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.

地球表面的很大一部分被季节性或永久冻土覆盖。考虑到气候变化的负面影响，这些地区的未来发展可以通过精确分析冻融土壤中热量和水分传输的数学方法来支撑。本文报道了一种新颖的非饱和土壤中水和热传输的非局域公式。该公式使用基于键的近场动力学 (PD)，并由一组能量和质量守恒的积分差分公式组成。冻结/解冻土壤的具体特征由 van Genuthcen 和 Clausius-Clapeyron 关系结合起来。将计算结果与四组实验室实验进行比较，以证明所开发方法的效率。该模型可用于分析多年冻土融化过程中水流对土壤传热的影响。此外，它还可以应用于气候变化影响建模，并可用于构建耦合物理合理的冻胀模型。