Steven L. Kramer University of .Loss model Loss curve – » Cost vs Cost...

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Transcript of Steven L. Kramer University of .Loss model Loss curve – » Cost vs Cost...

  • 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