VI CONGRESO DE 1/10 Investigaciones y estudios GRAIN SILOS TESTS UNDER SHAKING TABLE LOADS Salvador IVORRA CHORRO Dr. Ingeniero Industrial Universidad de Alicante Catedrático de Universidad [email protected]Stefano SILVESTRI Ms Civil Engineer, PhD Università di Bologna Richercatore CONFIRMATO [email protected]Tomaso TROMBETTI . Ms Civil Engineer, PhD Università di Bologna Profesor [email protected]M Giada GASPARINI . Ms Civil Engineer, PhD Università di Bologna Richercatore CONFIRMATO [email protected]Dora FOTI Ms Civil Engineer, PhD Politecnico di Bari Profesor [email protected]RESUMEN This paper reports describes a series of shaking table tests performed at the EQUALS lab of Bristol University in the framework of the SERIES FP7 project. The experimental test campaign was devoted to the evaluation of the effective behavior of flat-bottom silos filled of grain up to a certain height under base dynamic excitation, and to the experimental verification of the results obtained in a previous analytical research work by the authors. The analyses are developed by simulating the earthquake ground motion with time constant vertical and horizontal accelerations and are carried out by means of simple dynamic equilibrium equations that take into consideration the specific mutual actions developing in the ensiled grain. Different series of tests have been performed with different heights of the ensiled material to simulate a silo more or less squat. In this paper, the silo specimen and the test instrumentation are described, and the test program and the results are presented. Strong qualitative indications are obtained which basically confirm that the wall-grain friction coefficient plays an important role in the actions at the base of the silo walls. KEYWORDS: Grain silo, dynamic tests, earthquake tests, dynamic loads, flat-bottom silos, grain- like material, seismic response, shaking-table tests, friction coefficient.
Transcript
VI CONGRESO DE 1/10
Investigaciones y estudios
GRAIN SILOS TESTS UNDER SHAKING TABLE LOADS Salvador IVORRA CHORRO Dr. Ingeniero Industrial Universidad de Alicante Catedrático de Universidad [email protected]
Stefano SILVESTRI Ms Civil Engineer, PhD Università di Bologna Richercatore CONFIRMATO [email protected]
Tomaso TROMBETTI . Ms Civil Engineer, PhD Università di Bologna Profesor [email protected]
M Giada GASPARINI . Ms Civil Engineer, PhD Università di Bologna Richercatore CONFIRMATO [email protected]
Dora FOTI Ms Civil Engineer, PhD Politecnico di Bari Profesor [email protected]
RESUMEN
This paper reports describes a series of shaking table tests performed at the EQUALS lab of Bristol University in the framework of the SERIES FP7 project. The experimental test campaign was devoted to the evaluation of the effective behavior of flat-bottom silos filled of grain up to a certain height under base dynamic excitation, and to the experimental verification of the results obtained in a previous analytical research work by the authors. The analyses are developed by simulating the earthquake ground motion with time constant vertical and horizontal accelerations and are carried out by means of simple dynamic equilibrium equations that take into consideration the specific mutual actions developing in the ensiled grain. Different series of tests have been performed with different heights of the ensiled material to simulate a silo more or less squat. In this paper, the silo specimen and the test instrumentation are described, and the test program and the results are presented. Strong qualitative indications are obtained which basically confirm that the wall-grain friction coefficient plays an important role in the actions at the base of the silo walls.
1. Introduction In the general issue of the actions exerted by grain-like materials on the walls of flat-bottom silos during an earthquake, the assessment of the horizontal interaction is of particular interest. This interest is based on the possibility of providing more appropriate design rules closer to the effective seismic behaviour of silos. A careful evaluation of the forces produced by the material in the silos makes it possible to safely design silos in a seismic area without waste of material and excessive redundancy. In a previous research work [1], the authors developed an analytical theory with the aim of evaluating the interaction between the ensiled material and the silo-walls surface. Since the analytical theory is focused on a simplified idealized system, the design issues of the silo specimen have to deal with the differences between the idealized model and the characteristics of an actual silo subjected to earthquake ground motion. It is clear that a real silo is characterized by compressible (soft) grain material, flexible walls and, during an earthquake, is subjected to a seismic acceleration time-history. On the other hand, the theory developed by [1] has been developed with reference to the following strong assumptions (i.e. the ideal model deals with three fundamental hypotheses) of (i) incompressible material (in dry conditions, compact, without voids, as it were composed by a number of infinitely stiff and infinitely resistant spherical balls), (ii) infinitely stiff walls, (iii) time-constant acceleration. For these reasons, the shaking table tests and thus the test specimens have been designed both to meet the ideal conditions of the analytical theory and to investigate the influence of the type of input. Consequently, the two objectives of the experimental tests are:
• to verify the findings of the analytical theory developed by [1]; • to evaluate the influence of the assumption made on the base input (earthquake vs.
sinusoidal/constant) for the transition from ideal model case to the actual case.
2. Test set-up
2.1 The specimen: geometry and materials
Given that the dimensions of the EQUALS shaking-table is 3m x 3m, a scaled (roughly 1/10) circular tank specimen has been designed. The specimen consists in a 1.2 m diameter, 1.6 m tall, 3 mm wall thickness polycarbonate container fabricated for the project. Polycarbonate (E = 2.3GPa) has been selected as material for the walls in order to increase strains and thus to facilitate their measuring. The circular tank has been obtained by folding two single sheets on themselves to create two U sections, which have been interlocked and cemented with a 50 mm seam using epoxy and bolts. A ring is placed at the top of the specimen to avoid strong local deformations. Ballotini glass has been chosen as ensiled material to simulate incompressible grain-like material (Fig. 1). Furthermore, Ballottini glass is very close to the idealized ensiled material and its weight (20 kN) leads to horizontal forces which are compatible with the capacity of the shaking table system (150 kN). A 0.4-0.6 mm diameter for the particles of the Ballotini glass content has been selected for scaling reasons.
a) b) c) Figure 1. (a) The silo specimen; (b) the setup of the instrumentations (c) the insertion of the Ballotini glass. The specimen tank has been filled up to different heights h during the tests:
• h = 1.2 m, to obtain a slenderness ratio equal to 1 (Fig. 4); • h = 0.6 m, to obtain a slenderness ratio equal to 0.5 (Fig. 5).
The following table summarizes the reasonable values that can be assumed for the parameters involved in the analytical formulations to be validated.
2.2 The test instrumentation The test setup has been designed in order to provide measures of table, structure and grain accelerations at different locations; structure deformation at different locations; displacement of the rigid circular ring at the top of the silo; local pressures exerted by the grain on the walls. Figures 2 and 3 shows the instrumentation configuration.
Figure 2. The instrumentation set-up (a) Initial configuration. (b) Second set-up
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For this purpose, the following instrumentation was installed: • mono-directional accelerometers which are located at the shaking-table foundation, glued to
the silo walls and placed inside the Ballotini glass; • vertical and horizontal strain gauges positioned on the exterior side of the walls at four
different heights; • LVDT placed at the top of the structure; film and Flexi Force pressure sensors placed on the
interior side of the walls.
2.3 The test sessions
Three sessions of tests have been performed on the same specimen:
(1) first session: the silo is characterised by smooth walls (grain-wall friction coefficient: μGW=0.3) and filled with Ballotini glass up to a height equal to 120 cm (Figure 4a) has been tested under white noises, sinusoidal inputs and earthquake accelerogram, as applied along the horizontal direction only.
(2) second session: the silo is characterised by roughened walls (grain-wall friction coefficient: μGW=0.45) and filled with Ballotini glass up to a height equal to 60 cm (Figure 5a) has been tested under white noises, sinusoidal inputs and earthquake accelerogram, as applied along both the horizontal and the vertical directions.
(3) third session: the silo is characterised by roughened walls (grain-wall friction coefficient: μGW=0.45) and filled with Ballotini glass up to a height equal to 120 cm (Figure 4b)has been tested under systematic sinusoidal input, along the horizontal direction only.
The purpose of the first session of tests was to determine the dynamic properties of the silo specimen and to observe the variation in the dynamic properties of the prototype silo.
The objectives of the second session of test were to analyse the repeatability and the initial conditions of the silo and monitor the effect of a lower slenderness ratio (Ballotini up to 0.6m). To understand if the compaction of the ensiled material could affect the results, three repetitions of the same input were done. Also for this purpose the initial tests were repeated at the end of the campaign.
The aim of the third session of tests was to analyse the same conditions presented in the first session of tests (Ballotini up to 1.2 m) with a particular attention on the effect of the increased roughness and the changed internal friction coefficient of the ensiled material on the behaviour of the flat-bottom silo.
Figure 3. a)The specimen filled with Ballotini glass in the first session, b) The specimen filled with Ballotini glass in the second and third sessions.
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Figure 4. a)The specimen filled with Ballotini glass up to 0.6m with roughed walls b) The specimen filled with Ballotini glass up to 1.6m with roughened walls
2.4 The test input As illustrative example, Table 2 gives details about the tests sequence performed for the first configuration. This list is here provided in order to better contextualize the selected results which will be described in next section 5 (especially, the ones concerning frequency changes, grain compaction, and accelerations).
INPUT Tests No. PGA White noise N1 - N5 0.05 g – 0.30 g 1 HZ sinusoidal (Y) S1 - S8 0.05 g – 0.40 g White noise N6 0.30 g 1 HZ sinusoidal (Y) S9 0.03 g 0.5 HZ sinusoidal (Y) S10 – S13 0.01 g – 0.15 g White noise N7 0.30 g 1 HZ sinusoidal (Y) S14 0.50 g White noise N8 0.30 g Earthquake input E1- E18 0.04 g – 0.40 g White noise N9 0.30 g
Table 2. Test input for the first configuration of tests
We have developed more than 150 tests with different inputs and configurations.
3. Experimental results 3.1. Frequency
At first a white noise input was used in order to evaluate the dynamic properties of the silo. The first initial frequency was about 12÷13 Hz. Table n.3 reports the own frequency of the silo for the different sessions achieved by white noise at 0.3g:
WHITE NOISE ENSILED MATERIAL FREQUENCY (Hz)First Session (AUGUST 2012) Full Ballotini 12,72 Hz - 43.9 HzSecond Session (JANUARY 2013) Half Ballotini 28 HzThird Session (FEBRUARY 2013) Full Ballotini 16 Hz - 45,43 Hz
Table 3: Own frequency of the silo for each session of tests
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The grain inside the silo seems to act as a stiff material. No differences in the acceleration time-history were significantly observed during all tests performed under different base excitation (white noises, sinusoidal inputs and earthquake ground motions).
3.2. Grain compaction
During the first session of tests, instantaneously after the repetitions of the first tests a residual deformation was shown probably due to the compaction of the grain. The compaction was measured in 13 positions (p.1 - p.13), in terms of distance from a reference ideal line on the top ring of the silo and the average compacted thickness of the grain was around 3 ÷ 4cm. During the second session of tests, grain compaction due to dynamic excitation and its effects on the dynamic frequencies of the silo have been sistematically faced. Then among white noise, sinusoidal input and earthquake simulation the settlement of Ballotini glass into the silo was measured. An average of 3-4 cm was detected.
3.3. Acceleration Sinusoidal input The following pictures (Figures 5, 6) represent the profile of the acceleration versus time from which it is possible to figure out the type of input used for the test (sinusoidal).
0 5 10 15 20 25 30 35 40-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
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0.4Accelerometers y=0.6(LEFT)- test - S9 - a =0.339g
Time (s)
Hor
izon
tal A
ccel
erat
ion
(g)
h=0h=0.44h=0.84h=1.24h=1.54
0 5 10 15 20 25 30 35 40-0.4
-0.3
-0.2
-0.1
0
0.1
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0.4Accelerometers y=-0.6(RIGHT)- test - S9 - a =0.339g
Time (s)
Hor
izon
tal A
ccel
erat
ion
(g)
h=0h=0.44h=0.84h=1.24h=1.54
Figure 5. Accelerometers inside the silo at different heights (Left and Right in reference with Fig. 2a).
a)-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
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0.6
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1
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2max/min horizontal accelerations. Filtered t=0- test - S9 - a =0.339g
Acceleration (g)
h (m
)
max y=0.6(LEFT)min y=0.6(LEFT)max y=-0.6(RIGHT)min y=-0.6(RIGHT)
b)-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
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1
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2max/min horizontal accelerations. Filtered t=0 test S50 a = 0.2747 g
Acceleration (g)
h (m
)
max y=0.6(LEFT)min y=0.6(LEFT)max y=-0.6(RIGHT)min y=-0.6(RIGHT)
c)-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.2
0.4
0.6
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1
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1.8
2max/min horizontal accelerations. Filtered t=0 test S4 a = 0.325 g
Acceleration (g)
h (m
)
max y=0.6(LEFT)min y=0.6(LEFT)max y=-0.6(RIGHT)min y=-0.6(RIGHT)
Figure 6. Peak amplification profile and Maximum and minimum horizontal acceleration profile a) first session b) second session c) third session In this case, from the analysis made, the silo's behaviour validates the hypothesis to assumed an infinitely stiff silo. No amplification has to be considered and spectral acceleration coincides with ground acceleration (i.e. the response of the acceleration of the silo does not vary along the height of the silo). Furthermore the behaviour of the two parts of the silo is identical. The previous figures are representative not only for the reported test but for the 149 sinusoidal tests. Then the following
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conclusion can be achieved: the vertical profile of the horizontal acceleration under horizontal sinusoidal input is constant.
3.4. Vertical Strains Figures 7 - 9 represent the registered vertical strain gauges values in time for the right and left part of the silo with reference to figure 3a. It can be seen that the maximum vertical strain is reached at height 0.18 m (the lowest one), on the contrary the lowest vertical strain is set at height 0.92 m.
0 5 10 15 20 25 30 35 40-150
-100
-50
0
50
100
150
200
250Vertical strain-gauges, y=0.6(LEFT) filt. t=0 - test S9 - a = 0.339g
Time (s)
Vert
ical
mic
ro-s
trai
n
h=0.18mh=0.32mh=0.62mh=0.92m
0 5 10 15 20 25 30 35 40-150
-100
-50
0
50
100
150
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250Vertical strain-gauges, y=-0.6 filt. t=0- test - S9 - a =0.339g
Time (s)
Vert
ical
mic
ro-s
trai
n
h=0.18mh=0.32mh=0.62mh=0.92m
Figure 7. Vertical strain at different heights (Left and Right in reference with figure 2a) First session of test
0 5 10 15 20 25-100
-80
-60
-40
-20
0
20
40
60
80Vertical strain-gauges, y=0.6(LEFT) filt. t=0 test S50 a = 0.2747 g
Time (s)
Vert
ical
mic
ro-s
trai
n
h=0.18mh=0.32mh=0.62m
0 5 10 15 20 25-100
-80
-60
-40
-20
0
20
40
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80Vertical strain-gauges, y=-0.6 filt. t=0 test S50 a = 0.2747 g
Time (s)
Vert
ical
mic
ro-s
trai
n
h=0.18mh=0.32mh=0.62m
Figure 8. Vertical strain at different heights (Left and Right in reference with figure 2a) Second session of test
0 5 10 15 20 25 30 35 40-250
-200
-150
-100
-50
0
50
100
150
200
250Vertical strain-gauges, y=0.6(LEFT) filt. t=0 test S4 a = 0.325 g
Time (s)
Vert
ical
mic
ro-s
trai
n
h=0.18mh=0.32mh=0.62mh=0.92m
0 5 10 15 20 25 30 35 40-250
-200
-150
-100
-50
0
50
100
150
200
250Vertical strain-gauges, y=-0.6 filt. t=0 test S4 a = 0.325 g
Time (s)
Vert
ical
mic
ro-s
trai
n
h=0.18mh=0.32mh=0.62mh=0.92m
Figure 9. Vertical strain at different heights (Left and Right in reference with figure 5a) Third session of test These figures are representative not only for the reported test but for 149 sinusoidal tests, the residual has been erased to remove the static condition. Then the following conclusion can be achieved: by looking at the response of strain gauges placed at the base of the silo, it seems that the assumption of “plane sections remain plane” cannot be applied to such systems.
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3.5. The influence of the wall-grain friction coefficient Figure 10 compares the experimental base bending moments as reconstructed from the base strain values, for the following sessions:
• FIRST SESSION: Ballotini height equal to 1.2 m and smooth walls (black line) • SECOND SESSION: Ballotini height equal to 0.6 m and roughened walls (blue line) • THIRD SESSION: Ballotini height equal to 1.2 m and roughened walls (red line)
as obtained in the case of 1 Hz sinusoid input (only horizontal direction along the Y axis) at acceleration 0.33 g (first session test n. 9 vs. third session test n. 4) The results of the reconstruction and comparison of the base bending moment clearly indicate that the wall-grain friction coefficient strongly affects the experimental base bending moment. Then the following conclusions can be drawn:
• The experimental results do not match with Eurocode 8 [2] prescriptions which do not take into account the wall-grain friction coefficient at all.
• From a qualitative point of view, according to the analytical theory suggested by the authors [1], higher wall-grain friction coefficient (roughened walls) leads to higher actions inside the walls.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104
-3
-2
-1
0
1
2
3x 104Comparison of M(t) as re-constructed from base strains for 1° & 3° session of tests, a=0.2g, 1Hz
t [s]
M [kgcm]
first session: smooth walls (h=1.2m)second session: roughened walls (h=1.2m)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 104
-3
-2
-1
0
1
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3x 104Comparison of M(t) as re-constructed from base strains for 1° & 3° session of tests, a=0.3g, 1Hz
t [s]
M [kgcm]
first session: smooth walls (h=1.2m)second session: roughened walls (h=1.2m)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104
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-1
0
1
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3x 104Comparison of M(t) as re-constructed from base strains for 1° & 3° session of tests, a=0.4g, 1Hz
t [s]
M [kgcm]
first session: smooth walls (h=1.2m)second session: roughened walls (h=1.2m)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104
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3x 104Comparison of M(t) as re-constructed from base strains for 1° & 3° session of tests, a=0.5g, 1Hz
t [s]
M [kgcm]
first session: smooth walls (h=1.2m)second session: roughened walls (h=1.2m)
Figure 10. Comparison between First Second and Third session base bending moment at 1Hz and PGA equal to 0.2g (a), 0.3g (b), 0.4g (c) and 0.5g (d). 3.6. The base bending moment Figure 11 represents the reconstructed base bending moment with respect to the provisions of Eurocode 8 (simplified and accurate version) and the prediction of [1]. It is possible to note the significant difference in the magnitude of the base bending moment under the same base acceleration and low frequency equal to 1Hz. As showed, at different input frequencies and accelerations the value of the experimental bending moment at the base of the silo is much closer to the value given by the analytical theory [1] than to the two values (simplified and accurate procedures) given by the Eurocode 8 prescriptions. For the tests for which the value of the acceleration does not exceed the value of 0.30 g, the experimental
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value of the bending moment are even smaller than the value given by the analytical theory. On the contrary, when the acceleration reaches values of about 0.4 ÷ 0.5 g, the experimental value of the bending moment exceeds the analytical one. This is maybe due to the fact that the analytical theory is valid for small values of acceleration, basically ascribable to the values of the grain-grain and grain-base friction coefficients [1].
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104
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-1
0
1
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5x 104 M(t) as re-constructed from base strains a = 0.2g 1Hz
t [s]
M [kgcm]
first session: smooth walls (h=1.2m)third session: roughened walls (h=1.2m)M analyticalM EC8 simplifiedM EC8 accurate
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104
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5x 104 M(t) as re-constructed from base strains a = 0.3g 1Hz
t [s]
M [kgcm]
first session: smooth walls (h=1.2m)third session: roughened walls (h=1.2m)M analyticalM EC8 simplifiedM EC8 accurate
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104
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5x 104 M(t) as re-constructed from base strains a = 0.4g 1Hz
t [s]
M [kgcm]
first session: smooth walls (h=1.2m)third session: roughened walls (h=1.2m)M analyticalM EC8 simplifiedM EC8 accurate
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104
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-4
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5x 104 M(t) as re-constructed from base strains a = 0.5g 1Hz
t [s]
M [kgcm]
first session: smooth wallsthird session: roughened wallsM analyticalM EC8 simplifiedM EC8 accurate
Figure 11. comparison of Base bending moment in case of smooth and roughened surface of silo wall, with respect to expected value of Eurocode 8 (accurate and simplified version) and the analytical provision
4. Conclusions
The objective of the shaking-table tests was to investigate the pressures given by a grain-like material, under constant horizontal acceleration, confined in a stiff cylindrical element, in order to compare them with the analytical formulation and with the Eurocode 8 provisions. The following concluding remarks containing indications can be drawn from the experimental campaign:
1. The grain inside the silo seems to act as a stiff material. No differences in the acceleration time-history were significantly observed during all tests performed under different base excitation (white noises, sinusoidal inputs and earthquake ground motions).
2. Grain compaction occurs under dynamic excitation.
3. The vertical profile of the horizontal acceleration under horizontal sinusoidal input is constant. No acceleration amplification has to be considered for the dynamic system silo+grain and spectral acceleration coincides with ground acceleration.
4. By looking at the response of strain gauges placed at the base of the silo, it seems that the assumption of “plane sections remain plane” cannot be applied to such systems.
5. The experimental results clearly indicate that the wall-grain friction coefficient strongly affects the experimental base bending moment. This does not match with Eurocode 8 prescriptions which do not take into account the wall-grain friction coefficient at all. .
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6. From a qualitative point of view, according to the analytical theory suggested by the authors [1], higher wall-grain friction coefficient leads to higher actions inside the walls.
7. For a height h = 1.2 m of Ballotini glass inside the silo, the experimental bending moment is much closer to the prediction given by the analytical formulas provided by the authors [1] rather than to the values corresponding to the Eurocode 8 provisions.
8. For a height h = 0.6 m of Ballotini glass inside the silo, some strange interaction seems to occur between the mass of grain and the stiff circular ring at the top of the silo, whose presence seems to be no more negligble.
ACKNOWLEDGEMENTS
The authors acknowledge the financial support received from the European Community’s Seventh Framework Program [FP7/2007-2013] under grant agreement n° 227887 for the SERIES Project and thank Prof. Colin Taylor and Dr. Matt Dietz of the Bristol Laboratory of Civil Engineering (EQUALS). Also, the authors acknowledge the University of Alicante for the partial financial support by the grant nº ACIE12-04.
References
[1] Silvestri S., Gasparini G., Trombetti T., Foti D. (2012) On the evaluation of the horizontal forces produced by grain-like material inside silos during earthquakes. Bulletin of Earthquake Engineering, vol. 10, p. 1535-1560.
[2] EN 1998-4 (2006) Eurocode 8. Design of structures for earthquake resistance, Part 4 -Silos, tanks and pipelines, CEN, Brussels.
