Modelling - Universität Stuttgart

 Invited Lecture
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Modelling
Proceedings of the XVI ECSMGE
Geotechnical Engineering for Infrastructure and Development
ISBN 978-0-7277-6067-8
© The authors and ICE Publishing: All rights reserved, 2015
doi:10.1680/ecsmge.60678
Numerical investigation of track bed stability
on soft soils
Etude numérique de la piste stabilité de lit sur sols mous
J. Aschrafi*1 , F. Hamad1 , C. Moormann1 , S. Rapp2 and U. Martin2
1
2
University of Stuttgart, Institute for Geotechnical Engineering, Stuttgart, Germany
University of Stuttgart, City, Institute for Railway and Transportation Engineering, Stuttgart, Germany
*
Corresponding Author
ABSTRACT Track bed stability is of major importance for the safety and comfort of rail traffic. Quasi-static and dynamic loads from
train-traffic are applied to the entire track system: superstructure, substructure and subsoil. Owing to the dynamic loads on the track system
and lack of maintenance of the track bed, an accumulation of excess pore water pressure can develop within the substructure. Furthermore,
a pumping effect exerted on the track system, which depends on the axle load and velocity of the vehicle, may cause in mud hole formation, rising of the underlying soil, ballast contamination and the clogging of gravel bed pores. Consequently, the subgrade resistance is
reduced and hence the system loading capacity. The main objective is to detect mud holes, as early as possible, by non-invasive, nondestructive measurements. The plastic deformation induced by the development of the mud holes is investigated by simulating the complex
track-subsoil interaction with the finite element method (FEM). In this analysis, the advanced hypoplastic model has been used. More focus
will be paid on the effect of the boundary condition on the dynamic wave propagation. For this purpose, a one-dimensional problem is investigated. The time-dependent problem is studied next by considering the real load history of the rail traffic.
RÉSUMÉ Suivre la stabilité du lit est d'une importance majeure pour la sécurité et le confort du trafic ferroviaire. Les charges quasi - statiques et dynamiques de la gare de la circulation sont appliquées au système de piste entière: superstructure , infrastructure et le sous-sol.
En raison des charges dynamiques sur le système de voie et de l'absence d'entretien de l' assiette de la voie, une accumulation de pression
d'eau des pores en excès peut se développer à l'intérieur de la sous-structure. En outre, un effet de pompage exercée sur le système de rails,
qui dépend de la charge à l'essieu et la vitesse du véhicule, peut entraîner la formation de trous de boue, l'augmentation du sol sous-jacent,
la contamination du ballast et le colmatage des pores du lit de gravier. Par conséquent, la résistance à la plate-forme est réduite et par conséquent la capacité de charge du système. L'objectif principal est de détecter les trous de boue, le plus tôt possible, par des mesures non destructives et non - invasives. La déformation plastique induite par le développement des trous de boue est étudiée par simulation de l' interaction complexe de piste du sous-sol par la méthode des éléments finis ( FEM). Dans cette analyse, le modèle hypoplasie avancée a été
utilisé. Plus d'attention sera portée sur l'effet de la condition limite de la propagation des ondes dynamique. A cette fin, un problème unidimensionnel est étudié. A cette fin, un problème unidimensionnel est étudié. Le problème de dépendance du temps est ensuite examiné en
considérant l'historique de la charge réelle du trafic ferroviaire.
1
INTRODUCTION
Loads from train-traffic are applied to the entire track
system: ballast, sub-ballast and subgrade (Adam &
Kopf 2003, Adolfsson et al. 1999, Lieberenz et al.
2005). Climate factors affect the condition of existing
track structures. Rainfall and temperature have different influences on the ballast track system components for conventional construction methods (Knothe
2001, Göbel & Lieberenz 2013). For fine-grained soil
subgrades, rainfall can influence the consistency of
the soil. On the other hand temperature might affect
both, the soil, i.e. due to frost heaving, and the rail,
i.e. due to tensile and compressive forces.
If the ballast track is overstressed by traffic loads
and/or climate factors, plastic deformations accumulate in the interface ballast-subgrade (Cantrell Rail
Services, Inc. 2001). The process of in situ soil softening at the interface starts, such as the rising of soil
materials in track bed under traffic load (mud pump3797
Geotechnical Engineering for Infrastructure and Development
ing). The volume of voids in the ballast bed will be
closed stepwise. The stability of track bed is affected
by the degree of contamination, causing a reduction
of the friction force in the ballast. In addition, the water accumulation in the track bed reduces the stability
of the entire track system (Figure 1). If a certain degree of contamination of the ballast is recognized not
sufficiently early, the track after local maintenance
will return to its pre-maintenance condition
(Lichtberger 2007; Tzanakakis 2013). The latter causes a reduction in the ballast elasticity, which imposes higher stresses in the subgrade. This results in the
settlement of the railway track causing larger plastic
and elastic deformations along the track bed. Furthermore an increase of vertical acceleration due to
traffic loads occurs and eventually a loss of serviceability and load bearing capacity.
Track bed damages, associated to conventional
ballasted track construction methods, are in need of
extensive redevelopment. This is of particular importance if higher costs related to train operation disruption, elaborate construction methods and intensive
maintenance works are to be mitigated.
2
Different approaches for detection of irregularities on
railway tracks are available in literature.
Long-wave track irregularities are currently not
evaluated under the regular track geometry inspection done by the Deutsche Bahn AG (German Railways). In a study, Kipper explores the detection and
valuation of long-wave track-deformations by using
actual data measured through a measuring vehicle.
By establishing reference values for long-wave longitudinal irregularities, this method could be applied to
the regular German Railways’ track geometry inspection (Kipper 2014).
The determination of dynamic wheel-rail forces at
track level during the passage of a train is developed
by Liu et al. (2014). A multi-flexible, parameterized
finite element track model in combination with multi
body simulation and field measurements, allows for
the determination of the wheel-track forces and their
load distribution.
A guide by Deutsche Bahn AG is given for the
qualitative proof of dynamic stability of railway
tracks built on soft soils in ballast tracks conventional
construction methods. For simplification the modelling is split in two sub-models: Track dynamic (see
section 2.1) and soil dynamic model (Vogel et
al. 2013).
2.1
Figure 1. a) Mudregion (Göbel & Lieberenz 2013); b) initial state
(top): genesis of plastic deformations and leaching of small soil
particles; final state (bottom): water accumulation in track bed.
3798
INTERACTION VEHICLE-TRACK-SUBSOIL
Vehicle - track interaction
The operating program provides information on the
speed on the routes and the traffic volume of the
railway line. The result is the number of trains (timedependent stress) and the different train classes occurring (force diagram) with their corresponding axle
load (Göbel & Lieberenz 2013). With increasing
speed, the dynamic impact rises. The overlapping
frequencies propagate vibrations within the structure
of the track. The individual frequencies can be divided into low, medium and high frequencies. Lowfrequencies are caused for example by wagon length
and axle spacing. Middle and high frequencies result
from wheel flat, sleeper distance and local unevenness along the railway (Müller-Boruttau & Breitsamter 2000).
The stress caused by the vehicle-track interaction
is the sum of the quasi-static (lower frequency) and
dynamic (higher frequency) forces. The quasi-static
Aschrafi et al.
loads are simplified by Fryba (Fryba 1999), as determined by the continuously elastic embedded beam
model. The higher frequency effects could be determined according to Knothe through the simplified
frequency domain method (Knothe 2001).
2.2
Track - subsoil interaction
According to Vogel et al. (2010) deformations in
sub-ballast / subgrade should not exceed the admissible value in order to ensure high track quality (Vogel
et al. 2010). The overlay, the soft soil depth, ground
water level and the impact of traffic load influence
the dynamic stability. Due to large vibration paths,
vibration speeds and vibration acceleration, on the
existing track system, elastic and plastic deformations might develop in the vicinity of water accumulations (Vogel et al. 2013; Weisemann & Wegener 2005; Vogel et al. 2011; Wegener 2009). By increasing water content under dynamic impacts, the
consistency of the existing soil changes from solid to
plastic solid down to the liquid state. For soils in the
subgrade frequencies up to 120 Hz are relevant
(Göbel & Lieberenz 2013).
3
NUMERICAL SIMULATION
Complex three-dimensional numerical modelling of
dynamic loads on the track including the subsurface
is a very complex and computationally expensive
task. For engineering practice the overall modelling
can therefore be composed of two substructures of a
track dynamic model for the determination of the stationary excitation and a FE model for the subsurface
(Vogel et al. 2013).
3.1
General requirements
In the numerical modelling of wave propagation
problems the mesh fineness and the time step size
play an essential role. Extensive studies on the general one-dimensional and two-dimensional wave
propagation in soils are among others shown by e.g.
Wegener (2013); Wegener & Herle (2010, 2013);
Shan (2013) and Henke & Grabe (2009).
In the following, basic investigations on the influence of boundary conditions on the wave propagation
are shown for the one-dimensional case. The investi-
gations were carried out using the FE software package PLAXIS (Vermeer & Brinkgreve 2012).
3.2
Boundary value problem (1d)
Loads from a four-axle locomotive with attached
four-axle cars have been applied on top of a column.
At the bottom of the column (Figure 2, left) dashpots were placed, whereas rollers were applied to the
left and the right of the column.
Figure 2. Geometry of a single column for numerical simulation
of 1d wave propagation with different boundary conditions at the
bottom; left: fully fixed (reflecting) boundary / absorbing boundaries (dashpots); middle: extra soil layer without Rayleigh-damping;
right: extra soil layer with Rayleigh-damping.
As material description for the gravel and the sand
the hypoplastic model (von Wolffersdorff 1997) with
a modification by Niemunis and Herle to account for
the intergranular strain in soils (Niemunis & Herle
1997) was applied. High initial strength at small
strains, the decrease of stiffness due to an increase of
shear strain and an accumulation of plastic deformations and pore water pressure under cyclic dynamic loads are essential for the numerical simulation
(Wegener 2013). The material parameters for a
Hochstetten sand were taken for the gravel and sand
(Niemunis & Herle 1997).
For the clay layer below the gravel (superstructure) the hypoplastic constitutive law is applied after
Masin (2005) to take account of the relevant strain
areas. For this study the material parameters of London clay were applied to the clay layer (Masin 2005).
In general mud pumping is a problem for fine soils;
however silt is more sensitive than clay to dynamic
loads. Nevertheless, clay was chosen for the determi-
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Geotechnical Engineering for Infrastructure and Development
nation of the limiting behaviour of local instabilities
development.
Figure 3 shows a graph with the input load and the
resulting stresses at the bottom. The bottom stress is
shifted up (~208 kPa initial stress) and 0.03s left.
This 0.03s is apparently the time the wave needs to
travel to the bottom. After these shifts, the load/stress
at b nearly coincide. The displacements increase
when the stress is higher than the initial value. When
the wave has passed (~initial stress), the displacements ´stop´.
It is obvious that this type of boundary condition
(dashpot at the bottom of the column) is unsuitable
due to the continuous creep. Therefore, three further
boundary conditions are examined in more details
next.
3.2.4 Results
The oscillating vertical stresses in the time domain of
the simulated train crossing are shown in Figure 4 for
the above mentioned variants. The calculated stresses
at point b of the column (without initial stress) are
generally higher and with a small phase shift in accordance to the applied load at point a.
Figure 4. Oscillating vertical stresses at point b of the column in
the time domain.
Figure 3. Stresses and displacements with dashpot at bottom of the
column. Dynamic loads from a four-axle locomotive with attached
four-axle cars train from calculations with a track dynamic model.
3.2.1 Fully fixed boundary
In the first variant, in contrast to the variant with
dampers (shown in Figure 2, left) a non-absorbing
fixed boundary was applied to the bottom.
3.2.2 Extra soil layer without Rayleigh-damping
For the case with an extra layer of soil (Figure 2,
middle), a 7 m thick soil layer was added.
3.2.3 Extra soil layer with Rayleigh-damping
As a third variant, the material of the aforementioned
variant with an extra layer was then provided with a
Rayleigh-damping (Figure 2, right).
3800
In the case of the hypoplastic constitutive law with
stress- directional stiffness energy is dissipated even
in more cyclic loading. In case of additional Rayleigh-damping (Figure 2, right), stress oscillation
goes back to zero when load is off.
Overall, the calculated stresses and deformations
are significantly larger than in the case of two- or
three-dimensional wave propagation, since due to the
one-dimensionality of the problem the energy remains in the column (Wegner 2013). Extra soil layer
with Rayleigh-damping is in our experience the best
solution and applied to the following two-dimensional model of a railway track system.
In Figure 5, it is clear that all cases overestimate
the final settlement, which can be attributed to the
version of the hypoplastic model and the material parameters. However, adding extra layer at the boundary with Rayleigh-damping improves the boundary
condition as compared to the other two cases.
Aschrafi et al.
Strictly speaking, this means, that e.g. no geosynthetic reinforced layer or fleece was placed below the
gravel of the track bed and consequently soft soil underlies directly the pending superstructure (Figure 6).
For the soft cohesive clay layer an undrained material behaviour was assumed. An extra boundary
layer of 7 m with Rayleigh-damping was applied to
the bottom and the right boundary of the FE model
(not shown in Figure 6).
Figure 5. Oscillating vertical displacements at point a of the column for hypoplastic simulation in the time domain.
4
CASE STUDY: TRACK-SUBSOIL
INTERACTION
The overall modelling was carried out from 2 substructures consisting of a track dynamic model for
the determination of the stationary excitation and a
FE model, with the wave propagation in the track bed
and upcoming ground.
As the interface of both models, the threshold’s
lower edge is selected. In the track dynamic model
the vertical stress-time curve from Figure 3 is applied
as input for the dynamic FE-calculation. After the
calculation is checked whether the resulting deformation of both models at this interface (thresholds
lower edge) is of proximately the same size and shear
strains have not exceeded a critical value or whether
a recalculation with appropriate adjustment of the
load of the track-dynamic model is necessary.
This article will discuss only the numerical modelling with a simplified soil dynamic 2d FE-model,
since a three-dimensional numerical track bed model
including the ground with changing of stiffness along
the railway track takes significantly more computational time than a two-dimensional calculation (Holm
et al. 2002).
4.1
Boundary conditions
For the presented 2d calculations, a typical structure
was chosen, that is highly susceptible to mud spots.
Figure 6. Boundaries of FE-model (not true to scale); extra layer
with Rayleigh-damping not shown.
4.2
Results
Figure 7 shows the results of the two-dimensional
calculation in the time domain of 0-2.4s. The vertical
deformations of the roadbed due to the dynamic action of the train crossing at the time t = 2.4s are
shown.
Figure 7. Vertical displacements of the numerical simulation
(loads from a four-axle locomotive with attached four-axle cars
train).
Due to two-dimensional wave propagation, displacements are less than for the one-dimensional column (Figure 5).
3801
Geotechnical Engineering for Infrastructure and Development
5
CONCLUSION AND OUTLOOK
This paper presents the correlation between the analytical calculation of cyclic dynamic impacts, the detection of irregularities on railway tracks and the numerical simulation, which shows the influence and
the characteristics of local instabilities.
In the numerical modelling of wave propagation
problems many factors play a role on the result of the
numerical simulation. Basic simplified dynamic studies for track bed have been performed. In particular,
it has been studied among other:
 Using a hypoplastic material model (clay and sand)
for dynamic simulation.
 Studies and recommendations on three different
boundary conditions have been made.
Transport processes of cohesive soils in the superstructure ballast cannot be represented with the classical FE method. Following aspects have to be considered in the future when performing FE analyses
for structures with selective instabilities in the future:
 3D modelling of the entire track system and advanced boundary conditions (e.g. infinite elements).
 Advanced modelling techniques as Coupled Eulerian-Lagrangian (CEL) and Material Point method
(MPM) to take into account material transport etc.
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