A Review on the Angle of Repose of Granular Materials
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Powder Technology 330 (2018) 397–417 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec Review A review on the angle of repose of granular materials Hamzah M. Beakawi Al-Hashemi ⁎,1, Omar S. Baghabra Al-Amoudi 2 Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia article info abstract Article history: The abundance of granular materials and powders that are being used in several fields, along with their broad Received 17 September 2017 applications, requires a comprehensive understanding of both their macro- and micro-mechanical behavior. Received in revised form 28 January 2018 The fabric and structural properties, or the inter-particle properties, such as the angle of repose, do affect the be- Accepted 2 February 2018 havior of granular materials. This comprehensive review indicates that the angle of repose of granular material is Available online 27 February 2018 an essential parameter to understand the micro-behavior of the granular material and, then, to relate it with the fi Keywords: macro-behavior. Therefore, this extensive review was prepared about the repose angle theory, its de nitions, fl Angle of repose method of measurements, appropriate applications and the in uencing factors. Geotechnical © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license Granular (http://creativecommons.org/licenses/by/4.0/). Measurements Contents 1. Introduction.............................................................. 398 1.1. Granularmaterials........................................................ 398 1.2. Definitionsofangleofrepose................................................... 398 2. Measurementoftheangleofrepose................................................... 399 2.1. State-of-thepracticemethods................................................... 399 2.1.1. Tiltingboxmethod.................................................... 399 2.1.2. Fixedfunnelmethod................................................... 399 2.1.3. Revolvingcylinder/drummethod............................................. 400 2.1.4. Hollowcylindermethod................................................. 401 2.1.5. Tiltingcylindermethod.................................................. 401 2.1.6. Comparison....................................................... 402 2.2. State-of-the-artmethods..................................................... 402 3. Applicationsoftheangleofrepose.................................................... 403 3.1. Majorapplications........................................................ 403 3.1.1. Agriculturalengineering................................................. 403 3.1.2. Entomology....................................................... 403 3.1.3. Geotechnicalengineering................................................. 403 3.1.4. Hydrodynamicsandsedimentology............................................ 403 3.1.5. Particletechnologyandmaterialsscience......................................... 404 3.2. Otherapplications........................................................ 405 3.3. Calibrationofnumericalmodelsandsimulations.......................................... 406 4. Influentialfactors............................................................ 407 4.1. Geometricalpropertiesoftheparticles............................................... 407 4.1.1. Particleroundness.................................................... 408 4.1.2. Sphericityofparticles.................................................. 411 4.1.3. Roughness....................................................... 411 ⁎ Corresponding author. E-mail address: [email protected] (H.M. Beakawi Al-Hashemi). 1 0000-0002-3991-1712 2 0000-0001-5078-9204 https://doi.org/10.1016/j.powtec.2018.02.003 0032-5910/© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 398 H.M. Beakawi Al-Hashemi, O.S. Baghabra Al-Amoudi / Powder Technology 330 (2018) 397–417 4.2. Particlesize........................................................... 411 4.3. Friction coefficients........................................................ 412 4.3.1. Sliding (Coulomb) friction coefficients........................................... 412 4.3.2. Rolling friction coefficient................................................. 412 4.3.3. Angleofinternalfriction................................................. 412 4.4. Coefficientofrestitution(damping)................................................ 413 4.5. Numberofparticles........................................................ 413 4.6. Moisture content and air flow................................................... 413 4.7. Methodsofmeasurement..................................................... 413 5. Conclusions............................................................... 413 6. Recommendationsforfutureresearch................................................... 413 Acknowledgments.............................................................. 414 References.................................................................. 414 1. Introduction descriptions of the angle of repose are associated with specific applica- tions and the corresponding behavior (i.e., flowability, friction, etc.). In industrial and engineering applications, the use of granular mate- Therefore, the objectives of studying and determining the angle of re- rials such as powders, seeds, and soils is unavoidable [1]. Therefore, fur- pose of any granular material should be predetermined so that an ap- ther studies and improvements are currently needed to optimize and propriate and relevant definition can be adopted in the context of facilitate the process of handling and manufacturing bulk granular mate- those objectives. Physically, the angle of repose can be defined as the rials. Such improvements are contingent on the elucidation of the various angle that differentiates the transitions between phases of the granular properties and mechanical behavior of these materials. The challenges of material [7]. One of the most commonly used definitions of the angle of handling and manufacturing granular materials arise when the materials repose is the steepest slope of the unconfined material, measured from are sheared or disturbed because they will behave as non-Newtonian the horizontal plane on which the material can be heaped without fluids instead of stable, solid materials [2]. Moreover, the stress distribu- collapsing [8]. tion in granular materials is not uniform but is distributed along the force For powders, which can be defined as small-sized granular materials chains [3], which depend on the particle contacts and packing arrange- subject to cohesion and suspension in a gas, the definition of the angle of ment. The flowability of granules is dependent on a set of parameters, repose is frequently linked with the Hausner ratio or the tapped-to-bulk one of which is the angle of repose [4]. Therefore, while the angle of re- density ratio [9], and the powders will flow at angles greater than the pose can be used as an indication of flowability, this angle is controlled angle of repose [10]. The angle of repose can also indicate the cohesive- by numerous factors and has different definitions, methods of measure- ness of the granular material [11], referring to the Carr classification of ment, and applications that are discussed in this review. flowability [12,13]showninTable 1. However, for cohesive materials, the angle of repose is hard to obtain. Hence, indirect methods are 1.1. Granular materials often used, such as the angle-composition plot method [14], which is based on mixing the cohesive material with granular material and plot- While the primary material used in industry is fluid, the second most ting the composition against the respective angle of repose to indirectly widely used material is of granular nature [1]. Granular material is a obtain the angle of repose of the cohesive material. cluster of distinct particles that lose energy when interacting with In soil mechanics, Karl Terzaghi defined the angle of repose as a spe- other particles [5]. Commonly, the particle size determines if a material cial internal friction angle that is acquired under extreme (loosest state) is considered granular. The minimum particle size of the granular mate- conditions [15]. Additionally, it may be defined as the angle of rial is 1 μm, and materials with a smaller particle size may be subjected maximum slope inclination at which the soil is barely stable [16]. to thermal motion oscillations. For instance, soils are called granular, Geotechnically, the primary application of the angle of repose is in the coarse-grained, or cohesionless when N50% of the weight of the soil is determination of slope stability and design of retaining structures [17]. sand and gravel that have sizes ranging from 0.07 to 5 mm and 5 to Generally, the angle of repose is related to the static friction coefficient 75 mm, respectively [6]. Granular soils are often non-plastic and will and the angle of internal friction. In the literature, the angle of repose not form coherent matter when wet. The permeability of the granular is often assumed to be equal to the residual internal friction angle or soil is high to moderate due to the presence of voids. Nonetheless, a the constant volume angle in a critical state [18–20]. This assumption small amount of fine material, such