geo-dynamic modelling of track bed and...

Geo-dynamic Modelling of Track Bed

and Earthworks Document no.: C469-HWU-PM-REP-000001 FINAL DRAFT

Revision Author Date Issued for/Revision details

P01 Peter Woodward

Heriot-Watt University

4/6/2014

Po2

FINAL DRAFT

Peter Woodward

Heriot-Watt University

24/2/2015 1) Further strain plots and ground

contour plots added

2) Thalys runs updated to remove

instability

3) General report text updated

SECURITY CLASSIFICATION: OFFICIAL SENSITIVE

Handling instructions: Internal

Geodynamic Modelling of Track Bed and Earthworks

Document no.:

C469-HWU-PM-REP-000001

Rev:P02 FINAL DRAFT

Uncontrolled when printed

Page 1

Contents

Contents 1

1 Executive Summary 3

2 Abbreviations and Descriptions 4

3 Introduction 5

4 Numerical Simulation Procedure 5

4.1 DART3D 5

4.1.1 Rayleigh-waves 7

4.1.2 What this means for current theory 9

5 Computer Simulations 10

5.1 Stage 1 Simulations 10

5.1.1 Simulation S1.1 13








5.1.9 Discussion of Stage 1 simulations 53

5.2 Stage 2 Simulations 54

5.2.1 Simulation Analysis S2.1.1 54







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6 Implications for Ground Stiffness 79

7 Implications for Track Type 79

8 Implications for Track Geometry Retention 80

9 Cost Reduction Design Methodology 80

10 Track Type Recommendation 81

11 Suggested Further Work 81

12 References 82

Appendix A: Stage 1 Vertical Strain Verses Depth 83


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1 Executive Summary In this report the dynamic behaviour of various track structures have been investigated using a

three-dimensional dynamic finite element program. This limited study allows preliminary

comparisons to be made into the simulated behaviour of different trains and structures for a

given set of assumptions. Soil stiffness variations from 20 MPa through to 80 MPa were

investigated and typical outputs include the transient response of the sleepers, strains at

various depths within the structure & in-situ soil and typical ground surface contour plots of

displacement to highlight ground wave development. The simulations clearly show the

development of Rayleigh wave effects leading to increased track response. The development

of critical track velocity effects was also highlighted and the importance of calibration work to

assess the upper track bending stiffness to determine the exact trans-seismic response for a

particular track type and structure was discussed. For the purposes of this report assumptions

over this stiffness were made and kept consistent across each analysis to allow direct

comparisons from one track structure to another. Verification of the DART3D program was

included by reference to work on modelling the Ledsgard site at critical velocity. The Stage 2

simulations were based on the results and experience gained during the Stage 1 analysis.

Graphs of permissible train speed versus in-situ Young’s modulus confirmed (theoretically)

that an in-situ Young’s modulus greater than 100 MPa would be required to significantly

reduce Rayleigh wave effects. However the adoption of an appropriate lower stiffness (based

on the assumptions and parameters in this study >70 MPa was sufficient within the Rayleigh

wave depth) combined with a higher upper track Young’s modulus (concrete slab-track) may

represent an appropriate method to resolve geo-dynamic issues for the new line. However

further assessment work is required for confirmation of this and for design purposes.

In addition assessment work on the lateral ground vibration propagation would be required.

For concrete slab-track this would involve, for example, the determination of the track

receptance in order to assess potential resonant frequencies. Determination of the in-situ

ground natural frequencies will allow determination of ground wave propagation. Analysis of

ballasted track suggests that very high ground stiffness is required to prevent the induced

strains from exceeding limit values and hence reduce the plastic yielding of the geo-materials.

Without this high stiffness excessive geometry correction through differential movement may

result at the 360 km/h line speed. This is because the upper track stiffness of ballasted track is

much less than that of concrete slab-track. For the HS2 line the characteristic ground

wavelengths need to be determined and compared to the train characteristic lengths.

The dynamic behaviour of the embankments will require special attention due to the lack of

lateral support giving rise to potential issues over compaction stiffness; leading to both

reduced Rayleigh wave velocities and track critical velocities. It may be possible to optimise

the shape and/or structure of the embankment, combined with an appropriate geomaterial

stiffness, to provide enhanced dynamic support while reducing costs. The issue to be

addressed is when the embankment stiffness itself is not sufficient for the line speed

(guidance can be sought from the non-embankment simulations). Again a way forward may


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be to adopt slab-track which allows a further increase in the upper track stiffness above that

of ballasted track on the embankment. However in this study no concrete slab-track on

embankment simulations were performed to confirm this.

2 Abbreviations and descriptions Rayleigh ground wave velocity (critical velocity of the subgrade – first phase)

Critical track velocity (critical velocity for the combined track structure and subgrade)

Resonant train-track velocity (potential dynamic amplification due to coincidence of loading

and natural frequencies of a structure)

Characteristic wavelength (Rayleigh wavelength compared to the characteristic wavelengths

of the train)

Analysis *:E50-POINT (moving point load at primary Esubgrade=50 MPa)

Analysis *:E20-THALYS (Thalys train at primary Esubgrade=20 MPa)

Analysis *:E50-THALYS (Thalys train at primary Esubgrade=50 MPa)

Analysis *:E50-X2000 (X-2000 train at primary Esubgrade=50 MPa)

Analysis *:E60-HS2 (HS2 supplied train at primary Esubgrade=60 MPa)



EX strain in the x-direction (lateral strains)

EY strain in the y-direction (longitudinal strains along the track)

EZ strain in the z-direction (vertical strains)

DSTAIN Calculated deviatoric strains converted to equivalent triaxial values to represent an

upper calculated limit to shear strain

ESTAIN Estimated deviatoric strains

Stiffness all descriptions and values of stiffness referred to in this report are in terms of the

Young’s Modulus


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3 Introduction In September 2013 work began at the request of High Speed 2 Ltd to use a more advanced

numerical analysis of train-track interaction to perform a limited study into the behaviour of

soft soil locations and track structures with increases in train speed, than is normally adopted.

The purpose of the work is to help compare and contrast different track structure types in

terms of their geodynamic performance. In particular the work was to examine the effect of

ground geometry and stiffness on the ground-borne vibration (so called critical velocity

effects). The soil stiffness for each studied case was based on very conservative ground

conditions, including deep alluvium and glacial lake deposits. Both non-embankment and

embankment structures were considered and a degree of ground improvement as

appropriate. The runs consisted of eight analyses types in Phase 1, seven based on a ballasted

track structure and one based on concrete slab-track and 7 in Phase 2, with a greater emphasis

on concrete slab-track and an asphalt simulation. The specification for the train loading was

for a 17 tonne axle load travelling at 360 km/h (100 m/s).

The report details the results of the simulations in terms of time histories of the transient

response of a typical sleeper and strains within the track structure. Typical plots of ground

displacement contours are also included to highlight Rayleigh wave effects and resonant

responses. The report discusses how the model works and the types of phenomena it predicts

are primarily taken from several references; this section is presented before the main body of

the report detailing the results and discussion of each analysis type. The train types

considered were a single axle, X-2000, Thalys and Zefiro. The exact amount of track uplift

predicted is related to the critical track velocity and how the upper track bending stiffness is

modelled in the trans-seismic zone. It is normal that a calibration procedure is adopted for

simulation purposes, however this was not possible in this report and hence it is

recommended that a sensitivity analysis be performed for future analysis as this could

influence the overall predicted response.

4 Numerical Simulation Procedure 4.1 DART3D

DART3D (Dynamic Analysis of Railway Track 3-dimensional) is a dynamic time domain

research program developed to look at the linear and non-linear behaviour of railway track

using 3-dimensional finite elements coupled to a vertical train model. It is important to note

that only a very limited number of critical velocity measurement sites are reported in the

literature (it is normal to simply apply a line speed restriction to reduce their effect or

significantly reinforce the track structure to increase subgrade stiffness). This can make model

calibration more difficult.


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One would have assumed that all numerical programs would give similar responses to a

particular site, however differences between integration types, constitutive models, time

domain and frequency domain solutions (especially when a frequency domain transfer

function needs to be defined) can lead to differences between program outputs. The need for

more experimental and site measurement is therefore desirable. In frequency domain

solutions the ground dispersion curve is normally calculated and its relationship to the train

speed computed; this is normally applied in (for example) a 2.5D finite element program. The

DART3D code solves the time domain equation directly using an explicit time integration

scheme. While it can be argued that this approach is more robust it is more time consuming

especially when simulating 3D effects.

Details of the DART3D model have been published in the international literature [1,2, 3].

Coupling of the train and the track is through the following equations

−

−+−

−

+

−

−+−

−

ww

bw

cw

bcbc

bcccbccc

cccc

ww

bw

cw

bkbk

bkckbkck

ckck

&

&

&

0

0

0

0

+

+

=

wrFgwm

gbm

gcm

ww

bw

cw

wm

cm

bm

&&

&&

&&

0

00

0

0

0

(1)

For a quarter model, wc, wb and ww are the vertical displacements of the car body, bogie and

wheel, mw is the wheel mass, cmand bm

are representations of the car body and bogie

masses ( 8/cc mm = and 4/bb mm = ). kb and kc are the primary and secondary suspension

stiffness and cb and cc the corresponding damping coefficients. In Stage 1 analysis two train

types were considered one representing Thalys and the other an X-2000. However single axle

simulations were also performed in order to examine the Rayleigh-wave front (i.e.

independent to any potential axle resonant effect). In Stage 2 a different train configuration

was applied, as supplied by HS2 directly based on the Zefiro train type. Rayleigh damping is

used in the analysis with frequencies of ω1=32 rad/s and ω2=34 rad/s, and with 3% target

damping. The coefficients α and β can be found from Equations (2) & (3)

(2)

and

(3)

Where ω1 & ω2 are the two frequencies defining the damping curve and ξ is the target

damping ratio.

)(100

2

21

21

ωω

ξωωα

+=

)(100

2

21ωω

ξβ

+=


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Calibration of the upper track bending stiffness

Experience has shown that the DART3D code can model the geo-dynamic behaviour of

railway track very well. In particular it can simulate the critical speeds, such as the natural

ground Rayleigh wave velocity and the higher track critical velocity. It is also able to simulate

the train and track dynamic response (such as the transient sleeper and bogie deflections,

strains etc.) at these critical speeds (an example validation is given in Section 5.1). In order to

capture the track dynamics (i.e. the behaviour within the trans-seismic zone) to a high degree

of accurately it may be necessary to calibrate the rail system bending stiffness correctly. In

order to do this it is necessary to calibrate this upper track bending stiffness for the particular

type of track under consideration. In this report this calibration was not possible (the design of

the upper track components was unknown) and hence no modification was applied; this had

the benefit of ensuring consistency across the simulations. However better predictions can be

achieved against any physical measurements taken once the designed upper track structure is

known and hence the code can be fully calibrated.

4.1.1 Rayleigh-waves

The Rayleigh wave velocity for an elastic soil can be found from

( )νρν

ν

+

+

+=

121

12.187.0 EVR

(4)

This equation is used for a homogeneous soil layer and does not take into account any

stiffening effect from the upper track structure, i.e. the ballast or embankment (i.e. it is not

the critical track velocity). In this report, the parameter termed η is used to specify a maximum

permissible train speed VT(max) based on a percentage ONLY of the Rayleigh wave velocity (i.e.

50%, 70%, 100% etc.) where

RT VV η (max) = (5)

To give

( )νρν

νη

+

+

+=

121

12.187.0(max)

EVT

(6)

VT(max) therefore represents the maximum permissible train speed for a homogeneous soil

deposit for a given ratio assigned through the parameter η. The parameterη can be thought

of as the inverse of the factor of safety with respect to speed and hence its value is ≤ 1. For

example, if the intention was to run at 70% of the Rayleigh wave velocity VT(max)=0.7VR.

The latter part of Equation (6) represents the elastic shear modulus G calculated from:


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)1(2 v

EG

+= (7)

Note, in this report all stiffness referred to are Young’s Modulus in MPa.

In Figure 1 the Rayleigh wave velocity (Equation (6)) is plotted against the Young’s Modulus E

for η=1.0, 0.7, 0.5, with υ=0.45 and ρ=1600, 1800 & 2000 kg/m3.

Figure 1: Permissible train speed taken purely as a percentage of the Rayleigh-wave velocity

(the red line indicates a permissible speed of 100 m/s)

The graphs also indicate approximate ranges of clay stiffness for the assumed Poisson’s ratio.

The actual stiffness used at any particular site depends on the strain range, which in itself,

depends on the train speed and overall dynamic behaviour. As a general guide for a clay with a

plasticity index PI=30% the following can be assumed; linear behaviour for shear strains less

than 5.0e-5; with non-linear behaviour occurring between 5.0e-5 and 5.0e-4; and highly non-

linear behaviour for shear strains over 5.0e-4. The decision over what stiffness to use in any

0 20 40 60 80 100 120 140 160 180 200

Young's Modulus E (MPa)

0

20

40

60

80

100

120

140

160

Perm

issi

ble

Maxi

mum

Tra

in S

peed V

T(m

ax)

m/s

n=0.5;

Density :

1600

1800

2000

n=0.7;

Density :

1600

1800

2000

n=1.0; Density : 1600 1800 2000

soft

firm

stiff

very stiff

Approximate range

for dif ferent clay

stif fness values - shear

strain dependent

It is important that the correct value of stif fness E is applied based

on the anticipated induced shear strains for the different train speeds

The actual transient def lection can be estimated f rom the 'static'

def lection: note this maybe relatively low for high stif fness soils

Poisson's Ratio = 0.45

No Dynamic Effect

Some Dynamic

Effect

Increasingly Significant

Dynamic Effect

Passing Rayleigh

Wave Velocity


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analysis is therefore critical; this can be challenging for new high-speed lines where Rayleigh

wave effects are of concern. In-situ Rayleigh wave velocity measurements should therefore be

taken wherever possible and numerical analysis performed to assess dynamic effects with

train speed (for the particular train likely to be used). This is the starting point for calculating

the critical track velocity due to the addition of the upper track stiffness. In this report the

Rayleigh wave Number MRSM is defined through the Rayleigh subgrade velocity given by

R

TRSM

V

VM =

(8)

The equation represents a ratio for defining trains speeds running above or below the

Rayleigh ground wave speed. Similar expressions could be used for defining the critical track

velocity ratio; the natural frequency ratio; and the characteristic wavelength ratio. Reference

to these terms and their effect on the track response are given in reference [8].

The increase in the simulated dynamic track response is highlighted in Figure 2 which shows

the increase in transient displacements with speed for a constant damping ratio and stiffness.

This type of behaviour (i.e. the J-curve) has been observed on site.

Figure 2: (Dynamic / Static) displacement ratio verses the (Loading speed / Rayleigh wave

velocity). Note in this graph critical track velocity ≈ Rayleigh ground wave velocity

The J-curve in Figure 2 highlights the shape of the graphs in Figure 1 for the various η values.

4.1.2 What this means for current theory

The theoretical graphs (Figure 1) suggest that as the train speed increases considerably higher

stiffness (at the appropriate shear strain range) is required to ensure no Rayleigh wave issues

are generated. The curves are non-linear due to the Rayleigh wave velocity being related to

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Point Load Speed / Rayleigh Ground Wave Velocity

0

1

2

3

4

5

6

Dyn

am

ic D

ispla

cem

ents

/ S

tatic

Dis

pla

cem

ents

Ground Mach Cone

Formed


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the square root of the stiffness E and inversely proportional to the square root of the density.

The graphs suggest that Young’s Modulus values exceeding 100 MPa are required to fully

prevent Rayleigh-waves effects from forming for train speeds above 100 m/s (360 km/h) – for

low upper stiffness tracks. However, larger values of the Young’s modulus E mean that the

absolute magnitude of the transient deflection will reduce because the low speed ‘static’

deflection is small, i.e. even though multiples of the static deflection are applied the absolute

magnitude may still yield relatively low transient deflections at high-speed. Current theory

predicts that past the critical speeds the dynamic transient response reduces. These two

interesting observations suggest that some existing high-speed lines may actually be running

with Rayleigh wave effects but because the transient deflections are relatively low, due to the

higher ground stiffness, they have not been observed. The latter effect with dynamic

reductions past the critical speed is a possible explanation as to why very high train speed test

runs can occur.

The addition of embankments and stiff structures like concrete slab-track can shift the critical

speed above the Rayleigh ground wave velocity towards a higher value called the critical track

velocity. This technique can therefore be used to increase the train speed over poor ground in

addition to / or replacement of ground reinforcement such as CMCs or VCCs.

For ballasted track if particle velocities are relatively high then the ballast may still migrate

leading to a higher maintenance regime than desired. This aspect requires further

investigation as it has a significant impact when running high-speed trains on ballasted track

with a high track usage (such as HS2). Studies on the ballast Peak Particle Velocity (PPV) and

Peak Particle Acceleration (PPA) required to generate ballast movement have been reported

by several researchers. References [4, 5] reported values of PPV above 15–18 mm/s as causing

ballast deterioration and loss of compaction and more recently [6] reported that if ballast

accelerations exceed 0.7 to 0.8g the ballast will start to decompact; a limit of 0.35g was

therefore suggested. It is important to note however that the studies on particle acceleration

were performed by exciting the ballast layer via a shake table (i.e. from below). It is possible

that relatively high values of PPV and PPA would make conditions of ballast flight (combined

with high wind shear from passing trains) easier to occur. What would be of interest is to

examine relatively stiff tracks where Rayleigh wave velocities are still likely being exceeded

and measure the ballast particle velocity close to the sleepers (such as SNCF tracks). If the

PPV was relatively high it would be interesting to compare this to the track maintenance

regime to look for possible correlations. Other issues such as resonant effects discussed

earlier also need to be investigated as they may have a significant effect on track behaviour,

however DART3D predicts that these will be site and train specific.


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5 Computer Simulations 5.1 Stage 1 Simulations

The analyses were run on an 8-core Intel I7 Processor desk top computer. An explicit time

integration algorithm was used with a time step of ∆t=8 x 10-6 s for all the analyses presented.

Typically each computer simulation took between 2 to 3 weeks to run due to the sequential

nature of the processor (i.e the code is not yet parallelised) and the time period required; for

the train analyses a period of 1.4-1.6s was simulated. Table 1 shows the geometric depths and

material properties assumed in each analysis.

Table 1: Material properties assumed in the computer analysis (Run 1 – 8). p=density in kg/m3

For the general cases of Esubgrade=20 MPa and Esubgrade=50 MPa, the Rayleigh wave velocities are

calculated as VR(20)=59 m/s (MRSM=1.69) and VR(50)=93 m/s (MRSM=1.08) using Equation 4. In both

cases the Rayleigh wave velocity is therefore exceeded at a train speed of 100 m/s.

In the moving point load analyses a single axle load travelling at 100 m/s was simulated. The

purpose of these simulations was to explore critical speed development for all eight cases and

to investigate the level of shear strain development due to critical velocity effects only. The

mesh and element sizes are therefore set to model lower frequency critical velocity and track

critical velocity effects. For the moving point load analysis PL=210 kN per axle. For the train

analyses two trains were considered, one for a train similar to Thalys and the other for the X-

2000. The axle configuration for Thalys is shown in Figure 3a and for the X-2000 in Figure 3b.

(a) Thalys

(m) (m) (m) (m) (m) (m) (m) (m)

1 2 3 4 5 6 7 8 E (Mpa) v p

slab 0.45 20,000 0.25 2400

Rail 210,000 0.28 7850

Sleeper 20,000 0.25 2400

HBL 0.3 5,000 0.25 2200

Ballast 0.35 0.35 0.35 0.35 0.35 0.35 0.35 none 200 0.3 1600

Subballast 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 130 0.3 2000

Subgrade 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 90 0.3 2000

Improved soil layer none 1 4 1 4 1 4 1 80 0.3 1850

Embankment top none none none 5 5 5 5 50 0.3 1900

Embankment bottom none none none none 5 none 5 30 0.4 1850

Alluvium 1 7 6 3 6 3 9 6 9 20 0.4 1800

Alluvium 2 none none none none none 10 10 10 26 0.4 1800

Alluvium 3 none none none none none 10 10 10 34 0.4 1800

Material properties


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(b) X-2000

Figure 5: Train types simulated

For a given train speed the primary loading frequency for the Thalys train will be lower than

the X-2000 train since the maximum distance between two adjacent bogies for the Thalys

train is 18.7m; for the X-2000 it is 14.8m. The relationship between the train loading

frequencies, the Rayleigh wave velocity, the critical track velocity, the resonant train-track

velocity, the sleeper spacing, the characteristic wavelengths and the train suspension system

dynamics is the subject of current research by the Heriot-Watt University research group.

Typical axle loads are: (i) Thalys, 167 kN; (ii) X2000, power car 181 kN and coach 122 kN. The

moving point load was run until 0.8s. In all analyses linear properties were assumed, damping

was kept constant at 3% and a half mesh assumption was applied due to symmetry about the

track centre-line. Substructure element numbers ranged from 34,350 to 51,525 20-noded

brick elements, and lateral absorbing boundaries were applied to all runs.

Validation of the DART3D Code

Details about validation of the DART3D code can be found in reference [8] where verification

using linear and non-linear analyses of the Ledsgard site on the Swedish West Coast Main Line

are presented. For the purposes of this report Figure 5a shows part of this validation for the

sleeper deflection at critical velocity (using the same DART3D code as the one in this report).

Figure 5a: Example validation of the linear part of DART3D for the Ledsgard site at 51 m/s [8]

0 1 2 3 4Time (s)

-20

-10

0

10

Sle

eper

Defle

ctio

n (

mm

)

Simulated

Measured


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5.1.1 Simulation Analysis S1.1

A schematic of Run 1 is shown in Figure 4

Figure 4: Run 1 simulation

The material properties used are shown in Table 1 and the results of the analysis are shown in

Figures 5-7.

(a) E20-THALYS

Subgrade

Subballast

Ballast

Subgrade

Subballast

Ballast

Alluvium (7m)

Bedrock

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)


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(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT

Figure 5: Typical transient sleeper response time history at the mesh mid-point for each train

loading condition for Analysis 1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Deflection (

mm

)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time (s)

-10

-8

-6

-4

-2

0

2

Deflection (

mm

)


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(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT

Figure 6: Typical transient shear strain time history for the subgrade at the mesh mid-point for

each train loading condition for Analysis 1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Time(s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time(s)

-0.001

0.000

0.001

0.002

Str

ain

EX

EY

EZ

DSTAIN


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(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT

Figure 7: Analysis 1 Ground Surface Displacement Contour Plots for each train loading

condition


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Figure 5a shows that the code predicts a very high transient track response when the primary

stiffness of the clay subgrade is E=20 MPa and a Thalys train is simulated. This is because

MRSM=1.69 and the clay stiffness is very low. In reality the development of plasticity would

increase hysteretic damping within the soil, however the clay stiffness would reduce due to

this plasticity. While the response has reduced in Figure 5b (E=50 MPa) compared to Figure 5a

it is still relatively high since the ground Rayleigh wave velocity has been exceeded (see Figure

4) with MRSM=1.08.

The X-2000 train in Figure 5c indicates a reduced (but still relatively high) transient track

response. The high response from the moving point load analysis also shows that the Rayleigh

wave velocity has been exceeded. Figure 6a-d shows the corresponding transient dynamic

strain responses for the clay subgrade at a depth of 2.5m below ground level.

For all cases shown in Figure 6 significant strains are predicted indicating that high levels of

track non-linearity are being developed. Again this should be expected given that Rayleigh

wave velocities are being exceeded and subgrade stiffness is relatively low. Increasing

damping would reduce the predicted values.

Appendix A presents vertical strain time histories with depth.

The ground surface contour plots shown in Figure 7a-c shows that critical conditions have

been achieved. Figure 7d clearly shows cone development (note this analysis does not

simulate resonant conditions as only a single moving axle load is simulated).


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Figures 9-11.

(a) E20-THALYS

Subgrade

Subballast

Ballast

Subgrade

Subballast

Ballast

Alluvium (6m)

Bedrock

Ground improved layer (1

m)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 19

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Deflection (

mm

)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time (s)

-10

-8

-6

-4

-2

0

2

Deflection (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 20

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT

Figure 10: Typical transient shear strain time history for the subgrade at the mesh mid-point

for each train loading condition for Analysis 2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Time(s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time(s)

-0.001

0.000

0.001

0.002

Str

ain

EX

EY

EZ

DSTAIN


Document no.:


Rev:P02 FINAL DRAFT


Page 21

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT


condition


Document no.:


Rev:P02 FINAL DRAFT


Page 22

In this analysis the upper formation layer has been improved to a depth of 1m.

Figures 9a&b show that the program predicts significant dynamic sleeper deflections and the

overall performance is similar to that of Analysis 1. Uplift of the sleepers due to critical velocity

conditions is clearly evident. It should be noted that at the Ledsgard site a 2m deep

embankment, with a significantly higher material stiffness, increased the critical velocity to a

higher value but critical velocity conditions were still achieved.

Track strains are presented in Figure 10a-d for a soil element approximately 2.5m below

ground level (i.e. below the improved layer). All presented strains are relatively high indicating

non-linear behavior.


In Figure 11a-d cone formation is evident (particularly in Figure 11a&d) and strong Rayleigh

wave propagation for Thalys is seen. The X-2000 plot shown in Figure 11c shows notably lower

dynamic effects.


Document no.:


Rev:P02 FINAL DRAFT


Page 23





Figures 13-15.

(a) E20-THALYS

Subgrade

Subballast

Ballast

Subgrade

Subballast

Ballast

Alluvium (3m)

Bedrock


m)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 24

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Deflectio

n (

mm

)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time (s)

-10

-8

-6

-4

-2

0

2

Defl

ecti

on (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 25

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Time(s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time(s)

-0.001

0.000

0.001

0.002

Str

ain

EX

EY

EZ

DSTAIN


Document no.:


Rev:P02 FINAL DRAFT


Page 26

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT


condition

In this analysis the upper formation layer has been improved to a depth of 4m.


Document no.:


Rev:P02 FINAL DRAFT


Page 27

Figures 13a-d show that increasing the improved depth from 1m (Analysis 2) to 4m has

reduced the transient sleeper deflections for the 20 MPa subgrade stiffness; but has had a

limited effect on the 50 MPa stiffness subgrade layer due to the relatively small differential

between the 50 and 80 MPa stiffness. However it is noted that uplift has reduced. Strains 2.5m

below the ground surface are presented in Figure 14a-d and are lower for both the Thalys and

X-2000 trains when compared to the 1m ground improvement case.


Ground surface contours are presented in Figure 15a-d.


Document no.:


Rev:P02 FINAL DRAFT


Page 28





Figures 17-19.

(a) E20-THALYS

Subgrade

Subballast

Ballast

Embankment (5m)

Subgrade

Subballast

Ballast

Alluvium (6m)

Bedrock


m)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 29

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

De

flect

ion (

mm

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Time (s)

-25.00

-16.25

-7.50

1.25

10.00

De

flect

ion

(m

m)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time (s)

-10

-8

-6

-4

-2

0

2

Defle

cti

on (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 30

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Time(s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time(s)

-0.001

0.000

0.001

0.002

Str

ain

EX

EY

EZ

DSTAIN


Document no.:


Rev:P02 FINAL DRAFT


Page 31

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT


condition


Document no.:


Rev:P02 FINAL DRAFT


Page 32

In this analysis a 5m high embankment is simulated with an improved 1m depth soil layer.

Figures 17a-d show the dynamic transient sleeper deflection. The stiffness of the

embankment is primarily 50 MPa, i.e. below the critical speed value and hence DART3D will

predict critical velocity development due to the Rayleigh wave velocity being exceeded in the

embankment (as well as the subgrade). The elevated response is clearly shown in Figure 17.

It is interesting to note that even when a single moving axle load is simulated an oscillation in

the embankment response is predicted (Figure 17d), i.e. it is vibrating at its natural frequency

which can be estimated by analysing the oscillating tail after the axle has passed. The analysis

suggests that the embankment is not stiff enough to prevent Rayleigh wave development at

the simulated speed.

The strains are presented in Figure 18a-d for the clay layer 7m below the embankment top

(this explains their relatively low values compared to earlier analysis). This point was chosen to

enable a direct comparison to the clay soil strains presented in the earlier track structure

analyses. The low strain values suggest that the embankment is able to reduce the dynamic

shear strains in the clay subgrade (similar to a ground improvement case), but due to the

embankment’s low stiffness, is unable to prevent critical velocity development. As with

previous studies increasing damping will help reduce overall transient deflections and strains.


Figures 19a-d show the ground surface displacement contours and clearly indicate cone

development. Of interest is that the majority of the cone appears to be forming in the

embankment. It is therefore possible that the embankment is causing the Rayleigh wave to be

‘guided’.


Document no.:


Rev:P02 FINAL DRAFT


Page 33





Figures 21-23.

(a) E20-THALYS

Subgrade

Subballast

Ballast

Embankment (10m)

Subgrade

Subballast

Ballast

Alluvium (3m)

Bedrock


m)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 34

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Deflection (

mm

)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time (s)

-10

-8

-6

-4

-2

0

2

De

fle

ctio

n (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 35

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT

Figure 22: Typical transient shear strain time history for the clay subgrade at the mesh mid-

point for each train loading condition for Analysis 5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Time(s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time(s)

-0.001

0.000

0.001

0.002

Str

ain

EX

EY

EZ

DSTAIN


Document no.:


Rev:P02 FINAL DRAFT


Page 36

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT


condition


Document no.:


Rev:P02 FINAL DRAFT


Page 37

In this analysis a 10m high embankment is simulated with an improved 4m depth soil layer.

The lower 5m embankment stiffness is 30 MPa.

Figure 21a-c show the transient displacement response for the 4 cases considered. The

embankment stiffness is relatively low for the speed simulated: 50 MPa for the upper 5m

embankment height and 30 MPa for the lower 5m embankment height; this latter stiffness

being significantly below the stiffness required to prevent Rayleigh wave formation in the

embankment. As such the transient track response is relatively high with a high degree of

track interaction. As with the previous embankment case, signs of strong embankment

participation are evident by oscillations in the sleeper response for the single axle case (Figure

21d) when the load has passed over the observation point. However the improved soil layer

has obviously had some effect in helping to control overall track behaviour.

The strains are shown in Figure 22a-d for the soil in the lower embankment layer, i.e. 8m

below the ground level and Figure 23a-d shows the ground surface contour plots of

displacement indicating cone formation, especially for the 20 MPa stiffness subgrade.



Document no.:


Rev:P02 FINAL DRAFT


Page 38





Figures 25-27.

(a) E20-THALYS

Subgrade

Subballast

Ballast

Embankment (5m)

Subgrade

Subballast

Ballast

Alluvium (29m)

Bedrock


m)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

De

flect

ion (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 39

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

cti

on (

mm

)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time (s)

-10

-8

-6

-4

-2

0

2

Defl

ec

tio

n (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 40

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Time(s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time(s)

-0.001

0.000

0.001

0.002

Str

ain

EX

EY

EZ

DSTAIN


Document no.:


Rev:P02 FINAL DRAFT


Page 41

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT


condition


Document no.:


Rev:P02 FINAL DRAFT


Page 42

In this analysis the depth of subgrade clay has been significantly extended and a 5m high

embankment is simulated with a 1m improved layer.

Figures 25 shows the dynamic transient sleeper response for the cases considered.

Examination of the cone development in Figure 25a&b indicate that large parts of the

embankment are participating, especially when the subgrade stiffness is 20 MPa. The

interpretation of this analysis (for the damping level considered) is that the dynamic

excitation would eventually lead to significant damage of the support structure. Issues around

the numerical stability are evident when E=20 MPa due to the high embankment

participation. The X-2000 simulations also show a high degree of transient deflection. It is

thought that the low level of ground improvement is not sufficient to effectively support the

embankment at the simulated speeds.

The strain level for the soil 7m below the embankment ground surface are shown in Figures

26a-d. The strain levels indicate that a significant amount of the deformation is occurring in

the embankment and as before it appears that the embankment is acting as a Rayleigh wave

guide.


The ground surface contour plots for all the simulations considered in Analysis 6 are shown in

Figures 27a-d. Cone generation is clearly observed.


Document no.:


Rev:P02 FINAL DRAFT


Page 43





Figures 29-31.

(a) E20-THALYS

Subgrade

Subballast

Ballast

Embankment (10m)

Subgrade

Subballast

Ballast

Alluvium (26m)

Bedrock


m)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 44

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

De

flect

ion (

mm

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Time (s)

-25.00

-16.25

-7.50

1.25

10.00

De

flect

ion

(m

m)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time (s)

-10

-8

-6

-4

-2

0

2

Deflec

tion (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 45

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time(s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time(s)

-0.001

0.000

0.001

0.002

Str

ain

EX

EY

EZ

DSTAIN


Document no.:


Rev:P02 FINAL DRAFT


Page 46

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT


condition

In this analysis the depth of subgrade clay has been significantly extended and a 10m high

embankment is simulated with a 4m improved layer.


Document no.:


Rev:P02 FINAL DRAFT


Page 47

The transient sleeper results are shown in Figures 29a-d. Although the ground has been

improved, the 5m lower embankment stiffness is only 30 MPa, again well below the stiffness

required to prevent Rayleigh ground waves from forming. Consequently the predicted

transient track response is high; this combined with the increased depth (especially for the 20

MPa case) gives the response shown. The X-2000 simulation shows good stability, but

deflections are high.

The computed strains are shown in Figure 30a-d for a soil element approximately 8m below

the embankment ground surface and Figure 31a-d shows ground cone formation in all cases

considered due to the low embankment stiffness, again signs of guided waves are observed.



Document no.:


Rev:P02 FINAL DRAFT


Page 48





Figures 33-35.

(a) E20-THALYS

Subgrade

Subballast

Ballast

Subgrade

Subballast

Slab

Alluvium (29m)

Bedrock


m)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 49

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-25.00

-16.25

-7.50

1.25

10.00

Defle

ctio

n (

mm

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Time (s)

-25.00

-16.25

-7.50

1.25

10.00

De

flect

ion

(m

m)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time (s)

-10

-8

-6

-4

-2

0

2

Defl

ec

tio

n (

mm

)


Document no.:


Rev:P02 FINAL DRAFT


Page 50

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time(s)

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

EX

EY

EZ

DSTAIN

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Time(s)

-0.001

0.000

0.001

0.002

Str

ain

EX

EY

EZ

DSTAIN


Document no.:


Rev:P02 FINAL DRAFT


Page 51

(a) E20-THALYS

(b) E50-THALYS

(c) E50-X2000

(d) E50-POINT


condition


Document no.:


Rev:P02 FINAL DRAFT


Page 52

In this analysis the depth of subgrade clay has been significantly extended and concrete slab-

track has been simulated with a 1m improved ground layer.

Figure 33a-d shows the transient sleeper response. It is immediately clear that the program

predicts a difference in the dynamic performance of concrete slab-track to that of ballasted

track (although all the ballast cases modelled in Stage 1 would need to simulated to confirm

that this is the case for all track structures considered). For both simulated trains the Rayleigh

wave effects do not appear to be as high as those of the ballasted track, especially for the

E=50 MPa analysis, using this finite element mesh. The sleeper response appears to be similar

to that of sub-critical velocities (albeit at higher overall deflections due to the low subgrade

stiffness).

Figure 34a-d shows the strains 3m below the slab-track surface (i.e. below the improved

layer). Again lower values are predicted than those of the ballasted track due to the superior

load distributing properties of the slab-track compared to the ballasted track.


Figure 35a-d shows the ground contour plots of displacement. When the subgrade stiffness is

20 MPa Rayleigh wave propagation is evident, this reduces significantly when the subgrade

stiffness is 50 MPa. The plots indicate that some ground propagation will still occur even when

concrete slab-track is used (the train speed is still higher than the in-situ ground Rayleigh wave

velocity) however propagation due to critical velocity effects would appear to be less than

those of ballasted track.

While further simulation work is required to verify the dynamic performance of the slab-track

analysis (at the required 360 km/h speed and track conditions) this limited study in Stage 1 has

highlighted that significant benefits may be achievable, in terms of geo-dynamic

performance, using a concrete track rather than a ballasted track form.


Document no.:


Rev:P02 FINAL DRAFT


Page 53

5.1.9 Discussion of Stage 1 simulations

In Stage 1 three loading conditions were considered: (i) a single moving axle load; (ii) an axle

load and configuration representing a Thalys train; (iii) an axle load and configuration

representing an X-2000 train. For the majority of cases studied the primary soil stiffness has

been below the stiffness required to prevent cone formation (critical velocity effects) and

hence the computer simulations have predicted relatively large sleeper displacements for

ballasted track. Evidence of ground cones was seen in nearly all the ground contour plots

presented. Evidence of guided Rayleigh waves in the embankments was also observed, likely

due to the low stiffness simulated particularly for the lower embankment sections (which

were only at a stiffness of 30 MPa). Deeper clay soil subgrades were seen to adversely affect

the transient sleeper response. For the Thalys simulations some numerical instabilities were

observed for the low track stiffness simulations, this can be addressed using a smaller time

step. It is recommended that additional studies are performed to assess the sensitivity of the

critical track velocity by varying the upper track bending stiffness.

The final set of computer simulations concerning concrete slab-track indicated a significant

improvement in dynamic track response due to the higher stiffness (for the analysis case

considered). The transient sleeper response indicated a significant reduction in deflection

when compared to ballasted track (although each analysis case would need to be simulated to

confirm this). The strains also indicated a reduction in magnitude when compared to ballasted

track. This part of the study suggests that significantly stiffening the upper track structure, for

the two primary ground stiffness values of 20 and 50 MPa used in these analyses, is required

to run at 360 km/h. In addition a concrete slab-track track form may give better overall track

dynamic performance than a ballasted track due to this higher upper track structure stiffness.

geo-dynamic modelling of track bed and...

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