Abstract
As the demand of exploitation and utilization of geothermal energy increases, more geothermal-related earth structures occur recently. The design of the structures depends upon an accurate prediction of soil thermal conductivity. The existing soil thermal conductivity models were mostly developed by empirical fits to datasets of soil thermal conductivity measurements. Due to the gaps in measured thermal conductivities between any two tested natural soils, the models may not provide accurate prediction for other soils, and the predicted thermal conductivity might not be continuous over the entire range of soil type. In this research, a generalized soil thermal conductivity model was proposed based on a series of laboratory experiments on sand, kaolin clay and sand–kaolin clay mixtures using a newly designed thermo-time domain reflectometry probe. The model was then validated with respect to k dry–n (thermal conductivity of dry soils and porosity) and k r–S r (normalized thermal conductivity and degree of saturation) relationships by comparing with previous experimental studies. The predicted thermal conductivities were found to be in a good agreement with the experimental data collected from both this study and the other literatures with at least 85% confidence interval. It is concluded that the proposed model accounts for the effects of both environmental factors (i.e., moisture content and dry density) and compositional factors (i.e., quartz content and soil type) on soil thermal conductivity, and it has a great potential in predicting soil thermal conductivity more accurately for geothermal applications.
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References
ASTM C778-13 (2013) Standard specification for standard sand. ASTM International, West Conshohocken
ASTM D698-12e2 (2012) Standard test methods for laboratory compaction characteristics of soil using standard effort (12400 ft-lbf/ft3 (600 kN-m/m3)). ASTM International, West Conshohocken
Amatya BL, Soga K, Bourne-Webb PJ, Amis T, Laloui L (2012) Thermo-mechanical behavior of energy piles. Geotechnique 62(6):503–519
Baker JM, Lascano RJ (1989) The spatial sensitivity of time-domain reflectometry. Soil Sci Soc Am J 147(5):378–384
Balland V, Arp PA (2005) Modeling soil thermal conductivities over a wide range of conditions. J Environ Eng Sci 4(6):549–558
Bauer S, Urquhart A (2016) Thermal and physical properties of reconsolidated crushed rock salt as a function of porosity and temperature. Acta Geotech 11(4):913–924
Brandl H (2006) Energy foundations and other thermo-active ground structures. Geotechnique 56(2):81–122
Bristow KL (2002) Thermal conductivity. In: Dane JH, Topp GC (eds) Methods of soil analysis. Part 4. SSSA Book Ser. 5. SSSA and ASA, Madison, WI, pp 1209–1226
Bristow KL, Kluitenberg GJ, Horton R (1994) Measurement of soil thermal properties with a dual-probe heat-pulse technique. Soil Sci Soc Am J 58(5):1288–1294
Bristow KL, Bilskie JR, Kluitenberg GJ, Horton R (1995) Comparison of techniques for extracting soil thermal properties from dual-probe heat-pulse data. Soil Sci 160(1):1–7
Chen SX (2008) Thermal conductivity of sands. Heat Mass Transfer 44(10):1241–1246
Choo J, Kim YJ, Lee JH et al (2013) Stress-induced evolution of anisotropic thermal conductivity of dry granular materials. Acta Geotech 8(1):91–106
Cote J, Konrad JM (2005) A generalized thermal conductivity model for soils and construction materials. Can Geotech J 42(2):443–458
De Vries DA (1952) A nonstationary method for determining thermal conductivity of soil in situ. Soil Sci 73(2):83–89
De Vries DA (1963) Thermal properties of soils. In: Van Wijk WR (ed) Physics of plant environment. Wiley, New York, pp 210–235
Donazzi F, Occhini E, Seppi A (1979) Soil thermal and hydrological characteristics in designing underground cables. Proc Inst Electr Eng 126(6):506–516
Dong Y, Pamukcu S (2015) Thermal and electrical conduction in unsaturated sand controlled by surface wettability. Acta Geotech 10(6):821–829
Gangadhara Rao MVBB, Singh DN (1999) A generalized relationship to estimate thermal resistivity of soils. Can Geotech J 36(4):767–773
Gemant A (1950) The thermal conductivity of soils. J Appl Phys 21(8):750–752
Gori F (1983) A theoretical model for predicting the effective thermal conductivity of unsaturated frozen soils. In: Proceedings of 4th international conference on permafrost Fairbanks, AL. Natl. Acad. Press, Washington, DC, pp 363–368
Haigh SK (2012) Thermal conductivity of sands. Geotechnique 62(7):617–625
Heimovaara TJ (1993) Design of triple-wire time domain reflectometry probes in practice and theory. Soil Sci Soc Am J 57(6):1410–1417
Johansen O (1977) Thermal conductivity of soils. Ph.D. thesis, University of Trondheim, Trondheim, Norway. US Army Corps of Engineers, Cold Regions Research and Engineering Laboratory, Hanover, N. H. CRREL Draft English Translation 637
Kersten MS (1949) Laboratory research for the determination of the thermal properties of soils, Bulletin No. 28. Minneapolis, MN: University of Minnesota Engineering Experiment Station
Kluitenberg GJ, Ham JM, Bristow KL (1993) Error analysis of the heat pulse method for measuring soil volumetric heat capacity. Soil Sci Soc Am J 57(6):1444–1451
Kömle NI, Bing H, Feng WJ et al (2007) Thermal conductivity measurements of road construction materials in frozen and unfrozen state. Acta Geotech 2(2):127–138
Lee J, Kim YS, Kim HS, Kang JM, Bae GJ (2012) Assessment of calculation methods for thermal conductivity of saturated kaolinite. Int J Offshore Polar Eng 22(2):172–175
Low JE, Loveridge FA, Powrie W et al (2015) A comparison of laboratory and in situ methods to determine soil thermal conductivity for energy foundations and other ground heat exchanger applications. Acta Geotech 10(2):209–218
Lu N, Dong Y (2015) Closed-form equation for thermal conductivity of unsaturated soils at room temperature. J Geotech Geoenviron Eng. doi:10.1061/(ASCE)GT.1943-5606.0001295,04015016
Lu S, Ren T, Gong Y (2007) An improved model for predicting soil thermal conductivity from water content at room temperature. Soil Sci Soc Am J 71(1):8–14
Malicki MA, Skierucha WM (1989) A manually controlled TDR soil moisture meter operating with 300 ps rise-time needle pulse. Irrig Sci 10(2):153–163
Ren T, Noborio K, Horton R (1999) Measuring soil water content, electrical conductivity, and thermal properties with a thermo-time domain reflectometry probe. Soil Sci Soc Am J 63(3):450–457
Revil A, Lu N (2013) Unified water isotherms for clayey porous materials. Water Resour Res 49(9):5685–5699
Sass JH, Lachenbruch AH, Munroe RJ (1971) Thermal conductivity of rocks from measurements on fragments and its application to heat-flow determinations. J Geophys Res 76(14):3391–3401
Smith WO (1942) The thermal conductivity of dry soil. Soil Sci 53(6):435–460
Smith WO, Byers HG (1939) The thermal conductivity of dry soils of certain of the great soil groups. Soil Sci Soc Am J 3(C):13–19
Tarnawski VR, Momose T, Leong WH (2009) Assessing the impact of quartz content on the prediction of soil thermal conductivity. Geotechnique 59(4):331–338
Tong F, Jing L, Zimmerman RW (2009) An effective thermal conductivity model of geological porous media for coupled thermo-hydro-mechanical systems with multiphase flow. Int J Rock Mech Min Sci 46(8):1358–1369
Topp GC, Davis JL, Annan P (1980) Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour Res 16(3):574–582
Topp GC, Davis JL, Annan AP (1982) Electromagnetic determination of soil water content using TDR: evaluation of installation and configuration of parallel transmission lines. Soil Sci Soc Am J 46(4):678–684
Welch SM, Kluitenberg GJ, Bristow KL (1996) Rapid numerical estimation of soil thermal properties for a broad class of heat pulse emitter geometries. Meas Sci Technol 7(6):932–938
Yu X, Zhang N, Pradhan A (2014) Development and evaluation of a thermo-TDR probe. In: Soil Behavior and Geomechanics, Geo-Shanghai 2014, pp 434–444
Yu X, Zhang N, Pradhan A, Thapa B, Tjuatja S (2015) Design and evaluation of a thermo-TDR probe for geothermal applications. Geotech Test J 38(6):864–877
Yu X, Pradhan A, Zhang N, Thapa B, Tjuatja S (2014) Thermo-TDR probe for measurement of soil moisture, density, and thermal properties. In: Geo-Congress 2014, pp 2804–2813
Zegelin SJ, White I, Kenkins DJ (1989) Improved field probe for soil water content and electrical conductivity measurement using time domain reflectometry. Water Resour Res 25(11):2367–2376
Zhang N, Yu X, Pradhan A, Puppala AJ (2015) Thermal conductivity of quartz sands by thermo-time domain reflectometry probe and model prediction. J Mater Civ Eng ASCE. doi:10.1061/(ASCE)MT.1943-5533.0001332
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Zhang, N., Yu, X., Pradhan, A. et al. A new generalized soil thermal conductivity model for sand–kaolin clay mixtures using thermo-time domain reflectometry probe test. Acta Geotech. 12, 739–752 (2017). https://doi.org/10.1007/s11440-016-0506-0
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DOI: https://doi.org/10.1007/s11440-016-0506-0