Will Performance-Based Engineering Break the Power Law?

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Will Performance-Based Engineering Break the
Power Law?

• Tom Heaton
• John Hall
• Anna Olsen
• Masumi Yamada
• Georgia Cua

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½ of the deaths occurred in the 7 deadliest
earthquakes
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Designing for Long-Period Ground Motions

• Two worlds Short-period world and Long-period
  world
• Physics of short-period world is not understood,
  but the statistics are normal (Gaussian)
• Physics of the long-period world are better
  known, but the statistics are power law
• Cannot achieve performance based engineering
  for power law phenomena

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Performance-Based Earthquake Engineering
Seismic Hazard
Performance Simulation
Impact Assessment
Borrowed from Greg Deierlein at Stanford
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Engineering Short-Period World

• Short and stiff buildings
• Design is based on rules developed from
  experience in earthquakes
• Fma
• High yield strength compared to the weight of the
  building

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Engineering Long-Period World

• Flexible wave equation
• Design to limit deformation
• Probabilistic description of ground motion
• Statistics are power law, but few understand what
  that means

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Magnitude-dependent saturation of rock and soil
sites (S-waves)
Short period
horizontal S-wave acceleration
horizontal S-wave velocity
Long period

• Short-period motions saturate with magnitude at
  close distance
• Long-period motions at far distances are
  proportional to M0, or M3/2
• Long-period motions at near distances are
  proportional to M01/3, or M 1/2

From Georgia Cua
horizontal S-wave displacement
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All strong motions recorded at less than 10 km
from rupture from Mgt6
From Masumi Yamada
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PDF of near-source Displacement

• If D is fault slip, then
• If N is the number of earthquakes between M
  and M?M, then Log N a bM
• If , then
• If , then
• The total area of fault rupture between M and
  M?M is then
• If fault slip occurs at a point, it is equally
  likely that it is from any magnitude earthquake
• If slip occurs at a point, then any slip is
  equally likely!

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All strong motions recorded at less than 10 km
from rupture from Mgt6
From Masumi Yamada
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Two Statistical WorldsNormal Gaussian

• All events are independent (short-range
  interactions)
• Most action is within a std. deviation
• Low-probability events are not important
• Heart attacks, auto accidents
• Short-period ground motions
• Short-period buildings

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Two Statistical WorldsPower Law Pareto

• Px-b
• Events are connected to each other long-range
  interactions
• Most action is in the most improbable events
• Contagious disease (bird flu), war, fire
• Tsunami deaths (Sumatra)
• Long-period ground motion
• Long-period buildings?

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• John Halls design of a 20-story steel MRF
  building

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20-story steel-frame building subjected to a
2-meter near-source displacement pulse (from
Hall)

• triangles on the frame indicate the failures of
  welded column-beam connections (loss of
  stiffness).

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Large displacements can overwhelm base isolation
systems

• 2-meter displacement pulse as input for a
  simulation of the deformation of a 3-story
  base-isolated building (Hall, Heaton, Wald, and
  Halling
• The Sylmar record from the 1994 Northridge
  earthquake also causes the building to collide
  with the stops

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Pt Reyes Station 1906
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1906 ground motion simulation from Brad Aagaard
(USGS)
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Peak Ground Displacement
Bodega Bay
San Juan Bautista
Golden Gate
Ground motions From Brad Aagaard
meters
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Peak Ground Velocities
Golden Gate
Bodega Bay
San Juan Bautista
m/s
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Other factors that may increase the building
deformation

• There is no soil layer no bay mud
• The ground motions are heavily filtered at
  frequencies higher than ½ Hz
• Sub-shear rupture velocities may increase the
  strength of directivity pulses

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Faults Modeled
Day and others, 2005

• 1. Sierra Madre (7.0)
• 2. Santa Monica SW (6.3)
• 3. Hollywood (6.4)
• 4. Raymond (6.6)
• 5. Puente Hills I (6.8)
• 6. Puente Hills II (6.7)
• 7. Puente Hills (all) (7.1)
• 8. Compton (6.9)
• 9. Newport-Inglewood (6.9)
• 10. Whittier (6.7)

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Have we broken the Power Law?

• If power law catastrophes occur because we make
  systematic errors in our designs (we were
  surprised, just how many unknown faults are
  there in LA?), then I suspect that we have not
  broken the power law.
• Should we be doing something different?

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Designing for the Known

• Architect chooses the geometry of a design
• Define probability of forces that design will be
  subjected to
• Determine the size of elements that will satisfy
  statistical limits

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All strong motions recorded at less than 10 km
from rupture from Mgt6
From Masumi Yamada
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Designing for the Unknown

• Determine the functional requirements of a
  structure
• Consider several geometries of the structure
  (different architectures)
• Determine the cost of different designs
• Assess the strengths and weaknesses of different
  designs
• Choose the design that is most robust

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Conclusions

• End-to-End simulations of plausible earthquakes
  indicate that flexible buildings can be deformed
  far more than has been seen in previous
  earthquakes (blind luck)
• Fix the brittle welds
• We are a long way from being able to achieve
  performance based engineering for tall buildings