# Modeling Wicking Fabric Inhibition Effect on Frost Heave
## Coupled THM Modeling
### Actual Evaporation of WF  
The wetting process describes the movement of absorbed water in the geotextile. Geotextiles can remove water through gravity drainage and evaporation during a wet period. In saturated soils, gravity drainage occurs if sufficient water is supplied and the rate of water flow onto an exposed geotextile is greater than the evaporation rate. WF and conventional geotextiles can both provide gravity drainage. Besides serving as a gravity drainage device, WF can remove water in unsaturated soils by sucking it into the fibers. The WF water migration process is illustrated in Figure 2a, which is modified from Guo [37]. The water is transported to an exposed portion of the WF and evaporates into the air. In this study, the water removed by WF is described as an evaporating process, as illustrated in Figure 2a. The model test simulation was simplified by using the following assumption for the evaporation process of WF: water evaporation from WF exposed to air (\(X\)) equals the water absorbed from WF buried in the soil (\(Y\)), as shown in Figure 2b. Accordingly, the numerical model calculated the evaporation of WF exposed to air and applied it to the WF buried in the soil as a line source. However, this simplification is limited. As the model assumes that the rate of evaporation from the WF is the same as the rate of water removal from the soil, this assumption only holds true when the area of WF exposed to air (\(La\)) is not less than the area buried in the soil (\(Ls\)). Therefore, when the area of the WF exposed to air is smaller than that buried in the soil, the evaporation amount calculated by this method will be higher than reality. Accordingly, the WF appears to be more effective at suppressing frost heave in the calculation than it is. Figure 2: \(Cont.\)  
Referring to [PERSON] et al. [38], the actual evaporation rate can be expressed in the form of the thermodynamic equilibrium relationship between the relative humidity and total suction,  
\[AE=PE\times\exp^{(\frac{-\epsilon g\omega_{n}}{\zeta(1-SH_{T0})RT})} \tag{22}\]  
The widely used equation to calculate the potential evaporation rate was proposed by [PERSON] [39], which is written as  
\[PE=\frac{\Gamma\Omega_{n}+\eta_{e}E_{a}}{\Gamma+\eta_{e}} \tag{23}\]  
where \(E_{a}\) can be expressed as  
\[E_{a}=3.5(1+0.146U_{a})(e_{a0}-e_{a}) \tag{24}\]  
The heat budget is caused by the net radiant energy available at the surface. The heat budget and the wind speed are neglected in the freezing process, so Equation (23) can be simplified as  
\[PE=\frac{\eta_{e}3.5(e_{a0}-e_{a})}{\Gamma+\eta_{e}} \tag{25}\]  
[PERSON] [40] estimated \(\Gamma\) based on the air temperature as follows:  
\[\Gamma=\frac{4098e_{a0}}{\left(273.15+T_{a}\right)^{2}} \tag{26}\]  
and  
\[e_{a0}=\frac{e^{0}(T_{amax})+e^{0}(T_{amin})}{2} \tag{27}\] \[e_{a}=\frac{e^{0}(T_{amax})\frac{RH_{amax}}{100}+e^{0}(T_{amin}) \frac{RH_{amin}}{100}}{2}\] (28) \[e^{0}(T_{a})=0.6108\exp\biggl{(}\frac{17.27T_{a}}{T_{a}+273.15} \biggr{)} \tag{29}\]  
This study simulates the absorption of water by WF as an evaporation process and models this process numerically. In contrast to the evaporation process occurring under  
Figure 2: Schematic of water transport and evaporation in wicking geotextile. (**a**) Water transport and evaporation in wicking geotextile 5. (**b**) Simplified schematic of the evaporation model. saturated conditions with sufficient water supply, the unsaturated soil evaporation model is coupled with the evaporation process of the WF. In addition, this study presents a numerical simulation of the WF evaporation process under unsaturated conditions. The model includes both the evaporation and freezing processes. Thus, the proposed model can be used to simulate the water uptake of WF in unsaturated soil during the freezing process. Table 1 contains all abbreviations or symbols applied to variables and parameters, and Table 2 contains the fixed parameters which are employed in the model.