Page 1
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
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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
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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
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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#
Page 5
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
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All-Granular
• Traditional Track structure
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Asphalt• Underlayment
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Combination
• Contains an asphalt layer and a granular
subballast layer
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Kentrack Theory• Superposition of Loads
P
PS
P
PSS 2
41
2
'
1
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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
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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
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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
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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
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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
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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
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Kentrack Theory
• Predicted number of repetitions
•Each car equals one repetition
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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
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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
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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
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Failure Criteria
• All-Granular Trackbed
• Vertical Compressive Stress on Subgrade
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Failure Criteria
• Asphalt Trackbed
• Vertical Compressive Stress on Subgrade,
Tensile Strain at Bottom of Asphalt
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Kentrack Theory
• Combination Trackbed
• Vertical Compressive Stress on Subgrade,
Tensile Strain at Bottom of Asphalt
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Typical cross section
• All-Granular TrackbedSub. Mod. = 15,000 psi
28.6 MGT/yr
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Typical cross section
• Asphalt Trackbed Sub. Mod. = 15,000 psi
28.6 MGT/yr
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Typical cross section
• Combination Trackbed Sub. Mod. = 15,000 psi
28.6 MGT/yr
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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
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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
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Effect of Subgrade Modulus on Subgrade
Compressive Stress
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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
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Effect of Subgrade Modulus on Asphalt Tensile
Strain
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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
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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
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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
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Asphalt Trackbed Tutorial
• Start the
program
• Select the
trackbed to be
analyzed
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Thank You
Questions?