土体一维冻结问题温度场半解析解

针对土体的一维冻结过程，采用考虑土体冻结状态下未冻水存在的等效热容模型，建立了其温度场计算的半解析方法, 并与相关文献中的数值解进行了对比，验证了方法的正确性。对等效热容模型与显热容模型进行了对比, 计算结果表明：在瞬态阶段，显热容模型计算的冻结锋面推进速度较等效热容模型慢；而在接近稳态阶段，显热容模型计算的冻土区厚度较等效热容模型厚。在冻结诱导水流较弱的情形下，土体冻结状态下的持水特性越好，采用显热容模型进行温度场计算产生的误差越显著，并且其计算结果应用于人工冻结设计是偏于不安全的

Semi-analytical solution for temperature field of one-dimensional soil freezing problem

In order to calculate the temperature of the one-dimensional soil freezing process, the equivalent heat capacity model which considers the unfrozen water content has been applied; and the semi-analytical solution for the temperature field has been obtained. The solution procedure has been based on the Fourier method, and the solution has been confirmed by comparing with the numerical solution in some references. The comparison between the equivalent heat capacity model and the apparent heat capacity model has been made; and the results indicate that, during the transient stage, the advancing velocity of the freezing front calculated from the apparent heat capacity model is smaller than that of the equivalent heat capacity model; during the steady stage, the thickness of the frozen zone calculated from the apparent heat capacity model is larger than that of the equivalent heat capacity model. Considering the situation that the water flow induced by the freezing process is weak, then the better the soil freezing characteristic is, the larger the error gets when the apparent heat capacity model is used to calculate the temperature field; and the results are unsafe for the design of the artificial ground freezing engineering.