Performance of earth pressure cell as grain pressure transducer in a model silo
ABSTRACT Numerous methods have been proposed for determining the pressure exerted by grain at discrete locations in a storage structure, but few satisfactory solutions have been found. Earth pressure cells were tested as potential measurement devices for grain bins. Earth pressure cells are commercial transducers designed for geotechnical applications. Calibration of the earth pressure cell was performed in a pressurized chamber filled with wheat under normal load as well as shear load. The cell was tested in a model grain silo 1.83 m in diameter d with a height hc of 5.75 m. Vertical floor pressures and horizontal wall pressures were measured at different points in the model bin. The vertical floor pressure pvi was measured at two different radial locations and horizontal wall pressure ph was measured at four different wall heights. The vertical floor pressure obtained using the earth pressure cell was in good agreement with the mean floor pressure pv calculated using load cells that supported the entire floor or the bin. Considerable variation in the vertical floor pressure along the silo floor radius was observed. The variation of the lateral-to-vertical pressure ratio, K, was monitored during each fill-unload cycle of the model silo. In the case of the maximum h/d ratio of 2, K increased during filling and stabilized after reaching a grain h/d ratio of 1.3. At the onset of discharge, the pressure ratio immediately increased up to value of approximately 0.7, and remained stable during unloading down to a h/d ratio of approximately 0.65 when K decreased rapidly.
A b s t r a c t. Numerous methods have been proposed for
Earth pressure cells were tested as potential measurement devices
for grain bins. Earth pressure cells are commercial transducers
designed for geotechnical applications. Calibration of the earth
pressure cell was performed in a pressurized chamber filled with
wheat under normal load as well as shear load. The cell was tested
Vertical floor pressures and horizontal wall pressures were
measured at different points in the model bin. The vertical floor
pressure pviwas measured at two different radial locations and
horizontal wall pressure phwas measured at four different wall
heights. The vertical floor pressure obtained using the earth
Considerable variation in the vertical floor pressure along the silo
floor radius was observed. The variation of the lateral-to-vertical
pressure ratio, K, was monitored during each fill-unload cycle of
the model silo. In the case of the maximum h/d ratio of 2, K
increased during filling and stabilized after reaching a grain h/d
ratio of 1.3. At the onset of discharge, the pressure ratio imme-
diately increased up to value of approximately 0.7, and remained
stable during unloading down to a h/d ratio of approximately 0.65
when K decreased rapidly.
K e y w o r d s: bulk solids, granular material, pressure ratio,
pressure cell, silo loads
Information on the level and distribution of pressures
ries early theoretical considerations of storage pressures
required pressure measurements. Ketchum (1919) gave an
beginning of 20th century. In the chapter concerning expe-
riments on the pressure of grain in deep bins, this author re-
viewed results of nine projects, and in three of them authors
used hydraulic pressure transducers. Ketchum (1919) re-
ported that Jamieson and Lufft, used similar techniques
independent of each other at approximately the same time.
Jamieson performed his tests in Montreal, Canada in 1900
using a rubber diaphragm to transfer the grain pressure
through water to a mercury gage. Lufft performed his ex-
periments in full-size bins in Buenos Aires, Argentina in
1902 in which rubber diaphragms mounted inside the wall
transferred the grain pressure to a mercury column through
glycerine. Since that time, a significant amount of research
has been performed using pressure transducers for bulk
ducers pressure exerted on a circular surface is measured.
Two types of transducers are commonly employed: stiff
plate supported on force transducer or an elastic membrane.
Transducers for measuring pressure of bulk solids are not
widespread on the market, but one solution are earth pres-
elastic diaphragm where the deflection of the diaphragm
creates fluid pressure that is converted by the pressure
transducer into an electrical signal. Earth pressure cells are
meant to provide a direct means of measuring total pressure
in geotechnical applications.
The objective of this project was to validate the
applicability of earth pressure cells for determination of
grain pressure exerted on a silo wall and floor. Performance
of the EPC in four experimental conditions were tested:
radial distribution of vertical floor pressure, variation in the
horizontal wall load during filling and discharge of the
model silo, dynamic response of horizontal wall load at
initiation of discharge and variation of lateral pressure ratio
during a typical fill - unload cycle of a model silo.
Int. Agrophysics, 2007, 21, 73-79
Performance of earth pressure cell as grain pressure transducer in a model silo**
M. Molenda1*, M.D. Montross2and J. Horabik1
1Institute of Agrophysics, Polish Academy of Sciences, Doœwiadczalna 4, 20-290 Lublin 27, Poland
2Biosystems and Agricultural Engineering Department, University of Kentucky, Lexington, KY, USA
Received October 26, 2006; accepted December 30, 2006
© 2007 Institute of Agrophysics, Polish Academy of Sciences
*Corresponding author’s e-mail: email@example.com
**The investigations reported in this paper were made in College
of Agriculture, University of Kentucky, USA.
I I IN N NT T TE E ER R RN N NA A AT T TI I IO O ON N NA A AL L L
A A Ag g gr r ro o op p ph h hy y ys s si i ic c cs s s
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Geokon 3510 earth pressure cell with a diameter of 203
mm was used as the grain pressure transducer. The cell was
transducer was attached to the sample tray of the apparatus.
To produce a shear load the tray was pulled and the pulling
force recorded. The test for the applied normal load was
completed when the force required to slide grain across the
surface of the transducer stabilized. Tests were performed
to 48 kPa. The procedure was repeated three times and
transducer output versus normal pressure recorded.
Additional tests were conducted in a cylindrical, flat
diameter and 5.75 m high (Fig. 1). The wall corrugations
were 13 mm high with a period of 67.7 mm. The cylindrical
wall of the silo and the flat floor were each supported
independently from each other to isolate the wall and floor
loads. Both the wall and floor of the model grain silo were
supported by 3 load cells spaced at an angle of 120° around
the circumference of the silo. Load cells F1, F2and F3
support the floor of the bin, while load cells F4, F5and F6
support the walls of the bin. Soft red winter wheat with
bulk density of 750 kg m-3was used in the tests.
in the center of the silo at a rate of 1100 N min-1, which pro-
duced a sliding velocity of 2.8 m h-1along the silo wall du-
tion and discharge were measured at a 30 s interval until
of the loads at the start of grain discharge, loads were mea-
sured at a frequency of 0.7 s prior to opening the unloading
orifice and for one minute after the start of discharge. The
loads were measured with an accuracy of ? 50 N.
Locations of the EPC within the model silo used in the
under vertical floor pressure pvin the model silo was
performed at two radial locations of eccentricity ratios ( er -
of silo radius) of 0.33 and 0.67. Testing of the cell under
horizontal wall pressure phwas performed at four height-
to-diameter (h/d) locations on the silo wall of 0.1, 0.6, 1 and
1.25. Each test was repeated two times, and in case of noted
discrepancies between two replications a third test was
conducted. Results of one of the two tests will be shown in
Calibration of earth pressure cell under normal
and shear load
The earth pressure cell was calibrated under a pressu-
rized mass of grain under normal pressure only and under
normal pressure with shear stress. The cell was loaded with
eight levels of normal pressure from 0 to 48 kPa and then
and the transducer output (mV) against normal pressure
(kPa) recorded. Linear regression was performed and calib-
ration parameters obtained. Coefficients of linear correla-
calibration. No significant hysteresis was observed during
load increase – decrease cycles. Presence of shear stress
during calibration resulted in pressure readings that were
1.023 greater than readings under pure normal load.
74 M. MOLENDA et al.
d =1.83 m
h = d
h = 0.6d
h = 0.1d
h = 1.25d
Fig. 1. Schematic diagram of the model silo showing locations of
earth pressure cell tested in the project. F1, F2and F3are load cells
supporting the floor, while F4, F5and F6are load cells supporting
Vertical floor pressure during filing and discharge
a function of grain height-to-diameter ratio are shown in
Figs 2 and 3. Vertical floor pressure pviwas measured with
the EPC at two locations on the floor: er= 0.33 (0.305 m
from the silo axis, Fig. 2) and at er = 0.67 (0.61 m from the
silo axis, Fig. 3). The vertical floor pressures at discrete
locations were compared to the mean vertical floor pressure
pvin the bin by summing the vertical floor load from the
the silo floor area. At both test locations the EPC measured
floor pressures (pv1and pv2)were higher during filling than
the mean vertical floor pressure pv.Maximum floor pres-
sures pv1of 19.2 and pv2of 17.4 kPa were observed at the
end of filling at er = 0.33 and er = 0.67, respectively. The
mean vertical floor pressure pvwas found equal to 16.5 kPa
at the end of filling. During discharge the mean pressure pv
was greater than the pressure pv1and lower than pv2, both
measured using the EPC. This behavior confirmed earlier
a bin was not constant, contrary to Janssen’s assumption.
pressures on a flat floor but recommend that the design
vertical floor load in a bin is calculated using Janssen’s and
taken as uniform, except when the silo is squat or inter-
mediate slenderness. Australian Standard AS 3774 (1996)
recommended the following equation for determination of
where: pvix– mean initial pressure on the base at distance x
from center, kPa; x – radial coordinate in a circular
container, meters; dc – container diameter, meters; pv–
mean vertical floor pressure using Janssen’s equation and
the suggested grain coefficients.
PERFORMANCE OF EARTH PRESSURE CELL AS GRAIN PRESSURE TRANSDUCER IN A MODEL SILO75
Height to diameter ratio, h/d
Floor pressure (kPa)
(er = 0.33) and mean vertical pressure pvdetermined using the three load cells supporting the floor.
Height to diameter ratio, h/d
Floor pressure (kPa)
Fig. 3. Vertical floor pressure pv2measured with the EPC during filling and discharge at a distance of 0.67 radius from centerline
(er = 0.67) and mean vertical pressure pvdetermined using three load cells supporting the floor.
pressure) and radial coordinates of x1= 0.305 and x2= 0.61
kPa higher and 0.4 kPa lower than measured with the EPC.
The pressure distribution observed in the experiment was
flatter than the distribution suggested by the Australian
standard. At the initiation of discharge a sharp decrease in
the floor pressures was observed. The mean vertical floor
pressure pvdecreased from 16.5 to 13.7 kPa. Vertical
pressure at er = 0.67 (pv2) decreased from 17.4 to 15.2 kPa,
while at er = 0.33 the vertical pressure decreased from 19.2
to 9.2 kPa. A larger decrease in floor pressure closer to the
discharge orifice is a typical response during discharge.
Dynamic response of vertical floor pressure
to discharge initiation
Ratios of dynamic vertical floor pressure to static floor
in Fig. 4 for two radial locations of the pressure cell at er of
0.33 and er of 0.67.
Distinct differences in the dynamic to static floor
pressure ratio (dsr) for the two locations of the EPC were
silo axis the dsr decreased to 0.48 of its static value
immediately (within 1.5 s of discharge), while at an er of
0.67 the vertical floor pressure was still 0.99 of its static
value after 13 s of discharge. At the end of the recording
illustrated the strong dampening action of stagnant grain
covering the pressure cell. Change in stress state from static
to dynamic after discharge initiation had little effect on the
grain bulk located deeper in the stagnant zone. Propagation
of pressure wave in the network of intergranular forces was
weakened by friction between grains due to the increased
distance from the source of disturbance.
Horizontal wall pressures at various vertical
This set of tests were performed with the pressure cell
attached to the silo wall at height to diameter ratios (h/d) of
0.1, 0.6, 1 or 1.25. Measurements were taken during filling,
detention and discharge of the silo. Characteristics of
shown in Fig. 5a for filling and in Fig. 5b for discharge.
During filling, fluctuations in horizontal pressure were
observed due to the forming and collapsing of unstable
structures in the top layer of wheat. During the detention
period of 30 min horizontal pressure decreased by
approximately 15% in all cases except h/d of 0.1. This was
due to consolidation of grain in a direction of higher
principal stress ie in the vertical direction. This decrease in
horizontal pressure phwas accompanied by an increase in
vertical pressure pvand floor load. At the initiation of
discharge a sharp increase in horizontal pressure was
observed. Maximum dynamic to static pressure ratios (dsr)
1 and 1.25 were found to be 1.15, 1.5, 2.3 and 1.7, res-
pectively. This result is in disagreement with the opinion
that the highest increase in horizontal pressure occurred at
the transition from parallel to converging flow (h/d of
that a dynamic increase in horizontal pressure should not
occur at initial grain heights of less than h/d of 2.0 (EP433,
1997). Relatively small dynamic increase in horizontal
pressure phat the lowest h/d of 0.1 may be explained by the
muffling action of stagnant grain covering the pressure cell
in this case. At h/d of 0.6, 1 and 1.25 pressure fluctuations
were observed from the initiation of discharge until the
change in flow pattern from mass flow to funnel flow, at
which time these pressure fluctuations ceased. Cessation of
mass flow and initiation of funnel flow resulted in a steady
76M. MOLENDA et al.
0 10 20 3040 5060
Static to dynamic pressure ratio
er = 0.67
er = 0.33
Initiation of discharge
er = 0.33 and e r= 0.67.
decreased smoothly to 0 at which time the EPC surface was
uncovered. For the majority of tests after unloading the
pressure cell returned value between 100 and 500 Pa. This
pressure and temperature during testing that would
influence closed hydraulic system.
Dynamic pressure increase at the onset of discharge
The dynamic to static horizontal pressure ratios (dsr)
measured at an interval of 0.7 s during the first minute of
discharge and at four vertical locations of the pressure cell
floor (h/d = 0.1) the horizontal pressure phramped up after
discharge was initiated to 1.45 of the static value, and
of discharge. The dsr for the cell location at h/d = 0.6 also
and remained approximately stable with some fluctuations
extremes, with the largest 2.3 times the static value that was
observed after 23 s of discharge. Smaller fluctuations in dsr
were observed at the cell location of h/d = 1.25 where
PERFORMANCE OF EARTH PRESSURE CELL AS GRAIN PRESSURE TRANSDUCER IN A MODEL SILO 77
0 0,51 1,52
Height to diameter ratio, h/d
h/d = 1.25 h/d = 1.0
h/d = 0.1
h/d = 0.6
Height to diameter ratio, h/d
Lateral pressure (kPa)
h/d = 0.1 h/d = 0.6
h/d = 1.0
h/d = 1.25
1.25. Arrows pointing to the right indicate filling, and arrows pointing to the left indicate discharge.
0 10 2030 40 5060
dsr of horizontal pressure
h/d = 1.25
h/d = 0.6
h/d = 1.0
h/d = 0.1
1 and 1.25.
a minimum of 0.7 and a maximum of 1.6 were observed.
Data presented in Fig. 6 were for individual tests and were
representative of the duplicate. This silo discharged in mass
flow until the grain level reached a value of h/d of
approximately 1.5, and effective transition was observed at
smooth nature of the dsr at h/d of 0.1 was a result of cell
location in stagnant grain. Greater fluctuation was observed
for h/d of 0.6 because this was slightly below the transition.
The largest dsr fluctuations were found in the area of mass
flow (above h/d of 0.7) where grain was sliding against the
wall (and the cell surface) and where fluctuations of stress
state due to non-uniform wall shape and variation in wall
friction occurred. Eurocode 1 (2003) recommended that
increased discharge load should be used to account for
possible transitory increases in pressure on the silo walls
during discharge. The discharge factor Chof 1.15 for hori-
zontal pressure in slender silos and typical conditions has
recommended. ASAE standard EP 433 (1997) recommen-
ded an overpressure factor of 1.4 and in flat bottom mass
surface to within a distance of d/4 from the bottom. Results
of the current tests have shown that values of local dynamic
pressure increases were larger and occurred at a lower level
than recommended by conventional design codes.
Lateral pressure ratio, K, during filling
and discharge of the model silo
Eurocode 1 defines the lateral pressure ratio as the ratio
of the horizontal pressure on the vertical wall of a silo to the
active (or static) stress exists during filling, while a passive
(or dynamic) stress field develops during discharge. The
when the higher principal stress ?1is oriented vertically,
while ?2which is known as the passive stress is oriented
horizontally (Drescher, 1991). These states of stress are
accompanied by active and passive stress ratios. Figure 7
shows the stress ratio K against h/d ratio from experimental
results for filling and discharge of the model silo. For
calculation of K, values of lateral pressure measured at an
as the ratio of vertical floor load to silo floor area. During
filling of the silo, K increased with some fluctuations and
slow local decreases until it stabilized at a value of approxi-
mately 0.43 at an h/d ratio of approximately 1.4. During the
0.41. After initiation of discharge, K immediately increased
to a value of 0.63 and slowly increased during continuous
unloading to a value of 0.73. After the grain level decreased
down to an h/d of approximately 0.7, the pressure ratio
recommended by Eurocode 1. The dynamic to static wall
pressure ratio measured was 0.73/0.41 = 1.78 that was also
higher than the over pressure factor of 1.4 recommended by
EP 433 or 1.15 recommended by Eurocode 1. This discre-
pancy in results may be attributed to the relatively low level
of vertical pressure under which tests in the model silo were
reported that typical storage conditions in a full size
corrugated bin with a 15 m grain height, a vertical floor
pressure of approximately 100 kPa was observed. The floor
pressure in the 1.83 in diameter model was more than seven
times lower than in field conditions. Mechanical behaviour
78M. MOLENDA et al.
Height to diameter ratio, h/d
Pressure ratio, K
Fig. 7. Pressure ratio, K, produced during filling and discharge of the model silo.
1. The earth pressure cell (EPC) was found to be an
efficient transducer for measuring pressures exerted by
EPC were reliable in calibration tests with shear stress
application of EPC as a grain pressure transducer may be its
susceptibility to variation in reading due to ambient
temperature and atmospheric pressure.
2. Radial distribution of static vertical floor pressure
was found to vary contrary to Janssen’s assumption. In the
were found near the centerline.
3. Ramps in lateral pressure were observed in response
1 and 1.25 were found of 1.15, 1.5, 2.3 and 1.7, respecti-
vely. This finding is in disagreement with the claim that the
from mass to funnel flow, as well as with an opinion that
dynamic increase in lateral pressure for silos with an h/d
equal to 2 or lower would be negligible. Weaker dynamic
increase in phfor the lowest location of the pressure cell at
h/d of 0.1 may be explained by muffling action of the
stagnant bulk of grain covering the pressure cell.
4. The variation in the lateral-to-vertical pressure ratio,
K, was monitored during filling and discharge of the model
silo. K increased with small fluctuations during filling and
approximately 0.7, remained stable during unloading down
AS 3774, 1996. Australian Standard, Loads on bulk solids con-
tainers. Standards Association of Australia, 1 The Crescent,
Homebush, NSW 2140.
Drescher A., 1991 Analytical Methods in Bin-Load Analysis.
Elsevier, Amsterdam-Oxford-New York-Tokyo.
EP433, 2001. Loads Exerted by Free-Flowing Grain on Bins.
ASAE. 2950 Niles Road, Saint Joseph, MI 49085.
Eurocode 1, 2003. Actions on structures. Part 4: Actions on silos
and tanks. European Committee for Standardization,
Ketchum M., 1919. The Design of Walls, Bins and Grain
Elevators. McGraw-Hill Book Comp. Inc., New York.
Molenda M., Thompson S.A., and Ross I.J., 2000. Friction of
wheat on corrugated and smooth galvanized stell surfaces.
J. Agric. Eng. Res., 77(2), 209-219.
Thompson S. A., Galili N., and Williams R.A.. 1997. Lateral and
vertical pressures in two different full-scale grain bins during
loading. Food Sci. Technol. Int., 3(5), October, 371-379.
PERFORMANCE OF EARTH PRESSURE CELL AS GRAIN PRESSURE TRANSDUCER IN A MODEL SILO79