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Mechanical Properties of Granular Materials and Their Impact on Load Distribution in Silo: a Review MECHANICAL PROPERTIES OF GRANULAR MATERIALS AND THEIR IMPACT ON LOAD DISTRIBUTION IN SILO: A REVIEW J. Horabik, M. Molenda Polish Academy of Sciences, Institute of Agrophysics, Lublin, Poland Mechanical properties of granular materials and their impact on load distribution in storage silo were discussed with special focus on materials of biological origin. Granular materials classification was briefly outlined. The evolution of constitutive models of granular materials developed in the frame of mechanics of continuum was addressed. Analytical methods, Finite El- ement Methods (FEM), and Discrete Element Methods (DEM) of estimation of silo pressure were discussed. Special attention was paid to the following issues: dynamic pressure switch in the first moment of silo discharge, asymmetry of loads due to ec- centric discharge, and impact of uncontrolled increase of moisture content of grain on silo pressures. granular material; cereal grain; silo; pressure distribution; DEM doi: 10.1515/sab-2015-0001 Received for publication on September 2, 2014 Accepted for publication on September 21, 2014 INTRODUCTION Storage, handling, and processing of granular ma- terials are procedures required in numerous industries The term granular material includes a large group and are of interest to various branches of science and of materials of particular physical, chemical, and technology such as physics, chemistry, mechanics, mechanical properties. Granular material can be char- agriculture, and engineering. Agriculture and food acterized as a three-phase system composed of grains industry are, next to chemical, power, and pharma- creating a skeleton and a liquid or gases which fill ceutical industries, the largest producers and users voids. Grain size may range from several meters to of granular materials. The equipment for storage and several microns. Granular materials can be found processing of granular materials should meet two across a wide range of scales: in kitchen (sugar, salt), basic conditions: predictable and safe operations and geophysics (sand, gravel), as well as for example in high quality of finished products. Due to globalization astrophysics (asteroids). processes the industrial companies handling particulate A specific behaviour of granular media which ex- materials have been under severe pressure to reduce hibit some properties of gases, liquids, and solids costs while enhancing the quality of their products. is in the background of considerations that granular Granular materials of biological origin are distin- materials are the fourth state of matter (J a e g e r et guished by large deformability of particles and strong al., 1996). That opinion is supported by the following dependence of their mechanical properties on moisture properties of the material: existence of static friction, content. Contrary to materials of mineral origin, mois- inelastic collisions, and a very small energy of thermal ture penetrates inside grain, leading in some cases to motions in comparison to potential energy of gravi- qualitative changes in its physical properties. These tational field. Granular materials behave like a liquid specific behaviour of granular materials of biological or like a solid dependently on parameters such as the origin need to be considered when adjusting material density of the system, moisture, etc. As compared to models, experimental techniques, and technological a liquid, granular material shows three distinct differ- solutions. The most important is that stored grain ences in mechanical behaviour: existence of internal is a respiring biological material subjected to mi- friction, shear strength dependent on the mean stress crobiological activity. For high-quality preservation and independent on velocity of deformation, cohesion during storage, a multidisciplinary approach based that allows to maintain shape enforced under load (for on knowledge from several fields(biology, chemistry, example ratholes or channels). toxicology, engineering, and mathematical model- SCIENTIA AGRICULTURAE BOHEMICA, 45, 2014 (4): 203–211 203 ling) is necessary to study the complex interactions • fluidlike flooding among physical, chemical, and biological variables • very free flowing FF > 10 in a stored-grain ecosystem (J i a n , J a y a s , 2012). • free flowing 10 > FF > 4 The main objective of the paper was to describe • average flowing 4 > FF > 2 the evolution and the current state of knowledge re- • poor flowing 2 > FF garding mechanical properties of granular materials • sluggish/interlocked with special focus on agro and food biologically based granular materials and their influence on loads in silos. In the case of agricultural and food raw materials The paper presents a review of experimental studies and products, apart from the classifications mentioned and numerical modelling of mechanical properties above, attention should be paid also to a number of of granular solids. Special attention was paid to the additional features, such as: effects typically found in deposits of cereal grains. • possibility of freezing, • hygroscopicity, Classification of granular materials • toxic properties, • properties conducive to spontaneous combustion, Due to the variety of the granular materials and • explosive properties. their properties, their defining and description are rather difficult. The properties of granular materi- Constitutive models of granular materials als vary within a very broad range, depending on the origin of a material, the processes of production Modelling mechanical properties of granular ma- and processing applied, and on external factors and terials starts from the Mohr-Coulomb criterion of conditions. The classification of materials is based plasticity assuming that shear strength τ is a linear on different physico-chemical, mechanical, and geo- function of normal stress σ metrical properties. The parameters which are taken tan C into account for classification of granular materials are: size of particles, shape, density, flowability, abra- siveness, toxicity, etc. where: Based on ISO classification (I S O 3 5 3 5 , 1977), the φ = internal friction angle Mechanical Handling Engineers’ Association (MHEA), C = cohesion UK divided the granular material according to the di- Resistance resulting from internal friction and co- mension of particles (D) into ten cathegories, however hesion is overcome by external forces in the moment C h a t t o p a d h y a y et al. (1994) proposed the five of attaining the yield strength. The Drucker-Prager following groups: criterion of yielding (D r u c k e r , P r a g e r , 1952) representing surface of cone in the principal stress • dust D ≤ 0.42 mm space enables researchers to avoid several problems • grain D ≤ 3.35 mm occurring during the application of the Mohr-Coulomb • lump D ≤ 40 mm plasticity criterion representing a pyramid in the prin- • clump D ≤ 200 mm cipal stress space (Fig. 1). • block D > 200 mm Further developement of mechanics of granular materials resulted in many constitutive models describ- The classification of granular materials according ing real properties of the granular system: nonlinearly to bulk density (ρ) is as follows: elastic, viscoelastic, elasto-plastic, viscoplastic, and hypoplastic. Among the more advanced elasto-plastic –3 • light ρ < 600 kg m models having a broader application for granular mate- –3 –3 • medium 600 kg m < ρ ≤ 1100 kg m rials of plant origin, the models of Ghaboussi-Momen –3 –3 • heavy 1100 kg m < ρ ≤ 2000 kg m and Lade should be mentioned. They were applied –3 • very heavy ρ > 2000 kg m by Z h a n g et al. (1994) to describe the stress–strain The flowability defined as a motion of particles with relationship for wheat grain mass. The mentioned models assume that total strain ε reference to neighbouring particles or along surfaces ij is a sum of elastic εe and plastic strains εp : is the next parameter describing granular materials ij ij (P e l e g , 1985). It has a huge influence on processes e p. occurring during storage and handling of materials in ij ij ij industry and agriculture. The conventional classifica- The model of Ghaboussi and Momen adopts the tions of materials according to flowability are derived Drucker-Prager yield condition and describes phenom- from the classification based on the flow function (FF) ena typical for isotropic and kinematic hardening. It proposed by Jenike (1961). Chattopadhyay et describes especially well the anisotropy of material, al. (1994) extended J e n i k e ’s (1961) classification the hysteresis of stress-strain cycle, and the evolution adding two extreme classes: of hysteresis loop in the course of multiple loadings. 204 SCIENTIA AGRICULTURAE BOHEMICA, 45, 2014 (4): 203–211 p The model of Lade presents plastic strain ε ij as a turbance of motion of a single grain does not reach sum of plastic strain related with the compaction of further than to the nearest neighbours. This is the key c material ε ij and the plastic strain related to dilation assumption of the method that permits the description d of material ε ij: of nonlinear interactions occurring among a large p c d number of elements without excessive requirements ij ij ij . concerning the calculation memory power. In this approach all the forces acting on a given granule are Despite of obtaining fairly good descriptions of the considered – those resulting from gravity, from interac- behaviour of the material, the key parameter of the tions with neighbouring granules, and those resulting material – the microstructure
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