FRICTION PROPERTIES OF FERTILIZERS

E.B. Moysey and Shane Hiltz

AgriculturalEngineeringDepartment, University of Saskatchewan, Saskatoon, Sask. S7N 0W0

Received 20 August 1984, accepted 11 June 1985

Moysey, E.B. and Shane Hiltz. 1985. Friction properties of fertilizers. Can. Agric. Eng. 27: 79-84.

The internal friction angleof four fertilizers, as determined by the standard shearbox test, is considerably affectedbythepacking arrangement of theparticles. Angleofrepose approximates theminimum frictionanglemeasured by theshearboxmethod, but thefabric created bydensepacking canproduce considerably largerangles.Loadon the samplehadlittleeffect on the friction angle, but an increase in relative humidity increased the friction slightly. Coefficients of friction offertilizers on common wall materials are appreciablylarger than for cereal grains.

INTRODUCTION

Farmers in western Canada are usingmuch more commercial fertilizer than theydid 20 yr ago. Consequently, storage offertilizer in bulk is now common both in

small towns and on farms. Knowledge ofthe frictional properties of fertilizers isneeded if bulk storages are to be designedby engineering methods. Common formulae for estimating pressures in granularmaterials depend on the internal frictionangle, the co-efficient of friction of thegranular medium on the bin walls and theratio of lateral to vertical pressure. Thisratio is usually calculated from the internalfriction angle, and sometimes from boththe internal and wall friction angles. Information on these is therefore essential to

pressure calculations.

LITERATURE REVIEW

Friction properties are of major importance in the study of soil mechanics, andthere is a great body of technical literaturein this area. Soils come in a variety ofsizes, shapes, densities and moisture contents, much more so than fertilizers, so

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presumably the properties of fertilizersshould extend over a narrower range. Soilmechanics studies of interest include the

work of Persons (1936), in which he foundthat the internal friction angle in sand wasessentially independent of the normalpressure applied during a test. Casagrande(1936) noted that during tests in a standardshear box a loose sample of sand consolidated but a dense sample expanded.Roscoe et al. (1958) suggested what whena sample expands or settles during a sheartest, some of the work apparently done inshearing the sample is actually involved inraising or lowering the applied normalload. A correction must therefore be made

to the observed shear force to account for

this. Rowe et al. (1964) made a furtherrefinement to correct for the friction work

in the vertical direction. When both of

these corrections are made we are presumably left with the value of the minimumfriction force in the direction of sliding.Rowe et al. (1964) state that use of theseequations permits separation of the energycomponents so that resistance due to friction can be distinguished from that due to

(a)

Figure1. Three methods of determining angle of repose.

CANADIAN AGRICULTURAL ENGINEERING, VOL. 27, NO. 2, FALL 1985

the structure or fabric created by interlocking of the individual grains.

Packing arrangement of particles andthe associated differences in bulk densities

will produce some variation in the internalfriction angle. When spheres are stackedin a square arrangement there will be sixpoints of contact on each sphere. For thedensest possible hexagonal packing, 12points of contact are possible. The theoretical porosity is 47.6% in the first caseand 25.9% in the second. If one imaginesspheres sliding over one another as theywould during a shear box test, the initialpacking arrangement could be expected tohave a substantial effect on the apparentfriction force. When packed in the densehexagonal arrangement, each spherewould have to slide up and over to get pastits neighbors, while with the less densesquare packing there should be much lessresistance to sliding. Oda (1977) showedthat the internal friction angle for glassbeads could be related to the averagenumber of contacts per bead and to theuniformity of the number of contacts.

It has often been suggested that the

(c)

79

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The shear test apparatus is equippedwith a gearbox on the drive system whichpermits a wide range of shear rates to beemployed. Most of our tests were conducted at a shear rate of 0.4 mm/min.

A series of tests was also run to determine thecoefficientof friction of twotypesof fertilizer on various bin surface materials. The test procedure was the same asfor internal friction except that the bottomof the shear box was shimmed up so thatthe surface under study was level with theshear plane.

The voltage outputs from the LVDT andthe forcetransducer werecollectedusingaFluke datalogger and a Hewlett-Packard

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Figure 2. Schematic of shearbox apparatus.

angle of repose of a granular material is agood measure of the internal frictionangle. The difficulty with this is that thereare a number of ways of measuring theangle of repose. Figure 1(a) shows themethod used by Fowler and Wyatt (1960).In this case, a conical pile of the material isleft on the circular platform. Figure 1(b)shows the reverse situation, where a conicaldepression is left in the material. Sing-ley and Chapman (1982) analyzed theforces on the particles at the surface ofsuchacone and showed that theoretically asteeper angle of repose would be measuredwith the apparatus of Fig. 1(b) than that ofFig. 1(a). They also showed that the surface will be slightly curved near the outlet.A third method of measuring angle ofrepose is shown in Fig. 1(c). In this caseone end of a box is made removable so that

a plane surface is produced, rather than acone. It has also been suggested that theemptying angle of repose is largerthan thefilling or piling angle, e.g. Stahl (1950),which adds to the confusion.

APPARATUS AND PROCEDURE

Shear Box Tests

To determine the angle of internal friction, a Wykeham-Farrance standard sheartest apparatus was used. Figure 2 is a schematic of the shearbox; it is 100mm squareand the depth of fertilizer was 30 mm. Theshear plane was 5.5 mm from the bottom.The top and bottom of the shear box wereof porous sandstone to prevent the sampleslipping at the boundaries. The standardshear apparatus uses a proving ring anddial gauge to measure force and a dialgauge to measure consolidation or expansion of the sample during shear. To recordand process data more effectively thesefeatures were deleted. Force was measured

with a strain-gauge-type force transducer(Interface model SSM-500) and settlement/expansion of the sample by a linearvariable differential transformer (LVDT).

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HORIZONTAL DISPLACEMENT, mmTypical shearresults for monoammonium phosphate; loose fill, 430N normal load.

CANADIAN AGRICULTURAL ENGINEERING, VOL. 27, NO. 2, FALL 1985

minicomputer. The system was programmed to take a set of readings every 15 sec.Other programs were used to convert themillivolt readings to force and to outputthe results in tabular and graphical form.

All tests were performed in a controlledenvironment room, at a temperature of20°C and the desired relative humidity.

Previous experience with cereal grainshad shown that method of filling the shearbox affected the measured friction angle.To obtain a very loose fill, the outlet of afunnel was placed on the bottom of theshear box, the funnel was filled with fertilizer and then slowly raised. A sprinkle fillsimilar to what might be obtained with agrain spreader was achieved by using ascreen with 6-mm mesh. The screen was

mounted 150 mm above the box and the

fertilizer was poured slowly from 150 mmabove the screen. This caused the particlesto bounce around and come to rest in a

preferred orientation.

Angle of ReposeEmptying angle of repose was deter

mined using a rectangular box made fromplexiglas, similar to Fig. 1(c). Box dimensions were 300 x 200 x 250 mm. Lines

scribed on the sides of the box at angles of27-36 degrees in three-degree incrementspermitted estimation of the angle to withinabout one-half degree.

The filling angle of repose was measured using a simple scissors device fastened together with a bolt and wing nut. Acone of fertilizer was formed on the floor

using a funnel with a 20-mm dischargeopening. The hopper of the funnel waskept full until a pile large enough for accurate measurement had formed. The outlet

of the funnel was 800 mm above the floor

for all tests. The scissors device was

carefully placed on the cone of fertilizer,clamped and removed. The angle couldthen be read from a large protractor. Readings were repeatable within 1or 2 degrees.

RESULTS AND DISCUSSION

Shear Box Tests

Results typical of shear box tests onmonoammonium phosphate, 11-48-0, areshown in Figs. 3 and 4, Fig. 3 being forloose fill and Fig. 4 for sprinkle fill. Theupper half of the diagram shows verticalmovement of the load on the sample ineach case, and the lower half shows shearforce as the two halves of the box were

displaced relative to one another. Note thatthe one curve shows the measured force

whereas the second curve is for the force

corrected according to the method ofRoscoe et al. (1958). The forces increasequickly during the first 2 mm of displace-

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Figure 4. Typical shear results for monoammonium phosphate; sprinkle fill, 430N normal load.

ment but are essentially constant between3 and 4 mm. The loose sample settledslightly and then expanded during shear, asshown in the top half of the figure. Thedense sample expanded much morerapidly, as expected, which resulted in agreater difference between the measuredand corrected curves (Fig. 4). If the tabulated values of shear force are averagedbetween the 3- and 4-mm displacementsand divided by the normal load of 430 N,the coefficient of friction is obtained; taking the inverse tangent gives the frictionangle. For the tests shown in Figs. 3 and 4these values are 39 and 33 for the loose fill

and 50 and 41 for the sprinkle fill. Averaged values for several tests are given in

Table I.

The normal load of 430 N used in the

previous example gives a pressure of43 kPa, well within the range that might befound in a large bin of fertilizer. In order toestablish whether magnitude of the normalpressure had any effect on the frictionangle, a number of tests were run at pressures of 33 and 53 kPa. Results are given inTable I. There was essentially no difference between the values for loose fill

and only a very slight difference for sprinkle fill. It was therefore concluded that

normal pressure, within this range, atleast, had minimal effect on the shear boxresults.

Relative humidity of the ambient air is a

CANADIAN AGRICULTURAL ENGINEERING, VOL. 27, NO. 2, FALL 1985

TABLE I. EFFECT OF PRESSURE ON INTERNAL FRICTION ANGLE OFMONOAMMONIUM PHOSPHATE, 11-48-0

No. of runs Fill method

Internal friction angleNormal pressure

(kPa) ObservedCorrected(Roscoe)

334353

5

4

5

4

4

4

LooseLooseLoose

Mean

SprinkleSprinkleSprinkle

Mean

39.841.440.1

33.534.434.4

33

4354

40.4

49.649.1

50.4

34.1

41.1

40.3

41.8

49.7 41.1

TABLE II. EFFECT OF PRESSURE AND RELATIVE HUMIDITY ON THE INTERNALFRICTION ANGLE OF UREA (48-0-0)

Pressure

(kPa)

3333

3333

3333

3333

43

43

53

53

Relativehumidity

5555

6565

7575

7878

6565

65

65

No. of

runs

Internal friction angle

Fill method Observed

LooseSprinkle

33.846.2

Loose

Sprinkle34.549.5

LooseSprinkle

38.249.4

LooseSprinkle

36.547.4

Loose

Sprinkle36.548.1

Loose

Sprinkle35.848.8

Corrected(Roscoe)

29.837.3

31.640.7

32.540.6

32.040.2

30.139.2

30.8

40.0

TABLE IH. INTERNAL FRICTION ANGLES FOR FOUR TYPES OF FERTILIZERS

Internal friction angle

Fertilizer PressureNo. of

runs Fill method ObservedCorrected(Roscoe)

Potash0-0-60

4343

22

LooseSprinkle

38.0

51.732.843.1

Amm. phos.16-20-0-14

4343

22

LooseSprinkle

35.346.7

29.836.2

Monoamm. ph.11-48-0

allall

14

12Loose

Sprinkle40.4

49.734.141.1

Urea48-0-0

allall

10

11LooseSprinkle

35.748.4

30.939.6

TABLE IV. ANGLES OF REPOSE COMPARED TO INTERNAL FRICTION ANGLES

Angle of repose Internal friction angle (corr.)

Fertilizer Piling Emptying Loose Sprinkle

16-20-0 33 33 29.8 36.2

11-48-0 35 33.5 34.1 41.1

48-0-0 36 36.5 30.9 39.6

0-0-60 33 31.5 32.8 43.1

concern in the storage of some types offertilizer, particularly urea. For this reasonshear box tests on urea were conducted atfour levels of humidity as well as at threenormal pressures. Results are shown in

Table II. Above a relative humidity of 78%the particles soften, so these values werenot included in the average shown in thenext table. Values in Table II indicate that

the friction angle increases slightly as the

relative humidity increases from 55 to75%, but only slightly.

Some friction angle tests were alsodone on potash, 0-0-60, and on ammonium phosphate sulphate, 16-20-0. Resultsof these tests are shown in Table III, whichincludes a summary of the data in Tables Iand II.

The striking feature of all the shear boxresults is the marked difference thatmethod of fill has on the measured frictionangle. Sprinkle fill consistently gave friction angles 9-13 degrees larger than loosefill. The method of fill has more effect thanthe type of fertilizer; measured values forall types with sprinkle fill were about 50degrees, even though there was a decideddifference in particle shape. The sampleofurea used was a prill form, essentiallyspherical in shape, whereas the potash wasa crushed product, with long, narrow,angular particles. When the friction angleis corrected for vertical movement of thenormal load according to the Roscoemethod, a considerably smaller value isobtained, but the angle for sprinkle is stillconsistently greater than for loose fill. Afurther correction using the method ofRowe et al. (1964) reduces the angles butdoes not completely eliminate the difference between methods of fill. For exam

ple, in the 11-48-0tests, the angles go from40 to 34.4 to 30.8 with loose fill as the two

corrections are made. With sprinkle fill theangles go from 49.5 to 41 to 32. Thissuggests that the true friction angle forlarge flat pieces of ammonium phosphatewould be 31 or 32 degrees but when particles are packed together in a densearrangement, the effective friction anglecan be as high as 49 degrees.

Angle of ReposeTable IV shows results of the experi

ments on measuring angle of repose duringfilling and emptying, along with internalfriction angle from the shear box tests,corrected by the Roscoe method. Since theprocedure for filling angle was by pouring,a loose fill was also used for the emptyingangle tests. The two angles are so close asto be within the limits of experimentalerror. They are also remarkably close tothe corrected shear box angle for loose fill,with the exception of urea. This is whatone would expect: angle of repose appliesto a free surface where the fabric generatedby interlocking of particles has little or noeffect. Within a mass of particles subjected to pressure in two or more directions, the fabric or structure will have amore pronounced influence and may considerably increase the apparent friction.

82 CANADIAN AGRICULTURAL ENGINEERING, VOL. 27, NO. 2, FALL 1985

Wall Friction

Results of surface friction tests on urea

(48-0-0) and monoammonium phosphate(11-48-0) are shown in Table V. The friction coefficient for urea was lower in all

cases, perhaps because of the difference inshape and apparent roughness of the twofertilizers. If a surface is very rough, sliding will presumably occur within the granular mass, a small distance from thesurface, so the coefficient of friction of thefertilizer on itself should be the upperbound. Painted plywood had the largestcoefficient of those tested, and it approximated this limit. The value for polyethylene was larger than expected,possibly because of the softness of thebacking. In previous tests on wheat,coefficients of approximately 0.35 for galvanized steel and 0.40 for wood were mea

sured; values for oilseeds were lower still.Lateral pressures on the walls of deep

bins are usually calculated by Janssen'sformula, which states that the pressurevaries directly as the unit weight andhydraulic radius, but inversely as the wallfriction coefficient. A large value for thiscoefficient is therefore desirable from this

standpoint.

Bulk DensityMeasurement of bulk density is com

monly made in the industry by filling aone-cubic-foot box from a funnel mounted

6 inches above the top of the box. Thedischarge opening of the funnel is 3 inchesin diameter. Table VI shows values from an

industry source, presumably determinedin the above manner, as well as our measurements. Loose and sprinkle fills wereobtained in the manner previously described. Vibrated fill was produced using asieve shaker with a frequency of 60 Hz.Samples were shaken for 30 sec. Results inTable VI show that industry values compare best with our loose fill. Vibrating thesample increased the density by about 13%for both potash and 11-48-0, compared toloose fill. Sprinkle fill increased the density of 11-48-0by 11% but for potash, only4%. This difference is no doubt due to the

size and shape of particles. Previous workhas shown that sprinkling increases thebulk density by about 7% compared toloose fill if the particles are reasonablyuniform in size and shape, but by as muchas 14% in an ungraded sand. Crushedpotash particles, as previously stated, arelong, narrow, angular and irregular inshape and apparently did not fall into acompact arrangement due to sprinklingaction.

An increase in bulk density should presumably cause an increase in wall pres-

TABLE V. COEFFICIENT OF FRICTION OF TWO FERTILIZERS ON BIN WALLMATERIALS

Type of fertilizer

Surface

Urea

48-0-0

Monoamm. phosphate11-48-0

Galvanized steel sheet 0.52 0.62

Plywood, parallel to grainSmooth

Rough0.44

0.530.53

0.57

Oil-base paint on plywood 0.60 0.71

Polyethylene over plywood 0.48 0.60

Fiberglas-reinforced plastic 0.44 0.67

Tangent of internal friction angleloose fill, Roscoe corrected 0.60 0.68

TABLE VI. BULK DENSITY OF SOME FERTILIZERS

Bulk density

Type of fertilizer Loose SprinkleSprinklevibrated Industry

11-48-0 940 1040 1040 960

34-0-0 prills34-0-0 mix

824

845

907

945

922

976

16-20-0 934 1008 1048 930

27-14-0 mix 924 1002 1030

0-0-60 1062 1100 1210 1070

sure; however, the accompanying increasein internal friction may more than offsetthis effect.

CONCLUSIONS

When the standard shear box is used to

determine the internal friction angle ingranular materials, care must be taken ininterpreting the results. The gross measured value is likely to be considerablygreater than the angle of repose found byletting the material flow out one end of abox. If a correction is made for dilation of

the sample during shear, the angle will beclose to the angle of repose. For structuraldesign purposes, this minimum frictionangle would represent the worst condition,since it implies a large ratio of lateral tovertical pressure. In many situations theeffective angle of internal friction will beseveral degrees larger than the angle ofrepose, and this reduces the calculatedwall pressure. Specifically:

(1) Method of filling the shear box hada pronounced effect on friction angle. Filling with a sprinkling action, as occurswhen using a grain spreader, produced amore dense fill with more intimate contactbetween particles, resulting in larger friction angles than if a poured or loose fill wasused.

(2) Particle shape has less effect onfriction angle than expected. There waslittle difference between fertilizers con

sisting of spherical particles and those withrough, angular surfaces, particularly at thehigher bulk densities.

(3) Coefficients of friction of fertilizerson common wall materials are appreciablylarger than for wheat on these materials.Calculated wall pressures will therefore beslightly less with most fertilizers than withwheat, even though the bulk densities aregreater.

(4) Pressures calculated using angle ofrepose as the friction angle will likely overestimate lateral pressure and underestimate vertical pressure.

(5) For the one fertilizer tested,increasing the relative humidity from 55 to75% increased the friction angle onlyslightly.

REFERENCES

CASAGRANDE, A. 1936. Notes on theshearing resistance and the stability of cohe-sionless soils. Proceedings of InternationalConference on Soil Mechanics and Foundation Engineering. Harvard University,pp. 55-60.

FOWLER, A.T. and F.A. WYATT. 1960. Theeffect of moisture content on the angle ofrepose of granular solids. Aust. J. Chem.Eng. June pp. 5-8.

ODA,M. 1977. Co-ordination number and itsrelation to shear strength of granular materials. Soils and Foundations 17:2:29-42.

PARSONS, JAMES D. 1963. Progress reporton an investigation of the shearing resis-

CANADIAN AGRICULTURAL ENGINEERING, VOL. 27, NO. 2, FALL 1985 83

tance of cohesionless soils. Proceedings of Geotechnique 8:22-53. 1982. The flow of particulate materials.International Conference onSoil Mechanics ROWE, PW, L. BARDEN, and l.K. LEE. Trans. ASAE (Am. Soc. Agric. Eng.)and Foundation Engineering. Harvard Uni- 1964. Energycomponentsduringthe triax- 25:1360-1373.versity. pp. 282-285. ialcell anddirect shear tests. Geotechnique STAHL, BENTON M. 1950. Grain bin

ROSCOE, K.H., A.N. SCHOFIELD, andC.P 14:247-261. requirements. U.S. Department of Agri-WROTH. 1958. On the yielding of soils. SINGLEY, MARK E. and R.V. CHAPLIN. culture, Washington, D.C. Circ. 835.

84 CANADIAN AGRICULTURAL ENGINEERING, VOL. 27, NO. 2, FALL 1985