Abstract The relationship between the unfrozen water content in frozen soil and negative temperature is defined as the soil freezing characteristic curve (SFCC). The SFCC plays a crucial role in understanding the hydrothermal migration, frost heaving and constitutive relations of frozen soil. The mechanism of the SFCC is less understood, especially in the low-temperature range. Considering the adsorption and capillary action between soil particles and the ice interface, a new SFCC model for saturated frozen soil is proposed from the pore scale. The predicted results of the model show that the unfrozen water content gradually decreases with the increasing particle radius at the same temperature. The SFCC of monodisperse silica microspheres and quartz sand samples were tested based on nuclear magnetic resonance technology. The experimental results were compared with the mathematical model, which showed that the new SFCC model is in good agreement with the experimental results. The new model has a clear physical meaning and can provide a theoretical basis for understanding the phase change process in frozen soils, which is of great significance to the application of the proposed model.

中文翻译：

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土壤冻结特性曲线的数学模型：吸附和毛细作用的作用

摘要 冻土中未冻水含量与负温之间的关系定义为土壤冻结特征曲线（SFCC）。SFCC 在理解冻土的热液迁移、冻胀和本构关系方面起着至关重要的作用。SFCC 的机制尚不清楚，尤其是在低温范围内。考虑土壤颗粒与冰界面之间的吸附和毛细作用，从孔隙尺度提出了一种新的饱和冻土SFCC模型。模型预测结果表明，在相同温度下，随着颗粒半径的增加，未冻水含量逐渐降低。基于核磁共振技术测试了单分散二氧化硅微球和石英砂样品的SFCC。将实验结果与数学模型进行了对比，表明新的SFCC模型与实验结果吻合较好。新模型物理意义明确，可为理解冻土相变过程提供理论依据，对模型的应用具有重要意义。