Acta Geotechnica

, Volume 14, Issue 6, pp 2007–2029 | Cite as

Improving a thermal conductivity model of unsaturated soils based on multivariate distribution analysis

  • Haifeng Zou
  • Nan ZhangEmail author
  • Anand J. Puppala
Research Paper


Soil thermal conductivity (k) is a key parameter for the design of energy geo-structures, and it depends on many soil properties such as saturation degree, porosity, mineralogical composition, soil type and others. Capturing these diversified influencing factors in a soil thermal conductivity model is a challenging task for engineers due to the nonlinear dependencies. In this study, a multivariate distribution approach was utilized to improve an existing soil thermal conductivity model, Cote and Konrad model, by quantitatively considering the impacts of dry density (ρd), porosity (n), saturation degree (Sr), quartz content (mq), sand content (ms) and clay content (mc) on thermal conductivity of unsaturated soils. A large database containing these seven soil parameters was compiled from the literature to support the multivariate analysis. Simplified bivariate and multivariate correlations for improving the Cote and Konrad model were derived analytically and numerically to consider different influencing factors. By incorporating these simplified correlations, the predicted k values were more concentrated around the measured values with the coefficient of determination (R2) increased from 0.83 to 0.95. It is concluded that the developed correlations with the information of different soil properties provide an efficient, rational and simple way to predict soil thermal conductivity more accurately. Moreover, the quartz content is a more important factor than the porosity that shall be considered in the establishment of thermal conductivity models for unsaturated soils with high quartz content.


Multivariate correlations Numerical simulation Quartz content Soil thermal conductivity Unsaturated soils 



Majority of the work presented in this paper was funded by the National Key R&D Program of China (2016YFC0800200) and the National Natural Science Foundation of China (Grant No. 41672294). These financial supports are gratefully acknowledged. The authors would like to acknowledge the researchers who published the data in the literature but findings and conclusions expressed in this paper do not reflect the views of those researchers.


  1. 1.
    Barry-Macaulay D, Bouazza A, Wang B, Singh RM (2015) Evaluation of soil thermal conductivity models. Can Geotech J 52(11):1892–1900CrossRefGoogle Scholar
  2. 2.
    Bi J, Zhang MY, Chen WW, Lu JG, Lai YM (2018) A new model to determine the thermal conductivity of fine-grained soils. Int J Heat Mass Transf 123:407–417CrossRefGoogle Scholar
  3. 3.
    Box GEP, Cox DR (1964) An analysis of transformations. J R Stat Soc Ser B26(2):211–252zbMATHGoogle Scholar
  4. 4.
    Chen SX (2008) Thermal conductivity of sands. Heat Mass Transf 44(10):1241–1246CrossRefGoogle Scholar
  5. 5.
    Ching JY, Phoon KK (2014) Correlations among some clay parameters—the multivariate distribution. Can Geotech J 51:686–704CrossRefGoogle Scholar
  6. 6.
    Ching JY, Phoon KK, Chen CH (2014) Modeling piezocone cone penetration (CPTU) parameters of clays as a multivariate normal distribution. Can Geotech J 51(1):77–91CrossRefGoogle Scholar
  7. 7.
    Cote J, Konrad JM (2005) A generalized thermal conductivity model for soils and construction materials. Can Geotech J 42(2):443–458CrossRefGoogle Scholar
  8. 8.
    Farouki OT (1981) Thermal properties of soils, CRREL Monograph 81-1. US Army Corps of Engineers, Cold Regions Research and Engineering Laboratory, Hanover, NHCrossRefGoogle Scholar
  9. 9.
    Grabarczyk M, Furmanski P (2013) Predicting the effective thermal conductivity of dry granular media using artificial neural networks. J Power Technol 93(2):59–66Google Scholar
  10. 10.
    He HL, Zhao Y, Dyck MF, Si BC, Jin HJ, Lv JL, Wang JX (2017) A modified normalized model for predicting effective soil thermal conductivity. Acta Geotech 12:1281–1300CrossRefGoogle Scholar
  11. 11.
    He HL, Dyck MF, Horton R, Ren TS, Bristow KL, Lv J, Si B (2018) Development and application of the heat pulse method for soil physical measurements. Rev Geophys 56(4):567–620CrossRefGoogle Scholar
  12. 12.
    He HL, Dyck MF, Horton R, Li M, Jin HJ, Si BC (2018) Distributed temperature sensing for soil physical measurements and its similarity to heat pulse method. In: Sparks DL (ed) Advances in Agronomy. Academic Press, Cambridge, pp 173–230Google Scholar
  13. 13.
    Johansen O (1975) 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
  14. 14.
    Liu SY, Zou HF, Cai GJ, Bheemasetti T, Puppala AJ, Lin J (2016) Multivariate correlation among resilient modulus and cone penetration test parameters of cohesive subgrade soils. Eng Geol 209:128–142CrossRefGoogle Scholar
  15. 15.
    Lu N, Dong Y (2015) Closed-form equation for thermal conductivity of unsaturated soils at room temperature. J Geotech Geoenviron Eng 141(6):04015016CrossRefGoogle Scholar
  16. 16.
    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
  17. 17.
    Mishra PN, Surendran S, Gadi VK, Joseph RA, Arnepalli DN (2017) Generalized approach for determination of thermal conductivity of buffer materials. J Hazard Toxic Radioact Waste 21(4):04017005CrossRefGoogle Scholar
  18. 18.
    Ochsner TE, Horton R, Ren T (2001) A new perspective on soil thermal properties. Soil Sci Soc Am J 65(6):1641–1647CrossRefGoogle Scholar
  19. 19.
    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
  20. 20.
    Tarnawski VR, Momose T, McCombie ML, Leong WH (2015) Canadian field soils III. Thermal-conductivity data and modeling. Int J Thermophys 36:119–156CrossRefGoogle Scholar
  21. 21.
    Zhang N (2015) Development and validation of TDR based sensors for thermal conductivity and soil suction measurements. Ph.D. Thesis, University of Texas at Arlington, ArlingtonGoogle Scholar
  22. 22.
    Zhang N, Yu XB, Pradhan A, Puppala AJ (2015) Effects of particle size and fines content on thermal conductivity of quartz sands. Transp Res Rec J Transp Res Board 2510:36–43CrossRefGoogle Scholar
  23. 23.
    Zhang N, Yu XB, Pradhan A, Puppala AJ (2015) Thermal conductivity of quartz sands by thermo-TDR probe and model prediction. ASCE J Mater Civ Eng 27(12):04015059CrossRefGoogle Scholar
  24. 24.
    Zhang N, Wang ZY (2017) Review of soil thermal conductivity and predictive models. Int J Therm Sci 117:172–183CrossRefGoogle Scholar
  25. 25.
    Zhang N, Yu XB, Pradhan A, Puppala AJ (2017) A new generalized soil thermal conductivity model for sand-kaolin clay mixtures using thermo-TDR probe. Acta Geotech 12(4):739–752CrossRefGoogle Scholar
  26. 26.
    Zou HF, Liu SY, Cai GJ, Puppala AJ, Bheemasetti T (2017) Multivariate correlation analysis of seismic piezocone penetration (SCPTU) parameters and design properties of Jiangsu quaternary cohesive soils. Eng Geol 228:11–38CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringThe Hong Kong University of Science and TechnologyClear Water BayChina
  2. 2.Institute of Geotechnical EngineeringSoutheast UniversityNanjingChina
  3. 3.Department of Civil EngineeringThe University of Texas at ArlingtonArlingtonUSA

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