory sand tank test investigation was conducted to simulate water flow and thermal dynamics in the riparian zone. The sand temperature (ST) data generated were used to validate and compare HYDRUS-2D, a physically based numerical model, with Lu et al.’s (Soil Sci Soc Am J 71(1):8–14, 2007) soil thermal conductivity model under different water temperature, hydraulic head and radiation temperature conditions. The Richards model and the heat conduction model were coupled through the Horton thermal conductivity model and the Lu et al. (Soil Sci Soc Am J 71(1):8–14, 2007) model, respectively. The results demonstrated the success of model coupling and its application for investigating water flow and thermal dynamics in the riparian zone. The Lu et al. (Soil Sci Soc Am J 71(1):8–14, 2007) model based on COMSOL and the Horton thermal conductivity model based on HYDRUS each had their own advantages. Global analysis showed that the Lu et al. (Soil Sci Soc Am J 71(1):8–14, 2007) model was better able to simulate the riparian zone temperature field under the investigated experimental conditions. The sensitivity analysis results showed that the parameters nv, T and H had a considerable influence on the temperature field in the model, of which nv was the most sensitive, whereas the parameters ks, α, θs, and θr were relatively less sensitive to the temperature field.

Effective thermal conductivity of unsaturated granular geocomposite using lattice element method

Soil thermal conductivity has an important role in geo-energy applications and heat transfer modelling. The performances and efficiencies of such applications are strongly affected by the saturation conditions, especially at the lower saturation, which can negatively affect the soil thermal conductivity. Therefore, it is essential to improve the soil thermal conductivity at lower saturation levels. Here, we investigate the effect of the fillers, soil gradation and the water saturation on the thermal conductivity of sand as an innovative improvement method. The experimental results show a significant improvement in the thermal conductivity at dry and lower saturation degrees and a considerable improvement in the case of full saturation. The improvement in the thermal conductivity is comparatively high in dry state and is decreasing with increase in the saturation. The existing soil thermal conductivity models, which are limited to a specific boundary conditions and soil types, fail to consider the effect of soil filler composite behaviour. Therefore, a mesoscale numerical method is developed to model the change in effective thermal conductivity. The developed model shows a good agreement with the measured thermal conductivity values.

Selected soil thermal conductivity models

The paper presents collected from the literature models of soil thermal conductivity. This is a very important parameter, which allows one to assess how much heat can be transferred from the underground power cables through the soil. The models are presented in table form, thus when the properties of the soil are given, it is possible to select the most accurate method of calculating its thermal conductivity. Precise determination of this parameter results in designing the cable line in such a way that it does not occur the process of cable overheating.

Deriving pedotransfer functions for soil quartz fraction in southern France from reverse modeling

Abstract. The quartz fraction in soils is a key parameter of soil thermal conductivity models. Because it is difficult to measure the quartz fraction in soils, this information is usually unavailable. This source of uncertainty impacts the simulation of sensible heat flux, evapotranspiration and land surface temperature in numerical simulations of the Earth system. Improving the estimation of soil quartz fraction is needed for practical applications in meteorology, hydrology and climate modeling. This paper investigates the use of long time series of routine ground observations made in weather stations to retrieve the soil quartz fraction. Profile soil temperature and water content were monitored at 21 weather stations in southern France. Soil thermal diffusivity was derived from the temperature profiles. Using observations of bulk density, soil texture, and fractions of gravel and soil organic matter, soil heat capacity and thermal conductivity were estimated. The quartz fraction was inversely estimated using an empirical geometric mean thermal conductivity model. Several pedotransfer functions for estimating quartz content from gravimetric or volumetric fractions of soil particles (e.g., sand) were analyzed. The soil volumetric fraction of quartz (fq) was systematically better correlated with soil characteristics than the gravimetric fraction of quartz. More than 60 % of the variance of fq could be explained using indicators based on the sand fraction. It was shown that soil organic matter and/or gravels may have a marked impact on thermal conductivity values depending on which predictor of fq is used. For the grassland soils examined in this study, the ratio of sand-to-soil organic matter fractions was the best predictor of fq, followed by the gravimetric fraction of sand. An error propagation analysis and a comparison with independent data from other tested models showed that the gravimetric fraction of sand is the best predictor of fq when a larger variety of soil types is considered.

A new generalized soil thermal conductivity model for sand–kaolin clay mixtures using thermo-time domain reflectometry probe test

As the demand of exploitation and utilization of geothermal energy increases, more geothermal-related earth structures occur recently. The design of the structures depends upon an accurate prediction of soil thermal conductivity. The existing soil thermal conductivity models were mostly developed by empirical fits to datasets of soil thermal conductivity measurements. Due to the gaps in measured thermal conductivities between any two tested natural soils, the models may not provide accurate prediction for other soils, and the predicted thermal conductivity might not be continuous over the entire range of soil type. In this research, a generalized soil thermal conductivity model was proposed based on a series of laboratory experiments on sand, kaolin clay and sand–kaolin clay mixtures using a newly designed thermo-time domain reflectometry probe. The model was then validated with respect to k dry–n (thermal conductivity of dry soils and porosity) and k r–S r (normalized thermal conductivity and degree of saturation) relationships by comparing with previous experimental studies. The predicted thermal conductivities were found to be in a good agreement with the experimental data collected from both this study and the other literatures with at least 85% confidence interval. It is concluded that the proposed model accounts for the effects of both environmental factors (i.e., moisture content and dry density) and compositional factors (i.e., quartz content and soil type) on soil thermal conductivity, and it has a great potential in predicting soil thermal conductivity more accurately for geothermal applications.

Thermal conductivity of sand–kaolin clay mixtures

Thermal conductivity is a key parameter for the design of various geothermal structures such as geothermal energy piles, ground source heat pumps and soil borehole thermal energy storage. In this paper, the thermal conductivity of sand–kaolin clay mixtures prepared at varied moisture content, dry density and clay content was measured using a newly designed thermo-time domain reflectometry probe. The data revealed that the thermal conductivity of the sand–kaolin clay mixtures increased with an increase in moisture content and dry density. The thermal conductivity of the moist sand–kaolin mixtures decreased with an increase in clay content in two distinct regimes including a slow decrease in thermal conductivity above a critical clay content, which was found to be 10%. Five soil thermal conductivity models were selected to predict the thermal conductivity of the sand–kaolin clay mixtures, and the predictions were compared with the experimental results. Two models were modified to account for the effect of clay content on the thermal conductivity of the sand-clay mixtures. Recommendations regarding the design of energy geostructures were made based on the measured thermal conductivity data.

Assessment of some soil thermal conductivity models via variations in temperature and bulk density at low moisture range

Simulation of heat transfer in soil under steady and unsteady situations requires reliable estimate of soil thermal conductivity (λ) at varying environmental conditions. In the current work several soil thermal conductivity predicting models including I) de Vries, II) Campbell, III) combined de Vries and Campbell and IV) de Vries-Nobre were evaluated for the four soils of coarse sand, sandy loam, loam and clay loam textured at varying in temperature and bulk density at low moisture range. Thermal conductivities measured by the cylindrical probe method served as the reference for models assessment. Results showed that approximately same thermal conductivities obtained by the five methods at low moisture range (θ ≤ 0.05 m3/m3). Also the de Vries and de Vries-Campbell models produced accurate than Campbell and de vries-Nobre models. The accuracy of the two models increased with soil compaction but decreased with temperature rise. Campbell model showed more reliability at higher (311.16 and 321.16 K) temperatures; but its accuracy declined with soil compaction in current work. It seems that assuming needle shape for the soil particles is far away from the reality whereas assuming spherical shapes may be more realistic and produced more satisfactory prediction of thermal conductivity. The compaction would alter particle arrangement and may increase the contact area of particles; and then make them behave more or less spherical shape.it seems thermal conductivity in solid particles increase via increasing in temperature. Since a modified mineral shape factor, gm, was developed as a combination between sphere and needle according to geometric mean particle diameter as well as bulk density and temperature as modifying factors. This factor increased the accuracy of de Vries-Nobre model up to 10.37%. Regarding nonlinear regression model, moisture content, bulk density, temperature and quartz content demonstrated significant effect on soil thermal conductivity in our investigation.