The rheological characteristics of debris flow are the basis of the analysis of debris flow initiation, migration and deposition process. In order to explore the rheological characteristics of debris flow mud, according to the shear characteristics of debris flow fluid in different stages, taking Nanyang expansive soil mud as experimental material and using mcr702 rheometer blade rotor system, rheological experiments (twice increasing shear and once decreasing shear) were carried out on mud with different solid volume concentrations. According to the experimental results, the effects of different experimental processes and solid volume concentration on mud rheological parameters are analyzed, and the following conclusions are obtained: In the process of increasing shear rate, when the shear rate is less than 0.002s-1, the first shear stress is lower than the second shear stress; However, the first shear stress is higher than the second shear stress if the shear rate exceeds 0.002s-1. When the shear rate is greater than 1.83s-1, the mud is in the stable flow stage, the shear stress has a power-law relationship with the shear rate, and its rheological parameters increase exponentially with the volume concentration of mud. In the process of decelerating shear, the shear stress decreases in power law with the decrease of shear rate, which is a group of parallel lines in the double logarithmic coordinate system. Its flow index is less affected by solid volume concentration. The static yield stress of mud (the peak shear stress of the first increasing speed) is much larger than the stable flow yield stress (the shear stress value corresponding to the critical shear rate of 1.83s-1), and the difference decreases with the decrease of the volume concentration of mud solids. The static yield stress and steady flow yield stress of mud increase exponentially with the volume concentration of solid.
Article
Analysis of mud rheological characteristics based on debris flow migration process
https://doi.org/10.21203/rs.3.rs-2376078/v1
This work is licensed under a CC BY 4.0 License
Version 1
posted
You are reading this latest preprint version
Debris flow mud
Rheological experiment
Rheological properties
Solid volume concentration
Nanyang expansive soil slurry
Debris flows occur all over the world due to heavy rainfall. The dynamic process of debris flow (initiation, migration and accumulation) is the basic content of this kind of disaster prevention and control research. The basic structural model of debris flow is composed of fine-grained soil water mixed mud and coarse-grained particles (Shen, 1989; Wang, 1982). The cognition of mud rheological characteristics is very important for understanding and analyzing debris flow movement. It is the basis for determining debris flow velocity, impact force and outflow distance, and is helpful to evaluate the risks related to debris flow movement. Forterre, Y.; Pouliquen, O (2008) pointed out that the flow behavior of debris flow is controlled by the rheological characteristics of mud. Based on the analysis of the movement mechanism of such disasters, Ji et al (2012) has confirmed through model experiments that the mud moisture content affects the movement form, speed and range of such disasters (Ji, et al, 2013,2015). Ji, et al (2021) took Chengdu clay mud as an example to study its applicable rheological model. The rheological characteristics of mud will help to better understand the flow characteristics of debris flow. The rheological model thus obtained can indeed be input into the numerical simulation to predict the characteristics of debris flow events and draw the dangerous area map (Laigle et al., 2003; Rickenmann et al., 2006; Scot, et al, 2012).
The start-up process of debris flow is the process of debris flow fluid from static state to stable motion state in a short time. The shear rate acting on debris flow slurry increases rapidly from zero to the critical shear rate to maintain stable flow. The migration process of debris flow is a stable flow process of debris flow, and the shear rate is maintained above the critical shear rate. The accumulation process of debris flow is the process of debris flow fluid changing from moving state to static state. The shear rate acting on debris flow mud gradually decreases from the critical shear rate of maintaining stable movement to zero. Mud is the basic component of debris flow. How the shear stress of mud changes with the shear rate during the initiation, migration and accumulation of debris flow, how the solid volume concentration of debris flow affects the rheological parameters, and how to determine the static yield stress, stable flow yield stress and corresponding critical shear rate of mud are still the basic problems concerned in the analysis of debris flow disaster process. Therefore, combined with the shear rate change characteristics of mud in the process of debris flow startup, migration and accumulation, this paper takes Nanyang expansive soil as mud material to make mud samples with different solid volume concentrations, and carries out continuous shear rheological test with Antonpa mcr702 rheometer. The test includes three processes: increasing shear, decreasing shear and increasing shear again. Analyze the rheological characteristics of mud in different movement processes. In addition, the influence of filling mud on mud structure is not considered.
Nanyang is located in a semi-arid area. The soil layer exposed on the surface of this area is mainly expansive soil. The expansive soil is mainly composed of montmorillonite and illite. It has strong water absorption, high plasticity, rapid disintegration and violent expansion and contraction. The free expansion rate is 72%, the plastic limit is 26.5%, the liquid limit is 58.3%, and the particle density is 2.7g/cm3, through the liquid plastic limit test, expansibility test and particle density test. The soil samples used in the test were taken from Jingang village, Wolong District, Nanyang City (Nanyang section of the middle line of the South-to-North Water Transfer Project).The natural water content (\({w_0}\)) is measured in the laboratory. After drying, grinding and soaking, the composition of particulate matter is analyzed by Mastersizer 3000 laser diffraction particle size analyzer (see Fig. 1).
Soak the retrieved soil sample in water for 48 hours to make it fully saturated and fully stirred. Determine the initial moisture content of the soil sample after saturation (\({w_0}\): mass of water in unit volume and mass percentage of dry soil). In order to analyze the rheological properties of Nanyang expansive soil slurry with different solid volume concentrations, several saturated and softened soil samples were taken, placed in five measuring cups, and a certain amount of water was added to the cups respectively. According to the initial water content(\({w_0}\)) and the added water content, calculate the water content of the mud test sample in each measuring cup(\({w_1}\). The solid volume concentration\({C_{\text{s}}}\) of mud test samples is calculated by using water content \({w_1}\)and particle density \({d}_{s}\) (see Table 1).
| Slurry sample | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| solid volume concentration /% | 37 | 34 | 31 | 29 | 27 |
3.1 Experiment instrument
The experimental equipment adopts the Austrian Antonpa Mcr702 rheometer of the geotechnical Laboratory of Nanyang Institute of technology. The rheometer adopts modular and intelligent design and is composed of temperature control system, fixture system and test system. The blade rotor rheological measurement system is adopted. It consists of four thin blades arranged equiangularly around the axis of a small cylinder; Blade diameter D1 = 10 mm, blade height L = 9 mm; diameter of cup D2 = 25 mm (see Fig. 2). The rheometer adopts air bearing, and the minimum torque is 0.002 µ Nm, maximum torque: 200mnm, deflection angle (preset): 0.1 to ∞ µ Rad, minimum speed (CSS): 10 − 7 rpm, minimum speed (CSR): 10 − 6 rpm, maximum speed: 3000rpm, minimum frequency: 10 − 5 Hz, maximum frequency: 100Hz, normal stress range: 0.01-50n, normal stress accuracy: 0.002n, temperature range: − 150 ℃ ~ 1000 ℃.
In the rheological test, the wall slip problem (Ovarlez, 2011) resulted in the measured apparent shear rate being higher than the real shear rate inside the material (Choitre, 2017; Bonn, 2017). However, the vane viscometer has the least interference to the material structure during the insertion process, and can reduce the influence of wall slip on the test results to the greatest extent. It is still widely used to study the rheological properties of gel and thixotropic materials [Alderman et al (1991); Stokes &Telford (2004); Koehler et al (2006); Estellé et al (2008); wallevik (2008); Jau and Yang (2010)]. Therefore, the influence of wall slip on the experimental results is not considered. The normal stress difference without inertia effect is assumed in the rheological test.
3.2 Experimental scheme
This paper aims to analyze the rheological characteristics of mud in the process of initiation, migration and deposition of debris flow. During the start-up of debris flow, the debris flow 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; The migration process of debris flow is a stable shear process of debris flow; 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. The observed velocity of debris flow is usually between 0.5 and 20 m / S (Lorenzini & mazza2004, Ochiai et al 2004). According to the estimation of flow velocity and flow depth, the shear rate of moving debris flow slurry is usually between 0.1 and 20 S-1. In order to explore the variation process of shear stress with shear rate during the initiation, migration and accumulation of debris flow slurry, the rheological experiments of increasing shear (twice) and decreasing shear (once) were carried out continuously by using the blade rotor test system of mrc702 rheometer and the method of continuous shear experiment. Before the experiment, fully manually stir the prepared mud sample for 2 minutes, immediately take an appropriate amount of mud into the outer cylinder of the blade test system, lower the blade rotor, and completely immerse the rotor in the mud. The whole experiment is divided into three stages: two increasing shear and one decreasing shear. The change process of shear rate in each stage is as follows: the first shear is accelerated shear, the shear rate increases from 0 to 30s-1 in a logarithmic manner (stage 1: accelerated shear), and then the shear rate decreases from 30s-1 to 0s-1 in a logarithmic manner (stage 2: deceleration shear). After the end of the second stage, the blade rotor stands still for 4 minutes and starts the second speed-up shear. The change of shear rate is the same as that of the first stage (stage 3: speed-up shear)., The dynamic change process of shear stress with the increase and decrease of shear rate was recorded during the test. This experimental process is not complicated in operation, but the transient response of the sample and the shear induced solid-liquid phase transition are mixed in the shear process (divoux et al. 2013). Therefore, it is necessary to pay special attention to the change process of shear stress in the process of increasing shear rate. The whole experimental process reflects the rheological process of debris flow slurry in the initiation, migration and accumulation of debris flow. For all tests, the sample temperature is kept constant at 20 ℃ through the water circulation system.
4.1 Comparison and stage division of shear stress in increasing shear
According to the experimental scheme designed above, the variation process of the first and second increasing shear stress of mud with different solid volume concentration with shear rate is shown in Fig. 3. a-e。 Fig. 3. f is the change process of viscosity with shear rate in the second increasing shear process.
For all solid volume concentration slurries, the dynamic change process of shear stress with shear rate in the two increasing shear processes is similar, and the shear stress crosses near the shear rate of 0.002s-1. When the shear rate is less than 0.002s-1, the first increasing shear stress is lower than the second stress, but when the shear rate exceeds 0.002s-1, the first increasing shear stress is higher than the second shear stress (Fig. 3. a-e).
The shear stress of mud with each solid volume concentration changes abruptly twice each time it is sheared. In the first and second increasing shear processes, the maximum shear stress appears near 0.225s-1 and 0.1s-1 respectively. However, the minimum value of shear stress appears near 1.83s-1 in both increasing shear. Take Nanyang expansive soil slurry with solid volume concentration of 37% as an example. In the first increasing shear process, the shear stress increases rapidly from 0 to 1647pa (shear stress increase stage) when the shear rate increases from 0 to 0.225s-1. The shear stress decreases from 1647pa to 908pa (shear stress reduction stage) when the shear rate increases from 0.225s-1 to 1.83s-1. The shear stress increases from 908pa to 1145pa (shear stress increase stage) when the shear rate increases from 1.83s-1 to 30s-1. In the second increasing shear process, The shear stress increases rapidly from 678pa to 990pa when the shear rate increases from 0 to 0.1s-1. The shear stress decreases from 990pa to 252pa (shear stress reduction stage) when the shear rate increases from 0.1s-1 to 1.83s-1. The shear stress increases from 252pa to 776pa (shear stress increase stage) when the shear rate increases from 1.83s-1 to 30s-1. Cheng C H (1986) described this change process as three stages: stress growth, stress attenuation and stable flow. Jeo (2017,2019) carried out rheological experiment on tailings waste by using mcr301 spherical lateral volume system. With the increase of shear rate, the shear stress also shows an increase stage and a decrease stage, and then reaches a stable flow state. Taking the lowest shear stress as the dividing point, the change process of shear stress is divided into failure stage and stable flow stage after failure. The mud shear zone is formed in the failure stage, and the shear stress first increases and then decreases with the shear rate. It is two completely different processes of the formation of the shear zone. The shear stress growth (strain hardening) process is a dynamic failure process of slurry microstructure. With the increase of failure degree, the required shear stress increases (Bonn 2009). The process of shear stress reduction (strain softening) is not a unique phenomenon in the process of mud shear. Moller et al. (2009) found this negative slope in the rheological test of colloidal gel materials (the shear stress decreases with the increase of shear rate). (G. Ovarlez, et al, 2015; H. Hafid, et al, 2015; O.H. Wallevik, et al, 2015; J. Spangenberg, et al, 2012; Qian Y & Kawashima S, 2018) it is confirmed that this process is the migration of coarse particles from high shear rate region to low shear rate region. Chen Xiaoqing (2006) found that there was a sudden increase of pore water pressure during the start-up of debris flow. Therefore, the migration of coarse particles and the increase of pore water pressure are the reasons for the decrease of shear stress (strain softening) with the increase of shear rate in the flow curve. Scotto di santolo et al. (2012) observed similar behavior in the study of debris flow mixture and assumed that it was caused by the crushing and liquefaction of debris flow suspension. The area where the shear rate is greater than 1.83s-1 (as shown in Fig. 3.a-e and the shaded part in Fig. 4) represents the third stage of the first increasing shear: stable flow stage. Although the change of shear stress with shear rate is not stable, and even the shear stress decreases continuously with the increase of shear rate (Fig. 3. b-e), it is likely to be the continuation of coarse particle migration and shear liquefaction process. In view of this, the variation process of mud shear stress of Nanyang expansive soil with shear rate is divided into: strain hardening stage, strain softening stage and stable flow stage (see Fig. 4).
4.2 Effect of solid volume concentration on rheological parameters of shear stable flow
Proper rheological model is the key to analyze debris flow movement. From the above experimental results, it is difficult to use a unified model to describe the increase and decrease of shear stress in different shear rate ranges in the process of increasing shear rate. The failure stage is the formation process of shear zone and the focus of debris flow initiation process. The rheological characteristics of mud in stable flow stage are more suitable for the analysis of debris flow movement process. The commonly used rheological models in this stage mainly include Bingham model( \({\tau }={\tau }_{c}+k\dot{\gamma }\)), Herschel – Bulkley model(\({\tau }={\tau }_{c}+k{\dot{\gamma }}^{n}\)) and Power law model(\({\tau }=k{\dot{\gamma }}^{n}\)). According to the analysis in Section 4.1, the second increasing shear stable flow stage (shear rate is more than 1.83s-1) is selected as the representative to analyze the variation process of shear stress with shear rate (see Fig. 5).
In order to analyze the applicable rheological model and the influence of solid volume concentration on rheological parameters, the variation process of shear stress and shear rate is plotted in the double logarithmic coordinate system (Fig. 5). Figure 5 shows that the slope decreases with the decrease of solid volume concentration, and there is a good power-law relationship between shear stress and shear rate: \({\tau }=k{\dot{\gamma }}^{n}\)), and has a good correlation. In order to distinguish from the analysis of deceleration shear process in the next section, the rheological parameters of this stage (stable flow) are marked as: \({\text{k}}_{1}\),\({n}_{1}.\) The rheological parameters\({\text{k}}_{1}\) and \({n}_{1}\) of slurries with different solid volume concentrations are summarized in Table 2. In the stable flow stage, the rheological parameters \({\text{k}}_{1}\) and \({\text{n}}_{1}\) have an exponential relationship with the solid volume concentration (\({C}_{s}\)), where\({\text{k}}_{1}=0.1582{e}^{{19.473C}_{s}}\), \({\text{n}}_{1}=0.0017{e}^{{14.376C}_{s}}\)) (see Fig. 6. a and b). That is, the relationship between shear stress and shear rate related to solid volume concentration in the accelerated shear stable flow stage can be expressed as:
$${\tau }=0.1582{e}^{{19.473C}_{s}}\bullet {\dot{\gamma }}^{0.0017{e}^{{14.376C}_{s}}}$$
| Solid volume concentration(\({C}_{s}\)×100%) | \({\text{k}}_{1}\) | \({\text{n}}_{1}\) |
|---|---|---|
| 0.37 | 310.86 | 0.2919 |
| 0.34 | 105.59 | 0.2533 |
| 0.31 | 51.162 | 0.1625 |
| 0.29 | 36.701 | 0.1142 |
| 0.27 | 29.835 | 0.069 |
Jeong (2009) conducted a coaxial cylinder rheological experiment on Jonquiere clay (Eastern Canada) using rotovisco rv-12 rheometer. When the shear rate is in the range of 1 to 500s-1, the rheological curves of slurries with different liquid index (liquid index) in the double logarithmic coordinate system are a group of basically parallel lines, and the viscosity decreases with the increase of liquid index. The liquid index increases with the increase of water content, and the solid volume concentration decreases with the increase of liquid index. Figure 6A shows that the rheological parameter \({\text{k}}_{1}\) of Nanyang expansive soil slurry increases with the increase of solid volume concentration, which is consistent with Jeong (2009). However, the mud flow index \({n}_{1}\) of Nanyang expansive soil decreases with the decrease of solid volume concentration (Fig. 6. b), which is inconsistent with the result of Jeong (2009) that the flow index is 0.09.
4.3 Rheological properties of decreasing shear
The desilting process of debris flow is the process of debris flow fluid from stable flow state to static state. The change process of shear stress of debris flow slurry with the decrease of shear rate is the fundamental problem that must be concerned about the desilting condition and accumulation range of debris flow. Therefore, after the first speed increasing shear, the shear rate immediately decreases from 30s-1 to 0 in a logarithmic manner. The dynamic change process of shear stress and viscosity with the decrease of shear rate is shown in Fig. 7a, b。
In the process of decelerating shear, the shear stress decreases with the decrease of shear rate. The relationship between mud shear stress and shear rate is power-law. In the double logarithmic coordinate system, the shear stress, viscosity and shear rate of mud with each solid volume concentration are a group of nearly parallel parallel lines (Fig. 7. a, b). The relationship between shear stress and shear rate can be expressed as:
$${\tau }={\text{k}}_{2}\bullet {\dot{\gamma }}^{{n}_{2}}$$
Where \({\text{k}}_{2}\) and \({n}_{2}\) are the rheological parameters in the deceleration shear stage. The rheological parameters \({\text{k}}_{2}\) and \({n}_{2}\) of slurries with different solid volume concentrations are listed in Table 3. Parameter \({\text{k}}_{2}\) is closely related to the slurry solid volume concentration, which increases in a power-law relationship with the increase of solid volume concentration (see Fig. 8). The relationship between parameter \({\text{k}}_{2}\) and slurry solid volume concentration can be expressed as:\({\text{k}}_{2}={0.0144e}^{30.031{C}_{s}}\)。In the range of 27% − 37% of solid volume concentration, the value of rheological parameter \({n}_{2}\) is between 0.0271–0.0333 (see Table 3), which is less affected by solid volume concentration. Since the relationship between shear stress and shear rate is a group of approximately parallel lines (Fig. 7. a), the rheological parameter \({n}_{2}\) can be taken as its average value (0.0289) in the analysis of desilting process. According to the above analysis, in the process of deceleration shear, the shear stress can be expressed by solid volume concentration and shear rate. The formula is as follows:
$${\tau }={0.0144e}^{30.031{C}_{s}}\bullet {\dot{\gamma }}^{0.0289}$$
| Solid volume concentration(\({C}_{s}\)×100%) | \({\text{k}}_{2}\) | \({n}_{2}\) |
|---|---|---|
| 0.37 | 1072.7 | 0.0333 |
| 0.34 | 368.68 | 0.0284 |
| 0.31 | 137.11 | 0.0278 |
| 0.29 | 82.065 | 0.0277 |
| 0.27 | 55.469 | 0.0271 |
| average value | —— | 0.0289 |
The above analysis shows that there is a great difference between the increasing shear stress and decreasing shear stress of Nanyang expansive soil slurry with the change of shear rate. There are two sudden change points of shear stress in the increasing shear process, although it is difficult to use a unified model to express the change process of shear stress with the shear rate. However, there is a good power-law relationship between shear stress and shear rate in the steady flow stage of increasing shear rate and decelerating shear process. A unified power-law model can be used to describe the variation process of shear stress with shear rate.
4.4 Characteristic value of mud shear stress
The stress conditions such as starting, maintaining stable flow and deposition of debris flow are the basic problems often concerned in the whole process analysis of debris flow. According to the above analysis of the variation process of shear stress and viscosity with shear rate (two increasing shear and one decreasing shear), Nanyang expansive soil slurry is a thixotropic non-Newtonian fluid with yield stress (H.A. Barnes, 2007). Bonn (2017) described in detail the physical behavior of thixotropic non-Newtonian fluid materials with yield stress, and summarized the experimental techniques that can be used for yield stress testing. For thixotropic mud, the determination of yield stress depends on the accurate experimental scheme (Joshi, 2018). At present, there is a consensus on distinguishing the yield stress measured by the solid to liquid (or yield) transition from the yield stress measured during the liquid to solid transition. Mud yield stress can be described as static or dynamic yield stress (Bonnecaze and Brady 1992; Pham et al. 2008). The static yield stress can be regarded as the static yield stress according to the shear stress under the actual shear rate through the continuous shear test (Bonn, 2017). Although the determination of static yield stress depends on the shear rate applied and the "sample age" (Benzi et al. 2021a, 2021b). However, in the analysis of debris flow start-up process, the stress value represents the shear stress that must be overcome by debris flow start-up. In this experiment, two increasing shear were carried out, and the stress development process was similar (Fig. 3). Before the formation of the shear band (stable flow), both experienced the process of strain hardening and strain softening (Fig. 4). There was a peak shear stress, which can be used to represent the maximum shear stress that the mud must overcome from the formation of the shear band to the stage of stable flow, that is, the static yield stress. Although there is a peak stress in each increasing shear, and the peak stress of the first increasing shear is much greater than that of the second. However, for the analysis of debris flow start-up process, it can be considered that the mud is the primary shear, so it is more reasonable to use the first stress peak to analyze the debris flow start-up process. Therefore, the maximum shear stress of the first increasing shear is taken as the static yield stress of Nanyang expansive soil slurry( \({\tau }_{1}\))。Static yield stress of Nanyang expansive soil slurry with each solid volume concentration(\({\tau }_{1}\)) See Table 4.
The dynamic yield stress represents the critical stress value of the material gradually entering the deposited solid state from the flowing liquid state. Theoretically, it is the shear stress value when the shear rate approaches zero []. However, in the actual test, it is impossible to obtain the shear stress of mud at zero shear rate. Usually, the shear stress when the shear rate is close to 0 or the intercept of the stress axis is taken as the dynamic yield stress value.
In this experiment, when the shear rate increases from 0 to 30s-1 (the first increasing shear), the shear rate decreases from 30s-1 to 0 (decelerating shear). According to the above method, the intercept of the shear stress axis or the shear stress value with the shear rate close to 0 can be taken as the dynamic yield stress of the mud. From the variation process of increasing shear stress with shear rate (Fig. 3), it can be seen that the shear rate is in the range of 0-1.83s-1, which is the formation process of mud shear zone. During the formation stage of shear zone, the mud is in an unstable flow state (Jeo 2017, Leo 2020). Therefore, the dynamic yield stress determined by the shear rate of 0 or the intercept from the shear stress axis cannot be used for the analysis of the stable movement process of debris flow (Pell, 2018). According to the analysis of the development process of twice increasing shear stress (Section 4.1), when the shear rate exceeds the critical shear rate (1.83s-1), the shear zone is formed and the mud enters a stable flow state. The shear stress value corresponding to the critical shear rate represents the minimum stress value to maintain the stable movement of mud, which is more practical (Jeo, 2017). In order to distinguish the concept of dynamic yield stress, the shear stress corresponding to the critical shear rate is called stable flow yield stress(\({\tau }_{2}\)). From the start-up to the stable flow stage of debris flow, the mud must undergo a complex shear process, and the original microstructure of the mud is damaged by multiple shear. Therefore, in this paper, the shear stress corresponding to the critical shear rate in the secondary increasing shear process is taken as the stable flow yield stress. Stable flow yield stress of Nanyang expansive soil slurry with each solid volume concentration(\({\tau }_{2}\)) See Table 4. In order to compare the difference between static yield stress and stable flow yield stress, for Nanyang expansive soil slurry with various solid volume concentrations, the difference(\(\varDelta {\tau }\)) between static yield stress(\({\tau }_{1}\)) and stable flow yield stress ( \({\tau }_{2}\))is shown in Table 4.
| solid volume concentration /% | 37 | 34 | 31 | 29 | 27 |
|---|---|---|---|---|---|
| Static yield stress(\({\tau }_{1})\)/Pa | 1606 | 550 | 207 | 125 | 76 |
| Steady flow yield stress(\({\tau }_{2})\)/Pa | 352 | 125 | 53 | 39 | 30 |
| \(\varDelta {\tau }\) /Pa | 1254 | 425 | 154 | 86 | 46 |
The effect of solid volume concentration on static yield stress (\({\tau }_{1}\)) and steady flow yield stress (\({\tau }_{2}\)) is shown in Fig. 9.
Table 4 and Fig. 9 confirm that the static yield stress and stable flow yield stress of mud increase exponentially with solid volume concentration (Fig. 9). The static yield stress is much greater than the steady flow yield stress, and this difference decreases with the decrease of slurry solid volume concentration (Table 4). (J.J. Assaad et al 2006)。The static yield stress and stable flow yield stress of mud have the following relationship with the volume concentration of mud solid: static yield stress:, 
\({R^2}=0.9937\);Steady flow yield stres, :\({\tau _2}=0.0301{e^{24.84{C_s}}}\)༌ \({R^2}=0.9663\)。
Combined with the shear rate change process of mud in the process of debris flow startup, migration and accumulation, taking Nanyang expansive soil mud as the experimental material and using the blade rotor test system of mcr702 rheometer, the rheological experiments of increasing shear (twice) and reducing shear (once) are carried out for mud with different solid volume concentration, and the change process of mud shear stress with the increase and decrease of shear rate is analyzed. According to the experimental results, the change process of shear stress of Nanyang expansive soil slurry and the influence of solid volume concentration on rheological parameters are analyzed, and the following conclusions are obtained:
For all solid volume concentration slurries, the dynamic change process of shear stress with shear rate is similar in the two speed-up shear processes, and there is shear stress crossover near the shear rate of 0.002s-1. When the shear rate is less than 0.002s-1, the first increasing shear stress is lower than the second stress. When the shear rate exceeds 0.002s-1, the first increasing shear stress is higher than the second stress.
In the process of increasing shear rate, there are two abrupt changes (maximum and minimum) in shear stress with the increase of shear rate due to the damage of slurry microstructure, particle migration and liquefaction. The variation process of mud shear stress with shear rate can be divided into strain hardening stage, strain softening stage and stable flow stage. When the shear rate is greater than the critical shear rate (1.83s-1), the mud enters the stable flow stage and is in a stable flow state. In the steady flow stage, the shear stress and shear rate have a good power-law relationship, and the rheological parameters \({k}_{1}\) and \({n}_{1}\) increase exponentially with the increase of solid volume concentration. The relationship between shear stress and shear rate can be expressed as:
$${\tau }={k}_{1}\bullet {\dot{\gamma }}^{{n}_{1}}=0.1582{e}^{{19.473C}_{s}}\bullet {\dot{\gamma }}^{0.0017{e}^{{14.376C}_{s}}}$$
In the process of decelerating shear, the shear stress and shear rate have a good power-law relationship. The rheological parameter \({k}_{2}\) increases exponentially with the solid volume concentration, and the solid volume concentration has little effect on the rheological parameter \({n}_{2}\). The relationship between shear stress and shear rate can be expressed as:
$${\tau }={{k}_{2}\bullet {\dot{\gamma }}^{{n}_{2}}=0.0144e}^{30.031{C}_{s}}\bullet {\dot{\gamma }}^{0.02886}$$
The static yield stress and steady flow yield stress of mud increase exponentially with the volume concentration of solid. The relationship between mud static yield stress, stable flow yield stress and mud solid volume concentration can be expressed as follows:
Static yield stress:,
Steady flow yield stress:\({\tau _2}=0.0301{e^{24.84{C_s}}}\)。
Acknowledgments
We gratefully wish to acknowledge the Natural Science Foundation (Grant No.41672357), and the Henan Provincial Department of Science and Technology Research Project（Grant No. 212102310030,162102310253, 182102310779）
Data Availability Statement
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
- SHEN Shouchang. Experiment of rheology of debris flow [J].Journal of Hydraulic Engineering,1989, (9):7-13. (in Chinese)
- WANG Yuyi. The rheological characteristics of debris flow slurry [J]. Journal of Sediment Research,1982, (2)：74-78. (in Chinese)
- Jop P , Forterre Y , Pouliquen O . Initiation of granular surface flows in a narrow channel[J]. Physics of Fluids, 2007, 19(8):088102-
- JI Xianjun,Ou Guoqiang.etal.Research Status and Prospect on Moving Process of Landslip-collapse Soil along Slope[J].Journal of mountain science. 2012. 30（3）, 361-368.
- JI Xianjun, OU Guoqiang, YANG Shun, et al. Comparison Analysis of the Motion Process about Viscous and No-viscous Landslip-collapse Soil based on PFC3D[J]. Journal of Sichuan university (Engineering Science Edition), 2013,45(supp.1),67-73.
- JI Xianjun, LIANG Ying, OU Guoqiang, et al. Numerical simulation and verification about viscous debris motion process on slope[J]. Rock and Soil Mechanics, 2015,36(8), 2402-2408
- Ji, X., Liang, Y., Cao, W. Effect of Solid Volume Concentration on Rheological Properties of Chengdu Clay Slurry. Processes 2022, 10, 425. https://doi.org/10.3390/pr10020425
- Laigle D , Hector A F , J Hübl, et al. Comparison of numerical simulation of muddy debris flow spreading to records of real events[C]// 3rd International Conference “Debris-Flow Hazards Mitigation”. 2003.
- Kasim N , Taib K A , Mukhlisin M . COMPARISON OF DEBRIS FLOW SIMULATION MODEL WITH FIELD EVENT IN KUALA KUBU BARU, MALAYSIA[C]// The 9th International Conference of Geotechnical & Transportation Engineering (GEOTROPIKA) and The 1st International Conference on Construction and Building Engineering (ICONBUILD) – GEOCON2013. 2013.
- Rickenmann, D., Laigle, D., McArdell, B. W. & Hubl, J. (). Comparison of 2D debris-flow simulation models with field events. Comput. Geosci. 2006, 10(2), 241–264.
- Ovarlez G , Mahaut F , Bertrand, François, et al. Flows and heterogeneities with a vane tool: Magnetic resonance imaging measurements[J]. Journal of Rheology (1978-present), 2012, 55(2):197-223.
- Cloitre M , Bonnecaze R T . A review on wall slip in high solid dispersions[J]. Rheologica Acta, 2017.
- D Bonn, Denn M M , Berthier L , et al. Yield Stress Materials in Soft Condensed Matter[J]. Rev.mod.phys, 2017, 89(3):035005.
- Alderman N J, Meeten G H, Sherwood J. Vane rheometry of bentonite gels[J]. Journal of Non-newtonian Fluid Mechanics, 1991, 39(3): 291-310.
- Stokes J R , Telford J H . Measuring the yield behaviour of structured fluids[J]. Journal of Non-Newtonian Fluid Mechanics, 2004, 124(1-3):137-146.
- Koehler, Fowler, Ferraris A , et al. A NEW, PORTABLE RHEOMETER FOR FRESH SELF-CONSOLIDATING CONCRETE A NEW, PORTABLE RHEOMETER FOR FRESH SELF-CONSOLIDATING CONCRETE[J]. Aci Materials Journal, 2006, 233.
- Patrice Estellé, Lanos C , Perrot A , et al. Processing the vane shear flow data from Couette analogy[J]. Applied Rheology, 2008, 18(3):34037.
- Wallevik J E . Minimizing end-effects in the coaxial cylinders viscometer: Viscoplastic flow inside the ConTec BML Viscometer 3[J]. Journal of Non-Newtonian Fluid Mechanics, 2008, 155(3):116-123.
- Jau W C , Yang C T . Development of a Modified Concrete Rheometer to Measure the Rheological Behavior of Fresh Concrete. 2010.
- Lorenzini, G., and Mazza, N. 2004. Debris flow: Phenomenology and rheological modeling. WIT Press, Southampton, UK.
- Ochiai H , Okada Y , Furuya G , et al. A fluidized landslide on a natural slope by artificial rainfall[J]. Landslides, 2004, 1(3):211-219.
- Divoux T , Grenard V , Manneville S . Rheological hysteresis in soft glassy materials[J]. Physical Review Letters, 2013, 110(1):018304.
- Cheng C H. Yield stress: A time-dependent property and how to measure it[J]. Rheologica Acta, 1986, 25(5):542-554.
- Jeong S W , Wu Y H , Cho Y C , et al. Flow behavior and mobility of contaminated waste rock materials in the abandoned Imgi mine in Korea[J]. Geomorphology, 2018, 301(jan.15):79-91.
- Jeong S W. Shear Rate-Dependent Rheological Properties of Mine Tailings: Determination of Dynamic and Static Yield Stresses[J]. Applied Sciences, 2019, 9(22):4744.
- Daniel, Bonn, Morton, et al. Yield Stress Fluids Slowly Yield to Analysis[J]. Science, 2009, 324(Jun.12 TN.5933):1366-1367.
- Moller P C F, Fall A , Bonn D . Origin of apparent viscosity in yield stress fluids below yielding[J]. EPL (Europhysics Letters), 2009, 87(3):38004.
- G. Ovarlez, F. Mahaut, S. Deboeuf, N. Lenoir, S. Hormozi, X. Chateau, Flows of suspensions of particles in yield stress fluids, J. Rheology (1978-present) 59 (2015) 1449e1486.
- H. Hafid, G. Ovarlez, F. Toussaint, P. Jezequel, N. Roussel, Assessment of potential concrete and mortar rheometry artifacts using magnetic resonance imaging, Cem. Concr. Res. 71 (2015) 29-35.
- O.H. Wallevik, D. Feys, J.E. Wallevik, K.H. Khayat, Avoiding inaccurate interpretations of rheological measurements for cement-based materials, Cem.Concr. Res. (2015).
- J. Spangenberg, N. Roussel, J. Hattel, H. Stang, J. Skocek, M. Geiker, Flow induced particle migration in fresh concrete: theoretical frame, numerical simulations and experimental results on model fluids, Cem. Concr. Res. 42 (2012) 633-641.
- Qian Y , Kawashima S . Distinguishing dynamic and static yield stress of fresh cement mortars through thixotropy[J]. Cement & Concrete Composites, 2018, 86:288-296.
- Chen Xiaoqing Experimental study on starting mechanism of landslide transformed debris flow [D] Southwest Jiaotong University, 2006(in Chinese)
- Scotto di Santolo A, Pellegrino A M, Evangelista A, et al. Rheological behaviour of reconstituted pyroclastic debris flow[J]. Geotechnique, 2012, 62(1): 19-27.
- Jeong S W , Leroueil S , Locat J . Applicability of power law for describing the rheology of soils of different origins and characteristics[J]. Canadian Geotechnical Journal, 2009, 46(9):1011-1023.
- H.A. Barnes, The yield stress Myth?'Papere21 Years on, Appl. Rheol. 17 (2007),43110-44250.
- Joshi Y M , George P . Yield stress fluids and ageing[J]. Rheologica Acta, 2018, 57:521-549.
- Bonnecaze, R. T . Yield stresses in electrorheological fluids[J]. Journal of Rheology, 1992, 36(1):73-115.
- Pham K N , Petekidis G , Vlassopoulos D , et al. Yielding behavior of repulsion- and attraction-dominated colloidal glasses[J]. Journal of Rheology, 2008, 52(2):649-676.
- Benzi R , Divoux T , Barentin C , et al. Stress Overshoots in Simple Yield Stress Fluids[J]. Physical Review Letters, 2021, 127.
- Benzi R , Divoux T , Barentin C , et al. Continuum modeling of shear startup in soft glassy materials[J]. Physical Review E, 2021, 104.
- Schippa L . Modeling the effect of sediment concentration on the flow-like behavior of natural debris flow[J]. International Journal of Sediment Research, 2020, 35( 4):315-327.
- Anna P , Leonardo S . Rheological Modeling of Macro Viscous Flows of Granular Suspension of Regular and Irregular Particles[J]. Water, 2017, 10(1):21.
- Assaad J J, Khayat K H. Effect of Viscosity-Enhancing Admixtures on Formwork Pressure and Thixotropy of Self-Consolidating Concrete[J]. Aci Materials Journal, 2006, 103(4):280-287.
No competing interests reported.