Heat and Mass Transfer

, Volume 54, Issue 9, pp 2845–2852 | Cite as

Stochastic analysis of uncertain thermal parameters for random thermal regime of frozen soil around a single freezing pipe

  • Tao WangEmail author
  • Guoqing Zhou
  • Jianzhou Wang
  • Lei Zhou


The artificial ground freezing method (AGF) is widely used in civil and mining engineering, and the thermal regime of frozen soil around the freezing pipe affects the safety of design and construction. The thermal parameters can be truly random due to heterogeneity of the soil properties, which lead to the randomness of thermal regime of frozen soil around the freezing pipe. The purpose of this paper is to study the one-dimensional (1D) random thermal regime problem on the basis of a stochastic analysis model and the Monte Carlo (MC) method. Considering the uncertain thermal parameters of frozen soil as random variables, stochastic processes and random fields, the corresponding stochastic thermal regime of frozen soil around a single freezing pipe are obtained and analyzed. Taking the variability of each stochastic parameter into account individually, the influences of each stochastic thermal parameter on stochastic thermal regime are investigated. The results show that the mean temperatures of frozen soil around the single freezing pipe with three analogy method are the same while the standard deviations are different. The distributions of standard deviation have a great difference at different radial coordinate location and the larger standard deviations are mainly at the phase change area. The computed data with random variable method and stochastic process method have a great difference from the measured data while the computed data with random field method well agree with the measured data. Each uncertain thermal parameter has a different effect on the standard deviation of frozen soil temperature around the single freezing pipe. These results can provide a theoretical basis for the design and construction of AGF.



Heat capacity in the frozen area, [J/(m3·°C)]


Heat capacity in the unfrozen area, [J/(m3·°C)]


Latent heat of melting, [J/m3]


Outer diameter of freezing pipe, [m]


Temperature, [oC]


Temperature in the frontal freezing surface, [°C]


Phase transition temperature range, [°C]


Temperature for the outside surface of freezing pipe, [°C]


Initial temperature for the soil around freezing pipe, [°C]


Time, [s]

Li, Lj

Length of local average element, [m]


Center of local average element, [m]



Thermal conductivity in the frozen area, [W/(m·°C)]


Thermal conductivity in the unfrozen area, [W/(m·°C)]


Scale of fluctuation for random field, [m]



The authors thank the three anonymous reviewers for their comments and advice. This research was supported by the National Natural Science Foundation of China (Grant No. 51604265 and 51323004), the 111 Project (Grant No. B14021) and the China Postdoctoral Science Foundation funded project (Grant No. 2017M620229).


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Copyright information

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

Authors and Affiliations

  • Tao Wang
    • 1
    • 2
    Email author
  • Guoqing Zhou
    • 1
  • Jianzhou Wang
    • 1
  • Lei Zhou
    • 2
  1. 1.State Key Laboratory for Geomechanics and Deep Underground EngineeringChina University of Mining and TechnologyXuzhouChina
  2. 2.School of Mechanics and Civil EngineeringChina University of Mining and TechnologyXuzhouChina

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