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2/18/2011
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Soil Damping Ratio: Theoretical Aspect and Measurement - 2
A Two Day Workshop on SASW for Practicing Engineer
17 - 18 February 2011, Faculty of Engineering and Built Environment,
Universiti Kebangsaan Malaysia
Sri Atmaja P. Rosyidi, Ph.D.Assistant Professor, Universitas Muhammadiyah Yogyakarta
Damping Measurement Presentation outline
• Soil damping measurement
• Interpretation techniques
• In situ measurement
• Case study: field measurement and data interpretation
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement Soil damping measurement
Soil damping measurement
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Laboratory testing:- Resonant column test- Torsional shear test- Bender element test- Cyclic triaxial test- etc.
Field (in situ) testing:- Crosshole test- Surface wave test- etc.
Damping Measurement Resonant Column/ Torsional Shear Testing System
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement Resonant Column/ Torsional Shear Testing System
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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The resonant column test is the most commonly used laboratory test for measuring the low-strain properties of soils.
Damping Measurement Comparison with other laboratory tests
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Resonant column tests are used to determine laboratory values of soil stiffness (modulus) and damping ratio at very small strains.
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Damping Measurement RC Types
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement Principal in determining damping ratio
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Free Vibration Decay Method
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Damping Measurement Principal in determining damping ratio
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Half Power Bandwidth Method
n
12
2f
ffD
Damping Measurement Free Vibration Decay Method versus
Half Power Bandwidth Method
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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• Free vibration method :- based on the amplitude logarithmic decrement- appropriate for large strain measurement (more than 0.01 %)
• Half Power Bandwidth method :- the amplitude spectrum of the free vibration decay - appropriate for small strain measurement (less than 0.01 %)
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Damping Measurement In situ damping measurement test
• Surface wave measurement for damping ratio (Rix, 2000)
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement
Modelling the soil as a layered linear viscoelastic system
• Displacements for a harmonic point source
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement Damping ratio profile calculation (Foti, 2004)
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement
Modelling the soil as a layered linear viscoelastic system
• Displacements for a impact source
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement Find K( )
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement Example of regression result
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement Fourier Amplitude
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
Am
plit
ud
e
Frequency, Hz
Damping Measurement
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 5 10 15 20 25
Fi/F
1 (
Am
plit
ud
e R
atio
)
Offset, m
11 Hz
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Damping Measurement Attenuation Curve
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 20 40 60 80
Att
en
uat
ion
, 1/m
Frequency, Hz
Damping Measurement Attenuation Inversion
1s
Vk
N
1j s
s1p
Vkp
pN
1j
1R
j
pj
j
j
sj
jQ
V
c
c
VQ
V
c
c
VQ
j
pj
j
j
sj
j
f s
Vf
N
1j s2
s
p
Vf
N
1j p2
p
R DV
c
c
VD
V
c
c
Vf2
Anderson et al. (1965)
Mitchell (1975)
20
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
2/18/2011
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Damping Measurement Attenuation Inversion
Linear Problem
MR
2R
1R
sN
2s
1s
D
D
D
dm
dGm
21
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
Damping Measurement Least Squares
Define two objective functions as follows:
M
1i
2i
2N
1jjiji
2 mGdX
i = uncertainty in di
NxN
21
N
1j
21jj1
11
11
11
0
mR
mmR
22
M21
WGmWdX
1,1,1diagW
Minimize ‘roughness” Minimize data misfit
22
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
2/18/2011
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Damping Measurement Constrained Least Squares
Use a Lagrange multiplier to combine the two objective functions:
2*
212XWGmWdmmU
Setting the derivative of U(m) equal to zero to find the minimum yields:
WdWGWGWGm̂
0WdWGmm
mU
T1TT
TT
23
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
Damping Measurement Least Squares
d Gmtheoretical
0
3
6
9
12
15
0.0% 0.5% 1.0% 1.5% 2.0%
Shear Damping Ratio (%)
Depth
(m
)
0
5
10
15
20
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Attenuation Coefficient (1/m)
Wav
ele
ng
th (
m)
Experimental
Theoretical
24
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
2/18/2011
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Damping Measurement Residual soil (UKM)
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 20 40 60 80
Att
en
uat
ion
, 1/m
Frequency, Hz
0
2
4
6
8
10
12
14
16
0.00 0.01 0.02 0.03 0.04 0.05 0.06
De
pth
, m
Damping Ratio (D)
Damping Measurement Note for damping measurement by surface wave method
• the predicted damping ratio based on attenuation – amplitude decay (radiation/geometric damping)
• some assumptions:– the geometric spreading function to be inversely
proportional to the square root of the distance from the source
– The implicit dependence of the complex-valued phase angle on the source-to-receiver distance is eliminated by assuming: Ψ(r,ω) ≈ K(ω)r.
• appropriate for non-complex soil profiles
• the best data of damping – RC laboratory test
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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Damping Measurement Damping Ratio Comparison
0
3
6
9
12
15
0% 2% 4% 6% 8% 10%
Shear Damping Ratio (%)
Depth
(m
)
Surface Wave
Crosshole
Resonant Column
Torsional Shear
27
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
Damping Measurement Developed procedure on attenuation analysis by
wavelet transform
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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),(
),(
*1
*1
su
X
f
su
Y
f
W
W
dts
ut
stX
dts
ut
stY
fX
fYfH
),(),(
),(
,
,,
*
,,
suWsuW
esuW
suW
suWsuH
X
f
X
f
babaiXY
f
XX
f
XY
fXY
tRkiRf
nreeRKIGRG
R
ARA 0,
21
2
1ln,
,ln
1
2
RRfRKIGRGR
R
suW
suWn
R
f
R
f
2/18/2011
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Damping Measurement Attenuation analysis
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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y = -0.0118x + 3.6795
R2 = 0.67
2.5
3
3.5
4
4.5
5
0 2 4 6 8 10 12 14 16 18 20
Frekuensi, Hz
Nis
bah
(A
2/A
1)
da
lam
LN
alpha-0.005
data
alpha-0.03
alpha-0.05
regresi eksperimen
= 0.05 = 0.03
= 0.005
Damping Measurement RMS error during matching process
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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0
1
2
3
4
5
6
00.020.040.060.080.10.12
Pekali pengurangan, (s/m)
RM
S (
nis
ba
h a
mp
litu
d)
2/18/2011
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Damping Measurement Attenuation curve
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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0
5
10
15
20
25
30
0 0.1 0.2 0.3
Pekali pengurangan bersandar frekuensi
( ), 1/mP
an
jan
g g
elo
mb
an
g,
m
0
10
20
30
40
50
60
70
80
90
100
0 0.2 0.4 0.6 0.8
Pekali pengurangan bersandar frekuensi
( ), 1/m
Frek
uen
si,
Hz
Damping Measurement Inversion and damping ratio profile
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
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0
5
10
15
20
25
30
0 0.1 0.2 0.3
Pekali pengurangan bersandar frekuensi
( ), 1/m
Pa
nja
ng
gel
om
ba
ng
, m
data
model teori
model
mula
lelaran 1
lelaran 3
lelaran 4
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0.00% 2.00% 4.00% 6.00% 8.00%
Nisbah redaman (%)
Ked
ala
ma
n,
m
2/18/2011
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Damping Measurement
Sri Atmaja P. Rosyidi, Ph.D. • Universitas Muhammadiyah Yogyakarta •
330
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0% 2% 4% 6% 8%
Ked
ala
ma
n, m
Nisbah Redaman (%)
Kaedah fungsi perpindahan (Rix & Lai
1998)
Kaedah CWSASW (Kajian ini)
Kaedah Nisbah Spektrum
Thank you
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