Model tests and similarity criteria for nonlinear freezing of rock and soil

The specific heat and thermal conductivity of soil change constantly in a freezing process due to the significant difference in the specific heat and thermal conductivity between ice and water. The similarity criterion of the temperature field, built upon constant thermal parameters, can't accurately describe the evolution of the temperature field caused by nonlinear thermal parameters in a freezing process. Based on the heat conduction differential equation that considers the nonlinear behaviour of thermal parameters, the similarity criterion of temperature field of frozen soil model test was derived. The derivation was conducted by using the similar transformation method. The similarity relation between the prototype and the model was given when the original soil was used for model test. Meanwhile, the similarity conditions of thermophysical properties of the model soil were derived, considering the influence of the third boundary condition on the similarity criterion. On this basis, the temperature fields of the prototype and the model were simulated by ABAQUS, which considers the linearity, nonlinearity and the third boundary condition, and analyzed the temperature evolution of characteristic points in the freezing process. The results show that, the established nonlinear similarity criterion of heat conduction accurately reflects the temperature field development of the prototype frozen soil, and indicate the calculation method of thermal parameters of model soil is reasonable. Meanwhile, the nonlinear freezing similarity criterion that satisfies the third boundary condition has definite physical significance and higher practical values. This study provides a practical and meaningful calculation method for the preparation of model soil in the frozen soil model test. It also provides the theoretical basis and technical support for the design and implementation of temperature-moisture-stress coupling test in frozen soil. © 2019, Engineering Mechanics Press. All right reserved.