Shaking Hazard Compatible Methodology for Probabilistic Assessment of Fault Displacement Hazard

Transcription

1 Surface Fault Displacement Hazard Workshop PEER, Berkeley, May 20-21, 2009 Shaking Hazard Compatible Methodology for Probabilistic Assessment of Fault Displacement Hazard Maria Todorovska Civil & Environmental Engineering Department University of Southern California Los Angeles, CA

2 Credits USC Strong Motion Research Group (Earthquake Engineering and Engineering Seismology) Misha Trifunac Vincent Lee Work supported by METRANS - Metropolitan Transportation Research Center, a U.S. Department of Transportation designated university transportation center (Grant 03-27; PI-s: Trifunac and Todorovska). Numerous discussions on the application aspects of this project with Anoosh Shamsabadi Caltrans.

3 Publications Todorovska MI, Trifunac MD, and Lee VW (2007). Shaking hazard compatible methodology for probabilistic assessment of permanent ground displacement across earthquake faults, Soil Dynam. and Earthqu. Eng., 27(6), Todorovska MI, Trifunac MD (2006). A note on probabilistic assessment of fault displacement hazard, Proc. 8 th National Conference on Earthquake Engineering (commemorating the 100th anniversary of the 1906 earthquake), April 18-22, 2006, San Francisco California, Paper Number: 8NCEE , pp. 10. Proc. Earthquake Engineering in the 21st Century (EE- 21C), Skopje-Ohrid, Macedonia, August 27-September 1, 2005, pp. 11.

4 Relation to previous published work on PFDH Previous published work on PFDH: Youngs et al., Earthquake Spectra, 2003, 19(1): Stepp et al., Earthquake Spectra 2001; 17(1): Methodology and results aimed at application to the potential Yucca Mountain nuclear waste repository site in Nevada. Our work scaling models specific for California, and compatible with our scaling models we use for the other modules of our EQRISK program for assessment of: ground shaking, liquefaction initiation, and peak ground strain hazard (Lee and Trifunac, 1987; Trifunac, 1991; Todorovska and Trifunac, 1996, 1999).

5 Outline General methodology. Considers only earthquakes on the main fault, which are the main cause for the dislocation across the fault (principal faulting in Youngs et al.). Simpler than PSHA for ground shaking involves only one fault. Results for two hypothetical faults, Class A and B Class A: the most active faults, with average slip rate > 5 mm/year (like the San Andreas Flt). Class B: all other faults (like the Palos Verdes Flt crossed by the Vincent Thomas Bridge).

6 Motivation Vincent Thomas Bridge, crosses the Palos Verdes Fault in Los Angeles Area San Diego Coronado Bay Bridge, Rose Canyon Fault Zone Bart Tunnel, and Clermont Water Tunnel, both crossing the Hayward Fault in northern California

7 Model

8 Methodology D - random variable representing, for an earthquake that has ruptured the ground surface, the absolute value of the displacement across the rupture at the ground surface D site - displacement at the site, which may or may not have been affected by the earthquake p dt P D dt (, ) = { > } site

9 Methodology Assumption: Earthquakes occurrence is a Poissonian or a generalized Poissonian process. Then { D } is Selective Poissonian process site > d t Expected number of exceedances n ( t) = expected number of earthquakes i mdt ( ) q( dn ) ( t) of magnitude M during exposure t, i L, = i= 1 we get it from the adopted Gutenberg-Richter law for the fault q ( d) = prorating factor, a conditional probability. i i i

10 Methodology Conditional probability { > = } q ( d) P D d event M M has occurred i site { event occurred } = P D> d M = M i i P rupture breaks rupture extends P ground surface horizontally to the site

11 Methodology Finally: p dt, = Probab. of exceedance during exposure ( ) = 1 mt () e t mdt (, ) t = average occurrence rate of the exceedance t Td ( ) = = aver. return period of the exceedance mdt (, )

12 Probability that rupture breaks the surface for a generic model P rupture breaks W ( ) R M = min 1, ground surface W r W W, W ( ) R W W R = = fault width rupture width

13 Probability that rupture extends to the site for a generic model rupture 1, LR ( M) L extends LR ( M) L P = min 1,, LR M L, x LR M horizontally L LR ( M) < 2 to the site L x min 1, 2 L, LR M < L, x > LR M L LR ( M) 2 L (,, ) r L L x R ( ) ( ) ( ) ( ) L L R = fault length = rupture length x = distance of the site from the center of the fault

14 Rupture length and width, LR and WR

15 Rupture length and width We use our fit through a subset of the data in Wells and Coppersmith, 1994, for California earthquakes: log L ( M) = M R log W ( M) = M R

16 If we want to consider the uncertainty in in rupture length and width estimates rupture breaks P = r (, ) ( ) W W y fw y dy R ground surface 0 rupture extends P = r (, ) ( ) L W y fl y dy R horizontally to the site 0 f y L L R ( ) = Prob. density function for f ( y)= Prob. density function for W W R R R

17 Displacement across fault, D

18 Displacement across fault at surface Lee et al. (1995) with Mag + site + soil + % rock path model D = 2 d ( L L L) max log10 dmax = M log 10( Δ/ LR ) M s v M +. S +. S +. S + [ r (1 r)] R/ R + HR + S Δ= S ln R + HR + S0 12 / H = focal depth S = source dimension R =representative source to station distance S 0 = source coherence radius

19 Displacement across fault at surface D is lognormal: 10 ( δ ) μ = M log Δ M, R = 0, H = 0.5 W sin, S, S / L 10 R R 0 R M * v M log σ = event M = Ml occurred P D> d and ruptured the surface logd 1 1 = exp 2πσ 2 ( log x μ ) 2 σ dx

20 Results for two hypothetical faults (vertical) Fault I (Class B) 2/3 and 1/3 partitioning of seismic moment between characteristic and Gutenberg-Richter events L = 100 km; W = 13 km M = b= dyn cm/yr t = Exposure = 50 yrs Fault II (Class A) three variants of distribution of seismic moment L = 100 km; W = 18 km M GR = 24 0 ( ) dyn cm/yr M Char = 24 0 ( ) dyn cm/yr

21 Fault I (Class B): earthquake rates 10 2 Expected number of earthquakes during exposure Exposure = 50 years n i Hypothetical Fault I (Class B) M i

22 Fault I (Class B): P(site will be affected) Probabilities that a rupture will affect the site L =100 km W =13 km x-km r W r L M

23 Fault I (Class B): Results All events G-R contribution Characteristic contribution Hypothetical Fault I (Class B) 10 0 m (d,t) 0.2 p (d,t) t = 50 years 10-5 x = d - m d - m

24 Fault I (Class B): Results (cont.) x=0 x=25 km x=40 km Hypothetical Fault I (Class B) 10 0 m (d,t) 0.2 p (d,t) All events d - m d - m

25 Fault II (Class A): earthquake rates 10 3 Expected number of earthquakes during exposure Exposure = 50 years n i Seism. model 1 Seism. model 2 Seism. model M i

26 Fault II (Class A): P(site will be affected) Probabilities that a rupture will affect the site x=0 L =100 km W =18 km r W r L r L * r W M

27 Fault II (Class A): Results Seism. model IIa Seism. model IIb Seism. model IIc Hypothetical Fault II (Class A) 10 1 m (d,t) 1 p (d,t) x = d - m d - m

28 Conclusions Fault displacement hazard is generally small as only one fault contributes to the hazard, and not every earthquake affects the site. The results are quite sensitive to how the seismic moment is distributed over earthquake magnitudes. The hazard is the largest near the center of the fault.

29 Conclusions For a specific application, fault specific information should be used, to the extent possible, e.g. to define probabilities that rupture will break the ground surface and will affect the site, and for distribution of rupture along the fault.

30 References (principal) Todorovska M.I., M.D. Trifunac M.D., and V.W. Lee, Shaking hazard compatible methodology for probabilistic assessment of permanent ground displacement across earthquake faults, Soil Dynam. and Earthqu. Eng., accepted for publication. Lee V.W., M.D. Trifunac, M.I. Todorovska, and E.I. Novikova, Empirical equations describing attenuation of the peaks of strong ground motion, in terms of magnitude, distance, path effects and site conditions, Dept. Civil Eng. Report No , Univ. Southern California, Los Angeles, California. Wells D.L., and K.J. Coppersmith, New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. Seism. Soc. Am. 84(4),