## 2 Tests on the Effects of ADNB on the Slip Resistance of Borrowed Soil of Rock Slopes
### Analysis of the Test Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Group**} & \multicolumn{8}{c}{**Polymer Content**} \\ \cline{3-10}  & & **0\%** & **0.05\%** & **0.1\%** & **0.25\%** & **0.5\%** & **1\%** & **2.5\%** & **5\%** \\ \hline \multirow{2}{*}{\(d_{50}\)} & Mixing (mm) & 0.3 & 2.6 & 2.6 & 3.0 & 3.2 & 3.6 & 3.8 & 3.5 \\  & Spraying (mm) & 0.4 & 0.6 & 0.8 & 0.9 & 1.0 & 1.2 & 2.0 & 2.3 \\ \hline \multirow{2}{*}{\(K_{T}\)} & Mixing (\(\times 10^{-4}\) mm) & 0.97 & 4.88 & 5.58 & 6.66 & 8.19 & 9.98 & 15.90 & 21.80 \\  & Spraying (\(\times 10^{-4}\) mm) & 0.95 & 2.17 & 3.26 & 3.02 & 0.09 & 0.06 & 0.04 & 0.03 \\ \hline \multirow{2}{*}{\(c\)} & Mixing (mm) & 19.0 & 26.8 & 29.6 & 30.3 & 32.3 & 33.3 & 36.0 & 38.2 \\  & Spraying (mm) & 19.1 & 22.1 & 23.5 & 26.2 & 27.8 & 29.1 & 30.8 & 32.6 \\ \hline \multirow{2}{*}{\(\varphi\)} & Mixing (\({}^{\circ}\)) & 11.9 & 13.8 & 15.1 & 16.6 & 16.8 & 19.4 & 21.0 & 21.3 \\  & Spraying (\({}^{\circ}\)) & 11.9 & 12.5 & 12.6 & 13.0 & 13.3 & 13.6 & 14.2 & 14.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter changes after soil sample treatment. Equations (2)-(5) describe the change trends of the average particle diameter, permeability coefficient, cohesive force, and internal friction angle after soil improvement. Most of the \(R\) values were close to 1, and thus the correlation as a result of data fitting is reliable. According to the Mohr-Coulomb principle, as shown in Equation (6), the shear strength of soil was determined by the cohesive force and internal friction angle. By substituting Equations (3) and (4) into Equation (6), the shear strength growth model of the soil mass after improvement could be obtained, as shown in Equation (7). \[\tau=c+\sigma\tan(\varphi), \tag{6}\]  
\[\left\{ \begin{array}{l}\tau=c_{M}+\sigma\tan(\varphi_{M})\\ \tau=c_{S}+\sigma\tan(\varphi_{S})\end{array} \right., \tag{7}\]  
where \(\tau\) is the shear strength (kPa) and \(\sigma\) is the normal stress (kPa). After the borrowed soil was improved, the average particle diameter, permeability coefficient, and shear strength of the soil could be quantitatively analyzed according to the above quantitative characterization models. Thus, we avoided a large number of repeated experiments to determine the amount of material as well as the improvement effect. According to our construction experience, the ADNB content should not be higher than 5% when applied in the mixing process. When the content of ADNB was higher than 5%, an excessive soil viscosity was observed. This phenomenon would result in blockage of the pipelines that were used to transport the borrowed soil. Even though the slip resistance of borrowed soil improved when the content of ADNB was high, construction progress would be delayed. Increased material consumption and longer construction periods would lead to high costs. Therefore, in the mixing process, the material content should not be higher than 5%, and we thus determined the optimal addition amount range to be 0-5%. In the permeability tests, when the content of ADNB was higher than 0.1%, the permeability of the soil decreased. Therefore, in the spraying process, the optimal addition amount range was 0-0.1%. Based on the above analysis, Equation (7) should be limited to:  
\[\left\{ \begin{array}{l}\tau=c_{M}+\sigma\tan(\varphi_{M})\quad(0\leq x\leq 5 \%)\\ \tau=c_{S}+\sigma\tan(\varphi_{S})\quad(0\leq x\leq 0.1\%)\end{array} \right., \tag{8}\]  
During construction design, the construction process should be selected based on the site construction, geological, and climatic conditions. For example, in a slope with a certain thickness of soil attached, it would no longer be necessary to supplement with borrowed soil. However, spraying ADNB could indeed improve the slip resistance of the existing soil. This approach would reduce erosion damage. On the other hand, in a sand slope subject to heavy rainfall, it is necessary to mix ADNB in the borrowed soil, which could improve the slip resistance and reduce soil loss.