116G Attenuation Analysis Sri Atmaja
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The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of the well-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe(1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure based on Wavelet Spectrogram
Sri Atmaja P. Rosyidi, Ph.D.Presented in KoNTekS 7, Universitas Sebelas Maret, 24 October
2013
Department of Civil EngineeringUniversitas Muhammadiyah Yogyakarta
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet SpectrumThe SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
Outline
• Introduction• Research Methods• Results and Discussion• Conclusion
2
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet SpectrumThe SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
GeoEarthquake Engineering
3
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet SpectrumThe SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
Geo-Disaster
4
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
5
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
6
Soil Dynamic Parameters
Diubahsuai daripada Ishihara (1996)
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
In Situ Te
st !
Lab !
7
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
8
Soil damping measurementSoil damping measurement
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.
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
9
Resonant Column/ Torsional Shear Testing System
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
10 10
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
11
Non-Invasive (Surface) Methods
Refraction (ASTM D5777)
Reflection
Surface Wave
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
12
Seismic Wave Propagation
(from Woods, 1968)
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
13
Surface Wave MeasurementsParticleMotion
ParticleMotion
Layer 1
Layer 2
Layer 3
Depth Depth
lshort
llong
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet SpectrumThe SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
Research Methods
14
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
1515
Data Collection of SASW Measurement
d1 d2
Time, sec0.0 0.5 1.0
(Portable Device Configuration)
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
ADC & Spectrum Analysis
Geophones
Accelerometer
Sources Sensors
16
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
17
Damping ratio profile calculation
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
18
In situ damping measurement test• Surface wave measurement for damping ratio (Rix, 2000)
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
19
Modelling the soil as a layered linear viscoelastic system
• Displacements for a harmonic point source
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
20
Example of regression result
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
21
Continuous Wavelets Transform (CWT)
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
22
Example of regression result
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
23
Attenuation Analysis using Wavelet Spectrum
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reeRKIGRGR
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The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
24
Developed procedure on attenuation analysis by wavelet transform
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The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
25
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Isyarat Asal
Isyarat Buatan Terbina Kembali (Reconstructed Synthetic Signal)
.Continuous Wavelet Transform Filtration (CWT-F) Technique
CW T
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
26
data_signal1_2m.xls
Continuous Wavelet Time-Frequency Spectrum
Integrated Power, Time=0,3.99805
2.5564,1.4524e-09
52.784,2.0271e-11
123.51,6.7838e-13 186.04,2.76e-13
0.1 1 10 100 1000Frekuensi
0
0.5
1
1.5
2
2.5
3
3.5
4
Mas
a
-5e-10
0
5e-10
1e-09
1.5e-09
Mag
nitu
d
data_signal2_2m.xls
Continuous Wavelet Time-Frequency Spectrum
Integrated Power, Time=0,3.99805
3.9708,1.6402e-10
6.0219,1.8062e-10
23.969,1.8439e-11 54.736,1.0822e-11
0.1 1 10 100 1000Frekuensi
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0.5
1
1.5
2
2.5
3
3.5
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Mas
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0
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Mag
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0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
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0 10 20 30 40 50
Frekuensi, Hz
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agn
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The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
27
Attenuation Curve
10 20 30 40 50 60 70 800
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Frequency, Hz
Att
enua
tion,
1/m
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
28
Attenuation Inversion
1s
Vk
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Vf
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c
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Vc
c
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Anderson et al. (1965)
Mitchell (1975)
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
29
Attenuation Inversion
Linear Problem
MR
2R
1R
sN
2s
1s
D
D
D
dm
dGm
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
30
Least SquaresDefine two objective functions as follows:
M
1i
2i
2N
1jjiji
2 mGdX
si = 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
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
31
Constrained Least SquaresUse a Lagrange multiplier to combine the two objective functions:
2*
212 XWGmWdmmU
Setting the derivative of U(m) equal to zero to find the minimum yields:
WdWGWGWGm̂
0WdWGmmmU
T1TT
TT
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
32
Least Squares
d Gmtheoretical
0
3
6
9
12
15
0.0% 0.5% 1.0% 1.5% 2.0%
Shear Damping Ratio (%)
Dep
th (
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
elen
gth
(m)
Experimental
Theoretical
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
33
Residual soil (UKM)
10 20 30 40 50 60 70 800
0.020.040.060.08
0.10.120.14
Frequency, Hz
Att
enua
tion,
1/m
0.01 0.02 0.03 0.04 0.05 0.060
2
4
6
8
10
12
14
16
Damping Ratio (D)
Dept
h, m
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
34
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
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
35
Damping Ratio Comparison
0
3
6
9
12
15
0% 2% 4% 6% 8% 10%Shear Damping Ratio (%)
Dep
th (
m)
Surface Wave
Crosshole
Resonant Column
Torsional Shear
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
36
Developed procedure on attenuation analysis by wavelet transform
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),(
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The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
37
data_signal1_2m.xls
Continuous Wavelet Time-Frequency Spectrum
Integrated Power, Time=0,3.99805
2.5564,1.4524e-09
52.784,2.0271e-11
123.51,6.7838e-13 186.04,2.76e-13
0.1 1 10 100 1000Frekuensi
0
0.5
1
1.5
2
2.5
3
3.5
4
Mas
a
-5e-10
0
5e-10
1e-09
1.5e-09
Mag
nitu
d
data_signal2_2m.xls
Continuous Wavelet Time-Frequency Spectrum
Integrated Power, Time=0,3.99805
3.9708,1.6402e-10
6.0219,1.8062e-10
23.969,1.8439e-11 54.736,1.0822e-11
0.1 1 10 100 1000Frekuensi
0
0.5
1
1.5
2
2.5
3
3.5
4
Mas
a
-5e-11
0
5e-11
1e-10
1.5e-10
2e-10M
agni
tud
fsuW
suWRf
Rf 0118.068.3
,
,ln
1
2
kfkRfsuW
suWRf
Rf
02
,
,ln
1
2
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
38
Attenuation analysis
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
(A2/
A1)
dal
am L
N
alpha-0.005dataalpha-0.03
alpha-0.05regresi eksperimen
0 = 0.050 = 0.03
0 = 0.005
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
39
RMS error during matching process
0
1
2
3
4
5
6
00.020.040.060.080.10.12
Pekali pengurangan, 0 (s/m)
RM
S (
nis
bah
am
pli
tud
)
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
40
Attenuation curve
0
5
10
15
20
25
30
0 0.1 0.2 0.3
Pekali pengurangan bersandar frekuensi ( ), 1/m
Pan
jan
g ge
lom
ban
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
Fre
kuen
si, H
z
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
41
Inversion and damping ratio profile
0
5
10
15
20
25
30
0 0.1 0.2 0.3
Pekali pengurangan bersandar frekuensi ( ), 1/m
Pan
jan
g ge
lom
ban
g, m
datamodel 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
alam
an, m
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
42
PerbandingandenganKajianSebelumnya
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Halaju Gelombang Ricih, m/s
o (sa
at/m
)
Athanasopoulos et al. (2000)
Yang (1995)
Kelas 4
Kelas 2
Kelas 3
A
B
Woods & Jedele (1985);Woods (1997)Lempung lembut Kelang
(Kelang soft clay)
- Kajian ini
Kelompok Batuan (Rocks) daripada Shale, Limestones & Sandstone
Kelas 1
Hasil kajian
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
43
Shear Damping Profile
Kaedahnisbahspektrum (Champanella et al. 1994)
Kaedahfungsiperpindahan (Rix et al. 2002)
Kaedah CWSASW
0
5
10
15
20
25
30
0 0.1 0.2 0.3
Pekali pengurangan bersandar frekuensi ( ), 1/m
Pan
jang
gel
omba
ng, m
Kaedahfungsiperpindahan
Kaedah CWSASW
GeophonesShaker
SignalAnalyzer
r
Accelerometer
1
,
,
1
rrKi
l
i erG
rG
F
F
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
44
2 D Shear Wave Velocity
Contour Graph 1
Jarak Keratan (m)
0 5 10 15 20 25
Ked
ala
man
(m
)
0
2
4
6
8
10
12
14
16
40 60 80 100 120 140 160 180
ν12GE
ρVM
ρVG
maxmax
2pmax
2smax
ν12GE
ρVM
ρVG
maxmax
2pmax
2smax
Elastic Theory
S
zs V
u = 1.48 10-5
%.
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
45
2 D Shear Modulus and Damping
Contour Graph 2
Jarak Keratan (m)
0 5 10 15 20 25
Ked
ala
man
(m
)
0
2
4
6
8
10
12
14
16
2 4 6 8 10 12 14 16 18
Contour Graph 3
Jarak Keratan (m)
0 5 10 15 20 25K
ed
ala
man
(m
)
0
2
4
6
8
10
12
14
16
0.036 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.054
G (MPa) D [%]
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
46
Comparing with MASW (SurfSeis), KGS
(a) Profile from MASW (b) Profile from CWSASW
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
47
Lengkung Pekali Pengurangan dan Prosedur Songsangan
Lengkung serakan teori pekali
pengurangan vs frekuensi/panjang
gelombang
Profil kekukuhan anggaran
Proses songsangan
Lengkung serakan pekali pengurangan
tak bergantung f
Lengkung serakan eksperimen pekali
pengurangan vs frekuensi/panjang
gelombang
Proses perpadanan
ralat RMS
Profil nisbah redakam, halaju
gelombang R, ricih, dan mampatan
Profil 1-D redaman tanah
Analisis gandingan
Tidak diterima
Diterima
i
N
i iS
RiS
iP
RiP
R
DV
VVK
V
VV
V
ff ,,2
2
D, VR, VP, VS
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
Songsangan Pekali Pengurangan
j
pj
jj
sj
jf s
Vf
N
1j s2
sp
Vf
N
1j p2
pR D
Vc
c
VD
Vc
c
Vf2
Mitchell (1975)
Masalah Lelurus dalam Songsangan :
MR
2R
1R
sN
2s
1s
D
D
D
dm
dGm
i
N
i iS
RiS
iP
RiP
R
DV
VVK
V
VV
V
ff ,,2
2Rix et al. (2000)
48
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
49
Profil Nisbah Redaman
0
5
10
15
20
25
30
0 0.1 0.2 0.3
Pekali pengurangan bersandar frekuensi ( ), 1/m
Pan
jan
g ge
lom
ban
g, m
datamodel teori
model mula
lelaran 1
lelaran 3
lelaran 40
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
alam
an, m
0
0.4
0.8
1.2
1.6
2
0 1 2 3 4
Lelaran
Ral
at R
MS
(p
ekal
i p
engu
ran
gan
, 1/
m)
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
50
Pengesahan Profil Nisbah Redaman
Kaedah nisbah spektrum (Champanella et al. 1994)
Kaedah fungsi perpindahan (Rix et al. 2002)
Kaedah CWSASW
0
5
10
15
20
25
30
0 0.1 0.2 0.3
Pekali pengurangan bersandar frekuensi ( ), 1/m
Pan
jang
gel
omba
ng, m
Kaedah fungsi perpindahan
Kaedah CWSASW
GeophonesShaker
SignalAnalyzer
r
Accelerometer
1
,
,
1
rrKi
l
i erG
rG
F
F
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
51
Tomografi 2-D Parameter VS
Contour Graph 1
Jarak Keratan (m)
0 5 10 15 20 25
Ked
ala
man
(m
)
0
2
4
6
8
10
12
14
16
40 60 80 100 120 140 160 180
ν12GE
ρVM
ρVG
maxmax
2pmax
2smax
ν12GE
ρVM
ρVG
maxmax
2pmax
2smax
Teori Elastik
S
zs V
u = 1.48 10-5
%.
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
Attenuation Analysis on Soil Structure Based on Wavelet Spectrum
52
Tomografi 2-D Parameter G dan D
Contour Graph 2
Jarak Keratan (m)
0 5 10 15 20 25
Ked
ala
man
(m
)
0
2
4
6
8
10
12
14
16
2 4 6 8 10 12 14 16 18
Contour Graph 3
Jarak Keratan (m)
0 5 10 15 20 25K
ed
ala
man
(m
)
0
2
4
6
8
10
12
14
16
0.036 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.054
Profil Modulus Ricih (MPa) Profil Nisbah Redaman
The SASW method has been utilized in different applications over the past decade after the advancement and improvement of the well-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe(1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by
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