Steven L. Kramer University of Washingtonpeer.berkeley.edu/events/pdf/10-2009/Kramer.pdf · Loss...
Transcript of Steven L. Kramer University of Washingtonpeer.berkeley.edu/events/pdf/10-2009/Kramer.pdf · Loss...
Loss model
Loss curve – λCost vs
Cost
Seismic hazard
curve – λSa 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 σln IM
Desirable Characteristics
Predictability – given some scenario, how accurately can we predict IM?
Attenuation relationships
Uncertainty decreases with magnitude
Predictability increases with magnitude
σlnSa ~ 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 σEDP|IM1 Low σEDP|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
λIM(im) = ko(im)-k
λIM(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 σln edp|im)
Closed-form solution
Then median RM hazard curve can be expressed in closed form as
λIM(im)
im
edp
im
λEDP(edp)
edp
Closed-form solution
Then median RM hazard curve can be expressed in closed form as
λEDP(edp)
edp
Based on median IM and EDP-IM
relationship
EDP “amplifier” based on uncertainty in EDP|
IM relationship
A portion of λEDP 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 (σln EDP|IM = σln 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