Thermal conductivity of soils: A simplified unit cell model

A modified calculation model for the saturation-dependent thermal conductivity of fine-textured soils

Soil thermal conductivity is a property that represents a soil’s capability of transferring energy and has been a common subject of study in soil science, geotechnical engineering, and geology. In this study, the quantitative effects of density, water content, saturation, and porosity on thermal conductivity of soil in Fengxian County are investigated by the field and laboratory tests. A new model for predicting soil thermal conductivity from its porosity, saturation, and quartz content is developed. In the field test, the thermal conductivity has a linear relationship with water content due to the increase in thickness of hydration film which decreases the thermal contact resistance between particles. A good logarithmic function is found for the relationship between thermal conductivity and natural density of silty clay soil in Fengxian County. In the laboratory test, there is a linear function for the relationship between thermal conductivity and density of silty clay soil. The thermal conductivity linearly increases with water content and decreases slightly when water content exceeds 17.65% due to the decreased density. The predicted thermal conductivity with the new model is compared with measured thermal conductivity from the field and laboratory tests. The root mean square error (RMSE) of the new model is 0.098 and 0.096 W m−1 K−1, respectively, which indicates that the new model provides accurate approximations of soil thermal conductivity in Fengxian County, China.

Thermal properties of soft clayey soils from the former Lake Texcoco in Mexico

Thermal conductivity is one of the basic thermal properties of soil. For a buried pipeline, the thermal conductivity of the surrounding soil is the most important factor determining the overall heat transfer from the pipeline, and plays an important role in assessing the safety and energy consumption of pipeline operation. For providing reliable basic data for the commissioning and the operation of a waxy crude oil pipeline stretching in southwest Sahara Desert, six phases of thermal conductivity testing were performed along the pipeline route, respectively in February, March, April, May, July and September, 2011. The pipeline is 462.5km long and 323.9mm outside diameter. The pipeline route crosses tropical desert and grassland. Test points are located at roughly equal spaces along the pipeline route, and additional test points are located in seasonal river beds and rugged terrains. The soil temperature and thermal conductivity were tested simultaneously at a depth of about130cm below soil surface, which is also near to the pipeline centerline. The test equipment used was a field thermal needle system FTN01 for thermal conductivity made in Holland. For a given location along the pipeline route, the soil thermal conductivities have different values in dry season and rainy season. The average soil thermal conductivities for the pipeline route between two stations ranges from 0.5 to 1.1W/(m·°C) in rainy season, and from 0.4 to 0.8 W/(m·°C) in dry season. The test results show that the change of soil moisture content has significant impact on soil thermal conductivity. Because other properties of the tested soil along the pipeline route such as soil mineral composition, particle size distribution and density have no significant change, these factors have little effect on soil thermal conductivity.

Thermal properties of soil in the Murrumbidgee River Catchment (Australia)

Core Ideas Biochar may change the surface soil heat balance. Biochar significantly decreased soil thermal conductivity and thermal diffusivity. Changes were mainly attributed to soil bulk density and the biochar itself. Few studies have examined the effects of biochar amendment on soil thermal properties. Soil thermal properties dominate the storage and conduction of heat in soil, affect soil temperature and water and heat movement, and consequently influence plant growth and soil biochemical processes. A 7‐yr field experiment was performed to investigate the effects on soil thermal properties of biochar amendment at three application rates: 0 (control), 4.5 t ha −1 yr −1 (B4.5), and 9.0 t ha −1 yr −1 (B9.0). Soil heat capacity ( C ), thermal conductivity (λ), and thermal diffusivity (α) of the 0‐ to 5‐cm‐depth topsoil were determined throughout a corn ( Zea mays L.)–wheat ( Triticum aestivum L.) growing period using a heat pulse method. The results showed that soil bulk density was decreased significantly by biochar ( P < 0.05). There was no significant difference in soil water content between the control and biochar treatments. There was no significant difference in the soil volumetric heat capacity between the control and biochar treatments. Soil thermal conductivity and thermal diffusivity were decreased significantly by biochar ( P < 0.05). There was a strong positive relationship between soil thermal conductivity and bulk density, and between soil thermal conductivity and water content ( P < 0.001, n = 99). In contrast, there was a strong negative relationship between soil thermal conductivity and biochar amount ( P < 0.001, n = 99). The reduction in soil thermal diffusivity may be attributed largely to the low thermal diffusivity of biochar and the decrease in soil bulk density caused by biochar.

Hydraulic and thermal regimes are coupled in surface soil. Accurate measurement of soil volumetric water content (θ) and thermal properties will improve our understanding of the hydraulic and thermal regimes. A thermo‐time domain reflectometry (TDR) probe was developed to simultaneously measure θ, bulk electrical conductivity (σ), thermal conductivity (λ), heat capacity (ρ c ), and thermal diffusivity (α). Time domain reflectometry was used to measure θ and σ, and the dual‐probe heat pulse (DPHP) method was used to determine λ, ρ c , and α. Laboratory tests on two soils showed that the probe determined θ accurately and the measured σ values of saturated soil correlated well with values determined by a four‐electrode probe. Measurements in agar‐immobilized water produced values of λ and ρ c that closely corresponded with standard values of these properties for water, an indication of the sensor's functionality in other media. Soil thermal properties as a function of θ also are presented. The results of these laboratory tests suggest that the thermo‐TDR probe can be a valuable tool for simultaneously monitoring θ, σ, and soil thermal properties.

The thermal conductivity of soils is a key factor in calculating soil heat transfer and analyzing the temperature fields in geotechnical engineering projects in cold regions. In this study, investigations have been carried out with respect to the effect of temperature (T), concentration of sodium chloride (C), and water content (w) on the thermal conductivity of clay soil. A series model is applied to develop a new theoretical equation that relates thermal conductivity to the water content and temperature. In addition, ultrasonic testing is used to determine the volume of unfrozen water in frozen soil. The results show that the freezing temperatures of samples with an NaCl salt concentration of 0%, 2%, and 5% are − 2 °C, − 4 °C, and − 8 °C respectively. The theoretical equation can explain the relationship between the thermal conductivity and temperature and water content of frozen soil. There is an exponential function for the relationship between thermal conductivity and temperature of clay samples at temperatures below freezing. There is a small reduction in the thermal conductivity of the salt-free samples due to the propagation of frost heave cracks from − 6 to − 10 °C. An increase in the electrolyte concentration of the solution would compress the electrical double layer, thus leading to the increase in contact between the surface of the soil particles. When the salt concentration is increased to 5%, flocculation occurs between clay particles. There is a quadratic function for the relationship between thermal conductivity and NaCl concentration of clay soil. The thermal conductivity of the salt-free samples increases with higher water content at temperatures above freezing and decreases with higher water content due to the propagation of frost heave cracks when the samples are frozen. The generalized relationships between thermal conductivity and NaCl concentration and temperature can be used to evaluate the thermal conductivity in frozen saline soil.

지중 토양의 열 물리적 성질 중 열전도도(thermal conductivity)는 지열 히트펌프 시스템(ground-coupled heat pump systems)의 지중열교환기 설계 과정에서 매우 중요한 변수다. 토양의 열전도도는 3상 구조로 인해 함수비와 건조밀도의 영향을 많이 받는다. 본 논문에서는 수평형 지중열교환기의 트렌치 뒤채움재로 사용되는 9종류의 토양(모래-물혼합물)을 대상으로 열전도도 측정결과와 기존 상관식에 의한 계산결과를 비교하였다. 건조토인 경우, 2상 구조의 열전도도 예측모델인 준이론 모델에 의한 열전도도 계산 결과는 측정 결과와 큰 차이를 보였다. 불포화토인 경우, 기존 모델 중 Cote와 Konrad가 제시한 모델에 의한 계산 결과가 측정 결과와 가장 잘 일치하였다. 또한 토양의 열전도도와 함수비, 종류 등이 수평형 지중열교환기의 설계 길이에 미치는 영향을 고찰하였다. 뒤채움재로 사용되는 토양의 열전도도가 증가할수록 수평형 지중열 교환기의 설계 길이는 감소하였다. Among the various thermal properties, thermal conductivity of soils is one of the most important parameters to design a horizontal ground heat exchanger for ground-coupled heat pump systems. It is well known that the thermal conductivity of soil is strongly influenced by its density and water content because of its particulate structure. This paper evaluates some of the well-known prediction models for the thermal conductivity of particulate media such as soils along with the experimental results. The semi-theoretical models for two-component materials were found inappropriate to estimate the thermal conductivity of dry soils. It comes out that the model developed by Cote and Konrad provides the best overall prediction for unsaturated sands available in the literature. Also, a parametric analysis is conducted to investigate the effect of thermal conductivity, water content and soil type on the horizontal ground heat exchanger design. The results show that a design pipe length for the horizontal ground heat exchanger can be reduced with an increase in soil thermal conductivity. The current research concludes that the dimension of the horizontal ground heat exchanger can be reduced to a certain extent by backfilling materials with a higher thermal conductivity of solid particles.

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.

Stress effects on thermal conductivity of soils and heat transfer efficiency of energy piles in the saturated and unsaturated soils

Effects of Drying-induced Shrinkage on Thermal and Hydraulic Properties of Clayey Soils

Summary There is no simple and general relationship between the thermal conductivity of a soil, λ , and its volumetric water content, θ , because the porosity, n , and the thermal conductivity of the solid fraction, λ s , play a major part. Experimental data including measurements of all the variables are scarce. Using a numerical modelling approach, we have shown that the microscopic arrangement of water influences the relation between λ and θ . Simulated values for n ranging from 0.4 to 0.6, λ s ranging from 2 to 5 W m −1 K −1 and θ from 0.1 to 0.4 can be fitted by a simple linear formula that takes into account n , λ s and θ . The results given by this formula and by the quadratic parallel (QP) model widely used in physical property studies are in satisfactory agreement with published data both for saturated rocks and for unsaturated soils. Consequently, the linear formula and the QP model can be used as practical and efficient tools to investigate the effects of water content and porosity on the thermal conductivity of the soil and hence to optimize the design of thermal in situ techniques for monitoring water content.

Thermal properties of the soil gain great importance in engineering projects and situations where heat transfer may take place and affect the soil properties on the whole. Soil gets affected, for example, during laying of bituminous roads, airfield strips, gas or steam pipelines and/or hot water and cold gas lines in unfrozen grounds. In-situ determination of thermal properties of soil is not only time consuming, but in certain cases, costly. The purpose of this study is to understand the variation in thermal properties of virgin soil with addition of different carbonates like potassium carbonate, sodium carbonate and ammonium carbonate using laboratory based Lee’s and Charlton’s apparatus. It is observed that increase in density of soil with any of the three chemicals increases the thermal conductivity, however with the selected chemical the increase is limited to a certain percentage addition after which it does not show any changes as compared to virgin soil.

The permafrost types in the Arctic and Qinghai-Tibet Plateau (QTP) are different, resulting in significant differences in their thermal characteristics. Soil thermal conductivity (STC) is a key physical parameter in land surface processes that controls the storage and conduction of heat in soil, and it is of great significance for simulating the thermal state of frozen soil. Here,a comparative study on STC of the active layer surface soil between the Arctic tundra and alpine meadow in hinterland of the QTP was conducted. Results show that the STC of the Arctic tundra and the alpine meadow in  hinterland of the QTP exhibit an opposite patterns. During study period,  monthly average STC of the Arctic tundra varied significantly with seasons, reaching a maximum of 1.989 Wm-1K-1 in cold season and a minimum of 0.761 Wm-1K-1 in warmer season, with an annual average of 1.541 Wm-1K-1. For Arctic tundra, STC in frozen state was 1.787 Wm-1K-1, while in the unfrozen state, it was 0.802 Wm-1K-1. In contrast, the monthly average STC for alpine meadow in the hinterland of the QTP showed opposite pattern, with the minimum value of 0.933 Wm-1K-1 occurred in January and the maximum value of 1.375 Wm-1K-1 occurred in September, and an annual average of 1.151 Wm-1K-1. In frozen state STC was 0.962 Wm-1K-1 while in unfrozen state such value was 1.341 Wm-1K-1. Field observation experiments in both regions found that STC is strongly dependent on soil moisture content. The initial frozen water content of the Bylot tundra in the Arctic was approximately 0.531 m3m-3 (0.495~ 0.565 m3m-3), while that of the Tanggula alpine meadow in the hinterland of the QTP was 0.142 m3m-3 (0.167~0.115 m3m-3), only 26.7% of the Arctic tundra. This significant difference in initial frozen water content is the main reason for the difference in STC between the two regions. Additionally, rapid changes in unfrozen water content have a great impact on STC during freezing process. For the Arctic tundra observation site, the STC increased by 0.273 Wm-1K-1 (0.247~0.300 Wm-1K-1) for every 0.100 m3m-3 decrease in unfrozen water content. While for the alpine meadow of the QTP, the STC decreased by 0.163 Wm-1K-1 for every 0.100 m3m-3 decrease in unfrozen water content. On average, in the Arctic tundra, the STC of the active layer surface decreases with increasing soil liquid water content, while in the alpine meadow of the QTP, it increases with increasing soil liquid water content. In frozen state for Arctic tundra, the contribution of soil ice content and unfrozen water to thermal conductivity is 75.6% and 5.2%, respectively. It can be seen that STC of the Arctic tundra active layer is mainly controlled by the ice content. As for the QTP meadow, such values were 25.9% and 41.8%, respectively. That means unfrozen water content is the dominant factor for STC changes in the QTP meadow. Furthermore, the Kerstern number scheme was optimized based on the STC data obtained from in-situ observations and KD2 Pro dehumidification experiments of soil samples under different soil moisture conditions.