By Ray Ruichong ZHANG Colorado School of Mines, Colorado, USA HHT-based Characterization of Soil Nonlinearity and Liquefaction in Earthquake Recordings US-Taiwan Workshop on Soil Liquefaction National Chiao Tung University, Hsin-Chu, Taiwan, November 3-5, 2003

2 Site 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 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 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)  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) Fourier Amplitude Spectrum Hilbert Amplitude Spectrum Instantaneous vs. constant Marginal spectrum w/ integration of Hilbert amplitude spectrum over t j: IMF/Fourier Component

7 Hilbert Amplitude and Damping Spectra 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 Components Time (s) IMF Components 1st IMF=noise2nd IMF=waves 3 rd, 4 th and 5 th IMFs=numerical errors w/ small amplitudes Nonlinear waves + noise Recording= Nonlinear waves + noise at frequency [1+0.5cos(2  t)] + 15 Hz i.e., at freq. 0.5 to 1.5 Hz + 15 Hz Amplitude

9 HHT: Hilbert and Marginal Spectra Time (s)Freq. (Hz) Hilbert Amplitude Spectrum Marginal Hilbert Amplitude Spectrum vs. Fourier Amplitude Spectrum Noise at 15 Hz Waves at Hz 1) No physical meaning, making up for nonlinear waveform, 2) Overestimates high-freq. 3) Distorts freq-related damping Amplitude

10 Example of HHT Analysis High-frequency Motion Low-frequency Motion Time (s) Freq. (Hz) 1964 Niigata Earthquake Record High-frequency Spike Hilbert Amplitude Spectrum Amplitude

11 Marginal 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 motion Amplitude

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 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 Time (s) Acc (g) Symptom of Nonlinear site in S-coda waves 1 st IMF singles out abnormal high-frequency spikes 2001 Nisqually Mainshock: NS-Acc. Record 1 st IMF Acc (g) Record

14 Time (s) Acc (g) 1 st IMF Not clear on abnormal high- frequency spikes 1 st IMF singles out abnormal high-frequency spikes Nonlinearity Detection w/ IMF 2001 Nisqually Mainshock: EW-Acc. Record Record

15 Nonlinearity Detection w/ IMF 2001 Nisqually Aftershock: NS-Acc. Record Acc (g) Time (s) 1 st IMF No abnormal high- frequency spikes in S- coda waves Record

16 Nonlinearity Detection w/ Hilbert Spectra Time (s) Abnormal high-frequency spikes can be identified from Hilbert Spectra Hilbert Spectra Record Acc (g) Freq. (Hz) Hilbert Amplitude Spectrum Time (s) Amplitude

17 Nonlinearity Quantification at Soft Soil Freq. (Hz) Mainshock Aftershock Site Amplification (HHT) Frequency Downshift Amplitude Downshift

18 Nonlinearity Quantification at Stiff Soil AftershockMainshock Frequency Downshift Amplitude Downshift Freq. (Hz) Site Amplification (HHT)

19 Marginal vs. Fourier Ratio at Soft Soil Freq. (Hz) Marginal Spectral RatioFourier 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 Site Amplification

20 Marginal vs. Fourier Ratio at Stiff Soil Marginal Spectral RatioFourier 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) Site Amplification

21 Frequency Downshift of Mainshock from Aftershock

22 Average HHT-based Site Amplification of Mainshock and Aftershock Freq. (Hz) Site Amplification Mainshock on Soft Soil Aftershock on Soft Soil Mainshock on Stiff Soil Aftershock on Stiff Soil

23 Average Fourier-based Site Amplification of Mainshock and Aftershock Freq. (Hz) Site Amplification Mainshock on Soft Soil Aftershock on Soft Soil Mainshock on Stiff Soil Aftershock on Stiff Soil

24 Damping at Soft vs. Stiff Soil Site Damping at Soft SoilSite Damping at Stiff Soil 1)Increased damping at soft soil for nonlinear mainshock from linear aftershock 2)No Change in stiff rock Mainshock Aftershock Mainshock Aftershock Damping Freq. (Hz)

25 Concluding 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 downshift Increased damping For nonlinear sites, Fourier-based Approach  underestimates site amplification  distorts physics at high frequencies  Twists damping

26 Acknowledgments  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 of 1989 Superstition Hills (Bennett et al., 1984)

28 Excessive Pore Water Pressure Ratio at P5 Excessive Pore Pressure Time

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

30 Instantaneous Frequencies of Surface and Downhole UD Acceleration Recordings Instantaneous Frequency at Surface Instantaneous Frequency at Downhole Time