Determining frost heave classification by using ratio of frost heave to square root of time

The frost heave classification is the critical index for the design of foundation engineering in cold regions. At present, it is considered as a basic property of materials. Many criteria belong to empirical or semi-empirical methods and lack theoretical support. The frost heave tests are tedious and long time-consuming, and are not easily operated. To propose a rational and simple frost heave classification index, from the frost heave mechanism, an analytical model for unsaturated frozen soil is established and validated. Then a new frost heave classification index R (mm/h^0.5), which is the ratio of frost heave to square root of time, is identified based on the proposed model. Through comparison with the large number of frost heave results, the value of R less than 0.21 indicates the low frost heave classification, that between 0.21 and 1.18 represents the medium heave classification, and that greater than 1.18 means the high frost heave classification. From a statistical probability perspective, the probability density distribution of the values of each classification index is analyzed, and their trends are also compared. It is found that the concentration and stability of the new index R are the highest during freezing process. The new index R has theoretical support and simultaneously couples the basic soil properties and freezing environmental factors. It breaks through the limitation of the existing indexes, and enriches the frost heave classification system, and provides theoretical support for the engineering design in cold regions.