performance-based trackbed structural design and analysis
TRANSCRIPT
Performance-Based Trackbed Structural Design and Analysis Utilizing Kentrack
Dr. Jerry G. Rose, P.E. Professor of Civil Engineering
261 Raymond Building University of Kentucky Lexington, KY 40506
859-257-4278
[email protected] www.engr.uky.edu/~jrose
REES 2 2012
Kentrack
• 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 at Various Interfaces within the Track Structure
• Design Lives are Predicted • Based on Fatigue Effects (Cumulative Damage
Criteria) of Repeated Loadings • Uses DAMA Program – Developed for Highway
Pavements (Applicability for RR Trackbeds?)
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
Kentrack Theory • Superposition of Loads
PPS
PPSS 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
Hzn-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
21
KKE θ=)21( 0321 Kz ++++= γσσσθ
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
orNNNL
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 σ
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 ε
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
Figure 4a. Effect of Subgrade Modulus on Subgrade Compressive Stress.
Figure 4b. Effect of Subgrade Modulus on Asphalt Tensile Strain.
Figure 5a. Effect of Subgrade Modulus on Subgrade Design Life.
Figure 5b Effect of Subgrade Modulus on Asphalt Design Life.
Figure 6a. Effect of Ballast Thickness and Subgrade Modulus on Subgrade Compressive Stress for All-Granular Trackbed.
Figure 6b. Effect of Ballast Thickness and Subgrade Modulus on SubgradeDesign Life for All-Granular Trackbed.
Figure 7a. Effect of Asphalt Thickness and Subgrade Modulus on SubgradeCompressive Stress for Asphalt Trackbed.
Figure 7b. Effect of Asphalt Thickness and Subgrade Modulus on Subgrade Design Life for Asphalt Trackbed.
Figure 7c. Effect of Asphalt Thickness and Subgrade Modulus on Asphalt Tensile Strain for Asphalt Trackbed.
Figure 7d. Effect of Asphalt Thickness and Subgrade Modulus on Asphalt Design Life for Asphalt Trackbed.
Figure 8a. Effect of Ballast Thickness and Subgrade Modulus on Subgrade Compressive Stress for Asphalt Trackbed.
Figure 8b. Effect of Ballast Thickness and Subgrade Modulus on Subgrade Design Life for Asphalt Trackbed.
Figure 8c. Effect of Ballast Thickness and Subgrade Modulus on Asphalt Tensile Strain for Asphalt Trackbed.
Figure 8d. Effect of Ballast Thickness and Subgrade Modulus on Asphalt Design Life for Asphalt Trackbed.
SUMMARY Kentrack --- Layer-Elastic, Finite Element Computer Program Highway Structural Design Program Adapted to Railroad Loading
Configurations and Magnitudes Considers the Fatigue Lives of Various Layers for Repeated Loadings Damage Analysis Predictions Based on Highway Failure Criteria Uses the DAMA Program Believed to be More Severe than Rail-Road Loadings and
Environments Thus -- Conservative Analysis?
Kentrack --- Outputs are Performance Based • Calculate Stresses and Strains within the Track
Structure • Predict Design Lives of Various Layers
• Evaluate Effects of Varying Loadings and Track
Parameters
• Principle Factor -- Limit Subgrade Stress
Asphalt Trackbed Tutorial • Start the program • Select the
trackbed to be analyzed
