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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
Theory behind KENTRACK
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
Theory behind KENTRACK
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
Theory behind KENTRACK
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
Theory behind KENTRACK
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
Theory behind KENTRACK
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
Theory behind KENTRACK
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
Theory behind KENTRACK
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)
Subgrade Modulus 6000 psiSubgrade Modulus 12000 psiSubgrade Modulus 18000 psi
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)
Subgrade Modulus 6000 psiSubgrade Modulus 12000 psiSubgrade Modulus 18000 psi
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)
Subgrade Modulus 6000 psiSubgrade Modulus 12000 psiSubgrade Modulus 18000 psi
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
Subgrade Modulus 12000 psi
Subgrade Modulus 15000 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
20.42Service life of Asphalt Layer
11.9Compressive Stress on Subgrade
0.000183Tensile Strain in the asphalt
Asphalt Thickness - 6 Ballast Thickness - 8
10.36Service life of subgrade layer
23.77Service life of Asphalt Layer
12.6Compressive Stress on Subgrade
0.000167Tensile Strain in the asphalt
Asphalt Thickness - 4 Ballast Thickness - 10
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
13.5Compressive Stress on Subgrade
23.4Compressive Stress on Subballast
Subballast Thickness - 8 Ballast Thickness - 6
5.72Service life of subgrade layer
2.13Service life of Subballast Layer
13.7Compressive Stress on Subgrade
20.1Compressive Stress on Subballast
Subballast Thickness - 6 Ballast Thickness - 8
5.56Service life of subgrade layer
N/AService life of Subballast Layer
13.8Compressive Stress on Subgrade
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 ?