wall loads on bunker silos due to compaction · 2014. 11. 6. · wall loads on bunker silos due to...

Wall loads on bunker silos due to compactionQ. ZHAO1 and J.C. JOFRIET2

2Gore and Storrie LTD., 255 Consumers Road, North York, Toronto, ON, Canada M2J 5B6; and 2School of Engineering,University ofGuelph, Guelph, ON, Canada NIG 2W1. Received 1August 1990; accepted 25June 1991.

Zhao, Q., and Jofriet, J.C. 1992. Wall loads on bunker silos due tocompaction. Can. Agric. Eng. 34:083-094. Mechanical compaction ofsilage in a bunker silo adds considerable wall loadto thatexerted bythesilage.The Boussinesqequationswereused to carryout a comprehensive study of wall pressures in bunker silos caused by thecompaction equipment. Fifteen analyses witha tracked bulldozer andthirty analyses with a tractorwerecarriedout. Distance betweenwalland vehicle and wall slope were the major parameters of this study.Analytical results were compared with experimental field test data.Reasonable agreement was found. The results show that the wallpressures are a function of the wheel load, or the applied pressureunder a bulldozer track, and the distance of the vehicle from the wall.For a tracked compactionvehicle the wall pressure can be as high as40%of thepressureunder the track.The effectof compaction becamenegligible at 2.0m depth below the silage surface. For a tractor 50%of the wheel load acts as a normal pressure on about an area 1 m by 1m of the wall. The wall pressure became insignificant at about 1 mdepth. The tracked compaction vehicle wall pressure increased about14% asthewall slope decreased from 90°(vertical) to70°. Fortractorsthis increase was almost 40%.

Keywords: silagecompaction,compactionpressures,bunker silos,Boussinesq

Le compactage mecanique d'ensilage, dans un silo bunker, au-gmente considerablement la charge exercee par Tensilage sur lesparois. A Taide des equations de Boussinesq, on a etudie la pressionexercee sur des parois de silos par Tequipement de compactage.Quinze analyses avec un bouteur a chenille et trente analyses avec untracteur furent effectuees. Les parametres principaux de Fetude etaientla distance entre les parois et les vehicules, et rinclinaison des parois.es analysesont ete comparees a des donnees d'essai sur le terrainet ontproduit des concordances raisonnables. Lesresultatsindiquent que lespressions exercees sur les parois sont fonctionde la chargedes roues,ou de la pression appliquee sous la chenille du bouteur, ainsi que de ladistance entre le vehicule et la paroi. Pour un vehicule de compactagea chenille, la pression exercee sur les parois peut atteindre 40 % de lapression sous la chenille.L'effet du compactagedevientnegligeable a2 m de profondeursous la surface de Fensilage. Pour un tracteur,50% de la charge des roues agit comme une pression normale sur unesurface murale d' environ 1 m sur 1 m. La pression sur la paroi devientinsignifiantea environ 1 m de profondeur. Dans le cas du vehicule decompactage a chenille, elle a augmente d'environ 14 % a mesure querinclinaison de la paroi decroissait de 90° (verticalement) a 70°' etpour les tracteurs, cette augmentation etait de pres de 40 %.

INTRODUCTION

Mechanical compaction is common practice for silage storedin bunker silos. It enhances the silage quality and increases thesilo capacity. Both wheeled tractors and tracked bulldozers areused. The mass of these wheeled and tracked compactors rangefrom 4 to 25 tonnes.

As a compactor moves close to a silo wall, it causes temporarily high, localized pressures on that wall. Compactionpressures have not been studied in great depth. Esmay et al.

(1956) carried out experiments on a 2-m high bunker silo andused a tractor with 11 kN wheel loads for silage compaction.They reported that the maximum wall pressure due to compaction, acting on a 0.3 m by 3 m long horizontal plank, variedfrom 6 kPa to 7.2 kPa. Messer and Hawkins (1977) conductedfull-scale silo experiments with several commercial silos withwalls up to 3 m high. A 5.4 tonne wheeled tractor was used forcompaction of silage in those silos. They recorded a maximumwall pressure equivalent to a point load of 5.9 kN. Kangro(1986) used a 7.5 tonne tractor for silage compaction in hisexperiments with a 2 m high silo. The maximum compactionwallpoint force was measured to be 13.3kN for grass silage,12 kN for corn silage and 14.5 kN for beet pulp.

The results of these earlier experiments are limited to thecompactionvehicles and conditions under which the measurements were made. A comprehensive study includingexperimental and analytical work has not been reported thusfar. As a result, design information on wall normal pressures(or wall loads) due to compaction equipment is sketchy andquite variable from code to code.

The objectives of this paper are:

a. to illustrate the use of the Boussinesq method for predicting silo wall pressures due to the weight of compactionvehicles, and

b. to determine by Boussinesq method the magnitude andextent of normal wall pressures exerted by different compaction vehicles.

The results from the analyses with the Boussinesq formulaewill be comparedwith the results from a full-scale bunker siloexperiment.As well, wall pressure profiles due to wheeledandtrackedcompaction vehicles will be presented. Finally, recommendations will be made for design loads for bunker silo wallsdue to the compaction operation.

METHOD

Boussinesq formulae for point loads

Boussinesq (1885) derived expressions (Eqs. 1 to 4) for computing the vertical, radial and circumferential stresses at apoint in an elastic material due to a point load acting on thesurface. Using the assumption that silage material is linearelastic, isotropic and that the induced strains are small, thoseformulae are used to estimate the stresses at the silage-wallinterface induced by the compacting loads acting on the silagesurface. Westergaard (1938) provided another solution to thesame problem. He assumed that the soil was an elastic massreinforced laterally by horizontal inelastic sheets spaced at

CANADIAN AGRICULTURAL ENGINEERING Vol. 34, No. 1, JANUARY/FEBRUARY/MARCH 1992 S3

close intervals to simulate anisotropy in the soil. This solutiongives lower stresses than the Boussinesq values. The realconditionprobably lies between the two extremes representedby the Boussinesq and Westergaard solutions (Craig 1978).The Boussinesq approach was used here because it providesconservative values suitable for design.

Stressesinside the silage materialdue to a point load, g, ona semi-infinite space are (Boussinesq 1885):

Oz-32

2KZ1

5/2

1+ {r/zf(1)

*=%tfz l-2v

(r2 +z2)5/2 tZ +z2 +2(^+z2).24/2 (2)

ae=-=£(l-2v*(r2 +z2)3/2 r2 +Z2 +z(r2 +Z2)1/2

(3)

Trz_ 2nrz

L(r2 +z2)5/2 (4)

where:

Gz = vertical stress at depth z below surface and a distancer from line of action of load,

Or = radial stress at same point,a = circumferential stress,

Trz= shear stress, and

v = Poisson ratio.

For a tracked compactor, the weight of the vehicle is assumed tobecarried evenly byboth tracks forflatsurfaces (Fig.1). Each track area is discretized into a number of equalsub-areas (12 sub-areas shown in Fig. 2). The total load oneach sub-area is treated as a point load acting at the centreofthe sub-area. The pressureat eachpoint of the silo wallcan be

0.5 m 1.5 m 0.5 m

calculated by applying Eqs. 1 to 4 to the point load on each ofthe sub-areas and by summingthe corresponding stresses.

For a wheeled compactor, the load under each wheel can beconsidered a surface point load and the effects of the wheelson the wall surface can be summed.

The existence of the wall prevents the silage mass at thewall-silage interface from moving horizontally. To obtain thelateral pressure on a rigid structure (zero lateral strain), asecond load with the same magnitude of Q must be imaginedat an equal distance on the other side of the rigid structure(Craig 1978). Thus, the calculated horizontal stress normal tothe wall by the Boussinesq formulae should be doubled. Thena three-dimensional stress transformation is used to calculatethe pressure normal to the wall. The formulae for the three-dimensional stress transformation are from Boresi and Chong(1987).

Comparison of experimental with analytical resultsTo obtain the normal wall pressures, a small computer program was written in BASIC to perform the Boussinesqcalculations and the necessary stress transformations. Inputincluded the wall slope, the wall height, the wall-track cleardistance, and the desired location of wallpressures.

A comprehensive research project carried out at the University of Guelph included the determination of bunker silo wallloads by analysis and experiment. The compaction vehicle intheexperiments was a bulldozer (Zhao et al. 1989). Figure 1shows thedimensions andweight of thedozer. Theweight oneach track was 104 kN. Assuming a uniform distribution, thepressure under each track was 70 kPa. The results that followwere obtained by dividing the contact area of each of the twotracks with the silage surface into 24 subdivisions. A Poissonratio of 0.34 (Zhao 1990) was used in the calculations.

Figures 3 to 6 show the normal wall pressures calculatedwith theBoussinesq formulae and thepressures obtained fromthe experiment. The Boussinesq results are the resultant normal wall pressures due to the pressure under both tracks of a21 tonne bulldozer. Theanalytical results at the points on thewall for which the stresses were calculated are connected by

O O O "7"

2£ZjSi

3.0 m

Fig. 1. Dimensions andweight of the 21 tonne bulldozer compaction vehicle.

84ZHAO and JOFRIET

track II

i

X

f

o- .0.

G- •O::

EO- • O*.

m ©• •O-

a ••<*•'

1

0* '©'

m m

0.5 m 1.5 m 0.5 m

:lear wall dist.

Fig. 2. Plan viewof bulldozer tracks and subdivision oftracks into subareas, each represented by aconcentrated load in the Boussinesq equations.

straight lines. The experimental results were obtained in afull-scale experiment on a largebunkersilowithwalls 4.83mhigh (Zhao et al. 1989). Themeasured valuesin the figures areaverages of threemeasurements on eachof six levels, andareindicated with a diamond shaped mark. The experimentalresults were obtained by subtracting the wall pressures whenthe bulldozer was absent from those when the bulldozer waspositioned on thesilage surface nearthewall. Thetotal silagedepth was about 5.0 m at the time the measurements weremade.

InFig.3, thedistance between the edgeof the tracknearestto the wall and the wall surface (referred to as wall-trackdistance) was0.33 m. The calculatedand the measuredresultsagree well at level 2; the measured values at level 1and 3 are24% and 50% lower than those calculated. The calculatedmaximum wallpressure is about 19kPa at 0.25 m depthfromthesilage surface. Both themeasured andthecalculated resultsshow a rapid decrease of the normal wall pressures with increase of depth. Below a depth of 2 m, the wall pressuresreduce to a negligible value.

Figure 4 shows thepressures fora wall-track distance of0.6m.Excellent agreement between the measured and the calculatedresults is again evident at level 2. The measured valuesat levels 1 and 3 are smaller than the calculated values. Themaximum calculated pressure is 13 kPa at a depth of 0.5 mfrom the surface. Results for wall-track distances of 1.0 m and2.3 m are displayed in Figs. 5 and 6, respectively.The calculated wall pressures in both figures agree well with thecorresponding measured wall pressures.

In judging the quality of the simulation results it is well toremember that the experimental results were obtained by subtracting silage pressure observations made without thecompacting equipmentpresent from those with the equipmentin place. At the uppermost sensor (level 1) the silage pressureis of the order of 5 kPa and the additional pressures caused bythe compacting equipment are greater than 5 kPa when thewall-track distance is 0.6 m or less. For a wall-track distance

wall

NORMAL PRESSURE, kPa

0 5 10 15 20 25 30 35

0 1 1 1 1 1 1

level 1

F

2

level 2

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level 3

2:0CE

Xr—

level 4

LU

O

_J<CJ

level 5

»—l

h-rxUJ>

• I 0

4 level 6• 0

Fig.3. Calculated and measured wall pressures due to a21 tonne bulldozer compaction vehicle stationed0.33 m from the wall.

of 1 m they are about the same. At the lowest sensor (level 6)thesilage pressure is about28kPa.Themeasured (bysubtraction) pressure from thecompaction equipment is about 2 kPa,more than an order of magnitude smaller than the two measured pressures thatwere subtracted. Theexperimental resultsat the lowest 3 levels, therefore, are unreliable. Keeping this inmind,it mustbe concludedthat the comparisons of simulatedwith experimental results at the upper three levels with awall-track distance of less than 1 m are the only ones of value.

At level 1 the ratio of simulated to experimentalpressurefora wall-track distance of 0.33 m (Fig. 3) is 1.2. The ratios atlevel 2 are 0.95,1.0, 1.31 for wall-track distances of 0.33 m,0.6 m, 1.0m,respectively. This goodagreement indicates thatthe Boussinesq equations (Eqs. 1 to 4) are a very useful toolfor estimatingwall pressures on a bunker silo wall fromcompacting equipment. Errors in the calculated pressures tend tobe on the conservative side, as was pointed out by Craig(1978).

PARAMETRIC STUDY

A parametric study of normal wall pressureswas carriedoutwiththe solutionprocedurebased on the Boussinesqformulae.The parameters that were considered were the wall-track dis-

CANADIAN AGRICULTURAL ENGINEERING Vol. 34, No. 1, JANUARY/FEBRUARY/MARCH 1992 85

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xZ3CO

2:orxu_

Xr-

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0 5 10

1

15

1

20

1

25

1

30 31

0 -

0

level 1

level 2

2 - 0

level 3

level 4

-

level 5

4 -•lo •

level 6

Fig. 4. Calculated and measured wall pressures due to a21 tonne bulldozer compaction vehicle stationed0.6 m from the wall.

tance, the depth and the horizontal distance from the centre ofthe track of a bulldozer. Clear distances between track andwall of 0.2,0.4,0.6,0.8,1.0,1.2,1.4,1.6,1.8,2.0,2.2 and 2.4m were considered with a wall slope of 80°. Silo wall slopesof90° (vertical), 85°, 75°, and 70° were used in analyses inwhich the track-wall clear distancewas 0.2 m. The studyalsoincluded the predictions of wall pressures due to a wheeledtractor with the same range of the parameters clear distanceand wall slope. As well, the orientation of the tractor withrespect to the silo wall was considered. The results are presented in this section.

Compaction wall pressures from tracked vehicles

Sixteen analyses were carried out to determinethe wall pressure resulting from compaction by a 21 tonne bulldozer. Thewall-track clear distance (referred to in the figures as cleardistance) and wall slope were the variables in the analyses.The wall pressure variation with depth and with the horizontaldistance from the centre of the track of the vehicle will bereported. The wall slope with the horizontal was 80° in theanalyses in which the clear distance was varied. In the fouranalyses in which the wall slope was varied the clear distancewasmaintained at 0.2 m. Thedimensionsand the weightof thedozer were the same as those of the dozer used in the full-scale

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10

_L_

15

L_

20

L_

25

1

30 35

level 1


experiment described in the previous section. The analyseswere carried out with 24 subdivisions of the contact area ofeach track. Therefore, the point load acting at the centre ofeachof the subdivisions was 4.35 kN; i.e., l/48th the weightof the bulldozer. The wall pressure was calculated at 1025points on the wall, arranged in a grid of 25 vertical and 41horizontal points. The normal wall pressure from compactionat eachpointon thewallsurfacewasobtained by summing thenormal wall pressures due to each of the 48 point loads.

Figures 7 and 8 show the normal wall pressures due tocompaction versus the distance from the centre of the track ofthe vehicle, for two clear distances, 0.2 and 0.4 m. In thesefigures the wall pressure variations at six depths are presented.

The results for the clear distance of 0.2 m are presented inFig. 7. The effect of the discrete surface load points can beseen from the curve at a depth of 0.2 m below surface. The wallpressure at that depth is almost a constant 28 kPa over adistance of 3.0 m, which equals the length of the tracks of thebulldozer. This uniformity of pressure is consistent with thecompaction pressures measured in the full-scale experimentreported by Zhao et al. (1989). The three transducers spaced0.91m apart at the top levelsdid not give appreciablydifferentwall pressures when the 21 tonne bulldozer was located symmetrically about the middle sensor.

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_1_

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level 1

level 2

35

level 3

level 4

level 5

level 6


Beyond the 3.0-m length of high pressure, the wall pressuredrops drastically. At a 2-m distance from the centre, the pressure is about 5 kPa, only 18% of the maximum. The maximumnormal wall pressure at the depth of 0.2 m is about 40% of thecontact pressure under the track of the bulldozer.

The maximum wall pressure at a depth 0.6 m in Fig. 7 isabout 11 kPa. The shape of the wall pressure diagram becomesflatter and smoother at greater depths. It is obvious that theeffect of the compaction bulldozer becomes less significantwith depth. At 3.0 m depth the maximumpressure is less than2kPa.

Figure8 showsthe wall normal pressurewhenthe bulldozeris 0.4 m awayfrom the wall, twice the clear distancein Fig.7.Except at the0.2-mdepth, the magnitudes of thepressures forall depths are greater than those in Fig. 7 by about 25%.Thewall pressureat a depth of 0.2 m, however, is less; the maximum is only 15kPa.

The results for clear distances of 0.6 m, 1.0 m and 2.0 mwere also studied. The magnitudes of the wall compactionpressures reduced by almost 50% as the clear distance increased from 1.0 m to 2.0 m. The effect of the compactionbulldozer is almost a uniform 4 kPa when the bulldozer is 2.0m away from the wall.

The normal wall pressure distributions with depth at thecentreof the trackare plotted in Figs. 9 and 10.Figure9 showspressures forcleardistances of0.2,0.4,0.6,0.8,1.0 and1.2 m.Figure 10shows thepressures forcleardistances of 1.4,1.6,1.8,2.0,2.2 and 2.4 m. The effect of the clear distance on thewall pressures is evident. At thecentre of the track themaximum wall pressure decreased from 28kPato4 kPaasthecleardistance increased from 0.2 m to 2.4 m. The position of thepeak wall pressure also shifts downward from 0.2m to 1.5 mfrom the silage surface as a result of the increase in thecleardistance. The decrease in pressure with depth is faster with thecompactor positioned close tothewall. This indicates theeffectof compaction is more localized near the surface when the

DEPTH m

D 0 2+ 0 60 1 0

A 1 4

X 2 2

V 3 0

NORMAL PRESSURE. kPa

35-t

30-

/ 25-

20-

15-

^^^to1

rf*""""*"-! 1 0 1 1 n3*

DIST FROM CENTRE, m

DOZER WEIGHT: 208 kN

CLEAR DIST.: 0.2m

Fig. 7. Calculated normal wall pressures due toa 21 tonne bulldozer compaction vehicle positioned 0.2 m from thewall.

CANADIAN AGRICULTURAL ENGINEERING Vol.34, No. 1, JANUARY/FEBRUARY/MARCH 1992 87

DEPTH, m

° 0.2♦ 0.6« 1.0

A 1.4x 2.2v 3.0


35 T

30--

20-

-B-U&

-1 0 1

DIST. FROM CENTRE, m


CLEAR DIST.: 0.4 m

Fig. 8. Calculated normal wall pressures due to a 21tonne bulldozercompaction vehicle positioned 0.4 m from the wall.

<Li.crZ)CO

o

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a

CELU>

4 -


35

CLEAR DIST. m

0.2

0.4

0.60.8

1.0

1.2


POSITION: CENTRE

Fig. 9. Calculated normal wall pressures versus depth atthe centre of a 21 tonne bulldozer compactionvehicle positioned at distances ranging from0.2 -1.2 m from the wall.

88

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4 -


10

I

15 20

L_

25

L_

30

1

35

CLEAR DIST. m

2.4


POSITION: CENTRE

Fig. 10. Calculatednormal wall pressures versus depth atthe centre of a 21 tonne bulldozer compactionvehicle positioned at distances ranging from1.4 - 2.4 m from the wall.

ZHAO and JOFRIET

compactor is closer to the wall. In general, the effect of compaction diminishes to a negligible level at depths over 2.0 m.

The vertical pressure diagram remains much the same for ahorizontal length approximately equal to that of the tracks ofthe bulldozer. Beyond that length, the wall pressures at alldepths is reduced considerably.

Table I. Maximum pressure due to compaction by a21 tonne bulldozer

Wall Slope 90° 85° 80° 75° 70°

Max. Pressure

(kPa) 26.1 27.3 28.3 29.1 29.8

Four more analyses were carried out to determine the wallpressures from compaction with the wall slope varying from70°to90°with thehorizontal. Themaximum pressures resulting from these analyses are displayed in Table I.

These maximum pressures caused by a 21 tonne bulldozeroccurred at a depth of 0.2 m from the silage surface and witha clear distance of 0.2 m. As in the previous analyses, theextent of the maximum pressure along the wall equals thelength of the tracks of the bulldozer. The results in Table Ishow that the maximum normal wall pressure varies fromabout 26 kPa for the vertical wall to about 30 kPa for the wallsloped 70° with the horizontal. The increase in maximumpressure as thewall slope changed from 90° to 85°, from 90°to 80°, from 90° to 75° and from 90° to 70° is 5%, 8%, 11%and 14%, respectively.

The Boussinesq formulae indicate that the maximum normal wall pressure is a linear function of the applied surfaceload and, therefore, of the vehicle weight. The length overwhich the wall pressure acts is about equal to the length of thetracks of the compactor. These two observations will allow thedetermination of wall pressures from tracked vehicles of different weight and track geometry.

Compaction wall pressures from wheeled vehicles

Thirty analyses were carried out to investigate the wall pressures that would result from compaction of the silage with awheeled vehicle. The distance between the vehicle and the

wall, the vehicle orientation and wall slope were the variablesin these analyses. The assumed arrangement of the wheels isshown in Fig. 11. The wheel loads used in the analyses were16 kN (gross tractor mass of 4600 kg, 4 wheels), selectedaccording to NRC (1983). Two point loads, 2.0 m apart representing two rear wheels of a tractor, were placed on the surfaceof the silage at six different distances from the wall surface.The calculations were carried out for two orientations of the

two wheels, one parallel to the wall surface (Fig. 1la) and oneperpendicular (Fig. 1lb). The silowallhada slopeof 80° withthe horizontal. As before, pressures were calculated at 1025points.

Figures 12 and 13 present the normal wall pressures versusthe horizontal distance from the centre of the wheels which are

oriented parallel to the wall (Fig. 1la). In Fig. 12, the pressuresare with the nearest wheel load placed 0.2 m from the face ofthe wall measured at the silage surface. This distance is referred to as clear distance in the figures. In Fig. 13 the loadposition is 0.4 m from the wall. The maximum wall pressure

rear wheels of a tractor

2 m- ^—^—&-

/top edge ofwall

v-center of

wall panel

wall dist.

(a) wheels parallel to wall surface

v\\\ \ w. ....Ml)* v//// /

rear wheels of a tractor

wall dist.

top edge of

-center of

wall panel

(b) wheels perpendicular to wall surface

Fig. 11. Tractor wheel orientations with respect to the silowall.

in Fig. 12 reached 26 kPa at 0.2 m depth; its location, ofcourse, coincides with the position of the loads. The base ofthe triangular-shaped pressure diagram is about 1.0 m. Themaximum wall pressure dropped rapidly to 5 kPa as the depthincreased to 0.6 m. At a depth of 1.0 m, it was insignificant.The maximum pressure in Fig. 13 is only about 9.0 kPa at 0.2m depth. At greater depths the pressures on the wall are lesssensitive to the distance the load is positioned from the wall.

Figure 14 shows the vertical variation of the normal wallpressure at the location of the wheel loads. Six pressure curvesare shown for six distances between the wall and the nearestwheel. As this point load moved from 0.2 m to 0.4 m themaximum wall pressure dropped from 26 kPa to 12 kPa, adecrease of 54%. The figure also shows that the influence ofcompaction becomes negligible below a depth of about 1.5 m.

Figures 15 and 16 display the profiles of normal wall pressures from two wheels stationed perpendicularly to the wallsurface (Fig. lib). In Fig. 15 the pressures are the result ofplacing the wheel loads 0.2 m from the face of the wall at thesilage surface. In Fig. 16 the loads act at a point 0.4 m from thewall. Compared to the wheel orientation in Fig. 1la, instead ofone peak there are two peak pressures, 2 m apart. This corresponds exactly to the two wheel load positions. In Fig. 15 themaximum value at a depth of 0.2 m is about 26 kPa, the sameas the maximum value shown in Fig. 12. Each wheel has a near

CANADIAN AGRICULTURAL ENGINEERING Vol. 34, No. 1, JANUARY/FEBRUARY/MARCH 1992


35tWHEEL LOAD: 16 kN

WHEEL DIST.: 2.0 m

WHEEL ORIENT.: PARALLEL

CLEAR DIST.: 0.2 m

f • l|l • f I l|l • f2 3 4

M ii I f I II • f I-4 -3 -2 -1 0 1


Fig. 12. Calculated normal wall pressures due to a 32-kN axle load compaction vehicle positioned 0.2 m from the wall.Axle perpendicular to wall.


DEPTH, m

0.2

0.6

1.0

1.4

2.2

3.0

y • ii i f i II I | I-4 -3 -2

35T

25

20

15

0 1

FROM CENTRE, m

WHEEL LOAD 16 kN

WHEEL DIST. 2.0 m

WHEEL ORIENT. PARALLEL

CLEAR DIST. 0.4 m

~»l« ' I • •!• • I •4

Fig. 13. Calculated normal wall pressures due to a 32-kN axle load compaction vehicle positioned 0.4 m from the wall.Axle perpendicular to wall.

triangular pressure diagram with a base of 1.0 m wide. Theinfluence of the compaction at a point midway between thewheels is 2 kPa, a value quite small compared to the peakpressure.

Figure 16 shows the six profiles of the normal wall pressures for six depths when the point loads are 0.4 m from thewall surface. The major influence of compaction is at a pointabout 2 m each side from the centre line of the vehicle.

Figure 17 presents the normal wall pressure distributionwith depth along a vertical line centred on one wheel load.The effects of depth and load distance from the wall areobvious in the figure. The maximum value reached 26 kPa forthe load applied 0.2 m from the wall; this maximum decreased

90

to 12 kPa (54% decrease) as the distance increased to 0.4 m.The compaction effect diminished to a negligible level belowa depth of 1.5 m. The pressure diagrams in Figs. 14 and 17 arevery similar in shape and magnitude. It is therefore sufficientto study only the loading effect of the wheel closest to the wall.If the wheel spacing is so small to cause significant superposition the separate effects of two single wheel loads can simplybe added.

Using the same tractor specifications, the normal wall pressures due to the weight of the tractor were calculated fordifferent wall slopes. The maximum compaction wall pressures at a depth of 0.2 m from the silage surface are presented

ZHAO and JOFRIET

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WALL DIST..

0.

0.

0.

0.

1.

1.

WHEEL LOAD: 16 kN

WHEEL DIST.: 2.0 m

WHEEL ORIENT: PARALLEL

Fig. 14. Calculated normal wall pressures versus depth atthe centre of a 32-kN axle load compactionvehicle positioned at distances ranging from0.2 -1.2 m from the wall. Axle perpendicular towall.

in Table II. The clear distance used in calculating the maximum values was 0.2 m.

As expected, the maximum normal wall pressure was theleast, 21.7 kPa, for a vertical wall and the largest, 30.1 kPa, fora wall with a slope of 70°. The changes in the maximum wallpressure for thechange in the wallslope from 90°to 85°, from90° to 80°, from 90° to 75° and from 90° to 70° were 9%, 19%,29%, and 39%, respectively. The effect of wall slope appearsto be much greater for a wheeled vehicle than for a trackedvehicle.

For compaction with tractors of different weight, the maximum wall pressures can be obtained by proportioning thepressures up or down since the wall pressure varies linearlywith wheel load. The base of the triangular wall pressuredistribution near the surface is approximately 1.0 m regardlessof wheel load.

DESIGN CONSIDERATIONS

For design purposes it is necessary to have a simple designformula. Therefore, the difficult to handle distributed normalwall pressures were summed to a resultant concentrated force

in the caseof wheel loads and to a line load for trackedvehicleloads. This was done by an approximate integration of thevolume enclosed by the horizontal and vertical pressure diagrams. Also, it isconvenient to use asimilar concept to that ofthe pressure ratio used for silage pressures (Zhao et al. 1989).Here, a ratio of the resultant of wall pressure to the appliedsurface load is appropriate. The ratio will be referred to asforce ratio.

The normal wall pressures due to the compaction by a 21tonne bulldozer are shown versus vertical depth in Fig. 9 andversus horizontal distance from the centre of the track in Fig.7. The total force on the track with a contact area of 3.0 m x0.5 m is 104kN. The appliedresultant line loadon the surfaceof the silage is therefore:

V = (104 kN)/(3.0 m) = 34.7 kN/m

The maximum wall pressure for a clearwall-trackdistance of0.2 m is 28 kPa, 40% of the pressure under the tracks of thebulldozer. The prismatic pressure diagram canbe integrated toa resultantline load(Fig. 9). The areais simplified to a trianglewith a peakof 28 kPa anda base of about 1.15 m, so:

L = (28 kPa>(1.15 m/2) = 16 kN/m

This wall line load acts on a length equal to that of the track(3.0 m). The ratioof the normal wall line load to the appliedline load on the surface (i.e. the force ratio) at the closestwall-track distance is:

K = L/L/ = (16 kN/m)/(34.7 kN/m) = 0.46

For a 16-kN wheel load placed 0.2 m from the wall theintegrated resultant force is 7.8 kN acting normal to the wallabout 0.3 m below the surface of the silage. Similarly, forcesof 3.3 kN and 1.9 kN resulted from the same point load of 16kN acting at distances of 0.4 m and 0.6 m from the wall,respectively.

The ratios of the three resultants of the normal pressure tothe applied surfacevertical wheel loads at distancesof0.2,0.4m, and 0.6 m (force ratios) are 0.49, 0.21 and 0.12, respectively. The highest force ratio (0.49) is very similar to thatfound for the tracked vehicle placed similarly close to the wall.

Esmay et al. (1956) reported that the maximum wall pressure acting on a 0.3-m by 3-m horizontal plank, due tocompaction by a tractor with 11 kN wheel loads, varied from6 kPa to 7.2 kPa. A concentrated force due to compaction canbe computed as:

P=(0.3 m)(3 m)(6.0 kN/m2) =5.4 kN

and

P=(0.3 m)(3 m)(7.2 kN/m2) =6.48 kN

Dividing the forces by the wheel load of 11 kN gives the rangeof the force ratio as 0.49 < K < 0.59.

Messer and Hawkins (1977) recorded a maximum wallpressure equivalent to a point load of 5.9 kN, caused by a5.4tonne (53-kN) tractor. If the weight of the tractor distributesitself equally among the four wheels, the force ratio is:

K = (5.9 kN)/(0.25-53 kN) = 0.45

If the weight of the tractor is considered to be carriedonly bythe two rear wheels, the ratio is 0.23. Therefore, it is reason-



WHEEL LOAD:

WHEEL DIST.:

WHEEL ORIENT.:

CLEAR DIST.:

16 kN

2.0 m

PERPEND.

0.2 m


Fig. 15. Calculated normalwall pressures due to a 32-kN axle load compaction vehicle positioned 0.2m from the wall.Axle parallel to wall.


30

20--

15-

WHEEL LOAD: 16 kN

WHEEL DIST.: 2.0 m

WHEEL ORIENT.: PERPEND.

CLEAR DIST.: 0.4 m

-1 0

DIST. FROM CENTRE.

Fig. 16. Calculated normal wall pressures due to a 32-kN axle load compaction vehicle positioned 0.4 m from the wall.Axle parallel to wall.

able to say that the force ratio, K, from Messer and Hawkins'results was somewhere between 0.23 to 0.45, and probablycloser to 0.45 than to 0.23.

Kangro (1986) measured a maximum compaction wall loadof 13.3 kN from a 7.5 tonne (74-kN) tractor. An equal four-wheel weight distribution gives a force ratio of:

K = (13.3 kN)/(0.25-74 kN) = 0.72

92

A two-wheel weight distribution gives a ratio of 0.36. Therange for the force ratio from Kangro's results is therefore 0.36to 0.72.

A comparison of the force ratio of 0.41 computed by theBoussinesq formulae for a vertical wall (Table II) agrees verywell with the ratios from the experiments carried out by others.

It is evident that the wall loading becomes extremely highas the compactor moves within 0.5 m of the wall. This fact isrecognized in the British design code BS 5502 (BSI 1987).

ZHAO and JOFRIET

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WALL DIST.

•

+

o

A

X

V

WHEEL LOAD: 16 kN

WHEEL DIST.: 2.0 m

WHEEL ORIENT: PERPEND.

Fig. 17. Calculated normal wall pressures versus depth atthe centre of a 32-kN axle load compactionvehicle positioned at distances ranging from0.2 -1.2 m from the wall. Axle parallel to wall.

Table II. Maximum pressure due a 16-kN wheel load

Wall Slope 90° 85° 80° 75° 70°

Max. Pressure

(kPa) 21.7 23.7 25.8 27.8 30.1

Compaction

Force Ratio 0.41 0.45 0.49 0.53 0.57

The Canadian Farm Building Code (NRC 1983) suggests that30% of the wheel load is imposed normal to the wall which isabout equal to the calculated fraction for a distance from thewall of 0.3 m.

SUMMARY AND CONCLUSIONS

The results of the analyses can be summarized as:

l.The calculated maximum normal wall pressure on a wallsloped 80° withthehorizontal dueto compaction bya 21tonne bulldozer was 28 kPa, about 40% of the pressure

under the tracks of the bulldozer when the nearest trackwas 0.2 m from the wall.

2. The vertical pressure diagrams for different positionsofthe tracked compactor from the wall, remained almostunchangedover die length of the tracks. Beyond that,theeffect of compactiondecreased drastically. The effect ofcompaction became negligible at depths greater 2.0 mfrom the surface.

3.The maximum normal pressure onawall sloped 80° withthe horizontal due to a wheel load of 16 kN had a maximum value of 26 kPa when the wheel load was 0.2 mfrom the face of the wall. The force ratio of 0.41 for avertical wall, computed with the Boussinesq formulae,agreed well with those computed from experiments carried out by others.

4. A wheel load acting less than 0.5 m from the wall causedextremely high normal wall loading. About 50% of thewheel load was imposed on the wall when the wheel loadacted 0.2 m from the wall. The compaction pressure actedon an area about 1 x 1 m.

5. Maximum wall pressure from compaction by trackedvehicles was 14% greater for awallsloped 70°than for avertical wall. For wheeled vehicles it was 39% greater.

6. The influence of compaction was localized within the top2 m of the silage. At greater depths the compaction effectwas negligible.

Conclusions reached from this work are:

1. The wall pressures due to the weight of compactionvehicles can be estimated quite well by the Boussinesqformulae.

2. The maximum normal wall pressure due to the weight ofa tracked compaction vehicle can be as high as 40% ofthe pressure under the tracks.

3. The effect of tracked compaction vehicle on the wallextends to a horizontal length equal to the length of thetracks; it can be approximated by a line load of the samelength, acting normal to the wall.

4. About 50% of the wheel load of a wheeled compactionvehicle is imposed normal to the wall.

5. The wall pressure caused by a wheel point load takes aprismatic shape which acts on an area about 1 m x 1 m.

6. A wheel point load acted 2 m or more away from the wallhas little effect on the wall pressures.

7. The maximum wall pressure due to compaction increaseswith the decrease of the wall slope with the horizontal.

ACKNOWLEDGEMENT

Funds provided by Alberta Agriculture, the Ontario Ministryof Agriculture and Food, and the Natural Sciences and Engineering Council of Canada made this project possible.

REFERENCES

Boussinesq, J. 1883. Application des Potentials a L'Etude deVEquilibre et due Mouvement des Solides Elastiques.Paris, France: Gauthier-Villars.


Boresi, A.P. and K.P. Chong. 1987. Elasticity in EngineeringMechanics. New York, NY: Elsevier Science Publishers.

BSI. 1987. BS 5502, Code ofPractice For Design ofBuildingsand Structures for Agriculture. London, UK: BritishStandards Institution.

Craig, R.F. 1978. Soil Mechanics. New York, NY: VanNostrandReinhold Company.

Esmay, M.L., D.B. Brooker and J.S. McKibben. 1956. Designof above-ground horizontal silos. AgriculturalEngineering 37(5):325-327,333.

Kangro, A. 1986. Load measurements in bunker silos forsilage. Report 48. Division of Agricultural BuildingTechnology, Swedish University of Agricultural Science,Lund, Sweden.

Messer, HJ.M. and J.C. Hawkins. 1977. The loads exerted bygrass silage on bunker silowalls. Journal ofAgriculturalEngineering Research 22:327-339.

94

NRC. 1983. Canadian Farm Building Code, - NRCC No.21312.Ottawa,ON: NationalResearchCouncil ofCanada.

Westergaard, H.M. 1938. A problem of elasticity suggestedby a problem in soil mechanics: A soft materialreinforcedby numerous strong horizontal sheets. In Mechanics ofSolids, ed. S. Timoshenko. New York, NY: Macmillan.

Zhao, Q. 1990. Bunker (horizontal) wall loads. UnpublishedPh.D. thesis, School of Engineering, University ofGuelph,Guelph, ON.

Zhao, Q., J.C. Jofriet, D. Darby and H. Bellman. 1989. Bunkersilo wall loads by finite element analysis. ASAEPaper No.89-4010. St. Joseph, MI: ASAE.

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