Engineering Characteriza.on of Spa.ally Variable Ground Mo.on

Transcription

1 Engineering Characteriza.on of Spa.ally Variable Ground Mo.on Timothy D. Ancheta PEER Center, UC Berkeley Jonathan P. Stewart UCLA Civil & Environmental Engineering Department Norman A. Abrahamson Pacific Gas & Electric Co., San Francisco, CA ESG4 Conference Santa Barbara, CA. August

2 Acknowledgements to: Robert L. Nigbor and Jamie Steidl for providing access to Borrego Valley Differen.al Array data CEA for project funding

3 Outline Mo.va.on Metrics of spa.al variability in ground mo.ons (SVGM) Simula.on procedure for genera.ng SVGMs Inves.ga.on of seismic ground strains Conclusions

4 Kato et al., 1998 Mo.va.on

5 Example applica5ons Seismic demands on buried structures (pipelines, tunnels) e.g., Hashash et al., 2001 O Rourke and Deyoe, 2004

6 Example applica5ons Seismic demands on buried structures (pipelines, tunnels) Mul.- support excita.on for extended structures (bridges) e.g., Der Kiureghian & Neuenhofer, 2004

7 Example applica5ons Seismic demands on buried structures (pipelines, tunnels) Mul.- support excita.on for extended structures (bridges) Founda.on level ground mo.on reduc.on from kinema.c soil- structure interac.on e.g., ASCE- 41

8 Rancho Cucamonga Law & Jus.ce Center 1987 Whiber Earthquake

9 Outline Mo.va.on Metrics of spa-al variability in ground mo-ons (SVGM) Simula.on procedure for genera.ng SVGMs Inves.ga.on of seismic ground strains Conclusions

10 Metrics of SVGM Wave passage Lagged coherency Amplitude variability Correla.ons

11 Wave passage Zerva, 2009 V app Vapp, θ = sinθ

12 Wave passage

13 Wave passage V app,θ

14 Wave passage Arrival -me perturba-on, ATP

15 Wave passage Sensi.ve to waveform dura.on full signal or S- window Can have poor results if varying site condi.ons

16 Wave passage Lotung SMART 1 data: Boissieres and Vanmarcke (1995) Slope ranges from km/s

17 Wave passage Lotung SMART 1 data: Boissieres and Vanmarcke (1995) Std dev reflects arrival 5me perturba5ons

18 Wave passage BVDA and LSST Data (this study) BVDA Event θ (deg.) V app, θ (m/sec) V app (m/sec) LSST Event θ (deg.) V app, θ (m/sec) V app (m/sec) σ lnv = Med.= na na na na σ lnv = Med.= Lower σ lnv for V app preferred to V app,θ V app = km/s σ lnv =

19 Wave passage BVDA and LSST Residuals (this study) Negligible ATP for ξ < 50 m

20 Lagged Coherency Reflects phase variability that remains aher aligning sta.ons (removing wave passage and ATP).

21 Lagged Coherency Derived from smoothed power spectral density func.ons Sjk ( f ) γ jk ( f ) = ( ) ( ) 1 2 S f S f jj (, f ) = (, f ) exp i (, f ) γ ξ γ ξ θ ξ kk jk jk jk Sensi.ve to level of smoothing, windowing procedures, etc.

22 Lagged Coherency Complex sta.s.cal proper.es 10 Hz 20 Hz Kernal density es.mate of PDF

23 Lagged Coherency Complex sta.s.cal proper.es 10 Hz 20 Hz Transforma5on using tanh - 1 produces normal distribu5on

24 Lagged Coherency Trends with frequency and distance (BVDA data) Model bias for f < 10 Hz and ξ < 30 m

25 Lagged Coherency Chiba and LSST array data Bias for Chiba; no bias for LSST

26 Lagged Coherency Model adjustment ( ) ( ) ( ) { } ( ) 1 c tanh γ f, ξ = a ξ exp b ξ f + d ξ f + k ( ξ )

27 Lagged Coherency Model adjustment ( ) ( ) ( ) { } ( ) 1 c tanh γ f, ξ = a ξ exp b ξ f + d ξ f + k No change in b, c, d ( ξ )

28 Lagged Coherency Adjusted model compared to data

29 Lagged Coherency Adjusted model compared to data

30 Amplitude Variability Fourier amplitude varia.on in pair, ΔA(ξ, f)

31 Amplitude Variability Fourier amplitude varia.on in pair, ΔA(ξ, f) Distribu.on of ΔA(ξ, f) has mean zero and σ ΔA

32 Amplitude Variability BVDA & LSST data A Bf ( f ) = A( e ) σ Δ 1 B= b1+ bξ 2

33 Correla5ons Frequency- to- frequency correla.ons for coherency or amplitude variability Calculated for frequency steps Weak correla5on Coherency ΔA

34 Correla5ons Frequency- to- frequency correla.ons for coherency or amplitude variability Amplitude variability coherency correla.on No apparent correla5on

35 Outline Mo.va.on Metrics of spa.al variability in ground mo.ons (SVGM) Simula-on procedure for genera-ng SVGMs Inves.ga.on of seismic ground strains Conclusions

36 SVGM Simula.ons Objec.ve Phase modifica.on Amplitude modifica.on Frequency- dependent windowing

37 Objec5ve Given seed accelerogram, generate simulated mo.on compa.ble with γ and ΔA models Useful for response history analysis of structures Useful for es.ma.on of ground strains

38 Phase Modifica5on j n ( f, ξ ) = φ ( f ) + ε ( f, ξ ) + πfδt φ 2 i ij Phase of seed record

39 Phase Modifica5on j n ( f, ξ ) = φ ( f ) + ε ( f, ξ ) + πfδt φ 2 i ij Random phase change. Zero Mean Standard devia5on σ φ

40 Normal distribu5on Appears uniform at high frequency due to wrapping

41 Phase Modifica5on j n ( f, ξ ) = φ ( f ) + ε ( f, ξ ) + πfδt φ 2 i ij Wave passage. Δt from ξ and V app,θ

42 Phase Modifica5on Result of phase modifica.on (full dura.on): Unrealis5c high frequency energy at start and end of record

43 Amplitude Modifica5on 1 Aj f Ai f ij f σ Δ A f 2 A ( ) = exp ln ( ) + ε ( ) g ( ) Amplitude of seed record

44 Amplitude Modifica5on 1 Aj f Ai f ij f σ Δ A f 2 A ( ) = exp ln ( ) + ε ( ) g ( ) Gaussian random number. Mean zero Standard devia5on of unity

45 Amplitude Modifica5on 1 Aj f Ai f ij f σ Δ A f 2 A ( ) = exp ln ( ) + ε ( ) g ( ) From amplitude variability model

46 Amplitude Modifica5on 1 Aj f Ai f ij f σ Δ A f 2 A ( ) = exp ln ( ) + ε ( ) g ( ) To represent single sta5on amplitude variability

47 Amplitude Modifica5on Result of amplitude modifica.on (full dura.on): Pronounced 5me- domain leakage effect

48 Frequency Dependent Windowing

49 Frequency Dependent Windowing Seed Mo5on

50 Frequency Dependent Windowing Window Time Series Window length related to freq. band S.T. Fourier trans. Modify A & φ

51 Frequency Dependent Windowing S5tch together modified A & φ Inverse Fourier trans. to 5me domain

52 Frequency Dependent Windowing Cri5cal details: Windowing procedure Recombina.on procedure Details in Ancheta et al. (2011, Earthquake Spectra, in review)

53 Frequency Dependent Windowing Leakage removed

54 Frequency Dependent Windowing Compare simula.ons to underlying models

55 Outline Mo.va.on Metrics of spa.al variability in ground mo.ons (SVGM) Simula.on procedure for genera.ng SVGMs Inves-ga-on of seismic ground strains Conclusions

56 Seismic Ground Strains Previous work Procedure for simula.on- based strain es.ma.on Simula.on results & predic.on equa.ons Verifica.on using array data

57 Previous Work Strains from wave passage Newmark, 1967 PGS = PGV A V app Yeh (1974) St. John and Zahrah (1987) Trifunac and Lee (1996) Hashash et al. (2001)

58 Previous Work Strains from wave passage Inference of strains from arrays using geode.c approach O Rourke et al. (1984) Bodin et al. (1997) Gomberg et al. (1999) Paolucci and Smerzini (2008)

59 Previous Work Strains much higher than an5cipated from wave passage. Limited to modest PGV levels Paolucci and Smerzini (2008)

60 Strain Es5ma5on from Simula5ons 1. N i seed mo.ons selected for j=1..n e events 2. For each seed mo.on, simulate N s mo.ons for suites of separa.on distances (ξ = 6, 10, 20, 40, 80 m) and apparent veloci.es (V app ). 3. Each seed- simulated mo.on integrated twice to displacement & normalized by ξ to calculate strain history. Peak is PGS.

61 Strain Es5ma5on from Simula5ons Events M 4.9 Anza, CA M 4.9 Big Bear City, CA M 6.0 Whiber, CA M 6.1 North Palm Springs, CA M 6.5 Big Bear City, CA M 6.7 Northridge, CA M 6.9 Loma Prieta, CA M 7.5 Kocaeli, Turkey M 7.6 Chi Chi, Taiwan M 7.9 Denali, AL Soil sites selected 135 mojons

62 Results of Simula5ons Affected by ξ Satura.on effect for PGV > 80 cm/s

63 Fifng of Model α + βln PGV + ε for PGV < PGV ln PGSijk ξ = ψ otherwise ijk ijk L Final coefficients from random effects analysis. FOSM used to represent range of V app in data set.

64 Fifng of Model

65

66 Verifica5on of ξ- Dependence LSST data Calculate differen.al displacement from pairs & normalize by ξ. Sta.s.cally significant difference for low ξ; not for ξ > 20 m.

67 Outline Mo.va.on Metrics of spa.al variability in ground mo.ons (SVGM) Simula.on procedure for genera.ng SVGMs Inves.ga.on of seismic ground strains Conclusions

68 Summary of Key Results Three key metrics of SVGM. Wave passage: Recommenda.ons on V app, σ lnv, and importance of ATP Modest adjustment of previous γ model Model for amplitude variability Simula.on procedure provides realis.c spa.ally variable waveforms including amplitude variability. New insights on ground strain: Separa.on distance dependence Satura.on at large PGV

69 More Informa.on Metrics of SVGM: this conference SVGM simula.ons: Ancheta et al., Earthquake Spectra, in review Ground strains: Ancheta (2010) disserta.on; soon in PEER report