冻土导热系数的聚合模型研究及试验验证

为揭示土体冻结过程中导热系数的变化规律，建立基于均质球形颗粒的聚合几何模型。该模型由若干半径相等的球形土颗粒在正交方向上堆积而成，且土颗粒之外的区域全部被液态水填充。依据孔隙水首先在远离土颗粒的区域开始冻结的客观规律，建立冻结核在球形颗粒之间的几何中心产生并呈同心球向外扩展的聚合模型。基于土颗粒、水、冰的三相组成，从饱和冻土的组成和球形颗粒之间的接触等微观角度出发，建立导热系数的混合流计算方法。依据建立的几何模型和未冻水含量测试结果，结合给出的导热系数混合流计算方法，能够确定冻土在不同负温阶段的导热系数。另外，给出修正的正交热传导几何模型以计算不同干密度冻土的导热系数，并将混合流计算方法得出的预测值分别与Johansen法、Wiener法的预测值和探针法的实测值进行比较。研究结果表明：提出的混合流计算方法能够高精度地预测高温冻结阶段砂土的导热系数；聚合几何模型解答了干密度较大的土体冻实后的导热系数不一定较大的现象，具象地揭示出冻土导热系数随不同负温变化的原因是土中冰体含量的动态变化；依据冻结核产生位置建立的混合流导热系数计算方法，赋予了Wiener法在冻土导热系数预测中的具体物理意义；聚合模型和混合流导热系数计算方法能够对冻土在不同负温阶段的导热系数进行可靠预测，该研究期望为寒区和冻结法中的水-热-力耦合问题研究提供保证。

Aggregation Model Research and Experimental Verification of Frozen Soil Thermal Conductivity

An aggregation geometric model is established based on homogeneous spherical particles to reveal the variation in the thermal conductivity in the process of soil freezing. The model is composed of multiple spherical soil particles having equal radius, which are stacked in the orthogonal direction, and the remaining area is filled with liquid water. Based on the objective law that pore water begins to freeze in the region away from the soil particles, the aggregation model of the frozen core in the center of the spherical particles and the outward expansion of the concentric spheres are established. In view of the three-phase composition of soil particles, water, and ice, the mixed flow calculation method for thermal conductivity is proposed according to the microscopic properties such as the composition of the saturated frozen soil and contact between spherical particles. Based on the results of the homogeneous spherical aggregation geometry model and unfrozen water content of the frozen soil, the thermal conductivity of the frozen soil at different negative temperatures can be determined by using the method of mixed flow calculation, as proposed in this paper. A modified orthogonal heat conduction geometry model is proposed to satisfy the calculation of thermal conductivity at different dry densities of the soil. The predicted values for the flow calculation method were respectively compared with the predicted values of the Johansen method, Wiener method, and measured values of the probe method. The result shows that the mixed flow calculation method proposed in this paper can accurately predict the thermal conductivity of frozen sand in the high-temperature frozen stage. The aggregation geometric model explains the phenomenon that the thermal conductivity of the soil with a higher dry density is not necessarily increased after freezing. It concretely shows that the thermal conductivity of the frozen soil varies with different negative temperatures is the dynamic change in the ice content in the soil. Concurrently, the mixed flow calculation method established based on the location of the frozen nucleus provides the physical significance of the Wiener method for the prediction of the frozen soil thermal conductivity. The aggregation model and mixed flow calculation method for thermal conductivity can reliably predict the thermal conductivity of frozen soil at different negative temperatures. It is expected to ensure the study of the moisture-heat-stress coupling problem in the cold zone and freezing process.