Non Axial Stress State in a Model Silo G
291
Part. Part. Syst. Charact. 24 (2007) 291–295
Non-Axial Stress State in a Model Silo Generated by Eccentric
Filling and Internal Inserts
Marek Molenda*, Michael D. Montross**, Józef Horabik*
(Received: 20 December 2006; in revised form: 15 June 2007; accepted: 18 June 2007)
DOI: 10.1002/ppsc.200601113
Abstract
Dangerous nonuniformity of grain loads within a silo
may be caused by eccentric discharge, eccentric loading,
eccentric structural members fastened to the wall, geometrical imperfections or nonuniformity of the frictional
conditions. Some of these effects have been quantified
based on testing corrugated-walled, flat floor model silos filled with wheat. In this type of silo, filling above a
height to diameter ratio of H/D = 2.0 resulted in mixed
flow (following the terminology of Eurocode 1) where
grain slides along the wall during discharge above the effective transition and remains stagnant below the effective transition – located at H/D = ca. 0.7 (more details in
[1]).
The degree of load asymmetry due to eccentric filling is
demonstrated and compared to the worst case observed,
i.e., eccentric discharge through an orifice located at a
distance of 0.7 of the floor radius from the silo centerline. The presence of a nonsymmetric flow obstruction
on the silo wall is found to cause dangerous local loads
similar to eccentric discharge. Considerable nonuniformity in the load is observed during testing of a cylindrical obstruction immersed in grain supported on the silo
floor with its axis parallel to the silo centerline. The mechanisms of these phenomena are still poorly understood, and a satisfactory theoretical description cannot
be given.
Keywords: granular flow, horizontal pressure, load asymmetry, pressure distribution, silo
1 Introduction
According to Rotter [2], a silo wall is a shell that presents some of the most complicated mechanics for a
structural engineer. Rotter listed numerous new research areas and the need for general discussion of appropriate analysis methods that operate within standards, i.e., Eurocode 1. Unsymmetrical normal pressures
on the wall under symmetrical conditions of discharge,
eccentric discharge pressure regimes and nonuniform
stress states were some of the major areas that need to
be addressed. Sundaresan [3] focused attention on gaps
*
**
Assoc. Prof. M. Molenda (corresponding author), Prof. J.
Horabik, Institute of Agrophysics, Polish Academy of
Sciences, Doswiadczalna 4, 20-290 Lublin (Poland).
E-mail: mmolenda@demeter.ipan.lublin.pl
Assoc. Prof. M. D. Montross, 128 Barnhart Building, Biosystems and Agricultural Engineering, University of Kentucky,
Lexington KY (USA).
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
in the understanding of the mechanics of particulate systems, its translation into mathematical models and the
solution of such models. In the area of storage and discharge of granular materials, Sundaresan pointed out
several problems that still remain a challenge. One major problem is the inability to characterize how secondary variables (such as small changes in humidity level)
affect the deformation characteristics of the grain bulk.
Standard procedures for the estimation of loads on silo
walls are based on the rigid-perfectly plastic material
model [4]. Beginning with Coulomb as far back as 1771,
part of this model, the yield condition, was used to determine limiting stresses in soils. Load determination
methods in silos based on the Mohr–Coulomb yield condition are still widely used in practice, and in general,
provide a good estimation of loads. However in some
cases such as the dynamic load shift at the beginning of
discharge, the loads on objects immersed in grain or development of stagnant zones on flat inserts cannot be
predicted [5]. Haydl [6] suggested that even currently
http://www.ppsc-journal.com
292
observed progress in design would not bring about significantly better designs since the inaccuracy of the analysis was due to the uncertainty in the magnitude or distribution of the loading. To account for the inherent
variability of granular material properties, recently formulated codes (e.g., Eurocode 1 [7]) that recommended
using upper and lower estimates of parameters were applicable for obtaining maximum loads.
The results presented in this paper were selected from
several different research projects that demonstrate
asymmetric pressure distribution in flat floor, corrugated-walled, metal silos created by additional sources
within the grain mass.
2 Equipment and Procedure
The majority of tests reported in this article were conducted in a flat floor, corrugated-walled model silo
which was 1.83 m in diameter and 5.75 m in height
(filled to a maximum H/D of 3.0). These bins exhibited
mixed flow [7] during discharge with the grain sliding
along the wall above the effective transition and grain
remaining stagnant below the effective transition (located at a height to diameter ratio, H/D of ca. 0.7, see
[1]). The wall and floor of the silo were each supported
independently on three load cells, Figure 1. The silo was
constructed to isolate the vertical wall loads from the
floor loads. The load cells supporting the silo wall and
silo floor are evenly spaced around the circumference of
the silo at an angular distance of 120°.
This type of experimental configuration allows for the
determination of vertical wall and vertical floor loads, as
Fig. 1: Schematic of the model silo showing the locations of discharge orifices, wall load cells, floor load cells, pressure cells and
the XY system of coordinates used for calculation of wall bending
moments.
http://www.ppsc-journal.com
Part. Part. Syst. Charact. 24 (2007) 291–295
well as the calculation of overturning moments on the
walls and floor of the silo. With the exception of the
tests involving eccentric filling, the silo was centrally
filled from a spout at a flow rate of ca. 2600 N/min, up
to an initial H/D value of 2.75 (if not stated otherwise).
After filling, the grain was allowed to equilibrate following detention for a period of 0.5 h. The silo was then discharged through a centric orifice that produced a sliding
velocity along the bin wall with a mass flow of 3.1 m/h.
The wall and floor loads were measured during loading,
detention and discharge at 30 s intervals, until discharge
was completed. In general, the loads were measured
with an accuracy of ± 20 N and ± 50 N in the larger silo.
Three studies are summarized below:
1. Tests with eccentric filling and eccentric discharge
were conducted in a 2.44 m diameter silo that was
filled to an H/D of 2.0 for each test. The model silo
was filled using a movable filling chute located along
the radial line, coinciding with one of the major axis
of the silo at an eccentricity ratio (ER – distance from
the bin centerline divided by the silo radius) of 0, 0.5
and 0.75. Grain was discharged from one of five discharge orifices located at an ER of 0, ± 0.5 and ± 0.75
(further details in Molenda et al. [8]).
2. Tests regarding load asymmetry due to obstructions
attached to the silo wall were conducted using plane,
i.e., two-dimensional or three-dimensional obstructions. The plane obstruction was an annular segment
spanning 60° along the wall circumference and had a
surface area of 0.189 m2 or 7.2% of the bin cross-sectional area. The three-dimensional obstruction
(block) used the base of the two-dimensional obstruction was 0.5 m high and constructed using smooth,
galvanized steel. Obstructions were attached to the
wall with their upper base at H/D ratios of 0.38, 0.81
and 1.26. These locations placed the obstructions
within the stagnant zone, within the transition zone
between stagnant grain and funnel flow, and in the mass
flow zone. The lateral pressure was measured using
earth pressure cells. Two Geokon 3500 pressure cells
(Lebanon, New Hampshire) with a 100 kPa range and
an accuracy of 0.25% of full scale (± 250 Pa), were
used for measuring the grain pressure.
3. The loads were determined on a cylindrical obstruction with a three-legged support structure that rested
on three load cells fixed to the silo floor. The obstruction had a diameter of 0.445 m and a height of
0.675 m, and its base positioned at an H/D of 0.38.
Two radial positions were tested: centerline (eccentricity ratio ER = 0) and at a distance of 0.5 times the
silo radius from the centerline (ER = 0.5).
All tests were conducted with soft red winter wheat with
a moisture content of ca. 13% (wet basis) and an uncompacted bulk density of ca. 760 kg/m3.
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
293
Part. Part. Syst. Charact. 24 (2007) 291–295
3 Results
3.1 Eccentric Loading and Discharge
Figure 2 shows the resultant wall moments for eccentric
discharge located at values of ER of +0.7 and –0.7, and
discharge through the orifice located at an ER value of
+0.75. For test condition A, the filling chute and discharge orifice were on the same side of the Y-axis
(marked as “+”), and the wall moment after initiation of
discharge increased from 6.95 to 17.50 kNm. As unloading continued, the wall moment decreased rapidly from
a maximum moment of 17.7 kNm at H/D = 2.0, down to
a moment of ca. 8.0 kNm, at H/D = 1.5. During the remainder of the unloading, the moments decreased at a
much slower rate. For the test condition B, in which the
location of the filling chute and discharge orifice are on
opposite sides of the Y-axis, the wall moment decreased
from 8.30 to 3.20 kNm, after discharge was initiated.
After the initial ramp down, the wall moment increased
slightly during discharge but never reached the static value measured during filling. Eccentric discharge followed by eccentric filling either magnified or reduced
the nonuniformity of the stress distribution within the
silo, depending on the location of the filling and discharge gates.
Fig. 3: Resultant wall moment M, and its components Mx and My
with (a) plane, and (b) a 3D obstruction attached to the silo wall
at H/D of 0.38.
wall moment that was observed in the bin with no obstruction. After discharge initiation, the resultant wall
moment rapidly decreased to 1.6 kNm and remained relatively constant until an H/D ratio of 1.8, when the moment ramped down to 1.0 kNm. During further discharge, the moment remained constant until an H/D
ratio of 1.0, when the moment decreased consistently to
zero. The resultant moment, M, and its components Mx
and My acting on the silo wall with a 3D obstruction attached at an H/D of 0.38 in the (+x, +y) quadrant, is
shown in Figure 3b. Under these conditions, M reached
a maximum of 2.7 kNm at the end of filling and detention, i.e., ca. 300% of the value of the wall moment observed in the bin with no obstruction. The initiation of
discharge resulted in an immediate decrease of M to
2.4 kNm, followed by a continuous decrease with some
fluctuations during mass flow. A ramp down from
1.9 kNm to 1.4 kNm was observed at an H/D of ca. 1.8,
coincident with the change in the flow pattern from
mass flow to funnel flow.
3.2.2 Wall Pressure Above and Below Obstruction
Fig. 2: Wall moments produced during eccentric filling and
eccentric unloading of the bin, through discharge orifices located
at an ER of 0.7, on common (A) and opposite (B) sides of the bin
axis.
3.2 Obstructions Attached to the Wall
3.2.1 Asymmetry of Wall Load
The components and resultant wall moment during
loading and discharge for a two-dimensional obstruction
mounted on the wall at H/D = 0.38 in the (+x,+y) quadrant, are shown in Figure 3a. This condition produced a
resultant wall moment reaching a maximum of 2.1 kNm
at the end of filling. This was approximately double the
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
The distribution of horizontal pressure within the bin
was significantly influenced by obstructions, Figure 4. In
the case without an obstruction, Figure 4a, both pressure
cells measured a value of ca. 5 kPa at the end of filling.
The onset of discharge resulted in a sharp increase in
the horizontal pressure measured at H/D values of 0.66
to 13 kPa. The pressure decreased with fluctuations until
an H/D of 1.8 when the flow pattern changed from mass
to funnel flow. The horizontal pressure at an H/D of 1.1
initially ramped up to 7.5 kPa, but decreased to less than
4 kPa during further unloading. With the plane obstruction mounted at an H/D of 0.81, Figure 4b, the horizontal pressure was ca. 5 kPa after filling. The initiation of
discharge resulted in the horizontal pressure increasing
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294
Fig. 4: Wall pressure measured at heights 1.2 m (H/D = 0.66) and
2.0 m (H/D = 1.1): (a) without an insert attached, and (b) with
plane insert attached at height of 1.5 m (H/D = 0.81).
by 440% to 24 kPa above the obstruction, and it remained above 10 kPa with considerable fluctuations until an H/D value of 1.8, when the pressure decreased rapidly to zero. Below the obstruction, the horizontal
pressure remained less than 6.5 kPa during unloading.
Large disturbances in the pressure distribution result in
bending moments acting on the wall shell both in the circumferential and meridional direction, which may lead
to damages such as those reported by Blight [9]. A four
to five fold change in local horizontal pressures recorded by the pressure cells at discharge initiation were
associated with a dynamic increase in the vertical wall
load of 110%. Figure 4 also shows Janssen’s estimation
of horizontal pressure (with values of m = 0.4 and K =
0.42) at a height of attachment of the lower pressure cell
of 1.2 m, i.e. an H/D of 0.66. The readings of the pressure cell show strong fluctuations and lie below the theoretical curve, particularly in the case where the obstruction was located above the cell, Figure 4b.
3.3 Loads on Cylindrical Insert Supported on the Bin
Floor
In Figure 5, the loads recorded by the three individual
load cells OC1, OC2 and OC3 (which supported a cylindrical shaped insert located at an H/D of 0.38) are
shown during filling, detention and centric discharge.
Figure 5a shows the loads acting on the obstruction located centrically, i.e., ER = 0. The forces increased
smoothly during filling and reached final values of 2.2,
1.6 and 1.0 kN for load cells OC1, OC2, and OC3, respectively. The twofold difference in vertical forces between OC1 and OC3 was attributed to imperfect centric
filling of the bin. During discharge, large irregular fluctuations in load were observed in each load cell, particu-
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Part. Part. Syst. Charact. 24 (2007) 291–295
Fig. 5: Vertical loads on the three load cells supporting the cylinder
with H/D =0.38, at radial locations of (a) ER = 0.0, and (b) ER =
0.5.
larly during mass flow discharge. These fluctuations
were attributed to the sliding of grain against the cylinder wall during discharge. Strong load asymmetry was
observed with the cylinder located at ER = 0.5, Figure
5b. The loads on OC2 and OC3 reached a maximum of
ca. 2.3 kN at the end of filling, while the load on OC1
(the closest to the silo axis) did not increase markedly
during filling and reached a maximum static value of ca.
0.3 kN. Upon initiation of discharge, the loads on OC2
and OC3 suddenly decreased to 1.0 and 1.4 kN, respectively, while the load on OC1 ramped up to a value of
1.7 kN. The decreased loads on OC2 and OC3 were a result of decreased vertical loads that were characteristic
of a dynamic stress state. The increased load on OC1
can be attributed to the switch to an axial-symmetric
stress state due to centric discharge. During further discharge, the loads continually decreased without large
fluctuations.
4 Summary and Conclusions
Due to the ability of granular materials to transfer shear
stress, the distribution of pressure in a silo may be uneven and discontinuous. Frictional forces act between individual grains at their points of contact and create internal friction. The magnitude and direction of these
forces are not defined until sliding occurs. Tests in model
silos filled with dry wheat have shown a considerable degree of load asymmetry generated by eccentric loading
and eccentric structural members attached to the wall,
as well as on an obstruction immersed in grain.
Eccentric filling of the silo at ER = 0.7 up to an H/D of
2.0 resulted in wall bending moments of up to 7.9 kNm.
Eccentric discharge, i.e., ER = 0.7, after centric filling
created a maximum dynamic wall moment of 11.3 kNm.
Eccentric filling followed by eccentric discharge either
magnified or reduced the nonuniformity of the stress
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
295
Part. Part. Syst. Charact. 24 (2007) 291–295
distribution in the silo, depending on the location of the
filling and discharge gates. In the case with both gates
on the same side of the silo, the wall moments increased
from 6.9 to 17.5 kNm. In the case where the filling chute
and discharge orifice were located on opposite sides of
the silo, the wall moments decreased from 8.3 to
3.2 kNm, following discharge initiation.
The attachment of a 2D or 3D obstruction to the wall resulted in considerable asymmetry of the wall load distribution. The plane obstruction had the form of an annulus segment of 60° in circumferential extension and a
width of 0.154 m (i.e., surface area of 7.2 % of the silo
floor area). A three-dimensional obstruction was shaped
as a block with two identical bases as the plane obstruction and a height of 0.5 m. The plane obstruction and
upper base of the block obstruction were attached to the
wall at H/D ratios of 1.26, 0.81 and 0.38. Wall overturning moments of ca. 1 kNm were observed during centric
loading with no obstruction, even in conditions of near
symmetry. The attachment of an obstruction resulted in
an increased moment. The highest wall moment of
2.7 kNm was found at the end of filling the bin with the
block attached at an H/D of 0.38. The moment with a
plane obstruction in the same condition was measured
as 2.1 kNm. The maximum moment measured in this bin
for eccentric unloading with no obstruction was
3.5 kNm. For higher locations of the obstruction on the
wall, the wall moments were approximately 50 % of the
value at an H/D of 0.38.
Meridional distribution of horizontal pressure for filling
was found at lower values than Janssen’s estimation,
particularly below the obstruction. A sudden increase in
horizontal pressure was observed at the onset of discharge. A maximum pressure increase of 2.5 times the
static pressure was observed in the case without an obstruction attached to the wall. The dynamic pressure increases above the obstruction reached a maximum of
four times the static pressure. Conversely, the dynamic
pressure increases below the obstruction were lower
than those observed without the obstruction attached.
The data indicated that there are considerable additional loads placed on a bin due to obstructions that
may form during storage, which are not considered in
the design codes.
The vertical loads on the cylinder at the initiation of discharge increased, with large fluctuations in vertical load-
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ing observed during unloading of the bin. For an eccentrically loaded cylinder, the vertical pressure was lower
at the eccentric positions than when located centrically
along the centerline of the bin. No clear tendencies were
observed with respect to the bending moments acting on
the cylinder.
While Janssen’s equation can provide a simple estimation of the loads that might act on obstruction buried in
granular materials, this technique fails to satisfactorily
predict a number of effects that alter the vertical loading
on these obstructions. Some of these effects include the
stress history of the bulk, peak loads at the beginning of
discharge, variations in the stress state in the stagnant
zone of the materials, load asymmetry and fluctuations
and the nonhomogeneity of the material properties originating from variability of the packing structure of the
bulk.
5 References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
M. Molenda, J. Horabik, I. J. Ross, Comparison of Loads
on Smooth- and Corrugated-Wall Model Grain Bins. Intern. Agrophys. 2001, 15, 95–100.
J. M. Rotter, Shell Structures: The New European Standard and Current Research Needs. Thin-Walled Struct.
1998, 31, 3–23.
S. Sundaresan, Some Outstanding Questions in Handling
of Cohesionless Particles. Powder Technol. 2001, 115,
2–7.
A. Drescher, Analytical Methods in Bin-Load Analysis.
Elsevier, Amsterdam-Oxford-New York-Tokyo, 1991,
p. 37.
J. Strutsch, J. Schwedes, The Use of Slice Element Methods for Calculating Insert Loads. Bulk Solids Handling
1994, 14, 505–512.
H. M. Haydl, Some Practical Aspects of Concrete Silo
Design. Bulk Solids Handling 1992, 12, 41–43.
Eurocode 1, Actions on Structures. Part 4. Actions on Silos and Tanks. EN 1991-4:2003, European Committee for
Standardization, Brussels, 2003.
M. Molenda J. Horabik, S. A. Thompson, I. J. Ross, Bin
Loads Induced by Eccentric Filling and Discharge of
Grain. Trans. ASAE 2002, 45, 781–785.
G. E. Blight, Partial Failures of Corrugated Steel Silos
Storing Sanola. Bulk Solids Handling 2004, 24, 86–90.
http://www.ppsc-journal.com
Part. Part. Syst. Charact. 24 (2007) 291–295
Non-Axial Stress State in a Model Silo Generated by Eccentric
Filling and Internal Inserts
Marek Molenda*, Michael D. Montross**, Józef Horabik*
(Received: 20 December 2006; in revised form: 15 June 2007; accepted: 18 June 2007)
DOI: 10.1002/ppsc.200601113
Abstract
Dangerous nonuniformity of grain loads within a silo
may be caused by eccentric discharge, eccentric loading,
eccentric structural members fastened to the wall, geometrical imperfections or nonuniformity of the frictional
conditions. Some of these effects have been quantified
based on testing corrugated-walled, flat floor model silos filled with wheat. In this type of silo, filling above a
height to diameter ratio of H/D = 2.0 resulted in mixed
flow (following the terminology of Eurocode 1) where
grain slides along the wall during discharge above the effective transition and remains stagnant below the effective transition – located at H/D = ca. 0.7 (more details in
[1]).
The degree of load asymmetry due to eccentric filling is
demonstrated and compared to the worst case observed,
i.e., eccentric discharge through an orifice located at a
distance of 0.7 of the floor radius from the silo centerline. The presence of a nonsymmetric flow obstruction
on the silo wall is found to cause dangerous local loads
similar to eccentric discharge. Considerable nonuniformity in the load is observed during testing of a cylindrical obstruction immersed in grain supported on the silo
floor with its axis parallel to the silo centerline. The mechanisms of these phenomena are still poorly understood, and a satisfactory theoretical description cannot
be given.
Keywords: granular flow, horizontal pressure, load asymmetry, pressure distribution, silo
1 Introduction
According to Rotter [2], a silo wall is a shell that presents some of the most complicated mechanics for a
structural engineer. Rotter listed numerous new research areas and the need for general discussion of appropriate analysis methods that operate within standards, i.e., Eurocode 1. Unsymmetrical normal pressures
on the wall under symmetrical conditions of discharge,
eccentric discharge pressure regimes and nonuniform
stress states were some of the major areas that need to
be addressed. Sundaresan [3] focused attention on gaps
*
**
Assoc. Prof. M. Molenda (corresponding author), Prof. J.
Horabik, Institute of Agrophysics, Polish Academy of
Sciences, Doswiadczalna 4, 20-290 Lublin (Poland).
E-mail: mmolenda@demeter.ipan.lublin.pl
Assoc. Prof. M. D. Montross, 128 Barnhart Building, Biosystems and Agricultural Engineering, University of Kentucky,
Lexington KY (USA).
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
in the understanding of the mechanics of particulate systems, its translation into mathematical models and the
solution of such models. In the area of storage and discharge of granular materials, Sundaresan pointed out
several problems that still remain a challenge. One major problem is the inability to characterize how secondary variables (such as small changes in humidity level)
affect the deformation characteristics of the grain bulk.
Standard procedures for the estimation of loads on silo
walls are based on the rigid-perfectly plastic material
model [4]. Beginning with Coulomb as far back as 1771,
part of this model, the yield condition, was used to determine limiting stresses in soils. Load determination
methods in silos based on the Mohr–Coulomb yield condition are still widely used in practice, and in general,
provide a good estimation of loads. However in some
cases such as the dynamic load shift at the beginning of
discharge, the loads on objects immersed in grain or development of stagnant zones on flat inserts cannot be
predicted [5]. Haydl [6] suggested that even currently
http://www.ppsc-journal.com
292
observed progress in design would not bring about significantly better designs since the inaccuracy of the analysis was due to the uncertainty in the magnitude or distribution of the loading. To account for the inherent
variability of granular material properties, recently formulated codes (e.g., Eurocode 1 [7]) that recommended
using upper and lower estimates of parameters were applicable for obtaining maximum loads.
The results presented in this paper were selected from
several different research projects that demonstrate
asymmetric pressure distribution in flat floor, corrugated-walled, metal silos created by additional sources
within the grain mass.
2 Equipment and Procedure
The majority of tests reported in this article were conducted in a flat floor, corrugated-walled model silo
which was 1.83 m in diameter and 5.75 m in height
(filled to a maximum H/D of 3.0). These bins exhibited
mixed flow [7] during discharge with the grain sliding
along the wall above the effective transition and grain
remaining stagnant below the effective transition (located at a height to diameter ratio, H/D of ca. 0.7, see
[1]). The wall and floor of the silo were each supported
independently on three load cells, Figure 1. The silo was
constructed to isolate the vertical wall loads from the
floor loads. The load cells supporting the silo wall and
silo floor are evenly spaced around the circumference of
the silo at an angular distance of 120°.
This type of experimental configuration allows for the
determination of vertical wall and vertical floor loads, as
Fig. 1: Schematic of the model silo showing the locations of discharge orifices, wall load cells, floor load cells, pressure cells and
the XY system of coordinates used for calculation of wall bending
moments.
http://www.ppsc-journal.com
Part. Part. Syst. Charact. 24 (2007) 291–295
well as the calculation of overturning moments on the
walls and floor of the silo. With the exception of the
tests involving eccentric filling, the silo was centrally
filled from a spout at a flow rate of ca. 2600 N/min, up
to an initial H/D value of 2.75 (if not stated otherwise).
After filling, the grain was allowed to equilibrate following detention for a period of 0.5 h. The silo was then discharged through a centric orifice that produced a sliding
velocity along the bin wall with a mass flow of 3.1 m/h.
The wall and floor loads were measured during loading,
detention and discharge at 30 s intervals, until discharge
was completed. In general, the loads were measured
with an accuracy of ± 20 N and ± 50 N in the larger silo.
Three studies are summarized below:
1. Tests with eccentric filling and eccentric discharge
were conducted in a 2.44 m diameter silo that was
filled to an H/D of 2.0 for each test. The model silo
was filled using a movable filling chute located along
the radial line, coinciding with one of the major axis
of the silo at an eccentricity ratio (ER – distance from
the bin centerline divided by the silo radius) of 0, 0.5
and 0.75. Grain was discharged from one of five discharge orifices located at an ER of 0, ± 0.5 and ± 0.75
(further details in Molenda et al. [8]).
2. Tests regarding load asymmetry due to obstructions
attached to the silo wall were conducted using plane,
i.e., two-dimensional or three-dimensional obstructions. The plane obstruction was an annular segment
spanning 60° along the wall circumference and had a
surface area of 0.189 m2 or 7.2% of the bin cross-sectional area. The three-dimensional obstruction
(block) used the base of the two-dimensional obstruction was 0.5 m high and constructed using smooth,
galvanized steel. Obstructions were attached to the
wall with their upper base at H/D ratios of 0.38, 0.81
and 1.26. These locations placed the obstructions
within the stagnant zone, within the transition zone
between stagnant grain and funnel flow, and in the mass
flow zone. The lateral pressure was measured using
earth pressure cells. Two Geokon 3500 pressure cells
(Lebanon, New Hampshire) with a 100 kPa range and
an accuracy of 0.25% of full scale (± 250 Pa), were
used for measuring the grain pressure.
3. The loads were determined on a cylindrical obstruction with a three-legged support structure that rested
on three load cells fixed to the silo floor. The obstruction had a diameter of 0.445 m and a height of
0.675 m, and its base positioned at an H/D of 0.38.
Two radial positions were tested: centerline (eccentricity ratio ER = 0) and at a distance of 0.5 times the
silo radius from the centerline (ER = 0.5).
All tests were conducted with soft red winter wheat with
a moisture content of ca. 13% (wet basis) and an uncompacted bulk density of ca. 760 kg/m3.
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
293
Part. Part. Syst. Charact. 24 (2007) 291–295
3 Results
3.1 Eccentric Loading and Discharge
Figure 2 shows the resultant wall moments for eccentric
discharge located at values of ER of +0.7 and –0.7, and
discharge through the orifice located at an ER value of
+0.75. For test condition A, the filling chute and discharge orifice were on the same side of the Y-axis
(marked as “+”), and the wall moment after initiation of
discharge increased from 6.95 to 17.50 kNm. As unloading continued, the wall moment decreased rapidly from
a maximum moment of 17.7 kNm at H/D = 2.0, down to
a moment of ca. 8.0 kNm, at H/D = 1.5. During the remainder of the unloading, the moments decreased at a
much slower rate. For the test condition B, in which the
location of the filling chute and discharge orifice are on
opposite sides of the Y-axis, the wall moment decreased
from 8.30 to 3.20 kNm, after discharge was initiated.
After the initial ramp down, the wall moment increased
slightly during discharge but never reached the static value measured during filling. Eccentric discharge followed by eccentric filling either magnified or reduced
the nonuniformity of the stress distribution within the
silo, depending on the location of the filling and discharge gates.
Fig. 3: Resultant wall moment M, and its components Mx and My
with (a) plane, and (b) a 3D obstruction attached to the silo wall
at H/D of 0.38.
wall moment that was observed in the bin with no obstruction. After discharge initiation, the resultant wall
moment rapidly decreased to 1.6 kNm and remained relatively constant until an H/D ratio of 1.8, when the moment ramped down to 1.0 kNm. During further discharge, the moment remained constant until an H/D
ratio of 1.0, when the moment decreased consistently to
zero. The resultant moment, M, and its components Mx
and My acting on the silo wall with a 3D obstruction attached at an H/D of 0.38 in the (+x, +y) quadrant, is
shown in Figure 3b. Under these conditions, M reached
a maximum of 2.7 kNm at the end of filling and detention, i.e., ca. 300% of the value of the wall moment observed in the bin with no obstruction. The initiation of
discharge resulted in an immediate decrease of M to
2.4 kNm, followed by a continuous decrease with some
fluctuations during mass flow. A ramp down from
1.9 kNm to 1.4 kNm was observed at an H/D of ca. 1.8,
coincident with the change in the flow pattern from
mass flow to funnel flow.
3.2.2 Wall Pressure Above and Below Obstruction
Fig. 2: Wall moments produced during eccentric filling and
eccentric unloading of the bin, through discharge orifices located
at an ER of 0.7, on common (A) and opposite (B) sides of the bin
axis.
3.2 Obstructions Attached to the Wall
3.2.1 Asymmetry of Wall Load
The components and resultant wall moment during
loading and discharge for a two-dimensional obstruction
mounted on the wall at H/D = 0.38 in the (+x,+y) quadrant, are shown in Figure 3a. This condition produced a
resultant wall moment reaching a maximum of 2.1 kNm
at the end of filling. This was approximately double the
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
The distribution of horizontal pressure within the bin
was significantly influenced by obstructions, Figure 4. In
the case without an obstruction, Figure 4a, both pressure
cells measured a value of ca. 5 kPa at the end of filling.
The onset of discharge resulted in a sharp increase in
the horizontal pressure measured at H/D values of 0.66
to 13 kPa. The pressure decreased with fluctuations until
an H/D of 1.8 when the flow pattern changed from mass
to funnel flow. The horizontal pressure at an H/D of 1.1
initially ramped up to 7.5 kPa, but decreased to less than
4 kPa during further unloading. With the plane obstruction mounted at an H/D of 0.81, Figure 4b, the horizontal pressure was ca. 5 kPa after filling. The initiation of
discharge resulted in the horizontal pressure increasing
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294
Fig. 4: Wall pressure measured at heights 1.2 m (H/D = 0.66) and
2.0 m (H/D = 1.1): (a) without an insert attached, and (b) with
plane insert attached at height of 1.5 m (H/D = 0.81).
by 440% to 24 kPa above the obstruction, and it remained above 10 kPa with considerable fluctuations until an H/D value of 1.8, when the pressure decreased rapidly to zero. Below the obstruction, the horizontal
pressure remained less than 6.5 kPa during unloading.
Large disturbances in the pressure distribution result in
bending moments acting on the wall shell both in the circumferential and meridional direction, which may lead
to damages such as those reported by Blight [9]. A four
to five fold change in local horizontal pressures recorded by the pressure cells at discharge initiation were
associated with a dynamic increase in the vertical wall
load of 110%. Figure 4 also shows Janssen’s estimation
of horizontal pressure (with values of m = 0.4 and K =
0.42) at a height of attachment of the lower pressure cell
of 1.2 m, i.e. an H/D of 0.66. The readings of the pressure cell show strong fluctuations and lie below the theoretical curve, particularly in the case where the obstruction was located above the cell, Figure 4b.
3.3 Loads on Cylindrical Insert Supported on the Bin
Floor
In Figure 5, the loads recorded by the three individual
load cells OC1, OC2 and OC3 (which supported a cylindrical shaped insert located at an H/D of 0.38) are
shown during filling, detention and centric discharge.
Figure 5a shows the loads acting on the obstruction located centrically, i.e., ER = 0. The forces increased
smoothly during filling and reached final values of 2.2,
1.6 and 1.0 kN for load cells OC1, OC2, and OC3, respectively. The twofold difference in vertical forces between OC1 and OC3 was attributed to imperfect centric
filling of the bin. During discharge, large irregular fluctuations in load were observed in each load cell, particu-
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Part. Part. Syst. Charact. 24 (2007) 291–295
Fig. 5: Vertical loads on the three load cells supporting the cylinder
with H/D =0.38, at radial locations of (a) ER = 0.0, and (b) ER =
0.5.
larly during mass flow discharge. These fluctuations
were attributed to the sliding of grain against the cylinder wall during discharge. Strong load asymmetry was
observed with the cylinder located at ER = 0.5, Figure
5b. The loads on OC2 and OC3 reached a maximum of
ca. 2.3 kN at the end of filling, while the load on OC1
(the closest to the silo axis) did not increase markedly
during filling and reached a maximum static value of ca.
0.3 kN. Upon initiation of discharge, the loads on OC2
and OC3 suddenly decreased to 1.0 and 1.4 kN, respectively, while the load on OC1 ramped up to a value of
1.7 kN. The decreased loads on OC2 and OC3 were a result of decreased vertical loads that were characteristic
of a dynamic stress state. The increased load on OC1
can be attributed to the switch to an axial-symmetric
stress state due to centric discharge. During further discharge, the loads continually decreased without large
fluctuations.
4 Summary and Conclusions
Due to the ability of granular materials to transfer shear
stress, the distribution of pressure in a silo may be uneven and discontinuous. Frictional forces act between individual grains at their points of contact and create internal friction. The magnitude and direction of these
forces are not defined until sliding occurs. Tests in model
silos filled with dry wheat have shown a considerable degree of load asymmetry generated by eccentric loading
and eccentric structural members attached to the wall,
as well as on an obstruction immersed in grain.
Eccentric filling of the silo at ER = 0.7 up to an H/D of
2.0 resulted in wall bending moments of up to 7.9 kNm.
Eccentric discharge, i.e., ER = 0.7, after centric filling
created a maximum dynamic wall moment of 11.3 kNm.
Eccentric filling followed by eccentric discharge either
magnified or reduced the nonuniformity of the stress
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
295
Part. Part. Syst. Charact. 24 (2007) 291–295
distribution in the silo, depending on the location of the
filling and discharge gates. In the case with both gates
on the same side of the silo, the wall moments increased
from 6.9 to 17.5 kNm. In the case where the filling chute
and discharge orifice were located on opposite sides of
the silo, the wall moments decreased from 8.3 to
3.2 kNm, following discharge initiation.
The attachment of a 2D or 3D obstruction to the wall resulted in considerable asymmetry of the wall load distribution. The plane obstruction had the form of an annulus segment of 60° in circumferential extension and a
width of 0.154 m (i.e., surface area of 7.2 % of the silo
floor area). A three-dimensional obstruction was shaped
as a block with two identical bases as the plane obstruction and a height of 0.5 m. The plane obstruction and
upper base of the block obstruction were attached to the
wall at H/D ratios of 1.26, 0.81 and 0.38. Wall overturning moments of ca. 1 kNm were observed during centric
loading with no obstruction, even in conditions of near
symmetry. The attachment of an obstruction resulted in
an increased moment. The highest wall moment of
2.7 kNm was found at the end of filling the bin with the
block attached at an H/D of 0.38. The moment with a
plane obstruction in the same condition was measured
as 2.1 kNm. The maximum moment measured in this bin
for eccentric unloading with no obstruction was
3.5 kNm. For higher locations of the obstruction on the
wall, the wall moments were approximately 50 % of the
value at an H/D of 0.38.
Meridional distribution of horizontal pressure for filling
was found at lower values than Janssen’s estimation,
particularly below the obstruction. A sudden increase in
horizontal pressure was observed at the onset of discharge. A maximum pressure increase of 2.5 times the
static pressure was observed in the case without an obstruction attached to the wall. The dynamic pressure increases above the obstruction reached a maximum of
four times the static pressure. Conversely, the dynamic
pressure increases below the obstruction were lower
than those observed without the obstruction attached.
The data indicated that there are considerable additional loads placed on a bin due to obstructions that
may form during storage, which are not considered in
the design codes.
The vertical loads on the cylinder at the initiation of discharge increased, with large fluctuations in vertical load-
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ing observed during unloading of the bin. For an eccentrically loaded cylinder, the vertical pressure was lower
at the eccentric positions than when located centrically
along the centerline of the bin. No clear tendencies were
observed with respect to the bending moments acting on
the cylinder.
While Janssen’s equation can provide a simple estimation of the loads that might act on obstruction buried in
granular materials, this technique fails to satisfactorily
predict a number of effects that alter the vertical loading
on these obstructions. Some of these effects include the
stress history of the bulk, peak loads at the beginning of
discharge, variations in the stress state in the stagnant
zone of the materials, load asymmetry and fluctuations
and the nonhomogeneity of the material properties originating from variability of the packing structure of the
bulk.
5 References
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[2]
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[5]
[6]
[7]
[8]
[9]
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J. M. Rotter, Shell Structures: The New European Standard and Current Research Needs. Thin-Walled Struct.
1998, 31, 3–23.
S. Sundaresan, Some Outstanding Questions in Handling
of Cohesionless Particles. Powder Technol. 2001, 115,
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A. Drescher, Analytical Methods in Bin-Load Analysis.
Elsevier, Amsterdam-Oxford-New York-Tokyo, 1991,
p. 37.
J. Strutsch, J. Schwedes, The Use of Slice Element Methods for Calculating Insert Loads. Bulk Solids Handling
1994, 14, 505–512.
H. M. Haydl, Some Practical Aspects of Concrete Silo
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Eurocode 1, Actions on Structures. Part 4. Actions on Silos and Tanks. EN 1991-4:2003, European Committee for
Standardization, Brussels, 2003.
M. Molenda J. Horabik, S. A. Thompson, I. J. Ross, Bin
Loads Induced by Eccentric Filling and Discharge of
Grain. Trans. ASAE 2002, 45, 781–785.
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