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

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42 5.2. Density of consolidated material The density of granular material is a monotonically increasing non-linear function of pressure. The function most frequently used for the description of the relation is a power, exponential or logarithmic function. Gu et al. [59] made a detailed analysis of empirical relationships used, determining for each the range of pressure values for which a given function best describes the change in density. Fig. 5.1. Bulk density values for wheat as a function of moisture content and pressure [161] In the case of materials of plant origin, another parameter – apart from pressure – that significantly affects the density of a deposit is the moisture content of the material. Thompson and Ross [161] made an in-depth study of the density of wheat grain deposit within the range of pressures from 0 to 170 kPa. They found that within the grain moisture range from 8% to 12% a half of the change in the density of the medium was attributable to reorientation of the grains, and the other half their elastic deformation. Increase in the grain moisture caused an increase in the contribution of deformation of the grains in the change of the density of the medium. At grain moisture level of 24% the contribution of deformation of the grains was about 70% of the change in density. For vertical pressure values below 100 kPa the authors found a distinct minimum of density at grain moisture levels within the range of 20-24%. With increasing pressure, the minimum shifted slightly towards lower values of moisture (fig. 5.1). The authors described the relation with a non-linear function. A similar course of the relation was determined – for corn – by Clower et al. [36] and by Loewer et al. [96]. The curve marked with the symbol 0 kPa in figure 5.1 presents bulk density decreasing with increasing grain moisture content.
43 Eurocode 1 [50] recommends direct application of bulk unit weight of granular materials, determined experimentally under uniaxial compression, for the calculation of pressure. It is also recommended to use the value of vertical pressure that will exist in the bottom part of the silo as the consolidation pressure. If the information is not available, pressure value of 100 kPa is recommended for use as reference pressure. Bulk unit weight determined in this manner is used for the determination of the upper limit of load. A sample of the material tested is placed in a cylindrical container with diameter D that is greater than the maximum grain size by a factor of at least 40. Height H of the sample should be in the range of 0.3-0.4D. After the filling of the container, without any vibration and application of compacting loads, the upper surface of the sample is loaded with normal force generating the reference pressure σ r (corresponding to maximum vertical pressure p v or to 100 kPa). Then the top plate of the apparatus is rotated three times by 10 o right and left for additional compaction of the material. Bulk unit weight is determined as the quotient of the weight of consolidated sample and its volume (Tab. 5.2). Table 5.2. Bulk unit weight γ of consolidated granular materials according to Eurocode 1 [50] Granular material Barley Flour Maize Soybeans Sugar Wheat Bulk unit weight γ (kN m -3 ) 7.0-8.0 6.5-7.0 7.0-8.0 7.0-8.0 8.0-9.5 7.5-9.0 6. COMPRESSIBILITY AND ELASTICITY Granular materials in storage get compacted under their own weight and/or under external loads. Compaction increases through a change in packing and through deformation of the grains. The resultant strain ε p is the sum of reversible deformation ε e , caused by the elastic deformation of grains and thus disappearing with the removal of the load, and of the permanent deformation ε p related to the change of mutual orientation of grains: e p (6.1) ε = ε + ε . p Figure 6.1 presents the curve of cyclic loading of wheat grain sample under the conditions of uniaxial compression. Irrespective of the type of material tested
Page 2 and 3: EC Centre of Excellence AGROPHYSICS
Page 4 and 5: 4 9.3. Factors influencing the coef
Page 6 and 7: 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 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 58 and 59: 58 near the box wall and lifted alo
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
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92 reliable processing and stable v
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94 unconfined yield strength to pow
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96 The Chute Index (CI) is recommen
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98 obtained the maximum deviation o
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100 efficient flow control using op
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102 In the field of experimental in
Page 104 and 105:
104 22. Britton M.G., Moysey E.B.:
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106 69. Horabik J., Rusinek R.: Pre
Page 108 and 109:
108 114. Morland L.W., Sawicki A.,
Page 110 and 111:
110 158. 6WSQLHZVNL$ Influence of m
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112 16. APPENDIX - Physical Propert
Page 114 and 115:
114 16.2. Density and porosity Tabl
Page 116 and 117:
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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