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2011

Development and validation of calibrationmethods for discrete element modellingAndrew GrimaUniversity of Wollongong, agrima@uow.edu.au

Peter W. WypychUniversity of Wollongong, peter_wypych@uow.edu.au

http://ro.uow.edu.au/engpapers/2690

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Publication DetailsGrima, A. Phillip. Wypych, P. Wilhelm. (2011). Development and validation of calibration methods for discrete element modelling.Granular Matter, 13 (2), 127-132. >

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Granular Matter (2011) 13:127132DOI 10.1007/s10035-010-0197-4

Development and validation of calibration methods for discreteelement modelling

Andrew Phillip Grima Peter Wilhelm Wypych

Received: 26 February 2010 / Published online: 23 July 2010 Springer-Verlag 2010

Abstract Discrete element method (DEM) is proving tobe a reliable and increasingly used tool to study and pre-dict the behaviour of granular materials. Numerous particle-scale mechanisms influence the bulk behaviour and flow ofbulk materials. It is important that the relevant measurableinput parameters for discrete element models be measured bylaboratory equipment or determined by physical calibrationexperiments for rational results. This paper describes someof the bench-scale experiments that have been developedto calibrate the DEM simulations to reflect actual dynamicbehaviour. Relevant parameters such as static and rollingcoefficients of friction, coefficient of restitution and inter-particle cohesion forces from the presence of liquid bridgeshave been investigated to model the bulk behaviour of dry andmoist granular materials. To validate the DEM models, theresults have been checked against experimental slump testsand hopper discharge experiments to quantitatively comparethe poured and drained angles of repose and solids mass flowrate. The calibration techniques presented have the capabilityto be scaled to model and fine tune DEM parameters of gran-ular materials of varying length scales to obtain equivalentstatic and dynamic behaviour.

Keywords Discrete element method Non-spherical Calibration Angle of repose Cohesion

A. P. Grima (B) P. W. WypychCentre for Bulk Solids and Particulate Technologies,Faculty of Engineering, University of Wollongong,Northfields Avenue, Wollongong, NSW, 2522, Australiae-mail: a.p.grima@gmail.com; apg037@uow.edu.au

P. W. Wypyche-mail: wypych@uow.edu.au

1 Introduction

The understanding of granular flows is of great importancein the industries that rely on bulk materials handling andprocessing. Continuous improvement and innovation in com-puter simulation software to analyse the performance of com-plex systems handling difficult granular products is requiredto improve process efficiency, reliability and assist in mini-mising the amount of waste material. Discrete element mod-elling is gaining interest in many industrial applications as avaluable numerical design and trouble-shooting tool for engi-neers. However, methods to accurately calibrate and numer-ically quantify the bulk mechanical behaviour of granularmaterials from measured properties are still a formidable taskwith many suspicions about the validity of measured param-eters and the subsequent simulations.

There are numerous validated continuum methods whichhave proven to be accurate and reliable over the years tostudy confined and unconfined granular flow. Unlike conven-tional continuum mechanics, DEM can be time consuming toset up detailed models and can be limited by computationalresources, which restricts the number of particles and thesize of a system that can be analysed. The distinct advantageof DEM is the ability to model individual particle dynam-ics/transients and local interactions with other particles andequipment surfaces. The DEM code has advanced signifi-cantly to have the ability to model irregular particles of vary-ing size distribution and mechanical properties. Non-contactparticle forces such as capillary forces from liquid bridges[1] have successfully been incorporated into the DEM codeto model a vast range of materials from dry fine powdersto wet granular products. Numerous calibration and valida-tion techniques have been previously investigated includinggranular pile formation [2] and direct shear tests [1,3]. Coet-zee and Els [3] have examined various techniques to validate

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128 A. P. Grima, P. W. Wypych

and select appropriate DEM model parameters to success-fully model granular flow. This paper investigates alternativesimple bench-scale experiments to directly tune or cali-brate DEM model parameters and optimise computationaltime by scaling methods.

2 Bulk material properties determination

Determination of key parameters of a bulk material is essen-tial when it comes to the analysis of granular flow using anynumerical method. For this investigation various tests wereconducted on dry and wet washed coal with a top size of 4 mm.These tests involved evaluating the particle size distribution(Fig. 1), solid and loose-poured bulk densities, particle shape,coefficient of restitution (CoR), static friction angle for parti-cle-to-particle and particle-to-boundary interactions, tensilestrength and bulk compressibility. Some of the experimentalparameters are listed in Table 1. The CoR has been determinedusing a high-speed camera to analyse the velocity just beforeand after impact as shown in [4]. Two reasonably flat particlesof varying size were placed securely on a plane and inclinedto the point of slippage to approximate the static friction anglebetween particles and likewise for a boundary material.

0

20

40

60

80

100

0 2 4 6 8 10

Minor Particle Diameter (mm)

% U

nder

size

Exp

Particle A - DEM

Particle B - DEM

Note: based on mass % for Exp

Fig. 1 Particle size distribution of washed coal and DEM scaled par-ticles

Table 1 Measured properties of washed coal

Parameter Value

Solids density, s(kg m3

)1,430

Loose-poured bulk density, 788 (Dry)

bl(kg m3

)662 (7.5% wb moisture content)

646 (15% wb moisture content)

Coefficient of restitution (CoR) 0.55 (particle-to-particle)

0.6 (particle-to-perspex)

Static friction coefficient (s) 0.58 (particle-to-particle, dry)

0.43 (particle-to-perspex, dry)

3 Setup of calibration apparatuses

To provide experimental data of granular flow and behaviourseveral bench-scale tests have been developed to examine themechanics of granular flow in various conditions and con-finements. The aim of these tests is to assist in the calibrationof numerical parameters required for DEM simulation usingnumerous experiments to isolate key properties such as par-ticle-to-particle static and rolling friction coefficients. Oncea suitable parameter is determined other interactions can beadditionally investigated including extra boundary materi-als, cohesion and alternative dynamic interactions, such asmulti-phase analysis and other non-contact environmentalconditions (e.g. electrostatics).

A common test to study the influence of particle frictionand rolling resistance on the formation of granular piles isa slump test where material is loosely poured into a tubeand lifted to allow material to form a pile under gravitationalforces. This is used primarily to examine the angle of reposeand pile height. The disadvantage of this arrangement is thatas the tube is lifted at a set rate the flow of material is influ-enced by friction between the particles and the tube wall andthe lifting velocity. To avoid these affects an alternative slumptester has been designed as shown in Figs. 2 and 3, where aperspex split tube is filled with material and released by thetwo halves pulling away laterally from each other around afixed point in an arc. High-speed photography has shown thatthe two halves pull away quickly enough to avoid any con-tact with the bulk material as shown in Fig. 3. A pipe filledwith granular material to form a flat surface under the slumptester is an effective method to solely calibrate the particle-to-particle interactions as other interactions are negligible.Once the pile is formed the profile can be quantified usingthe angle of repose and the contour of the pile. For this inves-tigation a 60 and 100 mm inside diameter (I.D.) tube has beenused to examine the effects the aspect ratio of the column of

Fig. 2 DEM model of swing-arm slump test after release. 60 mm I.D.tube, 150 mm I.D. base

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Development and validation of calibration methods for discrete element modelling 129

Fig. 3 Swing-arm slump tester after release. 60 mm I.D. tube, 150 mmI.D. base

material may have on particle flow and pile formation duringslumping.

To verify that the parameters obtained from the slump test(i.e. unconfined flow) are suitable for confined flow, a testapparatus was set up consisting of an adjustable perspex flat-based hopper elevated 200 mm above a flat load platformsupported by a load cell as shown in [4]. With an adjustableopening and a quick release gate the material discharge ratecan be varied to examine the drained angle of repose, dif-ferent flow behaviours and phenomena that may occur suchas cohesive or mechanical arching. The influence that dropheight has on the formation of a granular pile in comparisonto the piles formed by slump testing can also be examined.The profile of the material discharging from the hopper andthe duration of discharge can be recorded by a high-speedcamera to compare with numerical models and determinewhether the particle dynamics and contact physics are repre-sentative on a macro scale.

Conducting a variety of physical tests enables a data-base of information to be collected to assist in the selectionof appropriate parameters and material mechanical proper-ties for various environmental conditions, applications andnumerical optimisation. It is not expected that DEM param-eters determined from one type of experiment will be realisticto characterise the dynamics of a bulk material in gen-eral. Fine adjustment of parameters, including particle shapemay be required to achieve an accurate representation ofbulk behaviour from observations from various bench-scaleexperiments.

4 Numerical modelling

DEM is an effective tool to simulate granular flow of dryand moist materials. The commercial code utilised in thisstudy is EDEM [5]. The simplified non-linear visco-elas-tic Hertz-Mindlin no-slip model was adopted in the presentwork. Further details on this contact model are provided in[6]. To account for surface asperities and particle geometry

which can not be easily modelled in DEM simulations, roll-ing friction was necessary to apply a resisting rolling torqueto oppose the relative rotation between particles and betweenparticles and boundaries. A simple Coulomb-like rolling fric-tion model proposed by Zhou et al. [2] was implemented inaddition to using shaped particles. Additionally, to appropri-ately model the capillary forces and cohesion between par-ticles in wet granular materials, a simple approach affiliatedwith the EDEM code [5] has been adopted that increases thenormal contact force proportionally to the normal particleoverlap and subsequently increasing the tangential contactforce. According to Hertz theory of elastic contact [7], thecontact area radius can be evaluated by:

r2 = 2R h (1)where R is the particle radius and h is the normal overlap.The additional normal repulsive force is expressed as:

FN = r2Ce (2)where Ce is cohesive energy density

(J m3

). An approach

adopted in this investigation to approximate the cohesiveenergy required to simulate tensile strength in moist mate-rials is based on the general formula derived by Rumpf [8]to originally calculate the tensile stress of wet mono-sizedspherical particles. With an empirical correlation for the coor-dination number the tensile stress is related to the followingexpression:

N = 1

FNd2

(3)

where is the voidage of the granular material dependent onthe consolidation stress, FN is the bonding force of a liquidbridge and d is the particle diameter. Figure 4 provides acomparison between the minor principal tensile stress (i.e.perpendicular to the axis of consolidation) of washed coal at7.5 and 15% wet basis (wb) moisture content measured withan Ajax tensile tester [9]. The cohesion energy is also esti-mated using Eqs. 2 and 3 in Fig. 4 to provide a preliminaryguide to the selection of the correct additional force requiredto represent moist bulk material under various consolidationconditions.

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30 35Major Consolidation Stress (kPa)

Tens

ile S

tres

s (P

a)

0.0E+00

5.0E+05

1.0E+06

1.5E+06

2.0E+06

2.5E+06

3.0E+06

3.5E+06

Coh

esio

n E

nerg

y (J

m -3 )

t - 15% wb MCt - 7.5% wb MCCe -15% wb MCCe - 7.5% wb MC

Linear (t - 15% wb MC)Linear (t - 7.5% wb MC)

Fig. 4 Tensile stress and cohesion energy vs. major consolidationstress for moist washed coal: h 0.1m, d = 5 mm

123

130 A. P. Grima, P. W. Wypych

To represent particle shape two different simple particleshapes were created by clustering spheres, as shown in Fig. 1.The mean particle size was approximately scaled up by a fac-tor of 4 to reduce the number of particles required and thesimulation time. As no indentation or compression tests wereconducted to determine the stiffness of the washed coal, themodulus of elasticity and Poissons ratio were approximatedat 2.43 GPa and 0.35, respectively.

A series of simple simulations were conducted to quan-tify the CoR of the shaped particles and spherical particlesby dropping the particles in a fixed orientation onto a flatsurface. Comparisons of the impact and rebound velocityshowed that the CoR for spherical particles correlated wellto the input value unlike the shaped particles where the aver-age simulated CoR was lower than the input value. As energyis absorbed by rotational motion when two or more spheres ofa clustered particle collide within a short period resulting inan oblique impact, adjustments were made to the measuredCoR by increasing the particle-to-particle and particle-to-perspex CoR to 0.78 and 0.8, respectively. Increasing theCoR reduced the difference between the numerical reboundvelocity of shaped particles and the measured rebound veloc-ity of the coal particles. The sensitivity of the CoR on mod-elling granular flow using non-spherical particles with lowrelative collision velocities is also examined in this paper.

5 Results and discussion of slump tests

From a practical point of view, it is ideal if appropriate param-eters for a DEM model can be evaluated in the shortest periodpossible to minimise the cost of computational and humanresources. The approach adopted to minimise computationaltime was to set the particle-to-particle friction to the mea-sured static friction coefficient (s = 0.58) and arbitrarilyadjust the rolling friction coefficient (r) accordingly untilthe pile closely matched the experimental measured profile.The static friction coefficient and CoR were also adjusted toexamine the effects they had on the particle flow. For the drywashed coal there was some difference between the angle ofrepose and the pile height using a 60 mm I.D. tube (Fig. 5) anda 100 mm I.D. tube (Fig. 6) filled with material to a height of150 and 100 mm, respectively. The reason for the differencesis due to the difference in the potential energy of the systemsresulting in different average particle velocities during theslump tests.

Initially, r was set to 1% of s, however this was not suf-ficient even with high values of s. Increasing r resulted insignificant changes in the pile height compared to increasesof s that governed more the angle of repose. Figure 5 showsgreater increases in pile height with changes in r and s,unlike Fig. 6 where the increases result in minor changes inpile height. The effect that the CoR has on the angle of repose

0

10

20

30

40

50

60

-80 -60 -40 -20 0 20 40 60 80

DEM 1 s =0.7,r=0.05,CoR=0.78

DEM 2 s =0.5,r=0.1,CoR=0.78

DEM 3 s =0.6,r=0.1,CoR=0.78

DEM 4 s =0.6,r=0.1,CoR=0.55

Exp - Dry

Dimensions in millimetres

Fig. 5 Granular pile profiles for dry washed coal from slump test:60 mm I.D. tube, 150 mm initial fill height in tube

0

10

20

30

40

50

60

-80 -60 -40 -20 0 20 40 60 80

DEM 1 s =0.7,r=0.05,CoR=0.78DEM 2 s =0.5,r=0.1,CoR=0.78DEM 3 s =0.6,r=0.1,CoR=0.78DEM 4 s =0.6,r=0.1,CoR=0.55Exp - Dry

Dimensions in millimetres

Fig. 6 Granular pile profiles for dry washed coal from slump test:100 mm I.D. tube, 100 mm initial fill height in tube

0

10

20

30

40

50

60

-80 -60 -40 -20 0 20 40 60 80

DEM 1 Ce = 1.5E6

DEM 2 Ce = 2.0E6

DEM 3 Ce = 2.5E6

DEM 4 Ce = 3.0E6

Exp 7.5% wb MC

Exp 15% wb MC

Dimensions in millimetres

Fig. 7 Granular pile profiles for moist washed coal from slump test:60 mm I.D. tube, s = 0.6r = 0.1 CoR=0.78, 150 mm initial fillheight in tube

and the pile height is minor at relatively low collision veloc-ities. To select which set of parameters best depicts the bulkmaterial behaviour a comparison is made between the differ-ent slump tests and the bulk density measured when the parti-cles are loosely injected into the tube prior to the slump armsbeing released. Referring to Fig. 6 the measured bulk densi-ties for each DEM simulation were 819 (DEM 1), 810 (DEM2), 799 (DEM 3) and 777 kg m3 (DEM 4). Thus the set ofparticle parameters which best complies with the profiles andbulk density is s = 0.6,r = 0.1, CoR = 0.78 or 0.55.

Utilising the parameters determined for free-flowing drywashed coal the effects that adhesion and cohesion haveon flow were investigated to determine how much cohesionenergy is required to represent the liquid bridges betweenthe particles. Figures 7 and 8 show the DEM and experimen-tal profiles of the granular piles formed from moist washedcoal with varying moisture content and strength. Using theapproximated values of cohesion energy from Fig. 4 the DEM

123

Development and validation of calibration methods for discrete element modelling 131

0

10

20

30

40

50

60

70

80

90

-80 -60 -40 -20 0 20 40 60 80

DEM 1 Ce = 1.5E6

DEM 2 Ce = 1.75E6

DEM 3 Ce = 2.0E6

Exp 7.5% wb MC

Dimensions in millimetres

Fig. 8 Granular pile profiles for moist washed coal from slump test:100 mm I.D. tube, s = 0.6, r = 0.1, CoR = 0.78, 100 mm initial fillheight in tube

simulations and experiments were conducted using a similarmanner where the initial height of material in the tubes wasidentical. Figure 7 shows that the experimental profiles forwashed coal at 7.5 and 15% wb moisture contents were verysimilar in regard to pile height and angle of repose. With theaddition of 3 106 J m3 of cohesion energy to the particlecontacts the behaviour of the material slumping correlatedwell to the physical behaviour of the washed coal at 7.5 and15% wb moisture content from the 60 mm I.D. tube slumptest. A clear distinction in the height of the piles betweenthe dry and moist washed coal can be seen when comparingFigs. 5 and 7.

The unconfined strength of the moist washed coal wasnoticed when the bulk material did not fail successfully whenwashed coal with a moisture content of 15% wb was looselypoured into the 100 mm I.D. tube to a height of 100 mm in theswing-arm slump tester. However, at half the moist contentthe material successfully failed and formed a pile as shown inFig. 8. A cohesion energy of approximately 1.75106 J m3is required to model the flow behaviour of washed coal witha moisture content of 7.5% wb in the 100 mm I.D. tube slumptest which is significantly different from the 60 mm I.D. tubeslump tests. Between the 60 and 100 mm I.D. tube slumptests the deviation between the particle dynamics and the totalsystem energy result in marginally different particle normaloverlaps in the DEM simulations which govern the magni-tude of the additional cohesive normal force added betweenparticles during a collision. Consequently, a cohesion energydetermined suitable for one system may not be suitable foranother system. As it is complex to model transferable liquidbridges in DEM, the bulk density measured experimentallydecreases with increasing moisture content, however in theDEM simulations shown in Figs. 7 and 8 the bulk densityof the moist material varied between 715 and 793 kg m3which is greater than the measured values in Table 1.

Adjustments could be made to the solid density of theparticles to artificially modify the bulk density, however this

will alter the gravitational weight forces on the particles. Theunsuccessful failure of the column in the 100 mm I.D. tubeof the slump tester was successfully simulated numericallywhen the cohesion energy between the particles was greaterthan 3 106 J m3, showing that calibration of adhesionand cohesion in a granular material is dependent on the con-solidation state and environmental conditions. However, theevaluation of the cohesion energy via Rumpfs expression(Eq. 3) has shown to be a plausible method to approximatethe required additional particle tensile forces to replicatephysical particle mechanics for moist materials.

6 Results and discussion of discharge from hopper

To verify that the results obtained from the slump tests arevalid for confined flow various tests were conducted usingdry washed coal to examine the behaviour of material dis-charging from a hopper. As the hopper has a flat base andno sloped walls the particle-to-particle interactions could beexamined with minor influences from the hopper walls. Usingthe suitable parameters established in the slump tests, numer-ous DEM simulations of the hopper flow for dry washed coalwere conducted. Investigations found that a minor decrease inthe particle rolling friction coefficient to r = 0.05 achievedsimilar behaviour to the physical experiments. Figure 9shows a good comparison between the simulated and experi-mental drained angle of repose in the hopper with a dischargeopening of 40 mm. The discharge time between the experi-mental and numerical tests were within 15% of each otherwhere r had the greatest influence on the drained angle ofrepose in the hopper and the pile formed below the hop-per. The discharge characteristics of the dry washed coal areshown in Fig. 10 which indicates that the washed coal is afree flowing material when dry as the change of the normalforce on the load platform is quite rapid once the hopper gateopens. Figure 10 also shows the difference between the totalnormal forces exerted on the load platform below the hopperin the DEM simulations compared well to the experimentalforce.

Fig. 9 a DE model of angle of repose at discharge point in hopper:s = 0.6, r = 0.05, CoR = 0.78 and 0.55, b experimental profile ofdry washed coal: 40 mm opening

123

132 A. P. Grima, P. W. Wypych

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5Time (s)

Nor

mal

For

ce (

N)

DEM 1 s = 0.6; r = 0.05; CoR=0.55

DEM 2 s = 0.6; r = 0.05; CoR=0.78

Exp

Fig. 10 Force exerted on load platform below hopper. Gate opens attime = 0 s

0

10

20

30

40

50

60

70

-80 -60 -40 -20 0 20 40 60 80

DEM 1 s =0.6,r=0.05,CoR=0.78

DEM 2 s =0.6,r=0.1,CoR=0.78

DEM 3 s =0.6,r=0.2,CoR=0.78

DEM 4 s =0.6,r=0.05,CoR=0.55

Exp - Dry

Dimensions in millimetres

Fig. 11 Granular pile profiles for dry washed coal from hopper:200 mm drop height

The profile of the granular pile formed below the hop-per for dry washed coal is shown in Fig. 11. The differencebetween the piles in Fig. 11 is minor and the angles of reposeare similar for various alterations in r, however the set ofparameters which best matched the angle of repose in the hop-per and on the pile was s = 0.6;r = 0.05; CoR= 0.55.Although these parameters are slightly different to slumptest parameters, this implies that DEM parameters have tobe tuned according to the environmental conditions andapplication.

7 Conclusion

Numerous methods were presented in this paper to assist inthe calibration process to determining the material parame-ters needed in DEM simulations. Numerical results for bothcohesionless and cohesive granular materials were comparedto experimental data to validate the DEM parameters suchas the static friction coefficient, the rolling friction coeffi-cient and the CoR. The developed techniques have proven tobe successful for the calibration of material parameters butalso allow for scope to optimise simulation time by scalingparameters such as particle size and particle stiffness. It isshown that DEM can accurately model the flow of granu-lar material from discharge of a hopper and the formation

of granular piles from slumping. The best method to tuneDEM models to optimise time was to measure as many sin-gle particle properties as possible to develop an appropri-ate particle shape representation and size distribution. Oncekey parameters are determined, several simple experimentswhich best replicate the flow mechanisms of the system tobe modelled can be conducted using a trial-and-error processwhere minimal dependent parameters are altered such as therolling friction or cohesion energy as presented. Minimis-ing the number of types of particle interactions to calibrateduring a single experiment is ideal to effectively reduce thenumber of parameters which influence granular flow and thequantity of trial DEM simulations required. Other notableobservations from this study is that the CoR is not so influ-ential on the bulk behaviour during slump tests and hopperdischarge, thus the adjustments made to the CoR to accountfor the effects of clustering spheres was not critical. Scalingup the average particle size to reduce computational time andthe required number of particles proved to be plausible forunconfined flow but shows a tendency to restrict the flow ofparticles from a hopper which may be problematic for real-istic flow of large models. Further investigation is being con-ducted to access the validility and accuracy of the bench-scalecalibration techniques to model large-scale granular flow.

Acknowledgments A. P Grima is grateful to Technological ResourcesPty Ltd (subsidiary of Rio Tinto Ltd) for the financial support (scholar-ship) for the present work.

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University of WollongongResearch Online2011

Development and validation of calibration methods for discrete element modellingAndrew GrimaPeter W. WypychPublication Details