image aided discrete element modeling (dem) for railroad ballast by erol tutumluer hai huang youssef...

Image Aided Discrete Element Image Aided Discrete Element Modeling (DEM) for Railroad BallastModeling (DEM) for Railroad Ballast

ByByErol TutumluerErol Tutumluer

Hai HuangHai HuangYoussef HashashYoussef Hashash

Jamshid GhaboussiJamshid Ghaboussi

Association of American RailroadsAssociation of American Railroads

OutlineOutline• BackgroundBackground

• Problem Statement• Current Railroad Track Analysis Approach

– Finite Element (FEM)– Discrete Element (DEM)

» DEM Theory» Discrete Element Modeling for Railroad Track Analysis

• Image Aided DEM ApproachImage Aided DEM Approach – – Research in University of IllinoisResearch in University of Illinois

• Digitalized Image Technique for Aggregates• Image Aided DEM Approach• Approach Validation • Applications on Railroad Ballast

– Ballast Strength in terms of Aggregate ShapesBallast Strength in terms of Aggregate Shapes– Ballast Settlement under Moving LoadBallast Settlement under Moving Load

• Conclusions and Future WorkConclusions and Future Work• AcknowledgementAcknowledgement

Problem StatementProblem Statement

• A large portion of a railroad company’s annual budget to sustain thA large portion of a railroad company’s annual budget to sustain the railway track system goes into e railway track system goes into maintenance and renewal of track maintenance and renewal of track ballastballast

• A better basic understanding of the ballast behavior is essential for mitigating track problems and failures due to:

• Ballast movement and instability causing track buckle• Ballast deformation and degradation

• Factors affecting ballast strength and stability includes: ballast aggregate gradation, aggregate shape properties, and loading characters

• A more realistic computational tool is needed to consider all factors A more realistic computational tool is needed to consider all factors which may have impact on ballastwhich may have impact on ballast

Current Railroad Track Analysis Approach :Current Railroad Track Analysis Approach :- - Finite ElementFinite Element

• Finite element based numerical solution techniques used for the analysis of railroad tracks assume the railroad ballast bed to be an elastic homogeneous continuum

• ILLI-TRACK and GEO-TRACK

Longitudinal & Transverse 2-D Finite Element Meshes – IILI-TRACKLongitudinal & Transverse 2-D Finite Element Meshes – IILI-TRACK

Current Railroad Track Analysis Approach :Current Railroad Track Analysis Approach :- - Finite ElementFinite Element

3-D Finite Element Model – GEO – TRACK3-D Finite Element Model – GEO – TRACK

Continuum Solution:

Elastic Layers, E and

UnboundAggregateLayers

“Track Geotechnology and Track Management,” 2000, by Ernest T. Selig and John M. Waters

• Railroad ballast layers are actually particulate media where individual aggregate particles are surrounded by other particles in contact with air voids in between

• When ballast is strained due to rail buckle and train wheels, motion takes place that may involve one or all of the following modes:

• Inter-particle slippage,• Particle rotation, particle separation, and• Even fracture at particle contacts

Current Railroad Track Analysis Approach :Current Railroad Track Analysis Approach :- - Discrete ElementDiscrete Element

Discontinuous Ballast Layer

√ ×

Discrete Element Analysis Continuum Analysis


DEM TheoryDEM Theory::

• A DEM model simulates the mechanical response of a particulate medium by explicitly accounting for the dynamics of each particle in the system

F1

F1

F2

F2

F3

F3

F4

F4F5

F5

F6F6


• The interaction forces between two particles are represented by a damped spring in the normal direction and a spring in series with a frictional slider in the tangential (shear) direction


Fs

Fn

A

B

FF

F ][][

][][

Bn

An

Bn

An

n KK

KKK

][][

][][

Bs

As

Bs

As

s KK

KKK


• The acceleration forces of each particle is computed by dividing the net force caused by interactions among neighboring particles

• Having found the acceleration, the particles velocity and displacement are computed for each time step using explicit integration Newton’s laws of motion



Current DEM Research (3D):Current DEM Research (3D):

Research, using ITASCA’s “PFC3D” to model the

ballast-geogrid interlock effect, is currently underway


Current DEM Research (3D): Current DEM Research (3D):

Tie was modeled by

several big balls in the

upper layer.

Colors represent gradation.

Ballast and geogrid system.

(UK)


• Can only use spherical particles to model aggregate

• Particle rotation becomes dominant in contact between particles due to the spherical shape

• Calculation time is relatively long

• PLUS


• AREMA (2000) requires ballast material to be angular particles with sharp corners and cubic fragments with a minimum of flat and elongated pieces.

• Visual Inspection cause error and fairly low reliable result.

• Uncompacted Voids method is time and labor intensive, subjective, and has inter-lab variability and low repeatability.

SOLUTION? ------- Image-DEM Approach


Flat & Elongated (F&E) Ratio - ASTM D 4791Flat & Elongated (F&E) Ratio - ASTM D 4791

• F&E ratio = Maximum to F&E ratio = Maximum to minimum dimensionminimum dimension– 5:15:1– 3:13:1– 2:12:1

IntermediateIntermediateMaximumMaximum

MinimumMinimum

AREMA specs require maximum 5% by weight over 3:1 ratioAREMA specs require maximum 5% by weight over 3:1 ratio

Digitalized Image Technique for AggregatesDigitalized Image Technique for Aggregates

n = 1

2

3

n

4

a1

a2

a3

0% Crushed0% Crushed 100% with 2 or More 100% with 2 or More Crushed FacesCrushed Faces

0 100 200 300 400 500

Angularity Index

(

degr

ees)

4041424344454647 Crushed

Stone

Gravel

50-50 Blend

AREMA specs require ballast AREMA specs require ballast aggregates to be angular particles aggregates to be angular particles with sharp corners and cubical with sharp corners and cubical fragmentsfragments

Digitalized Image Technique for AggregatesDigitalized Image Technique for Aggregates

University of Illinois Aggregate Image AnalyzerUniversity of Illinois Aggregate Image Analyzer- UIAIA- UIAIA

• Conveyor speed of 3 in./second• Particles placed 10 in. apart• Images captured within 0.1 second in successionProgressive Scan

Video Camera

Angularity: 570Angularity: 570 F&E Ratio: 1:1F&E Ratio: 1:1

Top, front, and side images Top, front, and side images

of an aggregate particleof an aggregate particle

Image Aided DEM ApproachImage Aided DEM Approach

Library 2 Library 2 AI = 570AI = 570F&E = 1:1F&E = 1:1




Library 6 Library 6 AI = 570AI = 570F&E = 3 :1F&E = 3 :1







Three orthogonal views of a single aggregate particle obtained using Three orthogonal views of a single aggregate particle obtained using University of Illinois Aggregate Image Analyzer to construct 3D Shape University of Illinois Aggregate Image Analyzer to construct 3D Shape libraries for DEMlibraries for DEM

F&E: 1:1F&E: 1:1

F&E: 3:1F&E: 3:1

F&E: 5:1F&E: 5:1


Some applications of Image Aided DEM Approach

1. Drop Particles

2. Compaction

3. Tamping


Tie Pull-out Test Results –Tie Pull-out Test Results – Before & After TampingBefore & After Tamping

Tampi ng Eff ect on Ti e Shear Resi stance(3000N Normal Force)

0

200

400

600

800

1000

1 2 3 4 5 6 7 8 9 10 11

Bal l ast Aggregate Shape (Li brary)

Shea

r Fo

rce

(N) Shear Resi stance Bef ore Tampi ng

Shear Resi stance Af ter Tampi ng

F&E = 1:1

AI: 630-390

F&E = 3:1

AI: 620-347

F&E = 5:1

AI: 573-360

Tie Pull-out Tests – Tie Pull-out Tests – Effect of TampingEffect of Tamping

Ballast With Aggregate From Library 5

Before Tamping

Wheel Load

Ballast

Ballast With Aggregate From Library 5

After Tamping

Wheel Load

Ballast

Tie Pull-out Tests – Tie Pull-out Tests – Effect of TampingEffect of Tamping

Validation of Image Aided DEM Approach Validation of Image Aided DEM Approach

• Direct Shear Box laboratory tests characters• Humboldt HM-2560A direct shear device with 100 by

100 mm box • Aggregate size: 4.75 – 9.5 mm• Laboratory sample has an average AI of 535 and F&

E ratio of 1.4:1• Need sensitivity analysis to decide DEM parameters includi

ng: • Normal Contact Stiffness• Shear Contact Stiffness

• Final set of parameters should make all DEM simulation results close to the laboratory results

Real aggregate picture compared to Discrete Element Real aggregate picture compared to Discrete Element


Sensitivity Analysis

- First Trial

Normal Stiffness: 300000 N/m

Shear Stiffness:

300000 N/m

0

2000

4000

6000

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

Shear Strain (%)

Shea

r R

eact

ion

Forc

e (N

)

Lab data, 600 N normal load

Original stiffness



- Second Trial


Shear Stiffness:

500000 N/m

0

2000

4000

6000

0 1 2 3 4 5 6 7 8 9

Shear Strain (%)

Shea

r R

eact

ion

Forc

e (N

)

Increased shear stiffness

Lab data, 600 N normal load

Original stiffness



- First Trial


Shear Stiffness:

300000 N/m

0

2000

4000

6000

0 1 2 3 4 5 6 7 8 9

Shear Strain (%)

Shea

r R

eact

ion

Forc

e (N

)

Increased shear stiffnessLab data, 600 N normal loadIncreased noraml stiffnessOriginal stiffness


0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5 6 7 8 9

Percent Strain (%)

Shea

r For

ce (N

)

DEM 30 kPa Normal Stresslab 30 kPa Normal StressLab 400 kPa Normal StressDEM 400 kPa Normal StressDEM 600 kPa Normal forceLab 600 kPa Normal Force

Final Validation Results


Validated ParametersValidated Parameters

Normal Contact Stiffness 500 KN/m

Shear Contact Stiffness 300KN/m

Particle Size 4.75~9.5 mm

Angularity Index 535

Flat & Elongated Ratio 1:1.4

Tangent Surface Friction Angle 0.7


Ballast Strength in Terms of Aggregate ShapesBallast Strength in Terms of Aggregate Shapes

• Direct shear box simulations to investigate the effect of Surface Texture and Angularity

Fs

Fn

A

B

F

F

F


y = 0.3396x + 328.4

R2 = 0.9802

y = 0.4508x + 620.39

R2 = 0.987

y = 0.55x + 864.67

R2 = 0.9705

y = 0.4013x + 299.33

R2 = 0.9872

0

1000

2000

3000

4000

5000

0 2000 4000 6000 8000

Normal Force (N)

Shea

r Rea

ctio

n Fo

rce

(N)

Rough and Angular

Rough and Round

Smooth and Round

Smooth and Angular

AI =570, Surface Friction Angle = 40

AI =390, Surface Friction Angle = 15AI =390, Surface Friction Angle = 40AI =570, Surface Friction Angle = 15


• Rough and Angular


• Rough and Round


• Smooth and Angular


• Smooth and Round

- Plan View of Ballast Settlement DEM Simulation- Plan View of Ballast Settlement DEM Simulation

Center PlaneRail SeatTransverse Vertical Plane

Half Tie

0.61 m

Application on Railroad Ballast SettlementApplication on Railroad Ballast Settlement

Ballast Layer PreparationBallast Layer Preparation

- Ballast Sample of a Half Railroad Section with Angular and Cubical Aggregate- Ballast Sample of a Half Railroad Section with Angular and Cubical Aggregates of Shape Library 1s of Shape Library 1

• Need to solve “Moving Load on Track” problem to obtain the load profile on the top of one single tie

Application on Railroad Ballast SettlementApplication on Railroad Ballast Settlement

Observation Tie

Load: P; Speed: V; Duration: t

• Close Form Solution

• Unequal Tie Spacing

• Different Tie-Ballast Structure

• Thermal Stress

• Arbitrary Excitation

Moving Load on TrackMoving Load on Track

Observation Tie

Load: P; Speed: V; Duration: t

Tie Mass

Ballast Mass

m

mm xxavtxtfuuTuEIu )()()(''''''...

ptptm DuuKuua )()(..

......

)()()()( ttbbtbbtptpt umDuuKuuDuuKuu .....

)()( bbbbbbbbbbt umDuKuDuuKuu

Parameters: •EI rail bending rigidity•u rail vertical deflection•T rail axial thermal force•ρ rail unit mass •ε rail damping•f(t) excitation function•δ delta function•am reaction force from substructure•m number of ties•ut tie vertical deflection•ub ballast mass deflection•Kp rail pad stiffness•Kb ballast stiffness•Dp rail pad damping•Db ballast damping


0

20000

40000

60000

80000

100000

120000

140000

0 0.5 1

Time (sec)

Loa

d M

agni

tude

(N

)

Load Pulsein DEM

Loading Magnitude and Frequency in DEMLoading Magnitude and Frequency in DEM

Single Tie Load Pulse of a 286 kip Car Moving @ 28 km/h

Simulation Test MatrixSimulation Test Matrix

Load Magnitude (k

N)

Frequency (Hz) (Train Speed,

km/h)

Shape Library 1

(Cubical - Angular)

Shape Library 3

(Cubical - Rounded)

Shape Library 8 (Elongated -

Rounded)

90

1 (28) X X

5 (140) X X

10 (280) X X

120

1 (28) X X X

5 (140) X X X

10 (280) X X X

150

1(28) X X

5 (140) X X

10 (280) X X

Repeated Loading – Longitudinal viewRepeated Loading – Longitudinal view

CYCLE CYCLE 00


CYCLE CYCLE 2020


CYCLE CYCLE 4040


CYCLE CYCLE 6060


CYCLE CYCLE 8080


CYCLE CYCLE 100100


CYCLE CYCLE 200200


CYCLE CYCLE 400400


CYCLE CYCLE 600600


CYCLE CYCLE 800800

Repeated Loading – Side ViewRepeated Loading – Side View

CYCLE CYCLE 00


CYCLE CYCLE 2020


CYCLE CYCLE 4040


CYCLE CYCLE 6060CYCLE CYCLE 6060


CYCLE CYCLE 8080


CYCLE CYCLE 100100


CYCLE CYCLE 200200


CYCLE CYCLE 400400


CYCLE CYCLE 600600


CYCLE CYCLE 800800

Simulation Results and AnalysisSimulation Results and Analysis- Permanent Settlement of Ballast with Aggregate Shape Library 1 (Cubical – - Permanent Settlement of Ballast with Aggregate Shape Library 1 (Cubical – Angular) at three Different Loading FrequenciesAngular) at three Different Loading Frequencies

y = 22. 096x0. 4513

R2 = 0. 9953

y = 17. 263x0. 4937

R2 = 0. 9934

y = 15. 72x0. 4403

R2 = 0. 9966

40

60

80

100

120

140

160

180

0 20 40 60 80 100 120Loadi ng Cycl es

Rut

Dept

h (m

m)

1 Hz5 Hz10 Hz

Library 1 Rutting Trend Line

Critical Loading Critical Loading Frequency (?) for Frequency (?) for maximum ruttingmaximum rutting

f f = 1 - 5 Hz= 1 - 5 Hz

Library 1 AggregateLibrary 1 Aggregate

120 kN Load120 kN Load

Simulation Results and AnalysisSimulation Results and Analysis- Permanent Deformation Produced by the Static Load and the Same Magnitude - Permanent Deformation Produced by the Static Load and the Same Magnitude Dynamic Loads Applied at Different FrequenciesDynamic Loads Applied at Different Frequencies

Simulation Results and AnalysisSimulation Results and Analysis- - Comparisons of Ballast Settlement between Aggregate Shape Library 1 (CubicComparisons of Ballast Settlement between Aggregate Shape Library 1 (Cubical – Angular) and Shape Library 8 (Elongated – Rounded) at Three Loading Freqal – Angular) and Shape Library 8 (Elongated – Rounded) at Three Loading Frequenciesuencies

y = 17. 472x0. 4825

R2 = 0. 9838

y = 13. 979x0. 4841

R2 = 0. 9948

y = 12. 123x0. 4896

R2 = 0. 99

40

60

80

100

120

140

160

180

0 20 40 60 80 100 120Loadi ng Cycl es

Rutt

ing

Dept

h (m

m)

1 Hz Li b15 Hz Li b110 Hz Li b11 Hz l i b85 Hz l i b810 Hz l i b8


Simulation Results and AnalysisSimulation Results and Analysis- - Comparisons of Ballast Settlement between Aggregate Shape Library 1 (CubicComparisons of Ballast Settlement between Aggregate Shape Library 1 (Cubical – Angular) and Shape Library 3 (Cubical – Rounded) at Three Loading Frequeal – Angular) and Shape Library 3 (Cubical – Rounded) at Three Loading Frequenciesncies

y = 14. 827x0. 4372

R2 = 0. 9948

y = 10. 274x0. 4725

R2 = 0. 9915

y = 6. 171x0. 5117

R2 = 0. 9896

20

40

60

80

100

120

140

160

180

0 20 40 60 80 100 120Loadi ng Cycl es

Rutt

ing

Dept

h (m

m)

1 Hz Li b15 Hz Li b110 Hz Li b11 Hz Li b35 Hz Li b310 Hz Li b3


Simulation Results and AnalysisSimulation Results and Analysis

Only one tie is simulated in the train moving direction, the interactions between tOnly one tie is simulated in the train moving direction, the interactions between ties are not considered in the DEM simulations and the ballast aggregate movemeies are not considered in the DEM simulations and the ballast aggregate movement along the traffic direction is limited by the transverse planent along the traffic direction is limited by the transverse plane

20000

25000

30000

35000

40000

45000

0 20 40 60 80 100 120Loading Cycle

Library 3Library 1

Res

idua

l For

ce o

n T

rans

vers

e V

erti

cal P

lane

(T

he M

iddl

e P

lane

bet

wee

n T

wo

Tie

s) (

N)

More rounded Library 3 has higher lateral confinement to reMore rounded Library 3 has higher lateral confinement to reduce permanent deformation tendencyduce permanent deformation tendency

Transverse Vertical Plane

0.61 m

ConclusionsConclusions• Aggregate angularity was found to have significant impact on strength of aggre

gate assembly. Aggregate surface texture, defined as the friction between two particles in contact, was quantified from direct shear box DEM simulations to have even more pronounced impact on the strength of the assembly when compared to aggregate angularity.

• Reducing the train speed, such as in the slow orders, (or decreasing the

applied loading frequency by increasing the load pulse durations) often results in a significant increase in the rut accumulation. However, static loading induced smaller permanent deformations than the 1-Hz loading. Therefore, a critical loading frequency to give maximum rutting was found to be between 1 and 5 Hz loadings.

• Effects of ballast aggregate shape was also found to influence ballast settlement. The DEM simulations that considered single tie tests resulted in lower ballast settlements for rounded aggregate particles possible due to lesser tendency to shakedown and consolidate.

• For future ballast settlement simulations, it will be worthwhile to consider a modified ballast box for the half tie and half ballast width railroad track geometry with at least three ties included to model longitudinal confinement and movement of ballast aggregate.

Future WorkFuture Work• Fouling study by combining Image Aided DEM Simulation with Large

Direct Shear Box Tests.

• Field Validation of Image Aided DEM Approach in TTCI “FAST” Track.

The Authors would like to thank the Association of The Authors would like to thank the Association of American Railroad for their financial support of this American Railroad for their financial support of this research study through the AAR Affiliated Research research study through the AAR Affiliated Research Laboratory established at the University of Illinois at Laboratory established at the University of Illinois at Urbana-ChampaignUrbana-Champaign

AcknowledgementAcknowledgement

Association of American RailroadsAssociation of American Railroads

image aided discrete element modeling (dem) for railroad ballast by erol tutumluer hai huang youssef...

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