Determination of dynamic soil characteristics and … · 2 Laboratoria de Geotecnia, CEDEX, Spain 3...

$: Determination of dynamic soil characteristics and … · 2 Laboratoria de Geotecnia, CEDEX, Spain 3 D2S International, Belgium. Transfer functions ... Seismic refraction test t 1$
RIVAS Final Conference "Vibrations – Ways out of the annoyance"

Royal Flemish Academy of Belgium, Brussels, 21 November 2013

RIVAS Final Conference, 21 November 2013 1

Determination of dynamic soil characteristics and

transfer functions to support the evaluation of the

efficiency of vibration mitigation measures

H. Verbraken1, V. Cuellar2, B. Stallaert3, G. Lombaert1 and G. Degrande1

1 Department of Civil Engineering, KU Leuven, Belgium2 Laboratoria de Geotecnia, CEDEX, Spain3 D2S International, Belgium

Transfer functions


Numerical prediction [Many authors]

z

x

y

x

x′

gk(t)

v(x, t) =

na∑

k=1

∫t

−∞

HTv

(xk(τ), x, t − τ)gk(τ)dτ (1)

Transfer functions


Empirical prediction (e.g. FRA and FTA [Hanson et al., 2005, 2006])

• Prediction of the ground vibration velocity level in one-third octave bands:

Lv = LF + TML (2)

Measurement lineRail alignment

Impact locations

xy

z

TML = 10 log10

(

h

n∑

k=1

10TMPk

10

)

(3)

Transfer functions


Insertion loss for vibration mitigation measures [Stiebel al., 2012]

Before

After

Test site Reference site

TMtbP

TMtaP

TMrbP

TMraP

E1

E2

C1

C2

• Vibration isolation efficiency:

E = TMtaP − TMtb

P︸︷︷︸

E2

+ TMrbP − TMra

P︸︷︷︸

C2

(4)

E = TMtaP − TMra

P︸︷︷︸

E1

+ TMrbP − TMtb

P︸︷︷︸

C1

(5)

Dynamic soil characteristics


• (a) Dilatational and (b) shear wave in an elastic medium.

(a) (b)

• Dilatational and shear wave velocity:

Cp =

√

λ + 2µ

ρ=

√

M

ρ(6)

Cs =

√µ

ρ(7)



• (a) τ − γ curve under cyclic excitation and (b) shear modulus degradation curve and (b) material

damping ratio for Toyoura sand (Kokusho, 1980):

(a)

• Material damping ratio

(correspondence principle):

(λ + 2µ)⋆ = (λ + 2µ)(1 + 2βpi) (8)

(µ)⋆ = µ(1 + 2βsi) (9)

(b)

(c)



1. Archive records and test information.• Geological maps, results of previous geotechnical investigation.

• Estimation of the soil layering and the dynamic characteristics of each layer.

• Use of empirical relations cannot replace in situ or laboratory testing !

2. Classical soil mechanics tests on (undisturbed) soil samples.• At least one sample per soil layer; lateral sampling.

• Mass density, void ratio, degree of saturation, plasticity index,. . . .

3. Non-intrusive geophysical tests at small strain levels.• Combined surface wave - seismic refraction test.

• Measure input force.

4. Intrusive geophysical tests at small strain levels.• Seismic cone penetration test (SCPT).

• Down hole or cross hole test.

5. Dynamic laboratory experiments on (undisturbed) soil samples.• Resonant column test.

• Cyclic triaxial test.

• Bender element test.



Spectral Analysis of Surface Waves

Signal Analyzer

Impulse LoadNear Receiver Far Receiver



Shear wave velocity: frequency-wavenumber analysis

[Rix et al., JGGE, 2000; Lai et al., SDEE, 2002]

• Phase velocity CER(ω) from peaks of the transfer function HE

zz(kr, ω)::

HEzz(kr, ω) =

∫∞

0

HEzz(r, ω)J0(krr)r dr (10)

• (a) Transfer function HEzz(kr, ω), (b) phase velocity CE

R(ω), and (c) shear wave velocity profile::

(a) (b)0 20 40 60 80

0

100

200

300

Frequency [Hz]

Ph

ase

ve

loci

ty [

m/s

]

(c)0 100 200 300 400 500

0

1

2

3

4

5

Shear wave velocity [m/s]

De

pth

[m

]



Material damping ratio: Arias intensity [Badsar, 2012]

• Arias intensity IEzz(r):

IEzz(r) =

π

2g

∫∞

0

a2z(r, t)dt (11)

• (a) Displacement uz(r, t), (b) Arias intensity IEzz(r) and (c) material damping ratio profile:

(a) (b)0 20 40 60 80 100

10−5

100

105

Distance [m]

Normalized Arias intensity [−]

(c)0 0.05 0.1

0

1

2

3

4

5

Material damping ratio [−]

De

pth

[m

]



Seismic refraction test

t1

t2

t3

t4 t5 t6 t7 t8 t9 t10

t11

t12

xc

θcθc

Cp1

Cp2 > Cp1

impactdirect wave first refracted wave first

0 20 40 60 800

0.02

0.04

0.06

0.08

0.1

Distance [m]

Arr

ival

tim

e [s

]



Soil profile at the site in Lincent (Belgium)

• (a) Soil stratification, (b) shear wave velocity (SASW and SCPT), (c) dilatational wave velocity

(seismic refraction) and (d) material damping ratio (SASW and SCPT) profile.

(a)

0.00 m

Fine Sand

Quaternary

Deposits

FormationofHannut

(TertiaryDeposit)

Mean

Groundwater

10.40 m

Simplified Stratification

of Drilling B1108

1.20

3.20

7.50

8.50

10.00

15.00

Silt

Sequence of

Arenite / Clay

Clay

Fine Sand

Sequence of

Fine Sand / Clay

13.00

FormationofHeers

(TertiaryDeposit)

1.00

(Clayey Sand)

(Sandy Clay

to Silty Clay)

(Silty Clay)

(Silty Clay)

(b)0 100 200 300 400 500

0

1

2

3

4

5

6

7

8

Shear wave velocity [m/s]

Dep

th [m

]

SCPT1SCPT2SASW1SASW2

(c)0 500 1000 1500 2000

0

1

2

3

4

5

6

7

8

Longitudinal wave velocity [m/s]D

epth

[m]

SR1SR2

(d)0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

4

5

6

7

8

Material damping ratio [%]

Dep

th [m

]

SCPT2(MH)SCPT2(SH)SASW1SASW2

El Realengo test site


Test and reference site

• Conventional railway line (ADIF) between Murcia and Alicante.

• Low Segura river flood plain.

• S592 commuter train, S599 medium distance train and Talgo VI train.

• Construction of a new HST line between Madrid and Levante.

• Installation of a jet grouting wall next to track as a vibration mitigation measure.



Test and reference site



Shear wave velocity

• Spectral Analysis of Surface Waves (falling weight deflectometer, CEDEX).

• Seismic Cone Penetration Test (down-hole test, CEDEX).



Longitudinal wave velocity

• Seismic refraction test (CEDEX).

Identified soil profile

Layer h Cs Cp βs βp ρ[m] [m/s] [m/s] [−] [−] [kg/m3]

1 0.30 270 560 0.025 0.025 1800

2 1.20 150 470 0.025 0.025 1750

3 8.50 150 1560 0.025 0.025 1750

4 10.00 475 1560 0.025 0.025 1900

5 ∞ 550 2030 0.025 0.025 1900



Material damping ratio

• Measured Arias intensity at the test (red line) and reference (green line) section and predicted

Arias intensity (a) before and (b) after updating of the material damping ratio [Badsar, 2012].

(a)

0 10 20 30 40 50 60 7010

−17

10−16

10−15

10−14

10−13

10−12

10−11

Distance [m]

Aria

s in

tens

ity [m

/s]

(b)

0 10 20 30 40 50 60 7010

−17

10−16

10−15

10−14

10−13

10−12

10−11

Distance [m]

Aria

s in

tens

ity [m

/s]

Identified soil profile (update)

Layer h Cs Cp βs βp ρ[m] [m/s] [m/s] [−] [−] [kg/m3]

1 0.30 270 560 0.123 0.123 1800

2 1.20 150 470 0.112 0.112 1750

3 8.50 150 1560 0.014 0.014 1750

4 10.00 475 1560 0.010 0.010 1900

5 ∞ 550 2030 0.010 0.010 1900

Free field transfer functions


Measurement setup

• (a) Measurement setup, (b) falling weight deflectometer, (c) force during a single impact, and (d)

velocity stacked for 5 impacts.

(a)

(b) (c)0 1 2 3 4 5

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4x 10

5

Time [s]

For

ce [N

]

(d)

23468

1216

24

32

48

64

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

Dis

tanc

e [m

]

Time [s]



Numerical model for benchmarking

• 3D coupled finite element – boundary element method.

• Rigid foundation: finite element method.

• Layered elastic soil: boundary element formulation.

• Model and parameter uncertainty.




• Measured and predicted transfer function (narrow band)

at (a) 8 m, (b) 16 m, (c) 32 m, and (d) 64 m.

Measured results are shown for the test (red line) and reference (green

line) section. Predicted results are shown for initial (grey line) and up-

dated (black line) soil parameters.

(a)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 8m8m

(b)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 16m16m

(c)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 32m32m

(d)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 64m64m

6 m

FF64C

FF48C

32 m

16 m

8 m

2 m

3 m

C

4 m

12 m

24 m

Track – free field transfer functions


Track characteristics

• RN 45 rails:

EIr = 3.00 × 106 Nm2 and ρAr = 44.8 kg/m.

• Bi-block reinforced concrete sleepers:

msl = 200 kg and spacing d = 0.6 m.

• Rubber rail pads with a thickness of 4.5 mm and stiffness of

300 kN/mm.

• Ballast layer (d = 0.50 m, Cs = 250 m/s, ν = 0.2 and ρ =1600 kg/m3).

• Embankment (d = 0.50 m, Cs = 200 m/s, ν = 0.35 and ρ =1700 kg/m3).



Measurement setup

• (a) Measurement setup, (b) force during a single impact, and (c) velocity along line C stacked for

98 impacts.

(a)

(b)0 0.5 1 1.5 2

−0.5

0

0.5

1

1.5

2

2.5

3x 10

4

Time [s]

For

ce [N

]

(c)

10

16

24

32

48

64

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Dis

tanc

e [m

]

Time [s]



Variation along the track at the test section

• Comparison of the free field response for all impact locations and corresponding measurement

lines at (a) 10 m, (b) 16 m, (c) 24 m, and (d) 32 m from the track.

(a)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 10m

(b)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 16m

(c)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 24m

(d)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 32m



Numerical model

• 2.5D coupled finite element – boundary element method [François et al., CMAME, 2010].

• Track: finite element method.– rail and rail pad: Euler-Bernoulli beam and continuous spring-damper connection;

– sleeper: beam, rigid in plane of cross section;

– ballast: elastic continuum.

• Layered elastic soil: boundary element formulation.

• Model and parameter uncertainty.



Transfer functions

• Measured and predicted transfer function (narrow band)

at (a) 10 m, (b) 16 m, (c) 32 m, and (d) 64 m along line C.

Measured results are shown for the test (red line) and reference (green

line) section. Predicted results are shown for initial (grey line) and up-

dated (black line) track parameters.

(a)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 10C

(b)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 16C

(c)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 32C

(d)0 50 100 150 200

−50

−25

0

25

50

Frequency [Hz]

Mob

ility

[dB

ref

10−

8 m/s

/N] 64C

10 m

64 m

48 m

32 m

24 m

16 m

C



Installation of the jet grouting wall (November 2013)

Conclusion


• Determination of dynamic soil characteristics.– In situ geophysical techniques to determine the shear and dilatational wave velocity and

material damping ratio profile.

– Deliverable D1.1 "Test procedures for the determination of the dynamic soil characteristics"

(December 2011).

– Quantification of uncertainty on identified dynamic soil characteristics.

• Benchmark problems as a validation tool.– Free field and track – free field transfer functions.

– Deliberable D1.11 "Benchmark tests for soil properties, including recommendations for

standards and guidelines" (December 2013).

– Quantification of uncertainty on model predictions.

• Assessment of vibration isolation efficiency of mitigation measures:– Sheet pile wall at Furet (Sweden).

– Jet grouting wall at El Realengo (Spain).

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Determination of dynamic soil characteristics and … · 2 Laboratoria de Geotecnia, CEDEX, Spain 3...

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