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.