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Relationship between thermal conductivity and soil–water characteristic curve of pure bentonite-based grout
International Journal of Heat and Mass Transfer 84 (2015) 1049–1055
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Relationship between thermal conductivity and soil–water characteristic curve of pure bentonite-based grout Daehoon Kim, Gyoungman Kim, Hwanjo Baek ⇑ Department of Energy and Resources Engineering, Kangwon National University, Chuncheon, Republic of Korea
a r t i c l e
i n f o
Article history: Received 9 May 2014 Received in revised form 12 December 2014 Accepted 20 January 2015
Keywords: Bentonite–sand grout Thermal conductivity Soil–water characteristic curve Air-entry value Geothermal heat exchanger
a b s t r a c t The relationship between the soil–water characteristic curve (SWCC) and thermal conductivity of pure bentonite and bentonite–sand grouts used as backfilling materials in ground heat exchangers was investigated in a laboratory experiment. The mix proportions utilized in this study were bentonite to 20% and 30% of the total weight, adding quartzite sand to 30% and 50% of the total weight (bentonite + water). Mixed grout specimens were prepared in rectangular parallelepiped shapes. The thermal conductivity, volumetric water content and matric suction of unsaturated specimens were measured as the saturated specimens were slowly dried at room temperature until there was little change in the measured values. The matric suction and thermal conductivity showed a bilinear relationship, with a breaking point identifying the air-entry value (AEV) and the SWCC describing the relationship between the matric suction and the volumetric water content (VWC). As the matric suction slowly increased to the AEV, the VWC of the specimens decreased, whereas the thermal conductivity increased; then, beyond the AEV, it rapidly decreased again. That is, as the specimens dried out, attaining the maximum at the AEV, their thermal conductivity decreased. The thermal conductivity and the VWC showed a parabolic relationship with the maximum thermal conductivity value at around the VWC corresponding to the AEV of each specimen. Revised empirical equations representing the relationship between these two parameters were suggested for prediction of the thermal characteristics of bentonite-based grout in geothermal heat pump applications. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Due to environmental and energy-supply issues such as global warming and fossil-fuel depletion, geothermal energy is seeing increasing use as a sustainable resource. In this context, groundsource heat pump (GSHP) systems and geothermal heat pump (GHP) systems have been adapted for geothermal energy use. These are heating and cooling systems that provide residential and commercial buildings with heat in winter and cooling in summer. This technology relies on the fact that, at depth, the Earth has a relatively constant temperature, warmer than the air in winter and cooler than the air in summer. GHP systems exchange heat with the ground, often by means of vertical closed-loop geothermal systems such as a vertical U-tube borehole heat exchanger [1]. In this system, the borehole is backfilled with grouting materials, which provide a heat-transfer medium between the heat exchanger and the surrounding ground (e.g. soils or rock) and also ⇑ Corresponding author. E-mail addresses: [email protected] (D. Kim), [email protected] (G. Kim), [email protected] (H. Baek). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.01.091 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
controls groundwater movement to prevent contamination of water. Granular bentonite-water grouts are commonly used in GHP systems [2,3] as well as in other applications such as radioactive waste confinement [4]. Grouting materials’ thermal conductivity is one of the key properties of GSHP systems. Bentonite, for example, has a relatively low thermal conductivity that typically ranges from 0.65 to 0.90 W/mK under the saturated condition [5]. Because the low thermal conductivity of bentonite makes it unsuitable as a filler material for GSHP systems, some additives need to be mixed into bentonite grouts to improve it in them respect. In this context, the thermal characteristics of pure bentonite (bentonite only) and bentonite– sand grouts, in their varying mixed proportions, have been studied under both saturated and dried conditions [5–9]. The results indicated that adding sand as an additive improves the thermal conductivity of grouts, and that grouts under saturated conditions showed much higher thermal conductivity than those under dried conditions. Thus, the thermal conductivity of grouts varies with their mix proportions and water contents. The ground in which the borehole is dug is not completely saturated or dried; rather, those qualities vary with borehole depth
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and in situ ground-water conditions. As in situ ground-water conditions changes, the water condition of the ground varies accordingly. This variation can affect the water contents and thermal conductivity of grouting materials. Due to the fact that direct measurement of grouting materials’ thermal properties is practically impossible after installation, prior characterization of those properties for varying water contents is key to the performance prediction and efficiency maintenance of GHP systems [9]. However, the effects of varying water contents on the thermal properties of bentonite-based grout for GSHP systems under unsaturated conditions, have only rarely been investigated. Kim et al. [10] found a parabolic relationship between the thermal conductivity and volumetric water content (VWC) of bentonite grouts, [11–14], unlike the other studies, which showed that the thermal conductivity only decreased with decreasing VWC. Kim et al. [10] also speculated that this parabolic relationship might be related to the soil– water characteristic curve (SWCC). The SWCC is a conceptual and interpretative tool by which the behavior of unsaturated soils can be understood [15]; it defines the relationship between matric suction and VWC or the degree of saturation [16]. In this study, the effects of varying VWC and matric suction on the thermal conductivity of bentonite and bentonite–sand grouts were investigated. Also, the SWCC of the bentonite and bentonite–sand grouts was identified to explain the phenomenon of the parabolic relationship between the VWC and thermal conductivity.
largest pores, which are then occupied by air. The matric suction required for removing the water from the largest pores is known as the air entry value (AEV), and the area between the zero matric suction and the AEV is referred to as the saturated zone [18]. Beyond the AEV, the increase of matric suction causes a rapid rate of VWC loss until the residual water content is reached. Matric suction corresponding to residual water content is referred to as residual suction, by which the desaturation ends, and the water begins to be held in the soil by adsorption forces. The area between the AEV and the matric suction in which the residual condition is reached is called the transition zone. In the residual zone, the curve exhibits an asymptotic line at a low degree of saturation. Water still exists, but considerable matric suction is needed to drain even a small amount of water from the pores [19]. The pore water within unsaturated soils exists in three forms (Fig. 1): (a) bulk water within those void spaces that are completely flooded, (b) meniscus water surrounding all inter-particle contact points that are not covered by bulk water, and (c) adsorbed water, which, tightly bound to the soil particles, acts as parts of the soil skeleton. The relationship between the SWCC and the porewater forms is shown in Fig. 1 [20]. Fig 2 shows a typical SWCC, which depends on the size and arrangement of the pores, for three different types of soil. The AEV generally increases not only with the plasticity of the soils but with decreasing grain-size. Other factors such as the stress history also affect the shape of the SWCC [18,21].
2. Soil–water characteristic curve Fig. 1 shows a typical soil–water characteristic curve (SWCC), which is an important tool for evaluation of the engineering behaviors of unsaturated soils. The SWCC is generally defined as the relationship between the VWC and the matric suction of the soil. The VWC is defined as the ratio between the volume of water and the total volume of the specimen. The soil matric suction, one of the most important parameters of unsaturated soils [17], is defined as the difference between the pore-air pressure and the pore-water pressure. The SWCC consists of three zones: the saturated zone, the transition zone, and the residual zone. In the saturated zone, almost all the soil pores are filled with water. The pore-water is in tension in this zone; however, the soil, owing to capillary forces, remains essentially saturated. When matric suction is applied to the water in the soil pores, the water is first drained from the
3. Materials and methods 3.1. Grouting materials Bentonite is an absorbent aluminium phyllosilicate, essentially impure clay consisting mostly of montmorillonite [22]. VolclayÒ
Fig. 2. Typical SWCC for different types of soil [18].
Table 1 Physical properties of VolclayÒ bentonite. Permeability (cm/s) 51 10
7
Swelling (ml/g)
Montmorillonite content (%)
Thermal conductivity (W/ mK)
Specific gravity
12.5
590
0.74
2.60
Table 2 Chemical composition of quartzite sand. Chemical SiO2 Al2O3 Fe2O3 K2O TiO2 CaO composition (wt%) Fig. 1. Soil–water characteristic curve showing zones of unsaturation.
Quartzite sand
99.6 0.1
0.03
–
MgO Ig-loss Total
0.02 Trace Trace 0.1
99.85
D. Kim et al. / International Journal of Heat and Mass Transfer 84 (2015) 1049–1055
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Table 3 Mix proportions and properties of grout. Specimen No.
Bentonite (wt%)
Quartzite sand (wt%)
Water (wt%)
Dry unit weight (kN/m3)
Void ratio
Water content (%)
BN BN BN BN BN BN
20.0 15.4 13.3 30.0 23.1 20.0
0 23.1 33.3 0 23.1 33.3
80.0 61.5 53.3 70.0 53.8 46.6
2.16 4.80 6.17 3.43 5.88 7.25
10.80 4.37 3.16 6.53 3.35 2.54
400 160 114 233 117 87
20-0 20-30 20-50 30-0 30-30 30-50
bentonite, used in this study, is a 20% solid, polymer-free, singlecomponent commercial sodium bentonite available in powdered form. It is widely employed in geothermal heat pump installations and for geophysical site investigation purposes. The physical properties of VolclayÒ bentonite are listed in Table 1. As noted above, the thermal conductivity of pure-bentonite grout is markedly lower. Grout materials are required to have thermal conductivities similar to that of geologic formations (1.7–2.1 W/mK) in the ground [23]. In this study, quartzite sand was used as an additive to improve the thermal conductivity of the grout. Quartzite sand has a relatively high thermal conductivity that typically ranges from 2.5 to 3.1 W/mK depending on dry density [24]. Quartzite sand is artificially produced by crushing and milling silica rocks such as quartz dikes or quartzites, and its chemical composition is listed in Table 2. 3.2. Experimental methods The mix proportions of grout applied in this study were those used in a previous study [10], that is, bentonite to 20% and 30% of the total weight (bentonite + water), adding quartzite sand to 30% and 50% of the total weight. As the amount of quartzite sand increased, the total unit weight increased, whereas the void ratio and the water content decreased (Table 3). Specimens were formed by pouring mixed grout into rectangular parallelepiped molds (22 cm 6.5 cm 4 cm). A 5TE sensor and a MPS-1 sensor (both from Decagon Devices, Ltd.) were installed at the center of each specimen to measure the VWC and matric suction, respectively. After allowing for free swelling under the sealed condition for 24 h, the VWC, thermal conductivity and matric suction were measured at room temperature (20 ± 2 °C) for 14 days until the measured values showed little change. A Quick Thermal conductivity Meter (QTM-500, Kyoto Electronics Manufacturing Co., Ltd.) was used to measure thermal conductivity. QTM-500 is a probe-type device, which consists of single heater wire and thermocouple. While other two sensors measure the properties of the surrounding soil mass at the center of the specimen, this device measures the thermal conductivity by sticking sensor probe on the surface of the specimen. A possible mismatch
Fig. 4. Variation of (a) volumetric water content with time, (b) matric suction with time, and (c) thermal conductivity with time.
among the measured properties was assumed to be negligible considering the specimen thickness (see Fig. 3).
Fig. 3. Experimental set-up: (a) 5TE and MPS-1 sensors, (b) QTM-500.
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4. Results and discussion 4.1. Changes in VWC, matric suction and thermal conductivity with time Fig 4(a) plots the change in VWC of the specimens with time. As the specimens were becoming drier at room temperature, the VWC decreased nonlinearly. The VWC of BN20-0, BN20-30 and BN20-50 rapidly decreased at the elapsed time of around 160, 130 and 100 h, respectively. Also, BN30-0, BN30-30 and BN30-50 rapidly decreased at the elapsed time of around 140, 110 and 90 h, respectively. Thereafter, the VWC of all of the specimens converged at the elapsed time of around 200 h. Fig 4(b) plots the change in the matric suction of the specimens with time. As the specimens were becoming drier, the matric suction increased nonlinearly. The matric suction of all of the specimens increased rapidly at the elapsed time of around 50 h, finally converging at the elapsed time of around 200 h. The MPS-1 sensor reportedly measures matric suction from about 10–500 kPa [25]. However, in the present study, matric suction values above
500 kPa were measured using the same sensor. In fact, in a recent study, the MPS-1 delivered not only readings up to 1.2 MPa but also reliable results up to a matric suction of 600 kPa [26]. Hence, matric suction values up to 600 kPa were used in this study. Finally, Fig. 4(c) shows the change in the thermal conductivity of the specimens with time. The thermal conductivity of all specimens initially increased and, after reaching the maximum at a certain elapsed time, began to rapidly decrease. Thereafter, the thermal conductivity of all of the specimens was converged at the elapsed time of around 200 h. The elapsed time at which each specimen reached the maximum thermal conductivity was equal to the time at which the VWC of each specimen started to rapidly decrease. As the amounts of bentonite and quartzite sand of the specimens increased, the elapsed time at which the change in their VWC or thermal conductivity occurred was shorter. The results on the changes of VWC and thermal conductivity with time were similar to those of a previous study [10]. However, there was a minor difference in the elapsed time when the specimens’ VWC and thermal conductivity changed, presumably as a result of room humidity differences during the testing.
Fig. 5. SWCC of the specimens: (a) BN20, (b) BN30.
Fig. 6. Relationship between matric suction and thermal conductivity of the specimens: (a) BN-20, (b) BN-30.
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D. Kim et al. / International Journal of Heat and Mass Transfer 84 (2015) 1049–1055 Table 4 Equations for fitted lines obtained from bilinear regression of experimental data. Sample No.
(a) y = VWC x = Matric suction
BN20-0
y= y= y= y= y= y= y= y= y= y= y= y=
BN20-30 BN20-50 BN30-0 BN30-30 BN30-50
0.08ln(x) + 1.02 0.70ln(x) + 4.91 0.08ln(x) + 0.94 0.48ln(x) + 3.32 0.05ln(x) + 0.72 0.40ln(x) + 2.76 0.07ln(x) + 0.93 0.60ln(x) + 4.10 0.07ln(x) + 0.83 0.55ln(x) + 3.68 0.03ln(x) + 0.58 0.45ln(x) + 2.98
(<500 kPa) (>500 kPa) (<400 kPa) (>400 kPa) (<300 kPa) (>300 kPa) (<400 kPa) (>400 kPa) (<300 kPa) (>300 kPa) (<250 kPa) (>250 kPa)
R2
(b) y = Thermal conductivity x = Matric suction
R2
0.94 0.99 0.96 0.95 0.81 0.99 0.98 0.99 0.91 0.99 0.81 0.97
y = 0.04ln(x) + 0.70 (<500 kPa) y = 0.82ln(x) + 6.09 (>500 kPa) y = 0.17ln(x) + 0.64 (<400 kPa) y = 1.74ln(x) + 12.18 (>400 kPa) y = 0.17ln(x) + 0.87 (<300 kPa) y = 1.06ln(x) + 7.91 (>300 kPa) y = 0.08ln(x) + 0.63 (<400 kPa) y = 0.61ln(x) + 4.77 (>400 kPa) y = 0.16ln(x) + 0.62 (<300 kPa) y = 1.36ln(x) + 9.57 (>300 kPa) y = 0.16ln(x) + 1.01 (<250 kPa) y = 1.57ln(x) + 10.82 (>250 kPa)
0.87 0.86 0.97 0.90 0.87 0.96 0.85 0.97 0.95 0.95 0.74 0.94
4.2. Relationship between matric suction and thermal conductivity of bentonite–sand specimens Fig 5 shows the SWCC of the specimens, in which bilinear patterns are clearly depicted. As the VWC of the specimen decreased, the matric suction also steadily decreased. The point of intersection of the two straight lines is the AEV, which ranges from 300 to 500 kPa. The AEV decreased as the amount of bentonite and quartzite sand increased. Fig 6 shows the relationship between matric suction and thermal conductivity. Again, a bilinear pattern was observed for each specimen with a break point, closely corresponding to AEV in Fig. 5. As the specimen gradually dried up, both thermal conductivity and matric suction of the specimen simultaneously increased. However, after passing the break point, the thermal conductivity rapidly decreased. Table 4 lists the equations for fitted lines obtained from bilinear regression of each specimen’ experimental data in Figs. 5 and 6. The AEV separately calculated by the bilinear equations in Table 4 matched well to each other within ±50 kPa, as shown in Fig. 7. Table 5 lists the maximum thermal conductivity and corresponding VWC of each specimen calculated by the bilinear equations. The maximum thermal conductivity value of each specimen increased with increasing bentonite and quartzite sand contents, whereas the corresponding VWC decreased. As the soil moves from a saturated state to drier conditions, the distribution of soil, water, and air phases change as the stress state changes. The relationship among these phases takes on different forms, and, thereby, influences the engineering properties of unsaturated soils [27]. Also, the interactions between these phases affect the change in the thermal conductivity of soils [28,29]. The wetted area of contact between the soil particles decreases with increasing soil matric suction [15]; and with this decrease, the thermal conductivity of soil decreases [28]. Water is retained within the pores of soils under physicochemical influences such as capillary force acting at the water–air interface and the attraction of water molecules by the soil-particle surface force associated with van der Waals’ attraction, electrical double-layer repulsion, cementation, and other mechanisms [21] (Fig. 8). The capillary force is affected by pore size, and the surface force is affected by the surface properties or surface area of the soils. Clays such as bentonite are superior to other types of soils in the surface force [30]. Water in soil, in the forms of bulk water, meniscus water and adsorbed water depicted in Fig. 1, affects the deformational behavior of soil. The meniscus water that collects at the particle contacts increases the inter-granular force acting on the soil particles, thus increasing the stiffness of the soil skeleton. On the other hand, the bulk water filling the void spaces induces not only an increase in the stiffness of the soil skeleton but also a decrease in the volume of the soil mass, due to slippages between soil particles at the contact points. The influence of bulk water is equal to the effect of neg-
Fig. 7. Relationship of each AEV calculated by bilinear equations in Table 4.
Table 5 Maximum thermal conductivity calculated by bilinear equations in Table 4 and corresponding VWC for each specimen. Sample No.
VWC (m3/m3)
Thermal conductivity (W/mK)
BN20-0 BN20-30 BN20-50 BN30-0 BN30-30 BN30-50
0.54 0.47 0.43 0.50 0.44 0.40
0.94 1.65 1.84 1.10 1.54 1.89
ative pore water pressure [31]. Therefore, as the matric suction of the specimens increases with decreasing VWC, the soil particles adhere closely to each other by a complex interaction between the surface force of bentonite, quartzite sand and the capillary force occurring along the water–air interface (Fig. 8). That is, up to the AEV and within the saturated zone of the SWCC, the thermal conductivity of the specimens gradually increases, because the bentonite and quartzite sand adhere closely to each other by the effect of bulk water. Within the saturated zone, the water in the soil pores is not drained up to the AEV, though the VWC gradually decreases. Beyond the AEV, the VWC rapidly decreases within the transition zone of the SWCC; the thermal conductivity of the specimens also rapidly decreases with increasing matric suction, because water is drained from the pore spaces, which are then filled with air. Within the transition zone, the effect of bulk water
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4.3. Relationship between thermal conductivity and volumetric water content of bentonite–sand specimens
Fig. 8. Water held by capillary forces and surface forces [34].
disappears and that of meniscus water starts to be applied. Air has a much lower thermal conductivity than water: 0.025 W/mK versus 0.591 W/mK, respectively [32]; hence, as the amount of air in the pore spaces further increases, the thermal conductivity of the specimens decreases. In case of non-plastic soils, any increase in thermal conductivity up to the AEV does not occur. Rather, as the water content decreases, the thermal conductivity also decreases in logarithmic scale [33]. The increase in thermal conductivity observed in the present investigation, up to the AEV and within the saturated zone of the SWCC, can be attributed to the effect of bulk water caused by the substantial surface force of bentonite.
Fig 9 shows the relationship between the thermal conductivity and the VWC of the specimens obtained in the present investigation, combined with the data from the previous study [10]. Each specimen’s trend curve is in a parabolic relationship with the maximum thermal conductivity value. As the amounts of bentonite and quartzite sand decreased, the trend curve showed a gentler slope, and the VWC corresponding to the maximum thermal conductivity value increased. Also, as the amounts of bentonite and quartzite sand increased, the value of maximum thermal conductivity increased. Table 6 lists the regression equations for the specimens’ thermal conductivity and VWC with the determination coefficient, R2. Also listed in Table 6 are the maximum value of thermal conductivity and the corresponding VWC for each specimen, determined from the regression equation. The regression equations were determined from the combined test results of both present and previous studies. Also, each VWC calculated by the regression equation in Table 6 was almost equal to that in Table 4, whereas there were some differences in thermal conductivity. However, it was apparent that the maximum thermal conductivity value of each specimen increased with increasing bentonite and quartzite sand contents, whereas the corresponding VWC decreased. Also, it could be seen, in Table 5, that the VWC corresponding to the maximum thermal conductivity value of each specimen was closely related to the AEV of the SWCC, via the VWC corresponding to the AEV of the SWCC in Table 4. This means that as the specimens dried
Fig. 9. Relationship between the thermal conductivity and VWC: (a) BN20, (b) BN30.
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D. Kim et al. / International Journal of Heat and Mass Transfer 84 (2015) 1049–1055 Table 6 Regression equation with the maximum thermal conductivity and corresponding VWC. Sample No. BN20-0 BN20-30 BN20-50 BN30-0 BN30-30 BN30-50
Regression equation y= y= y= y= y= y=
2
2.64x + 3.06x + 0.04 6.53x2 + 6.14x + 0.09 7.94x2 + 6.78x + 0.18 3.75x2 + 3.79x + 0.10 8.37x2 + 7.03x + 0.08 10.66x2 + 8.24x + 0.09
R2
Maximum thermal conductivity (W/mK)
Corresponding VWC (m3/m3)
0.97 0.92 0.92 0.94 0.93 0.94
0.93 1.53 1.63 1.06 1.56 1.68
0.58 0.47 0.43 0.51 0.42 0.39
out after reaching the maximum at the VWC corresponding to the AEV of each specimen, their thermal conductivity decreased. 5. Conclusions In this study, the relationship between thermal conductivity and SWCC of pure bentonite and bentonite–sand grouts for use as backfilling materials in geothermal systems was investigated. Specimens of different mix proportions were tested to measure the VWC, matric suction and thermal conductivity under unsaturated conditions. In case of the SWCC, it was observed that the AEV decreased with increasing bentonite and quartzite sand contents. The shape of the SWCC of the specimens also depended on the quartzite sand and bentonite contents, because the gradient of the SWCC in the low matric suction range up to the AEV decreased with increasing bentonite and quartzite sand contents. The relationship between the matric suction and the thermal conductivity of the expansive soil (in the forms of the pure bentonite and bentonite–sand grouts) showed a bilinear relationship with the breaking point identifying the AEV as well as their SWCC. As the matric suction increased to the AEV, the thermal conductivity of the specimens increased by the effect of bulk water, thereby inducing a decrease in the volume of the soil mass, and thereafter decreasing again. Also, at the AEV, the maximum thermal conductivity increased with increasing bentonite and quartzite sand contents. The trend curve between the thermal conductivity and the VWC of the specimens showed a parabolic relationship with the maximum thermal conductivity value at the VWC corresponding to the AEV of each specimen. The revised empirical equations representing the relationship between the thermal conductivity and VWC were suggested by the results both of this study and a previous one. On this basis, the present results are expected to facilitate the construction of geothermal heat pump systems. References [1] H. Esen, M. Inalli, In-situ thermal response test for ground source heat pump system in Elazıg˘, Turkey, Energy Build. 41 (4) (2009) 395–401. [2] F. Eckhart, Grouting Procedures for Ground-source Heat Pump Systems, Ground Source Heat Pump Publications, Oklahoma State University, US, 1991. [3] V. Trillat-Berdal, B. Souyri, G. Achard, Coupling of geothermal heat pump with thermal solar collectors, Appl. Therm. Eng. 27 (10) (2007) 1750–1755. [4] M. Jobmann, G. Buntebarth, Influence of graphite and quartz addition on the thermal-physical properties of bentonite for sealing heat-generating radioactive waste, Appl. Clay Sci. 44 (3–4) (2009) 206–210. [5] C.P. Remund, J.T. Lund, Thermal enhancement of bentonite grouts for vertical GSHP system, in: ASME, Heat Pump and Refrigeration System-Design Analysis and Applications, vol. 29, 1993, pp. 95–106. [6] M.L. Allan, A. Philippacopoulos, Properties and performance of cement-based grouts for geothermal heat pump application, U.S. Department of Energy, Washington DC, 1999. [7] C.C. Hiller, Grouting for vertical geothermal heat pump systems: engineering design and field procedures manual, International Ground Source Heat Pump Association, Stillwater, Oklahoma, 2000. [8] B.H. Sohn, Thermal conductivity enhancement of bentonite grout using silica sands, in: Proceedings of the Conference of The Society of Air-Conditioning and Refrigerating Engineers of Korea Semiannual, Sarek, Korea, 2006, pp. 713–718.
[9] H.S. Choi, H.P. Choi, C.H. Lee, S.B. Woo, A study on the physical characteristics of grout material for backfilling ground heat exchanger, J. Korean Geotech. Soc. 24 (1) (2008) 37–49. [10] D.H. Kim, G.M. Kim, S.H. Park, H.J. Baek, Changes in the thermal conductivity of bentonite-based grouts with varying volumetric water content, Geosyst. Eng. 16 (4) (2013) 257–264. [11] M.S. Kersten, Thermal properties of soils, Engineering Experiment Station, University of Minnesota, US, 1949. [12] O. Johansen, Thermal conductivity of soils (Ph.D. thesis), Trondheim, Norway, ADA 044002, 1975. [13] G.S. Campbell, Soil Physics with Basic, Elsevier, Amsterdam, 1985. [14] Y.M. Tien, C.A. Chu, W.S. Chuang, The prediction model of thermal conductivity of sand-bentonite based buffer material, in: France Clays in Natural and Engineered Barriers for Radioactive Waste Confinement, 2005, pp. 657. [15] S.K. Vanapalli, D.G. Fredlund, D.E. Pufahl, The influence of soil structure and stress history on the soil–water characteristics of a compacted till, Geotechnique 49 (2) (1999) 143–159. [16] J.M. Tinjum, C.H. Benson, L.R. Blotz, Soil water characteristic curves for compacted clays, ASCE J. Geotech. Geoenviron. Eng. 123 (11) (1997) 1060– 1069. [17] M.A. Tekinsoy, T. Taskiran, C. Kayadelen, One dimensional non-linear consolidation of unsaturated fine grained soils, World Appl. Sci. J. 6 (10) (2009) 1388–1398. [18] D.G. Fredlund, A. Xing, Equations for the soil–water characteristic curve, Can. Geotech. J. 31 (4) (1994) 521–532. [19] Y.M. Purwana, Experimental study on unsaturated direct shear and California bearing ratio tests with suction monitoring on sand-kaolin clay mixtures (Ph.D. thesis), Curtin University, Australia, 2013. [20] S.J. Wheeler, D. Karube, Constitutive modelling, in: Unsaturated soils Proceedings of the First International Conference on Unsaturated Soils, Paris, France, 1996, pp. 1323–1356. [21] N. Lu, W.K. Likos, Unsaturated Soil Mechanics, Wiley, New York, 2004. [22] T. Panahi Osalo, E. Merufinia, M. Esmat Saatlo, Phosphorus removal from aqueous solutions by bentonite: effect of Al2O3 addition, J. Civ. Eng. Urban. 3 (5) (2013) 317–322. [23] C.H. Lee, K.J. Lee, H.S. Choi, H.P. Choi, Characteristics of thermally-enhanced bentonite grouts for geothermal heat exchanger in South Korea, Sci. China Tech. Sci. 53 (2010) 123–128. [24] B.H. Sohn, Predicting the effective thermal conductivity of some sand–water mixtures used for backfilling materials of ground heat exchanger, J. Soc. AirCondition. Refrig. Eng. Korea 20 (9) (2008) 614–623. [25] Decagon devices, Dielectric water potential sensor MPS-1 operator’s manual version 1.0, Inc. 2365 NE Hopkins Court, Pullman, WA 99163, 2008. [26] R. Nolz, G. Kammerer, P. Cepuder, Calibrating soil water potential sensors integrated into a wireless monitoring network, Agric. Water Manage. 116 (1) (2013) 12–20. [27] S.L. Barbour, Nineteenth Canadian geotechnical colloquium: the soil–water characteristic curve: a historical perspective, Can. Geotech. J. 35 (5) (1998) 873–894. [28] A.R. Sepaskhah, L. Boersma, Thermal conductivity of soils as a function of temperature and water content, Soil Sci. Soc. Am. J. 43 (1979) 439–444. [29] S. Lu, T. Ren, Y. Gong, R. Horton, An improved model for predicting soil thermal conductivity from water content at room temperature, Soil Sci. Soc. Am. J. 71 (2007) 8–14. [30] E.G. Kang, Construction of real time monitoring system and infiltration analysis of slope for protecting cultural assets (M.S. thesis), Korea Advanced Institute of Science and Technology, South Korea, 2008. [31] J.G. Chae, B.S. Kim, S.W. Park, S.J. Kato, Effect of suction on unconfined compressive strength in partly saturated soils, KSCE J. Civil Eng. 14 (3) (2010) 281–290. [32] J.H. Cha, S.J. An, M.H. Koo, H.C. Kim, Y.H. Song, M.S. Suh, Effects of porosity and water content on thermal conductivity of soils, J. Korean Soc. Soil Groundwater Environ. 13 (3) (2008) 27–36. [33] S. Lu, T. Ren, Y. Gong, R. Horton, An improved model for predicting soil thermal conductivity from water content at room temperature, Soil Sci. Soc. Am. J. 71 (1) (2007) 8–14. [34] G.L. Guymon, Unsaturated Zone Hydrology, Prentice-hall, 1994.
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Relationship between thermal conductivity and soil–water characteristic curve of pure bentonite-based grout Daehoon Kim, Gyoungman Kim, Hwanjo Baek ⇑ Department of Energy and Resources Engineering, Kangwon National University, Chuncheon, Republic of Korea
a r t i c l e
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Article history: Received 9 May 2014 Received in revised form 12 December 2014 Accepted 20 January 2015
Keywords: Bentonite–sand grout Thermal conductivity Soil–water characteristic curve Air-entry value Geothermal heat exchanger
a b s t r a c t The relationship between the soil–water characteristic curve (SWCC) and thermal conductivity of pure bentonite and bentonite–sand grouts used as backfilling materials in ground heat exchangers was investigated in a laboratory experiment. The mix proportions utilized in this study were bentonite to 20% and 30% of the total weight, adding quartzite sand to 30% and 50% of the total weight (bentonite + water). Mixed grout specimens were prepared in rectangular parallelepiped shapes. The thermal conductivity, volumetric water content and matric suction of unsaturated specimens were measured as the saturated specimens were slowly dried at room temperature until there was little change in the measured values. The matric suction and thermal conductivity showed a bilinear relationship, with a breaking point identifying the air-entry value (AEV) and the SWCC describing the relationship between the matric suction and the volumetric water content (VWC). As the matric suction slowly increased to the AEV, the VWC of the specimens decreased, whereas the thermal conductivity increased; then, beyond the AEV, it rapidly decreased again. That is, as the specimens dried out, attaining the maximum at the AEV, their thermal conductivity decreased. The thermal conductivity and the VWC showed a parabolic relationship with the maximum thermal conductivity value at around the VWC corresponding to the AEV of each specimen. Revised empirical equations representing the relationship between these two parameters were suggested for prediction of the thermal characteristics of bentonite-based grout in geothermal heat pump applications. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Due to environmental and energy-supply issues such as global warming and fossil-fuel depletion, geothermal energy is seeing increasing use as a sustainable resource. In this context, groundsource heat pump (GSHP) systems and geothermal heat pump (GHP) systems have been adapted for geothermal energy use. These are heating and cooling systems that provide residential and commercial buildings with heat in winter and cooling in summer. This technology relies on the fact that, at depth, the Earth has a relatively constant temperature, warmer than the air in winter and cooler than the air in summer. GHP systems exchange heat with the ground, often by means of vertical closed-loop geothermal systems such as a vertical U-tube borehole heat exchanger [1]. In this system, the borehole is backfilled with grouting materials, which provide a heat-transfer medium between the heat exchanger and the surrounding ground (e.g. soils or rock) and also ⇑ Corresponding author. E-mail addresses: [email protected] (D. Kim), [email protected] (G. Kim), [email protected] (H. Baek). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.01.091 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
controls groundwater movement to prevent contamination of water. Granular bentonite-water grouts are commonly used in GHP systems [2,3] as well as in other applications such as radioactive waste confinement [4]. Grouting materials’ thermal conductivity is one of the key properties of GSHP systems. Bentonite, for example, has a relatively low thermal conductivity that typically ranges from 0.65 to 0.90 W/mK under the saturated condition [5]. Because the low thermal conductivity of bentonite makes it unsuitable as a filler material for GSHP systems, some additives need to be mixed into bentonite grouts to improve it in them respect. In this context, the thermal characteristics of pure bentonite (bentonite only) and bentonite– sand grouts, in their varying mixed proportions, have been studied under both saturated and dried conditions [5–9]. The results indicated that adding sand as an additive improves the thermal conductivity of grouts, and that grouts under saturated conditions showed much higher thermal conductivity than those under dried conditions. Thus, the thermal conductivity of grouts varies with their mix proportions and water contents. The ground in which the borehole is dug is not completely saturated or dried; rather, those qualities vary with borehole depth
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and in situ ground-water conditions. As in situ ground-water conditions changes, the water condition of the ground varies accordingly. This variation can affect the water contents and thermal conductivity of grouting materials. Due to the fact that direct measurement of grouting materials’ thermal properties is practically impossible after installation, prior characterization of those properties for varying water contents is key to the performance prediction and efficiency maintenance of GHP systems [9]. However, the effects of varying water contents on the thermal properties of bentonite-based grout for GSHP systems under unsaturated conditions, have only rarely been investigated. Kim et al. [10] found a parabolic relationship between the thermal conductivity and volumetric water content (VWC) of bentonite grouts, [11–14], unlike the other studies, which showed that the thermal conductivity only decreased with decreasing VWC. Kim et al. [10] also speculated that this parabolic relationship might be related to the soil– water characteristic curve (SWCC). The SWCC is a conceptual and interpretative tool by which the behavior of unsaturated soils can be understood [15]; it defines the relationship between matric suction and VWC or the degree of saturation [16]. In this study, the effects of varying VWC and matric suction on the thermal conductivity of bentonite and bentonite–sand grouts were investigated. Also, the SWCC of the bentonite and bentonite–sand grouts was identified to explain the phenomenon of the parabolic relationship between the VWC and thermal conductivity.
largest pores, which are then occupied by air. The matric suction required for removing the water from the largest pores is known as the air entry value (AEV), and the area between the zero matric suction and the AEV is referred to as the saturated zone [18]. Beyond the AEV, the increase of matric suction causes a rapid rate of VWC loss until the residual water content is reached. Matric suction corresponding to residual water content is referred to as residual suction, by which the desaturation ends, and the water begins to be held in the soil by adsorption forces. The area between the AEV and the matric suction in which the residual condition is reached is called the transition zone. In the residual zone, the curve exhibits an asymptotic line at a low degree of saturation. Water still exists, but considerable matric suction is needed to drain even a small amount of water from the pores [19]. The pore water within unsaturated soils exists in three forms (Fig. 1): (a) bulk water within those void spaces that are completely flooded, (b) meniscus water surrounding all inter-particle contact points that are not covered by bulk water, and (c) adsorbed water, which, tightly bound to the soil particles, acts as parts of the soil skeleton. The relationship between the SWCC and the porewater forms is shown in Fig. 1 [20]. Fig 2 shows a typical SWCC, which depends on the size and arrangement of the pores, for three different types of soil. The AEV generally increases not only with the plasticity of the soils but with decreasing grain-size. Other factors such as the stress history also affect the shape of the SWCC [18,21].
2. Soil–water characteristic curve Fig. 1 shows a typical soil–water characteristic curve (SWCC), which is an important tool for evaluation of the engineering behaviors of unsaturated soils. The SWCC is generally defined as the relationship between the VWC and the matric suction of the soil. The VWC is defined as the ratio between the volume of water and the total volume of the specimen. The soil matric suction, one of the most important parameters of unsaturated soils [17], is defined as the difference between the pore-air pressure and the pore-water pressure. The SWCC consists of three zones: the saturated zone, the transition zone, and the residual zone. In the saturated zone, almost all the soil pores are filled with water. The pore-water is in tension in this zone; however, the soil, owing to capillary forces, remains essentially saturated. When matric suction is applied to the water in the soil pores, the water is first drained from the
3. Materials and methods 3.1. Grouting materials Bentonite is an absorbent aluminium phyllosilicate, essentially impure clay consisting mostly of montmorillonite [22]. VolclayÒ
Fig. 2. Typical SWCC for different types of soil [18].
Table 1 Physical properties of VolclayÒ bentonite. Permeability (cm/s) 51 10
7
Swelling (ml/g)
Montmorillonite content (%)
Thermal conductivity (W/ mK)
Specific gravity
12.5
590
0.74
2.60
Table 2 Chemical composition of quartzite sand. Chemical SiO2 Al2O3 Fe2O3 K2O TiO2 CaO composition (wt%) Fig. 1. Soil–water characteristic curve showing zones of unsaturation.
Quartzite sand
99.6 0.1
0.03
–
MgO Ig-loss Total
0.02 Trace Trace 0.1
99.85
D. Kim et al. / International Journal of Heat and Mass Transfer 84 (2015) 1049–1055
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Table 3 Mix proportions and properties of grout. Specimen No.
Bentonite (wt%)
Quartzite sand (wt%)
Water (wt%)
Dry unit weight (kN/m3)
Void ratio
Water content (%)
BN BN BN BN BN BN
20.0 15.4 13.3 30.0 23.1 20.0
0 23.1 33.3 0 23.1 33.3
80.0 61.5 53.3 70.0 53.8 46.6
2.16 4.80 6.17 3.43 5.88 7.25
10.80 4.37 3.16 6.53 3.35 2.54
400 160 114 233 117 87
20-0 20-30 20-50 30-0 30-30 30-50
bentonite, used in this study, is a 20% solid, polymer-free, singlecomponent commercial sodium bentonite available in powdered form. It is widely employed in geothermal heat pump installations and for geophysical site investigation purposes. The physical properties of VolclayÒ bentonite are listed in Table 1. As noted above, the thermal conductivity of pure-bentonite grout is markedly lower. Grout materials are required to have thermal conductivities similar to that of geologic formations (1.7–2.1 W/mK) in the ground [23]. In this study, quartzite sand was used as an additive to improve the thermal conductivity of the grout. Quartzite sand has a relatively high thermal conductivity that typically ranges from 2.5 to 3.1 W/mK depending on dry density [24]. Quartzite sand is artificially produced by crushing and milling silica rocks such as quartz dikes or quartzites, and its chemical composition is listed in Table 2. 3.2. Experimental methods The mix proportions of grout applied in this study were those used in a previous study [10], that is, bentonite to 20% and 30% of the total weight (bentonite + water), adding quartzite sand to 30% and 50% of the total weight. As the amount of quartzite sand increased, the total unit weight increased, whereas the void ratio and the water content decreased (Table 3). Specimens were formed by pouring mixed grout into rectangular parallelepiped molds (22 cm 6.5 cm 4 cm). A 5TE sensor and a MPS-1 sensor (both from Decagon Devices, Ltd.) were installed at the center of each specimen to measure the VWC and matric suction, respectively. After allowing for free swelling under the sealed condition for 24 h, the VWC, thermal conductivity and matric suction were measured at room temperature (20 ± 2 °C) for 14 days until the measured values showed little change. A Quick Thermal conductivity Meter (QTM-500, Kyoto Electronics Manufacturing Co., Ltd.) was used to measure thermal conductivity. QTM-500 is a probe-type device, which consists of single heater wire and thermocouple. While other two sensors measure the properties of the surrounding soil mass at the center of the specimen, this device measures the thermal conductivity by sticking sensor probe on the surface of the specimen. A possible mismatch
Fig. 4. Variation of (a) volumetric water content with time, (b) matric suction with time, and (c) thermal conductivity with time.
among the measured properties was assumed to be negligible considering the specimen thickness (see Fig. 3).
Fig. 3. Experimental set-up: (a) 5TE and MPS-1 sensors, (b) QTM-500.
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4. Results and discussion 4.1. Changes in VWC, matric suction and thermal conductivity with time Fig 4(a) plots the change in VWC of the specimens with time. As the specimens were becoming drier at room temperature, the VWC decreased nonlinearly. The VWC of BN20-0, BN20-30 and BN20-50 rapidly decreased at the elapsed time of around 160, 130 and 100 h, respectively. Also, BN30-0, BN30-30 and BN30-50 rapidly decreased at the elapsed time of around 140, 110 and 90 h, respectively. Thereafter, the VWC of all of the specimens converged at the elapsed time of around 200 h. Fig 4(b) plots the change in the matric suction of the specimens with time. As the specimens were becoming drier, the matric suction increased nonlinearly. The matric suction of all of the specimens increased rapidly at the elapsed time of around 50 h, finally converging at the elapsed time of around 200 h. The MPS-1 sensor reportedly measures matric suction from about 10–500 kPa [25]. However, in the present study, matric suction values above
500 kPa were measured using the same sensor. In fact, in a recent study, the MPS-1 delivered not only readings up to 1.2 MPa but also reliable results up to a matric suction of 600 kPa [26]. Hence, matric suction values up to 600 kPa were used in this study. Finally, Fig. 4(c) shows the change in the thermal conductivity of the specimens with time. The thermal conductivity of all specimens initially increased and, after reaching the maximum at a certain elapsed time, began to rapidly decrease. Thereafter, the thermal conductivity of all of the specimens was converged at the elapsed time of around 200 h. The elapsed time at which each specimen reached the maximum thermal conductivity was equal to the time at which the VWC of each specimen started to rapidly decrease. As the amounts of bentonite and quartzite sand of the specimens increased, the elapsed time at which the change in their VWC or thermal conductivity occurred was shorter. The results on the changes of VWC and thermal conductivity with time were similar to those of a previous study [10]. However, there was a minor difference in the elapsed time when the specimens’ VWC and thermal conductivity changed, presumably as a result of room humidity differences during the testing.
Fig. 5. SWCC of the specimens: (a) BN20, (b) BN30.
Fig. 6. Relationship between matric suction and thermal conductivity of the specimens: (a) BN-20, (b) BN-30.
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D. Kim et al. / International Journal of Heat and Mass Transfer 84 (2015) 1049–1055 Table 4 Equations for fitted lines obtained from bilinear regression of experimental data. Sample No.
(a) y = VWC x = Matric suction
BN20-0
y= y= y= y= y= y= y= y= y= y= y= y=
BN20-30 BN20-50 BN30-0 BN30-30 BN30-50
0.08ln(x) + 1.02 0.70ln(x) + 4.91 0.08ln(x) + 0.94 0.48ln(x) + 3.32 0.05ln(x) + 0.72 0.40ln(x) + 2.76 0.07ln(x) + 0.93 0.60ln(x) + 4.10 0.07ln(x) + 0.83 0.55ln(x) + 3.68 0.03ln(x) + 0.58 0.45ln(x) + 2.98
(<500 kPa) (>500 kPa) (<400 kPa) (>400 kPa) (<300 kPa) (>300 kPa) (<400 kPa) (>400 kPa) (<300 kPa) (>300 kPa) (<250 kPa) (>250 kPa)
R2
(b) y = Thermal conductivity x = Matric suction
R2
0.94 0.99 0.96 0.95 0.81 0.99 0.98 0.99 0.91 0.99 0.81 0.97
y = 0.04ln(x) + 0.70 (<500 kPa) y = 0.82ln(x) + 6.09 (>500 kPa) y = 0.17ln(x) + 0.64 (<400 kPa) y = 1.74ln(x) + 12.18 (>400 kPa) y = 0.17ln(x) + 0.87 (<300 kPa) y = 1.06ln(x) + 7.91 (>300 kPa) y = 0.08ln(x) + 0.63 (<400 kPa) y = 0.61ln(x) + 4.77 (>400 kPa) y = 0.16ln(x) + 0.62 (<300 kPa) y = 1.36ln(x) + 9.57 (>300 kPa) y = 0.16ln(x) + 1.01 (<250 kPa) y = 1.57ln(x) + 10.82 (>250 kPa)
0.87 0.86 0.97 0.90 0.87 0.96 0.85 0.97 0.95 0.95 0.74 0.94
4.2. Relationship between matric suction and thermal conductivity of bentonite–sand specimens Fig 5 shows the SWCC of the specimens, in which bilinear patterns are clearly depicted. As the VWC of the specimen decreased, the matric suction also steadily decreased. The point of intersection of the two straight lines is the AEV, which ranges from 300 to 500 kPa. The AEV decreased as the amount of bentonite and quartzite sand increased. Fig 6 shows the relationship between matric suction and thermal conductivity. Again, a bilinear pattern was observed for each specimen with a break point, closely corresponding to AEV in Fig. 5. As the specimen gradually dried up, both thermal conductivity and matric suction of the specimen simultaneously increased. However, after passing the break point, the thermal conductivity rapidly decreased. Table 4 lists the equations for fitted lines obtained from bilinear regression of each specimen’ experimental data in Figs. 5 and 6. The AEV separately calculated by the bilinear equations in Table 4 matched well to each other within ±50 kPa, as shown in Fig. 7. Table 5 lists the maximum thermal conductivity and corresponding VWC of each specimen calculated by the bilinear equations. The maximum thermal conductivity value of each specimen increased with increasing bentonite and quartzite sand contents, whereas the corresponding VWC decreased. As the soil moves from a saturated state to drier conditions, the distribution of soil, water, and air phases change as the stress state changes. The relationship among these phases takes on different forms, and, thereby, influences the engineering properties of unsaturated soils [27]. Also, the interactions between these phases affect the change in the thermal conductivity of soils [28,29]. The wetted area of contact between the soil particles decreases with increasing soil matric suction [15]; and with this decrease, the thermal conductivity of soil decreases [28]. Water is retained within the pores of soils under physicochemical influences such as capillary force acting at the water–air interface and the attraction of water molecules by the soil-particle surface force associated with van der Waals’ attraction, electrical double-layer repulsion, cementation, and other mechanisms [21] (Fig. 8). The capillary force is affected by pore size, and the surface force is affected by the surface properties or surface area of the soils. Clays such as bentonite are superior to other types of soils in the surface force [30]. Water in soil, in the forms of bulk water, meniscus water and adsorbed water depicted in Fig. 1, affects the deformational behavior of soil. The meniscus water that collects at the particle contacts increases the inter-granular force acting on the soil particles, thus increasing the stiffness of the soil skeleton. On the other hand, the bulk water filling the void spaces induces not only an increase in the stiffness of the soil skeleton but also a decrease in the volume of the soil mass, due to slippages between soil particles at the contact points. The influence of bulk water is equal to the effect of neg-
Fig. 7. Relationship of each AEV calculated by bilinear equations in Table 4.
Table 5 Maximum thermal conductivity calculated by bilinear equations in Table 4 and corresponding VWC for each specimen. Sample No.
VWC (m3/m3)
Thermal conductivity (W/mK)
BN20-0 BN20-30 BN20-50 BN30-0 BN30-30 BN30-50
0.54 0.47 0.43 0.50 0.44 0.40
0.94 1.65 1.84 1.10 1.54 1.89
ative pore water pressure [31]. Therefore, as the matric suction of the specimens increases with decreasing VWC, the soil particles adhere closely to each other by a complex interaction between the surface force of bentonite, quartzite sand and the capillary force occurring along the water–air interface (Fig. 8). That is, up to the AEV and within the saturated zone of the SWCC, the thermal conductivity of the specimens gradually increases, because the bentonite and quartzite sand adhere closely to each other by the effect of bulk water. Within the saturated zone, the water in the soil pores is not drained up to the AEV, though the VWC gradually decreases. Beyond the AEV, the VWC rapidly decreases within the transition zone of the SWCC; the thermal conductivity of the specimens also rapidly decreases with increasing matric suction, because water is drained from the pore spaces, which are then filled with air. Within the transition zone, the effect of bulk water
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4.3. Relationship between thermal conductivity and volumetric water content of bentonite–sand specimens
Fig. 8. Water held by capillary forces and surface forces [34].
disappears and that of meniscus water starts to be applied. Air has a much lower thermal conductivity than water: 0.025 W/mK versus 0.591 W/mK, respectively [32]; hence, as the amount of air in the pore spaces further increases, the thermal conductivity of the specimens decreases. In case of non-plastic soils, any increase in thermal conductivity up to the AEV does not occur. Rather, as the water content decreases, the thermal conductivity also decreases in logarithmic scale [33]. The increase in thermal conductivity observed in the present investigation, up to the AEV and within the saturated zone of the SWCC, can be attributed to the effect of bulk water caused by the substantial surface force of bentonite.
Fig 9 shows the relationship between the thermal conductivity and the VWC of the specimens obtained in the present investigation, combined with the data from the previous study [10]. Each specimen’s trend curve is in a parabolic relationship with the maximum thermal conductivity value. As the amounts of bentonite and quartzite sand decreased, the trend curve showed a gentler slope, and the VWC corresponding to the maximum thermal conductivity value increased. Also, as the amounts of bentonite and quartzite sand increased, the value of maximum thermal conductivity increased. Table 6 lists the regression equations for the specimens’ thermal conductivity and VWC with the determination coefficient, R2. Also listed in Table 6 are the maximum value of thermal conductivity and the corresponding VWC for each specimen, determined from the regression equation. The regression equations were determined from the combined test results of both present and previous studies. Also, each VWC calculated by the regression equation in Table 6 was almost equal to that in Table 4, whereas there were some differences in thermal conductivity. However, it was apparent that the maximum thermal conductivity value of each specimen increased with increasing bentonite and quartzite sand contents, whereas the corresponding VWC decreased. Also, it could be seen, in Table 5, that the VWC corresponding to the maximum thermal conductivity value of each specimen was closely related to the AEV of the SWCC, via the VWC corresponding to the AEV of the SWCC in Table 4. This means that as the specimens dried
Fig. 9. Relationship between the thermal conductivity and VWC: (a) BN20, (b) BN30.
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D. Kim et al. / International Journal of Heat and Mass Transfer 84 (2015) 1049–1055 Table 6 Regression equation with the maximum thermal conductivity and corresponding VWC. Sample No. BN20-0 BN20-30 BN20-50 BN30-0 BN30-30 BN30-50
Regression equation y= y= y= y= y= y=
2
2.64x + 3.06x + 0.04 6.53x2 + 6.14x + 0.09 7.94x2 + 6.78x + 0.18 3.75x2 + 3.79x + 0.10 8.37x2 + 7.03x + 0.08 10.66x2 + 8.24x + 0.09
R2
Maximum thermal conductivity (W/mK)
Corresponding VWC (m3/m3)
0.97 0.92 0.92 0.94 0.93 0.94
0.93 1.53 1.63 1.06 1.56 1.68
0.58 0.47 0.43 0.51 0.42 0.39
out after reaching the maximum at the VWC corresponding to the AEV of each specimen, their thermal conductivity decreased. 5. Conclusions In this study, the relationship between thermal conductivity and SWCC of pure bentonite and bentonite–sand grouts for use as backfilling materials in geothermal systems was investigated. Specimens of different mix proportions were tested to measure the VWC, matric suction and thermal conductivity under unsaturated conditions. In case of the SWCC, it was observed that the AEV decreased with increasing bentonite and quartzite sand contents. The shape of the SWCC of the specimens also depended on the quartzite sand and bentonite contents, because the gradient of the SWCC in the low matric suction range up to the AEV decreased with increasing bentonite and quartzite sand contents. The relationship between the matric suction and the thermal conductivity of the expansive soil (in the forms of the pure bentonite and bentonite–sand grouts) showed a bilinear relationship with the breaking point identifying the AEV as well as their SWCC. As the matric suction increased to the AEV, the thermal conductivity of the specimens increased by the effect of bulk water, thereby inducing a decrease in the volume of the soil mass, and thereafter decreasing again. Also, at the AEV, the maximum thermal conductivity increased with increasing bentonite and quartzite sand contents. The trend curve between the thermal conductivity and the VWC of the specimens showed a parabolic relationship with the maximum thermal conductivity value at the VWC corresponding to the AEV of each specimen. The revised empirical equations representing the relationship between the thermal conductivity and VWC were suggested by the results both of this study and a previous one. On this basis, the present results are expected to facilitate the construction of geothermal heat pump systems. References [1] H. Esen, M. Inalli, In-situ thermal response test for ground source heat pump system in Elazıg˘, Turkey, Energy Build. 41 (4) (2009) 395–401. [2] F. Eckhart, Grouting Procedures for Ground-source Heat Pump Systems, Ground Source Heat Pump Publications, Oklahoma State University, US, 1991. [3] V. Trillat-Berdal, B. Souyri, G. Achard, Coupling of geothermal heat pump with thermal solar collectors, Appl. Therm. Eng. 27 (10) (2007) 1750–1755. [4] M. Jobmann, G. Buntebarth, Influence of graphite and quartz addition on the thermal-physical properties of bentonite for sealing heat-generating radioactive waste, Appl. Clay Sci. 44 (3–4) (2009) 206–210. [5] C.P. Remund, J.T. Lund, Thermal enhancement of bentonite grouts for vertical GSHP system, in: ASME, Heat Pump and Refrigeration System-Design Analysis and Applications, vol. 29, 1993, pp. 95–106. [6] M.L. Allan, A. Philippacopoulos, Properties and performance of cement-based grouts for geothermal heat pump application, U.S. Department of Energy, Washington DC, 1999. [7] C.C. Hiller, Grouting for vertical geothermal heat pump systems: engineering design and field procedures manual, International Ground Source Heat Pump Association, Stillwater, Oklahoma, 2000. [8] B.H. Sohn, Thermal conductivity enhancement of bentonite grout using silica sands, in: Proceedings of the Conference of The Society of Air-Conditioning and Refrigerating Engineers of Korea Semiannual, Sarek, Korea, 2006, pp. 713–718.
[9] H.S. Choi, H.P. Choi, C.H. Lee, S.B. Woo, A study on the physical characteristics of grout material for backfilling ground heat exchanger, J. Korean Geotech. Soc. 24 (1) (2008) 37–49. [10] D.H. Kim, G.M. Kim, S.H. Park, H.J. Baek, Changes in the thermal conductivity of bentonite-based grouts with varying volumetric water content, Geosyst. Eng. 16 (4) (2013) 257–264. [11] M.S. Kersten, Thermal properties of soils, Engineering Experiment Station, University of Minnesota, US, 1949. [12] O. Johansen, Thermal conductivity of soils (Ph.D. thesis), Trondheim, Norway, ADA 044002, 1975. [13] G.S. Campbell, Soil Physics with Basic, Elsevier, Amsterdam, 1985. [14] Y.M. Tien, C.A. Chu, W.S. Chuang, The prediction model of thermal conductivity of sand-bentonite based buffer material, in: France Clays in Natural and Engineered Barriers for Radioactive Waste Confinement, 2005, pp. 657. [15] S.K. Vanapalli, D.G. Fredlund, D.E. Pufahl, The influence of soil structure and stress history on the soil–water characteristics of a compacted till, Geotechnique 49 (2) (1999) 143–159. [16] J.M. Tinjum, C.H. Benson, L.R. Blotz, Soil water characteristic curves for compacted clays, ASCE J. Geotech. Geoenviron. Eng. 123 (11) (1997) 1060– 1069. [17] M.A. Tekinsoy, T. Taskiran, C. Kayadelen, One dimensional non-linear consolidation of unsaturated fine grained soils, World Appl. Sci. J. 6 (10) (2009) 1388–1398. [18] D.G. Fredlund, A. Xing, Equations for the soil–water characteristic curve, Can. Geotech. J. 31 (4) (1994) 521–532. [19] Y.M. Purwana, Experimental study on unsaturated direct shear and California bearing ratio tests with suction monitoring on sand-kaolin clay mixtures (Ph.D. thesis), Curtin University, Australia, 2013. [20] S.J. Wheeler, D. Karube, Constitutive modelling, in: Unsaturated soils Proceedings of the First International Conference on Unsaturated Soils, Paris, France, 1996, pp. 1323–1356. [21] N. Lu, W.K. Likos, Unsaturated Soil Mechanics, Wiley, New York, 2004. [22] T. Panahi Osalo, E. Merufinia, M. Esmat Saatlo, Phosphorus removal from aqueous solutions by bentonite: effect of Al2O3 addition, J. Civ. Eng. Urban. 3 (5) (2013) 317–322. [23] C.H. Lee, K.J. Lee, H.S. Choi, H.P. Choi, Characteristics of thermally-enhanced bentonite grouts for geothermal heat exchanger in South Korea, Sci. China Tech. Sci. 53 (2010) 123–128. [24] B.H. Sohn, Predicting the effective thermal conductivity of some sand–water mixtures used for backfilling materials of ground heat exchanger, J. Soc. AirCondition. Refrig. Eng. Korea 20 (9) (2008) 614–623. [25] Decagon devices, Dielectric water potential sensor MPS-1 operator’s manual version 1.0, Inc. 2365 NE Hopkins Court, Pullman, WA 99163, 2008. [26] R. Nolz, G. Kammerer, P. Cepuder, Calibrating soil water potential sensors integrated into a wireless monitoring network, Agric. Water Manage. 116 (1) (2013) 12–20. [27] S.L. Barbour, Nineteenth Canadian geotechnical colloquium: the soil–water characteristic curve: a historical perspective, Can. Geotech. J. 35 (5) (1998) 873–894. [28] A.R. Sepaskhah, L. Boersma, Thermal conductivity of soils as a function of temperature and water content, Soil Sci. Soc. Am. J. 43 (1979) 439–444. [29] S. Lu, T. Ren, Y. Gong, R. Horton, An improved model for predicting soil thermal conductivity from water content at room temperature, Soil Sci. Soc. Am. J. 71 (2007) 8–14. [30] E.G. Kang, Construction of real time monitoring system and infiltration analysis of slope for protecting cultural assets (M.S. thesis), Korea Advanced Institute of Science and Technology, South Korea, 2008. [31] J.G. Chae, B.S. Kim, S.W. Park, S.J. Kato, Effect of suction on unconfined compressive strength in partly saturated soils, KSCE J. Civil Eng. 14 (3) (2010) 281–290. [32] J.H. Cha, S.J. An, M.H. Koo, H.C. Kim, Y.H. Song, M.S. Suh, Effects of porosity and water content on thermal conductivity of soils, J. Korean Soc. Soil Groundwater Environ. 13 (3) (2008) 27–36. [33] S. Lu, T. Ren, Y. Gong, R. Horton, An improved model for predicting soil thermal conductivity from water content at room temperature, Soil Sci. Soc. Am. J. 71 (1) (2007) 8–14. [34] G.L. Guymon, Unsaturated Zone Hydrology, Prentice-hall, 1994.