Thermophysical Properties of Bentonite–Sand/Fly Ash-Based Backfill Materials for Underground Power Cable

The surrounding (backfill) materials around the underground power cable systems are essential for dissipating the heat away from it, during the exertion phases. The heat dissipation restrains the thermal instability and risk of progressive drying of the backfill materials, thus reducing the thermal stress on the power cable. Thermal instability indicates the reduction in thermal properties (conductivity or diffusivity) due to the migration of moisture because of heat accumulation. Thus, the backfill materials should have adequate thermal properties and water retention capacity to transfer the heat from the heat source to the surrounding area with minimal moisture migration. The bentonite has high water retention capacity, but low thermal conductivity, whereas sand/fly ash exhibits low water retention and has higher thermal conductivity than bentonite. The addition of bentonite promotes the water holding capacity and thermophysical properties of sand and fly ash. Therefore, this study presents the thermal properties of backfill materials, bentonite–fly ash (B–F) and bentonite–sand (B–S), at varying weight-percent of sand and fly ash with bentonite. Various compositions of the mixtures were compacted to varying dry densities, and water contents and thermal properties variation of backfill materials were measured using a dual thermal needle probe ‘KD2 Pro’ at room temperature. The study deals with the systematic evaluation of the volumetric specific heat capacity, thermal conductivity, and diffusivity of backfill materials against varying dry density and water content. The threshold water content (TWC) has been determined from the thermal diffusivity–water content variation curve, and it has correlated with plastic limit (PL) and optimum moisture content (OMC). Thereafter, the efficacies of two thermal conductivity prediction models have also been evaluated statistically with respect to experimental results.


Introduction
The underground power cable systems are less susceptible to the environmental hazards as well as from the severe weather conditions such as heavy rain, thunderstorm, lighting, extreme wind and more. The underground power cable systems require less maintenance in comparison with the overhead power lines and also ensure the reliable and safe power transmission to the consumer [1][2][3][4]. However, the laying or installation of underground power cable necessitates the investigation of the thermophysical, hydraulic, and mechanical properties of thermal backfill materials, which surrounds the power cable systems and permits the heat dissipation away from the cables during the exertion phase [5][6][7]. The effective dissipation of heat away from the underground power cable restrains the thermal instability and reduces the risk of progressive drying of the backfill material, and hence, the surrounding temperature is maintained within the permissible limit [8]. Thermal stability shows the ability of backfill materials to maintain almost constant thermal properties during the heating effect, thereby enhancing the ampacity (current carrying capacity) of the underground power cable systems [9][10][11].
Previous studies depict that the higher value of thermal conductivity (λ) provides adequate heat transfer from the underground power cable to the surrounding area, which reduces the temperature of core conductor and hence restrains the thermal 57 Page 4 of 26 Zhou et al. [29] have measured the thermal properties of sand and peat materials with varying peat-sand ratios, moisture content, bulk density, and temperatures, and it was reported that the thermal conductivity increases exponentially with increasing volumetric water content (θ), whereas decreases with increasing peat-sand ratio. This study also revealed that the volumetric heat capacity increases linearly with w and also significantly affected by w rather than peat-sand ratios and γ d . Moreover, the thermal diffusivity of peat-sand mixtures showed an initially increasing trend, reaching a plateau and then exhibiting a decreasing trend with a further increase in w; this water content (w) is known as threshold water content (TWC) [23]. Further, the peak value of thermal diffusivity was found to be increased with γ d and f s in the peat-sand mixtures, whereas the lowest and the highest values of thermal diffusivity were reported for peat and sand, respectively. Similar observations have also been reported by Arkhangelskaya and Luckyashchenko [30,31]. Chen et al. [32] have studied the thermal conductivity of bentonite-added graphene oxide at different γ d ranging from 1.4 g·cm −3 to 1.9 g · cm −3 with the variation of graphene oxide content from 0% to 50%. It was found that the thermal conductivity increases from 11.94 W·m −1 ·K −1 to 21.66 W·m −1 ·K −1 by adding 50% graphene oxide to the bentonite at w = 10%. Peng et al. [33] have also examined the thermal conductivity (λ) of bentonite-graphite mixtures, and it was reported that when the graphite content was in the order of 0% to 20%, the λ increased from 0.534 W·m −1 ·K −1 to 1.386 W·m −1 ·K −1 at a void ratio (e) = 0.84 and w = 10%. However, this study also revealed that the thermal conductivity of bentonite-graphite/graphene oxide mixtures significantly decreased with a small reduction in moisture content; hence, it threatens the thermal stability of backfill materials [34]. Kolay and Singh [16] have studied the thermal conductivity of black cotton soil-fly ash mixture-based thermal backfills at varying dry density (γ d ) and water content (w). It was reported that the thermal conductivity of black cotton soil increases with increasing fly ash content, γ d and w. Wan et al. [35] have measured the thermal conductivity of mixtures of iron tailing and loess (0% to 100%, by weight) and reported the highest thermal conductivity for the mixture of 30% loess with 70% iron tailing. Do et al. [36] have studied the thermal conductivity of controlled low-strength materials (CSLM) that consist of cement (88 kg·m −3 ), fly ash (264-265 kg·m −3 ) and water (483 kg·m −3 ) with varying proportions of excavated soil (0% to 40% by weight) with pond ash (60% to 100% by weight). It was reported that the thermal conductivity decreases linearly with a decrease in saturation level, whereas increases with increasing amount of pond ash in the excavated soil of CSLM. Lee and Shang [37] have studied the thermal conductivity of compacted mine tailing-fly ash mixture, and it was reported that the soil specimens compacted under the optimum water content lead to higher thermal conductivity. Fall et al. [38] have also evaluated the application of bentonite-mine tailing paste in underground mining operations and concluded that the bentonite-mine tailing paste with 4% to 8% of bentonite showed the low hydraulic conductivity and high water retention capacity. Claude et al. [39] have further studied the thermal conductivity of cemented paste backfill materials composed of hydraulic binder, tailing and water. It was reported that the cemented paste components such as tailing type and tailing fineness have a great influence on the thermal conductivity of backfill. This study also revealed that the tailing with high quartz and larger particle size results in the higher thermal conductivity of cemented paste backfill materialsthan those made up with the finer tailing.
Several researchers have reviewed the thermal conductivity models for unsaturated soils, and it was concluded that the thermal conductivity of rock/soil is governed by several factors such as mineralogy, particle size and shape, grain size distribution, dry density (γ d ), water content (w), porosity (n), quartz content (q), and sand content (f s ) [40][41][42]. Based on these controlling factors, several thermal conductivity empirical models of geomaterials have been developed via regression analysis of experimental data of thermal conductivity for geomaterials [43][44][45][46][47][48][49][50][51]. Kersten [43] has proposed an empirical relationship between λ, w, and γ d for different soil types ranging from sand-clay-loam. Campbell [44] proposed a model based on the volumetric water content (θ) considering the effects of variation in soil texture, dry density, clay content, and critical water content on thermal conductivity (λ). Rao and Singh [45] have also established a relationship between λ and γ d incorporating w based on laboratory experiments, wherein λ was derived using the reciprocal correlation between thermal conductivity and resistivity. Johansen [46] has proposed a concept of normalized λ (or Kersten's number, λ n ), which is the function of λ of dry soils (λ dry ) and thermal conductivity of saturated soils (λ sat ). Johansen [46] has further studied the effects of soil type, γ d , degree of saturation (S r ), and mineral components on the soil's thermal conductivity in a unique manner through λ n -S r relationship. This model is only suitable for pure sandy soils or for fine-grained soils having a degree of saturation above 20% [47]. Cote and Konrad [47] have further studied λ of soils and construction materials and established a new relationship between λ n and S r , in logarithmic function, incorporating variable (κ) to account the soil type, particle shape and size effect. Its applicability is also limited to the soils with mixed compositions like bentonite-sand mixture [48]. Lu et al. [49] roughly divided soil into coarse-grained and fine-grained soil according to sand content and described the relationship between λ n and S r in the form of an exponential function. This model is limited to the prediction of the thermal conductivity of fine-grained soil since it underestimates the thermal conductivity of coarse-grained soils [52]. Further, Nikoosokhan et al. [50] have improved the Cote and Konrad [47] empirical model considering the effect of f s and γ d on λ dry , λ sat , and κ. Tarnawski et al. [51] have also developed an advanced geometric mean model to predict λ of unsaturated soil, wherein three soil structure-based parameters were used, namely an inter-particle thermal contact resistance factor, the degree of saturation of miniscule pore space, and the thermal conductivity of soil solids (λ s ). Moreover, the assessment of representative value of thermal conductivity of soil solids (λ s ) is very difficult, without knowing the mineralogy of soil [53]. Tarnawski et al. [54] refined the thermal conductivity modeling of soil based on weighted average model (WAM) of soil solids as the continuous medium considering the two distinct mineral groups, i.e., quartz and other minerals, due to higher thermal conductivity of quartz (7.7 W·m −1 ·K −1 ) with respect to other minerals (2.2 W·m −1 ·K −1 ).
Furthermore, the previous study revealed that the capability of storing and conducting the heat of backfill materials in the vicinity of power cable systems depend upon their thermal conductivity (λ), thermal diffusivity (D), and volumetric heat capacity (C v ), which are collectively referred to as thermophysical parameters [31, 57 Page 6 of 26 42,55]. The D simply represents the rate of heat spreading within a conductive medium. Moreover, the materials with high thermal diffusivity release heat rapidly in the vicinity of heat source or power cable and reduce the thermal stress on the power cable [56]. For the safe power distribution and reliable performance of the underground power cable systems for the long run, the backfill materials should have good heat-releasing capacity, which restrains moisture migration from the surrounding backfill materials in order to avoid thermal failure of cables [57,58]. Thus, understanding the variation of thermophysical properties is utmost important for the proper design of backfill material for the underground power cable systems and geothermal structures [59,60]. Although the research has been more focused on the thermal conductivity of bentonite-based backfill materials, there are very few studies investigated on the thermal diffusivity (D) and volumetric heat capacity (C v ). Moreover, the prediction of thermal conductivity is limited to specific and natural soil; very few studies also explored the accuracy of thermal properties prediction model for bentonite/clay-based backfill materials [41,61]. Therefore, this study focuses on the measurement of thermophysical properties of geomaterials and mixtures (such as bentonite, fly ash, sand, bentonite-sand, and bentonite-fly ash mixtures) at different values of γ d and w. Fly ash is a waste material generated from thermal power plant and intentionally tested to check its potential use as a backfill material along with bentonite. The thermophysical properties variation of backfill materials was measured against varying dry density (γ d ) and water content (w), using a dual thermal needle probe KD2 Pro [62] at room temperature. Based on the experimental results, the interrelationship between the thermal conductivity (λ), thermal diffusivity (D), and volumetric heat capacity (C v ) of bentonite-based backfill materials was discussed. The threshold water content (TWC) has been determined from D-w relationship. Further, TWC has been correlated with plastic limit (PL) and optimum moisture content (OMC). Finally, the efficacies of two selected prediction models for thermal conductivity were assessed. The best correlation (model) for the data of bentonite-based backfill materials such as bentonite-fly ash (B-F) and bentonite-sand (B-S) mixtures has also been discussed via statistical evaluation.

Physical Properties, Chemical and Mineralogical Composition of Geomaterials
The geomaterials such as sand (S), bentonite (B), and fly ash (F) have been used in this study. The S and F were collected from locally available construction site and the Farakka thermal power plant, National Thermal Power Corporation Ltd.
(NTPC), West Bengal, India, respectively, whereas B was commercially available. The X-ray fluorescence (XRF) tests were carried out on three identical samples, and the average chemical compositions (% by wt.) of F and B were reported with the variation of ± 3% to 4%. The chemical compositions (% by weight) of F and B are summarized in Table 1. According to Table 1, the fly ash is classified as a class F fly ash [63]. In India, F is majorly constituted of a varying percentage of minerals such as SiO 2 (21-61%), Al 2 O 3 (6-36%), Fe 2 O 3 (9-40%), CaO (1-11%), and MgO (0-6%) [64]. The data obtained in this study are within the range as reported in the literature [64]. XRF shows that the bentonite contains 71.29% and 1.32% (wt.) silica plus aluminum oxide and CaO, respectively, along with other components of sodium, iron, potassium, and magnesium oxides. Based on the chemical compositions, the bentonite used in this study can be categorized as a sodium bentonite. When compared to earlier research, sodium bentonite has nearly identical compositions, consisting of SiO 2 (71.8%), Al 2 O 3 (15.3%), Fe 2 O 3 (4.5%), and MgO (1.8%) [65]. The particle size distribution of the geomaterials and mixtures was conducted as per guidelines of Indian Standard [66]. The particle size distribution of geomaterials is presented in Fig. 1. Based on the particle size distribution (Fig. 1), both sand and fly ash were categorized as poorly graded soil. Bentonite constitutes 95% finer particles, having 64% clay particle below 2 μm in average diameter. Further, the laboratory experiments were performed on the geomaterials and mixtures of bentonite-fly ash (B-F) and bentonite-sand (B-S) at different proportions (% by wt.), as listed in Table 2. The Atterberg limits and specific gravity (G s ) of the parental materials and mixtures were determined as per Indian Standard [67] and [68], respectively; all the results have been summarized in Table 3. Based on the results presented in Table 3, B-F and B-S mixtures are classified as high-plastic cohesive soil, whereas both sand and fly ash are the non-plastic cohesionless geomaterials [66,67].
The maximum dry density (MDD) and optimum moisture content (OMC) of geomaterials and mixtures, mentioned in Table 3, have been estimated using Standard Proctor Test [69]. The MDD and OMC for both B-F and B-S mixtures were found to be increased with increasing bentonite content up to 30%; further MDD of soil mixes was found to be decreased. However, OMC was found to be increased with increasing bentonite content. Similar observations have also been reported by the previous literature [70]. Figure 2 presents XRD analysis of fly ash (F), bentonite (B) and sand (S). It shows that B consists mainly of montmorillonite mineral, followed by kaolinite, illite, and quartz. For the fly ash (F), the peak intensity was observed corresponding to mullite and quartz minerals (as shown in Fig. 2), followed by hematite and aragonite, whereas sand mainly consists of inert quartz mineral.

Thermophysical Properties Measurement Procedure
The geomaterials were dried in thermostatically controlled oven at 105 °C for 24 h and mixed with different proportions of geomaterials as shown in Table 2. The required amount of geomaterials was calculated based on targeted γ d and volume   of the mold (i.e., size of 15 × 15 × 4 cm). The targeted γ d of geomaterials (fly ash, bentonite, and sand) and mixes were in the range of 1.0-1.6 g·cm −3 , as mentioned in Table 4. Further, considering this targeted γ d , the sample of geomaterials and mixtures were prepared manually with the addition of certain amount of water that varies from zero (i.e., dry condition) to nearly plastic limit (PL) (see Table 4). The prepared homogenous mixtures of soils were then kept in an airtight plastic bag for 24 h to 48 h to ensure the uniformity in the moisture distribution. Thereafter, the samples were equally divided into three parts to fill the mold in three layers. Each layer has been compacted as per Standard Proctor Test [69], using laboratory earth rammer, to accommodate the soil mass (calculated at the targeted γ d ) into the mold. The thermal properties of geomaterials and mixtures were measured using dualneedle SH-1 sensor (KD2 Pro, 2008) developed by Decagon devices (Pullman, Washington), which is based on the transient heat flow methodology. This methodology is suitable for soils because of their relative simplicity and less time required for the measurement of thermal properties [71,72]. The thermal properties analyzer  consists of a handheld controller (which also serves as a read-out unit) and a needle probe that can be inserted into the compacted soil. The KD2 Pro sensor has two parallel needles, each having 30 mm long and 1.3 mm in diameter with 6 mm spacing. The thermophysical properties (λ, C v , and D) were estimated using built-in algorithm in KD2 Pro [62]. The algorithm uses nonlinear least-square method to fit the time and temperature data with an exponential integral function and provides the λ, C v , and D directly on the controller screen. The mathematical correlation estimates the thermal properties within ± 10% error. The measurement ranges for each parameter were as follows: thermal conductivity 0.02-2.0 W·m −1 ·K −1 , thermal diffusivity 0.1-1.0 mm 2 ·s −1 , and volumetric specific heat 0.5-4.0 M·J·m −3 ·K −1 . Figure 3 shows the schematic arrangement of SH-1 sensor used for the measurement of thermal properties of geomaterials and mixtures. For the sake of accuracy, the values of thermal properties presented in this study are the average of three readings of the thermal properties of the compacted soil sample. The relative difference between the average value of three readings and individual measured values less than ± 7% was considered to collect the data. After measurement, the sample was further ovendried for moisture content determination to ensure its negligible variation during measurement. The detailed explanation of thermal probe and the methodology to measure thermal properties have been discussed in Sah and Sreedeep [73]. Figure 4 presents the variations of λ and D with w corresponding at different γ d of geomaterials (F, S, and B). It shows that λ of geomaterials increases with increasing w and γ d . It also shows that the thermal conductivity increased rapidly for sand, fly ash, and bentonite for w up to 5%, 20%, and 45%, respectively. Thereafter, with a further increase in water content the thermal conductivity remains unchanged or decreases slowly; this water content is known as critical water content (CWC) [74,75]. From Fig. 4, it can also be noted that S has maximum λ followed by F and B for whole range of w at same γ d of 1.2 g·cm −3 . Similar findings were reported on different textured of forty Canadian soils by Tarnawski et al. [76] and Rao and Singh [45]. Figure 4 also shows that the thermal diffusivity (D = λ/C v ) of the geomaterials has nonlinear variations with w and D of sand was found to be significantly higher than that of B and F. From the thermal diffusivity-water content (D-w) relationships, it can be noticed that D increased significantly up to w = 6% to 7% and reached a maximum value at a specific threshold water content (TWC); with a further increase in water content beyond TWC, D starts to decrease. Similar observations have also been reported in the previous studies [60,77]. The peak value of D of sand was found to be 0.70 mm 2 ·s −1 at TWC = 8% for γ d = 1.2 g·cm −3 , whereas, for fly ash and bentonite, the peak value of D was found to be nearly 0.44 mm 2 ·s −1 and 0.32 mm 2 ·s −1 at TWC = 10% and 42%, respectively. Similar observations were demonstrated by Abu-Hamdeh [55]. Arkhangelskaya and Luckyashchenko [56] and Zhao and Si [60] have reported that the thermal diffusivity of sand was in the range of 0.30-0.80 mm 2 ·s −1 and 0.90-1.12 mm 2 ·s −1 , respectively. Further, Arkhangelskaya and Luckyashchenko [56] have reported that the thermal diffusivity of saturated light clay and loamy soil is lesser than the sandy soil, and similar observations have been noticed in this study. Figure 5 reveals that C v increases with an increase in w and γ d for geomaterials. However, no specific trend has been observed between γ d and w. The maximum value of C v of S, F, and B was found to be 1.75 MJ·m −3 ·K −1 , 2.4 MJ·m −3 ·K −1 , and 3.5 MJ·m −3 ·K −1 at w = 10%, 28%, and 53%, respectively. The variations in C v of geomaterials were found in the order of 1.00-1.25 MJ·m −3 ·K −1 at dry conditions (w = 0). Similar observations have been reported by López-Acosta et al. [78] for the former lake Texcoco soils. López-Acosta et al. [78] have also reported that the increase in porosity (decrease in γ d ) causes an increase in specific heat capacity. The rise in C v up to 3.2 MJ·m −3 ·K −1 , at full saturation level, for clayey soils has also been reported in the previous literature works [55,78,79]. Moreover, Zhou and Si [60] have also reported that the range of C v was in the order of 0.6-3.65 MJ·m −3 ·K −1 for peat, and further, it was reported that C v is strongly influenced by w rather than γ d , which is similar to the results observed in this study. Figure 6 shows the effect of water content and dry density on thermal conductivity and thermal diffusivity of bentonite-fly ash-based backfill materials. The thermal diffusivity of bentonite-fly ash mixtures has very marginal difference at dry condition, whereas significant differences were observed at TWC for the tested ranges of γ d . The maximum value of thermal conductivity was found to be 1.23 W·m −1 ·K −1 for B50-F50 mixture (in comparison with the other mixes) at γ d = 1.36 g·cm −3 and w = 31%. It can also be observed that the thermal conductivity increases with increasing fly ash content, water content, and dry density. This is attributed to the fact that the fly ash content in the mixture reduces the porosity (denser packing) and enhances the overall thermal conductivity of mixtures due to higher thermal conductivity of fly ash than bentonite and vice versa. Similar observations have been reported in the previous research works [16,36] for black cotton soil-fly ash mixture and CSLM. Moreover, the range of thermal conductivity and thermal diffusivity of bentonite-fly ash mixtures at TWC is summarized in Table 5. From Table 5, it can be noticed that the peak value of D was in the range of 0.33-0.36 mm 2 ·s −1 , 0.37-0.43 mm 2 ·s −1 , 0.40-0.47 mm 2 ·s −1 , and 0.37-0.45 mm 2 ·s −1 at TWC 37.99%, 27.91%, 24.82%, and 20.00% for B80-F20, B60-F40, B50-F50, and B30-F70, respectively. Figure 7 represents C v of B-F mixtures with varying amount of w at different range of γ d . It shows that C v increases with increasing w for any value of γ d . The value of C v reflects wide range of scatter, with increasing amount of F from 20% to  70% for any specific value of w and γ d . From Fig. 7, it can also be noticed that B-F mixtures show lower value of C v than the bentonite (see Fig. 5); this might be due to the lesser value of C v of fly ash than the bentonite. Therefore, it can be concluded that B-F mixtures will have lower heat storing capacity, but relatively higher heat conduction capacity than the bentonite. Moreover, the maximum value of C v was found to be 3.4 MJ·m −3 ·K −1 at w = 44% for the case of B80-F20 mixture, which is nearly equal to the maximum value of C v of bentonite, and it decreases with increasing fly ash content. Figure 8 presents the variations in the thermal conductivity (λ) of B-S mixtures at different water content (w) and dry density (γ d ). It shows that λ increases with increasing w and γ d for any ratio of B-S mixture. It can also be noticed that the variation of λ with w is marginally affected by γ d at higher value of w, if f s < 40%; however, γ d have pronounced effect on B-S mixture, if f s > 40%. This might be due to quartz and non-quartz sand content which have higher thermal conductivity compared to the bentonite or other fine-grained soil, resulting in high λ of mixtures. Nikoosokhan et al. [48] and Mishra et al. [57] have also reported that the thermal conductivity of bentonite or other soil is enhanced by adding sand. From Fig. 8, it can also be noticed that the thermal conductivity of B-S mixture reaches the maximum value in the order of 1.6 to 1.8 W·m −1 ·K −1 by mixing 70% S to B. Furthermore, Fig. 8 depicts that D increases with increasing w and γ d up to specific water content, i.e., TWC, and thereafter, it decreases with s further increase in water content. Similar responses were obtained for bentonite-fly ash (B-F) mixtures; however, the increasing rate of thermal diffusivity of B-S mixtures is higher than that of B-F mixtures. Moreover, the range of thermal conductivity and diffusivity of bentonite-sand mixtures at TWC is summarized in    Figure 9 represents the variations of C v of B-S mixtures with varying γ d and w. It can be observed that C v increases with increasing w for the tested range of γ d ; however, the variation of C v with w is negligibly affected by γ d for any ratio of B-S mixture. It can also be seen that the value of C v shows very narrow range of differences, with increasing amount of S from 20% to 70%, for any specific value of w. Further, it can be observed that the variation of C v of mixtures is in the order of 1.00-1.25 MJ·m −3 ·K −1 at dry conditions, whereas the maximum values of C v of mixes were found to be in the order of 3.00-3.40 MJ·m −3 ·K −1 at w = 35% to 44%. Similar findings were reported for peat-sand mixtures by Zhao and Si [60].

Discussion
Due to limited study on volumetric heat capacity (C v ) and thermal diffusivity (D) of bentonite-based backfill materials, a relationship between these two thermal properties (D and C v ) and thermal conductivity (λ) for bentonite-based materials was discussed in this study. The thermal conductivity of geomaterials and mixtures increases with larger rate up to TWC; however, beyond TWC, the rate of increase in thermal conductivity is relatively smaller. As such, water has higher thermal conductivity and specific heat capacity than the pore air, causing an improvement in thermal properties with increasing water content [78]. Moreover, the soil solid has higher thermal conductivity and specific heat capacity than the water; therefore, the water film around the particles as well as grain-to-grain contact promotes the thermal conductivity at lower water content and hence rapid improvement in the thermal conduction [73,76]. It can be stated that beyond TWC a further increase in dry density does not improve the effective contact area, whereas the heat transfer takes place predominately through the water, and hence the improvement rate of thermal conduction is very slow [55]. The volumetric heat capacity of geomaterials and mixtures increases with w and bentonite content, because high percentage of bentonite clay, in the mixture, leads to the absorption of more water due to its swelling potential and water retention properties. Since the contact between the solid particles diminished with increasing percentage of bentonite, due to the formation of double diffuse layer, the thermal conductivity of the mixtures is also reduced [80]. On the other hand, the rate of increase in thermal conductivity with respect to water content is relatively greater than the volumetric specific heat capacity before TWC, but after TWC, the rate of increase in thermal conductivity is relatively slower than the volumetric specific heat capacity [60]. Therefore, due to the combined action of thermal conductivity and volumetric heat capacity of geomaterials and mixtures, D-w curves showed a decreasing trend after TWC.
Further, it can be observed that TWC varies with the sand/fly ash content into the bentonite-based backfill materials (see Tables 5 and 6). It can also be noticed that TWC of B-F mixtures showed a higher value than B-S mixtures. In this study, the obtained TWC from D-w curves was correlated with PL and OMC, as shown in Fig. 10. It shows that OMC and PL exhibit better correlation with TWC with coefficients of regression equal to 0.97 and 0.96, respectively. These correlations are valid for γ d less than 1.5 g·cm −3 . The equations obtained from this study (in Fig. 10) can be used to estimate TWC for bentonite-based materials, which will help the engineers to evaluate the accurate value of thermal diffusivity and corresponding thermal conductivity for the safe design of thermal backfill with respect to γ d and w in the field.
Moreover, for effective heat transfer from underground power cable system to the surrounding, the thermal conductivity of thermal backfill should be in the range of 0.8 to 1.0 W·m −1 ·K −1 [2,57]. Figure 11 shows the average thermal conductivity of geomaterials and mixtures corresponding to TWC. It depicts that the bentonitebased backfills (such as bentonite-fly ash and bentonite-sand mixtures) can be a promising thermal backfill materials with λ values higher than 0.8 W·m −1 ·K −1 , which is the acceptable limit of thermal conductivity for thermal backfill materials reported by Zakarka et al. [2]. However, the compressive strength, water retention capacity, and swelling potential of backfill materials need to be estimated in the laboratory while used in the underground power cable application.

Kersten [43] Model
Kersten [43] has measured thermal conductivity of different soils such as sand, gravel, sandy loam, clay, crushed rock, and organic soil to develop empirical equations, as mentioned in Eqs. 1 and 2. Accetable range according to [2] 57 Page 20 of 26 w > 0. For intermediate soils, i.e., soils having a composition between the silt-clay group and the sandy group, Kersten [43] has suggested an interpolation technique between the respective values obtained by Eqs. 1 and 2 for silty clay and sandy soils, respectively. Figure 12a presents the comparison between the predicted thermal conductivity (λ p ) and measured thermal conductivity (λ m ) of geomaterials and mixtures of the tested samples prepared at different γ d and w. From Fig. 12a, it can be observed that the Kersten [43] model overestimates the thermal conductivity for the lower values of thermal conductivity, when f s becomes greater than 40%. However, the majority of thermal conductivity data for geomaterials and mixes are within the ± 20% error lines. Further, the statistical evaluation of prediction models was assessed using root-mean-square error (RMSE), mean absolute error (MAE), and coefficient

Nikoosokhan et al. [50] Model
Johansen [46] has proposed the concept of normalized thermal conductivity, λ n (i.e., the Kersten number) and established a relationship between λ and λ n for unsaturated soils, based on λ values at dry and saturated states: where λ dry and λ sat are the thermal conductivity of dry and saturated soils (W·m −1 ·K −1 ), respectively. Based on Johansen [46] normalized λ model theory, Nikoosokhan et al. [43] have improved the Cote and Konrad [47] model accounting sand content and dry density of soil in empirical equation.
where κ were calculated by the following equation: This equation is valid for the wide range of sand fraction and dry density (γ d ) ranging from 0 < f s < 1 and 1.1-2.0 g·cm −3 , respectively. Figure 13a presents the predicted results of λ, using the Nikoosokhan et al. [39] model, versus experimentally measured λ for the wide range of w. The values of RMSE, MAE, and R 2 for geomaterials and mixes are presented in Fig. 13b. It can be observed that the Nikoosokhan et al. [50] model gives better prediction of λ over the wide range of w and γ d than the Kersten [43] model for all geomaterials and mixtures with R 2 > 0.70 except fly ash (R 2 = 0.54). The scattering of data for mixtures is larger; however, the tendency in the variation of λ with w, γ d , and f S is similar to previous reported data [61,81,82]. The RMSE and MAE range from 0.105 to 0.185 W·m −1 ·K −1 and from 0.090 to 0.166 W·m −1 ·K −1 for F and B-F mixes, respectively. This model overestimates the thermal conductivity (corresponding data at lower w) by more than 20% since RMSE and MAE value are ranging from 0.123 to 0.212 W·m −1 ·K −1 and from 0.102 to 0.144 W·m −1 ·K −1 , respectively, when f s > 50% in B-S mixtures.
The statistical comparison of λ-model shows that the Nikoosokhan et al. [50] model is the best performing model, which is the improved model over the Cote and Konrad [47] model by incorporating κ, λ dry , λ sat , and f s , represented in Eqs. 4 and 5. However, the accuracy in the predictions of thermal conductivity (λ) is strongly influenced by the volume fraction of quartz, specific soil group, particle shape and size, water content, and dry density [52]. Therefore, it can be stated that further studies are required to improve λ-prediction models according to soil-specific group, e.g., the mixture of bentonite-sand/fly ash. Moreover, from this study, it can be concluded that the Kertsen [43] model is most appropriate for B-F mixtures, whereas Nikoosokhan et al. [50] model predicted well for B-S mixtures.

Summary and Conclusions
In this paper, bentonite-based backfill materials were prepared by adding different proportions of F and S with B. The thermal properties of geomaterials and mixes were measured using a thermal probe (i.e., KD2 Pro 2008), at different γ d and w, to see its potential application as a thermal backfill material. Based on the experimental results obtained from this study as well as the results presented in the existing literature works, it can be concluded that the thermophysical properties of geomaterials and mixtures are influenced by many factors such as soil compositions, dry density, water content, particle size distribution, and so on. Moreover, based on the results obtained from the experimental study, the following conclusions have been drawn.
• Thermal conductivity (λ) of B-S mixtures is higher than B-F mixtures at any specific w and γ d . The thermal conductivity of B-S mixture reaches the maximum value in the order of 1.6-1.8 W·m −1 ·K −1 with mixing 70% S to B, whereas, for B-F mixtures, maximum thermal conductivity was found to be nearly 1.10 W·m −1 ·K −1 to 1.23 W·m −1 ·K −1 at 50% addition of F with bentonite. Overall, it can be concluded that the bentonite-based backfill such as bentonite-fly ash and bentonite-sand mixtures can be promising thermal backfill materials with thermal conductivity values higher than 0.8 W·m −1 ·K −1 . • Thermal diffusivity (D) increases with increasing w up to TWC; thereafter, a further increase in w content causes a decrease in D. It has also been observed that TWC values are different for different bentonite-based backfill materials, which is influenced by the sand/fly ash content present into the bentonite. • The maximum value of D was in the range of 0.33-0.36 mm 2 ·s −1 , 0.37-0.43 mm 2 ·s −1 , 0.40-0.47 mm 2 ·s −1 , and 0.37-0.45 mm 2 ·s −1 at TWC = 37.99%, 27.91%, 24.82%, and 20.00% for B80-F20, B60-F40, B50-F50, and B30-F70, respectively. However, the maximum value of D was in the order of 0.35-0.38 mm 2 ·s −1 , 0.41-0.54 mm 2 ·s −1 , 0.45-0.55 mm 2 ·s −1 , and 0.58-0.68 mm 2 ·s −1 at TWC = 29.5%, 17.66%, 18.21%, and 14.6% for B80-S20, B60-S40, B50-S50, and B30-S70, respectively. • The variation of C v of geomaterials was found to be in the order of 1.00-1.25 MJ·m −3 ·K −1 at dry conditions (w = 0); however, C v value increased with increasing w and observed that C v of S, F, and B was 1.75 MJ·m −3 ·K −1 , 2.4 MJ·m −3 ·K −1 , and 3.5 MJ·m −3 ·K −1 at w = 10% , 28%, and 53%, respectively. The B-F mixtures showed lower value of C v than the bentonite; this is obvious because of that fly ash has lower C v than the bentonite. The maximum value of C v was found to be 3.4 MJ·m −3 ·K −1 at w = 44% for the case of B80-F20 mixture. Moreover, C v of B-S mixtures was in the order of 1.00-1.25 MJ·m −3 ·K −1 at dry conditions and the maximum value observed is 3.00-3.40 MJ·m −3 ·K −1 at w = 35% to 44%. However, C v is more sensitive to the variations of w than γ d . • It was found that OMC and PL exhibit better correlation with TWC with coefficients of regression equal to 0.97 and 0.96, respectively. These correlations are valid for γ d less than 1.5 g·cm −3 . The equations obtained in this study (in Fig. 10) can be used to estimate TWC for bentonite-based materials, which will help the engineers to evaluate the accurate value of thermal diffusivity and corresponding thermal conductivity for the safe design of thermal backfill with respect to γ d and w in the field. • Further, the thermal conductivity prediction models were selected and statistically evaluated with respect to the experimental results, and it was found that the Kertsen [43] and Nikoosokhan et al. [50] model are the best suitable model to predict λ for B-F mixes and B-S mixes, respectively.
Moreover, in the future work, a model to predict the thermophysical properties of bentonite-based backfill materials with dry density, water content, Atterberg limits, and clay content must be established.