# Regression Equations for Estimating Landslide-Triggering Factors Using Soil Characteristics
## 3 Results
### Derivation of Regression Equations for Evaluating Landslide-Triggering Factors
#### 3.5.2 Regression Equations of Shear Strength
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Soil Variable**} & \multirow{2}{*}{**Correlation**} & \multicolumn{2}{c}{**Cohesion, kN/m\({}^{2}\)**} & \multicolumn{2}{c}{**Internal Friction Angle, \({}^{\circ}\)**} \\ \cline{3-6}  & & **Gneiss** & **Granite** & **Gneiss** & **Granite** \\ \hline \multirow{2}{*}{Density} & \(r\) & 0.634 & 0.297 & 0.635 & 0.219 \\ \cline{2-6}  & \(F\) & 0.036 & 0.231 & 0.036 & 0.254 \\ \hline \multirow{2}{*}{Water Content, \%} & \(r\) & –0.409 & –0.642 & –0.403 & –0.351 \\ \cline{2-6}  & \(F\) & 0.211 & 0.004 & 0.219 & 0.062 \\ \hline \multirow{2}{*}{Void Ratio} & \(r\) & –0.272 & –0.093 & –0.935 & –0.808 \\ \cline{2-6}  & \(F\) & 0.418 & 0.713 & 0.000 & 0.000 \\ \hline \multirow{2}{*}{Porosity, \%} & \(r\) & 0.146 & 0.546 & –0.337 & –0.287 \\ \cline{2-6}  & \(F\) & 0.667 & 0.019 & 0.311 & 0.132 \\ \hline \multirow{2}{*}{Degree of Saturation, \%} & \(r\) & –0.234 & –0.687 & 0.112 & –0.113 \\ \cline{2-6}  & \(F\) & 0.489 & 0.002 & 0.743 & 0.559 \\ \hline \multirow{2}{*}{Wet Unit Weight, kN/m\({}^{3}\)} & \(r\) & 0.097 & –0.294 & 0.826 & 0.679 \\ \cline{2-6}  & \(F\) & 0.777 & 0.234 & 0.002 & 0.000 \\ \hline \multirow{2}{*}{Saturation Unit Weight, kN/m\({}^{3}\)} & \(r\) & 0.318 & 0.178 & 0.960 & 0.816 \\ \cline{2-6}  & \(F\) & 0.341 & 0.481 & 0.000 & 0.000 \\ \hline \multirow{2}{*}{Dry Unit Weight, kN/m\({}^{3}\)} & \(r\) & 0.071 & 0.136 & 0.925 & 0.844 \\ \cline{2-6}  & \(F\) & 0.837 & 0.590 & 0.000 & 0.000 \\ \hline \multirow{2}{*}{Liquid Limit} & \(r\) & –0.270 & 0.073 & –0.502 & –0.258 \\ \cline{2-6}  & \(F\) & 0.423 & 0.775 & 0.115 & 0.177 \\ \hline \multirow{2}{*}{Plastic Limit} & \(r\) & –0.151 & 0.309 & –0.475 & 0.247 \\ \cline{2-6}  & \(F\) & 0.658 & 0.213 & 0.139 & 0.196 \\ \hline \multirow{2}{*}{Gravel, \%} & \(r\) & 0.215 & 0.419 & 0.032 & –0.040 \\ \cline{2-6}  & \(F\) & 0.525 & 0.084 & 0.927 & 0.835 \\ \hline \multirow{2}{*}{Sand, \%} & \(r\) & 0.534 & 0.125 & 0.198 & 0.252 \\ \cline{2-6}  & \(F\) & 0.091 & 0.621 & 0.559 & 0.188 \\ \hline \multirow{2}{*}{Fine, \%} & \(r\) & –0.947 & –0.928 & –0.219 & –0.345 \\ \cline{2-6}  & \(F\) & 0.000 & 0.000 & 0.518 & 0.067 \\ \hline \multirow{2}{*}{Effective Grain Size, D\({}_{10}\), cm} & \(r\) & 0.480 & 0.606 & 0.599 & –0.043 \\ \cline{2-6}  & \(F\) & 0.135 & 0.008 & 0.052 & 0.826 \\ \hline \multirow{2}{*}{Coefficient of Uniformity, \(c_{u}\)} & \(r\) & –0.746 & –0.417 & –0.374 & –0.008 \\ \cline{2-6}  & \(F\) & 0.008 & 0.086 & 0.257 & 0.966 \\ \hline \multirow{2}{*}{Coefficient of Curvature, \(c_{g}\)} & \(r\) & 0.551 & –0.403 & 0.147 & 0.197 \\ \cline{2-6}  & \(F\) & 0.079 & 0.097 & 0.666 & 0.307 \\ \hline \end{tabular} Remarks: \(r\) is Pearson correlation coefficient, and \(F\) is significance.  
\end{table} 
Table 4: Correlation coefficient and significance between cohesion and internal friction angle and soil characteristics. soil content and saturation degree were selected as independent variables for regression analysis to simplify the equations. For the granite regions, soil properties with equally high significance levels for internal friction angle were the void ratio, dry unit weight, wet unit weight, and saturated unit weight. Hence, void ratio and dry unit weight were finalized as the independent variables for regression analysis to simplify the regression equation that is consistent with the gneiss model. As shown in Table 5, a simple regression analysis of the soils by geological feature was used to derive the ground variables with high correlations between soil properties to make a regression equation for estimating the cohesion and internal friction angles of the gneiss and granite soils. According to the regression analysis, the variance analysis, which is a measure of the accuracy of the gneiss cohesion model, showed a very good probability of P = 0.000, and the R-square representing the explanatory power was about 88%. Moreover, the regression equation for internal friction angles was deemed suitable with the probability of P = 0.000, and an R-square of about 96%.