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EARTHQUAKE SCIENCE-ENGINEERING INTERFACE:

STRUCTURAL ENGINEERING RESEARCH PERSPECTIVE

Allin Cornell

Stanford University

SCEC WORKSHOP

Oakland, CA

October, 2003

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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

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“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

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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

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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)

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Probabilistic Seismic Hazard Curves

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241241 241241 241241

157157

105105

105105

105105

106106

105105

105105

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

Seismic Design Assessment of RC Seismic Design Assessment of RC Structures.Structures.

( (Holiday Inn Hotel in Van NuysHoliday Inn Hotel in Van Nuys))

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Multiple Stripe Analysis Multiple Stripe Analysis

• The Statistical Parameters of the The Statistical Parameters of the “Stripes”“Stripes” are are

Used to Estimate the Median and Dispersion as Used to Estimate the Median and Dispersion as

a Function of the Spectral Acceleration, Sa1.a Function of the Spectral Acceleration, Sa1.

C

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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

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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?

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IM = Sa1 IM = g(Sd-inelastic; Sa2) (Luco, 2002)

BETTER SCALAR IM?

More Efficient?

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10-4

10-3

10-2

10-1

100

Van Nuys 7 Story

Maximum Story Drift Angle, max

Sa a

t T1=

0.8

se

con

ds

[g]

a = 0.0198 b = 1.05

ln(max

)|ln(Sa) = 0.2716

60 records with 5.7 < M < 7.3

Van Nuys Transverse Frame:

Pinchiera Degrading Strength Model; T = 0.8 sec.

60 PEER records as recorded 5.3<M<7.3.10-1

100

5.6

5.8

6

6.2

6.4

6.6

6.8

7

7.2

7.4

Sa at T

1=0.8 seconds [g]

Ma

gn

itud

e

Van Nuys 7 Story

a = 6.72 b = 0.127

M|ln(Sa) = 0.4188

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-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 110

-1

100

101

Residual of the regression of magnitude on ln Sa(FMF)

Re

sid

ua

l of t

he

"o

rig

ina

l" r

eg

ress

ion

on

S a (

FM

F)

Van Nuys 7 Story

a = 2.31e-015 b = 0.1443

ln residual|residual2 = 0.2648

b = 0.08303

one-sided p-value = 0.04378

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

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

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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

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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)

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Vector-Based Response Prediction

Vector-Valued PSHA

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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.

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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)

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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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Residual-residual plot: drift versus magnitude (given Sa) for 4-second, fracturing-connection model of SAC

LA20. Ductility range: 0.2 to 1.5. Same records.

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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.