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Volpe The National Transportation Systems Center. Finite Element Analysis of Wood and Concrete Crossties Subjected to Direct Rail Seat Pressure. U.S. Department of Transportation Research and Innovative Technology Administration John A. Volpe National Transportation Systems Center.

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Volpe the national transportation systems center

VolpeThe National Transportation Systems Center

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

U.S. Department of Transportation

Research and Innovative Technology Administration

John A. Volpe National Transportation Systems Center

Hailing Yu and David Jeong

Structures and Dynamics Division

VolpeThe National Transportation Systems Center

Advancing transportation innovation for the public good



  • Background

  • Finite element analyses

  • Results

  • Conclusions

  • Future work

  • Acknowledgements



  • Rail seat failure in ties can cause rail rollover derailments

    • Plate cutting in wood ties

    • Rail seat deterioration in concrete ties

      • Probable cause for two Amtrak derailment accidents in Washington in 2005 and 2006

      • Recently observed on the Northeast Corridor

  • Correlation of rail seat failure with rail seat load is needed



  • 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

Current simplifications

Current Simplifications

  • Fasteners are not modeled

  • Vertical load is applied as direct rail seat pressure

  • Lateral load is not applied

Directionality in wood material

Directionality in Wood Material




L: parallel to fiber

T: perpendicular to fiber and tangent to growth rings

R: normal to growth rings

Orthotropic elasticity

Orthotropic Elasticity

Orthotropic strength limits

Orthotropic Strength Limits

Representative wood properties

Representative Wood Properties

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.

Macroscopic heterogeneity and material nonlinearity in concrete ties

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

Quarter symmetric fe models of 8 strand and 24 wire concrete crossties

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

Concrete material models

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 variable

    d – stiffness degradation variable (a function of dt and dc)

Cohesive interface elements

Cohesive Interface Elements

n – normal direction

s, t – shear directions

Normal traction tn

Shear tractions ts, tt

Quadratic nominal stress criterion for damage initiation

Support to the ties

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

Material parameters

Material Parameters

  • All material parameters are obtained from open literature

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

Analysis steps

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)

Deformed concrete tie shape after pretension release

Deformed Concrete Tie Shape After Pretension Release

Compressive stress state in concrete after pretension release

Compressive Stress State in Concrete After Pretension Release

Ratio of pretension retention

Ratio of Pretension Retention

Predicted failure mode under rail seat pressure

Wood tie – compressive rail seat failure

Predicted Failure Mode Under Rail Seat Pressure

Predicted failure mode under rail seat pressure1

Concrete tie – tensile cracking at tie base

Predicted Failure Mode Under Rail Seat Pressure

Rail seat force vs displacement up to predicted failure

Rail Seat Force vs. Displacement Up To Predicted Failure

Absolute rail seat displacement

Rail seat displacement relative to tie base

Partition of tie ballast interface

Partition of Tie-Ballast Interface

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

  • Contact force calculated on each sub-surface

Contact force distribution on the lower surface of wood tie

Contact Force Distribution on the Lower Surface of Wood Tie



  • 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

Future work

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



  • 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.

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