# Modeling Wicking Fabric Inhibition Effect on Frost Heave
## 5 Results and Discussions  
### Reliability of the Proposed Model  
The numerical results were compared with the experimental data to validate the proposed model. All these experimental and numerical results were obtained from their respective single tests. Figure 6 shows comparisons of the temperature distribution for the soil columns at different observation points in the numerical and experimental studies. The simulation results for both the WWF and NWF models are consistent with the experimental results at each observation point. Additionally, the comparison of the results between the WWF model and the NWF model reveals that these two models do not show significant differences in the temperature distribution and variations during the freezing process. The results demonstrate that the proposed model can accurately simulate temperature changes in the WWF and NWF models during the freezing process. Figure 5: Numerical model and boundary conditions for frost heave tests. Figure 7 presents the volumetric water content variation in the freezing process at the different observation points of the simulation results and experimental results. In the WWF model, the simulation results for the water content at 125 mm differ significantly from the experimental results. The moisture sensor at this site was found to be broken when checking the experimental equipment after the test. However, the numerical calculations were consistent with the experimental results for other observation points. The results indicate that the proposed model is capable of predicting the development and distribution of the water content in the freezing process. In both the WWF and NWF models, the volumetric water content decreased rapidly once freezing began; the closer the observation point is to the cold end, the more significant the reduction in the volumetric water content. Furthermore, Table 4 presents the freezing rate (\(U_{0}\)), frost heave rate (\(U_{h}\)), frost heave ratio (\(\zeta\)), and frost penetration depth (\(l_{0}\)) in the model tests and numerical simulations. The freezing rate (\(U_{0}\)), frost heave rate (\(U_{h}\)), frost heave ratio (\(\zeta\)), and frost penetration depth (\(l_{0}\)) stand for the rate at which the freezing front advances into the unfrozen soil, the amount of frost heave per unit time, the increase in the volume of soil due to freezing expressed as a percentage of the volume before freezing, and the depth to which the groundwater in the soil is expected to freeze (JGS 0171-2009, JGS 0172-2009) [53; 54]. The freezing rate is determined by the freezing time and the frost penetration depth. Assuming the bottom surface as the origin and \(d\) as the distance from the origin, with upwards as positive, freezing begins at the top surface (\(d\) = 250 mm). The freezing rate was calculated by dividing the distance between \(d\) = 225 mm and \(d\) = 125 mm by the time differential between the freezing front developed at the two points. Multiplying  
Figure 6: Comparison of the simulated and tested temperature development at the different observation points. Figure 7: Comparison of the simulated and tested volumetric water content at the different observation points. the freezing rate by the freezing time (100 h) returns the frost penetration depth. Both in the simulations and model tests, the WWF model had a deeper frost penetration depth than the NWF model. As a result of the lower water content due to the WF, the heat capacity of the soil mixture in the WWF model was smaller than that in the NWF model, and the thermal conductivity was higher. Therefore, under the same freezing conditions, the WWF model took less time to freeze to the same height as the NWF model. Comparing at the same observation point and the same freezing time, the volumetric water content in the WWF model was much smaller than that in the NWF model. Additionally, the water content in both the WWF and NWF models decreased significantly with increasing freezing time.