Finite Element Analysis of Wood and Concrete
Crossties Subjected to Direct Rail Seat Pressure
Volpe The National Transportation Systems Center
Hailing Yu and David Jeong
Structures and Dynamics Division
Volpe The National Transportation Systems Center
Advancing transportation innovation for the public good
U.S. Department of Transportation
Research and Innovative Technology Administration
John A. Volpe National Transportation Systems Center
1
Overview
 Background
 Finite
element analyses
 Results
 Conclusions
 Future work
 Acknowledgements
2
Background

Rail seat failure in ties can
cause rail rollover
derailments
 Plate cutting in wood ties
 Rail seat deterioration in
concrete ties
o
o

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
3
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
4
Current Simplifications
 Fasteners
are not modeled
 Vertical load is applied as direct rail seat
pressure
 Lateral load is not applied
5
Directionality in Wood Material
R
L
T
L: parallel to fiber
T: perpendicular to fiber and tangent to growth rings
R: normal to growth rings
6
Orthotropic Elasticity
 1
 E
 L
 LR

 LL  
   EL
 RR    LT
 TT   EL
 
 LR   0
 LT  
  
 RT 
0


 0

 RL
ER
1
ER
 RT
ER
0
 TL
ET
 TR
ET
1
ET
0
0
0
0
0
0
0
1
GLR
0
0
0
0
1
GLT
0
0
0
0

0 

0   LL 

  RR 

0 
  TT 
  LR 

0 
  LT 



0  RT 

1 

GRT 
7
Orthotropic Strength Limits
Symbol
XLt
XLc
XRt
XRc
XTt
XTc
SLR
SLT
SRT
Description
Tensile strength in the fiber direction L
Compressive strength in the fiber direction L
Tensile strength in the radial direction R
Compressive strength in the radial direction R
Tensile strength in the tangential direction T
Compressive strength in the tangential direction T
Shear strength in the L-R plane
Shear strength in the L-T plane
Shear strength in the R-T plane
8
Representative Wood Properties
EL (psi)
1,958,000
ER (psi)
319,154
ET (psi)
140,976
LR
LT
RT
0.369
GLR (psi)
168,388
0.428
GLT (psi)
158,598
0.618
GRT (psi)
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.
9
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
10
Quarter Symmetric FE Models of 8Strand and 24-Wire Concrete Crossties
11
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 )
12
Cohesive Interface Elements
n – normal direction
s, t – shear directions
Normal traction tn
Shear tractions ts, tt
Quadratic nominal stress criterion for damage initiation
2
2
2
 t n   ts   t t 
 0    0    0   1, where  is theMacaulaybracket
 t n   ts   t t 
13
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
14
Material Parameters
 All
material parameters are obtained from
open literature
 There is insufficient data on the bond-slip
properties of steel tendon-concrete interfaces
15
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)
16
Deformed Concrete Tie Shape After
Pretension Release
17
Compressive Stress State in Concrete
After Pretension Release
18
Average ratio of pretension retention
Ratio of Pretension Retention
1
0.8
0.6
0.4
8-strand tie
24-wire tie
0.2
0
0
0.2
0.4
0.6
0.8
Relative distance to tie center (1=tie end)
1
19
Predicted Failure Mode Under Rail
Seat Pressure
 Wood
tie – compressive rail seat failure
20
Predicted Failure Mode Under Rail
Seat Pressure
 Concrete
tie – tensile cracking at tie base
21
Rail Seat Force vs. Displacement Up To
Predicted Failure
Absolute rail seat displacement
40
Rail seat displacement relative to
tie base
40
(a)
35
30
25
20
15
8-strand concrete tie
24-wire concrete tie
Wood tie
10
5
0
0
0.05
0.1
0.15
0.2
0.25
Rail seat displacement (inch)
0.3
Rail seat force (kip)
Rail seat force (kip)
35
(b)
30
25
20
15
10
5
0
0
0.005
0.01
0.015
0.02
0.025
Relative rail seat displacement (inch)
0.03
22
Partition of Tie-Ballast Interface
 Fifty-one
sub-surfaces on lower surface of
wood tie
 Contact force calculated on each sub-surface
23
Contact Force Distribution on the
Lower Surface of Wood Tie
24
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
25
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
26
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.
27