By

Ray Ruichong ZHANG

Colorado School of Mines, Colorado, USA

HHT-based Characterization HHT-based Characterization of Soil Nonlinearity and of Soil Nonlinearity and

Liquefaction Liquefaction in Earthquake Recordingsin Earthquake Recordings

US-Taiwan Workshop on Soil Liquefaction

National Chiao Tung University, Hsin-Chu, Taiwan, November 3-5, 2003

2

Site NonlinearitySite Nonlinearity

Terminology

Site Nonlinearity = Soil Nonlinearity and/or Liquefaction

Importance

A major factor in mapping seismic hazard and design codes

Issues

Distorted estimation of the extent of site nonlinearity resulted in underestimation of the level of site amplification and liquefaction

3

Site NonlinearitySite Nonlinearity

Terminology

Site Nonlinearity = Soil Nonlinearity and/or Liquefaction

Importance

A major factor in mapping seismic hazard and design codes

Issues

Distorted estimation of the extent of site nonlinearity resulted in underestimation of the level of site amplification and liquefaction

4

Nonlinearity CharacterizationNonlinearity Characterization

Symptom of Nonlinearity (vs. Linearity) Reduced Soil Strength Increased Soil Damping Deformed Waveform

The nonlinear symptom is observable only in a portion

of recording and in a certain frequency band

Measure in Recordings

Frequency Downshift Seismic Wave Amplitude Downshift Abnormal Cusped, High-Frequency Spikes

5

Hilbert-Huang Transform (HHT)Hilbert-Huang Transform (HHT)

Empirical Mode Decomposition (EMD)

Any data is decomposed into a few, different simple intrinsic mode functions (IMF) on the basis of local characteristic time scale of the data

Hilbert Spectral Analysis (HSA)

Hilbert transform of IMF components leads to

(1) Instantaneous frequency and damping(2) temporal-frequency amplitude/damping

spectra

6

HHT (top) vs. Fourier (bottom)HHT (top) vs. Fourier (bottom)

')'(

1

)()(dtti

n

jj

jetatX

tiN

jj

jeAtX

1

)(

Fourier Amplitude Spectrum

Hilbert Amplitude Spectrum

Instantaneous vs. constant

Marginal spectrum w/ integration of Hilbert amplitude spectrum over t

j: IMF/Fourier Component

7

')'(')'(

1

)(dttidtt

n

jj

jjet

Hilbert Amplitude and Damping SpectraHilbert Amplitude and Damping Spectra

')'(

1

)()(dtti

n

jj

jetatX

Hilbert Damping Spectrum, a part of Hilbert Amplitude Spectrum

Hilbert Amplitude Spectrum

Damping vs. Frequency

Marginal spectrum w/ integration of Hilbert amplitude spectrum over t

8

HHT: IMF ComponentsHHT: IMF Components

0 1 2 3 4 5 6 7 8 9 10 -1.5

-1

-0.5

0

0.5

1

1.5

Time(sec)

Am

plit

ude

-0.5

0

0.5

c1

-0.5 0

0.5

c2

-0.02

0

0.02

c3

-0.02

0

0.02

c4

0 1 2 3 4 5 6 7 8 9 10

0 5

10 x 10 -3

c5

Time (sec)

Time (s) Time (s)

IMF Components

1st IMF=noise 2nd IMF=waves

3rd, 4th and 5th IMFs=numerical errors w/ small amplitudes

Recording=Nonlinear waves + noiseNonlinear waves + noise

at frequency [1+0.5cos(2at frequency [1+0.5cos(2t)] + 15 Hzt)] + 15 Hz

i.e., at freq. 0.5 to 1.5 Hz + 15 Hzi.e., at freq. 0.5 to 1.5 Hz + 15 Hz

Am

plit

ude

9

HHT: Hilbert and Marginal SpectraHHT: Hilbert and Marginal Spectra

Time (s) Freq. (Hz)

Fre

q. (

Hz)

Hilbert Amplitude Spectrum Marginal Hilbert Amplitude Spectrum vs. Fourier Amplitude Spectrum

Noise at 15 Hz

Waves at 0.5-1.5 Hz

1) No physical meaning, making up for nonlinear waveform,

2) Overestimates high-freq.

3) Distorts freq-related damping

Am

plit

ude

10

Example of HHT AnalysisExample of HHT Analysis

High-frequency MotionLow-frequency Motion

Time (s) Time (s)F

req.

(H

z)

1964 Niigata Earthquake Record

High-frequency Spike

Hilbert Amplitude Spectrum

Am

plit

ude

Am

plit

ude

11

Marginal Hilbert vs. Fourier SpectraMarginal Hilbert vs. Fourier Spectra

Freq. (Hz)

Fourier Amplitude Spectrum

Marginal Hilbert Amplitude Spectrum

Freq. (Hz)

Fourier Spectrum overestimates high frequency and thus underestimate low frequency of nonlinear motionA

mpl

itud

e

12

Site Amplification = Marginal (Fourier) Spectral Ratio

=Marginal (Fourier) Amplitude Spectrum of Motion at Soil

Marginal (Fourier) Amplitude Spectrum of Motion at Rock

Alternative HHT-based ApproachAlternative HHT-based Approach

IMFs, Hilbert and Marginal Spectra for Detection and Quantification of Site Nonlinearity

Site Damping = Marginal Spectral Difference

= Marginal Hilbert Damping Spectrum of Motion at Soil

Marginal Hilbert Damping Spectrum of Motion at Rock

13

Nonlinearity Detection w/ IMF Nonlinearity Detection w/ IMF

Time (s)

Acc

(g)

Symptom of Nonlinear site in S-coda waves

1st IMF singles out abnormal high-frequency spikes

2001 Nisqually Mainshock: NS-Acc. Record

1st IMF

Acc

(g)

Record

14

Time (s)

Acc

(g)

Acc

(g)

1st IMF

Not clear on abnormal high-frequency spikes

1st IMF singles out abnormal high-frequency spikes

Nonlinearity Detection w/ IMFNonlinearity Detection w/ IMF

2001 Nisqually Mainshock: EW-Acc. Record

Record

15

Nonlinearity Detection w/ IMFNonlinearity Detection w/ IMF

2001 Nisqually Aftershock: NS-Acc. RecordA

cc (

g)A

cc (

g)

Time (s)

1st IMF

No abnormal high-frequency spikes in S-coda waves

Record

16

Nonlinearity Detection w/ Hilbert SpectraNonlinearity Detection w/ Hilbert Spectra

Time (s)

Abnormal high-frequency spikes can be identified from Hilbert Spectra

Hilbert Spectra

RecordA

cc (

g)F

req.

(H

z)

Hilbert Amplitude Spectrum

Time (s)

Am

plit

ude

17

Nonlinearity Quantification at Soft SoilNonlinearity Quantification at Soft Soil

Freq. (Hz)

Mainshock

Aftershock

Sit

e A

mpl

ific

atio

n (H

HT

)

Frequency Downshift Amplitude

Downshift

18

Nonlinearity Quantification at Stiff SoilNonlinearity Quantification at Stiff Soil

AftershockMainshock

Frequency Downshift

Amplitude Downshift

Freq. (Hz)

Sit

e A

mpl

ific

atio

n (H

HT

)

19

Marginal vs. Fourier Ratio at Soft SoilMarginal vs. Fourier Ratio at Soft Soil

Freq. (Hz)

Marginal Spectral Ratio Fourier Spectral Ratio

Difference

For Marginal Ratio w/ Fourier ratio as reference 1) Large Ratio, i.e., Large Site Amplification 2) Large Freq. Downshift (decreased strength) 3) Large Ampl. Downshift (increased damping) 4) No change at High Frequencies

Sit

e A

mpl

ific

atio

n

20

Marginal vs. Fourier Ratio at Stiff SoilMarginal vs. Fourier Ratio at Stiff Soil

Marginal Spectral Ratio Fourier Spectral Ratio

Similar at stiff soil site in terms of 1) ratio (i.e., site amplification), 2) frequency down-shift, 3) amplitude down/up-shift

Freq. (Hz)

Sit

e A

mpl

ific

atio

n

21

Frequency Downshift of Mainshock Frequency Downshift of Mainshock from Aftershockfrom Aftershock

Sites

Soft Soil NS EW HHT FourierBOE 0.19 0.19 0.33 0.15HAR 0.22 0.19 0.34 0.24KDK 0.19 0.15 0.33 0.13SDS 0.29 0.22 0.36 0.21AVERAGE 0.22 0.19 0.34 0.18

Stiff Soil NS EW HHT FourierBHD 0.15 0.17 0.19 0.25LAP 0.10 0.09 0.16 0.15SEU 0.10 0.10 0.12 0.10THO 0.09 0.12 0.18 0.15AVERAGE 0.11 0.12 0.16 0.16

Mainshock PGA (g) Freq. Downshift (Hz)

22

0.1

1

10

100

0.1 1 10

Frequency (Hz)

Sit

e A

mp

lific

ati

on

Mainshock on Stiff Soil

Aftershock on Stiff Soil

Mainshock on Soft Soil

Aftershock on Soft Soil

Average HHT-based Site Amplification of Average HHT-based Site Amplification of Mainshock and AftershockMainshock and Aftershock

Freq. (Hz)

Sit

e A

mpl

ific

atio

n

Mainshock on Soft Soil

Aftershock on Soft Soil

Mainshock on Stiff Soil Aftershock

on Stiff Soil

23

0.1

1

10

100

0.1 1 10

Frequency (Hz)

Sit

e A

mp

lifi

ca

tio

n

Mainshock on Stiff Soil

Aftershock on Stiff Soil

Mainshock on Soft Soil

Aftershock on Soft Soil

Average Fourier-based Site Amplification of Average Fourier-based Site Amplification of Mainshock and AftershockMainshock and Aftershock

Freq. (Hz)

Sit

e A

mpl

ific

atio

n

Mainshock on Soft Soil

Aftershock on Soft Soil

Mainshock on Stiff Soil

Aftershock on Stiff Soil

24

0 2 4 6 8 10 12 14 16 18 2010

-3

10-2

10-1

100

Diff

eren

ce M

argi

nal D

ampi

ng S

pect

ra

Frequency (Hz)

Nisqually Earthquake, Difference of Marginal Damping Spectra (LAP-SEW)

AftershockMainshock

0 2 4 6 8 10 12 14 16 18 2010

-3

10-2

10-1

100

Diff

eren

ce M

argi

nal D

ampi

ng S

pect

ra

Frequency (Hz)

Nisqually Earthquake - Difference of Damping Factor (SDS-SEW)

AftershockMainshock

Damping at Soft vs. Stiff SoilDamping at Soft vs. Stiff Soil

Site Damping at Soft Soil Site Damping at Stiff Soil

1) Increased damping at soft soil for nonlinear mainshock from linear aftershock

2) No Change in stiff rock

Mainshock

Aftershock

MainshockAftershock

Dam

ping

Freq. (Hz)

25

Concluding RemarksConcluding Remarks

An Alternative Approach for Characterizing Site Nonlinearity• Nonlinearity Detection

IMFs and Hilbert amplitude spectrum• Site Indices

Site Amplification = Marginal amplitude spectral Ratio

Site Damping = Marginal damping spectral Difference • Nonlinearity Quantification

Frequency and amplitude downshiftIncreased damping

For nonlinear sites, Fourier-based Approach underestimates site amplification distorts physics at high frequenciesTwists damping

26

AcknowledgmentsAcknowledgments

Data and Fourier Analyses were provided by

Arthur Frankel and Stephen Hartzell

U.S. Geological Survey (USGS)

Research was supported by

National Science Foundation (NSF)

Multidisciplinary Centre for Earthquake Engineering

Research (MCEER)

On-going Liquefaction Research is in 4 slides

27

Layout of Seismic Instrumentation at Wildlife Site Layout of Seismic Instrumentation at Wildlife Site of 1989 of 1989 Superstition HillsSuperstition Hills (Bennett et al., (Bennett et al., 1984)1984) Instrument house

SM2 Recorder

P5

P4

SM1

P1P3

P2

P6

SM: Strong motion seismometer P: Piezometer

0

5

10

15

Depth

(m

)

Silty Sand

Silt

Silty Clay

Silt

(liquefiable layer)

28

Excessive Pore Water Pressure Ratio at P5 Excessive Pore Water Pressure Ratio at P5 E

xces

sive

Por

e P

ress

ure

Time

29

Excessive Pore Pressure vs. Instantaneous Excessive Pore Pressure vs. Instantaneous Frequency of Surface NS Acceleration Recording Frequency of Surface NS Acceleration Recording

Time

Exc

essi

ve P

ore

Pre

ssur

e I

nsta

ntan

eous

F

requ

ency

30

Instantaneous Frequencies of Surface and Instantaneous Frequencies of Surface and Downhole UD Acceleration Recordings Downhole UD Acceleration Recordings

Instantaneous Frequency at Surface

Instantaneous Frequency at Downhole

Time