## 3 Experimental Results and Analysis
### The Effects of Solid Volume Concentration on the Rheological Behavior of Debris Flows  
The variation law of rheological parameters in debris flow slurry is mainly based on the relationship between yield stress, viscosity, and solid volume concentration, which are significantly affected by factors such as volume concentration, particle size distribution, and fine particle mineral composition [23]. Coarse and fine particles in a debris flow are the main solid components, and the maintenance and movement of a debris flow is related to their mixing with water and the buoyancy effect. Under certain concentration conditions, the interaction between fine particles and water can form a kind of non-sorting solid-liquid flow (i.e., a one-phase flow), which has a certain yield stress, and this is significant for the movement of the debris flow. Apart from buoyancy, the support force of solid particles can be the inter-particle discrete force generated by particle shear motion or the yield shear force of a high-concentration slurry that prevents particles from sinking, generating the so-called neutral suspension movement even at low slope conditions in the channel. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(C_{\text{v}}\) & 0.350 & 0.375 & 0.400 & 0.425 & 0.450 & 0.475 & 0.500 & 0.525 & 0.550 \\ \(a\) & 0.14058 & 0.31336 & 0.6224 & 0.80036 & 1.13374 & 1.3773 & 1.6229 & 1.89992 & 2.17517 \\ \(b\) & \(-0.7746\) & \(-0.7486\) & \(-0.8027\) & \(-0.8117\) & \(-0.8614\) & \(-0.8875\) & \(-0.9079\) & \(-0.9059\) & \(-0.9211\) \\ R\({}^{2}\) & 0.98838 & 0.98507 & 0.99095 & 0.99200 & 0.99529 & 0.99584 & 0.99785 & 0.99768 & 0.99796 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fitting parameters of the \(\eta_{\text{a}}\)–\(\gamma\) curves at different solid volume concentrations. Figure 9: (**a**) Relationship between apparent viscosity and shear rate; (**b**) relationship between the fitting parameters and solid volume concentration. The volume concentration of a debris flow slurry directly reflects the influence of the slurry moisture content on the slurry flow and transport capacity. As the solid volume concentration increases, the volume fraction of the solid phase increases, reducing the internal water content of the debris flow, increasing viscosity, and suppressing the turbulence of the debris flow. In Figure 4, it can be observed that most curves show a relatively smooth upward trend, which indirectly indicates that, for the Jiangjiagou diluted debris flow (with low solid volume concentration) and viscous debris flow (with high solid volume concentration) in this study, the impact of discrete stress generated by particle collision on the resistance of the debris flow is lower than that of particle contact friction and viscous shear. The enhanced viscosity of the liquid phase slurry in the Jiangjiagou debris flow reduces the flow turbulence and increases the viscous shear. Moreover, as the solid volume concentration of the viscous debris flow in Jiangjiagou increases, the amount of solid particles increases, resulting in a denser structure. The adhesive force between coarse particles also increases, leading to greater frictional force when the particles contact each other, hence, continuously increasing resistance. On another note, as the solid volume concentration gradually increases in the debris flow slurry, it becomes easier for particles to adhere to each other, forming aggregates. Moreover, the particles adhere to each other and to aggregates, forming a mesh-like structure. At this point, water is trapped in the grid structure formed between particles, which further increases with the concentration of the solid particles. Clusters combine to form cluster aggregates, thereby forming a flocculent network structure, and the density of this network structure increases with the rise in solid volume concentration. As the adhesive force between particles strengthens continuously, the viscosity of the slurry gradually increases.