Similarity criterion for the nonlinear thermal analysis of the soil freezing process: considering the dual effect of nonlinear thermal parameters and boundary conditions

Model tests are an important method to predict the design and long-term performance of structures and are widely used to analyze the seismic performance, wind resistance, etc., of special structures. For geomaterials, it is difficult to find a material with similar properties to soil in some dimensions. This shortage hinders several kinds of geotechnical model tests that should be implemented with the in situ soil in a 1:1 ratio. Thus, a long-term prediction for tens or hundreds of years cannot be achieved. To guide long-term prediction of freezing soil temperatures, considering the nonlinear change in thermal parameters and the effect of thermal boundary conditions during the soil freezing process, the similarity criterion of the heat conduction process in a frozen soil is derived based on similarity transformation theory. Additionally, for the simulation of frozen soil heat conduction, a general expression of the model soil thermal parameters is given. Based on model tests and numerical simulations, an indirect method is proposed to verify the similarity criterion deduced herein. The results show that the similarity criterion considering the influence of the third kind of boundary conditions is more suitable for engineering practice and can better reflect the evolution of soil freezing temperatures. This research has a theoretical effect on the model test design and model soil preparation of frozen soil temperature fields, and provides a useful method for the future performance prediction of frozen soil thermal problems.