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Review of Silo Loadings Associated with the Storage of Bulk Granular Materials

Alan W. Roberts

Emeritus Professor, TUNRA Bulk Solids Handling Research Associates The University of Newcastle, NSW, Australia

Email: Alan.Roberts@newcastle.edu.au Abstract This paper presents an overview of developments in silo wall load analysis and design over the period commencing with the 1880s to the present. The pioneering work of Janssen (1995) in establishing the basic theory of silo wall loads under static filling conditions and the important contributions by Jamieson (1902-1903) in identifying the overpressures during symmetrical discharge and the non-symmetry of the wall loads during eccentric discharge are highlighted. The work of Jenike et al (1961-1973) which commenced in the latter 1950s is of particular note. The identification of the basic flow patterns of discharging bulk solids and the linking of these flow patterns to specific bin and silo geometries is reviewed. The associated bin wall loads that are linked to the flow patterns is discussed. Particular mention is made of the complex loading problems that are associated with eccentric discharge and multi outlet bins. The problems of grain swelling due to moisture increases and silo wall expansion and contraction that accompany temperature variations are outlined. The application of anti-dynamic or tremmie tubes for controlling wall loads in tall grain silos is illustrated. The subject of dynamic loads in silos, in particular, the phenomenon of silo quaking is reviewed. Also discussed is the case of rapid discharge of bulk solids which gives rise to impact loads which must be considered in the design of bin an its support structure. Brief mention is made of the loads on structural members that are buried in bins, bulk storage sheds and stockpiles. Key Words: Silo loads; flow patterns; grain moisture effects; silo quaking; buried structures 1. Introduction

The design of silos for the storage of bulk granular materials and other bulk products has been the focus of research for more than 100 years with the early publications appearing in the literature spanning the period from the latter 1800s to the early 1900s. Notable is the well known work of the German engineer, H.A. Janssen (1895)[6], but also noteworthy is the lesser known work of other researchers notably that of the Canadian engineer J.A. Jamieson (1903-1904)[4,5]. While much of the early work focussed on free-flowing, non-cohesive granular materials, the recognition of the vast array of cohesive bulk materials handled by industry gave rise to a much wider focus of the research into silo loads. The research of Jenike et al (1961-73)[7-12] and Johanson (1064)[13], which began in the late 1950s, represents a major contribution. The identification of the flow patterns of mass-flow and funnel-flow that are a function of the silo geometry, and the way these flow modes are influenced by the flow properties of the bulk material, has had a significant influence on silo design. The recognition of the role these flow patterns play in controlling the loadings on silo walls has been the subject of ongoing research over the past 60 years. Despite this, the determination of silo wall loads remains a subject of considerable complexity as is evidenced by the number of failures that have occurred. The complexity of the loadings includes such influences and factors as

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Silo geometry in relation to the bulk material flow pattern whether, for example, mass-flow, funnel-flow or expanded-flow

Eccentricity of loading and unloading

Moisture variations in the stored product and, in particular regarding agricultural grains, the swelling effect due to increases in moisture within contained storage masses in silos

Silo expansion and contraction on a night-to-day basis and, in the case of long term storage, on a seasonal basis summer through to winter.

Non-uniformity of silo wall loads due to non-uniformity of the wall expansion and contraction with respect to the aspect of the silo in relation to the position of the sun

Dynamic effects, such as the natural occurrence of pulsating flows in granular discharge from silos that give rise to the phenomenon of silo quaking

The influence of significant draw-down loads that can occur on structural members buried in stored granular masses

The purpose of this paper is to present a brief overview of the subject of silo wall loads illustrating some of the foregoing aspects with case study examples. Some emphasis is given to the subject of silo quaking to explain how and why it occurs and how it can be predicted and accounted for at the silo design stage so as to ensure it will not be experienced in practice.

2. Early Silo Research While silos have been in existence for many centuries, the known published research into silo loads was performed over the period of some 30 years commencing in the early 1880s. A review of this early silo load research has been published by Roberts (1995,1999)[15,18]. The most widely known work in the early period of silo research is that due to the German Engineer, H.A. Janssen (1895)[6]. This work is significant in that it recognised some fundamental aspects of internal and boundary friction which limit the magnitude of the loads on silo floors and walls. Janssens test apparatus is shown in Figure 1.

Figure 1. Model Bin Silo used by Janssen

By comparison, little is known of the work of the Canadian Engineer, J.A. Jamieson (1903, 1904)[4,5] who conducted experiments using the test rig of Figure 2. Jamiesons contributions are twofold. Firstly, during symmetrical discharge he showed that the wall pressures increased above the filling pressures. Secondly, and even more significantly, he examined eccentric discharge and showed that the wall loads on the side nearest the discharge outlet are lower than those for symmetrical discharge, but greater on the opposite side. His test results are shown in Figure 3. Thus he demonstrated the non-symmetry of the

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wall pressures. Had his research been more widely known, some of the silo failures that occurred 80 or more years later may have been avoided.

Figure 2. Model Bin used by Jamieson Figure 3. Pressures during Fill and Eccentric Discharge 3. Silo Load Research over the Past 50 Years

Following the foundation work of Jenike, the study of bin wall loads gained new impetus (Jenike et al (1968-1973)[9-12]. With the flow modes clearly defined and the advantages of mass-flow being identified, the need for determining the wall loadings in mass-flow bins became a necessity. The stress fields associated with mass-flow, together with the corresponding normal wall pressures are shown in Figure 4.

Figure 4. Pressures Acting in Mass-Flow Bins

When a bin is initially filled from the empty condition, a peaked or active stress field occurs as in Figure 4(a), the major principal stress being almost vertical. When flow occurs, the support offered by the gate at the outlet is removed and the stress field in the hopper switches to an arch or passive stress field, the switch travelling up the hopper becoming locked in at the transition as in Figure 4(b). In the arched or passive stress field, the load is

Peaked or

Active Stress

Field

Arched or Passive

Stress Field

1

2

1

2

Gate

Closed

(a) Initial Filling (b) Flow (c) Normal Wall Pressure

1

Initial Fill ing

Flow

Radial

Stress

Field

Switch

Pressure

p p

ppnhnh

n n

z

z

h

H

hs

s

h

B

D

z

zv v

v hv h

p

pp

p yy

Ef f ectiv e Datum Actual Datum

c

gz

hh

h

4

transmitted to the hopper walls with the major principal stress acting more in a horizontal direction tangential to each arch as in Figure 4(b). Most of the surcharge load due to the cylinder is carried by the upper section of the hopper giving rise to the high switch stress.

Above the hopper, that is in the cylinder, the peaked or active stress field remains, although imperfections in the cylinder wall which result in localised flow convergences cause over-pressures to occur in the cylinder. Imperfections in bin walls, which lead to over-pressures, may be due to manufacturing and/or constructional details such as weld projections or plate shrinkages in the case of steel bins, or deformation of formwork in the case of concrete bins. Jenike et al used strain-energy methods to analyse these over-pressures during flow in the cylinder. To simplify the computations, design codes generally apply over-pressure factors to the filling pressures computed by Janssens equation to account for flow conditions in the cylinder. This is indicated by the upper bound pn curve for the cylinder in Figure 4(c). It is to

be noted that when the bin discharges and the flow is stopped, the stress fields and corresponding pressures shown in Figure 4(c) remain unchanged. The passive stress field does not revert to that of Figure 4(a). This only occurs if the bin is completely emptied and then filled again. A better understanding of the characteristics of funnel-flow and the definition of the effective transition provided the scope for formalising the computation of wall loads in funnel-flow bins. There was the realisation that bin wall loads are directly related to the flow pattern developed during discharge, and this led to the conclusion that, wherever possible, bin shapes should be kept as simple as possible. While symmetry of the flow channel is seen as a desirable goal, from a practical point of view, it is virtually impossible to guarantee symmetrical loading. For instance the filling of the bin needs to be exactly central which, from a practical point of view, is unlikely. Secondly, the interfacing of the hopper with the feeder may skew the flow pattern. The need for ongoing research into bin wall loads had also been encouraged, to a significant extent, by an increase in the number of reported bin and silo failures. As a result, there was a pressing need to revise existing bin load codes and to develop new codes in countries where such codes have not previously existed. The Australian Standard AS3774-(1996)[1] is one example of the latter. This Standard is quite comprehensive, addressing a wide range of silo loading conditions including eccentric loads due to non-symmetrical flow patterns. The new Eurocode (2005)[3] covers the subject of silo loadings in great detail. 4. Loadings Associated with Multi Outlets Bins Loading conditions in multi outlet bins are quite complex with design misjudgements having been made on some occasions in the past by assuming uniform, symmetrical loading of the bin walls. An example of this is the coal bin shown in Figure 5. The bin, constructed of concrete, is 15m internal diameter with a 25m storage height. The discharge is via seven vibratory feeders linked to the central reclaim belt conveyor. The walls were designed solely on the basis of hoop stress with single reinforcing located at the centre of the 250mm wall thickness. There was no allowance for bending. As Figure 5 shows, the wall pressures in the region of the outlets are proportional to the flow channel diameters, whereas the pressures in the stationary regions between the outlets are proportional to the bin diameter. As a result of the bending in the walls, severe cracking occurred within the first months of operation. This necessitated the installation of steel cables to strengthen the bin walls as shown. The failure of the raw sugar storage bin shown in Figure 6 occurred within the 10 days of being filled for the first time. The bin was 18m diameter and had 2 rows of 4 outlets on opposite sides of the centre line. Again, the non-uniformity of the wall loads contributed to the failure.

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Figure 5. Cracking Problem in Multi-Outlet Coal Silo

Figure 6. Failure of 8-Outlet Raw Sugar Bin 5. Influence of Moisture and Temperature Variations on Silo Loads Significant increases in wall loads may occur in grain silos due to increases in grain moisture content in combination with thermal expansion and contraction (Roberts (1998))[17]. An example of such loadings have been identified as a contributing factor to the failure and collapse of the steel wheat storage silo in Australia as shown in Figure 7. Wheat had been stored in the silo from mid summer to winter, the collapse occurring early morning when the atmospheric temperature was at its lowest. While the failure may be attributed to the thermal contraction of the silo walls, there was a period when the grain conditioning aeration fans were left running during a period of high humidity. This resulted in the moisture content of the wheat in the lower region of the silo to increase from 9% to 13%. Laboratory tests using a triaxial cell showed that a 4% increase of moisture content from 9% to 13% resulted in an increase in the lateral pressure of the wheat of nine times. Grain swelling that accompanies such a moisture increase results in a reversal of the direction of the wall shear stress. This leads to an exponential increase in lateral pressure as shown in Figure 8.

Conveyor

Feeders

Low Pressure

High Pressure

Plan View of Bin

Bending of Wall

Flow Channels

18 m

6

Wall loads in storage bins for bulk solids are subject to significant variations in wall loads due to thermal expansion and contraction. Measurements of wall pressures have shown that pressures reduce during the day as a bin expands and increase during the night when the ambient temperature reduces and the bin contracts. However, complete contraction of the bin may not occur owing to the resistance of the stored bulk solid which has settled during the expansion phase. Hence, wall loads may not only be influenced by daily temperature fluctuations, but may also be cumulative over extended periods of undisturbed storage. The influence of wall load increase due to expansion and contraction is likely to be more pronounced in the case of grain or relatively free flowing material which can settle more readily. In the case of grain, the influence can be of considerable significance when coupled with the effects of moisture increases as discussed above.

Figure 7. Collapsed Grain Silo Figure 8. Wall Pressures under both Normal and Reverse Friction When considering expansion and contraction of silos, it is often the case that only the lateral or radial expansion and contraction are considered. In addition to lateral expansion a bin or silo will expand upwardly in the longitudinal direction, the amount of longitudinal expansion, for most bin aspect ratios, being of the same order as the lateral expansion. This is illustrated in Figure 9. When the bin cools, not only does it contract laterally, but it also contracts vertically. As the bin walls pull down due to this latter action, there is a strong likelihood that the shear stress at the wall due to wall friction will change direction from up to down. This reverse friction is a piston effect which can result in wall pressures significantly higher than the hydrostatic pressures. Pressures due to reverse friction can significantly add to those induced by the lateral contraction of the silo.

p p

n n

Aeration Ducts

Expansion Contraction

Figure 9. Expansion and Contraction of a Silo It needs to be noted that the thermal expansion and contraction influences on wall loads are

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most likely to be non-uniform around the silo wall owing to the relative position of the sun with respect to the silo. Hence eccentric type loadings will be induced in this way. 6. Use of Anti-Dynamic Tubes for Controlling Wall Loads in Tall Grain Silos In tall grain silos, the effective transition occurs low down the silo walls. As a result, mass-flow of grain with flow along the walls occurs over a substantial height of the silo above the effective transition. The effect is to cause dynamic pressures to be generated, these pressures being in the order of two to three times the static pressures generated after the silo is filled from the empty condition.

Figure 10. Model Silo and Test Results Figure 11. Anti-Dynamic

Tube for Eccentric Discharge

One way of controlling the wall loads in existing silos is to employ anti-dynamic, tremmie tubes which extend slightly less than half the height of the silo. Research using this type of anti-dynamic tube was conducted by Ooms and Roberts (1985)[14]. Figure 10 shows, schematically, the 1.2m diameter by 3.5m tall model flat bottom test silo and a sample set of test results. The work was initiated in order to provide a simple and low cost solution to controlling the pressures in a number of badly cracked concrete grain silos approximately ten times the scale. In effect, the tremmie tube divides the tall funnel-flow silo into two squat silos in series. The top half of the silo discharges first followed by the bottom part once the level drops below the top of the tremmie tube and the tube empties. Ports in the bottom of the tube allow grain to flow laterally to the silo outlet. The design of the bottom ports and tube sizing in relation to the silo outlet dimension are important in order to promote automatic choking of the lateral flow at the bottom until the tube empties. No valves are necessary. The arrangement ensures that at no time does the effective transition intersect the walls of the silo and hence the pressures never exceed the values corresponding to the static or initial filling condition. This is illustrated in the test results of Figure 10. The anti-dynamic tube has also been successfully used to control the flow in silos having eccentric discharge, as in Figure 11, and multiple discharge points. Without the tube in place, the walls of such silos are subject to significant bending stresses in addition to the hoop stresses. It is to be noted that the anti-dynamic tube described here is suitable only for free flowing, cohesionless bulk solids such as grain. They should not be used for cohesive bulk solids. It is also important to note that the cumulative effect of shear stresses causes high draw-down forces which must be accounted for in their design and installation in the silo.

Measured

Pressures

Mean Static Pressure

Mean Flow Pressure(Tube Fitted)

Mean Flow Pressure(No Tube)

Pressure

Model Silo

Anti-DynamicTube

H

Ht = 0.41H

Lowest ObservedEffective Transition

q = 45o

q

1

2

8

7. Dynamic Effects The Silo Quaking Problem A recurring problem in bin and silo loadings is that due to the phenomenon of silo quaking. Gravity flow in bins and silos, characteristically, is a cyclic or pulsating type flow which arises as a result of changes in density during flow and by varying degrees of mobilisation of the internal friction and flow channel boundary surface friction. Quaking is known to occur in bins of all types, namely mass-flow, funnel-flow, expanded-flow and bins with single and multi-outlets. In general, the pulsating load problem is more pronounced at low flow rates where the period of pulsing may be from a few seconds to many seconds or even minutes. The consequence of the pulsating loads may range from nuisance value arising from the transmission of shock waves through the ground to disturb neighbouring areas, to structural fatigue failure when the natural frequencies of the silo and structure are excited by the flow pulses. An overview of the silo quaking problem, based on the work of Roberts and Wensrich (1996-2003)[16-20,24,25], is now presented. 7.1 Experimental Studies Quaking in tall mass-flow bins may be experienced when the height of fill is above a critical height Hcr where Hcr D, as depicted in Figure 12. Figure 12(a) shows the test bin of

dimensions 1.2m diameter by 3.5m high, the bin being fitted with a stainless steel hopper. Load cells which measure normal and shear stress simultaneously are fitted into the silo walls. Above the height Hcr, plug type flow occurs with the velocity profile substantially

uniform over the cross-section. Below the critical level in the region of the transition, the flow starts to converge due to the influence of the hopper and the velocity profile is no longer uniform. The velocity profile is further developed in the hopper as shown. As the flow pressures form in the hopper, dilation of the bulk solid occurs. As a result of this dilation, it is possible that the vertical supporting pressures decrease slightly thus reducing the support given to the plug of bulk solid in the cylinder. This causes the plug to drop momentarily giving rise to a load pulse. The cycle is then repeated.

(a) Test bin showing load cell locations (b) Velocity profiles

Figure 12. Mass-flow Test Bin

H

H

D

cr

Critical Level for Mass Flow

Velocity Profiles

9

Examples of wall pressure and shear stress records at locations 5 and 14 are shown in Figure 13. The pulsing was quite pronounced at location 14 well up the cylinder, but was less evident further down the cylinder. Virtually no pulsing was shown to occur at location 5 near the transition.

(a) Results for location 5 (b) Results for location 14

Figure 13. Sample of Normal Pressures and Shear Stresses at Two Locations

7.2 Dynamic Load Model

The dynamic load model proposed initially by Roberts (1996)[16] was later modified in the light of the work of Wensrich (2002)[24,25]. Wensrich showed that in tall mass-flow silos, shock waves travel upwards through the silo from the transition giving rise to an exponential

increase in the amplitude of the dynamic wall pressures as illustrated in Figure 14. The

amplitude of the pulse pressure pws is given by

wows

y/R K -e p p (1)

Figure 14. Dynamic Loads Induced in Silo

D

WH

h S

sh

y

Plane ofshock

pws

hs Hs

D

WH

h S

y

Plane ofshock

p

hs Hs

p

pws

wo

Shock pressure on walls growsexponentially

Increment due to shock(amplitude)

pwo

t

t

T = Shock period

Tp p

pws

Shock pressure on walls

Increment due to shock(amplitude)

pwo

t

t

T = Shock period

Tp

D

WH

h S

sh

y

Plane ofshock

pws

hs Hs

D

WH

h S

y

Plane ofshock

p

hs Hs

p

pws

wo

Shock pressure on walls growsexponentially

Increment due to shock(amplitude)

pwo

t

t

T = Shock period

Tp p

pws

Shock pressure on walls

Increment due to shock(amplitude)

pwo

t

t

T = Shock period

Tp

10

As yh, it is assumed that pws 'tails off' to approach the flow pressure at the top surface in

the cylinder. It is noted that pws is the additional wall pressure applied to the initial or static

pressure. Figure15 shows the measured values (plotted points) and calculated (full lines) wall pressure amplitudes for the wheat silo of Figure 12(a). The calculated values are based on the following values:

Hsh = 2.14 m (location 14 of Figure 12(a)); = 30o; = 0.85 t/m3; D = 1.2 m:

Overall fill height above transition, Hsh + h = 3.0 m: K = 0.4 ;kr = 0.29 kr = ratio of shear to normal stress amplitude. The agreement between the measured and calculated normal and shear stresses is considered very satisfactory.

Figure 15. Computed and Measured Figure16. Pulse Period Versus Velocity Normal and Shear Stress Amplitudes

7.3 Pulse Period

The following equation, proposed by Roberts (1996)[16], has been shown to be a good predictor of the pulse period.

)a

v t2(

a

v )

a

v (t T oo (2)

where )h (h

p a

s

vo

A

Q v

v

t

yo

a = acceleration of upper mass during pulse motion such that a g v = average velocity of bulk solid in the cylinder during discharge, Q = discharge rate to = time for motion of upper mass to be initiated

y = dynamic displacement of consolidated mass in vertical direction

0 0.5 1 1.5 2

0

0.5

1

1.5

2

2.5

Normal Stress Amplitude

Shear Stress AmplitudePredicted Normal Stress Amplitude

Predicted Shear Stress Amplitude

STRESS AMPLITUDE (kPa)

HE

IGH

T A

BO

VE

TR

AN

SIT

ION

(m

)

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5 3

y = 5 mm

y = 2.5 mm

y =1 mm

y = 0.5 mm

Velocity (mm/s)

Pu

lkse P

erio

d (s

ec.)

11

Since velocities in the upper cylindrical section are usually quite low, for most practical

cases, the ratio va 0. Hence T = to. That is,

v

T

y (3)

The parameter y is dependent the average particle size, void ratio and properties of the

boundary surface of the flow channel. A plot of pulse period versus average discharge velocity in the cylindrical section of a silo is presented in Figure 16. As shown by Roberts

(2003)[20], y is related to the contact stiffness at the boundary of the channel as follows:

K

T

ny (4)

where KT = contact stiffness (mm

kPa) and n = normal stress (kPa).

7.4 Controlling Shock Loads in Tall Mass-Flow Silo Case Study In order to attenuate the growth in shock wave amplitude up the silo, Roberts and Wensrich conducted experiments using a hopper insert which, in effect, divides a tall mass-flow silo into two squatter mass-flow silos. Laboratory experiments on a small scale silo showed that the acceleration amplitude above the insert is reduced by approximately 50%. These results formed the solution to the quaking problem being experienced by the 200 tonne wheat conditioning silo shown in Figure 17.

Figure 17. 200 tonne Wheat Conditioning Silo

Wheat is dosed with water prior to being fed into the top of the silo, the objective being to bring the wheat to a uniform moisture content of around 16% prior to discharge for the milling process. The magnitude of the shock loads were quite severe, particularly when the silo was full or near full. Observation showed the shock loads were transmitted through the ground into the neighbouring concrete silo structure leading to some cracking.

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Calculations showed that the vertical dynamic load for the full silo when discharging grain amounted to 30% of the full static load, thereby increasing the total vertical load to 130% of the static load, The load analysis indicated that if the silo is operated at reduced head or fill, the shock loads are significantly reduced. For instance, at 60% full, the dynamic load is 46% of its maximum value, whereas at 50% full, the dynamic load is only 21% of its maximum value. Obviously, operating at 50% full would be the preferred option provided the residence time of the wheat in the silo is still sufficient to achieve good conditioning. The vibration frequency of the silo structure due to the vertical motion and swaying varies with the degree of fill. The fundamental natural frequency of the silo when 100% full is estimated to be 40% of the corresponding frequency when the silo is empty. 8. Quaking in Other Types of Bins and Silos

A similar action to that described for mass-flow bins may occur in tall funnel-flow bins where the effective transition intersects the wall in the lower region of the silo. As a result, there is flow along the walls of a substantial mass of bulk solid above the effective transition. 8.1 Squat Funnel-Flow, Expanded-Flow and Intermediate-Flow Bins The flow-patterns in squat funnel-flow and expanded-flow bins are illustrated in Figure 18. During funnelflow with no flow along the walls, as depicted in Figure 18(a), dilation of the bulk solid occurs as it expands in the flow channel. As a result some reduction in the radial support given to the stationary material may occur. If the hopper is fairly steeply sloped, say

q)], then the stationary mass may slip momentarily causing the pressure in the flow channel to increase as a result of the 'squeezing' action. The cycle then repeats. A similar behaviour may occur in expanded flow bins, such as the bin depicted in Figure 18(b).

Figure 18. Funnel-flow and expanded-flow

A similar flow pattern is that of intermediate-flow as described by Benink (1989)[2]. This mode of flow, illustrated in Figure 19, is a special form of mass-flow which can occur in squat mass-flow bins in which the surcharge head H < Hcr. Such flow is defined by a rapid

flow in the central region of the hopper, and a slower flow in the outer regions as illustrated in Figure 19(a). Funnel-flow is really the special case of intermediate-flow in which the outer region is stationary.

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Figure 19. Intermediate-flow

8.2 Expanded-Flow Surge Bin Case Study The example of an expanded-flow surge bin handling Potash is now considered. The bin constructed of stainless steel, is shown in Figure 20. The relevant properties of the Potash are:

Bulk Density = 1.2t/m3; Flow Rate qm = 4000tph; Effective Angle of Internal friction = 45

o;

Hopper Half-Angle = 25o; Average Particle Size of Potash = 7.5mm. 8.2.1 Analysis of Loads due to Central Channel

Referring Figure 21, it is assumed that during discharge the central channel or plug acts as a dynamic mass moving under accelerated flow. The driving force is the weight of the material in the channel, the downward movement being resisted by the components of the shear and normal forces around the boundaries of the flow channel. The slope of the central inner

moving plug is defined by the angle

Figure 20. Expanded-Flow Surge Bin Figure 21. Loads Acting in Flow Channel

Slow Flow in

Outer Region

Pulsating Flow in

Central RegionHopper

(a) Flow Patterns (b) Effective Mass

12000 OD

5697 OD

4500

3264

1600

3500

44o

25oz

Inclined Slide

Gates

1500 OD

zh

Di

Do

D

Dy

y

pnpn

Fs

W

Inner MovingPlug

ps

vs vmvav

Velocity Profile

14

Since shear at the boundary is due to internal friction, it is assumed that slip and hence failure corresponds to the maximum shear stress, it follows from Mohr circle analysis that

= sin (5)

The corresponding boundary friction angle is

w = tan-1(sin ) (6)

The total support force provided by the flow channel boundary is

(7)

The solution of equation (7) leads to

[

] (8)

where

(9)

[

]

(10)

(16)

{ (

) }

(11)

[ (

)] (12)

The weight of the moving central core is

( )

(13)

where

and

The net dynamic force is

(14)

The dynamic load factor depends on the elasticity of the impact during the deceleration phase. For a suddenly applied load, kD = 1. The acceleration is given by

a = W

gF D (15)

where

= g = bulk specific weight, kN/m3 = bulk density, t/m

3

y = height of moving mass, m kh = pressure ratio defined by equation (6) pv = average vertical pressure pn = normal pressure ps = surcharge pressure, kPa m = 1

= half-angle of flow channel. = half-angle of hopper

w = friction angle at boundary = friction coefficient

15

8.2.2 Predicted Performance Results

Figure 22. Predicted Dynamic Parameters for the Potash Surge Bin

Referring to the potash surge bin of Figure 20, the slide gates are partially closed to control the discharge flow rate through the split chute to 4000tph. Based on the above analysis, the dynamic forces, accelerations, velocities and pulse frequencies have been computed for the for various central flow channel heights 0 to 8.5m, the results being presented in Figure 22.

Based on the effective angle of internal friction = 45o, the half-angle of the flow channel,

(Roberts (2005)([21]. The lower frequencies for the full flow channel are most likely to be the critical values for the bin design.

9. 6000 Tonne Multi-Outlet Coal Bin Case Study Silo-quaking problems have been known to occur in bins with multiple outlets. By way of illustration, a case study concerning a 6000 tonne coal bin is reviewed. The bin, illustrated in Figure 23, has seven outlets as shown. Coal is discharged by means of seven vibratory feeders onto a centrally located conveyor belt. When the bin was full or near full, severe shock loads were observed at approximately 3 second intervals during discharge. The discharge rate from each feeder was in the order of 300 t/h. When the level in the bin had dropped to approximately half the height, the shock loads had diminished significantly. With all the outlets operating, the effective transition was well down towards the bottom of the bin walls. Substantial flow occurred along the walls, and since the reclaim hoppers were at a critical slope for mass and funnel-flow as determined by flow property tests, the conditions were right for severe 'silo quaking' to occur. Confirmation of the mechanism of silo quaking was obtained in field trials conducted on the bin. A set of dynamic strain results is shown in Figure 24. In one series of tests the three feeders along the centre line parallel with the reclaim conveyor were operated, while the four outer feeders were not operated. This induced funnel-flow in a wedged-shaped pattern as indicated in Figure 23, with the effective transition occurring well up the bin walls, that is Hm< Hcr. The same was true when only the central feeder (Fdr. 1) was operated. In this

latter case the stationary material in the bin formed a conical shape. Under these conditions, the motion down the walls was greatly restricted and, as a result, the load pulsations were barely perceptible

0.1

0.2

0.3

0.4

0.5

0.6

10

20

30

40

50

60

70

0 2 4 6 8 10

Velocity (m/s)

Frequency (hz)

Velo

cit

y

(m/s

)

Fre

qu

en

cy

(hz)

Flow Channel Height z

0

5

10

15

20

0

2

4

6

8

10

0 2 4 6 8 10

FD (kN)

Acceleration (m/s^2)

Dyn

am

ic F

orc

e F

D

(kN

)

Accele

rati

on

(m

/s^

2)

Flow Channel Height z (m)

(a) Dynamic Force and Acceleration (b) Velocity and Frequency

16

Figure 23. 6000 Tonne Multi-Outlet Coal Bin

In a second set of trials, the three central feeders were left stationary, while the four outer feeders were operated. This gave rise to the triangular prism shaped dead region in the central region, with substantial mass-flow along the walls. The load pulsations were just as severe in this case as was the case with all feeders operating.

Figure 24. Variation in Dynamic Micro-Strain in Bin Column (peak to peak measurement)

A critical factor in the operation of quaking silos is the dynamic stability of the overall structure. The silo in question is supported on columns from a concrete base which, in turn, is supported on piles as illustrated in Figure 25. In view of the significant decrease in total mass of the silo from the full to empty condition, there will be a corresponding increase in the natural frequencies of the silo during the emptying process. The modes of vibration involve combinations of vertical, swaying and twisting modes which are induced as a result of non-symmetrical loading of the silo, the pulsating flow during discharge and variations in the ground stiffness in the zone of the supporting piles.

H

H

D

D Eff ective transition for central feeders operationg

Eff ective transition for all feeders or outside feeders operating

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FeedersConveyor

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cr

m

F

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Feeders

Plan View of Bin

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3

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7

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14

20 30 40 50 60 70 80 90 100

All Feeders

Feeders 4.5.6.7

Feeders 1,2,3

Feeder 1

BIN LEVEL %

DY

NA

MIC

MIC

RO

-ST

RA

IN

17

k

k

1

2

Sw aying Mode

Columns

Piles

Vertical Mode

Concrete Base

Ground

M

Figure 25. Silo Dynamic Mode

10. Dynamic Loads Due to High Load-Out Rates Dynamic loads also occur during flood type loading of mineral ores into rail wagons. As an illustration, the case of an iron ore train loading bin, illustrated in Figure 26, is considered (Roberts (2008))[22].

(a) Train Loading Bin (b) Bin Flow Patterns and Loads (a) Wagon Load Rates and Total Loads (d) Rail Wagon Load Patterns

Figure 26 . Load-Out Bin for Filling Iron Ore Rail Wagons

Vex

Vey

Voq= 50o

Fix

Fiy

FH

FV

Fic

Tic

TD Tvi

Fvi FD

Pivot Point for Swing Chute

Pivot Point for Clamshell

Top of WagonTrim Level

12000 dia

8000

10900

1770 sq

Vex

Vey

Voq= 50o

Fix

Fiy

FH

FV

Fic

Tic

TD Tvi

Fvi FD

Pivot Point for Swing Chute

Pivot Point for Clamshell

Top of WagonTrim Level

Vex

Vey

Voq= 50o

Fix

Fiy

Vex

Vey

Voq= 50o

Fix

Fiy

FH

FV

Fic

Tic

TD Tvi

Fvi FD

Pivot Point for Swing Chute

Pivot Point for Clamshell

Top of WagonTrim Level

12000 dia

8000

10900

1770 sq

0

10

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Total Load (tonne)

TIME (sec)

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AD

-OU

T R

AT

E (t

/h x

10

^3)

TO

TA

L D

ISC

HA

RG

E (t

onne)

Qaverage = 8.64 x 10^3 t/h

VT

Zone 130 t3.5 sec

Zone 216.5 t6.5 sec

Zone 357 t27 sec

Zone 416.5 t13 sec

18

Each wagon holds 120 tonne of ore, the filling time per wagon being approximately 50 sec. The load out is controlled by a clam shell gate operating on a swinging chute as depicted. As an empty wagon moves under the bin load-out chute, there is an initial surge in the flow rate peaking around 60,000 t/h. This causes high vertical and lateral impact loads. Once the chute chokes, the remainder of the wagon is loaded at a rate of approximately 7000 t/h, with the flow rate reduced to zero as the gate closes with the wagon full. The shock loads on the bin and structure need to be taken into account in the design.

10. Loads on Buried Structural Members

Large bulk storage facilities such as stockpiles, bulk storage sheds and bins often contain structural elements which become partly or totally buried by the bulk solid during the filling process. Typical examples include trestle support legs on stockpile load-out conveyors as in Figure 26 and support columns in bulk storage sheds as illustrated in Figure 27. The loads on these structural elements are quite complex and depend on a number of factors such as the methods of filling and reclaim, load settlement, the flow properties of the bulk solid and any lateral deflection of the structural element. Furthermore, the cumulative, in-plane type compressive loads due to the shear stresses acting along the structural members can contribute to the buckling loads, thus exacerbating the lateral bending. Depending on the method of reclaim employed, the lateral loads may increase further during the unloading process. These various loading conditions have been described and design equations presented by Roberts (2007)[23]. He examined the case of the bulk phosphate storage shed of Figure 28.

Figure 27. Conveyor Support Legs Buried in Iron Ore Stockpile

Load-OutLoad - Out

Trestle Legs

Conveyor

Stockpile

Trestle Legs

Conveyor

19

Figure 28. Bulk Phosphate Storage Shed The loads on the buried columns can be quite variable depending on the following conditions:

Variations in the flow properties of the material

Loading and unloading history and mechanism for loading and unloading

Length of time the bulk material remains undisturbed in the stockpile

Rigidity of the stockpile floor - whether any settlement has occurred

Variations in stress fields from active to passive The models for the active and passive states of stress on the upper loading face of the column are shown in Figure 29. In view of the uncertainty as to how the stockpile will be filled and reclaimed, it is necessary to consider both stress states. The degree of support provided by the bulk solid on the rear face of the column depends on the degree of cohesiveness of the bulk solid. Observations have shown that for free flowing granular materials, flow of the material to the back face is quite rapid and the rear support provided by the material is quite strong. On the other hand, cohesive materials do not back-fill so readily so that the degree of support is much weaker.

Figure 29. Stress States for Buried Column

Load -OutConveyor

Stockpile

Columns

Load -OutConveyor

Stockpile

Active Case

1

SettlementDuring Loading &Flow DuringUnloading

Column

z

pnl

l

u

pnu

vp

b

qR

Direction of Major Consolidation Stress

Passive Case

b

z

z

g

h

Column

1

1

sc

pns

pv

s

s

c

pnc

c

20

As an example of the loads that may occur, the case of the bulk phosphate storage shed of Figure 28 is illustrated. The support columns are 250mm square steel tubing buried to a depth of 13.5m. Figure 30 shows the loads acting on the leading side of the columns for both the active and passive states. The full lines depict the load conditions with some back support, whereas the dotted lines are the load conditions without rear support. In addition the compressive loads due to shear draw-down need to be considered since these contribute to the compressive buckling loads. In view of the slenderness of the support column in this case study, it is not surprising that some columns were deformed due to bending.

Figure 30. Lateral loads on Support Columns of Bulk Phosphate Storage Shed

11. Concluding Remarks

The aim of this review paper has been to highlight some salient aspects in the research into silo load analysis that have occurred since the early work of Janssen and others commencing in the latter part of the 19th century until the present. It is quite evident that significant progress has been made. Yet, at the same time, it is also evident that the subject of silo loads remains a subject of considerable complexity. Apart from the analysis and design of the bin or silo and its support structure, the complexity is greatly magnified by the difficulty of fully understanding the properties of the bulk material being stored and handled and the way these bulk materials are influenced by consolidation stresses particularly under such variable conditions of prolonged undisturbed storage coupled with moisture and temperature variations. While the loading of silo and bin walls may be confidently predicted in the case symmetrical, single centrally located outlets, the case of multi-outlet bins and bins with eccentric discharge points create significant design challenges. Other areas for research include the important subjects of dynamic loads and bulk material flow induced vibrations. Invariably, modern industrial development in the agricultural and process industries demands increased tonnage rates, coupled with more efficient, economic and trouble-free operation. This provides the impetus for more exacting analysis and design procedures. It is the driving force for more in-depth research into this important subject, that of silo load analysis. There exists a wealth of knowledge which provides the datum for future research directions. This coupled with modern computer technology and keen young engineering and science based intellect, advances in the important subject of silo design and related areas of bulk handling are assured.

0 10 20 30 40 50 60 70 80

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FT - Active (kN/m)FT - Passive (kN/m)FT1 - Active (kN/m)FT1 - Passive (kN/m)

LATERAL FORCE ON COLUMN (kN/m)

DE

PTH

z

(m)

Bulk Density = 2.1 t/m^3

21

12. References

1. Australian Standard (1996) AS3774, Loads on Bulk Solids Containers. Standards

Association of Australia

2. Benink, E.J. (1989). Flow and Stress Analysis of Cohesionless Bulk Materials in Silos Related to Codes. Doctoral Thesis, The University of Twente, Enschede, The Netherlands.

3. EN 1991-4, (2005) Eurocode 1 Actions on Structures. Part 4. Silos and Tanks. Final Draft

4. Jamieson, H.A. (1903). Grain Pressures in Deep Bins. Trans. Canadian Society of Civil Engineers, Vol. XVII.

5. Jamieson, J.A. (1904). Grain Pressures in Deep Bins. Engineering News. Vol. LI,

No.10, 236-243.

6. Janssen, H.A (1895). Versuche u ber Getreidedruck in Silozellen (On the Measurement of Pressures in Grain Silos). Zeitschrift des Vereines deutscher Ingenieure, 1045-1049.

7. Jenike, A.W. (1961). Gravity Flow of Bulk Solids. Bul. 108, The Univ. of Utah,Engng. Exp. Station, USA.

8. Jenike, A.W. (1964). Storage and Flow of Solids. Bul. 123, The Univ. of Utah,Engng. Exp. Station, USA.

9. Jenike, A.W. and Johanson, J.R. (1969). On the Theory of Bin Loads. Trans. ASME.,

Jnl. of Engng. for Industry. Series B. Vol.91, No.2. 339.

10. Jenike, A.W., Johanson,J.R. and Carson, J.W. (1973). Bin Loads - Part 2: Concepts. Trans. ASME., Jnl. of Engng. for Industry. Series B. Vol.95, No.1.

11. Jenike, A.W., Johanson, J.R. and Carson, J.W. (1973). Bin Loads - Part 3: Mass-Flow Bins. Trans. ASME., Jnl. of Engng. for Industry. Series B. Vol.95, No.1, 6.

12. Jenike, A.W., Johanson, J.R. and Carson, J.W. (1973). Bin Loads - Part 4: Funnel-Flow Bins. Trans. ASME., Jnl. of Engng. for Industry. Series B. Vol.95, No.1, 13.

13. Johanson, J.R. (1964). Stress and Velocity Fields in the Gravity Flow of Bulk Solids. ASME, Jnl. of Appl. Mechanics, Vol. 131, Ser. E, No. 3. 499-506.

14. Ooms, M. and Roberts. A.W. (1985. The Reduction and Control of Flow Pressures in Cracked Grain Silos. Bulk Solids Handling, Vol. 5. No.5. 1009-1016.

15. Roberts A.W. (1995) One Hundred Years of Janssen. Bulk Solids Handling 15(3) 369-383.

16. Roberts, A.W. (1996). Shock Loads in Silos - The 'Silo Quaking' Problem., Bulk Solids Handling, Vol 16, No. 2. 59-73.

17. Roberts, A.W. (1998), Basic Principles of Bulk Solids, Storage, Flow and Handling. The University of Newcastle Research Associates Ltd. (TUNRA)

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18. Roberts, A.W. (1999). Particle Technology Reflection and Horizons: An Engineering Perspective, Transactions, Institution of Chemical Engineering, Part A, Vol 76, No A7, 1999, 775- 796.

19. Roberts, A.W and Wensrich,C.M. (2002). Flow Dynamics or Quaking in Gravity Discharge from Bins. Chemical Engineering Science, Vol. 57.295-305.

20. Roberts, A.W. (2003). Review of the Silo Quaking Problem in Bins of Various Geometrical Shapes and Flow Pattern. Task Force Quarterly, Academic Computer Centre in Gdansk, Poland, Vol 7. 623-641.

21. Roberts, A.W. (2005). Characterisation for Hopper and Stockpile Design, Chapter 3, Characterisation of Bulk Solids, Ed D. McGlinchey, Blackwell Publishing. 85-131.

22. Roberts, A.W. (2008). Shock Loads in an Iron Ore train Loading Bin. Proc. Structures and Granular Solids Conference, Royal Society of Edinburgh. CRC Press, Taylor and Francis Group, London. 67-76.

23. Roberts, A.W. (2007). Loads on Support Structural Elements Buried in Stockpiles, Particle and Particle Systems Characterisation, 2 Vol 24, Issue 4-5, 352-359.

24. Wensrich, C.M. (2002). Analytical and Numerical Modelling of Quaking in Tall Silos. PhD Thesis, The University of Newcastle, Australia.

25. Wensrich, C.M. (2002), Experimental Behaviour of Quaking in Tall Silos. Powder Technology, Vol. 127, 87-94.