Outstanding Problems. APOSTOLOS S. PAPAGEORGIOU University of Patras

Transcription

1 NEAR-FAULT GROUND MOTIONS: Outstanding Problems APOSTOLOS S. PAPAGEORGIOU University of Patras

2 Outline Characteristics of near-fault ground motions Near-fault strong ground motion database A mathematical expression for near-fault ground motions: Calibration Scaling laws of the parameters Spectral properties Interpretation of empirical observations Elastic and inelastic response spectra Synthesis of near-fault ground motion time histories Conclusions Additional considerations Directions of future research

3 Characteristics of Near-Fault Ground Motions Significant seismic events where the special character of the near-fault ground motions was originally observed. Note the intense velocity and displacement pulses in near-field regions.

4 Characteristics of Near-Fault Ground Motions Forward Directivity it Effect: Fault rupture propagates toward a site with V r β(and slip vector points toward the site). Appears in the form of two-sided velocity pulse. Observed in the strike-normal direction for strike-slip and dip-slip faults. [References: e.g., Aki, 1968; Somerville & Graves, 1993; Somerville, 2000; Abrahamson, 2000]. Permanent Translation Effect: Related to the permanent tectonic deformation at a site. Appears in the form of step displacement and one-sided velocity ypulse. Observed in the strike-parallel and strike-normal directions for strike-slip and dip-slip faults, respectively. [Reference: Abrahamson, 2000]. Other factors that influence the near-fault ground motions: - Type of rupture: Shear dislocation vs. crack [Aki & Richards, 1980; Campillo et al., 1989]. - Hanging wall vs. Foot wall effect [Abrahamson & Somerville, 1996; Oglesby et al., 1998]. - Surface vs. buried faulting [Aki, 1980; Somerville, 2000]. - Surface or interface P-wave [Bouchon, 1978; Kawase & Aki, 1990]. - Special geometrical conditions [Oglesby & Archuleta, 1997]. - Supershear rupture velocity [Bouchon et al., 2001; O Connell and Ake, 2003].

5 Characteristics of Near-Fault Ground Motions: Examples of Directivity and Permanent Translation Effect

6 Near-Fault Strong Ground Motion Database Thorough documentation of the existing near-source recordings of moderate and large events (31 events worldwide; 165 stations; fault-to-station distance less than 20 km). Collection and uniform processing of these data and presentation in visually informative form relative to the causative faults. Approximately 40 near-source ground motion records (from 20 events worldwide) are characterized by distincti velocity pulses.

7 Near-Fault ltstrong Ground dmotion Database

8 Near-Fault Strong Ground Motion Database Near-fault ground motion records with distinct velocity pulses (incorporating forward directivity and permanent translation effects). Pulse characteristics: ti amplitude, duration, as well as number and phase of half cycles. These records are being used for the calibration of the proposed analytical model.

9 Near-fault velocity pulses: Iceland 2000 Significant coherent part in the near-fault ground motions during the 17 June and 21 June, 2000, Mw6.5 earthquakes (Halldorsson et al., 2007)

10 Velocity north-south Iceland 2008: Velocity strike-normal Halldorsson & Sigbjornsson (2009, SDEE) Halldorsson et al. (2009, in progress)

11 Iceland 2008: Velocity strike-normal Halldorsson et al. (2009, in progress)

12 An Analytical Model for Near-Fault Ground Motions Objective: Representation of near-source ground motions in terms of simple analytical waveforms, the parameters of which have an unambiguous physical meaning and scale (to the extent possible) with earthquake size. Advantages: - Objective assessment of duration and amplitude of pulse. - These models can be easily used to effectively generate near-fault ground motion time histories appropriate for engineering design. - These models facilitate the parametric study of the elastic and inelastic response of long-period structures subjected to near-fault ground motions.

13 An Analytical Model for Near-Fault Ground Motions: Mathematical Expression 1 2π f A 1 + cos v ( t ) = 2 γ where: P γ γ 0 P 0, t0 t t0 + with γ > 1 2 f P 2 f P otherwise ( t t ) cos [ 2π f ( t t ) + ν ] 0, A is the amplitude of the signal, f P is the frequency of the amplitude-modulated modulated harmonic (or the prevailing frequency of the signal), ν is the phase of the amplitude-modulated modulated harmonic, γ is a parameter that defines the oscillatory character (i.e., zero-crossings) of the signal, and t 0 specifies the epoch of the envelope s peak.

14 An Analytical Model for Near-Fault Ground Motions: Calibration The proposed analytical model has been fitted to the entire set of nearfault ground motions with distinct velocity pulse. It successfully simulates the displacement, velocity and the coherent component of acceleration time histories, as well as the elastic response spectra. As anticipated, tii tdthe proposed model does not replicate the incoherent (high-frequency) component of ground motion (clearly evident in the accelerograms and in the low-period range of the response spectra).

15 An Analytical Model for Near-Fault Ground Motions: Calibration Utilization of multiple synthetic pulses to fit more complicated waveforms. Two (2) and three (3) synthetic pulses have been combined to model the YPT (1999 Izmit, Turkey) and KOB (1995 Kobe, Japan) time histories, respectively.

16 An Analytical Model for Near-Fault Ground Motions: Regression Analysis & Scaling Laws log T = P M w The pulse duration is defined as the inverse of the prevailing frequency. Only forward directivity pulses have been considered for the derivation of the expression above. PGV cm/ s, for R 7 km Both forward directivity and fling pulses are illustrated. With the exemption of TCU052 and TCU068 stations, all other records are effectively described by a PGV of 100 cm/s. (Note: A PGV).

17 The Specific Barrier Model: Barrier Interval 2ρρ 0 vs. Moment Magnitude M w ( 2ρ ) = MW log 0 + According to the Specific Barrier Model the Rise Time τ is estimated as follows: ( ρ V ) τ ( 2 /V ) 0 / ρ0 We previously obtained: ( T P ) = M W log + Combining the above we obtain: 0.35T τ P T P Therefore, we propose: τ 0.5T P

18 An Analytical Model for Near-Fault Ground Motions: Spectral Properties Fourier Spectra Normalized Fourier amplitude spectrum of velocity pulse vs. normalized frequency for a suite of γ and ν values. Narrow-band velocity pulse with its bandwidth and Fourier amplitude being a function of γ for constant ω P and A values. The phase parameter ν affects the Fourier amplitude spectrum only when γ approaches unity and then only for periods longer than T P.

19 An Analytical Model for Near-Fault Ground Motions: Spectral Properties Response Spectra

20 An Analytical Model for Near-Fault Ground Motions: Spectral Properties Elastic Response Spectra

21 An Analytical Model for Near-Fault Ground Motions: Interpretation of Empirical Observations It has been observed (originally by Somerville, 2000) that: the near-source acceleration response spectra of moderate earthquakes are stronger than those of large earthquakes in the high-frequency range. This trend is reversed at longer periods, and the peak spectral acceleration values of moderate earthquakes are regularly higher than the corresponding values of large earthquakes. We may interpret the above observations through the mathematical formulation of our model: Consider 2 seismic events with M w1 > M w2 that produce near-source ground velocity pulses effectively replicated by the proposed analytical model.

22 Equal-Ductility Pseudo-Velocity Response Spectra of Elastic Perfectly Plastic SDOF Systems

23 Equal-Ductility Pseudo-Velocity Response Spectra of Elastic Perfectly Plastic SDOF Systems

24 Schematic Illustration of Idealized Response Spectra In Four-Way Logarithmic i Plots

25 Elastic Response Spectra (Damping Ratio ξ =5%)

26 Elastic Response Spectra (Damping Ratio ξ = 5%) Earthquake Characterization Moment Magnitude (M w ) (T n /T P ) a (T n /T P ) b (T n /T P ) c (T n /T P ) d (T n /T P ) f Moderate Moderate-to-Large Large All sizes Earthquake Characterization Moment Magnitude (M w ) α V,cd α V,b Moderate Moderate-to-Large Large All sizes

27 Strength Reduction Factor R y : Comparison With Veletsos-Newmark-Hall Design Equations

28 Synthesis of Near-Fault Ground Motion Time Histories: A Simplified Methodology for Engineering g Applications Demonstration Case A Generation of ground motion for a M w 6.8 earthquake event and for the fault-station geometry displayed d in the figure. The site characterization at the station is assumed to be NEHRP Site Class C. The selected values for the parameters of the Specific Barrier Model are consistent with those of Chin and Aki (1991) inferred for a comparable size Californian event. As expected, the incoherent component of motion controls the accelerations while the coherent component of motion controls the velocity and displacement.

29 Synthesis of Near-Fault Ground Motion Time Histories: A Simplified Methodology for Engineering Applications Demonstration Case B

30 Demonstration Case B (Cont d)

31 Fast and efficient simulation of broad-band near-fault ground motions Halldorsson, Mavroeidis & Papageorgiou (2009) Journal of Structural Engineering (in press)

32 Conclusions The proposed mathematical model describes adequately the nature of the impulsive near-fault ground motions both qualitatively and quantitatively. The model input parameters have an unambiguous physical meaning. The analytical model has been calibrated using alarge number of actual near-field ground motion records; itsuccessfullysimulatesthe entire set of available near-fault displacement, velocity and, in many cases, acceleration time histories, as well as the corresponding response spectra. The model dl can be used to explain analytically empirical observations that are based on available near-source records. Wehaveproposed elastic and inelastic response spectra for design. We have proposed a very simplified methodology for generating realistic synthetic ground motions that are adequate for engineering analysis and design.

33 Additional Considerations Additional Considerations: Scaling of Pulse Period T P vs. Moment Magnitude M w for Intra-Plate Earthquake Events

34 Additional Considerations Super-shear Rupture A supershear rupture leads to large amplitudes on both the FP and FN components of motion. [Taken from Durham and Archuleta (2005), GRL] Rupture growth into a region of increased stress drop triggers a set of transient diffractions that accelerate the rupture from sub-rayleigh to supershear velocities. This process is accompanied by the release of a Rayleigh wave on the fault surface. This appears as a secondary slip pulse that manifests itself primarily in FN ground motion, explaining late arriving FN pulses recorded at PS10 that are not explained in supershear kinematic models.

35 Additional Considerations Directions of Future Research (cont d) Seismic energy radiated from the high-isochrone-velocity region of the fault arrives at the receiver within a time interval that coincides with the time window of the ground motion pulse recorded d at the site. Near-fault strong motion pulses are strongly correlated with large slip on the fault plane locally driven by high stress drop. For smaller earthquakes, the area of the fault that contributes to the formation of the near-fault pulse encompasses more than one patches of significant moment release (subevents).

36 Additional Considerations Directions of Future Research (cont d)

37 Additional Considerations Directions of Future Research (cont d) For larger earthquakes, the area of the fault that contributes to the formation of the near fault pulse encompasses an individual patch of significant moment release (subevent). The foreshock and aftershock seismic activity in combination with the shear The foreshock and aftershock seismic activity in combination with the shearstress images may offer insight into the type of mechanism (i.e., barrier or asperity) that controlled the mainshock rupture.

38 Dynamic Ground Deformations in the Near-Fault Region: The 1979 Imperial Valley Earthquake Remarkable waveform similarity between velocity time histories and derivatives of the displacement components with respect to the x coordinate (Bouchon and Aki, 1982). This indicates that most of the energy (which controls the peak amplitudes of motion) propagates at each observation point within a relatively small range of phase velocities. X-axis in the Fault-Parallel direction Y-axis in the Fault-Normal direction Z-axis in the Vertical Direction

39 Dynamic Ground Deformations in the Near-Fault Region: The 1979 Imperial Valley Earthquake u 1 u xx c t i i The relationship is approximately valid, with c being the average phase velocity. The phase velocities are controlled either by the basement rock shear velocity or the rupture velocity and may be estimated from synthetic time histories. In our case, the estimated phase velocities are close to the shear wave velocity of the basement rock (4 to 5 km/s). The axial strain along the strike direction (ε xx = u x / x), the rocking about an axis along the transverse direction (ω y = - u z / x), and the torsional motion (ω z 05* u 0.5 y / x) may be estimated with reasonable accuracy via the above equation by using synthetic or recorded ground velocities and properly selected phase velocities. The analytical model for the representation of the long-period component of the nearfault ground motions proposed by Mavroeidis and Papageorgiou (2003) may be used to approximate the torsional component of the near fault ground motion; that is: 1 u y 1 u y 1 ω z = V 2 x 2 c t 2c g