EARTHQUAKE SCIENCE-ENGINEERING INTERFACE: STRUCTURAL ENGINEERING RESEARCH PERSPECTIVE Allin Cornell Stanford University

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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 Allin Cornell Stanford University

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EARTHQUAKE SCIENCE-ENGINEERING INTERFACE:

STRUCTURAL ENGINEERING RESEARCH PERSPECTIVE

Allin Cornell

Stanford University

SCEC WORKSHOP

Oakland, CA

October, 2003

Objective
• λC = mean annual rate of State C, e.g., collapse
• Two Steps: earth science and structural engineering: λC = ∫PC(X) dλ(X)
• Where X = Vector Describing Interface
“Best” Case
• X = {A1(t1), A2(t2), …Ai(ti)..}

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

∙ Integrate

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

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)

105

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Seismic Design Assessment of RC Structures. (Holiday Inn Hotel in Van Nuys)

• Beam Column Model with Stiffness
• and Strength Degradation in Shear and Flexure
• using DRAIN2D-UW by J. Pincheira et al.

Multiple Stripe Analysis

C

• The Statistical Parameters of the “Stripes” are Used to Estimate the Median and Dispersion as a Function of the Spectral Acceleration, Sa1.
Best “Research-for-Practice” (Cont’d) :
• Analysis: λC = ∫PC(IM) dλ(IM) ≈ ∑PC(IMk) ∆ λ(IMk)
• Purely Structural Engineering Research Questions:
• Accuracy of Numerical Models
• Computational Efficiency
Best “Research-for-Practice”:
• Analysis: λC = ∫PC(IM) dλ(IM)

≈ ∑PC(IMk) ∆ λ(IMk)

·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?

BETTER SCALAR IM?

More Efficient?

IM = Sa1

IM = g(Sd-inelastic; Sa2) (Luco, 2002)

• when IM1I&2E is employed in lieu of IM1E, (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

Sa

MAGNITUDE

DRIFT

Sa

Van Nuys Transverse Frame:

Pinchiera Degrading Strength Model; T = 0.8 sec.

60 PEER records as recorded 5.3<M<7.3.

DRIFT

MAGNITUDE

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

DRIFT

MAGNITUDE

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.)

DRIFT

MAGNITUDE

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

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)

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.
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)
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.

DRIFT

MAGNITUDE

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.