Similarity Criterion of Freezing Model Test considering Nonlinear Variation of Thermal Parameters with Temperature

The significant differences in specific heat and thermal conductivity of ice and water lead to the changes of specific heat and thermal conductivity of soil during the freezing process. This makes it hard for the temperature field similarity criterion based on constant thermal parameters to accurately reflect the temperature field evolution of soil mass caused by nonlinearity of thermal parameters in the process. Based on heat conduction differential equation considering nonlinear changes of thermal parameters, this paper uses similarity transformation method to derive the similarity criterion of the temperature field in the frozen soil model test and arrives at the conclusion that the prototype soil and model soil should meet when the original soil is used for the model test. At the same time, given the impact of the third boundary condition on the similarity criterion, the thermal physical similarity conditions for the model soil are derived. On this basis, ABAQUS finite element software is used to numerically simulate the linear and nonlinear prototype and model temperature fields. The third boundary condition considered the temperature evolution of the characteristic points during the freezing process is analyzed. The calculation results indicate that the nonlinear thermal conductivity similarity criterion established herein can correctly reflect the evolution process of the prototype frozen soil temperature field. It is also suggested that the model soil thermal parameters are reasonably calculated. At the same time, it shows that the nonlinear freezing similarity criterion of the soil, when the third boundary condition is satisfied, has clear physical meaning and higher practical value. The research results provide a practical and reasonable parameter calculation method for the model soil preparation in the frozen soil model test and a theoretical basis and technical support for the design and implementation of the water-heat-force coupling model test on frozen soil.