## 3 Experimental Results and Analysis  
### Rheological Curves at Different Volume Concentrations  
Figure 4 presents the rheological curves of the debris flow at various solid volume concentration (\(C_{\rm v}\)) conditions. It can be observed that, at different \(C_{\rm v}\) levels, the shear stress demonstrates a linear relationship with shear rate, conforming to the Bingham fluid model for all curves. Furthermore, with increasing \(C_{\rm v}\) values, the rheological curves increase continuously and become steeper. It is noteworthy that at lower \(C_{\rm v}\) values, the rheological curves remain relatively stable without significant fluctuations. However, as the \(C_{\rm v}\) values increase gradually, fluctuations begin to emerge in the initial shear stage of the rheological curves. Particularly, when \(C_{\rm v}\) = 0.550, the overall rheological curve shows a fluctuating upward trend. This is primarily due to the increased solid particle content, which enhances the likelihood of collisions between the rotor and the particles in the sample, resulting in increased resistance and, thus, data fluctuations.  
Figure 4: Rheological curves of the debris flow at different solid volume concentrations.  
Figure 3: Rheometer used in this paper.  
We found that compared with many debris flows of other regions, the shear stress of the Jiangjiagou debris flow is significantly greater than that of viscous debris flow under the same gravity and shear rate, which indicates that the Jiangjiagou debris flow has greater movement resistance. The main reason for this phenomenon is that the content of clay in the Jiangjiagou debris flow is high, and the slurry forming the debris flow is more abundant. Once the glacier debris flow breaks out, its movement velocity will be far greater than that of debris flows of other regions in the same state. Therefore, protection should be improved to ensure the safety of buildings and construction sites.  
To assess the influence of solid volume concentration on the shear stress of the debris flow under various shear rate conditions, the shear stress increment \(\Delta\tau\) (Equation (3)) at each solid volume concentration, relative to \(C_{\rm v}=0.350\), was calculated by subtracting the shear stress at a specific \(C_{\rm v}\) (\(\tau(C_{\rm vj})\)) from the shear stress at \(C_{\rm v}=0.350\) (\(\tau(C_{\rm v0})\))  
\[\Delta\tau=\tau(C_{\rm vj})-\tau(C_{\rm v0}) \tag{3}\]  
Here, \(\tau(C_{\rm vj})\) represents the shear stress at a given solid volume concentration at the same shear rate, while \(\tau(C_{\rm v0})\) denotes the shear stress at \(C_{\rm v}=0.350\) for that particular shear rate.  
Figure 5 depicts the variation in the shear stress increment \(\Delta\tau\) with solid volume concentration at different shear rates. It is evident that the increment \(\Delta\tau\) gradually increased with the rising solid concentration. Notably, during the transition of \(C_{\rm v}\) from 0.350 to 0.425, the differences in the increment at various shear rates were indistinct; the curve changed mildly, and the data points among different sets almost overlapped, suggesting a minimal impact of the shear rate elevation in this phase. However, as the solid volume concentration continued to rise from 0.450 to 0.550, the elevation in shear rate distinctly led to varying shear stress increments. Specifically, at higher shear rates and the same volume concentration, greater shear stress increments were observed.