Strona 2_redak - Instytut Agrofizyki im. Bohdana DobrzaÅskiego ...

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58 near the box wall and lifted along the wall generatrix so that the outlet was constantly approximately 20 mm above the surface of gathered grains. The grain was allowed to slide down the surface of natural repose to the front side of the box. Any change in the angle of inclination of the shear box to the horizontal resulted in a change of preferred inclination γ of long axes of grains to the bottom of the box. Examination of an influence of the angle of preferred grain orientation on the shear stress-strain characteristic was performed under the normal pressure of 100 kPa. Samples were prepared so that the preferred orientation of grain formed angles, γ, of inclination to the shearing direction of: 0, 10, 20, 30 and 40 degrees. To preserve the packing structure of the bedding no additional consolidation was applied. The angle of preferred orientation of grains was found to influence strongly the stress-strain characteristics as shown in figure 7.7. The strongest was the sample with γ of 40° showing maximum shear stress τ max of approximately 50 kPa, while the lowest τ max of approximately 30 kPa was found in the case of γ = 0°. The probable reason for the observed difference of behaviour is the distribution of contact normals. Fig 7.7. Relationships of shear stress versus ratio of displacement to the sample diameter ∆L/D. Samples of rye with an angle of preferred inclination of kernels long axes to horizontal ranging from 0 to 40 degrees Oda [126] suggested that, for a two dimensional system, the distribution of contact normals may be approximated by an ellipse. The major axis of such an ellipse is initially oriented normal to the bedding plane. The preferred orientation of the long axes of the particles is parallel to the bedding plane. In the process of biaxial deformation the distribution of the contact normals changes so that a greater number of contact normals tend to orient themselves in the direction of contact force. Testing with grain samples deposited in various ways and subsequently consolidated by twisting (as recommended by Eurocode 1 [50]) did not show any differences in stress-strain characteristics, and consequently in obtained values of
59 the angle of internal friction. This result shows that the consolidation procedure of Eurocode 1 erased all stress history similarly to pre-shearing to steady-state as recommended by Jenike [74]. 7.2.5. Surface properties of particles The inter-particle friction is an obvious component of shear strength and in 1960’s and 70’s attempts were undertaken to find a relationship of the two effects. Rowe [144] suggested that the primary task was to separate the strength component of particle structure from that of inter-particle friction. This author derived relationships of strength limits for loose and dense sands that gave “quite close” agreement over the range of the angle of inter-granular friction φ µ from 17° to 39° for cohesion-less soils. Apart from φ µ and density, Rowe considered measurement technique for the stress state of deformed sample and found that for dense sands triaxial compression and direct shear gave similar results. Feda [51] summarized results of efforts undertaken up to 1975. No substantial progress in theoretical description of internal friction took place after that time. The structural component (or packing structure) of internal friction remains difficult to describe and monitor, but these days may be treated by DEM. Analysis of force distributions in three-dimensional granular assemblies performed by Blair et al. [20] regarded the significance of inter-particle friction. The authors varied the coefficient of static friction between grains in such a way that for rough beads it was three times higher than for smooth ones. The resultant force distributions for rough beads were not significantly different from the distributions for the smooth beads. The tests have shown that particle deformation is the key factor for intergranular force distribution. Results of Blair et al. show that the phenomenon of internal friction still remains far from a conclusive description. 7.2.6. Formation of shear bands Granular materials are deformed in many ways during processing. For a small strain the deformation is usually uniform. For a larger strain the deformation localises into a narrow region of shearing band. This region separates almost rigid blocks of a granular material. An effective rupture zone called a boundary layer or shear zone forms along the rough or corrugated wall in a silo with plug flow when friction between wall and grain is higher than internal friction of grain [119]. There is always a shear zone of a width equal to a few particle diameters in which the velocity changes rapidly from that in the bulk to that at the wall. The thickness of the boundary layer was found to be dependent on the granular material. Zhang et al. [177] examined shear zones in wheat sliding against corrugated steel surface. The lower boundary of the shear zone was estimated at 4.5 mm below corrugation peaks
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EC Centre of Excellence AGROPHYSICS
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4 9.3. Factors influencing the coef
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6 BASIC NOTATION c - cohesion [kPa]
Page 8 and 9: 8 Numerous granular materials when
Page 10 and 11: 10 the tensor of plastic strain inc
Page 12 and 13: 12 Fig. 2.1. Yield curves with comp
Page 14 and 15: 14 Stable or unstable behaviour of
Page 16 and 17: 16 In turn, the model of Lade, also
Page 18 and 19: 18 same porosity need not have iden
Page 20 and 21: 20 where: A = ∫ E( β) sin βdβ
Page 22 and 23: 22 (β = 0 o ), positioning the out
Page 24 and 25: 24 grain was poured into the mould
Page 26 and 27: 26 axes of the ellipse characterizi
Page 28 and 29: 28 [176] for the determination of p
Page 30 and 31: 30 A different approach to the desc
Page 32 and 33: 32 where: I - moment of inertia, k
Page 34 and 35: 34 a) b) f s f s m M f n f n Contac
Page 36 and 37: 36 The micropolar model yields resu
Page 38 and 39: 38 Fig. 3.17. Model of shear band f
Page 40 and 41: 40 In the case of agricultural mate
Page 42 and 43: 42 5.2. Density of consolidated mat
Page 44 and 45: 44 (cereal grain, sand, soil), the
Page 46 and 47: 46 Multiple wetting and drying of g
Page 48 and 49: 48 vertical pressure within the ran
Page 50 and 51: 50 of the curve defined by A, where
Page 52 and 53: 52 6. Vertical consolidation refere
Page 54 and 55: 54 poured into the box without vibr
Page 56 and 57: 56 7.2.2. Bulk density Stress-strai
Page 60 and 61: 60 and the upper boundary was 18.5
Page 62 and 63: 62 A -1 5 -1 0 -5 1 0 5 -5 5 1 0 1
Page 64 and 65: 64 Fig. 8.2. Yield locus and effect
Page 66 and 67: 66 in such a way that friction woul
Page 68 and 69: 68 a) b) µ = tg ϕw ϕ w c) d) e)
Page 70 and 71: 70 9.3. Factors influencing the coe
Page 72 and 73: 72 galvanized steel received from d
Page 74 and 75: 74 9.3.4. Velocity of sliding Becau
Page 76 and 77: 76 1+ sinϕ k = . 1 − sinϕ (10.3
Page 78 and 79: 78 N ϕ VLQϕ 3UHVVXUHUDWLRN
Page 80 and 81: 80 10.4.1. Friction force mobilizat
Page 82 and 83: 82 10.4.3. Moisture content With in
Page 84 and 85: 84 Table 10.1. Measured (k s ) and
Page 86 and 87: 86 conventional engineering analyse
Page 88 and 89: 88 a, b - product-dependent coeffic
Page 90 and 91: 90 also be performed as a function
Page 92 and 93: 92 reliable processing and stable v
Page 94 and 95: 94 unconfined yield strength to pow
Page 96 and 97: 96 The Chute Index (CI) is recommen
Page 98 and 99: 98 obtained the maximum deviation o
Page 100 and 101: 100 efficient flow control using op
Page 102 and 103: 102 In the field of experimental in
Page 104 and 105: 104 22. Britton M.G., Moysey E.B.:
Page 106 and 107: 106 69. Horabik J., Rusinek R.: Pre
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108 114. Morland L.W., Sawicki A.,
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110 158. 6WSQLHZVNL$ Influence of m
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112 16. APPENDIX - Physical Propert
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114 16.2. Density and porosity Tabl
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116 Table 16.7. Mean values (±St.
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126 Table 16.16. Cont. 1 2 3 4 Icin
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136 Table 16.25. Cont. 1 2 3 4 Icin
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140 Table 16.29. Cont. Table sugar
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144 Table 16.35. Mean values (± St
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