基于离散元法的粉质粘土单向冻结过程水热耦合模拟

Hydrological–Thermal Coupling Simulation of Silty Clay during Unidirectional Freezing Based on the Discrete Element Method

Wei Shan ^1,2,3,4* , Shiyao Qu ¹ and Ying Guo ^1,2,3,4

2 Ministry of Education Observation and Research Station of Permafrost Geo-Environment System in Northeast China (MEORS-PGSNEC), Harbin 150040, China;

3 Collaborative Innovation Centre for Permafrost Environment and Road Construction and Maintenance in Northeast China (CIC-PERCM), Harbin 150040, China;

4 Low-Carbon Road Construction and Maintenance Engineering Technology Research Center in Northeast Permafrost Region of Heilongjiang Province (LCRCMT-HLJ), Harbin 150040, China;

* Correspondence: shanwei456@163.com.

Abstract: A hydrological–thermal coupling discrete element model depicting the unidirectional freezing process of unsaturated silty clay was developed in order to investigate the migration law of unfrozen water in unsaturated silty clay under unidirectional freezing circumstances. The model uses the contact heat transfer equation to calculate the heat transfer process while taking into account the latent heat of phase transition. To obtain the silty clay’s freezing characteristic curve, the model combines the unfrozen water content curve with the Clausius–Clapeyron equation. The water migration from the unfrozen zone to the frozen zone was calculated using Harlan’s model and the frozen fringe hypothesis. The discrete element application MatDEM 3.0 was used to incorporate the mathematical model for computation, and the output was compared to the result of indoor unidirectional freezing tests. The soil closest to the stable freezing front had the largest water content, according to the findings of numerical modeling and laboratory testing, and unfrozen water in the soil would move from the unfrozen zone to the frozen zone under the action of water potential difference. The results of laboratory tests and numerical simulations can accurately describe the temperature variation and water migration of soil during freezing, demonstrating the accuracy of the established discrete element model and proving the viability of the discrete element method in the

study of frozen soil.

FIGURE 6 Temperature distribution of samples after freezing at different cold end temperatures:(a) the cold end temperature is -5°C; (b) the cold end temperature is -7°C; (c) the cold end temperature is -10°C.

FIGURE 9 Distribution of water content along the height of the sample at different cold end temperatures: (a) cold end temperature of -5°C; (b) cold end temperature of -7°C; (c) cold end temperature of -10°C.