applied sciences

Article Shear Rate-Dependent Rheological Properties of Mine Tailings: Determination of Dynamic and Static Yield Stresses

Sueng-Won Jeong

Korea Institute of Geoscience and Mineral Resources, Daejeon 34132, Korea; [email protected]



Received: 9 August 2019; Accepted: 5 November 2019; Published: 7 November 2019


Abstract: In this paper, shear rate-dependent rheological properties of mine tailings taken from abandoned mine deposits prone to mass movements are examined using a commercial ball-measuring rheological system. The yield stresses (i.e., dynamic and static yield stresses) and viscosity of sand-rich materials are examined by the shear rate-controlled flow curve and time-dependent stress growth methods. Before yielding, the shear stress reaches a peak value (i.e., yield stress) observed for all flow curves. In the steady-state condition, the materials have a minimum shear stress (i.e., dynamic yield stress). The static yield stress can be determined under a constant applied shear rate with different 4 1 1 initial values ranging from 10− to 10− s− . As a result, the Bingham yield stress and viscosity can be used as a first approximation for estimating the debris flow mobility of post-failure materials. However, the Bingham yield stress is competitive with the static yield stress measured from stress growth methods. Upon comparison of the dynamic and static yield stresses, the static yield stress is approximately 35–45 times greater than the dynamic yield stress, and may be strongly related to microstructural changes (i.e., thixotropy). In this context, special attention must be paid to the determination of yield stresses in debris flow mitigation programs.

Keywords: dynamic yield stress; static yield stress; initial shear rate; mine tailings; debris flow

1. Introduction The yield stress is a special property associated with non-Newtonian fluids, such as clay suspensions, concrete cements, crude oil, foams, food, paints, pastes, and polymers [1–6]. In general, the yield stress is defined as the shear stress at the point where the applied stress exceeds the critical shear rate; in this case, the material starts to flow. Materials may deform elastically due to structural changes below the yield stress, but they may deform greatly and flow like liquids above the yield stress. There are numerous methods that can be employed to determine the yield stress of non-Newtonian fluids: model fitting, a slump test, an inclined plane test, a stress ramp test, a stress growth test, oscillation amplitude sweep, and creep tests. However, the yield stress is strongly dependent on the test conditions and techniques employed [7,8]. In addition, many non-Newtonian fluids are thixotropic [9,10]. Structural changes with time are unavoidable during shear. Time-dependent rheological characteristics make it difficult to find a robust method for determining the true yield stress [11]. This subject is still under debate in cement and concrete research (such as building materials) and disaster-prevention measures (such as debris flow analysis for estimating future catastrophic hazards). The dynamic and static yield stresses can be determined by equilibrium flow curves and stress growth methods. The dynamic yield stress is the minimum shear stress in the flow curve with a steady-state flow condition, while the static yield stress is the peak shear stress measured with a constant shearing time [12]. It is also well-known that the dynamic yield stress is associated with

Appl. Sci. 2019, 9, 4744; doi:10.3390/app9224744 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 4744 2 of 11

flow stopping, but the static yield stress is associated with flow starting [13]. According to previous studies [6], the dynamic and static yield stresses are related to the state before and after microstructural changes in materials. In addition, the conception of the time depending on the value of the yield stress has been pointed out by numerous studies [14–16]. As a result, it is expected that the value of dynamic yield stress is much lower than that of static yield stress with respect to the structural states. It is well-known that the yield stress is related to the structural change, that is, thixotropy. Rheological properties are essential in the fluid industry and natural disaster-related sciences. The rheological properties are examined for various materials, such as clay suspensions, muds, sand-rich materials, and reconstituted pyroclastic debris flows [13,17–20]. Water is typically a viscous liquid, while particle-bearing liquids typically behave as non-Newtonian fluids, indicating more complex rheological characteristics. Few studies have focused on the geotechnical and rheological properties of post-failure materials in mass movements, which can result in rapid complex fluid-like behavior as a kind of soil liquefaction. In the field of debris flows, a multiphase process in large particle-bearing debris flows is of paramount importance [21] because they are very dense and exhibit strong interactions between particles in the interstitial fluid. Rheological tests are often considered large particle-laden flows, e.g., the mean grain size of materials tested in rheometers has often been a typical sand with particle sizes from 0.075 to 2 mm in diameter. However, the change in rheological properties is significant when the solid fraction is slightly changed [13]. The disposal of mine tailings and waste rock materials involving sand- and gravel-size particles in open pits is a problem that needs to be managed. Severe erosion and mass movements in abandoned mine deposits can result in physicochemical contamination at and near the mine deposits [22]. In this case, the determination of flow properties is crucial for debris flow rheology [19] because the runout distances and speeds of debris flows are mainly estimated by yield stress and viscosity [23]. When estimating the runout distance of debris flows in coarse-grained sediments, the rheological characteristics are the decisive criteria for mitigating and managing future debris flow events in mountainous areas. However, the determination of dynamic and static yield stresses in debris flows is still poorly studied. In this study, the dynamic and static yield stresses of sand-rich materials taken from abandoned mine deposits are studied. First, the flow behaviors of the sand-rich materials are examined as a function of the shear rate (i.e., the flow curve) at the same solid volume concentration. Second, the rheological properties, i.e., yield stresses and viscosity, are determined using model fitting, including Bingham, Herschel–Bulkley, bilinear, modified Bingham, and power law models. The initial shear rate-dependent shear stress is examined. Third, under a constant applied shear rate, the stress build-up with time is monitored. The differences in dynamic and static yield stresses as a function of shear rate are highlighted. Finally, the shear strengths, including the undrained shear strength measured from fall cone tests, the Bingham yield stress, and the static yield stress in modeling the debris flow, are compared. Creep and recovery tests are not taken into account. It should also be noted that pre-shearing has an impact on the determination of yield stress with respect to the flocculation state in the materials. Therefore, only a limited situation can be discussed.

2. Materials and Methods

2.1. Materials The materials tested were mine tailings taken from an abandoned mine deposit site located in Busan Metropolitan City, Republic of Korea. The grain sizes were fine to coarse, and the shapes were subangular. The main mineralogical composition was quartz, pyrophyllite, pyrite, sericite, and kaolin clay [22,24]. The on-site materials are very coarse: 30% gravel, 60–70% sand, and 5% finer sizes (clay and silt particles). The natural water content is less than 10%, and the permeability (k) is very high (e.g., k 2 10 cm/s 1). In the waste rock dump with a low level of vegetation, abandoned mine deposits ≥ × − experience severe erosion. In addition, after torrential rainfall events in the summer monsoon season, several traces of mass movements (e.g., rotational slumps, slides, and debris flows) can be found on Appl. Sci. 2019, 9, 4744 3 of 11 natural slopes. Failed materials often flow and are deposited in a mountain stream at and near the waste rock dump. In brief, the materials can be gravelly sands; however, they are very difficult to test in conventional rheological tests because most rheometers are suitable for fine-grained sediments. To measure these materials, a series of rheometric tests was performed on the material passing through a No. 4 sieve (i.e., sand-rich materials) using a ball-penetrating torque-measured system called the “ball-measuring system (BMS)” in this study.

2.2. Methods Numerous testing methods and apparatuses have been designed for determining the soil resistance of debris flow materials in the range from microscale to macroscale measuring systems (e.g., plate-plate, cone-plate, cylinder, vane, stirrer, slump, and large-scale devices). Figure1 shows the rheometer used in this study. The commercial ball-measuring rheological system (BMS, RheolabQC, Anton Paar) consists of three balls and a container. The balls have three diameters, i.e., 10, 12, and 15 mm, whilst the container (cup) has a diameter of 115 mm with a sample volume of 500 cm3. In this system, a homogenous soil sample, the mixture of soil and water, is placed into the container and the ball is immersed into the soil sample. The depth of ball penetration is the same for all tests. The distance between the ball and the bottom of the container is 20 mm. Torques are automatically recorded when rotating the ball. The shear rate control or shear stress control mode can be applied. The measurement of shear stress and the shear rate in a ball-measuring system can be performed for 1–5 mm diameter soil samples. Similar tests for large-particle fluids using a ball-measuring system have been performed by [19,25,26]. The edge and slip effects are assumed to be negligible. Potential slipping and gliding problems are negligible because of the ideal spherical shape used to minimize the edge effect during shearing. The system displays a wide gap between the sensor and soil sample container. In this context, it is applicable for both fine-grained and coarse-grained sediments in debris flow materials. However, there are some limitations in performing such experiments. The normal pressure effect is not taken into account. The temperature is fixed at 20 ◦C during shearing. However, it is expected that the variation in temperature is one of minor effects in the rheological behavior of sediments with large particle sizes. Two simple test methods were applied to satisfy the purpose of the study. Two types of rheological tests were performed: a flow curve test and a stress growth test. The first test was conducted to determine the dynamic yield stress (e.g., the Bingham yield stress and viscosity), and the second test was conducted to determine the static yield stress (e.g., the peak and residual shear stresses). As a result, the flow curves and stress growth methods could produce shear stress vs. shear rate and shear stress vs. shearing time relationships, respectively. To determine the yield strength of waste rock materials, the rheological models considered are as follows: . Bingham : τ = τc + µ γ (1) h· . ! . n τc γ Bilinear : τ = τy + µh γ + . · . (2) · γ + γo   .   1 exp mγ   − −  . Modified Bingham : τ = µ + τc . γ (3)  γ 

. n Herschel-Bulkley : τ = τc + K γ (4) · . n Power law : τ = µ γ , (5) · . where τ is the shear stress (Pa), µ is the viscosity (Pa s), and γ is the shear rate (s 1). In Equation (1), · − τc is the yield stress (Pa), which is called the Bingham yield stress, and µ is the plastic viscosity (Pa s). h · In Equation (2), τy is the yield stress (Pa) obtained from the bilinear model, which is similar to the yield stress obtained from the Bingham fluid; the exponent n is the flow behavior index (dimensionless); . and γo is the shear rate related to the rheological transition from a Newtonian viscosity to an ideal Appl. Sci. 2019, 9, 4744 4 of 11 plastic viscosity. The exponent n is also used in the Herschel–Bulkley and power law models to describe the flow behavior, e.g., if n < 1, pseudoplastic (shear thinning) behavior occurs, and if n > 1, dilatant (shear thickening) behavior occurs. Equation (3) is the modified Bingham model. It is a well-known model used to describe the transition from the pseudo-viscosity regime (elastic-dominant slope before yielding)Appl. Sci. to 2019 yielding, 9, x FOR in PEER the REVIEW flowing region. The value of m is a parameter related to surface yielding4 of 11 in shear stress at relatively low shear rates (unit of time, s). In Equation (4), if n = 1, it is the same as the if n = 1, it is the same as the Bingham fluid, and if τc = 0, it reduces to the power law model. K is the Bingham fluid, and if τc = 0, it reduces to the power law model. K is the consistency coefficient (Pa s). consistency coefficient (Pa∙s). The exponent n is 0.3 for clays, 0.8 for silt-rich materials, and 0.8 for · The exponent n is 0.3 for clays, 0.8 for silt-rich materials, and 0.8 for bentonite [27]. In Equation (5), bentonite [27]. In Equation (5), if n = 1, it is a Newtonian viscosity model. if n = 1, it is a Newtonian viscosity model. The shear strengths measured from the BMS were compared with those obtained from fall cone testsThe with shear different strengths solid measured volume concentrations. from the BMS wereSwedish compared fall cones with were those used obtained at 60 degrees from with fall cone testsdifferent with di conefferent weights, solid such volume as 10, concentrations. 60, 100, and 400 Swedishg. The test fall procedures cones were were used identical at 60 to degrees those of with different[28]. cone weights, such as 10, 60, 100, and 400 g. The test procedures were identical to those of [28].

FigureFigure 1. Ball-measuring 1. Ball-measuring rheometric rheometric system:system: ( (aa)) Test Test procedure, procedure, (b ()b schematic) schematic view view of ball of ballrotation, rotation, (c) shear(c) shear layer layer formation formation (sliding (sliding plane plane inin aa steady-statesteady-state condition) condition) during during shearing, shearing, (d) (flowd) flow curve curve withwith Bingham Bingham fluid fluid and and ball ball rotation, rotation, ((ee)) shearshear stress–shear stress–shear rate rate plot, plot, and and (f) (viscosity–shearf) viscosity–shear rate rateplot. plot. TestedTested from fromOa toⓐOg to. ⓖ.

3. Results3. Results

3.1.3.1. Rheological Rheological Properties Properties of of Mine Mine Tailings: Tailings: YieldYield Stress and and Viscosity Viscosity FigureFigure2 presents 2 presents the the flow flow characteristics characteristics ofof wastewaste materials with with initial initial shear shear rates rates for fora water a water contentcontent of of 34% 34% (equivalent (equivalent toto aa solid volume volume concentration concentration of 52%). of 52%). At the At same the water same content water content(or (orsolid volume volume concentration), concentration), the flow the behavior flow behavior is very similar is very (Figure similar 2a). (Figure To examine2a). the To rheological examine the characteristics, the controlled shear rate mode was employed with a range of 10−4 to 1014 s−1. In1 1 rheological characteristics, the controlled shear rate mode was employed with a range of 10− to 10 s− . particular, five shear rates were applied as initial values from 0.0001 to 0.1 s−1. The1 measured In particular, five shear rates were applied as initial values from 0.0001 to 0.1 s− . The measured rheological properties, that is, the yield stress and plastic viscosity, range from 17 to 21 Pa and 1.0 to 1.2 Pa∙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 Appl. Sci. 2019, 9, 4744 5 of 11 rheological properties, that is, the yield stress and plastic viscosity, range from 17 to 21 Pa and 1.0 to 1.2 Pa s, respectively. The variations in yield stress and viscosity are relatively small. They can be · 1 dividedAppl. Sci. 2019 into, 9 two, x FOR regimes PEER REVIEW based on a shear rate of 1 s− : (a) the generation of a slip surface in response5 of 11 to a complete rotation of a penetrated ball (after one full revolution, i.e., onset of failure stage) and (b)(b) continuous continuous viscousviscous shearingshearing (post-failure stage) stage).. An An example example is is shown shown in in Figure Figure 2b.2b. Compared Compared toto . 1 thethe flowflow behavior behavior of of fine-grained fine-grained sediments, sediments, a a large large di differencefference is is shown shown before before yielding yielding (i.e., (i.e.,γ =𝛾 1= s1− ). −1 1 −1 Theres ). There is a distinct is a distinct peak peak value value of shear of shear stress stress at a relativelyat a relatively low shearlow shear rate regimerate regime (i.e., (i.e., 0.4 s −0.4). s After). theAfter peak the value, peak value, an abrupt an abrupt decrease decrease in shear in stressshear isstress observed. is observed. All processes All processes generate generate a slip a surface slip (i.e.,surface shear (i.e., banding shear formationbanding formation in Figure1 c)in in Figure a ball-measuring 1c) in a ball-measuring system. After onesystem. full revolutionAfter one offull the ball,revolution they behave of the ball, as an they ideal behave plastic asfluid, an ideal such plasti as ac Binghamfluid, such fluid as a Bingham [29]. To verify fluid [29]. the applicabilityTo verify the of theapplicability rheological of modelthe rheological for obtaining model flow for curves, obtaining the flow best fitcurves, was obtainedthe best fit with was the obtained Bingham, with bilinear, the Herschel–Bulkley,Bingham, bilinear, modifiedHerschel–Bulkl Bingham,ey, modified and power Bing lawham, models. and power As shownlaw models in Figure. As shown2b, most in Figure of them 1 −1 are2b, inmost good of agreementthem are in withgood theagreement test results with after the test the shearresults rate after of the 1 sshear− , but rate a large of 1 s scatter, but a is large found atscatter lower is shear found rates. at lower In this shear context, rates. In the this post-failure context, the characteristics post-failure characteristics are limited to are the limited flow behaviors to the observedflow behaviors after theobserved critical after deformation. the critical The deformat resultsion. of modelThe results fitting of withmodel respect fitting towith diff respecterent initial to different initial shear rates ranging4 from1 101 −4 to 10−1 s−1 are summarized in Table 1. Compared to the shear rates ranging from 10− to 10− s− are summarized in Table1. Compared to the rheological propertiesrheological of properties fine-grained of fine-grain sediments,ed sediments, the properties the properties of these materials of these arematerials slightly are higher. slightly According higher. toAccordingJeong et al.to [27Jeong], the et rheological al. [27], the compilation rheological of compilation clay-rich, silt-rich, of clay-rich, and sand-rich silt-rich, materialsand sand-rich shows materials shows viscosities of approximately 20, 200, and 2000 mPa∙s, respectively, in the case that viscosities of approximately 20, 200, and 2000 mPa s, respectively, in the case that the yield stress is the yield stress is equal to 20 Pa. In this study, the· materials tested were sand-rich materials (less equal to 20 Pa. In this study, the materials tested were sand-rich materials (less cohesive). The results cohesive). The results are in good agreement with the previous rheological compilation (especially are in good agreement with the previous rheological compilation (especially the yield stress–viscosity the yield stress–viscosity relationship for the sand-rich group). Uncertainties are higher for the relationship for the sand-rich group). Uncertainties are higher for the rheological properties measured rheological properties measured at lower shear rates because the variations in viscosity at low shear at lower shear rates because the variations in viscosity at low shear rates (less than 1 s 1) are significant. rates (less than 1 s−1) are significant. In an elastic regime, the structure begins to break− down, is In an elastic regime, the structure begins to break down, is subjected to shear localization, and creates subjected to shear localization, and creates partial shear-induced particle migration in the flow curves partial shear-induced particle migration in the flow curves when the shear strain approaches the critical when the shear strain approaches the critical shear strain [6]. In the transition from the solid-like to shear strain [6]. In the transition from the solid-like to liquid-like regime, there is a critical deformation. liquid-like regime, there is a critical deformation. The shear localization and shear banding (stick-slip Thebehavior) shear localizationare dependent and on shear increasi bandingng the (stick-slip apparent behavior) shear rate are [30]. dependent According on to increasing [31], shear the banding apparent shearinstability rate [can30]. be According divided into to [three31], shear regions, banding e.g., homogeneous, instability can wall be dividedslip, and into bulk three shear regions, banding. e.g., homogeneous,In this regard, wallthe term slip, “shear and bulk layer” shear in banding.Figure 1 Inis more this regard, appropriate the term and “shear could layer”describe in Figurethe area1 is morewhere appropriate the shear stresses and could (shear describe forces) the are area applied where to the the shear suspension stresses structure. (shear forces) At a arerelatively applied high to the suspensionshear rate, structure.the Bingham At a rheological relatively high concept shear is rate, well-matched. the Bingham The rheological viscosity concept before is 1 well-matched. s−1 can be 1 Theconsidered viscosity pseudo-Newtonian before 1 s− can be viscosity considered [27], pseudo-Newtonian which is defined asviscosity the slope[ of27 ],the which line fit is between defined asthe the slopeorigin of (0 the value line in fit flow between curves) the and origin the (0maximum value in flowvalue curves) reached and before the maximumthe critical valueshear reachedrates (in beforethis 1 thecase, critical 1 s−1). shearAs a result, rates (inthe this lower case, the 1 initial s− ). Asshear a result, rates are, the the lower higher the initialthe slopes shear (Table rates 1). are, This the result higher themay slopes occur (Table because1). Thisthe pseudo-Newtonian result may occur because viscosit they (i.e., pseudo-Newtonian the slope determined viscosity before (i.e., yielding) the slope determinedgradually approaches before yielding) the y-axis gradually as the initial approaches shear rates the y-axis decrease. as the initial shear rates decrease.

FigureFigure 2.2. FlowFlow curves and model fitting: fitting: (a (a) )Shear Shear stress stress and and shear shear rate rate relationships relationships with with the the mean mean valuevalue ofof flow flow equation; equation; (b )( modelb) model fitting fitting with with Bingham, Bingham, Bilinear, Bilinear, Herschel–Bulkley, Herschel–Bulkley, Modified Modified Bingham, andBingham, Power and law. Power law.

Appl. Sci. 2019, 9, 4744 6 of 11

Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 11 Table 1. Rheological properties obtained from different rheological models. Table 1. Rheological properties obtained from different rheological models. Bingham Bilinear Modified Bingham Herschel–Bulkley Power Law . Bingham . Bilinear Modified Bingham Herschel–Bulkley Power Law γ τc ηh γo c ηpN m τc-HB K-HB n-HB K n 𝜸 τc ηh 𝜸 c ηpN m τc-HB K-HB n-HB K n 0.1 22.39 1.34 0.47𝒐 10.43 49.4 10.43 23.0 0.83 1.14 11.04 0.52 0.010.1 19.7522.39 1.34 1.46 0.47 0.08 10.43 1.52 257.05 49.4 10. 1.5243 18.023.0 0.83 0.69 1.14 1.13 11.04 13.01 0.52 0.42 0.0010.01 15.3119.75 1.46 1.10 0.08 0.04 1.52 0.61 257.05 384.21 0.611.52 15.018.0 0.69 1.96 1.13 0.84 13.01 10.88 0.42 0.45 0.00010.001 17.0215.31 1.10 1.09 0.04 0.03 0.61 0.43 384.21 674.49 0.430.61 12.015.0 1.96 1.78 0.84 0.96 10.88 11.50 0.45 0.45 0.000010.0001 15.3317.02 1.09 1.13 0.03 0.01 0.43 0.14 1703.47 674.49 0.140.43 12.012.0 1.78 1.90 0.96 0.91 11.50 8.98 0.45 0.53 0.00001 .15.33 1.13 0.01 0.14 1703.47 0.14 12.0 1.90 0.91 8.98 0.53 Note: γo and c are bilinear constants; ηpN = pseudo-Newtonian viscosity obtained from the Bilinear model; m = model constant, τc-HB = Herschel–Bulkley yield stress; n-HB = flow behavior index in the Herschel–Bulkley Note: 𝛾 and c are bilinear constants; ηpN = pseudo-Newtonian viscosity obtained from the Bilinear model; K and n = flow behavior indices in the Power law model. model; m = model constant, τc-HB = Herschel–Bulkley yield stress; n-HB = flow behavior index in the Herschel–Bulkley model; K and n = flow behavior indices in the Power law model. 3.2. Shear Rate-Dependent Flow Behavior: Dynamic and Static Yield Stresses 3.2. ShearA series Rate-Dependent of ball-measuring Flow Beha rheometricvior: Dynamic tests wasand Static performed Yield Stresses to examine the shear rate dependency of rheologicalA series of behavior. ball-measuring Two tests rheometric were considered: tests was performed (a) flow to curve examine tests the with shear the rate initial dependency shear rate 5 4 3 2 1 1 graduallyof rheological increasing behavior. from Two 10− ,tests 10− were, 10− ,considered: and 10− to (a) 10− flows− ,curve and (b) tests stress with growth the initial tests atshear a constant rate sheargradually rate withincreasing shearing from time. 10−5, 10−4, 10−3, and 10−2 to 10−1 s−1, and (b) stress growth tests at a constant shear rate with shearing time. 3.2.1. Flow Curve Test: Initial Shear Rate Dependency 3.2.1.The Flow shear Curve rate Test: dependency Initial Shear of Rate shear Dependency stress was examined using different initial shear rates. FigureThe3 presents shear rate the sheardependency stress–shear of shear rate stress and viscosity–shearwas examined rateusing relationships. different initial Five shear initial rates. shear 5 4 3 2 1 1 rates,Figure consisting 3 presents of the 10 shear− , 10 stress–shear− , 10− , 10− rate, and and 10 vi−scosity–shears− , were applied rate relationships. to measure Five the flowinitial behavior. shear Therates, di ffconsistingerence in flowof 10 curves−5, 10−4, is10 much−3, 10−2 clearer, and 10 using−1 s−1, thewere plot applied of logarithmic to measure shear the stress flow andbehavior. logarithmic The sheardifference rate (Figurein flow3 curvesa). The is measurementmuch clearer using of shear the stressplot of depends logarithmic on theshear applied stress and initial logarithmic shear rate. 3 1 Forshear example, rate (Figure the first 3a). measurementThe measurement of shear of shear stress stress is equaldepends to1 on Pa the at applied approximately initial shear 10− rate.s− whenFor 5 1 anexample, initial shear the first rate measurement of 10− s− is of applied. shear stress Delayed is equal detection to 1 Pa at may approximately be removed 10 when−3 s−1 when the initial an initial shear 1 1 rateshear is rate increased of 10−5 (for s−1 is example, applied. initial Delayed shear detection rate of may 10− bes− removed). Interestingly, when the as initial shown shear in Figure rate is3b, aincreased pseudo-plateau (for example, regime initial is clearly shear shown rate of when 10−1 s the−1). Interestingly, initial shear rate as shown applied inis Figure increased. 3b, a Aspseudo- shown 1 inplateau Figure regime2, after is 1 clearly s − , the shown materials when behavethe initial as shear ideal rate plastic applied fluids. is increased. In this case, As theshown flow in behaviorFigure of2, sand-richafter 1 s−1, materialsthe materials can behave be governed as ideal by plastic the Binghamfluids. In this constitutive case, the lawflow withbehavior a yield of sand-rich stress and plasticmaterials viscosity. can be governed by the Bingham constitutive law with a yield stress and plastic viscosity.

FigureFigure 3. Shear3. Shear rate rate dependency dependency ofof rheological behavior behavior at at relatively relatively low low shear shear rates: rates: (a) Shear (a) Shear stress-shear ratestress-shear relationship rate and relationship (b) viscosity-shear and (b) viscosity-shear rate relationship rate relationship

3.2.2.3.2.2. StressStress GrowthGrowth Test: Time Dependency Flow-likeFlow-like sedimentssediments are well-known as as time-depen time-dependentdent materials materials (i.e., (i.e., thixotropic thixotropic materials). materials). TheThe timetime dependencydependency ofof the rheological behavior behavior of of waste waste materials materials at at a aconstant constant shear shear rate rate was was examined. The applied shear rates ranged from 0.001 to 1 s−1. The shear rate was continuously Appl. Sci. 2019, 9, 4744 7 of 11

Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 11 1 examined. The applied shear rates ranged from 0.001 to 1 s− . The shear rate was continuously applied, 1 −1 applied,and the torquesand the weretorques measured were measured for 350 s, for except 350 s, at except 0.5 s− at. Most 0.5 s rheological. Most rheological tests for tests coarse-grained for coarse- grainedsediments sediments are performed are performed for relatively for relatively short periods short periods of time, of such time, as such less as than less 1 than min. 1 If min. the shearIf the 3 1−3 −1 shearrate is rate less is than less 10than− s10− , s the, the test test is diisffi difficultcult to to carry carry out out with with a a time time constraint. constraint. FigureFigure4 4 shows shows the test results of of the the stress stress grow growthth method: method: shear shear stress stress with with time time and and viscosity viscosity with with time. time. There There is significantis significant fluctuation fluctuation during during shearing. shearing. This This large large scatter scatter (fluctuation) (fluctuation) is is observed observed for for each each flow flow curve. This feature may be due to interactions be betweentween large particles. The scatter may be minimized when the finefine content is increased. In Figure 44a,a, thethe flowflow behaviorbehavior isis quitequite didifferentfferent when different different continuous shear rates are applied at constant values during shearing. Typically, Typically, two types of shear behavior can be found for a givengiven rangerange ofof shearingshearing times:times: strain hardening and strain softening behavior. The firstfirst type has a peak value (i.e., the yield stress) in shear stress with time, and the second type has a peak and a steady-state value. The The latter latter is is very similar to the residual shear stress in soil mechanics. It It can can be defined defined as the minimum shear resistance of th thee materials along the previously existing slip slip surface. surface. Strain Strain hardening hardening is dominant is dominant for forrelatively relatively low low initial initial shear shear rates rates (i.e., shear (i.e.,shear rates −3 3 −2 −1 2 1 ofrates 10 of and 10− 10and s 10), −buts− strain), but softening strain softening is dominant is dominant for relatively for relatively high initial high shear initial rates shear (i.e., rates shear (i.e., −1 1 −1 1 −2 2 −1 −1 1 1 ratesshear of rates 10 of and 10− 1 ands ). 1The s− ).transitional The transitional behavior behavior occurs occurs between between 10 and 10− 10and s 10. −Thes− shear. The stress shear fluctuationstress fluctuation (vertical (vertical variation variation in shear in stress shear for stress a given for atime) given is time)large. isThis large. result This may result occur may because occur ofbecause particle–particle of particle–particle interaction interaction via the via nonslip the nonslip boundary boundary system, system, resulting resulting in in collisions collisions and fragmentation in coarse-grained sediments. The The viscosity viscosity is is also also very sensitive to the shearing time 3−3 −22 −11 (Figure4 4b).b). AtAtrelatively relatively low low shear shear rates rates (i.e., (i.e., shear shear rates rates of of 10 10− and and10 10− s− ),), the the viscosity viscosity gradually gradually increases with increasing shearing time; in both cases, no steady state appears for a given period of −1 shearing time. However, when the shearshear raterate isis largerlarger thanthan 0.10.1 ss− ,, the the viscosity viscosity reaches reaches a peak value and gradually decreases with shearing time. After a certain amount of time, the viscosity is almost −11 −1 1 −1 1 constant with time, e.g., after 250 s for 0.1 s− , ,70 70 s s for for 0.5 0.5 s s−, and, and 60 60 s sfor for 1 1s s−. .

Figure 4. Stress growth test: ( (aa)) Shear Shear stress–shearing stress–shearing time; ( b) viscosity–shearing time.

From the stress growth tests, the measurements of shear stress and viscosity are very sensitive to variations in the initial condition driven by shear. There are two shear stresses: a peak value and a Appl. Sci. 2019, 9, 4744 8 of 11

From the stress growth tests, the measurements of shear stress and viscosity are very sensitive toAppl. variations Sci. 2019, 9 in, x theFOR initial PEER REVIEW condition driven by shear. There are two shear stresses: a peak value8 of and11 a steady-state (i.e., residual) value. The latter can be obtained at the end of the tests. As shown in Figuresteady-state5a, the (i.e., peak residual) value of value. shear The stress latter obtained can be obtained from strain-hardening at the end of the tests. flow As behavior shown graduallyin Figure increases5a, the peak with value an increasing of shear stress shear obtained rate. The from residual strain-hardening shear stress flow obtained behavior from gradually the strain-softening increases flowwith behavior an increasing gradually shear decreases rate. The withresidual increasing shear stress shear obtained rates, except from for the the strain-softening lowest shear rateflow of behavior1 gradually decreases with increasing shear rates, except for the lowest shear rate of 0.001 s−1. 0.001 s− . It may have a very high value when a long shearing time can be applied. Interestingly, threeIt may strain-softening have a very high fluids value display when a similara long shearing range of time residual can be shear applied. stress Interestingly, (i.e., mean value three of strain- 283 Pa). softening fluids display a similar range of residual shear stress (i.e., mean value of 283 Pa). Similar Similar results can be observed for clayey soils [32]. Viscosity is also dependent on the shear rate results can be observed for clayey soils [32]. Viscosity is also dependent on the shear rate and time. and time. At low shear rates, the final viscosity rapidly decreases with an increasing shear rate; At low shear rates, the final viscosity rapidly decreases with an increasing shear1 rate; however, there however, there is no significant variation after an initial shear rate of 0.1 s− . In particular, there is a is no significant variation after an initial shear rate of 0.1 s−1. In particular, there is a pseudo- pseudo-Newtonian viscosity (not shown, but slopes may be found) in the elastic domain before the Newtonian viscosity (not shown, but slopes may be found) in the elastic domain before the static static yield stress for three higher shear rates. Interestingly, the pseudo-Newtonian viscosity increases yield stress for three higher shear rates. Interestingly, the pseudo-Newtonian viscosity increases with with an increasing shear rate (Figure4a). Compared to the Bingham yield stress and viscosity of an increasing shear rate (Figure 4a). Compared to the Bingham yield stress and viscosity of the sand- the sand-rich materials tested, the yield stress and viscosity obtained from stress growth tests are rich materials tested, the yield stress and viscosity obtained from stress growth tests are approximatelyapproximately 35–45 35–45 timestimes andand 100–35,000100–35,000 times higher, higher, respectively, respectively, than than those those obtained obtained from from flow flow curvecurve tests tests (Figure (Figure4). 4). Similar Similar results results have have been been observed observed for for other other thixotropic thixotropic materials. materials. According According to previousto previous studies studies [6,11 [6,11,13],,13], the the diff differenceerence between between static static and and dynamic dynamic yield yield stresses stresses ranges ranges between between 1.5 and1.5 2-fold.and 2-fold. It is, ofIt course,is, of believedcourse, believed that the dithatfference the difference is larger when is larger the solid when volume the solid concentration volume isconcentration greater. is greater.

FigureFigure 5. 5.Static Static andand dynamicdynamic rheologicalrheological properties of sand-rich sand-rich mine mine tailings: tailings: (a ()a )Peak, Peak, residual residual shear shear stress,stress, and and the the Bingham Bingham yield yield stresses;stresses; ((bb)) finalfinal viscosityviscosity and the Bingham Bingham viscosity. viscosity.

3.3.3.3. Rheological Rheological Properties Properties andand PossiblePossible ImplicationsImplications for Debris Flow Flow Modeling Modeling TheThe rheological rheological parametersparameters areare essentialessential for examining debris debris flow flow propagation propagation and and designing designing measuresmeasures for for future future catastrophiccatastrophic events.events. For many cases cases in in debris debris flow flow simulation, simulation, the the value value of of the the yieldyield stress stress is is fixed fixed during during thethe flowflow as a first first approximation approximation to to understand understand post-failure post-failure characteristics. characteristics. InIn this this case, case, the the determination determination of of yield yield stress stress is crucial.is crucial. Engineers Engineers could could obtain obtain the the shear shear strength strength from fieldfrom vane field tests vane under tests under in situ in conditions situ conditions and fall and cone fall tests cone in tests the in laboratory the laboratory as a priority, as a priority, which which would bewould more be reliable more reliable for debris for flowdebris initiation. flow initiation. For fine-grained For fine-grained sediments, sediments, the yield the yield stress stress obtained obtained from thefrom material, the material, which which is assumed is assumed to behave to behave as a Bingham as a Bingham fluid, fluid, is very is closevery close to the to undrained the undrained shear strengthshear strength determined determined by fall by cone falltests. cone tests. For a Fo givenr a given sand-rich sand-rich material, material the, Binghamthe Bingham yield yield stress stress and undrainedand undrained shear shear strength strength were comparedwere compared for a givenfor a given solid volumesolid volume concentration concentration ranging ranging from 50%from to 65%.50% Figureto 65%.6 presentsFigure 6 presents a comparison a comparison of the shear of the strength shear strength measured measured from the from Bingham the Bingham yield stress yield in flowstress curve in flow tests, curve the static tests, yield the stressstatic inyield time-dependent stress in time-dependent tests, and the tests, undrained and the shear undrained strength shear in fall strength in fall cone tests. A simple relationship can be expressed0.1 as Cvs = 74∙Su0.1 (kPa). For Cvs = 50%, cone tests. A simple relationship can be expressed as Cvs = 74 Su (kPa). For Cvs = 50%, the Bingham · yieldthe Bingham stress and yield undrained stress and shear undrained strength shear range strength between range 0.02 between and 0.06 0.02 kPa and (mean0.06 kPa value (mean of value 40 Pa); of 40 Pa); however, the static yield stress is approximately 0.6–0.9 kPa (mean value of 700 Pa). The difference is more than 10-fold. More interestingly, as described above, the sediments are much more resistant to flow when the shear rate is increased. These results suggest that more research is needed to understand the mechanism related to the high mobilization of debris flows, e.g., entrainment, Appl. Sci. 2019, 9, 4744 9 of 11 however, the static yield stress is approximately 0.6–0.9 kPa (mean value of 700 Pa). The difference is more than 10-fold. More interestingly, as described above, the sediments are much more resistant to flow when the shear rate is increased. These results suggest that more research is needed to understand Appl.the mechanismSci. 2019, 9, x FOR related PEER to REVIEW the high mobilization of debris flows, e.g., entrainment, hydroplaning,9 yield of 11 stress reduction, and wetting processes in debris flow motion. It is necessary to revisit the research hydroplaning, yield stress reduction, and wetting processes in debris flow motion. It is necessary to work ([24] see Figure 8 in the paper) on failure and post-failure characteristics of mine deposit areas revisit the research work ([24] see Figure 8 in the paper) on failure and post-failure characteristics of and to estimate the debris flow mobility for such areas. Using the same geometry for the initial slope mine deposit areas and to estimate the debris flow mobility for such areas. Using the same geometry and volume with different yield stresses, the debris flow propagation can be simply compared. For a for the initial slope and volume with different yield stresses, the debris flow propagation can be given yield stress of 50 Pa, the runout distance is approximately 700 m, but for a stress of 700 Pa, the simply compared. For a given yield stress of 50 Pa, the runout distance is approximately 700 m, but distance is approximately 100 m. The difference is more than 7-fold. The debris flow velocity is more for a stress of 700 Pa, the distance is approximately 100 m. The difference is more than 7-fold. The sensitive to the variation in yield stress. The difference is more than 10-fold. This result means that the debris flow velocity is more sensitive to the variation in yield stress. The difference is more than 10- debris flow impact can be determined by determining the yield stress. In this context, more precise fold. This result means that the debris flow impact can be determined by determining the yield stress. computational techniques based on rheological studies are required to avoid overdesigning for future In this context, more precise computational techniques based on rheological studies are required to disasters and to establish reasonable measures. avoid overdesigning for future disasters and to establish reasonable measures. It is very difficult to describe debris flow with one fixed rheological model, because it is expected It is very difficult to describe debris flow with one fixed rheological model, because it is expected that the flow behaviors of real debris flow are too complex. In particular, the influence of material that the flow behaviors of real debris flow are too complex. In particular, the influence of material parameters (such as the particle size distribution, change in water content, porosity, roughness, edge parameters (such as the particle size distribution, change in water content, porosity, roughness, edge and wall slip effects) in estimating the flow mobility should be scrutinized in future work. Even with a and wall slip effects) in estimating the flow mobility should be scrutinized in future work. Even with very simplified hypothesis in which many parameters, such as the particle size distribution, water a very simplified hypothesis in which many parameters, such as the particle size distribution, water content, porosity, roughness, solid concentration, and topographic characteristics are simplified with content, porosity, roughness, solid concentration, and topographic characteristics are simplified with ordinary constants, the research findings presented in this study can be simply applied to debris flow ordinary constants, the research findings presented in this study can be simply applied to debris flow mitigation in mine tailing. In addition, micro-structural evolution of the particles in terms of landslide mitigation in mine tailing. In addition, micro-structural evolution of the particles in terms of landslide mobilization has a substantial contribution in the destructuration–restructuration process [33]. mobilization has a substantial contribution in the destructuration–restructuration process [33].

FigureFigure 6. 6. RelationshipRelationship between between the the shear shear strength strength and and the the solid solid volume volume concentration. concentration.

4.4. Conclusions Conclusions TheThe dynamic dynamic and and static static yield yield stresses stresses of of mine mine ta tailings,ilings, which which are are exposed exposed on onnatural natural slopes slopes in abandonedin abandoned mine mine deposits deposits and and potentially potentially vulnerable vulnerable to to future future geochemical geochemical and and geophysical modification,modification, have have been been identified identified and and examined examined in in this this study. study. The The rheological rheological properties, properties, the the yield yield stressesstresses and and viscosity, viscosity, have been been determined determined using using the the ball-measuring ball-measuring system, system, which which is is a a well-known well-known piecepiece of of apparatus suitable suitable for for large large particles. Th Thee yield yield stresses stresses obtained obtained from from the the flow flow curve curve and and stressstress growth growth methods methods have have been been compared. compared. In the In pl theot of plot shear of shearstress stressand the and shear the rate shear (flow rate curve), (flow there is a peak value related to the generation of the slip surface due to the high percentage of soils; after the critical shear rate, the materials behave as Bingham fluids. The shear resistance before yielding is different from the applied initial shear rates. The pseudo-Newtonian viscosity increases with decreasing initial shear rates. However, the Bingham yield stress and viscosity are obtained within a similar range, regardless of the initial shear rates applied. Therefore, the Bingham rheology is applicable as a first approximation for debris flow motion to examine the post-failure Appl. Sci. 2019, 9, 4744 10 of 11 curve), there is a peak value related to the generation of the slip surface due to the high percentage of soils; after the critical shear rate, the materials behave as Bingham fluids. The shear resistance before yielding is different from the applied initial shear rates. The pseudo-Newtonian viscosity increases with decreasing initial shear rates. However, the Bingham yield stress and viscosity are obtained within a similar range, regardless of the initial shear rates applied. Therefore, the Bingham rheology is applicable as a first approximation for debris flow motion to examine the post-failure characteristics of mass movement. These results can be used from a very conservative point of view. The yield stress can be obtained from the stress growth tests (the measurement of shear stress with a constant shear rate). In this case, it is called the static yield stress. The static yield stresses are strongly affected by the shear rate. At relatively low shear rates, the flow curve seems to demonstrate Newtonian behavior for a given period of time. However, after a certain amount of time, the flow curve displays strain-softening behavior similar to that in soil mechanics. A large difference is found between the dynamic and static yield stresses. The largest difference is approximately 45-fold. In general, the static yield stress is related to the flow starting, but the dynamic yield stress is related to the flow stopping. This effect may result in an underestimation of the debris flow mobility if only the static yield stress and residual shear stress from the stress growth test are considered. In landslide dynamics, at the onset of slope failure, the undrained shear strength and static yield stress may be useful for examining the generation of slip surfaces; however, at the transition to flow conditions, the transition from the static yield stress to the Bingham yield stress should be considered. Yield stress reduction must be taken into account in highly mobile debris flow hazards, which are related to hydroplaning, particle migration, and wetting effects during flow.

Funding: This research was supported by the KIGAM Research project (19-3413). Acknowledgments: The author also extends special thanks to the anonymous reviewers and editor for their valuable comments and recommendations for publishing this paper. Conflicts of Interest: The author declares no conflicts of interest.

References

1. Barnes, H.A. The yield stress—A review or ‘παντα ρει’—Everything flows? J. Non-Newton. Fluid Mech. 1999, 81, 133–178. [CrossRef] 2. Coussot, P.; Nguyen, Q.D.; Huynh, H.T.; Bonn, D. Viscosity bifurcation in thixotropic, yielding fluids. J. Rheol. 2002, 46, 573–589. [CrossRef] 3. Moller, P.C.F.; Mewis, J.; Bonn, D. Yield stress and thixotropy: On the difficulty of measuring yield stresses in practice. Soft Matt. 2006, 2, 274–283. [CrossRef] 4. Mewis, J.; Wagner, N.J. Thixotropy. Adv. Colloid Interface Sci. 2009, 147–148, 214–227. 5. Qian, Y.; Kawashima, S. Use of creep recovery protocol to measure static yield stress and structural rebuilding of fresh cement pastes. Cem. Concr. Res. 2016, 90, 73–79. [CrossRef] 6. Qian, Y.; Kawashima, S. Distinguishing dynamic and static yield stress of fresh cement mortars through thixotropy. Cem. Concr. Comp. 2018, 86, 288–296. [CrossRef] 7. Nguyen, Q.D.; Boger, D.V. Measuring the Flow Properties of Yield Stress Fluids. Annu. Rev. Fluid Mech. 1992, 24, 47–88. [CrossRef] 8. Stokes, J.R.; Telford, J.H. Measuring the yield behaviour of structured fluids. J. Non-Newton. Fluid Mech. 2004, 124, 137–146. [CrossRef] 9. Mewis, J. Thixotropy—A general review. J. Non-Newton. Fluid Mech. 1979, 6, 1–20. [CrossRef] 10. Barnes, H.A. Thixotropy—A review. J. Non-Newton. Fluid Mech. 1997, 70, 1–33. [CrossRef] 11. Moller, P.; Fall, A.; Chikkadi, V.; Derks, D.; Bonn, D. An attempt to categorize yield stress fluid behaviour. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2009, 367, 5139–5155. [CrossRef][PubMed] 12. Cheng, D.C.H. Yield stress: A time-dependent property and how to measure it. Rheol. Acta 1986, 25, 542–554. [CrossRef] 13. Santolo, A.S.D.; Pellegrino, A.M.; Evangelista, A.; Coussot, P. Rheological behaviour of reconstituted pyroclastic debris flow. Géotechnique 2012, 62, 19–27. [CrossRef] Appl. Sci. 2019, 9, 4744 11 of 11

14. Barnes, H.A.; Walters, K. The yield stress myths? Rheol. Acta 1985, 24, 323–326. [CrossRef] 15. Astarita, G. Letter to the editor: The engineering reality of the yield stress. J. Rheol. 1990, 34, 275–277. [CrossRef] 16. De Souza Mendes, P.R. Modeling the thixotropic behavior of structured fluids. J. Non-Newton. Fluid Mech. 2009, 164, 66–75. [CrossRef] 17. O’Brien, J.S.; Julien, P.Y. Laboratory Analysis of Mudflow Properties. J. Hydraul. Eng. 1988, 114, 877–887. [CrossRef] 18. Coussot, P.; Piau, J.M. On the behavior of fine mud suspensions. Rheol. Acta 1994, 33, 175–184. [CrossRef] 19. Schatzmann, M.; Bezzola, G.R.; Minor, H.E.; Windhab, E.J.; Fischer, P. Rheometry for large-particulated fluids: Analysis of the ball measuring system and comparison to debris flow rheometry. Rheol. Acta 2009, 48, 715–733. [CrossRef] 20. Sosio, R.; Crosta, G.B. Rheology of concentrated granular suspensions and possible implications for debris flow modeling. Water Resour. Res. 2009, 45, W03412. [CrossRef] 21. Campbell, C.S. Rapid Granular Flows. Annu. Rev. Fluid Mech. 1990, 22, 57–90. [CrossRef] 22. Jeong, S.W.; Wu, Y.H.; Cho, Y.C.; Ji, S.W. Flow behavior and mobility of contaminated waste rock materials in the abandoned Imgi mine in Korea. Geomorphology 2018, 301, 79–91. [CrossRef] 23. Imran, J.; Parker, G.; Locat, J.; Lee, H. 1D Numerical Model of Muddy Subaqueous and Subaerial Debris Flows. J. Hydraul. Eng. 2001, 127, 959–968. [CrossRef] 24. Jeong, S.W. Geotechnical and rheological characteristics of waste rock deposits influencing potential debris flow occurrence at the abandoned Imgi Mine, Korea. Environ. Earth Sci. 2015, 73, 8299–8310. [CrossRef] 25. Bisantino, T.; Fischer, P.; Gentile, F. Rheological characteristics of debris-flow material in South-Gargano watersheds. Nat. Hazards 2010, 54, 209–223. [CrossRef] 26. Kaitna, R.; Rickenmann, D.; Schatzmann, M. Experimental study on rheologic behaviour of debris flow material. Acta Geotech. 2007, 2, 71–85. [CrossRef] 27. Jeong, S.W.; Locat, J.; Leroueil, S.; Malet, J.-P. Rheological properties of fine-grained sediment: The roles of texture and mineralogy. Can. Geotech. J. 2010, 47, 1085–1100. [CrossRef] 28. Locat, J.; Demers, D. Viscosity, yield stress, remolded strength, and liquidity index relationships for sensitive clays. Can. Geotech. J. 1988, 25, 799–806. [CrossRef] 29. Bingham, E.C. Fluidity and Plasticity; McGraw Hill: New York, NY, USA, 1922; p. 440. 30. Coussot, P.; Tocquer, L.; Lanos, C.; Ovarlez, G. Macroscopic vs. local rheology of yield stress fluids. J. Non-Newton. Fluid Mech. 2009, 158, 85–90. [CrossRef] 31. Germann, N. Shear banding in semidilute entangled polymer solutions. Curr. Opin. Colloid Interface Sci. 2019, 39, 1–10. [CrossRef] 32. Tika, T.E.; Vaughan, P.R.; Lemos, L.J.L.J. Fast shearing of pre-existing shear zones in soil. Géotechnique 1996, 46, 197–233. [CrossRef] 33. Huynh, H.T.; Roussel, N.; Coussot, P. Aging and free surface flow of a thixotropic fluid. Phys. Fluids 2005, 17, 033101. [CrossRef]

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