# Experimental and Modeling of Residual Deformation of Soil-Rock Mixture under Freeze-Thaw Cycles
## 1 Introduction  
In recent years, for the sake of adapting to the transition of our country's economic development model from fast to stable, construction of the transportation system, especially the high-speed railway, is increasing. However, the complex geographical conditions also bring more challenges to the project's construction. In particular, projects in seasonal permafrost areas also need to take into account the freezing and thawing deformation of foundation fill composed of soil-rock mixture. Therefore, it is necessary to fully explore the change law of the volume and strength of soil-rock mixture under the action of freeze-thaw cycles, and to grasp the influence of rock content on the residual deformation of the soil-rock mixture, so as to ensure the engineering quality and operation safety to the greatest extent. Many scholars at home and abroad have done plenty of research on the freeze-thaw cycle mechanism and theoretical model, and they usually focus on the basic theory of thesoil frost heave effect. There is still no systematic reference model for the research on the freeze-thaw cycle mechanism of soil-rock mixture. Foreign research on the mechanism of the freeze-thaw cycle roughly started in the 1960s. [PERSON] [1; 2] observed that the rocks in the soil were exposed to the surface due to repeated freezing and thawing in the cold winter area. After research, it was found that under the action of repeated freezing and thawing, when the soil contains enough water, the non-uniform soil particles will undergo vertical sorting of particle sizes. Further laboratory experiments determined the basic conditions for vertical sorting to occur, that is, the effects of the freezing rate range, water content on the frozen surface, and particle size on soil particle migration. [PERSON] and [PERSON] [3] proposed another explanation for this phenomenon, which was, assuming that the soil particles are spherical and are of sufficient mass, embedded in a cold mud composed of fine particles frozen from top to bottom, then the direction of the particles' movement is decided by the orientation of freezing and thawing, which is not determined by the direction of gravity. [PERSON] and [PERSON] [4] believe that, in addition to the freezing expansion of soil water, the frost heave effect of soil water on soil during the freezing process should also be taken into consideration. Due to the repulsion between ice and particles and the tension created by unfrozen water, larger particles tend to be sorted to the surface layer, while smaller particles are migrated deep into the soil. [PERSON] [5] expounded the frost heave theory from a geological point of view. That is to say, the separation of ice occurs during the frost heave process of soil. Different forms of separated ice such as ice layers and ice wedges will cause the soil to bulge with the continuous growth. With the seasonal freezing and thawing, the soil particles are sorted and the rocks in the soil are migrated. The study by [PERSON] [6] pointed out the soil conditions necessary for the uplift of the rock under the action of freeze-thaw cycles. The test results show that the void ratio of the soil is the key parameter that determines the upward or downward movement of the rock. In addition, the soil must contain enough water for ice to form and to cause frost heave. During the freeze-thaw cycle, vertical cracks are induced in the fine-grained soil, and the water in the soil continuously replenishes the water for the formation of ice lenses. This process causes the rock and coarse particles to continuously move towards the cold end, that is, generally towards the surface. An artificial neural network model was proposed and validated by [PERSON] et al. [7], who tested the modulus of elasticity of pavement subgrade soils in seasonal permafrost zones. Thus, the elastic modulus of the soil can be estimated under freeze-thaw cycling conditions by combining the initial moisture content of the specimen and the soil type.