Non-local modelling of freezing and thawing of unsaturated soils

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A large part of the earth’s surface is covered by seasonally or permanently frozen soils. Considering the negative impact of climate change, future development of such regions can be underpinned by mathematical methods for accurate analysis of heat and moisture transport in freezing and thawing soils. Reported in this paper is a novel non-local formulation of water and heat transport in unsaturated soils. The formulation uses bond-based peridynamics (PD) and consists of a set of integral-difference formulations of energy and mass conservation. Specific features of freezing/thawing soils are incorporated by a combination of van Genuthcen and Clausius-Clapeyron relations. Computational results are compared with four sets of laboratory experiments to demonstrate the efficiency of the developed approach. The model can be used to analyse the effect of water flow on heat transfer in soils during thawing of permafrost soils. Further, it can be applied in modelling climate change effects, and can be used for construction of coupled physically justified models of frost heave.
Original languageEnglish
Article number104614
Number of pages17
JournalAdvances in Water Resources
Publication statusPublished - 1 Feb 2024


  • Peridynamics
  • heat conduction
  • phase change
  • Stephan problem
  • water flow in porous medium
  • unsaturated soils

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  • Energy


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