# Stability Prediction of Soil Slopes Based on Digital Twinning and Deep Learning
### Digital Twins of Slopes  
Since the number of actual slopes collected was insufficient for CNN training, as shown in Figure 3, in this paper, the DT method was used to create digital models with similar characteristics to the actual slopes, and a group of multi-size models was created by inserting some random points to fine-tune the slope profiles. Each actual slope was extended to create 100 samples. This method was able to provide sufficient CNN training samples for slope stability prediction. First, the outer profile line of each soil layer was represented by a polyline connected by several points, and these points that formed the original slope were called control points. The existing control points were kept unchanged, and some random points were inserted between them to fine-tune the outer shape of the slope and its soil layers and increase the number of slope samples. It should be explained here that the positive \(x\)-axis of the slope coordinate system points horizontally in the direction of the landslide, and the positive y-axis points vertically downward. As shown in Figure 4, the number of randomly inserted points was determined by the quotient of the horizontal projection length between two connected control points divided \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Slope Name** &
\begin{tabular}{c} **Soil Layer** \\ **Number** \\ \end{tabular} & **c (kN/m2)** & **\(\varphi\) (°)** & **\(\gamma\) (kN/m3)** & **\(\gamma_{sat}\) (kN/m3)** \\ \hline \multirow{4}{*}{Lion Mountain} & 1 & 0.0 & 25.0 & 18.0 & 18.5 \\  & 2 & 20.0 & 22.0 & 19.3 & 20.1 \\  & 3 & 15.5 & 15.0 & 19.5 & 20.2 \\  & 4 & 300.0 & 35.0 & 23.0 & 23.25 \\ \hline \multirow{4}{*}{Tianshengqiao} & 1 & 19.6 & 21.8 & 18.1 & 19.0 \\  & 2 & 0.0 & 21.8 & 19.3 & 20.1 \\  & 3 & 29.4 & 20.8 & 18.1 & 19.0 \\  & 4 & 39.2 & 45.0 & 23.5 & 24.0 \\ \hline \multirow{4}{*}{Yanglu Expressway} & 1 & 22.0 & 30.0 & 19.4 & 20.0 \\  & 2 & 30.0 & 27.0 & 20.2 & 21.0 \\ \cline{1-1}  & 3 & 35.0 & 28.0 & 19.0 & 19.8 \\ \cline{1-1}  & 4 & 150.0 & 45.0 & 26.5 & 27.0 \\ \hline \hline \end{tabular} Notes: (1) c: cohesive force; (2) \(\varphi\) : internal friction angle; (3) \(\gamma\): natural unit weight; (4) \(\gamma_{sat}\): saturated unit weight.  
\end{table} 
Table 2: Physical and mechanical parameters of slope. Figure 3: DT of an actual slope. by the corresponding threshold. According to the total length \(L\) of the horizontal projection of the slope, the following threshold was set:  
\[f=\left\{ \begin{array}{l}50\;\mathrm{m}\;L>500\;\mathrm{m}\\ 20\;\mathrm{m}\;500\;\mathrm{m}\geq L>150\;\mathrm{m}\\ 10\;\mathrm{m}\;150\;\mathrm{m}\geq L>50\;\mathrm{m}\\ 3\;\mathrm{m}\;\;L\leq 50\;\mathrm{m}\end{array} \right. \tag{1}\]  
This method was used to fine-tune the outer contour of the slope and soil layers to generate a large number of slope models with profiles similar to the actual slope. To generate diverse samples, the vertical and horizontal coordinates of the insertion points were randomly generated within the range of the control points. In addition, it was necessary to ensure that the insertion point did not penetrate the soil layer and prevent reverse slope (Figure 5). For this reason, the following work was performed:  
Between each pair of control points, the x-coordinates of the insertion points were randomly generated according to their number. The number of insertion points \(=\)\(\frac{\text{the horizontal projection length between the control points}}{\text{the corresponding threshold}}\)  
\[x_{\mathrm{P(i)}}\geq x\;\text{coordinates of the insertion points}\geq x_{ \mathrm{P(i+1)}}\]  
As shown in Figure 6, random points were inserted from the higher control point \(\mathrm{P(i+1)}\) to the lower control point \(\mathrm{P(i)}\) of the slope, and the y-coordinates of the random points were generated:  
Figure 4: Insert random points to fine-tune the shape of the slope. Figure 5: Reverse slope.