Post on 13-May-2022
Quantifying Near-Surface Attenuation via SiteβSpecific Kappa (ΞΊ0) to Improve HighβFrequency Ground Motion Characterization in Central
and Eastern United States
Presented By
Sugandha Singh Abhinav Gupta Ashly Cabas
1
High Frequency Seismic Hazard
Source:- EPRI, 2015
2
3
Spectral Decay Factor, Kappa (ΞΊr_AS)
0 5 10 15 20 25 30
Frequency (Hz)
10-5
100
FA
S (
cm/s
2)
fE=10fmax=25
FAS (Acceleration) Fitted Spectral Decay
o The decay of acceleration spectrum is modeled as:
π΄π΄ ππ = π΄π΄0. exp βππππππo Kappa is related to the slope of ln(A) vs
frequency plot as:
ππππ_π΄π΄π΄π΄ = βππππ
Where,
ππ =Ξ lnπ΄π΄Ξππ
o The frequency range for evaluating kappa is dependent on corner frequency of ground motion and the database
4
SiteβSpecific Kappa (ΞΊ0_AS)
o Kappa (ππππ_π΄π΄π΄π΄) is assumed to depend on various physical factors relating to path and site
ππππ_π΄π΄π΄π΄ = ππ0_π΄π΄π΄π΄ + πππ π π΄π΄π΄π΄ .π π ππ (π π )
o ππ0_π΄π΄π΄π΄ represents the attenuation of S-waves travelling vertically through the shallow geology of the site
o πππ π _π΄π΄π΄π΄ is the slope of the regression model which corresponds to incremental regional along the path
o Requires availability of strong ground motion
5
Source: Ktenidou et al. (2012)
Effect of SiteβSpecific Kappa (ΞΊ0) on Response Spectra
oLowβtoβmoderate seismicity regions: a smaller number of records; requires stochastic stimulation or hostβtoβtarget adjustment of ground motions
o ΞΊ0 is an important factor in ground motion simulation
o ΞΊ0 affects the frequency at which peak spectral acceleration occurs
6
Source: Laurendau et al. (2013)
ΞΊ0
Transfer Function Method (ΞΊ0_TF)
0 5 10 15 20 25 30
Frequency (Hz)
10-2
100
102
104
Am
pli
fica
tion
fc fE=10 fmax=25
Transfer Function Fitted Spectral Decay
o Transfer function is the ratio of FAS of recorded acceleration motion at the surface by that of the bedrock
o ΞΊ0_TF is measured as the decaying peaks of the transfer function of a site at high frequencies
o Can be calculated with or without available ground motions
o ΞΊ0_TF represents attenuation between the bedrock and soil layer
7
Source: Drouet et al. (2010)
Objectives
8
Compare the kappa estimates from acceleration spectrum and transfer function methods
Use theoretical transfer functions to evaluate siteβspecific kappa (ΞΊ0_TF) using site parameters such as shearβwave velocity (Vs) and damping ratio (ΞΎ)
Compare probability density functions of empirical and theoretical data and quantify uncertainties in site parameters
KiKβnet Database
9
o The KiKβnet is a huge database of recorded motions at approximately 700 locations
o At each site, the seismic motions are recorded at a borehole as well as at the ground surface
o The database allows for our study to compare siteβspecific kappa evaluations from acceleration spectrum and transfer function method
o Linear elastic sites are selected for this study
Study Sites500 1000
Velocity (m/s)
0
200
400
600
Dep
th (m
)
(a) Site OSKH01
1000 2000
Velocity (m/s)
0
200
400D
epth
(m)
(b) Site SZOH25
200 600 1000
Velocity (m/s)
0
50
100Dep
th (m
)
(c) Site FKSH14
500 1500
Velocity (m/s)
0
200
400
Dep
th (m
)
(d) Site IBRH10
Profile Bedrock
Vs 3 0
Vs _ m e a n
Site Name Depth to Bedrock (m)
Vs30(m/s)
Vs_mean(m/s)
NEHRP Site Classification
OSKH01 550 500 500 C
SZOH25 328 347.3 589.1 D
FKSH14 106 251.3 654 D
IBRH10 518 200 531.3 D
10
Ground Motion Selection
o At least 10 ground motions are selected for each site
o The ground motion selection criteria are shown in the table
o The ground motions are further screened if amplification peaks occur beyond 10Hz
11
Parameter Value Reference
SNR <3 Ktenidou et al. (2012)
PGA <10cm/s2 Ktenidou et al. (2012)
Magnitude 3-5 Drouet et al. (2010)
Epicentral
Distance<180km
Anderson and Hough
(1984)
Shear Strain
Index<0.1% Cabas et al. (2017)
Empirical Evaluation of SiteβSpecific Kappa (ΞΞΊ0_AS andΞΊ0_TF)
12
H
Bedrock
Surface
Vs1, H1
Vs2,H2
Vs3, H3
5 10 15 20 25 30
Frequency (Hz)
0.5
1
1.5
2
FA
S
10-8
fE=10 fmax=25
FAS (Acceleration) Fitted Spectral Decay
5 10 15 20 25 30
Frequency (Hz)
2
4
6
8
FA
S
10-8
fE=10 fmax=25
FAS (Acceleration) Fitted Spectral Decay
ΞΊr_AS_bedrock
ΞΊr_AS_surface
5 10 15 20 25 30
Frequency (Hz)
3
4
5
Am
pli
fica
tio
n
fE=10 fmax=25
Transfer Function Fitted Spectral Decay
ΞΊ0_TF
βπΏπΏππ_π¨π¨π¨π¨ = πΏπΏπ¨π¨π¨π¨_ππππππππππππππ β πΏπΏπ¨π¨π¨π¨_ππππππππππππππ
βπΏπΏππ_π¨π¨π¨π¨ = πΏπΏππ_π»π»π»π»
Empirical Results
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055
0 _ T F (s)
0
10
20
30
40
PD
F
Acceleration Spectrum Method Transfer Function Method
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
0 _ T F (s)
0
20
40
60
80
PD
F
Histograms Lognormal Distribution Normal Distribution
13
o Results shown for low Vs gradient multiple layer site, SZOH25
o Study aims to compare probability density function of empirical results with theoretical results
o Both normal and lognormal distribution are fitted to ΞΊ0_TFestimates from recorded ground motions β normal distribution fits better
o ΞΞΊ0_AS and ΞΊ0_TF estimates are in good agreement if evaluated at same frequencies
Theoretical Evaluation of ΞΊ0_TFo Site Response Analysis
o All the study sites are analyzed in STRATAo Bedrock motions from KiKβnet data are applied o Unit weight is evaluated Boore (2016)
formulationso Minimum shear strain damping (ΞΎmin) from
laboratoryβbased Darendeli (2001) model is calculated for each layer
o Constant damping (ΞΎc) of 1% β 4% is added to all the layers
o ΞΊ0_TF Evaluationo Based on estimated transfer function, ΞΊ0_TF is
calculated at same frequencies as empirical calculations
14
H
Bedrock
Surface
Ξ³1, Vs1, H1
Ξ³2, Vs2,H2
Ξ³3, Vs3, H3
ππ1 = ππππππππ,1 + ππππ
ππ2 = ππππππππ,2 + ππππ
ππ3 = ππππππππ,3 + ππππ
Theoretical Site Response Analysis Results
15
o Normal distribution is fitted to ΞΊ0_TFestimates obtained from analysis of study sites as described in previous slide
o Significant difference between PDF of theoretical and empirical estimates β must consider uncertainty in site parameters
o The PDF of case with uncertainty in only damping is closest to empirical estimates
ClosedβForm Equation (ΞΊ0_TF_Eqn)o The peaks occur when πππ»π»
πππ π = ππ
2+ ππππ
o Hence, closed form equation to evaluate site-specific kappa is:
o ππ0_ππππ_πΈπΈπΈπΈππ =2π»π»βπΏπΏπΏπΏ ππππ ππ2
ππππ ππ1ππ(ππ2βππ1)πππ΄π΄
=
2π»π»βπΏπΏπΏπΏπππππ π
ππ2+ππ1ππ1+πππππ π
+πππΌπΌβπ π ππππππ2+ππ1ππ1+πππππ π
πππππ π ππ2+ππ2ππ1+πππππ π
+πππΌπΌβπ π ππππππ2+ππ2ππ1+πππππ π
ππ(ππ2βππ1)πππ΄π΄
o where,o VS = Shear Wave velocity of soil layero H = Soil Layer Thicknesso Ξ±* = Complex Impedance Ratio between Soil and Bedrocko ΞΎs = Damping Ratio of Soil Layer
16
ΞΊ0_TF
n1 = 1
n2 = 4
Single Layer Approximation
17
o The study sites are approximated as single layers based on site parameters:
o Vs_proxy = Vs30, Vs_mean
o ΞΎ = Kappaβconsistent damping from empirical data using the formula:
ππ =ππ0_ππππ
2βππ=1ππ π§π§πππππ π ππ
o Normal distribution of Vs and ΞΎ is considered as independent random variables and MonteβCarlo simulation is run
o PDF from Vs_mean is in better agreement with both empirical and site response analysis PDF
Single Layer Approximation
18
-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 _ T F (s)
0
10
20
30
PD
F
Empirical
Closed-Form Equation
(Vs _ m e a n
50%*CoV
V s _ m e a n @ )
Closed-Form Equation
(Vs _ m e a n
100%*CoV
V s _ m e a n @ )
o Site SZOH25 has low Vs gradient
o For sites such as FKSH14, Vsgradient is high
o Comparison of PDF of empirical results with closedβform equation results with 50% and 100% of coefficient of variation (CoV) in Vs
o Results with 50% CoV compares well with empirical results
o This relates to CoV of empirical ΞΊ0_TF data
-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
0 _ T F (s)
0
20
40
60
PD
F
(a) Site OSKH01 (Single Layer Site)
Empirical
Theoretical Site Response Analysis
(Vs
@ )
Closed-Form Equation
(Vs
@ )
-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06
0 _ T F (s)
0
20
40
PD
F
(c) Site FKSH14 (Multiple Layer Site: High Vs
Gradient)
Empirical
Theoretical Site Response Analysis
(Vs
@ = (Min. Darendeli Damping + 2%) )
Closed-Form Equation
(Vs _ m e a n
50%*CoV*V
s _ m e a n @ )
-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0 _ T F (s)
0
50
100
PD
F
(d) Site IBRH10 (Multiple Layer Site: High Vs
Gradient)
Empirical
Theoretical Site Response Analysis
(Vs
@ = (Min. Darendeli Damping + 2.6%) )
Closed-Form Equation
(Vs _ m e a n
50%*CoV*V
s _ m e a n @ )
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
0 _ T F (s)
0
20
40
PD
F
(b) Site SZOH25 (Multiple Layer Site: Low Vs
Gradient)
Empirical
Theoretical Site Response Analysis
(Vs
@ = (Min. Darendeli Damping + 2.5%) )
Closed-Form Equation
(Vs _ m e a n
50%*CoV*V
s _ m e a n @ )
19
Site IBRH10
20
o The empirical PDF at site is not in agreement with theoretical site response analysis
o The estimates from two ground motions have highβfrequency amplification β records are ignored
o The PDF of revised empirical data compare well with site response analysis
o CoV of new ΞΊ0_TF data = 6.32%
o Higher damping required for revised data
0 5 10 15 20 25 30
Frequency (Hz)
10-2
100
102
104
Am
plifi
catio
n
(a) Record #122539 (NS Direction)
fc
fE=10 fmax=25
Transfer Function Fitted Decay
0 5 10 15 20 25 30
Frequency (Hz)
10-2
100
102
104
Am
plifi
catio
n
(b) Record #128050 (NS Direction)
fc fE=10 fmax=25
Transfer Function Fitted Decay
0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085
0 _ T F (s)
0
50
100
PD
F
Empirical
Theoretical Site Response Analysis
(Vs
@ = (Min. Darendeli Damping + 2.6%) )
Closed-Form Equation
(Vs _ m e a n
50%*CoV*V
s _ m e a n @ )
0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085
0 _ T F (s)
0
50
100
PD
F
(a) Kappa-Consistent Damping ( =2.91%)
Empirical
Theoretical Site Response Analysis
(Vs
@ = (Min. Darendeli Damping + 2.6%) )
Closed-Form Equation
(Vs _ m e a n
6.32%*CoV*V
s _ m e a n @ )
0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085
0 _ T F (s)
0
50
100
PD
F
(b) Revised Damping ( =3.5%)
Empirical
Theoretical Site Response Analysis
(Vs
@ = (Min. Darendeli Damping + 2.6%) )
Closed-Form Equation
(Vs _ m e a n
6.32%*CoV*V
s _ m e a n @ )
Conclusionso Siteβspecific kappa from transfer function (ΞΊ0_TF) are in good agreement with
estimates from acceleration spectrum (ΞΞΊ0_AS) method for same frequency band
o PDF of siteβspecific kappa estimates from theoretical site response analysis are not found to be in good agreement with empirical results for deterministic values of site parameters (shearβ wave velocity and damping ratio)
o PDF obtained after considering uncertainty in both site parameters in site response analysis as well as closedβform equation are in good agreement with empirical results
o More study is required to assess appropriate site parameters as well as uncertainty in the parameters
o ΞΊ0_TF can be used to characterize nearβsurface attenuation in lowβtoβmoderate seismicity regions
21
Future Work
1.
Use of more study sites for evaluation of siteβspecific kappa from closedβform equation and propose appropriate values for site parameters for use in the equation
2.
Use kappa values obtained from closedβform equation for simulating ground motions at nuclear power plant sites and further apply simulated ground motions for analysis of buildingβcabinet system
22
Thank You23