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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?