# Assessment of Frost Depth and Frost Heave in Romania
## 4 Evaluation of Frost Heave/Freeze-Thaw Cycle (FTC)  
The freeze-thaw cycle (FTC) is defined as a cycle in which the temperature fluctuates both above and below 0 \({}^{\circ}\)C [12]. The minimum temperature of 0 \({}^{\circ}\)C is used as the threshold for freezing to increase the likelihood that water froze at the surface. The determination of the number of days with FTC occurrence potential, for each year, for a different investigated period, was calculated in accordance with the two measured parameters: daily maximum temperature (T\({}_{\text{max}}\)) and daily minimum temperature (T\({}_{\text{min}}\)) [13]. Figure 7 highlights the trend of the number of FTCs during the three investigated periods. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Investigated** \\ **Period** \\ \end{tabular} } & \multicolumn{6}{c}{**Depth of Frost (in cm)**} \\ \cline{2-13}  & \multicolumn{3}{c}{**Using AFI, Equation (1)**} & \multicolumn{3}{c}{**Using FI, Equation (4)**} & \multicolumn{3}{c}{**Using Fd\({}_{\text{d}}\)**} \\  & \multicolumn{3}{c}{**Equation (5)**} & \multicolumn{3}{c}{**Equation (6)**} & \multicolumn{3}{c}{**Equation (7)**} \\ \cline{2-13}  & \multicolumn{3}{c}{**\(\mathbf{d_{\text{front,100}}}\)**} & \multicolumn{3}{c}{**\(\mathbf{d_{\text{front,50}}}\)**} & \multicolumn{3}{c}{**\(\mathbf{d_{\text{front,10}}}\)**} & \multicolumn{3}{c}{**\(\mathbf{d_{\text{front,100}}}\)**} & \multicolumn{3}{c}{**\(\mathbf{d_{\text{front,50}}}\)**} & \multicolumn{3}{c}{**\(\mathbf{d_{\text{front,10}}}\)**} & \multicolumn{3}{c}{**\(\mathbf{d_{\text{front,10}}}\)**} & \multicolumn{3}{c}{**\(\mathbf{d_{\text{front,50}}}\)**} & \multicolumn{3}{c}{**\(\mathbf{d_{\text{front,10}}}\)**} & \multicolumn{3}{c}{**\(\mathbf{H}\)**} \\ \hline
1900–2020 & 110 & 100 & 87 & 76 & 117 & 109 & 89 & 110 & 88 & & \\
1950–2020 & 105 & 96 & 83 & 72 & 115 & 107 & 87 & 107 & 86 & 34 & 57 \\
1950–1990 & 113 & 103 & 89 & 78 & 124 & 117 & 96 & 117 & 96 & 3 & \\
1990–2020 & 88 & 80 & 71 & 62 & 84 & 79 & 64 & 78 & 63 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Frost depth for the Arad station. Figure 7: _Cont._  
The FTC10, FTC50, and FTC100 (FTCs with different return periods: 10 years, 50 years, and 100 years) for available meteorological stations are computed using generalized extreme value distribution analysis. Table 7 shows the statistical parameters (mean, standard deviation, and maximum recorded) of the yearly FTCs during different periods for the Arad Station. Also in Table 7, the FTC values are for 10-year, 50-year, and 100-year return periods. The 50-year return FTC values were calculated using the Gumbel value distribution for all 111 meteorological stations in Romania for the 1950-2020 period. Based on the simple kriging geostatistical method, Figure 8 presents the FTC\({}_{50}\) map of Romania. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Investigated**} & \multicolumn{3}{c}{**Yearly Number of FTCs**} & \multirow{2}{*}{**FTC\({}_{\mathbf{10}}\)**} & \multirow{2}{*}{**FTC\({}_{\mathbf{50}}\)**} & \multirow{2}{*}{**FTC\({}_{\mathbf{100}}\)**} \\ \cline{2-2} \cline{5-7}
**Period** & **Average** & **St. Dev** & **Maximum** & & & \\ \hline
1950–2020 & 66.53 & 12.29 & 98 & 83 & 98 & 105 \\
1950–1990 & 67.2 & 10.62 & 92 & 81 & 97 & 101 \\
1990–2020 & 65.63 & 14.02 & 98 & 84 & 102 & 110 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Arad station’s values for the statistical parameters (mean, standard deviation, and maximum recorded) of the yearly FTC during different time intervals. Figure 8: FTC\({}_{50}\) map of Romania for altitudes \(<\)1000 m.  
Figure 7: Number of FTCs during the three investigated periods at the Arad station. Sulina and Miercurea Ciuc stand out as the most extreme locations when considering winter parameters.