Thermal–physical properties of selected geomaterials: coal, sandstone and concrete based on basic series and parallel models

  • Zhaoxiang ChuEmail author
  • Guoqing Zhou
  • Yijiang Wang
  • Pin-Qiang Mo
  • Rui Tang
Original Article


Thermal diffusivity and thermal conductivity of three types of selected geomaterials: coking coal, sandstone and foamed concrete, are presented in this paper via water absorbability and thermal–physical property measurements. Experimental results show that the relationships among different thermal–physical properties of composite–porous geomaterials are consistent with the theoretical prediction and the previous experimental data. Based on the hypotheses of basic series and parallel heat propagation patterns, the harmonic approach between series and parallel thermal resistance models is performed. Under the combination of water-saturated and oven-drying conditions, this hypothetical model can be used to inversely calculate the effective/equivalent thermal conductivity (ETC) of the solid matrix with the acceptable accuracy compared with five other ETC prediction models based on mixing laws, especially for saturated samples. In addition, the rationality of the respective proportions of series and parallel heat propagation forms is also examined due to the acceptable accuracy of solid matrix inversely calculated ETC. Further validation on solid skeleton ETC of selected geomaterials indicates that the difference between two solid matrix ETC computational methods: namely the forward calculation using the XRD mineralogical composition data and inverse computation using the block sample ETC experimental results, is significant. Compared with the inverse calculation (overall relative uncertainty of 4.26%), the forward calculation results obtained using XRD data are not accurate enough (relative uncertainty is approximately 7.6–11.4%), which requires a large database for validation and further researches.


Geomaterials Porosity Thermal conductivity Series and parallel models XRD 

List of symbols



Heat flux (W)


Temperature (°C)


Area (m2)

Weight of series model (%)


Distance along heat flow (m)

Volume fraction (%)


Volume (m3)


Degree of saturation


Mass (kg)


Thermal diffusivity (m2 s−1)


Specific heat (J kg−1 K−1)

\( \overline{\Delta t} \)

Temperature increase (K)


Output power (W)


Sensor radius (m)






Range factor



Thermal conductivity (W m−1 K−1)


Thickness (m)


Effective porosity (%)


Water absorption (%)


Density (kg m−3)


Dimensionless specific time

\( \sigma \)

Standard deviation

\( \nu \)

Degree of freedom



ETC of series model


ETC of parallel model






nth component

No. of tests


ith component








Natural water absorption


Compulsory water absorption


Type A uncertainty method 1


Type A uncertainty method 2


Type B uncertainty


Overall uncertainty


Geometric mean


Square root mean



This work was financially supported by “The Fundamental Research Funds for the Central Universities” (2017BSCXB55) and “The Postgraduate Research & Practice Innovation Program of Jiangsu Province” (KYCX17_1527). Special thanks to the anonymous reviewers for their valuable comments and Prof. David C. Sego from University of Alberta for his proofreading.

Supplementary material

12665_2018_7337_MOESM1_ESM.mp4 (298 kb)
Supplementary material 1 (MP4 297 kb)

Supplementary material 2 (MP4 4171 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanics and Civil EngineeringChina University of Mining and TechnologyXuzhouPeople’s Republic of China
  2. 2.State Key Laboratory for Geo-Mechanics and Deep Underground EngineeringXuzhouPeople’s Republic of China

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