Table 1
Classification of silo action assessment class according to - Eurocode 1, Part 4 [11].
| Action assessment class | Class description |
|---|---|
| Action assessment class 3 (AAC3) | Silo with storage volume of >10,000 tons. |
| Silo with storage volume of >1,000 tons, with any of the following calculation situations: | |
| a) non-centric emptying at e0/dc > 0.25; | |
| b) low silos, with the eccentricity of the upper filling cone et/dc> 0.25. | |
| Action assessment class 2 (AAC2) | All silos mentioned in Eurocode 1, Part 4 [11] which are not assigned to a different class. |
| Action assessment class 1 (AAC1) | Silo with storage volume of <100 tons. |
Figure 1
Distribution of local pressure in the cylindrical silo chamber.
Figure 2
Non-centric flow channel during emptying and the distribution of pressure on the silo wall, according to Eurocode 1, Part 4 [11].
Table 2
Parameters specifying the geometry of the flow channel (AAC3 class) for the selected bulk solids for reinforced concrete silo wall (D3 wall category, according to Eurocode 1, Part 4 [11]).
| Type of bulk solid | μm | aμ | μd | ϕim | aϕ | ϕig | μ/tandϕig | ec/r | Angle θc[°] | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| G=0.25 | G=0.4 | G=0.6 | G=0.25 | G=0.4 | G=0.6 | ||||||||
| Barley | 0.48 | 1.16 | 0.410 | 28 | 1.14 | 31.92 | 0.658 | 0.790 | 0.660 | 0.479 | 8.9 | 14.8 | 24.9 |
| Corn | 0.53 | 1.12 | 0.470 | 31 | 1.14 | 35.34 | 0.663 | 0.789 | 0.659 | 0.478 | 8.5 | 14.8 | 24.8 |
| Wheat | 0.57 | 1.16 | 0.490 | 30 | 1.12 | 33.6 | 0.738 | 0.780 | 0.646 | 0.461 | 7.7 | 13.3 | 22.3 |
Figure 3
Distribution of pressure on the perimeter of the silo, taking into account a non-centric flow channel while emptying the wheat silo with a diameter of 10 m: a) rc = 0.25 r, b) rc = 0.4 r and c) rc = 0.6 r.
Figure 4
Calculation model of a free-standing silo with height H = 25 m and diameter dc = 10 m: a) model of the chamber using the finite element method; and b) levels of reference in the silo adopted for the analysis of internal forces.
Table 3
Data on discretisation of the silo model (finite element method).
| Number of elements (panels) | 15 (13 wall panels, 1 bottom plate panel, 1 cover plate panel) |
| Number of distribution nodes | 4,030 |
| Standard net dimensions | 40 cm × 131 cm |
| Thickened net dimensions | 20 cm × 65 cm |
| Number of stiff nodes (of edge elements) | 48 |
Table 4
Physicomechanical properties of wheat adopted to determine the pressure in the silo chamber according to Eurocode 1, Part 4, Annex E [11].
| Properties of bulk solid | Wheat | |||
|---|---|---|---|---|
| Average value | Parameter a | Upper value | Lower value | |
| Unit weight, γ [kN/m3] | - | - | 9.0 | 7.5 |
| Internal friction angle, ϕi [°] | 30 | 1.12 | 33.6 | 26.8 |
| Concrete wall friction coefficient, μ | 0.57 | 1.16 | 0.661 | 0.491 |
| (D3 wall type) | ||||
| Lateral pressure ratio, K | 0.54 | 1.11 | 0.599 | 0.486 |
| Angle of repose, ϕr [°] | 34 | |||
| Patch load solid reference factor, Cop | 0.5 | |||
Figure 5
Values of components of bulk solid pressure on the wall of the silo with diameter dc=10 m and height H=25 m during emptying on large eccentricities e0(2) = 0 . 375 d c : a) Combination I; b) Combination II.
Table 5
Extreme values of internal forces in the wall of the silo with diameter dc=10 m at selected levels from symmetrical pressure, taking into account the local load.
| Values of internal forces | Level z/hc | |||
|---|---|---|---|---|
| 0.25 | 0.75 | 0.5 | ||
| N [kN/m] | e0(1) = 0.25dc | -128.93 | -267.79 | -417.14 |
| e0(2) = 0.375dc | -137.93 | -276.44 | -426.79 | |
| e0(3) = 0.5dc | -146.39 | -284.68 | -431.66 | |
| R [kN/m] | e0(1) = 0.25dc | 126.82 | 213.18 | 228.26 |
| e0(2) = 0.375dc | 139.09 | 221.04 | 253.38 | |
| e0(3) = 0.5dc | 144.14 | 232.03 | 263.44 | |
| MN [kNm/m] | e0(1) = 0.25dc | 0.76 | 2.9 | 1.46 |
| e0(2) = 0.375dc | 1.83 | 3.61 | 3.57 | |
| e0(3) = 0.5dc | 2.32 | 4.61 | 4.47 | |
| MR [kNm/m] | e0(1) = 0.25dc | 4.43 | 9.05 | 6.76 |
| e0(2) = 0.375dc | 6.28 | 10.42 | 10.61 | |
| e0(3) = 0.5dc | 7.31 | 12.34 | 12.42 | |
Table 6
Extreme values of internal forces in the wall of the silo with the diameter dc=10 m emptied on a large eccentric taking into account the occurrence of non-centric flow channel.
| Values of internal forces | Level z/hc | |||
|---|---|---|---|---|
| 0.25 | 0.5 | 0.75 | ||
| N [kN/m] | G = 0.25 | –97.51 | –232.55 | –398.24 |
| G = 0.4 | –112.27 | –254.48 | –433.87 | |
| G = 0.6 | –131.26 | –308.19 | –487.33 | |
| R [kN/m] | G = 0.25 | 101.05 | 165.67 | 195.77 |
| G = 0.4 | 113.35 | 173.13 | 201.99 | |
| G = 0.6 | 113.5 | 173.39 | 205.98 | |
| MN [kNm/m] | G = 0.25 | –1.09 | –2.31 | –2.89 |
| G = 0.4 | –1.7 | –3.39 | –4.33 | |
| G = 0.6 | –2.39 | –4.65 | –5.58 | |
| MR [kNm/m] | G = 0.25 | –5.78 | –11.34 | –13.89 |
| G = 0.4 | –8.54 | –16.34 | –19.91 | |
| G = 0.6 | –11.47 | –20.82 | –23.05 | |
Table 7
Percentage comparison of values of hoop moments in the silo with the diameter dc=10 m, calculated taking into account the occurrence of flow channel with values calculated on the eccentricity limit e0(1) = 0.25dc.
| Level, z/hc | Values of hoop moments, MR [kNm/m] | ||||||
|---|---|---|---|---|---|---|---|
| e0(1)= 0.25dc | G=0.25 | % | G=0.4 | % | G=0.6 | % | |
| 0.25 | 4.43 | –5.78 | 30.5 | –8.54 | 92.8 | –11.47 | 158.9 |
| 0.5 | 9.05 | –11.34 | 25.3 | –16.34 | 80.6 | –20.82 | 130.1 |
| 0.75 | 6.76 | –13.89 | 105.5 | –19.91 | 194.5 | –23.05 | 241.0 |
Figure 6
Maps of internal forces during emptying of the silo with the diameter dc = 10 m on a large eccentric taking into account the occurrence of non-centric flow channel with the radius rc,3 = 0.6r (θ c = 22.3o): a) maps of vertical forces, N [kN/m]; b) maps of hoop forces, R [kN/m]; and c) maps of hoop moments, MR [kNm/m].
Figure 7
Diagrams of hoop moments, MR, kNm/m ( z / h c == 0.5 ): 1) G=0.25, 2) G=0.4 and 3) G=0.6.
Figure 8
Diagrams of vertical moments, MN, kNm/m ( z / h c = 0.5 ): 1) G=0.25, 2) G=0.4 and 3) G=0.6.
Figure 9
Diagrams of hoop forces, R, kN/m ( z / h c = 0.5 ): 1) G=0.25, 2) G=0.4 and 3) G=0.6.
Figure 10
Diagrams of moments in the silo wall calculated taking into account the occurrence of the flow channel: a) vertical moments; and b) hoop moments.