Jerry G. Rose

University of Kentucky

Lexington, KY USA

Kentrack, A Performance-Based Layered

Elastic Railway Trackbed Structural Design and

Analysis Procedure – A Tutorial

Nithin K. Agarwal

University of Kentucky

Lexington, KY USA

Prepared for the 2010 Joint Rail Conference

April 27-29 2010, Urbana, IL, USA

Copyright © 2010 by ASME

JRC2010-36067

Justin D. Brown

University of Kentucky

Lexington, KY USA

Neeharika Ilavala

University of Kentucky

Lexington, KY USA

Introduction

• Kentrack is a computer program designed

to analyze a railroad track segment as a

structure

• Uses Bousinessq’s Elastic Theory

• Uses Burmister’s Multi-Layer System and

Finite Element Analysis to perform

calculations

Introduction

• Critical Stresses and Strains are

Calculated

• Design Lives are Predicted

• Based on Fatigue Effects (Cumulative

Damage Criteria) of Repeated Loadings

• Uses DAMA Program – Developed for

Highway Pavements

Background

• Originally Kentrack was written in

FORTRAN for DOS operation

• Since been upgraded to a Windows

Platform

• 3.0 was written in Visual Studio using a

.Net Framework in C#

Background

• The original development goal was to

analyze traditional All-Granular trackbeds

and Asphalt Underlayment trackbeds

• 3.0 has the option for• All-Granular

• Asphalt Underlayment

• Combination – Granular & Asphalt

All-Granular

• Traditional Track structure

Asphalt• Underlayment

Combination

• Contains an asphalt layer and a granular

subballast layer

Kentrack Theory• Superposition of Loads

P

PS

P

PSS 2

41

2

'

1

w(P)

y(My)

z

y

xji

l

l

w(P) z

x(Mx)i

x

jy

RAIL:

TIE:

w(P)

i

j

SPRING:

Kentrack Theory• Finite Element Method

– Used to calculate the stress and strain in the

rail and tie

En-1 n-1

a

En n

E2

E1

H

zn-2

z2

z

z1

a

qr

Kentrack Theory• Multilayered System

– Used to calculate the stress and strain in each

layer

Kentrack Theory

• Each type of trackbed is composed of

different materials

– All-Granular trackbed layers include Ballast,

Subballast, and Subgrade

– Asphalt trackbed layers include Ballast,

Asphalt and Subgrade

– Combination trackbed layers include Ballast,

Asphalt, Subballast, and Subgrade

• Different equations are used to describe

the properties of each material

Kentrack Theory

• Ballast

– In new trackbeds the ballast behaves non-

linearly

– In aged trackbeds the ballast behaves linearly

• Subgrade

– Behaves as a linear elastic material

2

1

KKE

)21( 0321 Kz

Kentrack Theory

• Asphalt is a visco-elastic material

• The dynamic modulus depends on the

following:

– Temperature

– Aggregate passing the No. 200 sieve in %

– Volume of bitumen %

– Volume of air voids %

– Asphalt viscosity

– Load frequency

Kentrack Theory

• Damage Analysis

– Based on minor linear damage analysis

criteria

– Performance is based on periods

• For Kentrack this is four seasons

n

i da

p

orNN

NL

1

1

Kentrack Theory

• Predicted number of repetitions

•Each car equals one repetition

Kentrack Theory• Predicted 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

Subgrade Damage Analysis

• Excessive permanent deformation controls

failure

• Deformation is governed by the vertical

compressive stress on the top of the

subgrade

• Based on Highway experience

• The number of allowable repetitions before

failure

583.3734.3510837.4 scd EN

Asphalt Damage Analysis

• Fatigue cracking controls failure

• Fatigue cracking is governed by the tensile

strain in the bottom of the asphalt

• Based on highway experience

• The number of allowable repetitions before

failure

853.0291.30795.0 ata EN

Failure Criteria

• All-Granular Trackbed

• Vertical Compressive Stress on Subgrade

Failure Criteria

• Asphalt Trackbed

• Vertical Compressive Stress on Subgrade,

Tensile Strain at Bottom of Asphalt

Kentrack Theory

• Combination Trackbed

• Vertical Compressive Stress on Subgrade,

Tensile Strain at Bottom of Asphalt

Typical cross section

• All-Granular TrackbedSub. Mod. = 15,000 psi

28.6 MGT/yr

Typical cross section

• Asphalt Trackbed Sub. Mod. = 15,000 psi

28.6 MGT/yr

Typical cross section

• Combination Trackbed Sub. Mod. = 15,000 psi

28.6 MGT/yr

Critical Outputs*

VariableAll-Granular

Trackbed

Asphalt

Trackbed

Combination

Trackbed

Subgrade Vertical

Compressive Stress (psi)14.47 11.69 10.49

Asphalt Strain (in/in) N/A 0.000134 0.000116

Service life of Subgrade (yrs) 10.27 25.56 38.38

Service life of Asphalt (yrs) N/A 24.89 39.80

*Axle Load = 36 tons, Sub. Mod. = 15,000 psi, 28.6 MGT/yr

Material Properties

• Properties to be inputted are often industry

standards or specified by the railroad

• Several properties are set as defaults as

noted in the tutorial

• The majority of default values can be

changed by the user

Effect of Subgrade Modulus on Subgrade

Compressive Stress

Effect of Subgrade Modulus on Subgrade

Design Life

36 Ton Axle Load

28.6 MGT/yr

0

10

20

30

40

50

60

70

80

90

6000 12000 18000 21000

Sub

grad

e D

esig

n L

ife

(ye

ars)

Subgrade Modulus (psi)

Subgrade life in All Granular-Trackbed

Subgrade life in Asphalt Trackbed

Subgrade life in Combination Trackbed

Effect of Subgrade Modulus on Asphalt Tensile

Strain

0

10

20

30

40

50

60

70

6000 12000 18000 21000

Asp

hal

t Des

ign

Lif

e (

year

s)

Subgrade Modulus (psi)

Asphalt Life in Asphalt Trackbed

Asphalt Life in Combination Trackbed

Effect of Subgrade Modulus on Asphalt Design Life

36 Ton Axle Load

28.6 MGT/yr

Kentrack

• The output values are stored automatically

in a text file that is over written in each

new analysis

• The text file can be saved by the user after

the analysis

• Through the input process the program

validates inputs

• Results can be used for performance-

based structural design and analysis

Summary• Kentrack is a versatile program for the

design and analysis of All-Granular, Asphalt

Underlayment, and Combination Trackbeds

• Subgrade compressive stress, asphalt

tensile strain, and associated design lives

are computed

• Design lives are considered conservative

since they are based on highway failure

criteria

• The relative effects of varying input

parameters can be assessed

Asphalt Trackbed Tutorial

• Start the

program

• Select the

trackbed to be

analyzed

Thank You

Questions?