# 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
Therefore, the final regression equations for the cohesion and internal friction angle of gneiss soil are shown as Equations (4) and (5):  
\[\text{c}^{\prime}\text{gn}=(-0.712\times Fines)+(-0.131\times c_{u})+15.335 \tag{4}\]  
\[\varphi^{\prime}\text{gn}=(27.01\times r_{d})+(-12.594\times e)+6.018 \tag{5}\]  
where \(\text{c}^{\prime}\text{gn}\) is the cohesion of gneiss soil, \(\varphi^{\prime}\text{gn}\) is the internal friction angle of gneiss soil, \(Fines\) is fine-grained soil content, \(c_{u}\) is the uniformity coefficient, \(r_{d}\) is dry unit weight, and \(e\) is the void ratio, respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Geology**} & \multirow{2}{*}{**Soil Variable**} & \multicolumn{2}{c}{**Unstandardized**} & \multicolumn{2}{c}{**Standardized**} & \multirow{2}{*}{**Geefficients**} & \multirow{2}{*}{**t-value**} & \multirow{2}{*}{**Significance**} \\  & & & **Coefficients** & & & & & \\ \cline{3-8}  & & \multicolumn{1}{c}{**B**} & \multicolumn{1}{c}{**Standard**} & \multicolumn{1}{c}{**Beta**} & & & \\ \hline \multirow{8}{*}{**Gneiss**} & \multirow{4}{*}{**Cohesion,**} & (Constant) & 15.335 & 1.479 & & 10.369 & 0.000 \\ \cline{3-8}  & & Fine grain content, & \(Fines\) & \(-0.712\) & 0.130 & \(-0.851\) & \(-5.457\) & 0.001 \\ \cline{3-8}  & & Coefficient of & \(-0.131\) & 0.151 & \(-0.135\) & \(-0.863\) & 0.413 \\ \cline{2-8}  & & (Constant) & 6.018 & 10.509 & & 0.573 & 0.583 \\ \cline{2-8}  & **Internal Friction Angle,** & \(-12.594\) & 2.566 & \(-0.543\) & \(-4.909\) & 0.001 \\ \cline{2-8}  & & Dry unit weight, \(r_{d}\) & 27.010 & 6.047 & 0.494 & 4.466 & 0.002 \\ \hline \multirow{8}{*}{**Granite**} & \multirow{4}{*}{**Cohesion,**} & (Constant) & 18.590 & 0.871 & & 21.347 & 0.000 \\ \cline{3-8}  & & Fine grain content, & \(Fines\) & \(-0.698\) & 0.072 & \(-0.779\) & \(-9.701\) & 0.000 \\ \cline{1-1} \cline{2-8}  & & Degree of & \(-7.441\times 10^{-2}\) & 0.020 & \(-0.298\) & \(-3.709\) & 0.002 \\ \cline{1-1} \cline{2-8}  & & (Constant) & \(-9.685\) & 27.740 & & \(-0.349\) & 0.730 \\ \cline{1-1} \cline{2-8}  & **Friction Angle,** & \(-0.875\) & 9.138 & \(-0.033\) & \(-0.096\) & 0.924 \\ \cline{1-1} \cline{2-8}  & **Dry unit weight, \(r_{d}\)** & 33.640 & 14.381 & 0.813 & 2.339 & 0.027 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical results of shear strength with cohesion and internal friction angle using regression analysis of soils in different geological features. Meanwhile, the results of the regression analysis of the granite cohesion model showed a very good probability of P = 0.000 and an R-square of about 92%. For the internal friction angle, the probability of variance analysis showed P = 0.000, and the R-square about 70%. Finally, the regression equations for estimating the cohesion of granite soils is shown in Equation (6). On the other hand, the internal friction angle estimation equation of the granite soil is shown in Equation (7):  
\[\mathrm{c^{\prime}}_{\mathrm{gr}}=(-0.689\times Fines)+(-0.0744\times S)+18.590 \tag{6}\]  
\[\mathrm{\varphi^{\prime}}_{\mathrm{gr}}=(33.640\times r_{d})+(-0.875\times e)-9.685 \tag{7}\]  
where, \(\mathrm{c^{\prime}}_{\mathrm{gr}}\) is the cohesion of granite soil, \(\mathrm{\varphi^{\prime}}_{\mathrm{gr}}\) is the internal friction angle of granite soil, \(Fines\) is fine-grained soil content, \(S\) is the degree of saturation, \(r_{d}\) is dry unit weight, and \(e\) is the void ratio, respectively.