kentrack – a railway trackbed structural design program

KENTRACK – A Railway TrackbedStructural Design Program

Jerry G. Rose & Karthik C. Konduri

University of Kentucky

AREMA 2006 Annual ConferenceLouisville, KY

September 17-20, 2006

KENTRACKVersion 2.0.1

Railway Trackbed Structural Design Software

Introduction

Railroads

Track Superstructure

Track Substructure – support system

Research in the last 20 years

HMA Trackbeds

Overlayment- Ties placed directly over asphalt

- Ballast is only used for cribbing

HMA Trackbeds

Underlayment- HMA layer present between ballast and subgrade

- Preferred over overlayment

- Better service lifethan overlayment

HMA Trackbeds

Underlayment

HMA Trackbeds

Stronger support layerReduced stresses onto subgradeWaterproofing layerNo subgrade pumpingConfining layer for ballast

Background

Theoritical method Bousinessq’s Elastic TheoryDeficiencies:Assumes the support system to be elastic, isotropic

Background

Empirical equations- JNR Equation

- Talbot’s Equation

35.11050

hP

P mc +=

25.1

8.16h

PP m

c =

Background

ILLITRACK- Finite element method- Two dimensionalGEOTRACK- Multilayered theory - Three dimensional model- It was developed to analyze all-granulartrackbeds

Background

KENTRACKDeveloped specifically to analyze HMA trackbedsHas the versatility to analyze all-granular trackbedsInitially a DOS based programUpgraded to a windows based platform with a Graphic User Interface

Theory behind KENTRACKSuperposition of Loads

S4

S4

S2

S4

S4

S4

S3 S2

S2

S4

S3 S2 S1

S2S1 S3

7

S3

S1

S2

S2

P1

1 2 3

S4

S1 S2

S3

S3

4 5

P2

6

S3 S2 S1 S2 S3

P

108

P3

9

P4

S4PPS

PPSS 2

41

2'1 +=

Theory behind KENTRACK

Finite Element Method

w ( P )

y ( M y )

z

y

xji

l

l

w ( P ) z

x ( M x )i

x

jy

R A IL :

T IE :

w ( P )

i

j

S P R IN G :

- To calculate stresses and strains in rail and tie

Theory behind KENTRACKMultilayered System

En-1 n-1

a

En n

E2

E1

Hzn-2

z2

z

z1

a

qr

- To calculate stresses and strains in the layers


Material Properties- HMA trackbed is comprised of ballast, HMAand subgrade

- All-granular trackbed is comprised of ballast, subballast and subgrade

- Different equations are used to describe thematerial properties


Ballast- In a new trackbed it behaves non-linearly- In an aged trackbed it behaves linearly

21

KKE θ=

)21( 0321 Kz ++++= γσσσθ

Subgrade- Linearly elastic material


Hot Mix Asphalt (HMA)Visco-elastic material

The dynamic modulus of HMA depends on- Temperature- Aggregate passing No. 200 sieve in %- Volume of bitumen %- Volume of air voids %- Asphalt viscosity- Load frequency


Damage Analysis- Based on minor linear damage analysis

criteria- Performed by periods (seasons, months)

∑=

= n

i da

p

orNNNL

1

1

Theory behind KENTRACKPredicted number of repetitions

Wheel Load = 36000 lb/wheel

For one car the total weight = 36000 lb/wheel x 8 = 286,000 lb/rep / 2000 = 143 ton/rep

The number of repetitions assumed per year = 200,000 rep/yr

The traffic per year = 200,000 rep/yr x 143 ton/rep = 28,600,000 GT/yr / 1 x 106

= 28.6 MGT/yr


HMA Damage Analysis- Fatigue cracking controls failure- Fatigue cracking is governed by the tensile strain

at the bottom of HMA- Based on highway experience- Number of allowable repetitions (Na) before failure

853.0291.30795.0 −−= ata EN ε


Subgrade Damage Analysis- Excessive permanent deformation controls failure- Deformation is governed by the vertical

compressive stresss on top of subgrade- Based on highway experience- Number of allowable repetitions (Nd) before failure

583.3734.3510837.4 +−−×= scd EN σ


Stresses and Strains

Asphalt Trackbed All-Granular Trackbed

Methodology

HMA trackbed cross-section

Methodology

Ballast trackbed cross-section

Methodology

Critical outputs for the two sections

N/A19.8Service life of HMA (yrs)

5.615.2Service life of Subgrade (yrs)

N/A0.000183HMA Tensile Strain (in/in)

13.811.9Subgrade Vertical Compressive Stress (psi)

Standard Ballast Trackbed

Standard HMA trackbedVariable

Critical Outputs

Effect of Subgrade Modulus on σc

Axle Load – 36 tons

0

2

4

6

8

10

12

14

16

18

3000 6000 9000 12000 15000 18000 21000

Subgrade Modulus (psi)

Ver

tical

Com

pres

sive

Str

ess (

psi)

HMA TrackbedBallast Trackbed

Effect of Subgrade Modulus on L

Axle load - 36 tons

0

10

20

30

40

50

60

3000 6000 9000 12000 15000 18000 21000

Subgrade Modulus (psi)

Pre

dict

ed S

ervi

ce L

ife (y

rs)

Subgrade Life in Ballast TrackbedSubgrade Life in HMA TrackbedHMA Life in HMA Trackbed

Effect of Subgrade Modulus on εt

Axle load – 36 tons

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

3000 6000 9000 12000 15000 18000 21000

Subgrde Modulus (psi)

HM

A te

nsile

Str

ain

(in/in

)

Effect of Axle Load on σc

HMA Trackbed

0

2

4

6

8

10

12

14

16

33 36 39Axle Load (ton)

Subg

rade

Ver

tical

Com

pres

sive

Stre

ss

(psi)

Subgrde Modulus 6000 psiSubgrde Modulus 12000 psiSubgrde Modulus 18000 psi

0

2

4

6

8

10

12

14

16

18

33 36 39

Axle Load (ton)Su

bgra

de V

ertic

al C

ompr

essi

ve S

tres

s (ps

i)

Subgrade Modulus 6000 psiSubgrade Modulus 12000 psiSubgrade Modulus 18000 psi

Ballast Trackbed

Effect of Axle Load on εt

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

33 36 39Axle Load (ton)

HM

A T

ensi

le S

trai

n (in

/in)


Effect of Axle Load on La

05

101520253035404550

33 36 39

Axle Load (ton)

Pred

icte

d Se

rvic

e Li

fe o

f HM

A (y

rs)


Effect of Axle Load on Ld

0

10

20

30

40

50

60

33 36 39

Axle Load (ton)

Pred

icte

d Se

rvic

e Li

fe o

f Sub

grad

e (y

rs)


Ballast Trackbed

0

5

10

15

20

25

33 36 39

Axle Load (ton)Pr

edic

ted

Serv

ice

Life

of S

ubgr

ade

(yrs

)

Subgrade Modulus 6000 psi



HMA Trackbed

Effect of Ballast Thickness

23.3Service life of Subgrade layer

22.37Service life of Asphalt Layer

11.0Compressive Stress on Subgrade

0.000180Tensile Strain in the asphalt

Asphalt Thickness - 8 Ballast Thickness - 6

15.51Service life of subgrade layer










Asphalt Track Bed Subgrade Modulus 12000 psi, Axle Load 36 ton

Effect of Ballast Thickness

6.03Service life of Subgrade layer

1.26Service life of Subballast Layer


23.4Compressive Stress on Subballast

Subballast Thickness - 8 Ballast Thickness - 6


2.13Service life of Subballast Layer


20.1Compressive Stress on Subballast

Subballast Thickness - 6 Ballast Thickness - 8


N/AService life of Subballast Layer


N/ACompressive Stress on Subballast

Subballast Thickness - 0 Ballast Thickness – 14

Ballast Track BedSubgrade Modulus 12000 psi, Axle Load 36 ton

Predictive Values Versus In-track Data

11.7 / -22.0 / 15.048.7 / -10 / 8

13.6 / -21.0 / 16.047.9 / -10 / 5

Vertical Compressive Stress on Subgrade

KPV/TTD psi

Vertical Compressive Stress on HMAKPV/TTD psi

Vertical Compressive Stress on Ballast

KPV/TTD psi

Thickness Ballast-HMA inches

Comparison of the KENTRACK Predictive values (KPV) Versus In-Track Data (ITD) for the CSX Mainline at Conway, Kentucky

8.2 / 7.721.9 / 114.947.0 / -8 / 8

8.3 / 8.011.7 / 14.943.5 / -12 / 4

Vertical Compressive Stress on Subgrade

KPV/TTD psi

Vertical Compressive Stress on HMAKPV/TTD psi

Vertical Compressive Stress on Ballast

KPV/TTD psi

Thickness Ballast-HMA inches

Comparison of the KENTRACK Predictive values (KPV) Versus In-Track Data (ITD) at TTCI in Pueblo, Colorado

Summary

KENTRACK is a versatile program that can be used to analyze HMA and all-granular trackbedsHMA trackbeds improve the service life and perform better than all-granular trackbedsDamage analysis values are conservativeSubgrade modulus is a very important factor in trackbed design

Future Research

Study the aging of HMA in railroad trackbeds. Develop damage analysis equations for HMA and all-granular trackbeds.Attempt to incorporate dynamic factors in the analysis.

KENTRACK Version 2.0.1

Modified from DOS to Windows with a Graphic User InterfaceValues can be modified easier than the previous versionData files can be opened using the new versionInput and output files can be accessed easily

KENTRACK Version 2.0.1

Contains:

•Program

•Help File

•Example Data Files

Contact for a copy:

Jerry G. Rose, Ph.D., PE,

Department of Civil Engineering,

University of Kentucky,

Lexington, Kentucky.

40506-0281

(859) 257 – 4278 (Phone)

(859) 257 - 4404 (Fax)

[email protected] (e-mail)

Questions ?

kentrack – a railway trackbed structural design program

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