## 4 Discussion  
The soil clay content in the TGRA is very low (Table 3) due to the selective migration of fine fractions. An investigation [51] showed that the critical shear stress and critical flow force increase with increased particle size, whereby fine fractions transfer more quickly than other fractions in the process of loss [52], resulting in a lower proportion of finer fractions and a greater proportion of coarser fractions in the residual soil. In addition, the adhesion and deposition of organic matter in clay could reduce the risk of clay loss [53]. However, this phenomenon was not present in the study area, resulting in a high risk of clay loss. Generally speaking, the selective migration of fine fractions occurs continuously during the long-term cultivation process on slope farmland [54; 55]. At the same time, the low organic matter content in the soil aggravates the loss of fine fractions. Generally, under the combined action of these two factors, the clay content is low and the silt content is high [39; 53]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fractions**} & \multicolumn{4}{c}{**Langmuir Parameters**} & \multicolumn{4}{c}{**Freundlich Parameters**} \\ \cline{2-7}  & \(\mathbf{q_{m}/mg.g^{-1}}\) & \(\mathbf{K_{L}}\) & \(\mathbf{r^{2}}\) & \(\mathbf{K_{F}}\) & \(\mathbf{n}\) & \(\mathbf{r^{2}}\) \\ \hline Clay & 0.900 & 0.214 & 0.870 & 0.191 & 2.66 & 0.998 \\ Silt & 0.384 & 0.091 & 0.871 & 0.056 & 2.41 & 0.994 \\ Fine Sand & 0.304 & 0.042 & 0.932 & 0.029 & 2.06 & 0.980 \\ Coarse Sand & 0.204 & 0.048 & 0.920 & 0.021 & 2.12 & 0.974 \\ Bulk Soil-Sample A & 0.349 & 0.075 & 0.889 & 0.050 & 2.42 & 0.989 \\ Bulk Soil-Sample B & 0.351 & 0.074 & 0.889 & 0.049 & 2.40 & 0.985 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters in Langmuir and Freundlich isotherm models. Figure 5: Adsorption curves of different particle-size fractions at different initial P concentration (Ce: equilibrium concentration of the solution, \(\mathbf{q_{c}}\): phosphorus adsorption quantity of the sample under equilibrium conditions). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \(\mathbf{Ca_{x}}\)-P & \(\mathbf{Ca_{x}}\)-P & \(\mathbf{Ca_{x}}\)-P & \(\mathbf{Al}\)-P & Fe-P & O-P & \(\mathbf{Og}\)-P & \(\mathbf{Ca}\)-P & TP & \(\mathbf{q_{m}}\) & \(\mathbf{K_{L}}\) & \(\mathbf{K_{F}}\) \\ \hline Kaolinite & \(-0.908\,^{*}\) & \(-0.948\,^{*}\) & \(-0.957\,^{*}\) & 0.864 & 0.963 \({}^{**}\) & 0.595 & \(0.902\,^{*}\) & \(-0.961\,^{**}\) & \(-0.939\,^{*}\) & \(-0.521\,\) & \(0.940\,^{*}\) & \(0.962\,^{**}\) \\ Muscovite & 0.038 & \(-0.372\) & \(-0.242\) & 0.469 & 0.251 & 0.745 & 0.533 & \(-0.252\) & \(-0.016\) & \(0.606\,^{*}\) & \(-0.003\,^{*}\) & \(-0.057\,^{*}\) \\ Quartz & 0.935 & \({}^{*}\) & 0.918 & \({}^{*}\) & \(-0.855\,^{*}\) & \(-0.965\,^{**}\) & \(-0.527\) & \(-0.871\,\) & 0.936 & \({}^{*}\) & \(0.922\,^{*}\) & \(0.530\,^{*}\) & \(-0.962\,^{**}\) & \(-0.978\,^{*}\) \\ Calorie & 0.669 & 0.794 & 0.694 & \(-0.940\,^{*}\) & \(-0.850\) & \(-0.726\,^{*}\) & \(-0.909\,^{*}\) & 0.709 & 0.521 & \(-0.196\,^{*}\) & \(-0.701\,^{*}\) & \(-0.636\,^{*}\) \\ Dolomite & 0.701 & 0.989 \({}^{**}\) & 0.994 \({}^{**}\) & \(-0.792\,^{*}\) & \(-0.851\,\) & \(-0.826\,^{*}\) & \(-0.938\,^{*}\) & \(0.994\,^{**}\) & 0.949 \({}^{*}\) & 0.495 & \(-0.749\,^{*}\) & \(-0.805\,^{*}\) \\ Allite & 0.758 & 0.575 & 0.477 & \(-0.879\,^{*}\) & \(-0.816\,^{*}\) & \(-0.343\,^{*}\) & \(-0.708\,\) & 0.498 & 0.338 & \(-0.268\,^{*}\) & \(-0.765\,^{*}\) & \(-0.655\,^{*}\) \\ Orthoclase & 0.762 & 0.936 \({}^{*}\) & 0.873 & \(-0.961\,^{**}\) & \(-0.932\,^{*}\) & \(-0.799\,^{*}\) & \(-0.990\,^{**}\) & 0.884 \({}^{*}\) & 0.744 & \(0.087\,^{*}\) & \(-0.801\,^{*}\) & \(-0.779\,^{*}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Correlation matrix of phosphorus and adsorption to soil mineral.