Thermal Conductivity Of Unsaturated Soils Research Articles

Influence of degree of saturation on the thermal conductivity of soils: Experimental and comparative model analysis

The thermal conductivity can characterize thermal behaviour of soils in different engineering studies: environmental, geothermal, geotechnical and buildings construction. However, accurately measuring and predicting this parameter poses a challenging task. Measuring this parameter can be very complex, considering several factors, such as soil heterogeneity and external climatic conditions. In addition, predictions models may not capture all the nuances of real-world soil conditions, leading to less accurate predictions of ?. The objectives of this paper encompassed two primary aspects: (i) Evaluation of laboratory tests of thermal conductivity of unsaturated soil. (ii) Assessment of five highly recommended soil thermal conductivity models to determine their validity and strengthen their trustworthiness. The studied material consisted of calcareous tufa locally available in Beni-Saf region (Algeria). The tested samples were compacted to the Standard and Modified Proctor Optimum (SPO, MPO) followed by drying periods under laboratory conditions. The thermal conductivity of samples was evaluated using transient method. The models’ predictive results of the thermal conductivity were assessed with different criteria such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Coefficient of Determination R². Furthermore, this work also attempts to deliver an in-depth discussion of the effect of degree of saturation Sr on the thermal conductivity of soils.

Fractal thermal conductivity of unsaturated soils considering pore heterogeneity

Accurately predicting the thermal conductivity of unsaturated soils is crucial for assessing and simulating the long-term environmental impact of subterranean engineering structures. This study presents a fractal thermal conductivity model for unsaturated soils that considers the influence of heterogeneous pore topology, water content and volumetric deformation. Based on the results from the scanning electron microscopy (SEM) and mercury intrusion-extrusion cyclic porosimetry (MIECP) tests on Shanghai clay and Kaolin, we introduce the pore-throat structure to describe the soil heterogeneity and deal with the coupling of solid-pore thermal properties through the mixing law at the pore scale. Together with the self-similar fractal law, the thermal conductivity model is upscaled from the pore scale to the representative element volume (REV) scale. During the process, heterogeneity factors are introduced to describe differences between local and bulk properties, such as porosity and saturation. Thermal property tests of Shanghai clay and Kaolin with varying porosities are then conducted to validate the proposed thermal conductivity model. Additionally, nineteen published datasets on thermal conductivity are also utilized to confirm the adaptability and robustness of the model. The results show that the proposed model predicts well the thermal conductivity of unsaturated soils. Moreover, when compared to existing models, the proposed model offers superior performance in describing the thermal properties of unsaturated soils.

Excluding quartz content from the estimation of saturated soil thermal conductivity: Combined use of differential effective medium theory and geometric mean method

Saturated soil thermal conductivity (λsat) is the maximum soil thermal conductivity value of a given soil. Although it can be determined accurately with a heat pulse sensor, there are challenges to prepare fully saturated soil samples. Numerous models have been developed to estimate λsat, and among these, the geometric mean method (GMM) generally performs well. The GMM requires soil mineral composition or quartz content information, which is unavailable for most soils. Earlier studies commonly used assumed that quartz content (fquartz) was equal to sand content (fsand) or to 0.5 × fsand, which led to significant λsat estimation errors especially on coarse-textured soils. We derived a novel method to estimate λsat from soil porosity (ϕ) based on a combination of the GMM and differential effective medium theory (DEM). The new DEM-GMM approach has a single parameter, cementation exponent (m). Using a calibration dataset of 43 soils, we determined best fit m values for soils in three groups: 1.66 for Group I (fsand < 0.4), 1.62 for Group II (0.4 <= fsand < 1) and m = -1.34ϕ+1.70 for Group III (fsand = 1). Using best fit m values for different groups, the new model can estimate λsat values from ϕ. Independent validation results on another 46 soils showed that the new model outperformed the GMM method with the assumption that fquartz = fsand or fquartz = 0.5 × fsand. The mean RMSE, Bias and R2 values of the DEM-GMM approach were 0.202 W m−1 K−1, 0.013 W m−1 K−1 and 0.89, respectively, and corresponding values of the GMM with the two assumptions were 0.295 and 0.476 W m−1 K−1, 0.056 and -0.28 W m−1 K−1, 0.80 and 0.82, respectively. The robust performance of the DEM-GMM approach suggests that it can be incorporated into thermal conductivity models to accurately estimate the thermal conductivity of unsaturated soils.

Robust calibration and evaluation of a percolation-based effective‐medium approximation model for thermal conductivity of unsaturated soils

Thermal conductivity (λ) is a property characterizing heat transfer in porous media, such as soils and rocks, with broad applications to geothermal systems and aquifer characterizations. Numerous empirical and physically-based models have been developed for thermal conductivity in unsaturated soils. Recently, Ghanbarian and Daigle (G&D) proposed a theoretical model using the percolation-based effective-medium approximation. An explicit form of the G&D model relating λ to water content (θ) and equations to estimate the model parameters were also derived. In this study, we calibrated the G&D model and two widely applied empirical λ(θ) models using a robust calibration dataset of 41 soils. All three λ(θ) model performances were evaluated using a validation dataset of 58 soils. After calibration, the root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2) of the G&D model were 0.092 W−1 m−1 K−1, 0.067 W−1 m−1 K−1 and 0.97, respectively. For the two empirical models, RMSEs ranged from 0.086 to 0.096 W−1 m−1 K−1, MAEs from 0.063 to 0.071 W−1 m−1 K−1, and R2 values were about 0.97. All three metrics indicated that calibration improved the performance of the G&D model, and it had an accuracy similar to that of the two empirical λ(θ) models. Such a robust performance confirmed that the theoretically-based G&D model can be applied to study soil heat transfer and potentially other related fields.

Prediction of soil thermal conductivity using artificial intelligence approaches

In this study, three artificial intelligence models, namely group method of data handing (GMDH), multi expression programming (MEP) and random forest (RF), are proposed to predict soil thermal conductivity. A large database of 444 data samples collected from existing literature was used to construct the three models. Three statistical indexes were used to evaluate the performance of the proposed three models and the other five existing models. The results show that the predicted results of the three models are in good agreement with the experimental results, and the RF model has the best comprehensive performance. Therefore, RF model is recommended to predict the thermal conductivity of unsaturated soil. To facilitate practical engineering applications, we have built a web program for the three proposed models, and users can use these three models by visiting the website.

Comparison of Measured and Derived Thermal Conductivities in the Unsaturated Soil Zone of a Large-Scale Geothermal Collector System (LSC)

The design, energetic performance, and thermal impact of large-scale geothermal collector systems (LSCs) are dependent on the thermal conductivity of unsaturated soils (λ). The aim of this study was to investigate the benefits of two different λ measurement methods using single-needle sensor measuring devices on a laboratory scale. Since large-scale determinations are required in the context of LSCs, the potential for deriving λ from electrical resistivity tomography measurements (ERTs) was also examined. Using two approaches—the continuous evaporation method and the punctual method—thermal conductivities of soil samples from Bad Nauheim (Germany) were measured. The results were compared with averaged λ derived from three ERT sections. With the evaporation method, significant bulk density changes were observed during the experimental procedure, which were caused by the clay content and the use of repacked samples. The punctual method ensures a sufficiently constant bulk density during the measurements, but only provides a small number of measurement points. The thermal conductivities derived from ERTs show largely minor deviations from the laboratory measurements on average. If further research confirms the results of this study, ERTs could provide a non-invasive and unelaborate thermal exploration of the subsurface in the context of large-scale infrastructure projects such as LSCs.

Predicting the thermal conductivity of unsaturated soils considering wetting behavior: A meso‑scale study

Unsaturated soils are three-phase porous materials that consist of the solid phase, the liquid phase and the gas phase. While accurate predictions to the thermal conductivity of unsaturated soils are crucial for the analysis and design of geothermal systems, the distribution characteristics of the different phases can also significantly affect the thermal performance. In addition, the fact that soils are heterogeneous materials also adds to the challenges in the evaluation of the thermal conductivity of unsaturated soils. In this paper, a methodology is proposed to calculate the thermal conductivity of unsaturated soils. This methodology starts from identifying representative soil parameters based on microscopy images of soil specimens. The meso‑structures that consist of the different phases are then reconstructed in a finite-element model based on the identified characteristics. The Monte-Carlo-based finite-element analyses are then carried out to calculate the thermal conductivity of unsaturated soils while considering the wetting behavior between the solid and liquid phases, which is characterized using the hydrophilia coefficient. After validating the methodology using both the experimental and numerical results reported in the literature, a parametric analysis is conducted. The results indicate that a high quartz content improves the heat transfer, but the quartz content does not affect the heat transfer skeleton. Furthermore, an increase in the solid content and degree of saturation results in an increase in the density of the heat transfer skeleton, which leads to enhanced heat transfer efficiency. A reduction in the hydrophilia coefficient and the formation of liquid-bridges have a similar effect. Last, the effects of wetting are more evident in soils with high porosity and a low degree of saturation.

Energy pile groups for thermal energy storage in unsaturated soils

• Energy pile groups provide superior thermal energy storage performance over boreholes. • Both energy pile geometry and number of internal heat exchangers are important. • Lower thermal conductivity of unsaturated soils leads to higher heat retention. • Transient decreases in degree of saturation were observed over several years. • Heat transfer in unsaturated soil can be enhanced in some cases via vapor diffusion. A coupled heat transfer and water flow model implemented in COMSOL and validated against measurements from a tank scale test was applied to investigate the application of energy pile groups for thermal energy storage in unsaturated soil layers. The novel focus of the investigation was understanding the long-term thermo-hydraulic response of the unsaturated soil within the energy pile group during heat injection at high temperature up to 90 °C and associated impacts on the heat storage performance. Unsaturated soil layers are advantageous for thermal energy storage due to enhanced convective heat transfer during injection associated with vapor diffusion and favorable insulation properties during storage associated with lower thermal conductivity of soils surrounding a heat storage system. Evolutions in temperature and degree of saturation in soil layers having different hydraulic properties and water table depths were simulated during five years of operating a group of five energy piles with inlet fluid temperatures of 90 °C during heat injection and 30 °C during heat extraction. Transient fluctuations in the degree of saturation were observed in all soil layers simulated, but a permanent decrease was only observed for a soil layer having a greater air entry suction after several cycles of heating and cooling. While the heat storage in energy pile groups in unsaturated soil layers was always between that of dry and saturated soils with no groundwater flow, the soil hydraulic properties and water table depth were found to control both the rate of heat transfer and the total heat stored. When comparing the performance of energy pile groups with a group of borehole heat exchangers commonly used in heat storage applications, the energy piles were approximately 1.2 times more effective in extracting heat with a faster response confirming their suitability for heat storage.

Predicting the thermal conductivity of soils using integrated approach of ANN and PSO with adaptive and time-varying acceleration coefficients

This study aims to propose hybrid adaptive neuro swarm intelligence (HANSI) techniques for predicting the thermal conductivity of unsaturated soils. The novel contribution is made by integrating artificial neural networks (ANNs) and particle swarm optimisation (PSO) with adaptive and time-varying acceleration coefficients. Two HANSI techniques, namely ANN-IPSO (ANN optimised with improved PSO) and ANN-APSO (ANN optimised with adaptive PSO) were constructed. To train and validate the proposed models, a dataset of 257 measurements of the thermal conductivity of soils featuring 6 influencing factors was used. The proposed ANN-APSO model has the best prediction performance in both the training and testing stages, according to the results. Also, during the validation phase, the suggested ANN-APSO model attained the most accurate prediction with Adj. R2 = 0.9265, R2 = 0.9442, and RMSE = 0.0515. These results are significantly better than those obtained from other hybrid ANN models constructed with standard PSO, IPSO, new self-organizing hierarchical PSO, modified new self-organizing hierarchical PSO, genetic algorithm, biogeography-based optimisation, and firefly algorithm. Based on the experimental results, the newly constructed HANSI models, especially ANN-APSO can be considered as an alternate solution for predicting real-time engineering problems, including the thermal conductivity of unsaturated soils.

A novel technique based on the improved firefly algorithm coupled with extreme learning machine (ELM-IFF) for predicting the thermal conductivity of soil

Thermal conductivity is a specific thermal property of soil which controls the exchange of thermal energy. If predicted accurately, the thermal conductivity of soil has a significant effect on geothermal applications. Since the thermal conductivity is influenced by multiple variables including soil type and mineralogy, dry density, and water content, its precise prediction becomes a challenging problem. In this study, novel computational approaches including hybridisation of two metaheuristic optimisation algorithms, i.e. firefly algorithm (FF) and improved firefly algorithm (IFF), with conventional machine learning techniques including extreme learning machine (ELM), adaptive neuro-fuzzy interface system (ANFIS) and artificial neural network (ANN), are proposed to predict the thermal conductivity of unsaturated soils. FF and IFF are used to optimise the internal parameters of the ELM, ANFIS and ANN. These six hybrid models are applied to the dataset of 257 soil cases considering six influential variables for predicting the thermal conductivity of unsaturated soils. Several performance parameters are used to verify the predictive performance and generalisation capability of the developed hybrid models. The obtained results from the computational process confirmed that ELM-IFF attained the best predictive performance with a coefficient of determination = 0.9615, variance account for = 96.06%, root mean square error = 0.0428, and mean absolute error = 0.0316 on the testing dataset (validation phase). The results of the models are also visualised and analysed through different approaches using Taylor diagrams, regression error characteristic curves and area under curve scores, rank analysis and a novel method called accuracy matrix. It was found that all the proposed hybrid models have a great ability to be considered as alternatives for empirical relevant models. The developed ELM-IFF model can be employed in the initial stages of any engineering projects for fast determination of thermal conductivity.

Unsaturated cell model of effective thermal conductivity of soils

In this study, a cell model based on new physical conceptualizations is developed to calculate the effective thermal conductivity of unsaturated soils. The evolution of water phase saturation is treated using a cell model consisting of solid particle being enveloped by a mixture of water and air phases. The thermal conductivity of the mixed fluid phase is determined by the volume-weighted average of water and air thermal conductivities. The temperature distribution in the cell of soil and fluid mixture is solved along with boundary condition of linearly varying temperature field. The heat transfer through the cell is calculated by integration of the temperature gradient along with thermal conductivities of soil and fluid. The effective thermal conductivity of the unsaturated soils is determined by conceptualizing the soils as having the same heat transfer as the cell of solid particle and fluid mixture. The new model is compared with 268 data entries of unsaturated soil effective thermal conductivity measurements from the literature. The developed effective thermal conductivity model compares favorably with the experimental data. When the porosity is small, the increase in the effective thermal conductivity with water phase saturation is more significant and non-linear. When the porosity increases, the increases of effective thermal conductivity with water phase saturation approaches a linear relationship.

Effective thermal conductivity of unsaturated soils based on deep learning algorithm

Soil thermal conductivity plays a critical role in the design of geo-structures and energy transportation systems. Effective thermal conductivity (ETC) of soil depends primarily on the degree of saturation, porosity and mineralogical composition. These controlling parameters have nonlinear dependencies, thus making prediction a nontrivial task. In this study, an artificial neural network (ANN) model is developed based on the deep learning (DL) algorithm to predict the effective thermal conductivity of unsaturated soil. A large dataset is constructed including porosity, degree of saturation and quartz content from literature to train and validate the developed model. The model is constructed with a different number of hidden layers and neurons in each hidden layer. The standard errors for training and testing are calculated for each variation of hidden layers and neurons. The network with the least error is adopted for prediction. Two sand types independent of training and validation data reported in the literature are considered for prediction of the ETC. Five simulation runs are performed for each sand, and the computed results are plotted against the reported experimental results. The results conclude that the developed ANN model provides an efficient, easy and straightforward way to predict soil thermal conductivity with reasonable accuracy.

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.

Role of Nonequilibrium Water Vapor Diffusion in Thermal Energy Storage Systems in the Vadose Zone

AbstractAlthough siting of thermal energy storage systems in the vadose zone may be beneficial due to the low thermal conductivity of unsaturated soils, water phase change and vapor diffusion in so...

Transient Plane and Line Source Methods for Soil Thermal Conductivity

Abstract Experiments were conducted to compare two sensing techniques for measuring thermal conductivity of unsaturated soils: (i) a modified transient plane source (MTPS) method for non-destructive measurements using a planar, interfacial heat reflectance sensor, and (ii) a transient line source (TLS-SP) method utilizing an embedded single-probe heat source. Measurement protocols for coarse-grained and fine-grained soils were developed. Thermal conductivity dry-out curves (TCDCs) were measured for five soil types, including poorly graded sand, well-graded sand with silt, silty sand, silt, and clay. The MTPS sensor consistently produced higher thermal conductivity for degrees of saturation greater than about 50 % but lower thermal conductivity for saturations less than 50 %. Saturated thermal conductivity measured using the MTPS sensor ranged from 8 % to 26 % greater than values measured using the TLS-SP sensor. Dry thermal conductivity measurements were comparable (&amp;lt;5 % difference) for fine-grained soils but were consistently and appreciably greater using the TLS-SP for coarse-grained soils. Mechanisms responsible for these differences include thermally induced water migration, latent heat transfer, sensor-soil contact resistance, gravity-induced water migration, and specimen heterogeneity. Secondary experiments indicated that the effects of gravity-induced water migration were insignificant within the short (&amp;lt;5 min) time frame elapsed between sample preparation and measurement.

Advanced Geometric Mean Model for Predicting Thermal Conductivity of Unsaturated Soils

An advanced geometric mean model for predicting the effective thermal conductivity ( $$\lambda $$ ) of unsaturated soils has been developed and successfully verified against an experimental $$\lambda $$ database consisting of 40 Canadian soils, 15 American soils, 10 Chinese soils, four Japanese soils, three standard sands, and one pyroclastic soil (Pozzolana) from Italy (a total of 667 experimental $$\lambda $$ entries). Three soil structure-based parameters were used in the model, namely an inter-particle thermal contact resistance factor ( $$\alpha $$ ), the degree of saturation of a miniscule pore space $$(s_{\mathrm{r}})$$ , and the bulk thermal conductivity of soil solids $$(\lambda _{\mathrm{s}})$$ . The $$\alpha $$ factor strongly depended on the ratio of $$\lambda _{\mathrm{s}}$$ to $$\lambda _{\mathrm{f}}$$ (where $$\lambda _{\mathrm{f}}$$ is the thermal conductivity of interfacial fluid) and an inter-particle contact coefficient ( $$\varepsilon $$ ) whose value was obtained by reverse modeling of experimental $$\lambda $$ data of 40 Canadian soils; the average values of $$\varepsilon $$ varied between 0.988 and 0.994 for coarse and fine soils, respectively. In general, $$\varepsilon $$ depends on soil compaction, soil specific surface area, and grain size distribution. The use of $$\alpha $$ was essential for close $$\lambda $$ estimates of experimental data at a low range of degree of saturation $$(S_{\mathrm{r}})$$ . For $$\lambda _{\mathrm{s}}$$ estimates obtained from measured $$\lambda $$ at soil saturation or a complete soil mineral composition data or experimental quartz content, 69 % of $$\lambda $$ predictions were less than $$0.08\, \hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ , 15 % were between $$0.08\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ and $$0.13\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ , and 13 % were between $$0.13\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ and $$0.24\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ with respect to experimental data $$(\lambda _{\mathrm{exp}})$$ . The model gives close $$\lambda $$ estimates with an average root-mean-square error (RMSE) of $$0.051\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ for 22 Canadian fine soils and an average RMSE of $$0.092\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ for 18 Canadian coarse soils. In general, better $$\lambda $$ estimates were obtained for soils containing less content of quartz. Overall, the model estimates were good for all soils at dry state ( $$\hbox {RMSE} = 0.050\, \hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ ; 22 % of the average $$\lambda _{\mathrm{exp}}$$ ), saturated state ( $$\hbox {RMSE} = 0.090\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ ; 5 % of the average $$\lambda _{\mathrm{exp}}$$ ), soil field capacity ( $$\hbox {RMSE} = 0.105\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ ; 9 % of the average $$\lambda _{\mathrm{exp}}$$ ), and satisfactory near a critical degree of saturation, $$S_{\mathrm{r-cr}}$$ ( $$\hbox {RMSE} = 0.162\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$ ; 26 % of the average $$\lambda _{\mathrm{exp}}$$ ).

Introduction to the Special Issue of Geotechnical and Geological Engineering Entitled: “Thermo-Hydro-Mechanical Behavior of Soils and Energy Geostructures”

This special issue of Geotechnical and Geological Engineering highlights state-of-the-art research on the thermo-hydro-mechanical behavior of soils, rocks and energy geostructures. Although the impetus of the special issue was to collect journal papers on subjects related to an NSF-funded international workshop on ‘‘Thermally Active Geotechnical Systems for Near Surface Geothermal Energy’’ held in March 2013 at Ecole Polytechnique Federale de Lausanne in Switzerland, the special issue expanded to collect a broader set of papers from the field of Energy Geotechnics that involve thermal soil behavior. A total of 15 journal papers were selected to be published as part of the special issue, and went through the standard peer review process for the journal. Two papers focused on the thermal properties of unsaturated soils. Likos (2014) presented a pore-scale model for predicting the thermal conductivity of unsaturated sands using basic soil properties. Dong et al. (2014) presented an evaluation of various approaches to predict the thermal conductivity of unsaturated soils, and compared them with experimental data for sand, silt and clay. One paper was presented on the thermal volume change of unsaturated soils, and the impact of these volume changes on the response of a heated shallow foundation (Houston et al. 2014). Three papers were published on different aspects of geothermal heat exchangers in conventional applications (boreholes and horizontal trenches). Wu et al. (2014) studied relationships between the thermal conductivity dryout curve for unsaturated soils and the performance of geothermal heat exchangers in horizontal trenches, Ozudogru et al. (2014a) compared the performance of different numerical simulations to evaluate the response of geothermal heat exchangers in vertical boreholes, and Walker et al. (2014) studied the impact of different stratigraphic units on the overall thermal response of a geothermal heat exchanger in a vertical borehole. Seven papers were focused on the thermal and thermo-mechanical response of energy piles. Loveridge et al. (2014) analyzed the response of different types of auger cast piles that were converted into energy piles. Yu et al. (2015) used numerical modeling to evaluate the thermal conductivity of different soil layers from the analysis of a thermal response test on an energy pile. Kramer et al. (2014) evaluated the thermal response of an energy pile in sand constructed within a laboratory container. Murphy and McCartney (2014) studied the J. S. McCartney (&) Department of Structural Engineering, University of California San Diego, 9500 Gilman Dr, La Jolla, CA 92093-0085, USA e-mail: mccartney@ucsd.edu

Closed-Form Equation for Thermal Conductivity of Unsaturated Soils at Room Temperature

AbstractThermal conductivity is a fundamental physical property governing heat transfer in soil. It depends on soil types, pore structure, temperature, and moisture content, and can vary over an order of magnitude. Some theories have been established to address the effect of temperature on thermal conductivity. Other theoretical works focus on the effect of moisture content on thermal conductivity of different sandy and loamy soils. This work addresses the effect of all soil types and moisture content on thermal conductivity for ambient temperatures from 20 to 25°C. Thermal conductivity varies little within the hydration and capillary regimes, varies moderately within the funicular regime, and varies greatly within the pendular regime. A closed-form equation is proposed and validated by explicitly considering the soil-water retention regimes. Results taken from the literature for 25 soils and from the current study for two clay soils show that the closed-form equation can accurately predict thermal conduc...

Critical Review of Thermal Conductivity Models for Unsaturated Soils

Although it is well established that heat conduction in unsaturated soil depends on liquid saturation, there are several models available to consider the changes in thermal conductivity during drying and wetting. The key factors affecting thermal conductivity of unsaturated soil are evaluated through a critical examination of these different models and their development. Depending on the principles and assumptions employed, these models are categorized into three groups: mixing models involving series/parallel elements; empirical models where thermal conductivity values at dry and saturated states are used; and mathematical models based on phase volume fractions. Experimental data for different soils are used to assess the quality of prediction for these models. It is found that all the existing models do not realistically account for pore structure or interface properties, and thus are not capable of properly predicting thermal conductivity as a function of liquid saturation. A conceptual model based on soil–water retention mechanisms, is proposed to overcome the pitfalls of the existing models and can be used to establish quantitative thermal conductivity models for variably saturated soils in the future.

The Primary and Secondary Analysis of Uncertain Factors in Soil Thermal Properties for GSHP

In this paper, at first, an effective soil thermal conductivity model was established. Single factor regression analysis for 6 uncertain factors contained in the model was then conducted respectively. Finally, the primary and secondary characters of these uncertain factors were analyzed by using the orthogonal test. The analysis results show that the effective soil thermal conductivity has linear relationships with the saturation degree of unsaturated soil and the depth of water table and has power function relationships with other 4 uncertain factors; the porosity of unsaturated soil has the greatest effect on the effective soil thermal properties, followed by saturation degree of unsaturated soil, porosity of saturated soil, solid phase thermal conductivity of unsaturated soil, solid phase thermal conductivity of saturated soil and the depth of water table.