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

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76 1+ sinϕ k = . 1 − sinϕ (10.3) where 3 is the angle of internal friction. The commonly used assumption that the lateral stress is constant along the slice results in location of Mohr’s circle for stresses at the wall outside the yield locus [45]. This assumption does not adequately represent pressure distribution in granular material in a silo. $FWLYHFDVH 3DVVLYHFDVH a) b) c) d) Fig. 10.1. Mohr’s circles for active (a), (c) and passive (b), (d) stress cases, (a), (b) – yielding at the centre, (c), (d) – yielding at the wall [67] 10.2. Yielding at the silo wall Considering the assumption that yielding occurs at the silo wall, the stress ratio k can be determined from the Mohr’s circle construction as the function of the angle of internal friction and the angle of wall friction 3 w :
77 ƒ for the active case (fig. 10.1c): 1− sinϕ cosα k = , 1+ sinϕ cosα (10.4) where: sinϕw α = arcsin −ϕw, sinϕ (10.5) ƒ and for the passive case (fig. 10.1d): 1+ sinϕ cosα k = , 1−sinϕ cosα (10.6) where: sinϕw α = arcsin + ϕw. sinϕ (10.7) A plot of the pressure ratio for yielding at the silo wall and the active and the passive stress cases for typical range of values of the angle of internal friction and the angle of wall friction is shown in figure 10.2. The pressure ratio observed in practice varies in a considerably smaller range [91]. A plot of the stress ratio calculated from the angle of internal friction according to the simplified formula recommended by Eurocode 1 [50]: k ϕ = 1.1(1 − sinϕ), (10.8) is shown in figure 10.2. The angle of internal friction 3 used in this formula should be determined experimentally in the direct shear test or in the triaxial compression test. The plot of the pressure ratio obtained from formula (54) is located in the upper limit of theoretical values obtained for the active stress case and yielding at the wall (i.e. for the wall friction angle 3 w close to the internal friction angle 3).
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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]
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8 Numerous granular materials when
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10 the tensor of plastic strain inc
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12 Fig. 2.1. Yield curves with comp
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14 Stable or unstable behaviour of
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16 In turn, the model of Lade, also
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18 same porosity need not have iden
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20 where: A = ∫ E( β) sin βdβ
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22 (β = 0 o ), positioning the out
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24 grain was poured into the mould
Page 26 and 27: 26 axes of the ellipse characterizi
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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 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 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
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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
Page 108 and 109: 108 114. Morland L.W., Sawicki A.,
Page 110 and 111: 110 158. 6WSQLHZVNL$ Influence of m
Page 112 and 113: 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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128 Table 16.18. Mean values (±St.
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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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