# Shear Strength Analysis and Slope Stability Study of Straight Root Herbaceous Root Soil Composite
## 3 Results
### Significance and Correlation Analysis of Shear Resistance Indicators and Influencing Factors
#### 3.3.3 Multiple Linear Regression Analysis Results  
Linear models I and II were established with the root content and moisture content as independent variables and the cohesion or internal friction angle of undisturbed soil as the dependent variables. Table 4 reports the results. The equations for linear models I and II are \(y_{1}=2349.511\cdot x_{1}+11.038\cdot x_{2}+3.474\) and \(y_{2}=657.5393\cdot x_{1}-70.9555\cdot x_{2}+40.8992\), respectively, where \(x_{1}\) denotes root content and \(x_{2}\) denotes moisture content. The \(p\)-values indicate that the root content significantly affects the cohesion of undisturbed soil, whereas the influence of moisture content is relatively small. The influence of the moisture content on the internal friction angle of undisturbed soil is significant, while that of the root content is relatively weak. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Linear Model**} & \multirow{2}{*}{\begin{tabular}{c} **Shear Strength** \\ **Index** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Influence Factor** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Estimate** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Standard Error** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **\(t\)-Value** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **\(p\)-Value** \\ \end{tabular} } \\ \hline I & \multirow{2}{*}{\(c\)} & intercept & 3.474 & 1.343 & 2.586 & 0.0130 * \\  & & root content & 2349.511 & 276.746 & 8.490 & 6.75 \(\times\) 10\({}^{-11}\) *** \\  & & moisture content & 11.038 & 5.066 & 2.179 & 0.0346 * \\  & & intercept & 40.8992 & 0.3427 & 119.343 & 2 \(\times\) 10\({}^{-16}\) *** \\ II & \(\varphi\) & root content & 657.5393 & 70.6059 & 9.313 & 4.61 \(\times\) 10\({}^{-12}\) *** \\  & & moisture content & \(-\)70.9555 & 1.2926 & \(-\)54.894 & 2 \(\times\) 10\({}^{-16}\) *** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of linear regression analysis. Figure 7: Correlation analysis results between the shear strength index and the root content, moisture content, and root burial depth. Note: blue represents a positive correlation; red represents a negative correlation; darker color represents higher correlation; circle size represents the absolute value of the correlation; and the number represents the \(p\)-value. 3.4 Three-Dimensional Correlation between Shear Strength Parameters with Root Content and Moisture Content  
Figure 8 presents the three-dimensional relationship between USRS with different root and moisture contents, while Table 5 reports the surface-fitting results of the correlation data in Figure 8. The internal friction angle and cohesion were evaluated using the equation \(Y=Z+A\cdot r+B\cdot w+C\cdot r^{2}+D\cdot w^{2}+E\cdot r\cdot w\), where \(r\) is root content, \(w\) is moisture content, and \(Y\) is the internal friction angle or cohesion. The goodness-of-fit results for the relationship between the shear strength index and root content and moisture content were \(R^{2}>0.83\) and \(R^{2}>0.99\), respectively. This indicates a high level of reliability in the fitting results. The root content played a major role in cohesion, while moisture content exerted a great influence on the internal friction angle. Figure 9 presents the relationship of the failure deviation stress of USRS with root content and moisture content under different confining pressure conditions. Table 6 reports the surface-fitting results of the correlation data in Figure 9. The failure deviation stress was evaluated using equation \(Y=Z+A\cdot r+B\cdot w+C\cdot r^{2}+D\cdot w^{2}+E\cdot r\cdot w\), where \(r\) is root content, \(w\) is moisture content, and \(Y\) is the failure deviation stress. The goodness-of-fit for the relationship between root content, moisture content, and failure deviation stress was \(R^{2}>0.96\), indicating a high level of reliability in the fitting results.