1

Volpe The National Transportation Systems Center

Finite Element Analysis of Wood and Concrete Crossties Subjected to Direct Rail Seat Pressure

U.S. Department of TransportationResearch and Innovative Technology AdministrationJohn A. Volpe National Transportation Systems Center

Volpe The National Transportation Systems CenterAdvancing transportation innovation for the public good

Hailing Yu and David JeongStructures and Dynamics Division

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Overview

Background Finite element analyses Results Conclusions Future work Acknowledgements

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Background Rail seat failure in ties can

cause rail rollover derailments Plate cutting in wood ties Rail seat deterioration in

concrete tieso Probable cause for two Amtrak

derailment accidents in Washington in 2005 and 2006

o Recently observed on the Northeast Corridor

Correlation of rail seat failure with rail seat load is needed

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Objectives

Develop finite element (FE) models for wood and concrete ties in a ballasted track

Study failure mechanisms of railroad ties subjected to rail seat loading using the FE models

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Current Simplifications

Fasteners are not modeled Vertical load is applied as direct rail seat

pressure Lateral load is not applied

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Directionality in Wood Material

L: parallel to fiberT: perpendicular to fiber and tangent to growth ringsR: normal to growth rings

L

R

T

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Orthotropic Elasticity

RT

LT

LR

TT

RR

LL

RT

LT

LR

TR

RT

L

LT

T

TR

RL

LR

T

TL

R

RL

L

RT

LT

LR

TT

RR

LL

G

G

G

EEE

EEE

EEE

100000

010000

001000

0001

0001

0001

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Orthotropic Strength Limits

Symbol DescriptionXLt Tensile strength in the fiber direction LXLc Compressive strength in the fiber direction LXRt Tensile strength in the radial direction RXRc Compressive strength in the radial direction RXTt Tensile strength in the tangential direction TXTc Compressive strength in the tangential direction TSLR Shear strength in the L-R planeSLT Shear strength in the L-T planeSRT Shear strength in the R-T plane

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Representative Wood PropertiesEL (psi) ER (psi) ET (psi)

1,958,000 319,154 140,976LR LT RT

0.369 0.428 0.618GLR (psi) GLT (psi) GRT (psi)168,388 158,598 41,118

XLt (psi) XLc (psi) XRt, XTt (psi) XRc, XTc (psi) SLR, SLT (psi)15,200 7,440 800 1,070 2,000

Based on properties of the white oak species described in Bergman, R., et al., “Wood handbook - Wood as an engineering material,” General Technical Report FPL-GTR-190, U.S. Department of Agriculture, Forest Service, Forest Products Laboratory: 508 p. 2010.

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Macroscopic Heterogeneity and Material Nonlinearity in Concrete Ties Steel strands/wires

Linear elasticity with perfectly plastic yield strength

Concrete Linear elasticity followed by

damaged plasticity Interfaces

Bond-slip depicted in linear elasticity followed by initiation and evolution of damage to bond

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Quarter Symmetric FE Models of 8-Strand and 24-Wire Concrete Crossties

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Concrete Material Models Concrete damaged plasticity Uniaxial tension: linear elasticity

followed by tension stiffening Uniaxial compression: linear

elasticity followed first by strain hardening and then by strain softening

Multi-axial yield function dt – tensile damage variable

dc – compressive damage variabled – stiffness degradation variable (a function of dt and dc)

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Cohesive Interface Elements

n – normal directions, t – shear directions

Normal traction tn

Shear tractions ts, tt

bracketMacaulay theis where,12

0t

t

2

0s

s

2

0n

n

tt

tt

tt

Quadratic nominal stress criterion for damage initiation

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Support to the Ties Ballast

Extended Drucker-Prager model for granular, frictional materials

Subgrade Modeled as an elastic

half space using infinite elements

Transitional layers can be modeled if geometric and material properties are known

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Material Parameters

All material parameters are obtained from open literature

There is insufficient data on the bond-slip properties of steel tendon-concrete interfaces

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Analysis Steps Initial condition

Steel tendons pretensioned to requirements (concrete tie) First step (static analysis)

Pretension released in the tendons (concrete tie) Second step (dynamic analysis)

Uniformly distributed pressure loads applied on rail seats (wood and concrete ties)

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Deformed Concrete Tie Shape After Pretension Release

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Compressive Stress State in Concrete After Pretension Release

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Ratio of Pretension Retention

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

8-strand tie24-wire tie

Ave

rage

ratio

of p

rete

nsio

n re

tent

ion

Relative distance to tie center (1=tie end)

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Predicted Failure Mode Under Rail Seat Pressure

Wood tie – compressive rail seat failure

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Predicted Failure Mode Under Rail Seat Pressure

Concrete tie – tensile cracking at tie base

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Rail Seat Force vs. Displacement Up To Predicted Failure

Absolute rail seat displacement

0

5

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2 0.25 0.3

8-strand concrete tie24-wire concrete tieWood tie

Rai

l sea

t for

ce (k

ip)

Rail seat displacement (inch)

(a)

Rail seat displacement relative to tie base

0

5

10

15

20

25

30

35

40

0 0.005 0.01 0.015 0.02 0.025 0.03

Rai

l sea

t for

ce (k

ip)

Relative rail seat displacement (inch)

(b)

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Partition of Tie-Ballast Interface

Fifty-one sub-surfaces on lower surface of wood tie

Contact force calculated on each sub-surface

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Contact Force Distribution on the Lower Surface of Wood Tie

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Conclusions

FE analyses predict that under a uniform rail seat pressure load, The wood tie fails at the rail seats due to excessive

compressive stresses Tensile cracks form at the base of the concrete ties

The simplified loading application predicts rail seat failure in the wood tie but not in the concrete ties

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Future Work

Calibrate bond-slip relations in the steel tendon-concrete interfaces from tensioned or untensioned pullout tests

Incorporate fasteners and rails, and apply both vertical and lateral loading

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Acknowledgements

The Track Research Division in the Office of Research and Development of Federal Railroad Administration sponsored this research.

Technical discussions with Mr. Michael Coltman, Dr. Ted Sussmann and Mr. John Choros are gratefully acknowledged.