Fault Rupture Displacement Estimation: Caltrans’ Approach

1. Fault Rupture Displacement Estimation: Caltrans’ Approach Martha Merriam and Tom Shantz 2012 SSA Annual Meeting

2. Design criteria and references Caltrans bases the design fault rupture displacement on the larger of…. • mean Wells & Coppersmith (1994) • 5% in 50 year displacement hazard Probabilistic assessment based on… Abrahamson, N., 2006, Appendix C, Probabilistic Fault Rupture Hazard Analysis, San Francisco PUC, General Seismic Requirements for the Design on New Facilities and Upgrade of Existing Facilities….. Petersen, M., Dawson, T., Rui, C., Cao, T., Wills, C., Schwartz, D., Frankel, A., Displacement Hazard for Strike-Slip Faults, BSSA, Vol 101, No. 2, pp. 805-825, April 2011

3. Probabilistic Calculation (for 975 year displacement hazard) Assume 95% of seismic moment is released by characteristic earthquake Estimate MCHAR using fault dimensions and Hanks-Bakun (2002) Example 100 km MCHAR =7.3 Slip rate = 10 mm/yr 15 km Too small! Increase 15 to 20%. M0= 101.5MCHAR+16.05 Mag. Prob. Density M0= (0.95) mAD 7.3 Mw

4. Probabilistic Calculation (con’t) M0 mean recurrence interval = = 282 years M0 P[z > z0| EQCHAR] * 1/282 1/975 = Assume log-normal distribution of rupture displacement ( ) ( ) Annual rate of exceedence z > z0 Annual rate of EQCHAR What’s m and s? No measurements: sT= 0.39 (log10 units) se= 0.35 m = W&C (AD) sa= 0.17 With measurements: Z0 m = measavg epistemic aleatory

5. Probabilistic Calculation (con’t) Example con’t: assume no past rupture displacement measurements are available W&C (AD) = 1.8 m e= 0.55 Alt. 2: Alt. 1: z = 1.8 * 100.55*0.39 = 2.95 m Z% = m%* 100.55*sa Z50% = 1.8* 100.55*0.17 = 2.23 m Z70% = 1.8 *100.52*0.35* 100.55*0.17 = 3.40 m Uncertainty in fault location Per Petersen et. al (2011) we characterize fault mapping as either (1) Accurate, (2) Approximate, (3) Concealed, or (4) Inferred

6. Alder Creek Bridges, Mendocino County San Andreas Fault

7. Old Alder Creek Bridge 1905

8. Old Alder Creek Bridge 1906 Bancroft Library

9. Alder Creek State Bridge, built in 1947

10. San Andreas Fault parameters(North Coast section) • MMax 8 • Type strike-slip • Slip rate 24 mm/yr • Aseismic slip factor 0.0185 • Site-specific* measurements 3 • Average displacement 5 m *Within 1 km

11. Displacement at fault

12. 1974 Point Arena/Mallo Pass AP EFZ Maps

14. Displacement at Alder Creek Bridge

15. Recommendations to Engineer • For preliminary design use 5.4 m of right lateral offset perpendicular to bridge and beneath any portion of the bridge • Further investigation may refine location and reduce design offset

16. East Warren Avenue Undercrossing Sunol Grade Hwy 680, Hayward Fault

17. Hayward fault parameters(southern section) • MMax 7.3 • Type strike-slip • Slip rate 9.2 mm/yr • Aseismic slip factor 0.4

18. Displacement at fault

20. Displacement at East Warren Avenue Undercrossing

21. Pasadena Freeway Bridges Raymond fault 1977 Los Angeles AP EFZ Map

22. Raymond fault parameters • MMax 6.7 • Type strike-slip dips north 79 • Slip rate 1.5 mm/yr

23. Displacement at fault

25. Displacement at Pasadena Freeway Prospect Ave Overcrossing

27. Displacement on Pasadena Freeway Bridges 10 m from single trace

28. State Bridges With 1.8 m (6 feet) or more estimated offset

29. Issues • When is the assumption of characteristic magnitude-frequency behavior not justified? • Need method for when MCHAR recurrence period is longer than 975 years • What fractile (on epistemic uncertainty) should we use for displacement hazard? • Use of time dependent hazard models • Consideration of aseismic creep