# Study of the Effect of Cutting Frozen Soils on the Supports of Above-Ground Trunk Pipelines
## 3 Results
### Development of Above-Ground Trunk Pipeline Support Design
Figure 3:0 Distribution of equivalent stresses of the sharp edge in the most probable case of cutting frozen sand from frost heave forces at \(-10\)\({}^{\circ}\)C.  
Figure 3:1 Distribution of equivalent stresses of the sharp edge in the most probable case of cutting frozen clay from the frost heave forces at \(-10\)\({}^{\circ}\)C.  
To assess the accuracy of the mathematical model for calculating the design of the support slab in the PLAXIS environment, the final results of the finite-element model and the experimental measurement data were compared with the actual displacements of the support slab obtained through PC measurements (as presented in Table 2). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No. of Experience**} & \multirow{2}{*}{**Temperature of**} & \multirow{2}{*}{**Type of Frozen**} & \multirow{2}{*}{**Soil Fracture**} & \multirow{2}{*}{**Movements of the Press with**} \\  & & & & \\ \cline{3-4} \cline{5-5}  & & & & \\ \hline \multicolumn{4}{c}{Results of experimental measurements (initial data—given actual displacements of a sharp edge)} \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{\(-4\)} & Sand & 16,055 & 0.1014 \\ \cline{3-4} \cline{5-5}  & & Sandy loam & 17,085 & 0.1013 \\ \cline{3-4} \cline{5-5}  & & Clay & 25,091 & 0.1019 \\ \hline \multirow{4}{*}{2} & \multirow{4}{*}{\(-5\)} & Sand & 21,526 & 0.1016 \\ \cline{3-4} \cline{5-5}  & & Sandy loam & 30,768 & 0.1012 \\ \cline{3-4} \cline{5-5}  & & Clay & 48,355 & 0.1022 \\ \hline \multirow{4}{*}{3} & \multirow{4}{*}{\(-7\)} & Sand & 34,754 & 0.1013 \\ \cline{3-4} \cline{5-5}  & & Sandy loam & 49,886 & 0.1014 \\ \cline{3-4} \cline{5-5}  & & Clay & 73,976 & 0.1029 \\ \hline \multirow{4}{*}{4} & \multirow{4}{*}{\(-8\)} & Sand & 42,639 & 0.1012 \\ \cline{3-4} \cline{5-5}  & & Sandy loam & 56,868 & 0.1015 \\ \cline{3-4} \cline{5-5}  & & Clay & 91,669 & 0.1033 \\ \hline \multirow{4}{*}{5} & \multirow{4}{*}{\(-10\)} & Sand & 58,644 & 0.1011 \\ \cline{3-4} \cline{5-5}  & & Sandy loam & 78,647 & 0.1012 \\ \cline{3-4} \cline{5-5}  & & Clay & 119,148 & 0.1051 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the performance test of the computational model. Figure 12: Distribution of equivalent stresses of the sharp edge in the most probable case of cutting frozen sandy loam from the frost heave forces at \(-10\,^{\circ}\)C.  
The verification calculations demonstrate the reliability of the proposed above-ground pipeline support structure, specifically the support slab with a sharp edge, through the high level of convergence between the model and experimental measurements (as shown in Table 3). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No. of Experience**} & \multirow{2}{*}{**Temperature of**} & \multirow{2}{*}{**Type of Frozen**} & \multirow{2}{*}{**Soil Fracture**} & \multirow{2}{*}{**Movements of the Press with**} \\  & & & & \\ \cline{5-5}  & & & & \\ \hline \multicolumn{5}{c}{Calculation results in the PLAXIS final element model (input data—given actual sharp edge movements)} \\ \hline \hline \multirow{4}{*}{1} & \multirow{4}{*}{\(-4\)} & Sand & 16,695 & 0.1014 \\ \cline{3-5}  & & Sandy loam & 17,585 & 0.1013 \\ \cline{3-5}  & & Clay & 25,591 & 0.1019 \\ \hline \multirow{4}{*}{2} & \multirow{4}{*}{\(-5\)} & Sand & 22,026 & 0.1016 \\ \cline{3-5}  & & Sandy loam & 31,268 & 0.1012 \\ \cline{3-5}  & & Clay & 49,134 & 0.1022 \\ \hline \multirow{4}{*}{3} & \multirow{4}{*}{\(-7\)} & Sand & 35,223 & 0.1013 \\ \cline{3-5}  & & Sandy loam & 50,773 & 0.1014 \\ \cline{3-5}  & & Clay & 74,666 & 0.1029 \\ \hline \multirow{4}{*}{4} & \multirow{4}{*}{\(-8\)} & Sand & 43,358 & 0.1012 \\ \cline{3-5}  & & Sandy loam & 57,332 & 0.1015 \\ \cline{3-5}  & & Clay & 92,649 & 0.1033 \\ \hline \multirow{4}{*}{5} & \multirow{4}{*}{\(-10\)} & Sand & 59,234 & 0.1011 \\ \cline{3-5}  & & Sandy loam & 79,636 & 0.1012 \\ \cline{3-5}  & & Clay & 121,147 & 0.1051 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._