## 4 Results
### Analysis I: Comparison of Different Methods
This method also underestimated frost depth by 17% in the case of poorly graded gravel (GM), and overestimated by 28%, 12%, and 37% in the cases of silty sands (SP and SM) in different regions, respectively. For the poorly graded sandy soil type, the MTO method overestimated frost depth prediction by 24% in the Great Falls site but could almost perfectly predict the value for the case of Bemidji in Minnesota. Comparing the results obtained from the TCGA and MTO methods, it can be concluded that, regardless of soil type, these two methods consistently provided either an overestimation or underestimation of the frost penetration depth, which can be considered relatively similar to each other. More specifically, the TCAA method overestimated the frost depth penetration by 27% for CL soil and underestimated it by 4% and 12% in ML and CL soils, respectively. In the case of the poorly graded sands available in the Bemidji and Great Falls sites, TCGA overestimated frost depth by 5% and 17%, respectively, while for the poorly graded gravel in the New Haven site, it underestimated this value by 15%. Furthermore, the TCGA results exhibited overestimation in predicting frost depth in the range of 19% to 48% in the cases of the silty sands in Hamlin and Varden, respectively. Although both underestimation and overestimation of frost penetration depths can affect pavement design to some extent, an underestimation can be especially critical in the case of frost-susceptible soil types that are prone to the frost action and can lead to premature pavement failures. Finally, the MTQ method showed either close-to-field data or more conservative protection depths, in most cases. The only case among those evaluated where the method underestimated frost depth was GM soil from New Haven, Vermont (\(-\)7%). The MTQ method showed the best results within clays, silt, and gravel, with a difference of 3%, \(-\)1%, and \(-\)3% in cases of fat clay, sandy silt, and silty clay soil types, respectively, which can all be considered relatively very close to the actual measured depths in the field. In terms of the difference in magnitude between the predicted and measured field frost depths, the worst-case scenarios were regarding the sites with silty sands and poorly graded sands, with values being overestimated in the range of 15% to 44% higher than the field measured data. While this is still on the safe side for the purpose of frost protection, such overestimation can lead to overddesigned sections and consequently result in an unnecessary increase in  
Figure 4: Comparison between frost depth field data and prediction methods. pavement construction costs. Nevertheless, the results indicate that the MTQ method provides better estimation of the required frost protection for the case studies investigated in this research. Table 4 provides a general comparison between the accuracy of the predictions from the three methods investigated in this research, along with their maximum and minimum differences when compared with the data measured from the field, as well as the average difference and standard deviation, considering all values as positive. From Table 4, it is evident that all methods provided more accurate results when predicting the frost depth of the fine soils. Under the fine soil scenario, the MTQ method had the smallest average difference (2%), and a small standard deviation (1%). On the other hand, for the coarse-grained soil scenario, the MTO method led to the smallest average difference among the methods (20%); however, the TCGA method was not far behind (21%). Regardless of the magnitude differences, the MTQ method provided the most prudent results in terms of rarely underpredicting the frost depth in all evaluated scenarios.