## 3 Results  
### Rheological Properties of Mine Tailings: Yield Stress and Viscosity  
Figure 2 presents the flow characteristics of waste materials with initial shear rates for a water content of 34% (equivalent to a solid volume concentration of 52%). At the same water content (or solid volume concentration), the flow behavior is very similar (Figure 2a). To examine the rheological characteristics, the controlled shear rate mode was employed with a range of \(10^{-4}\) to \(10^{1}\) s\({}^{-1}\). In particular, five shear rates were applied as initial values from 0.0001 to 0.1 s\({}^{-1}\). The measured  
Figure 1: Ball-measuring rheometric system: (**a**) Test procedure, (**b**) schematic view of ball rotation, (**c**) shear layer formation (sliding plane in a steady-state condition) during shearing, (**d**) flow curve with Bingham fluid and ball rotation, (**e**) shear stress–shear rate plot, and (**f**) viscosity–shear rate plot. Tested from \⃝ to \⃝. rheological properties, that is, the yield stress and plastic viscosity, range from 17 to 21 Pa and 1.0 to 1.2 Pa\(\cdot\)s, respectively. The variations in yield stress and viscosity are relatively small. They can be divided into two regimes based on a shear rate of 1 s\({}^{-1}\): (a) the generation of a slip surface in response to a complete rotation of a penetrated ball (after one full revolution, i.e., onset of failure stage) and (b) continuous viscous shearing (post-failure stage). An example is shown in Figure 2b. Compared to the flow behavior of fine-grained sediments, a large difference is shown before yielding (i.e., \(\dot{\gamma}=1\) s\({}^{-1}\)). There is a distinct peak value of shear stress at a relatively low shear rate regime (i.e., 0.4 s\({}^{-1}\)). After the peak value, an abrupt decrease in shear stress is observed. All processes generate a slip surface (i.e., shear banding formation in Figure 1c) in a ball-measuring system. After one full revolution of the ball, they behave as an ideal plastic fluid, such as a Bingham fluid [29]. To verify the applicability of the rheological model for obtaining flow curves, the best fit was obtained with the Bingham, bilinear, Herschel-Bulkley, modified Bingham, and power law models. As shown in Figure 2b, most of them are in good agreement with the test results after the shear rate of 1 s\({}^{-1}\), but a large scatter is found at lower shear rates. In this context, the post-failure characteristics are limited to the flow behaviors observed after the critical deformation. The results of model fitting with respect to different initial shear rates ranging from 10\({}^{-4}\) to 10\({}^{-1}\) s\({}^{-1}\) are summarized in Table 1. Compared to the rheological properties of fine-grained sediments, the properties of these materials are slightly higher. According to [PERSON] et al. [27], the rheological compilation of clay-rich, silt-rich, and sand-rich materials shows viscosities of approximately 20, 200, and 2000 mPa\(\cdot\)s, respectively, in the case that the yield stress is equal to 20 Pa. In this study, the materials tested were sand-rich materials (less cohesive). The results are in good agreement with the previous rheological compilation (especially the yield stress-viscosity relationship for the sand-rich group). Uncertainties are higher for the rheological properties measured at lower shear rates because the variations in viscosity at low shear rates (less than 1 s\({}^{-1}\)) are significant. In an elastic regime, the structure begins to break down, is subjected to shear localization, and creates partial shear-induced particle migration in the flow curves when the shear strain approaches the critical shear strain [6]. In the transition from the solid-like to liquid-like regime, there is a critical deformation. The shear localization and shear banding (stick-slip behavior) are dependent on increasing the apparent shear rate [30]. According to [31], shear banding instability can be divided into three regions, e.g., homogeneous, wall slip, and bulk shear banding.