Quantifying Near-Surface Attenuation via Site–Specific Kappa (κ0) to Improve High–Frequency 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 (κr_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:

𝐴𝐴 𝑓𝑓 = 𝐴𝐴0. exp −𝜋𝜋𝜋𝜋𝑓𝑓o Kappa is related to the slope of ln(A) vs

frequency plot as:

𝜋𝜋𝑟𝑟_𝐴𝐴𝐴𝐴 = −𝜆𝜆𝜋𝜋

Where,

𝜆𝜆 =Δ ln𝐴𝐴Δ𝑓𝑓

o The frequency range for evaluating kappa is dependent on corner frequency of ground motion and the database

4

Site–Specific Kappa (κ0_AS)

o Kappa (𝜋𝜋𝑟𝑟_𝐴𝐴𝐴𝐴) is assumed to depend on various physical factors relating to path and site

𝜋𝜋𝑟𝑟_𝐴𝐴𝐴𝐴 = 𝜋𝜋0_𝐴𝐴𝐴𝐴 + 𝜋𝜋𝑅𝑅𝐴𝐴𝐴𝐴 .𝑅𝑅𝑒𝑒 (𝑠𝑠)

o 𝜋𝜋0_𝐴𝐴𝐴𝐴 represents the attenuation of S-waves travelling vertically through the shallow geology of the site

o 𝜋𝜋𝑅𝑅_𝐴𝐴𝐴𝐴 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 Site–Specific Kappa (κ0) on Response Spectra

oLow–to–moderate seismicity regions: a smaller number of records; requires stochastic stimulation or host–to–target adjustment of ground motions

o κ0 is an important factor in ground motion simulation

o κ0 affects the frequency at which peak spectral acceleration occurs

6

Source: Laurendau et al. (2013)

κ0

Transfer Function Method (κ0_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 κ0_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 κ0_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 site–specific kappa (κ0_TF) using site parameters such as shear–wave velocity (Vs) and damping ratio (ξ)

Compare probability density functions of empirical and theoretical data and quantify uncertainties in site parameters

KiK–net Database

9

o The KiK–net 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 site–specific 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 Site–Specific Kappa (Δκ0_AS andκ0_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

κr_AS_bedrock

κr_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

κ0_TF

∆𝜿𝜿𝟎𝟎_𝑨𝑨𝑨𝑨 = 𝜿𝜿𝑨𝑨𝑨𝑨_𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 − 𝜿𝜿𝑨𝑨𝑨𝑨_𝒃𝒃𝒔𝒔𝒃𝒃𝒔𝒔𝒃𝒃𝒔𝒔𝒃𝒃

∆𝜿𝜿𝟎𝟎_𝑨𝑨𝑨𝑨 = 𝜿𝜿𝟎𝟎_𝑻𝑻𝑻𝑻

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 κ0_TFestimates from recorded ground motions – normal distribution fits better

o Δκ0_AS and κ0_TF estimates are in good agreement if evaluated at same frequencies

Theoretical Evaluation of κ0_TFo Site Response Analysis

o All the study sites are analyzed in STRATAo Bedrock motions from KiK–net data are applied o Unit weight is evaluated Boore (2016)

formulationso Minimum shear strain damping (ξmin) from

laboratory–based Darendeli (2001) model is calculated for each layer

o Constant damping (ξc) of 1% – 4% is added to all the layers

o κ0_TF Evaluationo Based on estimated transfer function, κ0_TF is

calculated at same frequencies as empirical calculations

14

H

Bedrock

Surface

γ1, Vs1, H1

γ2, Vs2,H2

γ3, Vs3, H3

𝜉𝜉1 = 𝜉𝜉𝑚𝑚𝑚𝑚𝑚𝑚,1 + 𝜉𝜉𝑐𝑐

𝜉𝜉2 = 𝜉𝜉𝑚𝑚𝑚𝑚𝑚𝑚,2 + 𝜉𝜉𝑐𝑐

𝜉𝜉3 = 𝜉𝜉𝑚𝑚𝑚𝑚𝑚𝑚,3 + 𝜉𝜉𝑐𝑐

Theoretical Site Response Analysis Results

15

o Normal distribution is fitted to κ0_TFestimates obtained from analysis of study sites as described in previous slide

o Significant difference between PDF of theoretical and empirical estimates – must consider uncertainty in site parameters

o The PDF of case with uncertainty in only damping is closest to empirical estimates

Closed–Form Equation (κ0_TF_Eqn)o The peaks occur when 𝜔𝜔𝐻𝐻

𝑉𝑉𝑠𝑠= 𝜋𝜋

2+ 𝑛𝑛𝜋𝜋

o Hence, closed form equation to evaluate site-specific kappa is:

o 𝜋𝜋0_𝑇𝑇𝑇𝑇_𝐸𝐸𝐸𝐸𝑚𝑚 =2𝐻𝐻∗𝐿𝐿𝐿𝐿 𝑇𝑇𝑇𝑇 𝑛𝑛2

𝑇𝑇𝑇𝑇 𝑛𝑛1𝜋𝜋(𝑚𝑚2−𝑚𝑚1)𝑉𝑉𝐴𝐴

=

2𝐻𝐻∗𝐿𝐿𝐿𝐿𝑐𝑐𝑐𝑐𝑠𝑠

𝜋𝜋2+𝑛𝑛1𝜋𝜋1+𝑖𝑖𝜉𝜉𝑠𝑠

+𝑖𝑖𝛼𝛼∗𝑠𝑠𝑖𝑖𝑛𝑛𝜋𝜋2+𝑛𝑛1𝜋𝜋1+𝑖𝑖𝜉𝜉𝑠𝑠

𝑐𝑐𝑐𝑐𝑠𝑠𝜋𝜋2+𝑛𝑛2𝜋𝜋1+𝑖𝑖𝜉𝜉𝑠𝑠

+𝑖𝑖𝛼𝛼∗𝑠𝑠𝑖𝑖𝑛𝑛𝜋𝜋2+𝑛𝑛2𝜋𝜋1+𝑖𝑖𝜉𝜉𝑠𝑠

𝜋𝜋(𝑚𝑚2−𝑚𝑚1)𝑉𝑉𝐴𝐴

o where,o VS = Shear Wave velocity of soil layero H = Soil Layer Thicknesso α* = Complex Impedance Ratio between Soil and Bedrocko ξs = Damping Ratio of Soil Layer

16

κ0_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 ξ = Kappa–consistent damping from empirical data using the formula:

𝜉𝜉 =𝜋𝜋0_𝑇𝑇𝑇𝑇

2∑𝑚𝑚=1𝑚𝑚 𝑧𝑧𝑚𝑚𝑉𝑉𝑠𝑠𝑚𝑚

o Normal distribution of Vs and ξ is considered as independent random variables and Monte–Carlo 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 closed–form 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 κ0_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 high–frequency amplification – records are ignored

o The PDF of revised empirical data compare well with site response analysis

o CoV of new κ0_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 Site–specific kappa from transfer function (κ0_TF) are in good agreement with

estimates from acceleration spectrum (Δκ0_AS) method for same frequency band

o PDF of site–specific kappa estimates from theoretical site response analysis are not found to be in good agreement with empirical results for deterministic values of site parameters (shear– wave velocity and damping ratio)

o PDF obtained after considering uncertainty in both site parameters in site response analysis as well as closed–form 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 κ0_TF can be used to characterize near–surface attenuation in low–to–moderate seismicity regions

21

Future Work

1.

Use of more study sites for evaluation of site–specific kappa from closed–form equation and propose appropriate values for site parameters for use in the equation

2.

Use kappa values obtained from closed–form equation for simulating ground motions at nuclear power plant sites and further apply simulated ground motions for analysis of building–cabinet system

22

Thank You23