# Artificial Neural Network-Based Model for Prediction of Frost Heave Behavior of Silty Soil Specimen
## 5 Summary and Conclusions  
The present study evaluated the frost heave amount caused by the formation of an ice lens layer during the freezing process of soils. Through a parametric study, we analyzed the effects of geotechnical parameters on frost heave ratio in a quantitative manner. Furthermore, this study proposed a predictive model based on an artificial neural network capable of practically estimating frost heave ratio. The main conclusions drawn from this study are as follows. 1. A fully coupled THM model numerically evaluated various physical phenomena that occur during one\(-\)dimensional freezing. During the freezing process, the freezing front propagated rapidly when freezing initially began but came to a halt as it approached thermal equilibrium. The amount of frost heave increased steadily until thermal equilibrium was achieved, after which the freezing front stopped and no further severe frost heave occurred. 2. According to the results of the parametric study, the overall patterns of the predictive model are explained by preconditions for frost heave action. The amount of heave tended to decrease as particle thermal conductivity increased. This may have something to do with thermal conditions that prevent a sufficient inflow of water from external sources due to a high freezing rate. Additionally, the frost heave ratio tended to increase as the initial hydraulic conductivity increased. If the thermal conditions are the same yet the hydraulic conditions are varied, it could be judged that higher soil hydraulic conductivity would result in a higher frost heave ratio. 3. After evaluating the sensitivity of each parameter to frost heave behavior through multiple statistical analyses, an artificial neural network model was proposed to practically estimate frost heave behavior. According to the interpreting connection \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Hidden Node** & & & \\ \hline  & V1 & V2 & OUT \\ \hline \multicolumn{4}{l}{**Connection weights (Input to hidden)**} \\ \hline
1 & \(-\)1.3290 & 1.5107 & \(-\)0.5700 \\ \hline
2 & 1.1272 & \(-\)0.2495 & \(-\)1.1663 \\
3 & \(-\)0.8410 & \(-\)0.0200 & \(-\)0.4456 \\ \hline
4 & \(-\)0.9127 & 0.6520 & 1.2482 \\
5 & 0.7730 & 1.1022 & 0.5838 \\ \hline \multicolumn{4}{l}{**Absolute connection weights (input to hidden)**} \\ \hline
1 & 1.3290 & 1.5107 & 0.5700 \\ \hline
2 & 1.1272 & 0.2495 & 1.1663 \\
3 & 0.8410 & 0.0200 & 0.4456 \\ \hline
4 & 0.9127 & 0.6520 & 1.2482 \\
5 & 0.7730 & 1.1022 & 0.5838 \\ \hline \multicolumn{4}{l}{**Connection shares \({}^{*}\) hidden node input**} \\ \hline
1 & 0.2668 & 0.3032 & \\ \hline
2 & 0.9549 & 0.2114 & \\
3 & 0.4352 & 0.0104 & \\ \hline
4 & 0.7281 & 0.5201 & \\
5 & 0.2407 & 0.3431 & \\ \hline \multicolumn{4}{l}{**Sum:**} & **2.6257** & **1.3882** & \\ \hline \multicolumn{4}{l}{**Input node share of output layer connections, excluding bias ones**} \\ \hline  & **65.41\%** & & **34.59\%** \\ \hline  & \(k_{0}\) (m/s) & & \(\lambda_{s}\) (W/M\(\cdot\)K) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The interpreting neural\(-\)network connection weights. weights, the hydraulic conductivity in the unfrozen zone (\(k_{0}\)) was the most important input parameter that was a direct cause of the frost heave ratio \(\zeta\)(%), and the thermal conductivity of the soil particle (\(\lambda_{s}\)) was lesser importance. In order to evaluate the applicability of the artificial neural network model, the model was tested with datasets that had not been introduced during the training stage. According to the verification results, the trained network model demonstrated a reliable accuracy (R\({}^{2}\) = 0.893) in predicting frost heave ratio, even when the model used the test datasets that were not part of the training datasets. It is expected that this prediction model will be useful in many areas of research related to evaluating the frost heave behavior of saturated specimens. Conceptualization, G.-H.G. and S.Y. ; methodology, D.-V.L. ; software, G.-H.G. and D.-V.L. ; validation, S.Y. ; formal analysis, S.Y.