geotechnical challenges in high speed railway lines

Pedro Alves Costa

Geotechnical Challenges in High Speed Railway Lines:The critical speed issue

1. Introduction

1. Introduction

NEW PARADIGM – THE CRITICAL SPEED OF THE TRACK-GROUND SYSTEMS CAN EASILLY BE ACHIEVED!!

LOAD

Soil-

structure

Quasi-static mechanism

t

t

F

uPuw

F

1. Introduction

LOAD

Soil-

structure

Quasi-static mechanism

Dynamic mechanism

F

uP

t

t

1. Introduction

When the train speed reaches the "critical barrier", a radiation of energy

occurs, similar to...

…but it can be even more complex when dealing with geotechnical materials!

1. Introduction

2. Basics of Critical Speed

2. Basics of Critical speed

( ) ( )

<<−

×=0

||,||22

1

,0,,byaxctx

batyxpz

δ

( ) ( ) ( )111 ,,0,, ckykfykpz −= ωδω

2. Basics of Critical speed

Usually the ground is not homogeneous over depth…

2. Basics of Critical speed

Usually the ground is not homogeneous over depth…

0 0.2 0.4 0.6 0.8 1 1.2 1.40.5

1

1.5

2

M=c/Cs

Co

eficie

nte

s d

e a

mp

lific

ação

din

âm

ica

H=6 mH=3 m

y

x

z

2.0 m

2.0 mc

H=3.0m

E=200 MPa

ν=0.35

ρ=2000 kg/m

ξ=0.03

3

E=50 MPaν=0.35

ρ=2000 kg/m

ξ=0.03

3

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

f (Hz)

k1 (

/m)

M=0.5

M=0.7

M=0.934M=1.0

M=1.5

M=1.9

3. Track-ground critical speed

3. Track-ground critical speed

Pzc

xRail: EI , m

Railpad: k , c

Sleepers: mz

Ballast: E , ρ ,h hb b

s

p p

r r

Ground layer 1

Ground layer 2

Ground layer n

Simplified semi-analytical modelling

Sheng, X., C. Jones, and D. Thompson, A theoretical study on the influence of the track on train-induced ground vibration. Journal of Sound and Vibration, 2004. 272: p. 909-936.Costa, P. A., A. Colaço, R. Calçada and A. S. Cardoso 2015. Critical speed of railway tracks. Detailed and simplified approaches. Transportation Geotechnics 2: 30-46.

3. Track-ground critical speed

Simplified semi-analytical modelling

V1

(ballasted track)

V2

(slab track)

V3

(slab track)

Rail UIC60 UIC60 UIC60

msleeper (kg/m) 490 - -

hballast/slab (m) 0.35 0.35 0.44

Ebal/lastlslab (Pa) 130e6 30e9 30e9

ρρρρ ballast/lslab (kg/m3) 1700 2500 1990

3. Track-ground critical speed

Homogeneous ground

0.2 0.4 0.6 0.8 1 1.21

1.5

2

2.5

3

3.5

4

4.5

5

M=c/Cs

FD

A-v

ert

ica

l d

isp

lace

me

nt

Cr

Ballasted track

Slab track - V1

Slab track

(V2)

0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8

1

f (Hz)

k1 (

/m)

P-SV mode

(GROUND)

Ballasted track

Slab track - V2

Slab track

(V3)

The critical speed of the system is fully dominated by the properties of the

ground.

Costa, P. A., A. Colaço, R. Calçada and A. S. Cardoso 2015. Critical speed of railway tracks. Detailed and simplified approaches. Transportation Geotechnics 2: 30-46.Mezher, S. B., D. P. Connolly, P. K. Woodward, O. Laghrouche, J. Pombo and P. A. Costa. 2016. Railway critical velocity - Analytical prediction and analysis. Transportation Geotechnics 6: 84-96.

3. Track-ground critical speed

Non-homogeneous ground

The critical speed of the system is affected by the stiffness of the track.

The analysis of the critical speed can be performed by simplified methods.

0.5 1 1.5 20.8

1

1.2

1.4

1.6

1.8

2

M=c/Cs

FDA

- v

ert

ica

l dis

pla

cem

en

t

Ballasted trackSlab track Slab track

(V3)

0 10 20 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

f (Hz)

k1 (

/m) Ballasted track

P-SV mode

(ground)

Slab track

Slab track

(V3)

4. Track-embankment-ground critical speed

4. Track-embankment-ground critical speed

Numerical modelling

CL2.5D FEM

ITM

Ground

2.5 BEM

( ) ( )ω=ωω+ω−+++ ,kp~,ku~)),k(KMKkKkKikK( 1n1n1global5

global2global4

41

global3

21

global21

global1

Regular geometry – 2.5D BEM

Complex geometry – 2.5D FEMAlves Costa, P., R. Calçada, and A. Cardoso, Track–ground vibrations induced by railway traffic: In-situ measurements and validation of a 2.5D FEM-BEM model. Soil Dynamics and Earthquake Engineering, 2012. 32: p. 111-128.

4. Track-embankment-ground critical speed

Numerical modelling – the role of embankment properties

Continuos slabtrack

Vs={220;300} m/s

ρ=2000 kg/m3ν=0,35

ξ=0,03

Vs={185;220} m/s

ρ=2000 kg/m3

ν=0,35

ξ=0,03

Embankment 2

Embankment 1 h={1;2;3}m

h=2 m

Vs=variable

ρ=1900 kg/m3ν=0.45ξ=0.03In

-situ

so

il

-20 m

150 m/s

480 m/s

-3 m

Shear wave

velocity

z

AnalysisVS,Embankment1

(m/s)

VS,Embankment2

(m/s)

hEmbankment1

(m)

A1 220 185 1

A2 220 185 2

A3 220 185 3

A4 300 220 1

A5 300 220 2

A6 300 220 3

Does embankmentproperties affect the criticalspeed value?

4. Track-embankment-ground critical speed

Numerical modelling – the role of embankment properties

AnalysisVS,Embankment1

(m/s)

VS,Embankment2

(m/s)

hEmbankment1

(m)

A1 220 185 1

10 m/s160 m/s176 m/s195 m/s

Due to the track-embankment properties the critical speed can be larger

than the shear wave velocity in the shallow layer of the ground

4. Track-embankment-ground critical speed

Numerical modelling – the role of embankment properties

AnalysisVS,Embankment1

(m/s)

VS,Embankment2

(m/s)

hEmbankment1

(m)

A1 220 185 1

A2 220 185 2

A3 220 185 3

Analysis

Critical speed (m/s)

Error (%)Direct

approach

Simplified

approach

A1 176 164 -6.0

A2 181 173 -4.4

A3 182 181 -0.5

http://vcritical.simpleaxis.com/

Preliminiary assessement of

critical speed in few seconds

Colaço, A.; Alves Costa, P.; Geotechnical challenges in very high speed railway tracks. The

numerical modelling of critical speed issues. NUMGE 2018

4. Track-embankment-ground critical speed

Numerical modelling – the role of embankment properties

AnalysisVS,Embankment1

(m/s)

VS,Embankment2

(m/s)

hEmbankment1

(m)

A4 300 220 1

A5 300 220 2

A6 300 220 3

Analysis

Critical speed (m/s)

Error (%)Direct

approach

Simplified

approach

A4 195 188 -3.6

A5 204 199 -2.4

A6 206 201 -2.4

Embankment

height

Embankment

stiffness

Critical

Speed

5. The critical speed effects

5. The effects

5. The effects

Large rail displacements

Risk of derailment

Large strains and stresses in the

subgrade

Colaço, A., P. Alves Costa and P. Lopes, Dynamicground stress‐path evolution due to the railwaytraffic: A parametric study. Revista Internacional de Métodos Numéricos para Cálculo y Diseño enIngeniería, 2015. 31(2): p. 120-131.

Large rail displacements

Risk of derailment

Large strains and stresses in the

subgrade

Colaço, A., P. Alves Costa and P. Lopes, Dynamic ground stress‐path evolution due to therailway traffic: A parametric study. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 2015. 31(2): p. 120-131.

Shakedown limit can be achieved

Accumulation of plastic strains

Track deterioration

5. The effects

5. The effects

The critical speed and the shakedown limit

5. The effects

The critical speed and the shakedown limit

5. The effects

The critical speed and the shakedown limit

5. The effects

The critical speed and the shakedown limit

5. The effects

0.25

0.30

Slab: E= 30 GPa

ρ=2500 kg/m

ν=0.2; ξ=0.001

3

PCL: E= 5 GPa ρ=2500 kg/m

ν=0.2; ξ=0.001

3

Rail: UIC60

Railpad: k=40 kN/mm

c=8 kN.s/m

Ground: Cs=120 m/s

ρ=1900 kg/m ν=0.3; ξ=0.03

K =0.5

3

0

2.60

0 50 100 1500.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Velocity (m/s)

DA

F (

-)

Original scenario

Without poor

concrete layer

Critical

speed

20 40 60 80 100 1200

500

1000

1500

2000

2500

Velocity (m/s)

����

�

Original scenario

without poor concrete layer

Service speed should be around

0.6-0.7 of the critical speed to avoid

strong reduction of shakedown limit

VcrThe critical speed and the shakedown limit

Alves Costa, P.; Lopes, P. Silva Cardoso, A. Soil shakedown analysis of slab railway tracks:

numerical approach and parametric study. (2018) Computers and Geotechnics (submitted)

5. Case study - Ledsgard

Alves Costa, P., et al., Influence of soil non-linearity on the dynamic response of high-speed railway tracks.Soil Dynamics and Earthquake Engineering, 2010. 30(4): p. 221-235.

Alves Costa, P., R. Calçada, and A. Silva Cardoso, Track-ground vibrations induced by railway traffic, in

Applications of Computational Mechanics in Geotechnical Engineering,, L. Sousa, et al., Editors. 2012,

Balkema.

5. The effectsLedsgard - General description

2. Numerical Model

3,352,502,702,502,702,503,35

1,35

Via oriental

Travessase=0,67 m

Carris UIC60

Via ocidental

Sentido Norte -Sul

Camadas Granulares

Maciço de Fundação

10-4

10-3

10-2

10-1

100

101

0

0.2

0.4

0.6

0.8

1

Distorção (%)G

sec/

Gm

ax

Experimental results

0 5 10 15 20 25 30 35 40-15

-10

-5

0

5

10

15

Tempo (s)

De

slo

cam

en

to v

ert

ica

l (m

m)

0 1 2 3 4-15

-10

-5

0

5

10

15

Tempo (s)

De

slo

cam

en

to v

ert

ica

l (m

m)

0 50 100 150 200-15

-10

-5

0

5

10

15

Velocidade de circulação (km/h)

De

slo

cam

en

to d

e p

ico

(m

m)

Train speed (km/h)

Pe

ak v

ert

ica

l dis

pla

ce

me

nt (m

m)

Ve

rtic

al d

isp

lace

me

nt (m

m)

Ve

rtic

al d

isp

lace

me

nt (m

m)

5. The effectsLedsgard - Measurements

Ledsgard – Elastic numerical modelling

5. The effects

A

B

C

G Gm ax s ec

1 1

Shear strain

Shear stress

D amping

Strains 10-6 10-5 10-4 10-3 10-2 10-1

Small Medium High Failure

Elastic

Elastoplatic

Effect of

cyclic loading

Analysis

approach

Linear

elastic

Equivalent

linear analysis

Non-linear analysis

Soil behaviour is clearly non-linear;

Demand of new prediction

approaches

The critical speed is dependent on

train properties;

5. The effectsLedsgard – Non linear behaviour

5. Case study - Ledsgard

0 1 2 3 4-15

-10

-5

0

5

10

15

Tempo (s)

De

slo

ca

me

nto

ve

rtic

al (

mm

)

0 50 100 150 200 250-20

-15

-10

-5

0

5

10

15

Train speed (km/h)

Pe

ak

dis

pla

cem

en

t (m

m)

Ledsgard – Linear equivalent analysis

Time (s)

Time (s)

Vert

ical d

ispla

cem

ent (m

m)

Vert

ical d

ispla

cem

ent (m

m)

6. Some mitigation solutions

Wittenberge (High speed railway line Hamburg – Berlin, Germany):

6. Some mitigation solutionsStone columns

• Stone columns

• Diameter: 0.6m to 0.8m

• Spacing: 2.0m x 1.25m

[1] V.R. Raju – “Ground improvement techniques for railway embankments”,

Keller Grundbau GmbH, Technical Paper 10-59E

6. Some mitigation solutionsStone columns

Aterro

Sub-balastroBalastro

TravessaCarris

[m]

1,6 1,6 1,6 1,6 1,4 1,4 1,6 1,61,61,61,61,41,41,6

21,6

Colunas de brita

(Diâmetro = 0,8 m)

E [MPa] ρ [kg/m3] ν [-] D [-] Cs [m/s]

160 2000 0,3 0,03 175

Stone columns

Embankment

Cs = 100 m/s 12 m

Cs = 200 m/s

2 mCs = 178 m/s

5. Some mitigation solutionsStone columns

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Velocidade de circulação [m/s]

Fa

cto

r d

e A

mp

lific

açã

o D

inâ

mic

a [

-]

sem colunas

com colunas (E=160MPa)com colunas (E=240MPa)

com colunas (E=320MPa)

Load speed (m/s)

Dyn

am

ica

mp

lifica

tio

nfa

cto

r (-

)

Reference

scenario

Stone columns

E=160 MPa

Stone columns

E=240 MPa

Stone columns

E=320 MPa

In layered ground, installation of stone columns allows to increase the critical

speed

6. Some mitigation solutions

Cutter-Soil-Mixing (CSM)

6. Some mitigation solutions

Embankment reinforced with geogrids and deep soil mixing columns

1,6 1,6 1,6 1,6 1,4 1,4 1,6 1,61,61,61,61,41,41,6

21,6

Aterro

Sub-balastroBalastro

TravessaCarris

Barretas de DeepSoil Mixing

(Largura = 0,8 m)

[m]

6. Some mitigation solutions

Cutter-Soil-Mixing (CSM)

E [MPa] ρ [kg/m3] ν [-] D [-] Cs [m/s]

650 2000 0,3 0,03 354

1000 2000 0,3 0,03 439

CSM panels

Cs = 100 m/s 12 m

Cs = 200 m/s

2 mCs = 178 m/s

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Velocidade de circulação [m/s]

Fa

cto

r d

e A

mp

lific

aç

ão

Din

âm

ica

[-]

sem barretas

com barretas (E = 650 MPa)

com barretas (E = 1000 MPa)

Dyn

am

ica

mp

lifica

tio

nfa

cto

r (-

)

Load speed (m/s)

6. Some mitigation solutions

Cutter-Soil-Mixing (CSM)

Large increase of the critical speed

Critical speed is governed by the embankment properties

7. Conclusions

7. Conclusions

The problem of “critical speed” due to moving loads was revisited.

It was shown that the critical speed is equal to the lower phase velocity of the

system track-embankment-ground.

A simplified approach for the assessment of the critical speed of elastic linear

systems is proposed. This simplified approach can very useful for scoping

analysis, in order to identify the railway stretches that should be submitted to

detailed analysis.

It was shown that the critical speed should be assessed taking into account

the particular site conditions and not based in prescriptive rules. Critical

speed is governed by the ground stiffness and layering, embankment

properties and track type.

.

7. Conclusions

It was shown that when the train speed becomes close to the critical speed,

the strains experienced in the ground are not compatible with a linear

approach and that a strong reduction of the elastic shakedown limit load

occurs.

A numerical approach based on the 2.5D FEM, where the ground is

simulated by an equivalent linear model, is proposed as a suitable method

for the assessment of vibrations induced by very high-speed traffic.

Some measures to increase critical speed were presented and discussed. It

was shown that 2.5D approach is a suitable method for the support on the

design of new high-speed railway lines.

Thank you for your attention Pedro Alves Costa____________________Assistant ProfessorFaculty of EngineeringUniversity of PortoPortugal

Email: pacosta@fe.up.ptmobile: +351 962934245