PEER EARTHQUAKE SCIENCE-ENGINEERING INTERFACE: STRUCTURAL ENGINEERING RESEARCH PERSPECTIVE Allin Cornell Stanford University SCEC WORKSHOP Oakland, CA October, 2003

PEER Objective λ C = mean annual rate of State C, e.g., collapse Two Steps: earth science and structural engineering: λ C = ∫P C (X) dλ(X) Where X = Vector Describing Interface

PEER “Best” Case X = {A 1 (t 1 ), A 2 (t 2 ), …A i (t i )..} for all t i = i∆t, i = 1, 2, …n i.e., an accelerogram · dλ(x) = mean annual rate of observing a “specific” accelerogram, e.g., a(ti) < A(ti) <a(ti) + da for all ∙ Then engineer finds PC(x) for all x ∙ Integrate

PEER Current Best “Practice” (or Research for Practice) λ C = mean annual rate of State C, e.g., collapse Two Steps: earth science and structural engineering: λ C = ∫P C (IM) dλ(IM) IM = Scalar “Intensity Measure”, e.g., PGA or Sa1 λ(IM) from PSHA P C (IM) found from “random sample” of accelerograms = fraction of cases leading to C

PEER Current Best Seismology Practice*: ·Disaggregate PSHA at Sa1 at p o, say, 2% in 50 years, by M and R: f M,R|Sa. Repeat for several levels, Sa1 1, Sa1 2, … · For Each Level Select Sample of Records: from a “bin” near mean (or mode) M and R. Same faulting style, hanging/foot wall, soil type, … · Scale the records to the UHS (in some way, e.g., to the S a (T 1 )). *DOE, NRC, PEER, … e.g., see R.K. McGuire: “... Closing the Loop”( BSSA, 1996+/-); Kramer (Text book; /-); Stewart et al. (PEER Report, 2002)

PEER Probabilistic Seismic Hazard Curves

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PEER Beam Column Model with StiffnessBeam Column Model with Stiffness and Strength Degradation in Shear and Flexure using DRAIN2D-UW by J. Pincheira et al. Seismic Design Assessment of RC Structures. (Holiday Inn Hotel in Van Nuys)

PEER Multiple Stripe Analysis Multiple Stripe Analysis The Statistical Parameters of the “Stripes” are Used to Estimate the Median and Dispersion as a Function of the Spectral Acceleration, Sa1.The Statistical Parameters of the “Stripes” are Used to Estimate the Median and Dispersion as a Function of the Spectral Acceleration, Sa1. C

PEER Best “Research-for-Practice” (Cont’d) : Analysis: λ C = ∫P C (IM) dλ(IM) ≈ ∑PC(IM k ) ∆ λ(IM k ) Purely Structural Engineering Research Questions: –Accuracy of Numerical Models –Computational Efficiency

PEER Best “Research-for-Practice”: Analysis: λ C = ∫P C (IM) dλ(IM) ≈ ∑PC(IM k ) ∆ λ(IM k ) · Interface Questions: What are good choices for IM? Efficient? Sufficient? How does one obtain λ(IM) ? How does one do this transparently, easily and practically?

PEER  when IM 1I&2E is employed in lieu of IM 1E, (0.17/0.44) 2 ≈ 1/7 the number of earthquake records and NDA's are needed to estimate a with the same degree of precision IM = Sa1 IM = g(Sd-inelastic; Sa2) (Luco, 2002) BETTER SCALAR IM? More Efficient?

PEER Van Nuys Transverse Frame: Pinchiera Degrading Strength Model; T = 0.8 sec. 60 PEER records as recorded 5.3<M<7.3.

PEER Residual-residual plot: drift versus magnitude (given S a ) for Van Nuys. (Ductility range: 0.3 to 6 ) (60 PEER records, as recorded.)

PEER Residual-residual plot: drift versus magnitude (given S a ) of a very short period (0.1 sec) SDOF bilinear system. (Ductility range 1 to 20.) (47 PEER records, as recorded.)

PEER Residual-residual plot: drift versus magnitude (given S a ) for 4-second, fracturing-connection model of SAC LA20. Records scaled by 3. Ductility range: mostly 0.5 to 5

PEER What Can Be Done That is Still Better? Scalar to (Compact) Vector IM Interface Issues: What vector? How to find λ (IM)? Examples: {Sa1, M}, {Sa1, Sa2}, … · PSHA: λ(Sa1, M) = λ(Sa1) f(M| Sa1) (from “Deagg”) λ(Sa1, Sa2) Requires Vector PSHA (SCEC project)

PEER Vector-Based Response Prediction Vector-Valued PSHA

PEER Future Interface Needs Engineers: Need to identify “good” scalar IMs and IM vectors. In-house issues: what’s “wrong” with current candidates? When? Why? How to fix? How to make fast and easy, i.e., professionally useful.

PEER Future Interface Needs (con’t ) Help from Earth scientists: Guidance (e.g., what changes frequency content? Non- ”random” phasing? ) · Earth Science problems: How likely is it? λ(X) λ(X) = ∫P(X \ Y) dλ(Y) X = ground motion variables (ground motion prediction:empirical, synthetic) Y = source variables (e.g., RELM)

PEER Future Needs (Cont’d) Especially λ(X) for “bad” values of X (Or IM). · Some Special Problems: Nonlinear Soils, Strong Directivity, Aftershocks, Spatial Fields of X.

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PEER Residual-residual plot: drift versus magnitude (given S a ) for 4-second, fracturing-connection model of SAC LA20. Ductility range: 0.2 to 1.5. Same records.

PEER Non-Linear MDOF Conclusion: (Given S a (T 1 ) level) the median (displacement) EDP is apparently independent of event parameters such as M, R, …*. Implications: (1) the record set used need not be selected carefully selected to match these parameters to those relevant to the site and structure. Comments: Same conclusion found for transverse components. More periods and backbones and EDPs deserve testing to test the limits of applicability of this illustration. *Provisos: Magnitudes not too low relative to general range of usual interest; no directivity or shallow, soft soil issues.