Thermophysical Properties of Bentonite-sand/fly ash Based Backfill Materials for Underground Power Cable

doi:10.21203/rs.3.rs-2321894/v1

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Thermophysical Properties of Bentonite-sand/fly ash Based Backfill Materials for Underground Power Cable

https://doi.org/10.21203/rs.3.rs-2321894/v1

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published 24 Feb, 2023

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The surrounding (backfill) materials around the underground power cable systems are essential for dissipiating the heat away from it, during the exertion phases. The heat dissipiation restrains the thermal instability and risk of progressive drying of the backfill materials, thus, reduce thermal stress on power cable. Thermal instability is the reduction of thermal properties (conductivity or diffusivity) due to migration of moisture because of heat accumulation. Thus, the backfill materials should have adequate thermal properties and favorable water retention capacity, which will falicitate the heat transfer easily from the heat source to the surrounding area with minimal moisture migration. The bentonite have high water retention capacity, but low thermal conductivity. Sand/fly ash exhibit low water retention and have higher thermal conductivity than bentonite. The addition of bentonite promote the water holding capacity and thermo-physical 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 weigth-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 2008’ at room temperature. The study deals with 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 mosite conetn (OMC). Thereafter, the efficacy two thermal conductivity prediction models also were statistically evaluated with respect to experimental results.

Underground power cable

bentonite-based thermal backfill

bentonite-sand/fly ash

thermophysical properties

prediction

waste management

The underground power cable systems are less susceptible to environment hazards and severe weather conditions such as heavy rain, thunderstorm, lighting, extreme wind and more, thus ensuring the reliable and safe power transmission to the consumer and also required less maintenance in comparison to the overhead power lines [1–4]. However, the underground laying cables implies the necessity to investigate on the thermophysical, hydraulic and mechanical properties of thermal backfill materials (surrounding to the power cable and others), which allow the heat dissipation away from the cables, during the exertion phase [5–7]. The effective dissipation of heat away from the underground power cable restrains the thermal instability and reduces risk of progressive drying of the backfill material and thus, maintain surrounding temperature within the permissible limit [8]. Thermal stability is the ability of backfill materials to maintain relatively constant thermal properties during heating effect and hence, enhancing the amapacity (current carrying capacity) of these underground power cable system [9–11].

Previous studied depict that higher value of thermal conductivity provides adequate heat transfer from underground power cable to the surrounding area, thus reduced the temperature of core conductor and restrain the thermal failure during operation [12–14]. Generally, the temperature of the core conductor reduced from 64 ^οC to 48^οC, while the thermal conductivity of the surrounding backfill materials increased from 0.5 Wm^− 1K^− 1 to 1.0 Wm^− 1K^− 1 [12, 13]. On the other hand, the improper dissipation of heat causes the migration of moisture from the vicinity of the power cable and thus, dry zone formation occurred due to loss of moisture causes thermal instability [15–17]. Therefore, the thermal backfill materials should have adequate thermal properties and favorable water retention capacity, which will facilitate the heat transfer easily from the heat source to the surrounding area with minimal moisture migration [18, 19]. To mainatian the long-term stability of underground power cable system, the compressive strength and thermal conductivity should be greater than 0.5 MPa and 0.83 W/m^− 1K^− 1 respectively with favorable hydrological characteristics [2].

The clay soils (such as bentonite) have high water retention capacity but low thermal conductivity and strength whereas; the cohesionless materials (sand, fly ash and graphite) have higher thermal conductivity and strength than bentonite but low water retention capacity [20, 21]. The addition of bentonite promotes the water holding capacity, mechanical and thermophysical properties of sand and fly ash. Therefore, previous researchers reported that a mixture of bentonite/clay-based backfill material for various similar geothermal structures such as ground air heat exchanger (GAHE), high-level nuclear waste repository (HLWR) and ground source heat pump (GSHP) might be promising buffer and backfill material; due to its better performance over pure bentonite/clay with respect to heat storage-releasing abilities, swelling, water retention and mechanical properties [22–25]. Wang et al. [22] reported that mixture of sand and bentonite as backfill materials of borehole heat exchangers and observed that wet thermal conductivity of bentonite-sand showed higher value than normal sand-clay mixtures and found that the thermal conductivity increased 36.1%-26.7% by adding 10%-12% fine-coarse sand to bentonite. Agrawal et al. [23] studied the thermal performance of locally available wet soil and sand-bentonite mixtures (dry and wet both) for the application of ground air heat exchanger and found that wet sand-bentonite as optimal backfill materials than wet soil. Xu et al. [24] reported addition of sand to the bentonite increase the thermal conductivity of the mixture and sand content below 38% and 39% should also sufficient to achieve the swelling pressure above 1.0 MPa and the hydraulic conductivity lower than 10^− 12 m/s respectively. Liang et al. [25] studied the thermal and moisture diffusion properties of sand- kaolin mixture for the application of GSHP and observed that the thermal conductivity of sand-kaolin is 2.81 Wm^− 1K^− 1 with 10% water content, which is better than pure sand of thermal conductivity 1.81 Wm^− 1K^− 1. Cho et al. [26, 27] have studied the thermal conductivity of bentonite-sand mixes and found that the addition of sand with bentonite increases the thermal conductivity of mixtures at different γ_d and w. Yu et al. [28] have examined thermal conductivity of sand-kaolin mixture at varying clay contents, γ_d and w and, the results confirm that thermal conductivity of the mixture increases with an increase of γ_d, w, quartz content (q) and sand content (f_s). Zhou et al. [29] 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 thermal conductivity increases exponentially with increasing volumetric water content (θ) and subsequently decreases with increasing peat-sand ratios. These studies also claim that volumetric heat capcity linearly increases with w and significantly affected by w rather than peat-sand ratios and γ_d. Moreover, the thermal diffusivity of peat-sand mixtures showed initially increasing trend, reaching a plateau and then exhibiting decreasing trend with further increasing of w, this water content is known as threshold water content (TWC) [23]. Moreover, the peak value of thermal diffusivity was found to be increased with γ_d and f_s in the peat-sand mixtures and observed lowest and highest value for peat and sand respectively, the similar observations also reported by Arkhangelskaya and Luckyashchenko [30, 31]. Chen et al. [32] have studied the thermal conductivity of bentonite added graphene at different γ_d ranging from 1.4 gm/cm³ to 1.9 gm/cm³ with the variation of graphene oxide content from 0–50%. It was found that thermal conductivity increases from 11.94 Wm^− 1K^− 1 to 21.66 Wm^− 1K^− 1 by adding 50% graphene oxide to the bentonite at w = 10%. Peng et al. [33] have also examined λ of bentonite-graphite mixtures, when the graphite content was in the order of 0–20%, λ increased from 0.534 Wm^− 1K^− 1 to 1.386 Wm^− 1K^− 1 at a void ratio (e) = 0.84 and w = 10%. However, these studies also revealed that thermal conductivity of bentonite-graphite/geophene oxide mixtures significantly decreased with small reduction in moisture content; hence it threaten the thermal stability of backfill materials [34]. Kolay and Singh [16] studied thermal conductivity of black cotton soil-fly ash mixture based thermal backfills at varying dry density (γ_d) and water content (w) and reported that the thermal conductivity black cotton soil increasing fly ash content, γ_d and w. Wan et al. [35] measured the thermal conductivity of mixtures of iron tailing and losses (0%-100%, by weight) and reported the highest thermal conductivity for the mixture of 30% losses with 70% iron tailing. Do et al. [36] studied the thermal conductivity of controlled low strength materials (CSLM) consists of cement (88 kg/m³), fly ash (264–265 kg/m³) and water (483 kg /m³) with varying proportions of excavated soil (0–40% by weight) with pond ash (60–100% by weight). It was reported that the thermal conductivity decreases linearly with decrease in saturation and increases with increasing the amount of pond ash into the excavated soil of CSLM. Lee and Shang [37] studied the thermal conductivity of compacted mine tailing-fly ash mixture and reported that compacted specimen under the optimum water content leads to higher thermal conductivity. Fall et al. [38] have suggested that the bentonite-paste tailing as engineering barrier material for mine waste containment facilities. A significant decrease in hydraulic conductivity was observed due to reduction of voids, while bentonite of 4%-8% mixed with paste tailing.

Moreover, several researchers did a review on the thermal conductivity models for the unsaturated soil. These studied conclude that the thermal conductivity of rock-soil were governed by the factors including the mineralogy, particle size and shape, grain size distribution, dry density, water content, porosity (n), quartz content (q) and sand content (f_s) [39, 40]. Based these controlling factors, several thermal conductivity empirical models of geomaterials have been developed via regression analysis of experimental data of thermal conductivity for geomaterials [41–49]. Kersten [41] proposed an empirical relationship between λ, w and γ_d for different soil types ranging from sand-clay-loam. Campbell [42] 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 λ. Rao and Singh [43] established a relationship between thermal resistivity and γ_d incorporating w based on laboratory experiments; further, λ was derived according to the reciprocal correlation between thermal conductivity and resistivity. Johansen [44] 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 [44] has further studied the effects of soil type, γ_d, S_r and mineral component on soil thermal conductivity in a unique manner through λ_n-S_r relationship. This model is only suitable for pure sandy soils on one hand or for fined-grained soils having a degree of saturation above 20% [45]. Cote and Konrad [45] 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 also limited to the soils with mixed compostions like bentonite-sand mixture [46]. Lu et al. [47] 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 exponential function. This model also limited to predicting the thermal conductivities of fine-grained soil and underestimated the thermal condutivties prediction of coarse-grained soils [50]. Nikoosokhan et al. [48] have improved the Cote and Konrad [45] empirical model considering the effect of f_s and γ_d on λ_dry, λ_sat and κ. Tarnawski et al. [49] developed an advanced geometric mean model for predicting the λ of unsaturated soil. Three soil structure-based parameters used in the model, namely, an inter-particle thermal contact resistance factor, the degree of saturation of a 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 [51]. Therefore, Tarnawski et al. [52] 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 fact that higher thermal conductivity of quartz (7.7 Wm^− 1K^− 1) with respect to other minerals (2.2 Wm^− 1K^− 1) [44].

Furthermore, previous studied depict that the capability of storing heat and conducting heat of backfill material 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 refered to as thermophysical parameters [31, 53]. The D simply represent that rate of the spread of heat within a conductive medium. Materials with high thermal diffusivity releases heat rapidly in the vicinity of heat source or power cable and reduce the thermal stress on power cable [54]. For the perspective of safe, long-run and reliable performance of underground power cable systems, the backfill material are required to good heat-releasing capacity for restraining the moisture migration due improper heat-conduction. Thus, understanding the variation of thermophysical properties are crucial for a proper design of backfill material for a underground power cable systems and geothermal structures [55, 56]. Although, the research has been more focused on the thermal conductivity of bentonite-based backfill materials, there are very few studied were investigated the thermal diffusivity (D) and volumetric heat capacity (C_v). Moreover, the prediction of thermal conductivity limited to the specific and natural soil, very few studied were also explored the accuracy of thermal properties prediction model for the bentonite/clay-based backfill materials [40, 57]. 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. The fly ash is waste material generated from thermal power plant and intentionally tested for checking the potential of their mixture with bentonite for backfill materials. The thermophysical properties variation of backfill materials were measured for against varying dry density (γ_d) and water content (w), using a dual thermal needle probe KD2 Pro [58] at room temperature. Based on the experimental results, the inter-relationship between the thermal conductivity (λ), thermal diffusivity (D) and volumetric heat capacity (C_v) of bentonite-based backfill materials were discussed. The threshold water content (TWC) has been determined from the D-w relationship. TWC has been correlated with plastic limit (PL) and optimum moisture content (OMC). Finally, the efficacy of two selected prediction models for the thermal conductivity was assessed. The best correlation (model) for the data of bentonite based backfill materials (B-F and B-S mixtures) have also been discussed via statistical evaluation.

2.1 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 chemical compositions (% 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 [59].

Table 1

Chemical compositions of fly ash and bentonite
Chemical compositon (%weight)	Fly ash	Bentonite
SiO₂	46.47	52.23
Al₂O₃	27.49	19.06
Fe₂O₃	1.06	2.03
MnO	0.05	0.54
MgO	2.93	1.39
Cao	2.84	1.32
Na₂O	0.56	2.84
K₂O	0.84	1.44
TiO₂	6.58	2.76
P₂O₅	5.20	0.09
SiO₂ + Al₂O₃ + Fe₂O₃	75.02	73.32
Loss on Ignition	6.17	16.36

The particle size distribution [60] of geomaterials are presented in Fig. 1. Based on the particle size distribution (Fig. 1), both sand and fly ash exhibit poorly graded soil. The laboratory experiments were performed on the geomaterials and mixtures of Bentonite-Fly ash (B-F) and Bentonite-Sand (B-S) at different proportions, listed in Table 2.

Table 2

Designation of bentonite-fly ash-sand mixtures
Mix	Bentonite (%)	Fly ash (%)
B80-F20	80	20
B60-F40	60	40
B50-F50	50	50
B30-F70	30	70
Mix	Bentonite (%)	Sand (%)
B80-S20	80	20
B60-S40	60	40
B50-S50	50	50
B30-S70	30	70

The other important physical and geotechnical characteristics of geomaterials, B-F and B-S mixtures, such as particle size distribution, Atterberg limits [61], specific gravity (G_s) [62] and compaction characteristics [63] are 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 [60, 61]. The Maximum Dry Density (MDD) for both B-F and B-S mixtures were increased with increasing in bentonite content up to 30% and further MDD of soil mixes decreased however, the optimum moisture content (OMC) increased with increasing bentonite content (Table 3), the similar observations also reported by previous studied [64].

Table 3

Physical properties and classification of geomaterials and mixes.
Soil Identification	Particle size distribution (%)			Specific Gravity G_s	Liquid limit LL (%)	Plastic Index PI (%)	Soil Classification	Compaction characteristics
	Sand	Silt	Clay					Compaction characteristics
	4.75 − 0.075 mm	0.075 − 0.002 mm	< 0.002mm					MDD^c (gm/cm³)	OMC^d (%)
F	26	74	0	2.07	-	-	Class F^a	1.38	19.66
B	5	31	64	2.71	300	247	CH^b	1.27	37.50
S	100	0	0	2.62	-	-	SP	-	-
B80-F20	11	38	51	2.55	160	116	CH	1 .31	32.00
B60-F40	16	46	38	2.41	130	94	CH	1 .36	26.45
B50-F50	19	44	37	2.35	113	79	CH	1.39	25.10
B30-F70	22	58	20	2.23	80	50	CH	1.43	20.82
B80-S20	24	25	51	2.69	180	134	CH	1.38	32.33
B60-S40	43	17	40	2.67	145	105	CH	1.53	19.88
B50-S50	53	15	32	2.66	120	84	CH	1.63	18.29
B30-S70	72	7	21	2.64	98	66	CH	1.72	16.95
^aASTM (2010) ^bASTM (2008) ^cMaximum Dry Density ^dOptimum Moisture Content

The XRD analysis, shown in Fig. 2, depicts that the Bentonite (B) consists mainly of Montmorilonite mineral, followed by Kaolinite, Illite and Quartz. For Fly ash (F), the peak internsity corresponding to Mullite and Quartz minerals (as shown in Fig. 2), followed by Hematite and Aragonite. The sand mainly consists of inert quartz mineral

2.2 Thermophysical Properties Measurement Procedure

The pre-determined amount of geomaterials was mix with certain amount of water and the mixed sample was placed in an airtight bag for 24 to 48 h to ensure the uniformity in the moisture distribution. Afterward, the specimens of dimension 15×15×4 cm were prepared at a desired dry density (Fig. 3). The soil was filled, in three layers, in to the mold and each layer was undergone through the compaction. The compaction effort was adjusted based on free fall height and weight of the rammer. After compaction, the dry density and moisture content of the sample were measured. The compaction effort was adjusted based on height of free fall and weight of rammer. After compaction, the dry density and moisture content of the sample were measured.

The thermal properties of geomaterials and mixtures were measured using Dual-needle 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 [65, 66]. The thermal properties analyzer consists of a hand-held 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 (see Fig. 3), each having 30 mm long and 1.3 mm in diameter with 6 mm spacing and can measure λ, C_v and D by employing the dual needle heat pulse method. Figure 3 shows the schematic arrangement of SH-1 sensor used for measurement of thermal properties of geomaterials and mixes, the value of thermal properties presented in this study are the average of three readings of the thermal properties of the compacted soil sample. After measurement, the sample was further oven dried 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 [67].

3.1 Thermophysical Properties of Geomaterials

Figure 4 presents the variations of λ and D along with w corresponding to the different γ_d of geomaterials (F, S and B). Figure 4 reflects that λ of geomaterials increases with increasing w and γ_d. The thermal conductivity of increased rapidly for w below 5%, 20% and 45% for sand, fly ash and bentonite respectively. Thereafter beyond this, further increase in water content the thermal conductivity remain unchanged or decreases slowly; this water content is known as critical water content (CWC) [68, 69]. From Fig. 4, it can be noted that S has maximum λ followed by F and B for whole range of w at same γ_d of 1.2 gm/cm³. The similar findings were reported on different textured of forty Canadian soils by [70] and other [43]. Figure 4 also shows that the thermal diffusivity (D = λ/C_v) of the geomaterials have non-linear variations with w and it also showed that D of sand is significantly higher than that of B and F. The thermal diffusivity-water content (D-w) relationships demonstrated that the it has initially increased quickly at lower w and reaches peak at a certain threshold water content (TWC), the thermal diffusivity decreases upon further increases in the soil-water content, the similar trend has obtained by previous researches [56, 71]. The peak value of D of sand reaches to 0.70 mm²/s at TWC = 8%, at γ_d = 1.2 gm/cm³, followed, the peak value of D was found to be nearly 0.44 mm²/s and 0.32 mm²/s at TWC = 10% and 42% for fly ash and bentonite respectively, the similar observation demonstrated by [53]. Arkhangelskaya and Luckyashchenko [54] and Zhao and Si [56] reported that thermal diffusivity of the sand is between 0.30 mm²/s-0.80 mm²/s and 0.90 mm²/s-1.12 mm²/s respectively. Previous studied also depict that saturated light clay and loamy soil have lower thermal diffusivity than sandy soils [54], the similar has been found in this study.

Figure 5 reveals that C_v increases with an increasing w and γ_d for geomaterials. However, no specific trend has observed γ_d for tested range of w. However, C_v value increased with increasing w and observed that C_v of S, F and B was 1.75 MJ/m³K, 2.4 MJ/m³K and 3.5 MJ/m³K at w = 10%, 28% and 53% respectively. The variation of C_v of geomaterials were found in the order of 1.00-1.25 MJ/m³K at dry conditions (w = 0). Similar observations have been reported for former lake Texcoco soils that increase in porosity (decrease in γ_d) causes increase in specific heat capacity [72]. The rise in C_v might be upto 3.2 MJ/m³K at full saturation level for clayey soils have been observed [53, 72, 73]. Moreover, Zhou and Si [56] reported the C_v from 0.6 to 3.65 MJ/m³K for peat and it has observed that C_v strongly influenced by w rather than γ_d, similar trends were also found in this study.

3.2 Thermophysical Properties of Bentonite-fly ash Based Backfill

Figure 6 shows that effect water content and dry density on thermal conductivity and diffusivity of bentonite-fly ash based backfill materials. Figure 6 illustrated that the peak value of D were 0.33–0.36 mm²/s, 0.37–0.43 mm²/s, 0.40–0.47 mm²/s and 0.37–0.45 mm²/s at TWC 37.99%, 27.91%, 24.82% and 20.00% for B80-F20, B60-F40, B50-F50 and B30-F70 respectively. The thermal diffusivity of bentonite-fly ash mixtures have smaller difference at dry condition and it showed relatively larger differences at TWC for the tested ranges of γ_d. The maximum value of thermal conductivity was found to be 1.23 W/mK for B50-F50 mixture (in comparison to the other mixes) at dry density 1.36 gm/cm³ and w = 31%. It has also observed that, the thermal conductivity has increased with increasing fly ash content, water content and dry density. This because of fly ash content in the mixtures lowered the porosity (denser packing) and due to higher thermal conductivity of fly ash (than bentonite) promotes the thermal conductivity of mixtures and vice-versa. The similar observations are reported by previous research works [16, 36] for black cotton soil- fly ash mixture and CSLM respectively.

Figure 7 represents C_v of B-F mixtures with varying amount of w at different range of γ_d. It can be seen that the C_v increases with increasing in w for any value of γ_d. The C_v shows wide range of scatter, with increasing amount of F from 20–70% for any specific value of w and γ_d. The B-F mixtures showed lower C_v than bentonite, this is obious because of that fly ash has lower C_v than bentonite, thus mixtures showed lower C_v (see Fig. 7). Therefore, it can be concluded that B-F mixtures have lower heat storing capacity, but relatively higher heat conduction capacity than bentonite. The maximum values of C_v was found to be 3.4 MJ/m³K at w = 44% for the case of B80-F20 mixture.

3.2 Thermophysical Properties of Bentonite-Sand Based Backfill

From Fig. 8, it can be observed that λ increases with increasing w, for any ratio of B-S mixture, at the tested range of γ_d. It can also be noticed that the variations of λ with w is marginally affcetd by γ_d, if f_s<40% at higher w values however, γ_d have pronounced effect on B-S mixture, if f_s>40%. This might be due to quartz and non-quartz sand have higher thermal conductivity as compared to bentonite or other fine grained soil, thus thermal conductivity has enhanced by adding sand to the bentonite or other soil [48, 57]. The thermal conductivity of B-S mixture reaches the maximum value in the order of 1.6 Wm^− 1K^− 1- 1.8 Wm^− 1K⁻1 with mixing 70% S to B. Furthermore, Fig. 6 depict that D increases with increasing w and γ_d. The similar response was obtained as discussed above, however increasing rate of thermal diffusivity of B-S mixtures are higher than B-F mixtures. The peak value of D were 0.35–0.38 mm²/s, 0.41–0.54 mm²/s, 0.45–0.55 mm²/s and 0.58–0.68 mm²/s at TWC 29.5%, 17.66%, 18.21% and 14.6% for B80-S20, B60-S40, B50-S50 and B30-S70 respectively.

Figure 9 represents the C_v of the 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 variations of C_v with θ is negligibly affcetd by γ_d for any ratio of B-S mixture. It can also be seen that the value of C_v shows very narrow diffrences, with increasing amount of S from 20–70% for any specific value of w. Moreover, Fig. 9 also shows that the variation of C_v of mixtures was in the order of 1.00 MJ/m³K -1.25 MJ/m³K at dry conditions and maximum values observed 3.00 MJ/m³K − 3.40 MJ/m³K at w = 35%-44%. The similar findings were reported for peat-sand mixtures by [56].

3.4 Discusion

There are limited data on volumetric heat capacity and thermal diffusivity of bentonite-based backfill materials. The relationship between these two thermal properties (D and C_v) and thermal conductivity (λ) for bentonite-based materials were discussed in this study. The thermal conductivity of geomaterials and mixtures increases with larger rate upto the TWC, however it can be seen that increasing rate has relatively smaller after the TWC. As such as water has higher thermal conductivity and specific heat than air pores, causes improvement in thermal properties with increase of water content [72]. Moreover, the soil solid has higher thermal conductivity and specific heat than water, hence water film around the particles and grain to grain contact both promote the thermal conductivity at lower water content and the improvement on the thermal conduction is rapid [67, 70]. When w approaches TWC and thereafter the increase in dry density doesnot improved the effective contact area and heat transfer takes place predominately through water, thus thermal conduction increased slowly [53]. The volumetric heat capacity of geomaterials and mixtures increases with w and bentonite content, because of high percentage of bentonite clay in the mixture leads to absorption of more water due to its swelling potential and water retention properties. Although, the contact between the solid particles diminished with increasing of bentonite, due to formation of double diffuse layer, thereby reduced the thermal conductivity of the mixtures [74]. On the other hand, the rate of increase of thermal conductivity with respect to water content is relatively grater than of the volumetric specific heat capacity before TWC, but after TWC, increasing rate of thermal conductivity is relatively lower than the volumetric specific heat capacity [56]. Therefore, due to the combined action of thermal conductivity and volumetric heat capacity of geomaterials and mixtures, the D-w curves showed a decreasing trend after TWC .

Further, the TWC varied with the sand/fly ash content into the bentonite-based backfill materials. It is noted that the TWC of B-F mixtures showed higher value than B-S mixtures. In this study the obtained TWC from D-w curves were correlated with PL and OMC, as shown in Fig. 10. It is noted that OMC and PL exhibit better correlation with TWC with c coefficients of regression equal to 0.97 and 0.96 respectively (Fig. 10). These correlations valid for γ_d less than 1.5 gm/cm³. The Equations obtained from this study can be used as quick estimate of TWC for bentonite-based materials. It help to safe design of the thermal backfill with respect to γ_d and w in the field, to obtained the both peak or safe thermal diffusivity and corresponding thermal conductivity.

Figure 11 shows that average thermal c conductivity of geomaterials and mixtures corresponding to the TWC. Figure 11 also depict that bentonite-based like bentonite-fly ash and bentonite-sand mixtures were promising thermal backfill materials with thermal conductivity values higher than 0.8 Wm^− 1K^− 1 according to [2]. However, the compressive strength, water retention capacity and swelling potential need to measured in the laboratory while applied in the underground power cable application.

4.1 Kersten [41] Model

Kersten [41] has measured thermal conductivity of different soils such as sand, gravel, sandy loam, clay, crushed rock, organic soil, etc. to develop an empirical equations, as mentioned in Eqs. (1) and (2).

For silty and clayey soils;

$$\lambda =0.1442\left( {0.9\log w - 0.2} \right){.10^{0.6243{\gamma _d}}}$$

For sandy soil;

$$\lambda =0.1442\left( {0.7\log w+0.4} \right){.10^{0.6243{\gamma _d}}}$$

where, λ is the thermal conductivity of soils (Wm^− 1K^− 1), w is the water content (%) and γ_d is dry density (gm/cm³). Both the Eqs. (1) and (2) are only valid for w > 0. For intermediate soils i.e., soils having a composition between the silt-clay group and the sandy group, Kersten [41] has suggested an interpolation technique between the respective values obtained by Eq. (1) and Eq. (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. 10a, it can be observed that the Kersten [41] model overestimate the thermal conductivity, when f_s becomes greater than 40% at lower thermal conductivity values. However, the majority of thermal conductivity data for geomaterials and mixes are inside ± 20% error lines. Further, the statistical evaluation of prediction models were assessed using root mean square error (RMSE), mean absolute error (MAE)and R². As indicated in Fig. 12b, the Kersten [41] model reflects somewhat better prediction of λ for B, F and B-F mixes (0.70 < R² < 0.91) having RMSE and MAE ranging from 0.07–0.157 Wm^− 1K^− 1 and 0.09–0.147 Wm^− 1K^− 1, respectively. However, the model shows a poor performance for thermal conductivity of S and B-S mixtures with R² = 0.12 and 0.61 < R² < 0.71, respectively and indicating RMSE and MAE values ranging from 0.198–0.299 Wm^− 1K^− 1 and 0.164–0.285 Wm^− 1K^− 1. Moreover, the bentonite-sand mixtures reflecting large error arising out of overprediction with R² < 0.65, when f_s>40% suffers.

4.2 Nikoosokhan et al. [48] Model

Johansen [44] 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:

$$\lambda =\left( {{\lambda _{sat}} - {\lambda _{dry}}} \right){\lambda _n}+{\lambda _{dry}}$$

where, λ_dry and λ_sat are the thermal conductivity of dry and saturated soils (W/mK) respectively. Based on Johansen [44] normalized λ modeltheory, Nikoosokhan et al. [43] have improved the Cote and Konrad [45] model accounting sand content and dry density of soil in empirical equation.

$$\lambda =\left[ {\left( {0.53{f_s}+0.1{\gamma _d}} \right) - \left( {0.087{f_s}+0.019{\gamma _d}} \right)} \right]\left( {\frac{{\kappa {S_r}}}{{1+\left( {\kappa - 1} \right){S_r}}}} \right)+\left( {0.087{f_s}+0.019{\gamma _d}} \right)$$

where, κ were calculated by following equation:

$$\kappa =4.4{f_s}+0.4$$

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 gm/cm³ − 2.0 gm/cm³, respectively.

Figure 13a presents the predicted results of λ, using the Nikoosokhan et al. [39] model, versus the experimetally measured λ for the wide range of w. The values of RMSE, MAE and R² for geomaterials and mixes have been presented in Fig. 13b. It can be observed that the Nikoosokhan et al. [48] model gives better prediction of λ over the wide range of w and γ_d than the Kersten [41] model for all geomaterials and mixtures with R² > 0.70 except fly ash (R² = 0.54). The scattering of data for mixtures is larger, however the tendency in the varaiation of λ with w, γ_d and f_S is similar to previous reported data [57, 75, 76]. The RMSE and MAE ranging from 0.105–0.185 Wm^− 1K^− 1 and 0.09–0.166 Wm^− 1K^− 1 for F and B-F mixes, respectively. This model overestimated the thermal conductivity (corresponding data at lower w) more than 20% since, RMSE and MAE value are ranging from 0.123–0.212 and 0.102–0.144, repectively, when f_s>50% in B-S mixtures.

The statistical comparison of λ-model showed that the Nikoosokhan et al. [48] model is the best performing model, which has been improved over the Cote and Konrad [45] model by incorporating κ, λ_dry, λ_sat and f_s in Eqs. 4 and 5. However, the accuracy in the predictions of λ is strongly influenced by the volume fraction of quartz, specific soil-group, particle shape and size, water content and dry density as discussed in previous section. Therefore, further studies 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 [41] model is most appropriate for B-F mixtures and whereas, Nikoosokhan et al. [48] model predicted well for B-S mixtures.

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) corresponding to a particular γ_d and w thermal properties of bentonite based-thermal backfill materials were explored. Based on the experimental results with the thermo-physical properties geomaterials and mixtures are influenced by many factors, such as soil compositions, dry density, water conetnt, particle size distribution and so on. More precisely, the folowing conclusions can be made:

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 Wm^-1K^-1 with mixing 70% S to B, whereas, for B-F mixtures, maximum thermal conductivity was found to be nearly 1.10 Wm^-1K^-1 − 1.23 Wm^-1K^-1 at 50% addition of F with bentonite. Therefore, bentonite-based like bentonite-fly ash and bentonite-sand mixtures were promosing thermal backfill materials with thermal conductivity values higher than 0.8 Wm^-1K^-1.
Thermal diffusivity (D) increases with increasing w upto TWC, thereafter further increase of w content causes decrease in D. It has also observed the TWC values differed for different bentonite-based backfill materials and it has influenced by the content of sand/fly ash into bentonite.
The peak value of D were 0.33–0.36 mm²/s, 0.37–0.43 mm²/s, 0.40–0.47 mm²/s and 0.37–0.45 mm²/s at TWC 37.99%, 27.91%, 24.82% and 20.00% for B80-F20, B60-F40, B50-F50 and B30-F70 respectively. The peak value of D were 0.35–0.38 mm²/s, 0.41–0.54 mm²/s, 0.45–0.55 mm²/s and 0.58–0.68 mm²/s 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 were found to be in the order of 1.00-1.25 MJ/m³K 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/m³K, 2.4 MJ/m³K and 3.5 MJ/m³K at w = 10%, 28% and 53% respectively. The B-F mixtures showed lower C_v than bentonite, this is obvious because of that fly ash has lower C_v than bentonite. The maximum values of C_v was found to be 3.4 MJ/m³K at w = 44% for the case of B80-F20 mixture. Moreover, the C_v of B-S mixtures was in the order of 1.00 MJ/m³K -1.25 MJ/m³K at dry conditions and maximum values observed 3.00 MJ/m³K − 3.40 MJ/m³K at w = 35%-44%. However, C_v are more sensitive to an increase in w than γ_d have been observed.
It is noted that OMC and PL exhibit better correlation with TWC with coefficients of regression equal to 0.97 and 0.96 respectively. These correlations valid for γ_d less than 1.5 gm/cm³. The Equations obtained from this study can be used as quick estimate of TWC and corresponding thermophysical properties for bentonite-based materials.
Further, the thermal conductivity prediction models were selected and statistically evaluated with respect to experimental results and, it was found that the Kertsen [41] and Nikoosokhan et al. [48] model are the best suitable model to predicted λ for B-F mixes and B-S mixes, respectively.

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.

Acknowledgements

The authors are very thankful to Prof. Sreedeep S., Indian Institute of Technology Guwahati, Assam and also the Indian Institute of Technology Guwahati, Assam, for providing the facilities to conduct the experiments and their kind support during this study.

Declaration of competing interest

The authors declare that there are no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Thermophysical Properties of Bentonite-sand/fly ash Based Backfill Materials for Underground Power Cable

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Abstract

Figures

1 Introduction

2 Materials And Methods

2.1 Physical Properties, Chemical and Mineralogical Composition of Geomaterials

2.2 Thermophysical Properties Measurement Procedure

3 Experimental Results And Discussion

3.1 Thermophysical Properties of Geomaterials

3.2 Thermophysical Properties of Bentonite-fly ash Based Backfill

3.2 Thermophysical Properties of Bentonite-Sand Based Backfill

3.4 Discusion

4. Evaluation Of Thermal Conductivity Models Against Experiemntal Results

4.1 Kersten [41] Model

4.2 Nikoosokhan et al. [48] Model

5. Summary And Conclusions

Declarations

References

Additional Declarations

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