This document summarizes a simplified approach to assessing levee seismic vulnerability. The approach uses the Newmark method to estimate potential deformation from earthquakes and assess post-earthquake flood protection ability. Key steps include evaluating seismic hazard, liquefaction potential, earthquake loading, and calculating displacement based on factors like magnitude, levee properties, and ground motion. Charts and examples of results are presented.

1. SIMPLIFIED APPROACH TO ASSESS LEVEE SEISMIC VULNERABILITY Presentation for SAME Conference October 2009, Sacramento, California Scott Shewbridge, Jerry Wu [1] , Sujan Punyamurthula, Juan Vargas [2] , Steve Mahnke, and Mike Inamine [3] [1] URS Corporation, 1333 Broadway, Suite 800, Oakland, CA 94612, [email_address] and Jerry_Wu@urscorp.com [2] URS Corporation, 2870 Gateway Oaks Drive, Suite 150, Sacramento, CA, [email_address] and [email_address] [3] Department of Water Resources, Division of Flood Management, 2825 Watt Avenue #100, Sacramento, CA 95821 [email_address] and [email_address]

3. Newmark Approach Force = Mass * Acceleration Relative Acceleration – a = a y - a f Integrate once – Relative Velocity = at Integrate twice- Relative Displacement = ½ at 2 Relative Displacement

5. Estimates of Peak Ground Acceleration (PGA)

7. Example Finite Element Model Inputs & Results Calculated Peak Horizontal Acceleration 1979 Imperial Valley Earthquake, USGS 286 Station, 135-Degree Component Scaled to 0.5g Input Motion - - - 1100 125 Elastic Base Vucetic & Dobry, PI=30 0.45 - 900 125 Pleistocene (CL) Seed-Idriss Sand (mean) 0.35 50 - 125 Holocene (Medium Dense Sand) Seed-Idriss Sand (mean) 0.35 25 - 115 Levee Fill (Silt) G/Gmax and Damping Curves Poisson’s Ratio K 2 max Vs (ft/s) Unit Weight (pcf) Material

8. Estimate of Cyclic Stress Ratio (CSR)

10. How do we evaluate K y ? Limit Equilibrium – Increase seismic coefficient until FS = 1 Infinite Slope Multi-block Wedge

11. Use Slope Stability Program UTEXAS4 is the only currently authorized computer program

13. Evaluate Liquefaction Triggering Using Seed et al (2004)* Set Duration Weighting Factor = 1 All Events

14. Estimate Liquefied Soil Strengths using Seed and Harder (1990)

15. Use Undrained Residual Strength to Assess Post-Liquefaction Triggering K y Su = 250psf

18. Estimate of Site Response and 2-Dimensional Effects (K max )

19. Asymmetry/Stiffness Asymmetry may be important and can be considered. “ Stiffer” Asymmetric “ Stockton” “ Medium” Less Symmetric “ Marysville” “ Softer” Symmetric “ Sacramento”

20. Choose Model Based on Stiffness

22. Example Newmark Calculation Results

24. Displacement = (K y /K max )? YES K y /K max has an impact on K y /K max estimates of displacement

26. Displacement = f(Magnitude/Duration)? Yes for K y /K max < 0.4 Scaled PGA – 0.05 0.2 0.5 M6.5 M7.25 M8 Magnitude Magnitude / Duration has an apparent impact on K y /K max estimates of displacement

27. Displacement = f(Scaled Input PGA)? Yes, but… Scaled PGA – 0.05 0.2 0.5 M6.5 M7.25 M8 Magnitude Concern that Scaled Input PGA apparent impact on K y /K max estimates of displacement is only a numerical result Possible resolution – Spectral Matching and Arias Intensity screening

28. Use Model for Scaled Input Motion = 0.2g for Vulnerability Assessment Scaled PGA – 0.05 0.2 0.5 M6.5 M7.25 M8 Magnitude 0.2g scaled PGA model results are believed to provide a reasonable expected relationship for the study areas

29. Summary – Levee Deformation Evaluation Charts PGA = f(Return Period) CSR = f(PGA) K max = f(PGA, block depth, model stiffness) Displacement = f(K y /K max , Magnitude)

31. Vulnerability Assessment Compromised None Yes Unlimited (flow slide condition) Likely Compromised None Likely if existing 3’ to 10’ Possibly Compromised >1’ Possibly 1’ to 3’ Probably Uncompromised >1’ No <1’ POST SEISMIC FLOOD PROTECTION ABILITY REMAINING FREEBOARD FOR POST SEISMIC EVALUATION (2-YEAR FLOOD WATER SURFACE ELEVATION?) SIGNIFICANT DAMAGE TO INTERNAL STRUCTURES (E.G. CUTOFF WALLS AMOUNT OF DEFORMATION

32. Final Evaluation Charts PGA CSR K max Displacement

33. Questions / Discussion