Stress states caused in chamber of reinforced concrete grain silo by non-centric emptying on large eccentricities

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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

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.

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

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

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

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

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