## 3 Project Overview
### Model Training  
An input layer, hidden layers, and an output layer make up BP. The study's neural network topology is 6-10-5, meaning that there are six design parameters in the input layer, ten neurons in the hidden layer, and five evaluation indicators in the output layer. Figure 5 shows a schematic of the neural network structure. We created a computational model of the secondary embankment using the FLAC3D finite element program. Sixty-eight sets of design parameters were selected for the numerical simulations through orthogonal and control variable tests. The evaluation indicators were used to assess the calculation results. This process yielded 68 sets of sample data for model construction and training. Each data set included six input parameters to be optimized: wrapping thickness, slope ratio of the reinforced embankment, elastic modulus of the fill, reinforcement length, reinforcement elasticity modulus, and soil-reinforcement interface friction angle. The output data consisted of five optimization targets: maximum lateral displacement, maximum vertical displacement, maximum stress in the XZ direction, maximum shear strain increment, and the safety factor. The sample input and output data are listed in Tables 4 and 5, respectively. Due to space constraints, only a portion of the data are presented. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & \multirow{2}{*}{\begin{tabular}{c} **Wrapping** \\ **Thickness (m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Slope Ratio of** \\ **Reinforced** \\ **Embankment (-)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Modulus of** \\ **Ensistcity of the** \\ **Fill (MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Reinforcement** \\ **Strip Length (m)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Lasticity of** \\ **Reinforcement** \\ **Strip (MPa)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Interfacial** \\ **Friction Angle (°)** \\ \end{tabular} } \\ \hline
1 & 0.4 & 1:2.5 & 55 & 30 & 2600 & 5 \\ \hline
2 & 0.4 & 1:2 & 35 & 15 & 1000 & 4 \\ \hline
3 & 0.4 & 1:1.5 & 15 & 25 & 1400 & 3 \\ \hline
4 & 0.4 & 1:1 & 45 & 10 & 1800 & 2 \\ \hline
5 & 0.4 & 1:0.5 & 25 & 20 & 2200 & 1 \\ \hline
6 & 0.6 & 1:2.5 & 15 & 15 & 1800 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Sample input data. Figure 5: Schematic of the neural network. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample Number** & \begin{tabular}{c} **Wrapping** \\ **Thickness (m)** \\ \end{tabular} & \begin{tabular}{c} **Slope Ratio of** \\ **Reinforced** \\ **Emankment (-)** \\ \end{tabular} & \begin{tabular}{c} **Modulus of** \\ **Elasticity of the** \\ **Fill (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Reinforcement** \\ **Strip Length (m)** \\ \end{tabular} & \
\begin{tabular}{c} **Modulus of** \\ **Elasticity of** \\ **Reinforcement** \\ **Strip (MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Interfacial** \\ **Friction Angle (\({}^{\circ}\))** \\ \end{tabular} \\ \hline
7 & 0.6 & 1:2 & 45 & 25 & 2200 & 5 \\ \hline
8 & 0.6 & 1:1.5 & 25 & 10 & 2600 & 4 \\ \hline
9 & 0.6 & 1:1 & 55 & 20 & 1000 & 3 \\ \hline
10 & 0.6 & 1:0.5 & 35 & 30 & 1400 & 2 \\ \hline
59 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 0 \\ \hline
60 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 1 \\ \hline
61 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 2 \\ \hline
62 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 3 \\ \hline
63 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 4 \\ \hline
64 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 10 \\ \hline
65 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 15 \\ \hline
66 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 20 \\ \hline
67 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 25 \\ \hline
68 & 1.2 & 1:0.5 & 15 & 10 & 1000 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample Number** & \begin{tabular}{c} **Maximum Lateral** \\ **Displacement** \\ **(mm)** \\ \end{tabular}  & \begin{tabular}{c} **Maximum Vertical** \\ **Displacement (mm)** \\ \end{tabular}  & \