# Steven L. Kramer University of .Loss model Loss curve – λ Cost vs Cost Seismic hazard curve –

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06-Jun-2018Category

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Steven L. Kramer University of Washington

Loss model

Loss curve Cost vs

Cost

Seismic hazard

curve Sa vs Sa

Fragility curve interstory

drift given Sa

Fragility curve crack width

given interstory drift

Fragility curve repair cost given

crack width

PSHA Response model Damage model

Covers entire range of hazard (ground motion) levels

Accounts for uncertainty in parameters, relationships

$2.7M $5.8M

Common IMs

Peak ground acceleration, PGA Peak ground velocity, PGV Spectral acceleration, Sa(T)

Classes of IMs

Peak parameters: PGA, PGV, PGD Compound parameters: PGV/PGA Integral parameters: Ia, CAV Modified parameters: Sa, SI

Desirable Characteristics

Predictability given some scenario, how accurately can we predict IM?

Attenuation relationships

R

ln IM ln IM

Desirable Characteristics

Predictability given some scenario, how accurately can we predict IM?

Attenuation relationships

Uncertainty decreases with magnitude

Predictability increases with magnitude

lnSa ~ 0.5 0.7

68% within factor of 1.7 2.0

Desirable Characteristics

Predictability given some scenario, how accurately can we predict IM?

Attenuation relationships Predictability decreases with increasing period

Desirable Characteristics

Efficiency given some IM, how accurately can we predict response (EDP)?

IM1 Uncertainty in EDP for a given

IM1 is high

IM1 is an inefficient predictor of EDP

EDP

High EDP|IM1 Low EDP|IM2

EDP

IM2 Uncertainty in EDP for a given

IM2 is low

IM2 is an efficient predictor of EDP

Closed-form solution

Assume hazard curve is of power law form

IM(im) = ko(im)-k

IM(im)

im

edp

im

and response is related to intensity as

edp = a(im)b

with lognormal conditional uncertainty (ln edp is normally distributed with standard deviation ln edp|im)

Closed-form solution

Then median RM hazard curve can be expressed in closed form as

IM(im)

im

edp

im

EDP(edp)

edp

Closed-form solution

Then median RM hazard curve can be expressed in closed form as

EDP(edp)

edp

Based on median IM and EDP-IM

relationship

EDP amplifier based on uncertainty in EDP|

IM relationship

A portion of EDP is due to uncertainty reducing uncertainty can significantly reduce response

Effect of predictability on IM

Intensity Measure, IM

Effect of efficiency on EDP Effect of predictability on EDP

Hypothetical site

Hypothetical site

Increasing uncertainty in IM prediction

Increasing uncertainty in IM prediction Increasing uncertainty in

EDP prediction

Effect of predictability on IM

Effect of predictability on EDP Effect of efficiency on EDP

Hypothetical site

Base case Poor predictability, poor efficiency

Good predictability, good efficiency Poor predictability, good efficiency Good predictability, poor efficiency

EDP Hazard Curves 50-yr exceedance probabilities

For return periods of interest, EDPs are strongly driven by uncertainty in IM and EDP | IM

Reducing these uncertainties will lead to reduction in design requirements while maintaining consistent level of conservatism

PGA

Ia

Desirable Characteristics

Sufficiency how completely does IM predict response (EDP)?

An IM is sufficient if the addition of additional ground motion data does not improve its ability to predict EDP (ln EDP|IM = ln EDP|IM, X for all X)

PGA is an insufficient predictor of excess pore pressure overpredicts for short-duration events and underpredicts for long-duration events

Arias intensity is a more sufficient predictor of excess pore pressure. Ia is affected by duration (or number of cycles).

Which IMs are best?

Problem-dependent

Different for slope problems and liquefaction problems Different for different slope problems

Shallow failures Deep failures

Which IMs are best?

Slope Stability

Newmark analysis (non-strain-softening materials)

Makdisi-Seed approach

High uncertainty in displacement given PGA. Can we do better?

Which IMs are best?

Slope Stability

Newmark analysis (non-strain-softening materials)

Makdisi-Seed approach

Travasarou et al. (2003)

Arias intensity is a more efficient predictor than PGA or PGV2 for Newmark slope displacements for shallow slides

Wilson and Keefer, 1985; Harp and Wilson, 1995; Jibson and Jibson, 2003

Sa(1.5To) is not sufficient.. Adding Mw improves predictive capability

Which IMs are best?

Slope Stability

Newmark analysis (non-strain-softening materials)

Makdisi-Seed approach

Travasarou et al. (2003)

Bray and Travasarou (2007) Sa(1.5To) is a more efficient predictor than Ia or PGV for Newmark slope displacements for deep slides

Which IMs are best?

Slope Stability

Newmark analysis (non-strain-softening materials)

Makdisi-Seed approach

Travasarou et al. (2003)

Bray and Travasarou (2007)

Jibson (2007)

Used Arias intensity and PGA (vector)

Saygili and Rathje (2008)

Used PGA and PGV (vector)

Used PGA, PGV, and Ia (3-element vector)

Watson-Lamprey and Abrahamson (2006)

Used PGA, Sa(1.0), ARMS, Durky (4-element vector)

Saygili and Rathje (2008)

PGA

PGA, PGV

PGA, PGV, Ia

Substantial improvement in efficiency using

vector IM

Two approaches to improving efficiency:

Find more efficient scalar IMs

Find efficient vector IMs

More complicated than for scalar IMs

Need to integrate over all IMs

Conditional probability of exceeding edp given im1 and im2

Joint probability of im1 and im2

Need to know correlation between im1 and im2

Which IMs are best?

Liquefaction

Kramer and Mitchell, 2006

CAV5 is a more efficient predictor of excess pore pressure generation than PGA or Arias intensity

CAV5 is a more sufficient predictor of excess pore pressure generation than PGA or Arias intensity

Which IMs are best?

Pile Response

Bradley et al., 2008

VSI is an efficient and sufficient predictor of pile curvature during earthquake shaking

Which IMs are best? What characteristics do they share?

Common elements

Nearly all are correlated to lower frequencies than PGA Peak velocity Ia, CAV5 integrals of accelerations Sa(1.5To) extended site period VSI spectral velocities over 0.1 sec < T < 2.5 sec

Duration matters Integral parameters appear to work well Vector IMs including duration or integral parameters work well

New IMs are promising from accuracy standpoint More difficult to compute Unfamiliar to most Challenges in implementation for practical use

Thank you