The objective of Work
Package 3 is to extend, adapt, and couple two existing computer
codes with complementary features for numerical modelling of the
instrumented sites. The main contributors to this package are ECP
and LU who performed short-term and long-term non-linear analysis of
the track-system including train-track interaction. This WP is led
by ECP.
At LU
two track models are developed (Fig. 1):
In the smaller model it
is assumed that the track is symmetric along the centreline of the
track. The second model, however, is a larger model of a
double-track line. Both a French double-track line and a Spanish
double-track line are modelled.The
track models can be used to simulate both the short-term
behaviour
of the dynamic train/track system when a wheel or a train runs on
the track, and the long-term behaviour of the track due to many
wheel passages. The models are built up using the pre-processor TrueGrid, and the commercial finite element program LS-DYNA is used
to solve the dynamic train/track interaction problem
(Figure 1).
 
Figure 1:
Train/Track model with ballast bed of elastic-plastic material
View animation of vibration simulation
 Animation (4 mb) (right-click,
"Save target as..")
The
finite element model of the Spanish double-track line is verified by
use of the measured results from the test site. The track deflection
was measured when a six-axle locomotive is loading the track.
Typical results are presented in Figure 2.
 The
passage of the six axles can clearly be seen in the figure. The
calculations produce displacements of the same size as the measured
displacements. The observed difference is believed to be partly due
to the fact that the track was newly built and the track structure
(rails and sleepers) had not yet settled firmly onto the ballast.
Figure 2: Comparison between measured and
calculated track deflection of Spanish track
The research at LU also
includes modelling of the track settlement. In the finite element
model of the track an elastic-plastic material model is used for the
ballast layer along the central segment of the track (Fig. 1). In
the calculated results presented in Fig. 3 the yield limit of the
ballast material in this segment is selected so that the stress
beneath the sleepers exceeded the yield limit of the ballast
material when the wheel passes.
 The
computations show that the contact force between the ballast and the
first sleeper in the segment with low yield strength is zero after
the first wheel passage. The adjacent sleeper gets a lower (static)
sleeper/ballast contact force after the first wheel passage, and the
contact disappears after the second passage. The following sleepers
lose contact during these cycles, but the permanent deformation
(settlement) increases during the loading, see Fig. 3. The
settlement rate after each wheel passage is, however, decreasing.
Figure 3: Displacement of a
representative sleeper due to three wheel passages. The settlement
increases for each load cycle, but settlement rate decreases.
As an application study,
the influence of an unsupported (or “hanging”) sleeper on the
train/track dynamics is performed at LU. In practice, not all
sleepers are well supported by the ballast bed. In this study, one
sleeper (or several sleepers) is assumed not to be in contact with
the ballast. A gap of 0.5mm or 1mm is introduced between the sleeper
and the ballast, and the increase of dynamic forces due to this gap
is investigated. The hanging sleeper and the two adjacent sleepers
are made flexible, while the other sleepers of the track model are
rigid.
 The
wheel/rail contact force calculated using track model with one
hanging sleeper (No 15 in Fig. 1) is shown in Fig. 4. It is seen
that the contact force goes down when the wheel passes sleeper 15.
Moreover, there is a large impact when the wheel reaches sleeper 16
(where the wheel moving downwards should be turned to move upwards).
The increase loading of the ballast bed at sleeper 16 due to the
hanging sleeper 15 will of course induce permanent track
deformations at sleeper 16 (and later on also at other sleepers).
Figure 4:
Wheel/rail contact force: Hanging sleeper No. 15
is passed at time 0.085s and a large dynamic impact is seen when the
sleeper reaches sleeper No. 16.
The research work at ECP
covers the following topics:
- implementation and
validation of the 3-D linear (short-term) dynamic response of
track-ground,
- Calibration of the
constitutive model for granular material against lab data and
development of a numerical model for non-linear (long-term)
dynamic analysis of track
 The
3-D linear dynamic model is based on a geometrical periodic
formulation and takes into account the dynamic soil-structure
interaction. By this formulation, one can reduce the analysis for
the overall system to a problem posed on a generic cell (Fig. 5).
Figure 5: Periodic model bt ECP
The simulations are made
using the computer code MISS3D, developed at ECP. This software is
based on a sub-structuring method whereby the three-dimensional
domain (the generic cell) is decomposed into two sub-domains, namely
the track-structure and the soil. The boundary element method (BEM)
with special Green's functions is used for the soil while the
track-structure is modelled by using the finite element method (FEM)
and its dynamical behaviour is characterized by periodic modes.
Figure 6 shows snap
shots of an animation of the simulated response of the Swedish test
site at Ledsgård.
Figure 6: Numerical simulation of Swedish test
data
Animation (55 mb) (right-click,
"Save target as..")
The non-linear analyses
are based on the ECP’s elasto-plastic multi-mechanism model, the
so-called Hujeux model. The model, which is written in terms
of effective stress, is calibrated against the NGI’s lab data. The
representation of all irreversible phenomena is made by four coupled
elementary plastic mechanisms consisting of three plane-strain
deviatoric plastic deformation mechanisms in three orthogonal planes
and an isotropic one. The model uses a Coulomb type failure
criterion and the critical state concept. The evolution of hardening
is based on the plastic strain (deviatoric and volumetric strain for
the deviatoric mechanisms and volumetric strain for the isotropic
one). To take into account the cyclic behaviour, a kinematical
hardening based on the state variables at the last load reversal is
used.
Figure 7 plots the
response obtained by the above model together with the experimental
data from the vacuum tri-axial tests performed by NGI. Refined
calibration work is still under way at ECP
Figure 7: Comparison
between simulated test and NGI's experimental test on ballast
The above model is
implemented in ECP’s simulation code GEFDYN.
 Figure
8 displays a typical output of the numerical simulations made for
the Swedish test site. The figure shows the calculated vertical
stress at a given time. Work is underway at ECP to refine the
numerical model and verify its performance against long-term track
response collected at the Spanish and French sites.
Figure 8: Simulation of non-linear response
of track |
