The geometry of viscometer commonly used for yield stress fluid measurement includes concentric cylinder, cone and plate, blade shape, etc. [23] comprehensively introduced the principle and application of the above viscometers with different geometry used for viscosity measurement, and fully analyzed the source of experimental error. In hard particle suspensions, wall slip is a common main problem affecting rheological measurement [24]. Relevant scholars have adopted local measurement techniques (light scattering velocimetry in Couette geometry [25] and particle tracking velocimetry in cones and plates [26‐28] and flat plate geometry [29], It provides direct evidence for the wall slip of materials with different yield stress, and puts forward the quantitative measurement of sliding velocity. In the presence of wall slip, the measured apparent shear rate overestimates the true shear rate inside the material [9]. The vane viscometer consists of four blades arranged at an equal angle. Compared with other geometries, the vane viscometer has the advantages of minimal interference to the material structure during insertion, and can minimize the problem of wall slip. Although magnetic resonance imaging technology has found that wall slip phenomenon still exists [30], it is still widely used to study in gel and thixotropic materials; [31‐35].

According to the above analysis, the blade rotor system of mcr301 rotary rheometer in antonpa, Austria is used in this study- It is a stress-controlled rheometer by Anton Paar. The rheometer adopts modular and intelligent design and is composed of temperature control system, fixture system and test system. It consists of four thin blades arranged equiangularly around the axis of a small cylinder; Blade diameter d1 = 13 mm, blade height h = 48 mm; Cup mouth diameter d2 = 37 mm (see Figure 2). The rheometer adopts air bearing, and the minimum torque is 0.002 μNm, maximum torque: 200 mnm, deflection angle (preset): 0.1 to ∞ μRad, minimum speed (CSS): 10⁻⁷ rpm, minimum speed (CSR): 10⁻⁶ rpm, maximum speed: 3000 rpm, minimum frequency: 10⁻⁵ Hz, maximum frequency: 100 Hz, normal stress range: 0.01–50 N, normal stress accuracy: 0.002 N, temperature range: 150–1,000°C.

Assuming no inertia effect and ignoring the normal stress difference, the shear stress ( τ ) and shear rate ( γ ˙ ) are calculated as follows: τ = T 2 π R 1 2 L ;   γ ˙ = ω R 1 R 2 − R 1 Where T is the torque applied to the blade and ω is the angular velocity of the blade rotor.

In the past, many methods have been developed to measure yield stress, mainly including stress relaxation, creep/recovery test, stress growth test, continuous shear test and so on. The yield stress of stress relaxation experiment is defined as the residual ultimate stress after the fluid stops flowing. Creep/recovery test is to apply a constant shear stress to the fluid, the shear stress is higher than the yield stress, the material flows, the stress is lower than the yield stress, and the material behaves as a solid. The stress growth experiment is to shear the fluid at a constant shear rate during the rheological experiment, obtain the change process of shear stress with time, and determine the yield stress according to the change curve of stress with time. Continuous shear test is a process in which the shear rate continuously increases from zero to the set value (accelerated shear) or decreases from the set value to zero (decelerated shear) during the rheological experiment to obtain the variation of shear stress with the shear rate (increase or decrease). [36] summarized the advantages and disadvantages of each method. Although some methods are widely used, because the yield stress depends on its measurement method, especially whether it is determined during the solid-liquid transition or the opposite transition [9], no method is considered as a standard procedure for determining the yield stress. Aiming at the start-up and deposition process of debris flow, in the start-up process of debris flow, the debris flow fluid develops from static state to stable motion state in a short time, and the shear rate of debris flow slurry increases from zero to a large value; In the process of debris flow deposition, the moving debris flow fluid changes from moving state to static state, and the shear rate of debris flow slurry decreases from large value to zero. According to the field observation of field debris flow disasters by [3] and [37], it is estimated that the shear rate of moving debris flow slurry is usually between 0.1 and 20 S⁻¹ [38]. In order to explore the variation process of shear stress with shear rate during the start-up and accumulation of debris flow slurry, the rheological experiments of increasing shear (representing the start-up process of debris flow) and decreasing shear (representing the deposition process of debris flow) were carried out continuously by using the blade rotor of mrc301 rheometer and the method of continuous shear experiment. At the beginning of the test, the slurry with different solid volume concentrations is fully stirred, and then take an appropriate amount of prepared mud into the fixed outer cylinder of the blade rheometer, and immerse the blade rotor into the mud. In the test, the shear rate (blade rotor rotation rate) continuously increased from 0 to 30s⁻¹ (accelerated shear) in a logarithmic growth mode, and then the shear rate continuously decreased from 30 s to 1 to 0 (deceleration shear) in the same path. There is no time interval between increasing shear and decreasing shear. The dynamic change process of shear stress with the increase and decrease of shear rate was recorded. Although this process is not complicated, the scheme combines the complex transient response of the sample and the shear induced solid-liquid phase transition [39], but largely reflects the rheological process of debris flow slurry during debris flow initiation and accumulation. In the whole experimental process, the test temperature of the sample is constant at 20°C through the water circulation system.

The dynamic change process of shear stress 1) of Chengdu clay mud with shear rate 2) is shown in semi logarithmic coordinate system (Figure 3A–J). Figure 3 shows that Chengdu mud with all solid volume concentrations shows non-Newtonian behavior. At the same shear rate, the shear stress increases with the increase of mud solid concentration. The change of shear stress is completely different in the process of increasing shear and decreasing shear. In the process of increasing shear rate, the influence of solid volume concentration on the dynamic change of shear stress is obviously different. The main manifestations are: When the volume concentration of mud solid exceeds 35% and the shear rate is in the range of 0.01-1s-1, the shear stress increases rapidly to the maximum; When the shear rate exceeds 1s-1, the shear stress decays rapidly and tends to be stable (Figure 4A, B). For example, for the slurry with a solid volume concentration of 43%, when the shear rate is in the range of 0.01–1 s⁻¹, the shear stress increases rapidly from 2650 pa to nearly 9000 pa (Figure 4A, and then decreases to less than 4700 pa (Figure 4. b). When the solid volume concentration is less than 35% and the shear rate is less than 0.1 s⁻¹, the shear stress increases rapidly with the shear rate; When the shear rate exceeds 0.1 s⁻¹, although the shear stress increases with the increase of shear rate, the increase range is small. For example, when the solid volume concentration is 28%, the shear rate is in the range of 0.01–0.1 s⁻¹, and the shear stress increases rapidly from nearly 110 pa to nearly 270 pa. The shear rate is in the range of 0.1 s^–1 to 30 s⁻¹, and the shear stress increases slowly from 270 to 310 pa (Figure 3F). As the results of Jeong et al. 2010 on bentonite and illite natural clay, its flow behavior depends not only on the shear rate, but also on the particle concentration[40]. This result is consistent with the results of similar laboratory tests ([41,42]; Sueng won [43]). This result shows that Chengdu clay slurry is a typical non-Newtonian fluid with yield stress. In the process of decelerating shear, in the semi logarithmic coordinate system, the shear stress decreases steadily with the decrease of shear rate (filled with ● in Figure 3).

In the process of accelerated shear and decelerated shear, although the same shear rate change path is adopted, the increase (accelerated shear) and decrease (decelerated shear) of shear stress are completely inconsistent. The shear stress forms a hysteresis loop with the increase and decrease of shear rate (Figure 3), and the area of hysteresis loop decreases with the decrease of solid volume concentration. It shows that Chengdu clay mud has thixotropy, which decreases with the decrease of solid volume concentration. Relevant studies have shown that the response of thixotropic yield stress fluid will depend on the rate of stress rise and fall and the rest time between subsequent scans [8]. For the slurry with solid volume concentration lower than 35%, there is an intersection between the increasing shear stress curve and the decreasing shear stress curve (Figures 3E–J). [44] also observed similar behavior, and [45] reviewed the hysteresis loop in thixotropic fluid.

In addition, in order to analyze the viscosity change in the shear process, the viscosity change of Chengdu clay slurry with solid volume concentration of 43% and 28% respectively in the process of increasing and decreasing shear is plotted in Figure 5. Unfilled ○ in the figure represents the increasing shear process of slurry with solid volume concentration of 43%, and filled • presents its decreasing shear process; Unfilled △ represents the increasing shear process of slurry with solid volume concentration of 28%, and filled ▲ represents the decreasing shear process. Figure 5 shows that the viscosity of Chengdu clay slurry decreases with the increase of shear rate and increases with the decrease of shear rate, with typical shear thinning characteristics [46,47].

According to the experimental results and 4.1 analysis, the variation process of shear stress of mud with different concentrations with shear rate is not consistent. When the solid volume concentration is greater than 35%, the shear stress increases rapidly, then decreases gradually, and finally tends to be stable. This change process is more clearly shown by plotting the change of shear stress with shear rate in semi logarithmic coordinate system (Figure 4A, B). [48,49] described this change process: in viscoelastic thixotropic fluid or nonlinear viscoelastic fluid, there will be stress growth first, then stress attenuation, and then the stress change tends to be stable (equilibrium flow). Although the static yield stress of thixotropic fluid depends on the applied shear rate and sample age [20,21], it is one of the common methods to use the stress overshoot as the static yield stress of mud. In this paper, for the slurry with solid volume concentration greater than 35%, the peak stress (stress overshoot) in the process of accelerated shear is taken as its static yield stress. For the slurry with solid volume concentration less than 35%, the growth range of shear stress before the shear rate is less than 0.1 s⁻¹ and after the shear rate is greater than 0.1 s⁻¹ is obviously different. Therefore, the shear stress value with shear rate of 0.1 s^–1 is taken as its static yield stress. Combined with the start-up process of debris flow, the static yield stress value of mud with different solid volume concentration represents the minimum stress value that needs to be overcome when debris flow enters the flow state from start-up.

The dynamic yield stress value represents the stress threshold of the material gradually entering the solid state from the flowing liquid state. The shear stress value is measured by gradually reducing the shear rate to reach the limit. The stress value obtained by extrapolating the stress within the disappearance limit of the shear rate (the intercept from the shear stress axis) is usually called the stress value of dynamic yield stress. According to the variation process curve of shear stress with shear rate obtained from the deceleration shear rheological experiment of mud with different solid volume concentration (filled with ● Figure 3), the shear stress value with shear rate of 0.01 s^–1 is taken as the dynamic yield stress of mud.

Table 2 confirms that the solid volume concentration has a strong effect on the yield stress. For slurries with solid volume concentration greater than 35%, the dynamic yield stress is much smaller than the static yield stress [30,37,50–52], and this difference decreases with the decrease of concentration. The yield stress increases exponentially with particle concentration (Figure 4). [38] expressed the relationship between yield stress and solid volume concentration as: τ c = α ∙ e β ∙ C s , where α,βis an empirical coefficient, depending on sediment characteristics. eonardo. [53] used a rotary rheometer equipped with a blade rotor system, adopted the same experimental scheme, conducted rheological experiments on the slurry composed of fine pyroclastic particles with solid concentrations of 32%, 35%, 38%, 40% and 42% respectively, analyzed the influence of solid volume concentration on its static and dynamic yield stress, and obtained the conclusion consistent with this paper. The research results of Leonardo [53] on Nocera debris flow and [54] on Colorado debris flow are drawn in the same semi logarithmic coordinate diagram (Figure 6), and the influence of solid concentration on yield stress is compared. Empirical coefficient of static yield stress of Chengdu clay slurry varying with solid volume concentration α, β is 0.8317 and 0.223, respectively Empirical coefficient of dynamic yield stress with solid volume concentration α, β They are 1.433 and 0.1769 respectively. Empirical coefficient of variation of mud yield stress of Nocera debris flow and Colorado debris flow with solid volume concentration α,β See the fitting data in Figure 6. This result shows that due to the difference of mud composition, the effect of solid concentration on yield stress is quite different.