Advertisement

Acta Geotechnica

, Volume 12, Issue 4, pp 739–752 | Cite as

A new generalized soil thermal conductivity model for sand–kaolin clay mixtures using thermo-time domain reflectometry probe test

  • Nan Zhang
  • Xinbao YuEmail author
  • Asheesh Pradhan
  • Anand J. Puppala
Research Paper

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 dryn (thermal conductivity of dry soils and porosity) and k rS 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.

Keywords

Sand–kaolin clay mixtures Thermal conductivity model Thermo-TDR probe 

References

  1. 1.
    ASTM C778-13 (2013) Standard specification for standard sand. ASTM International, West ConshohockenGoogle Scholar
  2. 2.
    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 ConshohockenGoogle Scholar
  3. 3.
    Amatya BL, Soga K, Bourne-Webb PJ, Amis T, Laloui L (2012) Thermo-mechanical behavior of energy piles. Geotechnique 62(6):503–519CrossRefGoogle Scholar
  4. 4.
    Baker JM, Lascano RJ (1989) The spatial sensitivity of time-domain reflectometry. Soil Sci Soc Am J 147(5):378–384CrossRefGoogle Scholar
  5. 5.
    Balland V, Arp PA (2005) Modeling soil thermal conductivities over a wide range of conditions. J Environ Eng Sci 4(6):549–558CrossRefGoogle Scholar
  6. 6.
    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):913–924CrossRefGoogle Scholar
  7. 7.
    Brandl H (2006) Energy foundations and other thermo-active ground structures. Geotechnique 56(2):81–122CrossRefGoogle Scholar
  8. 8.
    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 1209–1226Google Scholar
  9. 9.
    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):1288–1294CrossRefGoogle Scholar
  10. 10.
    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):1–7CrossRefGoogle Scholar
  11. 11.
    Chen SX (2008) Thermal conductivity of sands. Heat Mass Transfer 44(10):1241–1246CrossRefGoogle Scholar
  12. 12.
    Choo J, Kim YJ, Lee JH et al (2013) Stress-induced evolution of anisotropic thermal conductivity of dry granular materials. Acta Geotech 8(1):91–106CrossRefGoogle Scholar
  13. 13.
    Cote J, Konrad JM (2005) A generalized thermal conductivity model for soils and construction materials. Can Geotech J 42(2):443–458CrossRefGoogle Scholar
  14. 14.
    De Vries DA (1952) A nonstationary method for determining thermal conductivity of soil in situ. Soil Sci 73(2):83–89CrossRefGoogle Scholar
  15. 15.
    De Vries DA (1963) Thermal properties of soils. In: Van Wijk WR (ed) Physics of plant environment. Wiley, New York, pp 210–235Google Scholar
  16. 16.
    Donazzi F, Occhini E, Seppi A (1979) Soil thermal and hydrological characteristics in designing underground cables. Proc Inst Electr Eng 126(6):506–516CrossRefGoogle Scholar
  17. 17.
    Dong Y, Pamukcu S (2015) Thermal and electrical conduction in unsaturated sand controlled by surface wettability. Acta Geotech 10(6):821–829CrossRefGoogle Scholar
  18. 18.
    Gangadhara Rao MVBB, Singh DN (1999) A generalized relationship to estimate thermal resistivity of soils. Can Geotech J 36(4):767–773CrossRefGoogle Scholar
  19. 19.
    Gemant A (1950) The thermal conductivity of soils. J Appl Phys 21(8):750–752CrossRefGoogle Scholar
  20. 20.
    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 363–368Google Scholar
  21. 21.
    Haigh SK (2012) Thermal conductivity of sands. Geotechnique 62(7):617–625CrossRefGoogle Scholar
  22. 22.
    Heimovaara TJ (1993) Design of triple-wire time domain reflectometry probes in practice and theory. Soil Sci Soc Am J 57(6):1410–1417CrossRefGoogle Scholar
  23. 23.
    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 637Google Scholar
  24. 24.
    Kersten MS (1949) Laboratory research for the determination of the thermal properties of soils, Bulletin No. 28. Minneapolis, MN: University of Minnesota Engineering Experiment StationGoogle Scholar
  25. 25.
    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):1444–1451CrossRefGoogle Scholar
  26. 26.
    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):127–138CrossRefGoogle Scholar
  27. 27.
    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):172–175Google Scholar
  28. 28.
    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):209–218CrossRefGoogle Scholar
  29. 29.
    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 Google Scholar
  30. 30.
    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):8–14CrossRefGoogle Scholar
  31. 31.
    Malicki MA, Skierucha WM (1989) A manually controlled TDR soil moisture meter operating with 300 ps rise-time needle pulse. Irrig Sci 10(2):153–163CrossRefGoogle Scholar
  32. 32.
    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):450–457CrossRefGoogle Scholar
  33. 33.
    Revil A, Lu N (2013) Unified water isotherms for clayey porous materials. Water Resour Res 49(9):5685–5699CrossRefGoogle Scholar
  34. 34.
    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):3391–3401CrossRefGoogle Scholar
  35. 35.
    Smith WO (1942) The thermal conductivity of dry soil. Soil Sci 53(6):435–460CrossRefGoogle Scholar
  36. 36.
    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):13–19CrossRefGoogle Scholar
  37. 37.
    Tarnawski VR, Momose T, Leong WH (2009) Assessing the impact of quartz content on the prediction of soil thermal conductivity. Geotechnique 59(4):331–338CrossRefGoogle Scholar
  38. 38.
    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):1358–1369CrossRefGoogle Scholar
  39. 39.
    Topp GC, Davis JL, Annan P (1980) Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour Res 16(3):574–582CrossRefGoogle Scholar
  40. 40.
    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):678–684CrossRefGoogle Scholar
  41. 41.
    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):932–938CrossRefGoogle Scholar
  42. 42.
    Yu X, Zhang N, Pradhan A (2014) Development and evaluation of a thermo-TDR probe. In: Soil Behavior and Geomechanics, Geo-Shanghai 2014, pp 434–444Google Scholar
  43. 43.
    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):864–877CrossRefGoogle Scholar
  44. 44.
    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 2804–2813Google Scholar
  45. 45.
    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):2367–2376CrossRefGoogle Scholar
  46. 46.
    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 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Civil EngineeringThe University of Texas at ArlingtonArlingtonUSA
  2. 2.Group Delta Consultants, Inc.IrvineUSA

Personalised recommendations