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Stochastic Simulation of Ground Motion Components for a Specified Design Scenario

Stochastic Simulation of Ground Motion Components for a Specified Design Scenario. Sanaz Rezaeian Armen Der Kiureghian (PI) University of California, Berkeley. Sponsor: State of California through Transportation Systems Research

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Stochastic Simulation of Ground Motion Components for a Specified Design Scenario

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  1. Stochastic Simulation of Ground Motion Components for a Specified Design Scenario SanazRezaeian ArmenDerKiureghian (PI) University of California, Berkeley Sponsor: State of California through Transportation Systems Research Program of Pacific Earthquake Engineering Research (PEER)

  2. Outline: • Motivation • Ground motion model • Extend to simulate multiple components • Principal axes of ground motions • High correlations between model parameters • Example • Conclusion

  3. Motivation: • In seismic hazard analysis, development of design ground motions is a crucial step. • High levels of intensity • Expected structural behavior: Nonlinear • Approach: Response-history dynamic analysis • Requires: Ground motion time-series

  4. Motivation: • In seismic hazard analysis, development of design ground motions is a crucial step. • High levels of intensity • Expected structural behavior: Nonlinear • Approach: Response-history dynamic analysis • Requires: Ground motion time-series • Difficulties come from scarcity of previously recorded motions. • Controversies come from methods of selecting and modifying real records. • Alternative: Use simulated time-series in conjunction or in the place of real records.

  5. Motivation: • In seismic hazard analysis, development of design ground motions is a crucial step. • High levels of intensity • Expected structural behavior: Nonlinear • Approach: Response-history dynamic analysis • Requires: Ground motion time-series • Our Goal: Earthquake and site characteristics  Suite of simulated time-series • (F, M, Rrup, Vs30) Site VS30: Shear wave velocity of top 30m Controlling Fault F: Faulting mechanism M: Moment magnitude … R: Closest distance to ruptured area

  6. Motivation: • In seismic hazard analysis, development of design ground motions is a crucial step. • High levels of intensity • Expected structural behavior: Nonlinear • Approach: Response-history dynamic analysis • Requires: Ground motion time-series • Our Goal: Earthquake and site characteristics  Suite of simulated time-series • (F, M, Rrup, Vs30) • For 2D/3D structural analysis, need ground motion components. Site VS30: Shear wave velocity of top 30m Controlling Fault F: Faulting mechanism M: Moment magnitude … R: Closest distance to ruptured area

  7. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008]

  8. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008] Acceleration time-series

  9. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008] Temporal non-stationarity: Variation of intensity in time Spectral non-stationarity: Variation of frequency content in time

  10. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008] Source of stochasticity

  11. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008] Impulse response function (IRF) corresponding to pseudo-acceleration response of a SDOF linear oscillator

  12. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008] Duhamel’s integral (superposition of filter responses to a sequence of statistically independent pulses with the time of application τ)

  13. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008]

  14. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008]

  15. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008] 0timetn

  16. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008] Non-zero residuals! Over estimates response spectrum at long periods!

  17. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008] Critically damped oscillator

  18. Ground Motion Model: [Rezaeian and Der Kiureghian, 2008]

  19. Model Parameters:

  20. Model Parameters: Modulating function parameters: Filter parameters: : Frequency at the middle of strong shaking : Arias intensity : Rate of change of frequency over time : Effective duration, between 5% to 95% Ia : Damping ratio : Time at the middle of strong shaking, at 45% Ia

  21. Model Parameters: Modulating function parameters: Filter parameters: : Frequency at the middle of strong shaking : Arias intensity : Rate of change of frequency over time : Effective duration, between 5% to 95% Ia : Damping ratio : Time at the middle of strong shaking, at 45% Ia

  22. Model Parameters: Modulating function parameters: Filter parameters: 0.15 0 Acceleration, g Recorded : Frequency at the middle of strong shaking : Arias intensity -0.25 0 40 Time, sec : Rate of change of frequency over time : Effective duration, between 5% to 95% Ia : Damping ratio : Time at the middle of strong shaking, at 45% Ia Model parameters are identified for many recorded motions to develop predictive equations in terms of F, M, R, VS30 • Match • statistical • characteristics • Representing: • Intensity • Frequency • Bandwidth Identify model parameters Ia, tmid, D5-95 ωmid, ω’, ζ

  23. Two Horizontal Components: Component 1: Component 2:

  24. Two Horizontal Components: Component 1: Component 2: source of stochasticity • w1(τ) and w2(τ) are statistically independent if along the principal axes.

  25. Two Horizontal Components: Component 1: Component 2: source of stochasticity Expected Epicenter Site Horizontal Plane • w1(τ) and w2(τ) are statistically independent if along the principal axes. • Principal Axes of Ground Motion: • A set of orthogonal axes along which the components are uncorrelated. Minor • Penzien and Watabe (1975) Major Intermediate

  26. Two Horizontal Components: Component 1: Component 2: source of stochasticity • w1(τ) and w2(τ) are statistically independent if along the principal axes. • Principal Axes of Ground Motion: • A set of orthogonal axes along which the components are uncorrelated. Rotate recorded motions in the database. a2,θ ρa1 , a2≠ 0 a2 θ Site ρa1,θ , a2,θ = 0 a1,θ Horizontal Plane a1

  27. Rotating Recorded Motions: Northridge earthquake recorded at Mt. Wilson Station

  28. Two Horizontal Components: Component 1: Component 2:

  29. Two Horizontal Components: Component 1: Component 2: • Predictive equations: if if

  30. Two Horizontal Components: Component 1: Component 2: • Predictive equations: if if Model parameter p transformed to the standard normal space

  31. Two Horizontal Components: Component 1: Component 2: • Predictive equations: if if Predicted mean conditioned on earthquake and site characteristics Independent normally-distributed errors

  32. Two Horizontal Components: Component 1: Component 2: • Predictive equations. • High correlations expected between parameters of the two components.

  33. Two Horizontal Components: Correlation Matrix: Major Component (larger Arias intensity) Intermediate Component (smaller Arias intensity) Major Component Symmetric Intermediate Component

  34. Two Horizontal Components: Correlation Matrix: Major Component (larger Arias intensity) Intermediate Component (smaller Arias intensity) Major Component Symmetric Intermediate Component

  35. Two Horizontal Components: Correlation Matrix: Major Component (larger Arias intensity) Intermediate Component (smaller Arias intensity) Major Component Symmetric Intermediate Component

  36. Two Horizontal Components: Correlation Matrix: Major Component (larger Arias intensity) Intermediate Component (smaller Arias intensity) Major Component Symmetric Intermediate Component

  37. Example: Design scenario: F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s

  38. Example: Design scenario: F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s Major Component Intermediate Component

  39. Example: Design scenario: F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s 0.1 Recorded Recorded Major Component Intermediate Component 0 -0.1 Acceleration, g 0.1 Simulated Simulated 0 -0.1 0 20 40 60 80 0 20 40 60 80 Time, s Time, s 0.05 Simulated Simulated 0 -0.05

  40. Example: Design scenario: F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s 0.01 Recorded Recorded Major Component Intermediate Component 0 -0.01 Simulated Simulated Velocity, m/s Simulated Simulated 0.05 0 -0.05 0 20 40 60 80 0 20 40 60 80 Time, s Time, s 0.05 0 -0.05

  41. Example: Design scenario: F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s 0.02 Recorded Recorded Major Component Intermediate Component 0 -0.02 Simulated Simulated Displacement, m Simulated Simulated 0.05 Time, s Time, s 0 -0.05 0.05 0 -0.05 0 20 40 60 80 0 20 40 60 80

  42. Conclusion: • Developed a stochastic model for earthquake ground motion components • Created a database of principal ground motion components • Identified model parameters for the records in the database •  predictive equations for model parameters in terms of F , M , R, VS30 • Identified correlation coefficients between model parameters of the components • For given F , M , R, VS30 , correlated model parameters are randomly simulated and used along with statistically independent white-noise processes to generate a pair of horizontal ground motion components in the directions of principal axes. • The proposed methods can be easily extended to simulate the vertical component.

  43. Related Publications: • Rezaeian S, DerKiureghian A. "A stochastic ground motion model with separable temporal and spectral nonstationarities”, Earthquake Engineering and Structural Dynamics, 2008, Vol. 37, pp. 1565-1584. Rezaeian S, DerKiureghian A. "Simulation of synthetic ground motions for specified earthquake and site characteristics”, Earthquake Engineering and Structural Dynamics, 2010, Vol. 39, pp. 1155-1180. Rezaeian S, DerKiureghian A. "Simulation of orthogonal horizontal ground motion components for specified earthquake and site characteristics”, Submitted to Earthquake Engineering and Structural Dynamics.

  44. Thank You • This project was made possible with support from: • State of California through Transportation Systems Research Program of Pacific Earthquake Engineering Research Center (PEER TSRP).

  45. Ground Motion Model: Advantages Extra • Small number of parameters that have physical meaning and can be easily identified by matching with features of a given accelerogram • Completely separable temporal and spectral nonstationary characteristics, which facilitates identification and interpretation of the parameters • No need for sophisticated processing of the target accelerogram, e.g. Fourier analysis or estimation of evolutionary PSD • Simple simulation of sample functions, requiring little more than generation of standard normal random variables • Form of the model facilitates nonlinear random vibration analysis (e.g., by using TELM).

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