International Journal of Heat and Mass Transfer 138 (2019) 562–570 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Effect of temperature on thermal conductivity of lateritic clays over a wide temperature range Yunshan Xu a, De’an Sun a,b,⇑, Zhaotian Zeng b,⇑, Haibo Lv b a b Department of Civil Engineering, Shanghai University, Shanghai 200444, China Guangxi Key Laboratory of New Energy and Building Energy Saving, Guilin University of Technology, Guilin 541004, China a r t i c l e i n f o Article history: Received 17 September 2018 Received in revised form 14 March 2019 Accepted 16 April 2019 Keywords: Lateritic clay Thermal conductivity Temperature effect Aggregate structure Model prediction a b s t r a c t The temperature dependence of the relationship between thermal conductivity and saturation of lateritic clays is more complex than that of other soils. This paper reports sample-scale measurements of thermal conductivity of two lateritic clays with aggregates and dual-porosity at different saturations and temperatures. Test results indicate that the thermal conductivity increases with increasing temperature. The effects of the latent heat transfer (LHT) of vapor on the thermal conductivity were more pronounced at intermediate saturations and temperatures above 60 °C. The thermal conductivity resulting from the LHT of vapor has obvious peak value with saturation, and its peak value and corresponding saturation are related to the clay content. The difference in the thermal conductivity from the LHT of vapor between two clays at a given temperature is due to the effect of the microstructure. The mercury intrusion porosimetry (MIP) tests were also performed to observe the pore-size distribution (PSD) of two lateritic clays, which can explain the difference in the temperature effect on thermal conductivity. The interparticle contact heat transfer (IPCHT) model provides good agreement with test data at temperatures ranging from 5 to 90 °C for two lateritic clays. The soil-water retention curves play an important role in predicting the thermal conductivity by the IPCHT model, which can be further improved by better consideration of the microstructure and phase configuration. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction Soil’s thermal conductivity (k) is an essential thermophysical parameter in characterizing the heat transfer or thermal diffusivity property of soils. During the past few decades much attention and research effort have been focused on the soil thermal property in the fields of geothermal, agricultural and civil engineering. Soil is a complex porous medium consisting of solid particles, water, and gas phase, and thus there are many factors affecting k. Previous studies have shown that k is affected by soil texture, mineralogical compositions, bulk density, particle-size distribution, salt content and saturation (S), etc. . The studies mentioned above mainly focused on the ambient temperatures ranging from 0 to 30 °C, although satisfactory experimental results and some well-known predictive models have been obtained. Little work was devoted to the study on the property of soil heat transfer at high temperatures (60–90 °C). Thorough knowledge of soil thermal properties at ⇑ Corresponding authors at: 99 Shangda Road, Shanghai 200444, China (D. Sun). 12 Jiangan Road, Guilin, Guangxi Province 541004, China (Z. Zeng). E-mail addresses: [email protected] (D. Sun), [email protected] (Z. Zeng). https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.077 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved. high temperatures is particularly required in several important processes, such as thermal treatment of contaminated soils , high-temperature thermal storage of soils  and long- or shortterm interactions between soil and ground-contact engineering facilities such as the high-level radioactive waste repositories  and buried high-voltage power cables . Over past few decades, few works have been conducted on the thermal conductivity measurements and predictive models at high temperatures. Philip and de Vries  observed that at intermediate water contents, water vapor flux is enhanced because of the effects of thermal gradients on the water vapor diffusion. Lu and Ren  confirmed that k increased dramatically with temperature in moist soil for loam samples, reaching values two to four times the 22 °C value when the temperature was 81 °C. Similar observations were also made by Hiraiwa and Kasubuchi  and Liu et al.  who investigated the temperature effect of k. Their results showed that the temperature effect on k is more pronounced at intermediate water contents, whereas k varies insignificantly with water content and temperature at low water contents. More recently, Smits et al.  measured k at temperatures varying from 30 to 70 °C for silica sand samples. They suggested that the thermal conductivity and diffusivity increased Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570 noticeably at temperatures above 50 °C due to the enhanced latent heat transfer (LHT). As for the study of k predictive models, de Vries  proposed a model that accounts for the enhanced heat transfer by vapor distillation in soils at high temperatures, but this model involves many parameters and is more dependent on the calculated value of the critical water content. Also, a new predictive model, based on a modified de Vries approach, was developed by Campbell et al. . This model was, however, designed to correlate with experimental data, and it cannot be strictly applied to different soils. It is of note that a simple inter-particle contact heat transfer (IPCHT) model for predicting k at different temperatures (0–90 °C) has been proposed by Tarnawski et al.  and Leong et al. . Based on the selfconsistent approximation model, the model considered synthetically the modified interparticle contact heat transfer and LHT of vapor. However, it has not been thoroughly verified by more accurately measured data for a wide variety of soils. It is generally recognized that k increases with temperatures due to the enhanced LHT. At elevated temperature, water evaporation and the associated LHT become an increasingly important or even dominant, contributing to an increase of heat transfer in the soil air compared to the moderate temperatures. Both the processes, the conduction and LHT, take place under the same temperature gradient . Thorough knowledge of the LHT of vapor at different temperatures is vital to understand these phenomena, and therefore corresponding work on this issue should be further studied. Natural soils are mainly characterized by soil structure and texture. For many of the multi-pore structured media, a unique permittivity response is exhibited on the relationship between volumetric water content (h) and dielectric permittivity . Similar observations about thermal properties were also made by Zeng et al.  who investigated the relationship between volumetric water content and thermal conductivity for four lateritic clays. In China, lateritic clay spreads in tropical and subtropical zones with an approximate area of 2,000,000 km2, and a number of works has been devoted to investigating the engineering property during the past few decades [18–20]. However, little work was devoted to the study on the thermal property of lateritic clay. Particularly, several engineering problems or environmental issues, such as the utilization of shallow geothermal energy, urban heat island effect and prevention of heat hazard in underground space, have not been effectively solved because of limited knowledge on the temperature dependence of thermal property of lateritic clay. Moreover, to the best of our knowledge, the lateritic clays are very unique soils in the microstructures and mineralogical compositions, which have a significant impact on engineering property and may have an influence on the temperature dependence of thermal property. Therefore, there is a great need for study on the temperature dependence of thermal property of lateritic clay and its LHT of vapor. This paper presents a study on the k -S relationship of two lateritic clays from Guanxi, China over a wide range of temperatures (5–90 °C) and tries to provide some more insight into the microscopic mechanism of the LHT of vapor affecting the k-S relationship. The thermal probe method was used to measure k. To this end, the application of the IPCHT model for predicting the k-S relationship was evaluated and thus its reliability was verified. Furthermore, probing the soil microstructures and soil-water retention behaviour can aid understanding the temperature effect on the LHT of vapor. In this study, the mercury intrusion porosimetry (MIP) tests were conducted to measure the micro-porosity structures, together with the measured soil-water retention curves (SWRCs), which were applied to reveal the temperature effect on the thermal property of lateritic clays. 563 2. Materials and method 2.1. Soil samples The lateritic clays used in this study were taken near the ground surface from Guilin and Liuzhou areas in Guangxi Autonomous region, China. The sampling sites are shown in Fig. 1. Prior to the commencement of laboratory tests on the soil samples, they were air-dried, passed through a required sieve (a 2-mm sieve for k measurement) and thoroughly mixed. Table 1 listed the sampling depth and major physical property indexes including liquid and plastic limits and grain fractions of two soils. The mineralogical compositions and their relative contents, determined using the X-ray diffraction (XRD) and chemistry analysis tests simultaneously, are listed in Table 2. The Lateritic clays were formed by the weathering and laterization of carbonate rocks under humid tropical climates, followed by eluviation or slope. The clay minerals, iron and manganese oxide minerals and gibbsite are the indicative minerals for three pedogenesis geochemical processes respectively: (i) enrichment of silicon and aluminum and depletion of calcium and magnesium, (ii) enrichment of iron and manganese, and (iii) enrichment of aluminum and depletion of silicon. It can be seen from Table 1 that the Guilin lateritic clay contains 11.44% gibbsite, whereas the Liuzhou lateritic clay contains no gibbsite. This indicated that the degree of laterization of Guilin lateritic clay is higher than that of Liuzhou lateritic clay, which may have an influence on the physical property indexes, as shown in Table 1. 2.2. Measurement of thermal conductivity Laboratory testing was performed to measure the values of k over a wide range of temperature (5–90 °C). The measurement of k was conducted using a commercially available non-steady-state thermal needle probe (KD2 Pro, Decagon Devices Inc., Pullman, WA), which is equipped with three types of thermal probes (i.e., KS-1, TR-1 and SH-1) for different test samples. Its operating principle is based on the hot wire method and the thermal conductivity can be obtained by heating the samples and monitoring tempera- Fig. 1. Sampling locations of two lateritic clays. 564 Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570 Table 1 Physical property indexes of soil samples studied. Soil Depth (m) Specific gravity Liquid limit (%) Plastic limit (%) Sand (%) Silt (%) Clay (%) Guilin lateritic clay Liuzhou lateritic clay 2–4 0–3 2.74 2.73 77.8 58.0 42.1 24.6 14.30 11.71 32.20 40.70 53.50 47.59 Table 2 Mineralogical compositions of soil samples studied. Soil Kaolinite (%) Gibbsite (%) Illite (%) Geothite (%) Quartz (%) Guilin lateritic clay Liuzhou lateritic clay 56.59 19.71 11.44 — — 23.1 15.61 7.45 12.45 44.0 ture variation during the linear heat transfer . The resolution of KD2 Pro is 0.001 W/(mK) for measurements of thermal conductivity. SH-1 type thermal probe is widely used for measuring thermal conductivity of soils with an accuracy of better than 5% in the range of 0.02 to 2 W/(mK), and was adopted in this study. SH-1 probe consists of dual needles with 30 mm length and 1.28 mm diameter, which are spaced 6 mm apart. In testing process, a current firstly passes through the heater in one of the needles for a set time (30 s) and the change in temperature is measured using a thermocouple in the other needle, and then the cooling period of 30 s lasted following the heating period. Through monitoring the heat dissipation of linear heat resource in specimens, the thermal conductivity of specimens was calculated and displayed on the controller’s screen. The test procedure for measuring the value of k is as follows: (i) a given amount of air-dried soil was put into a plastic bag; (ii) the required amount of distilled water was sprinkled on the soil to reach a specified gravimetric water content; (iii) the wet soil was kept in closed plastic bags for 72 h to allow uniform distribution of moisture throughout the soil mass; (iv) the wet soil was packed into the steel ring (90-mm in height, 75-mm inside diameter, 3mm in wall thickness) and then was compacted to desired bulk density of 1.1 g/cm3 for both lateritic clay by the static compaction method; and (v) the soil samples were tightly wrapped with plastic film and placed in a box with a constant temperature (controlled to ±0.1 °C), which was set from 5 to 90 °C for 48 h before the thermal conductivity measurement. Before the tests, SH-1 sensor was calibrated using the Delrin block. The thermal probe was inserted into the compacted soil col- Steel ring Support Fig. 2. Diagram for measuring thermal conductivity. Measurements of soil-water retention curves (SWRCs) were conducted for explaining the thermal properties and for being used in the prediction model of thermal conductivity. The compacted specimens of the lateritic clay were prepared with the same bulk density as the soil specimens for measuring k by the static compaction in a stainless-steel specimen ring (61.8-mm inside diameter and 20-mm height). For lateritic clay, a laboratory testing program consisting of several different methods for suction control or measurement was designed to measure the SWRCs over a wide suction range. The pressure plate method (PPM) was used to control the matric suction ranging from 0 to 1.5 MPa. The tests were performed by increasing the matric suction from 0 to 1.5 MPa by several steps at zero net stress. When the water content and the vertical deformation of the specimen reached equilibrium, the next suction level was applied. The filter paper method (FPM) was used to measure the matric suction ranging from 0.5 to 40 MPa. For details of the relative test devices and measurement procedures of PPM and FPM, see Sun et al. . The prediction model of k is useful for understanding the dependence of k on the water content (w), temperature (T) and soil physical property. Some prediction models of k based on physical theory have been proposed to describe the k-w relationship accounting for soil physical property [11–13]. Among various kinds of k predictive models, the inter-particle contact heat transfer (IPCHT) model  was adopted for its convenience since the model does not include any geometrical fitting parameter, and the effective thermal conductivity of soils (keff) was calculated as: Transmission cable Soil sample 2.3. Measurement of soil-water retention curve 2.4. Application of IPCHT model Constant temperature box Thermal probe umn and then k was measured, as shown in Fig. 2. After that, the water content and bulk density were determined by measuring the specimen volume and the specimen weights before and after drying the samples in an oven at 105 °C for 24 h. The results of repeated tests for measuring the thermal conductivity under respective the same condition are listed in Table 3. It can be seen from Table 3 that the standard deviation (SD) of the measured values is within 1%. To further improve the measurement accuracy, the obtained values of repeated measurements on thermal conductivity were averaged as the final value. KD2 Pro keff " #1 3 1 X hi ¼ 3 i¼1 2keff þ ki ð1Þ where ki and hi are the thermal conductivity and volumetric fraction of phase i, respectively. The volumetric fractions of solid (h1), water (h2) and air (h3) are defined and calculated as: 565 Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570 Table 3 Repeated tests for measuring thermal conductivity of Guilin lateritic clay under the same condition. Dry density (g/cm3) Saturation (%) Temperature (°C) 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 4.0 4.0 4.0 4.0 4.0 4.0 44.9 44.9 44.9 44.9 44.9 44.9 83.9 83.9 83.9 83.9 83.9 83.9 5 25 40 60 80 90 5 25 40 60 80 90 5 25 40 60 80 90 Thermal conductivity (Wm1K1) No.1 No.2 No.3 No.4 No.5 Mean 0.199 0.237 0.249 0.301 0.402 0.462 0.607 0.686 0.825 1.071 1.304 1.548 0.904 1.026 1.040 1.166 1.289 1.359 0.197 0.234 0.245 0.298 0.392 0.474 0.605 0.691 0.828 1.063 1.307 1.542 0.900 1.028 1.042 1.179 1.299 1.364 0.205 0.229 0.246 0.314 0.393 0.475 0.603 0.686 0.827 1.069 1.306 1.542 0.909 1.029 1.043 1.183 1.306 1.376 0.207 0.228 0.241 0.309 0.405 0.464 0.609 0.689 0.827 1.064 1.303 1.551 0.912 1.029 1.045 1.177 1.304 1.372 0.204 0.227 0.243 0.316 0.401 0.479 0.604 0.689 0.827 1.068 1.295 1.555 0.909 1.032 1.04 1.183 1.290 1.380 0.202 0.231 0.245 0.308 0.399 0.471 0.606 0.688 0.827 1.067 1.303 1.548 0.907 1.029 1.043 1.178 1.298 1.370 h1 ¼ Vs qd ¼ V v þ V s qw Gs ð2Þ h2 ¼ Vw SðGs qd =qw Þ ¼ Gs Vv þ Vs ð3Þ Va ¼ 1 ðh1 þ h2 Þ h3 ¼ Vv þ Vs ð4Þ where Vs, Vw and Vv are the volumes of solid, water and voids in soils, respectively. qd is the dry density of soil specimens, qw is the density of water, and Gs is the specific gravity. Thermal conductivity of soil solid (k1) is given by k1 ¼ aks ð5Þ where a is a dimensionless heat transfer correction factor of soils, representing reduction of heat flow due to an imperfect contact between soil particles, i.e., thermal contact resistance (TCR) and can be expressed as a function of saturation (S): a ¼ Keðasat adry Þ ð6Þ Ke ¼ 0:7logS þ 1 ð7Þ where Ke is the Kersten coefficient, asat and adry are the heat transfer correction factors of saturated and dry soils respectively, and are calculated as: adry ¼ 1 ðb=ks þ ð1 bÞ=kda Þks ð8Þ asat ¼ 1 ðb=ks þ ð1 bÞ=k2 Þks ð9Þ where kda and k2 is the thermal conductivities of dry air and water respectively, b is an effective solid fraction at the contact points of soil particles, and can be expressed as a function of soil porosity (u): b ¼ 1 0:12833u þ 0:06461u2 þ 0:06491u3 ð10Þ S is defined and calculated as: S¼ Vw wGs ¼ V v Gs qw =qd 1 ð11Þ ks is the average thermal conductivity of the solid particles, and ks ¼ khqq koml q 1h Standard deviation (%) ð12Þ 0.4 0.4 0.3 0.8 0.6 0.7 0.2 0.2 0.1 0.3 0.5 0.6 0.5 0.2 0.2 0.7 0.8 0.9 where kq is the thermal conductivity of quartz, koml is the thermal conductivity of other minerals in soils and hq is the volumetric fraction of quartz. Thermal conductivity of water (k2) is given by: k2 ¼ 0:569 þ 1:884 103 T 0:772 106 T 2 ð13Þ where T is temperature in Celsius. Thermal conductivity of air (k3) is given by: k3 ¼ kda þ hkvs ð14Þ where h is the relative humidity of soil air and kvs is the thermal conductivity of saturated water vapor. When applying the IPCHT model to the prediction, the values of kq and koml were respectively assumed 8.8 W/(mK) and 2.0 W/ (mK) for all the soils, which were used by de Vries . The value of h was estimated from the measured SWRCs. 3. Measured results of thermal conductivity and discussion 3.1. Effect of temperature on relation between thermal conductivity and saturation Fig. 3 presents the change in thermal conductivity (k) of two lateritic clays for each temperature (T) with saturation (S) from the KD2 pro measurements. It can be seen from Fig. 3 that for a given saturation (4–84%), measured k increases with increasing temperature. The increase in k with temperature is mainly seen at intermediate saturations and temperatures above 60 °C. At sample temperatures below 60 °C, the effect of temperature on the k-S relationship is small. When saturation is very high or low, the effect of temperature on the k-S relationship is relatively smaller. These results agree with Smits et al.  who suggested that the increase in k may be due to the additional heat transfer in the form of latent heat due to evaporation and condensation between the ‘‘liquid islands”. This process is so-called latent heat transfer (LHT) of vapor, which requires enough liquid water to form the liquid islands and void space in soils through which vapor can move. This can explain that temperature has little effect on k when the sample is very dry or wet. Also, this can explain why temperature effect on k is related to the saturation. It can be seen from Fig. 3 that except for some cases with high temperature and saturation, k increases with increasing saturation and tends to be constant when the saturation is near 100%. k starts 566 Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570 2.0 (a) λ (W/m·K) SFC SPWP 1.6 T decreasing 1.2 0.8 Temperature(ºC) 5 25 40 60 80 90 0.4 0.0 0 20 40 60 80 100 S (%) 2.5 (b) SFC SPWP 2.0 λ (W/m·K) T decreasing 1.5 1.0 Temperature(ºC) 5 25 40 60 80 90 0.5 0.0 0 20 40 60 80 100 S (%) Fig. 3. Change in thermal conductivity (mean ± standard deviation, n = 5) for each temperature with saturation for lateritic clays: (a) Guilin lateritic clay; (b) Liuzhou lateritic clay. The critical water contents were calculated using the empirical function of Rawls et al.  (short-dashed lines). to decrease from the saturation of about 54% at temperatures of 80 and 90 °C. This is because, the thermal conductivity of water in soils is much higher than that of air in the voids of unsaturated lateritic clays, leading to an increase in k as water replaces the air when the water content increases. At low saturation, water first coats the soil particles. When the particles are fully coated with water and a further increased water fills the voids in soil, resulting in a rapid increase in k. Finally, when all the voids are nearly full of water, further increasing the water content no longer increases the heat flow between the soil particles, and k does not appreciably increase. Hiraiwa and Kasubuchi  also observed that at volumetric water content (h) between 0.3 and 0.4 m3/m3 (from 0.33 m3/m3 to 0.42 m3/m3 in this study), k decreased with h at temperatures above 65 °C (above 60 °C in this study). A possible explanation is that the water in soils modifies the extent or quality of the LHT of vapor in soils and thus the effective heat flow paths. As reported by Blonquist et al. , the pore system in aggregated soils was separated into two types: intra-aggregate pores within an aggregate, and relatively larger inter-aggregate pores between aggregates. Accordingly, they suggested that at high saturation, a further increase in water content filled the inter-aggregate pores, resulting in an abrupt decrease in void space required for the LHT of vapor. As mentioned above, k increases with the LHT of vapor, which requires enough void space in soils. Therefore, at temperature above 60 °C k decreases severely when the saturation is beyond a given value (i.e., from 55% to 70%). Comparing Fig. 3(a) and (b) shows that for the same temperature and saturation, the thermal conductivity of Liuzhou lateritic clay is higher than that of Guilin lateritic clay. In general, the soil thermal conductivity depends on the mineralogical composition (especially for quartz), particle composition, water content, dry density and temperature. For the same water content, dry density and temperature, the mineralogical composition is an important factor that affects its thermal conductivity. As shown in Table 2, Liuzhou lateritic clay contains 40% quartz, while Guilin lateritic clay contains only 12.45% quartz. As the thermal conductivity of quartz (7.7 W/mK) is much higher than that of other minerals (2.0 W/mK), the proportion of quartz may significantly affect the thermal conductivity. Tang et al.  and Xu et al.  suggested that the bentonite with higher quartz content has the greater value of thermal conductivity. This can explain why Liuzhou lateritic clay has higher thermal conductivity than Guilin lateritic clay. Hiraiwa and Kasubuchi  observed that the change in k with water content was related to the critical water content corresponding to the permanent wilting point (PWP) and field capacity (FC). In Fig. 3, there exhibit some obvious inflection points in the k-S curves. Rawls et al.  suggested that the critical water content associated with the particle-size distribution, which can be calculated through the linear regression formulas. The critical water contents (SPWP and SFC) of two lateritic clays were estimated by the empirical function of Rawls et al. , which are also shown in Fig. 3. It can be seen from Fig. 3 that the change in k-S for each temperature can be divided into some characteristic intervals of saturations by calculated results of the critical water contents (Guilin lateritic clay: SPWP = 49.1%, SFC = 70.7%; Liuzhou lateritic clay: SPWP = 27.4%, SFC = 56.1%). This indicates that the heat conduction is also related to the form and distribution of water in soils. Conceptually, we outline five important physical stages of the lateritic clays with aggregate structure: (i) the soil is completely dry; (ii) in the moisture range from full dryness to the PWP, water in soil is hold tightly in the intra-aggregate pores and the formation of water micro-wedges between the contact points of the soil grains occurs (connects the primary particles effectively); (iii) for the moisture near FC (FC), the intra-aggregate pores are fully filled with water, while the inter-aggregate pores are nearly filled with air; (iv) the intra-aggregate pores are water saturated and the inter-aggregate pores are partly filled with water under gravity; (v) both intra and inter-aggregate pores are water saturated and there is no air in soils. Fig. 4 presents the detailed physical states during the saturation process for aggregated soil, and these physical states can be applied to provide some more insight in understanding the temperature effect on the k-S relationship of lateritic clays. 3.2. Effect of temperature on the LHT of vapor The thermal conductivity resulting from the LHT of vapor (kLHT) characterizes the contribution of LHT on the heat transfer in soils and can be separated from k by several methods in the literature. Cass et al.  considered that the temperature dependence of k was mainly attributed to kLHT, and suggested a separation method. Although, kLHT can be obtained by the separation method, its accuracy is not enough when investigating the temperature dependence of k. Hiraiwa and Kasubuchi  suggested that k can be separated into the thermal conductivity due to conduction (kC) and the LHT of vapor (kLHT). This separation method is based on the assumptions that the temperature dependence of kC is much smaller than that of kLHT, and at a low temperature the kLHT is negligibly small. Recently, the method of Hiraiwa and Kasubuchi  has been verified, and it is reliable in analyzing the temperature effect on the thermal conductivity . Therefore, in this paper, a similar method of separation was adopted, i.e., kLHT is obtained from k by subtracting the thermal conductivity near 5 °C (kT=5°C) (kLHT = k-kT=5°C). 567 Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570 Fig. 4. Five physical stages during saturation process for aggregated soils. 1.5 (a) λLHT (W/m·K) 1.2 0.9 Temperature(ºC) 25 Peak value decreasing 40 60 80 90 T decreasing 0.6 0.3 0.0 0 20 40 60 80 100 S (%) 2.4 (b) λLHT (W/m·K) 2.0 Temperature(ºC) 25 40 60 80 90 Peak value decreasing 1.6 1.2 T decreasing 0.8 0.4 as shown in Table 2. This is because the gaps between particles or soil aggregates can be filled with the relatively small clay particles effectively. The higher the clay content, the less the gaps between particles, resulting in a decrease in kLHT. On the other hand, it has been suggested that the water adsorption capacity of clayed soils is positively related to the specific surface area (SSA) of soils . Here, the SSAs of Guilin and Liuzhou lateritic clays are 78 and 40 respectively in m2/g, determined by the ethylene glycol monomethyl ether (EGME) adsorption method. Our results agree with Lv et al.  who suggested that the SSA of clayed soils increased with the clay content, resulting in an increase in water adsorption capacity. Therefore, for Guilin lateritic clay, it requires more water content to form the ‘‘liquid island”, which affects the LHT of vapor greatly. As mentioned above, the LHT of vapor requires enough material condition (vapor) and transmission space (pores in soils). Hence, this is capable of explaining why the temperature effect on kLHT is smaller at high or low saturations than that at intermediate saturations. The temperature dependence of kLHT-S relationship of soils is related to several factors such as soil type and soil microstructure, etc. For the same type of soil, the soil microstructure is an important factor that affects its kLHT-S relationship, and can be simply represented by the pore-size distribution (PSD), which can be determined by the mercury intrusion porosimetry (MIP) tests. Fig. 6 shows the PSDs of compacted Guilin and Liuzhou lateritic clays from the MIP tests. The specimen preparation for the MIP tests is the freeze-dried method and the MIP apparatus used in this 0.0 20 40 60 80 100 S (%) Fig. 5. Change in thermal conductivity resulting from the latent heat transfer of vapor for each temperature with saturation: (a) Guilin lateritic clay; and (b) Liuzhou lateritic clay. The k-S relationships at different temperatures were shown in Fig. 5. During the saturation process, kLHT increases with increasing temperature and temperature effect on kLHT becomes significant when temperature is above 60 °C. This is consistent with temperature dependence of k (see Fig. 3). For a given temperature, kLHT first increases rapidly as saturation increases, and then it reaches a peak value. Finally, kLHT decreases as saturation increases to near 100%. The peak value of kLHT at 90 °C is three to four times that at 5 °C. Moreover, the peak kLHT and its saturation are related to the clay content. That is, the peak kLHT decreases with increasing clay content, whereas its saturation increases with increasing clay content, Differential pore volume (mL/g) 0 0.8 0.7 Intra-aggregate pores Guilin lateritic clay Liuzhou lateritic clay 0.6 0.5 0.4 Inter-aggregate pores 0.3 0.2 0.1 0.0 -3 10 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 Pore diameter (μm) Fig. 6. Pore-size distribution of lateritic clays measured by MIP tests (dry density = 1.1 g/cm3). Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570 study was the Micromeritics AutoPore IV with a maximum intrusion pressure of 413.7 MPa. In Fig. 6, compacted Guilin and Liuzhou lateritic clays all shows a bimodal PSD, that means there are two peaks in their PSDs. According to Lloret and Villar  and Xu et al. , the pore system is simply separated into two types: intra-aggregate pores (at pore size r < 0.15 lm) within aggregates, and relatively larger inter-aggregate pores (at r > 0.15 lm) between aggregates. The amount of relatively larger interaggregate pores in Liuzhou lateritic clay is larger than that in Guilin lateritic clay. This implies that for Liuzhou lateritic clay, the number of gaps between particles or aggregates is greater, leading to a favorable transmission space for the enhanced LHT of vapor, whereas the volume fraction of intra-aggregate pores become reversed. Therefore, this can explain that for a given temperature the kLHT-S curve of Liuzhou lateritic clay is higher than that of Guilin lateritic clay (see Fig. 5). The results of d(kLHT)/dT (kLHT differentiated with T) was also calculated for analyzing the temperature dependence of kLHT, as shown in Fig. 7. It can be seen from Fig. 7 that d(kLHT)/dT increases with increasing temperature for the same saturation. This is because, the higher the temperature, the more significant the LHT of vapor. On the other hand, pores in the lateritic clays with the double porosity system are tortuous, resulting in a non-linear temperature dependence of kLHT and k. For the same temperature, d(kLHT)/dT increases firstly and then deceases with saturation. This indicates that the temperature effect on kLHT is also related to the saturation. At temperatures between 60 °C and 90 °C, d(kLHT)/dT of Liuzhou lateritic clay is nearly two times that of Guilin lateritic clay at intermediate saturations. This implies that the latent heat transfer of vapor for Liuzhou lateritic clay is more sensitive to temperature than that for Guilin lateritic clay. This can be explained by the difference in the soil-water retention curves of two lateritic clays, which will be discussed later. 3.3. Soil-water retention tests Fig. 8 shows the measured water retention behavior: the changes in saturation with suction of specimens with the dry density of 1.1 g/cm3 by using two methods (i.e., the PPM, and the FPM). In Fig. 8, it can be seen that the soil-water retention curves (SWRCs) exhibit different shapes for Guilin and Liuzhou lateritic clays, especially in the suction range from 102 to 104 kPa. The air-entry value of Guilin lateritic clay is different from that of Liuzhou lateritic clay. The air entry value of Guilin lateritic clay is about 30 kPa while the air entry value of Liuzhou lateritic clay is about 130 kPa, as shown in Fig. 8. This can be attributed mainly to the differences in the PSDs for soils used in the tests (see Fig. 7). Sun et al. LHT d(λ )/dT (W/m·K·ºC) 0.03 0.02 Temperature(ºC) Liuzhou Guilin 60 60 80 80 90 90 0.01 T decreasing 0.00 0 20 40 60 80 100 S (%) Fig. 7. Change in d(kLHT)/dT of two lateritic clays for each temperature with saturation. 100 Air entry value 80 Saturation (%) 568 60 40 20 0 0 10 Guilin lateritic clay Liuzhou lateritic clay 10 1 10 2 10 3 10 4 10 5 Suction (kPa) Fig. 8. Soil-water retention curves of Guilin and Liuzhou lateritic clays.  made an experimental study on the SWRCs and microstructures of compacted Guilin lateritic clay. They suggested that the SWRCs were related to the features of the PSDs and can be predicted by them. Furthermore, it can also be seen from Fig. 8 that the SWRCs of Guilin and Liuzhou lateritic clays differed significantly at intermediate saturations, which is consistent with the mentioned changes in d(kLHT)/dT with saturation. This can be explained by the difference in soil-water retention curves for two lateritic clays, and the difference causes variations in the evaporation and diffusion of water in soils. As shown in Fig. 8, the same amount of water added to Guilin lateritic clay will result in a greater decrease in the suction than that in Liuzhou lateritic clay at intermediate saturations. That is, water in soil changes more rapidly for Liuzhou lateritic clay, which causes rapid change in the relative humidity of air in soil, providing a favorable material condition for the LHT of vapor. Therefore, the LHT of vapor for Liuzhou lateritic clay is more sensitive to temperature than that for Guilin lateritic clay (see Fig. 7). Also, this is capable of explaining that saturations corresponding to peak kLHT of Liuzhou lateritic clay is smaller than that of Guilin lateritic clay (see Fig. 5). 4. Comparison of measured and predicted thermal conductivities Measured and predicted thermal conductivities of two lateritic clays are shown in Fig. 9(a) and (b). The predicted one is calculated by the IPCHT model. Verifications of the IPCHT model for unsaturated soils have been performed using measured thermal conductivities of sand and silty clay from Liu et al. , as shown in Fig. 9(c) and (d). ±5% lines from the isoline of measured and predicted values are plotted in Fig. 9. It can be seen from Fig. 9(a)–(c) that at temperatures ranging from 5 to 90 °C, the predicted k of finegrained soils (Guilin and Liuzhou lateritic clays, and silty clay) compares well with the measured k. However, for coarse-grained soil (sand), there is an obvious deviation between measured and predicted k, as shown in Fig. 9 (d). The predicted k is smaller than the measured k of coarsegrained soil. A possible explanation about lower accuracy of predicted results for sand is the uncertainty of soil-water retentions, which would result in considerable deviation in the determination of k (see Eq. (14)). As reported by Liu et al. , the soil-water retention curve of sand was estimated by the RETC code, which is a very crude. As reported by Tang and Cui , for given water contents the relative humidity h decreased with increasing temperature. In this study, the soil-water retention curves of lateritic clays were only conducted at room temperature (20 °C), without considering the 569 Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570 Predicted λ (W/m·K) 2.0 Temperature(ºC) 5 25 40 60 80 90 1.6 Table 4 Summary of RMSE of IPCHT model. +5% -5% Guilin lateritic clay Liuzhou lateritic clay Silty clay Sand 1.2 0.8 Dry density: 1.1g/cm Saturation: 4%~84% 0.4 (a) 0 0.8 1.2 1.6 Temperature(ºC) 5 25 40 60 80 90 2.5 2.0 +5% -5% 1.5 1.0 3 Dry density: 1.1g/cm Saturation: 10%~78% 0.5 (b) 0 0.5 1.0 1.5 2.0 2.5 3.0 Measured λ (W/m·K) 2.5 Temperature(ºC) 5 20 40 58 78 88 2.0 +5% -5% 1.5 1.0 Liu et al. (2011) 3 Dry density: 1.24g/cm Saturation: 11%~99% 0.5 (c) 0.0 0 0.5 1.0 1.5 2.0 2.5 Measured λ (W/m·K) 4.5 +5% Temperature(ºC) 5 20 40 58 78 88 3.6 -5% 2.7 1.8 Liu et al. (2011) 3 Dry density: 1.47g/cm Saturation: 1%~75% (d) 0.9 0.0 0 0.9 0 °C < T < 30 °C 30 °C T 90 °C 0 < T 90 °C 12 18 25 41 31 30 19 29 26 21 21 33 tions, which mainly depend on the microstructure and mineralogical compositions, play an important role when the IPCHT model is applied to predict the temperature dependence of thermal conductivity. For each type of soil, the fitness of the IPCHT model to measured data was evaluated by the root mean square error (RMSE): vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u n u1 X kexp kpre2 RMSE ¼ t n 1 kexp 0.0 Predicted λ (W/m·K) 2.0 Measured λ (W/m·K) 3.0 Predicted λ (W/m·K) 0.4 RMSE (%) 3 0.0 Predicted λ (W/m·K) Soil 1.8 2.7 3.6 ð15Þ where n is the number of observations, kexp and kpre are measured and predicted thermal conductivities. A summary of the RMSE error analyses is listed in Table 4. The RMSE provides useful information regarding the error extent. According to the RMSE in Table 4, at temperature between 0 and 90 °C, the IPCHT model can predict k within 30% RMSE for all types of soils, except for sand with 33% RMSE. However, the RMSEs of two lateritic clays from 30 to 90 °C are twice from 0 to 30 °C. This means that the applicability of the IPCHT model is limited for lateritic clays when the temperature is higher than 30 °C. This is mainly because the evaporation and the associated latent heat transfer become an increasingly complicated at elevated temperature due to the microstructure and phase configuration effects. Blonquist et al.  suggested that the microstructure and phase configuration play an important role in determining the dielectric response for their aggregated porous media. The heat conduction and dielectric response in soils are practically similar. Although the soil-water retentions were taken into account in the IPCHT model, it reflected partly the microstructure of soils. Accordingly, Blonquist et al.  proposed the extended dual three-layer composite sphere model to take into account water distribution and the processes of water filling in intra-aggregate and inter-aggregate pores. This model includes four-phase composite and used sigmodal functions as a weight function, which can describe aggregate structure effects on dielectric permittivity since there is an addition of a layer dividing water phase into intra-aggregate and inter-aggregate pores parts. Therefore, it is believed that the performance of the IPCHT model could be further improved by better consideration of the microstructure and phase configuration. More accurately measured data for a wide variety of aggregated soils are needed for further improvements of the IPCHT model. 4.5 Measured λ (W/m·K) Fig. 9. Measured and predicted thermal conductivity for each temperature: (a) Guilin lateritic clay; (b) Liuzhou lateritic clay; (c) Silty clay; and (d) Sand. effect of temperature when applying the IPCHT model. Therefore, at temperatures above 20 °C, most predictions are slightly below the measured values, as shown in Fig. 9(a) and (b). From the comparison of four soils, it can be deduced that the soil-water reten- 5. Conclusions The relationship between thermal conductivity (k) and saturation (S) for two lateritic clays at different temperatures was experimentally investigated. The effects of clay content, aggregate structure and mineralogical compositions on the temperature dependence of the k-S relationship were discussed, together with the predictions by the IPCHT model. The following conclusions can be obtained from this study: 570 Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570 (1) For lateritic clays, k increases with temperature due to the enhanced LHT of vapor. At temperatures ranging from 5 to 60 °C, k increases with S. At temperatures above 60 °C, k decreases with increasing saturation when S is beyond about 54%. (2) The soil heat conduction is related to the form and distribution of water in soil. The thermal conductivity resulting from the LHT of vapor has obvious peak value with saturation, and its peak value and corresponding saturation are related to the clay content. The peak value decreases with increasing clay content, whereas its saturation increases with increasing clay content. (3) The differences in PSDs and soil-water retentions of compacted lateritic clays demonstrated clearly that the more the water content and void space for LHT, the more obvious the temperature effect on the thermal conductivity. (4) The IPCHT model can provide good agreement with experimental data at different temperatures ranging from 5 to 90 °C. The accurate acquisition of the soil-water retentions can improve the agreement. Further work may aim toward the effects of the microstructure and phase configuration on the k prediction models. Acknowledgements This research was supported by National Natural Science Foundation of China (Grant No. 51568014, 41502284) and opening fund from Guangxi Key Laboratory of New Energy and Building Energy Saving (Guilin University of Technology) (Grant No. 17-J-22-1). Conflict of interest The authors declare that there is no conflict of interest. Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.077. References  T. Zhang, G. Cai, S. Liu, A.J. Puppala, Investigation on thermal characteristics and prediction models of soils, Int. J. Heat Mass Transfer 106 (2017) 1074– 1086.  P.P. 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