Will Performance-Based Engineering Break the Power Law? Tom Heaton John Hall Anna Olsen Masumi Yamada Georgia Cua

½ of the deaths occurred in the 7 deadliest earthquakes

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

Earth Sciences Engineering Social Sciences Seismic Hazard Performance Simulation Impact Assessment Seismic Event Transmission of Seismic Waves Site Response Soil-Foundation-Structure Interaction System Response Performance Modeling Consequences (Losses/Decisions) Performance-Based Earthquake Engineering “Borrowed” from Greg Deierlein at Stanford

Engineering Short-Period World Short and stiff buildings Design is based on rules developed from experience in earthquakes F=ma High yield strength compared to the weight of the building

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

Magnitude-dependent saturation of rock and soil sites (S-waves) horizontal S-wave accelerationhorizontal S-wave velocity horizontal S-wave displacement From Georgia Cua Short-period motions saturate with magnitude at close distance Long-period motions at far distances are proportional to M 0, or M 3/2 Long-period motions at near distances are proportional to M 0 1/3, or M 1/2 Short period Long period

All strong motions recorded at less than 10 km from rupture from M>6 From Masumi Yamada

PDF of near-source Displacement If D is fault slip, then If N’ is the number of earthquakes between M and M+ΔM, then Log N’ = a – bM If, then The total area of fault rupture between M and M+ΔM 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!

All strong motions recorded at less than 10 km from rupture from M>6 From Masumi Yamada

Two Statistical Worlds Normal … 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

Two Statistical Worlds Power Law … Pareto P=x -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?

John Hall’s design of a 20-story steel MRF building

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).

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

Pt Reyes Station 1906

1906 g1906 ground motion simulation from Brad Aagaard (USGS)

Peak Ground Displacement Bodega BaySan Juan BautistaGolden Gate meters Ground motions From Brad Aagaard

Peak Ground Velocities Bodega BaySan Juan Bautista Golden Gate m/s

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

Faults Modeled 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) Day and others, 2005

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?

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

All strong motions recorded at less than 10 km from rupture from M>6 From Masumi Yamada

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

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