SIM IMULATION of NEAR-FAULT GROUND MOTIONS for SPECIF IFIED EARTHQUAKE SOURCE and SIT ITE CHARACTERISTICS Mayssa Dabaghi Visiting Assistant Professor, American University of Beirut (AUB) Abdurrahman Almikati Graduate Student, American University of Beirut (AUB) Armen Der Kiureghian President, American University of Armenia Taisei Professor of Civil Engineering Emeritus, UC Berkeley Funding: Caltrans, PEER, AUB 8/17/2015 - ESG5, Taipei, Taiwan
Motivation Characteristics of near-fault (NF) ground motions (GM) are different from far-field GMs Rupture directivity effect Fling Step (after Somerville et al. [1997]). 2 (figure courtesy of Y. Bozorgnia, adopted from Somerville et al. [1997]).
Motivation NF effects not properly represented in modern codes and current ground motion prediction equations (GMPEs). May underestimate: Elastic demands on long period structures Damage potential to ductile short-period structures NF records from 2014 South Napa EQ vs. code spectra and UHS (directivity and/or site effects) (source: Bray et al., 2014). Attempt to develop NGA West2 directivity models (Spudich et al., 2014) 3
Motivation Recorded NF GMs remain scarce Ongoing effort to understand, model, and simulate NF GMs and their effects on the response of structures Proposed Methodology: Site-based stochastic model of NF GMs in 2 orthogonal horizontal directions Simulation procedure for specified EQ source and site characteristics References: Dabaghi M, Der Kiureghian A. (2016). Stochastic model for simulation of near-fault ground motions, submitted manuscript. Dabaghi M, Der Kiureghian A. (2014). Stochastic modeling and simulation of near-fault ground motions for performance- based earthquake engineering, PEER Report No. 2014/20 , Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA. Rezaeian S, Der Kiureghian A. (2010). Simulation of synthetic ground motions for specified earthquake and site 4 characteristics. Earthquake Engineering & Structural Dynamics ; 39 (10): 1155-1180.
Outline Overview of NF Ground Motion Model Overview of Simulation Framework Illustrative Examples #1: Forward vs. Backward Directivity Sites #2: Hypothetical M6.5 Strike-Slip Earthquake Event Summary and Conclusions 5
Overview of f Stochastic Model of NF Ground Motion Pulse-like and Non-pulse-like 6
Puls lse-like GM Model Pulse in at least one horizontal direction, due to rupture directivity… Model formulated in: .5 𝑏 𝑄𝑄 (𝑢) 0 direction of the largest pulse : 𝑏 𝑄𝑄 (𝑢) corresponding orthogonal direction: 𝑏 𝑄𝑃 (𝑢) .5 0 10 20 30 40 .5 𝑏 𝑄𝑃 (𝑢) 0 Simulated .5 0 10 20 30
Puls lse-like GM Model Pulse in at least one horizontal direction, due to rupture directivity Model formulated in: .5 𝑏 𝑄𝑄 (𝑢) 0 direction of the largest pulse : 𝑏 𝑄𝑄 (𝑢) corresponding orthogonal direction: 𝑏 𝑄𝑃 (𝑢) .5 0 10 20 30 40 .5 𝑏 𝑄𝑃 (𝑢) 0 Simulated .5 0 10 20 30 𝑏 𝑄𝑄 𝑢 𝑏 𝑠𝑓𝑡 (𝑢) 𝑏 𝑞𝑣𝑚(𝑢) .5 .5 .5 0 0 0 Simulated .5 .5 .5 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40 MFW : modified Rezaeian & Der mMP : modified Mavroeidis & Kiureghian (2010) modulated and Papageorgiou (2003) pulse model filtered white noise model ( 𝑊 𝑞 , 𝑈 𝑞 , 𝛿 , 𝜉 , 𝑢 𝑛𝑏𝑦,𝑞 ) 𝑛𝑗𝑒 , 𝑔 ′ , 𝜂 𝑔 ) ( 𝐽 𝑏 , 𝐸 5−95 , 𝐸 0−5 , 𝐸 0−30 , 𝑔 8
Puls lse-like GM Model Pulse in at least one horizontal direction, due to rupture directivity Model formulated in: .5 𝑏 𝑄𝑄 (𝑢) 0 direction of the largest pulse : 𝑏 𝑄𝑄 (𝑢) corresponding orthogonal direction: 𝑏 𝑄𝑃 (𝑢) .5 0 10 20 30 40 .5 𝑏 𝑄𝑃 (𝑢) 0 Simulated .5 0 10 20 30 𝑏 𝑄𝑃 𝑢 .5 .5 0 0 Simulated Simulated .5 .5 0 10 20 30 0 10 20 30 MFW : modified Rezaeian & Der Kiureghian (2010) modulated and filtered white noise model 𝑛𝑗𝑒 , 𝑔 ′ , 𝜂 𝑔 ) ( 𝐽 𝑏 , 𝐸 5−95 , 𝐸 0−5 , 𝐸 0−30 , 𝑔 9
Puls lse-like GM Model Complete list of the parameters 𝛽 𝑄,𝑗 of the pulse-like model, 𝑗 = 1, … , 19 . Table 1. Complete list of the parameters 𝛽 𝑄 , 𝑗 of the pulse-like model, 𝑗 = 1, … ,19 . 𝛽 𝑄 ,1 𝛽 𝑄 ,2 𝛽 𝑄 ,3 𝛽 𝑄 ,4 𝛽 𝑄 ,5 𝑏 𝑞𝑣𝑚 𝑢 : Pulse 𝑊 𝑈 𝑢 𝑛𝑏𝑦 , 𝑞 (s) ν / π (rad) 𝑞 (cm/s) 𝑞 (s) γ 𝛽 𝑄 ,6 𝛽 𝑄 ,7 𝛽 𝑄 ,8 𝛽 𝑄 ,9 𝛽 𝑄 ,10 𝛽 𝑄 ,11 𝛽 𝑄 ,12 𝑏 𝑠𝑓𝑡 𝑢 : Residual ′ (Hz/s) 𝜂 𝑔 , 𝑠𝑓𝑡 𝐽 𝑏 , 𝑠𝑓𝑡 (cm/s) 𝐸 5 − 95, 𝑠𝑓𝑡 (s) 𝐸 0 − 5, 𝑠𝑓𝑡 (s) 𝐸 0 − 30, 𝑠𝑓𝑡 (s) 𝑔 𝑛𝑗𝑒 , 𝑠𝑓𝑡 (Hz) 𝑔 𝑠𝑓𝑡 Orthogonal 𝛽 𝑄 ,13 𝛽 𝑄 ,14 𝛽 𝑄 ,15 𝛽 𝑄 ,16 𝛽 𝑄 ,17 𝛽 𝑄 ,18 𝛽 𝑄 ,19 𝑏 𝑄𝑃 𝑢 : ′ (Hz/s) 𝜂 𝑔 , 𝑄𝑃 𝐽 𝑏 , 𝑄𝑃 (cm/s) 𝐸 5 − 95, 𝑄𝑃 (s) 𝐸 0 − 5, 𝑄𝑃 (s) 𝐸 0 − 30, 𝑄𝑃 (s) 𝑔 𝑔 𝑛𝑗𝑒 , 𝑄𝑃 (Hz) 𝑄𝑃 10
Non-pulse-like GM Model No pulse in any horizontal direction Formulated in: 𝑏 𝑂𝑄1 (𝑢) Major principal direction: 𝑏 𝑂𝑄1 (𝑢) Intermediate principal direction: 𝑏 𝑂𝑄2 (𝑢) 𝑏 𝑂𝑄2 (𝑢) .5 𝑏 𝑂𝑄1 (𝑢) 0 .5 30 40 50 60 MFW : modified Rezaeian & Der .5 Kiureghian (2010) modulated and 𝑏 𝑂𝑄2 (𝑢) 0 filtered white noise model .5 𝑛𝑗𝑒 , 𝑔 ′ , 𝜂 𝑔 ) 30 40 50 60 ( 𝐽 𝑏 , 𝐸 5−95 , 𝐸 0−5 , 𝐸 0−30 , 𝑔 11
Non-pulse-like GM Model Complete list of the parameters 𝛽 𝑂𝑄,𝑗 of the non-pulse-like model, 𝑗 = 1, … , 14 . Table 1. Complete list of the parameters 𝛽 𝑂𝑄 , 𝑗 of the non-pulse-like model, 𝑗 = 1, … ,14 . 𝛽 𝑂𝑄 ,1 𝛽 𝑂𝑄 ,2 𝛽 𝑂𝑄 ,3 𝛽 𝑂𝑄 ,4 𝛽 𝑂𝑄 ,5 𝛽 𝑂𝑄 ,6 𝛽 𝑂𝑄 ,7 𝑏 𝑂𝑄1 (𝑢) : Major ′ 𝑛𝑗𝑒 , 𝑂𝑄 1 (Hz) 𝑔 𝐽 𝑏 , 𝑂𝑄 1 (cm/s) 𝐸 5 − 95, 𝑂𝑄 1 (s) 𝐸 0 − 5, 𝑂𝑄 1 (s) 𝐸 0 − 30, 𝑂𝑄 1 (s) 𝑔 (Hz/s) 𝜂 𝑔 , 𝑂𝑄 1 𝑂𝑄 1 𝛽 𝑂𝑄 ,8 𝛽 𝑂𝑄 ,9 𝛽 𝑂𝑄 ,10 𝛽 𝑂𝑄 ,11 𝛽 𝑂𝑄 ,12 𝛽 𝑂𝑄 ,13 𝛽 𝑂𝑄 ,14 𝑏 𝑂𝑄2 𝑢 : Intermediate ′ 𝐽 𝑏 , 𝑂𝑄 2 (cm/s) 𝐸 5 − 95, 𝑂𝑄 2 (s) 𝐸 0 − 5, 𝑂𝑄 2 (s) 𝐸 0 − 30, 𝑂𝑄 2 (s) 𝑔 𝑛𝑗𝑒 , 𝑂𝑄 2 (Hz) 𝑔 (Hz/s) 𝜂 𝑔 , 𝑂𝑄 2 𝑂𝑄 2 12
Overview of f Simulation Framework Simulation of 2 orthogonal NF GM components 13
Predictive Models Input: EQ source and site characteristics ( 𝐺 , 𝑁 𝑥 , 𝑎 𝑈𝑃𝑆 , 𝑆 𝑆𝑉𝑄 , 𝑊 𝑡30 , 𝑡 𝑝𝑠 𝑒 , 𝜄 𝑝𝑠 𝜚 ) Probability of occurrence of a pulse (Shahi and Baker, 2011) Empirical predictive relations: for both pulse-like and non-pulse-like model parameters Orientation of the simulated components with respect to fault strike 14
Input Parameters (o In (or Predictor Vari riables) EQ design scenario: ( 𝐺 , 𝑁 𝑥 , 𝑎 𝑈𝑃𝑆 , 𝑆 𝑆𝑉𝑄 , 𝑊 𝑡30 , 𝑡 𝑝𝑠 𝑒 , 𝜄 𝑝𝑠 𝜚 ) 𝑡 𝑝𝑠 𝑒 , 𝜄 𝑝𝑠 𝜚 ) description of the EQ source and site characteristics including directivity parameters Reverse Strike-Slip Reverse-Oblique For any style of faulting, we use: 𝑡 𝑝𝑠 𝑒 = max 𝑡, 𝑒 If 𝑡 𝑝𝑠 𝑒 = 𝑡 , 𝜄 𝑝𝑠 𝜚 = 𝜄 If 𝑡 𝑝𝑠 𝑒 = 𝑒 , 𝜄 𝑝𝑠 𝜚 = 𝜚 15
Puls lse Probability Model Input: ( 𝐺 , 𝑆 𝑆𝑉𝑄 , 𝑡 𝑝𝑠 𝑒 , 𝜄 𝑝𝑠 𝜚 ) Output: Probability of occurrence of a directivity pulse in at least one direction at a site (Shahi and Baker, 2011) Pr pulselike|𝐺, 𝑆 𝑆𝑉𝑄 , 𝑡 𝑝𝑠 𝑒, 𝜄 𝑝𝑠 𝜚 1 = (0.642+0.167𝑆 𝑆𝑉𝑄 −0.075𝑡 𝑝𝑠 𝑒) , 𝑗𝑔 𝐺 = 0 1+exp 1 = (0.128+0.055𝑆 𝑆𝑉𝑄 −0.061𝑡 𝑝𝑠 𝑒+0.036𝜄 𝑝𝑠 𝜚) , 𝑗𝑔 𝐺 = 1 1+exp 16
Empirical Predictive Relations for r Model Parameters Input: ( 𝐺 , 𝑁 𝑥 , 𝑎 𝑈𝑃𝑆 , 𝑆 𝑆𝑉𝑄 , 𝑊 𝑡30 , 𝑡 𝑝𝑠 𝑒 ) Using: results of regression and correlation analyses Output: simulated parameters of pulse-like and non-pulse-like GM models model parameters 𝑨 𝑄,𝑗 , 𝑨 𝑂𝑄,𝑗 in the normal space ( correlated, and with natural variability ) transformed to original parameter space: 𝛽 𝑄,𝑗 , 𝛽 𝑂𝑄,𝑗 Functional forms chosen to be consistent with seismological theory E 𝑨 = 𝛾 0 + 𝛾 1 𝑁 𝑥 + 𝛾 2 𝑁 𝑥 − 6.5 𝕁 𝑁 𝑥 > 6.5 + 𝛾 3 𝐺𝑔 𝑔𝑚𝑢,𝑎 𝑡30 ) 2 2 + ℎ 2 + ℎ 2 + 𝛾 4 ln 𝑆 𝑆𝑉𝑄 + 𝛾 5 𝑁 𝑥 . ln 𝑆 𝑆𝑉𝑄 + 𝛾 6 ln(𝑊 + 𝛾 7 𝑡 𝑝𝑠 𝑒 17
Sim imulation Procedure , , , , , , , , 30 , , 30 , , , , , Pulse Probability Model Yes Yes No Pulselike? e? Pulselike GM Model Non-Pulselike GM Model 30 30 30 30 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 18
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