EARTHQUAKE SCIENCE-ENGINEERING INTERFACE: STRUCTURAL ENGINEERING RESEARCH PERSPECTIVE Allin Cornell Stanford University SCEC WORKSHOP Oakland, CA October, 2003. Objective. λ C = mean annual rate of State C , e.g., collapse
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EARTHQUAKE SCIENCE-ENGINEERING INTERFACE:
STRUCTURAL ENGINEERING RESEARCH PERSPECTIVE
for all ti = 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
Current Best Seismology Practice*:
·Disaggregate PSHA at Sa1 at po, say, 2% in 50 years, by M and R: fM,R|Sa. Repeat for several levels, Sa11, Sa12, …
· 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 Sa(T1)).
*DOE, NRC, PEER, … e.g., see R.K. McGuire: “... Closing the Loop”( BSSA, 1996+/-); Kramer (Text book; 1996 +/-); Stewart et al. (PEER Report, 2002)
Probabilistic Seismic Hazard Curves
Seismic Design Assessment of RC Structures. (Holiday Inn Hotel in Van Nuys)
Multiple Stripe Analysis
≈ ∑PC(IMk) ∆ λ(IMk)
What are good choices for IM?
How does one obtain λ(IM) ?
How does one do this transparently, easily and practically?
BETTER SCALAR IM?
IM = Sa1
IM = g(Sd-inelastic; Sa2) (Luco, 2002)
Van Nuys Transverse Frame:
Pinchiera Degrading Strength Model; T = 0.8 sec.
60 PEER records as recorded 5.3<M<7.3.
Residual-residual plot: drift versus magnitude (given Sa) for Van Nuys. (Ductility range: 0.3 to 6) (60 PEER records, as recorded.)
Residual-residual plot: drift versus magnitude (given Sa) of a very short period (0.1 sec) SDOF bilinear system. (Ductility range 1to 20.) (47 PEER records, as recorded.)
Residual-residual plot: drift versus magnitude (given Sa) for 4-second, fracturing-connection model of SAC LA20. Records scaled by 3. Ductility range: mostly 0.5 to 5
λ(Sa1, M) = λ(Sa1) f(M| Sa1) (from “Deagg”)
λ(Sa1, Sa2) Requires Vector PSHA (SCEC project)
Vector-Based Response Prediction
· Earth Science problems:How likely is it? λ(X)
·Some Special Problems: Nonlinear Soils, Strong Directivity, Aftershocks, Spatial Fields of X.
Residual-residual plot: drift versus magnitude (given Sa) for 4-second, fracturing-connection model of SACLA20. Ductility range: 0.2 to 1.5. Same records.
Non-Linear MDOF Conclusion:
(Given Sa(T1) 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.