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Simulating the Earthquake
 Before the bridge's response can be simulated, the rupturing of an earthquake fault must be simulated to generate ground motion information. A rupture of the Hayward fault was simulated with the powerful E3D seismic code developed by Livermore computer scientist and geophysicist Shawn Larsen. The code incorporates three-dimensional (3D) information about propagation of seismic waves: how they are radiated from the earthquake's source to the surface, at what velocities they propagate, and how they interact with the geology and topography in their path. Because the simulation involves distances to several hundred kilometers and depths to 50 kilometers, accurately predicting the strength and geographic distribution of seismic waves demands robust computing.
E3D integrates seismic information through a complex 3D geologic model of the San Francisco Bay Area, which was developed at UC Berkeley by Professor Doug Dreger and graduate student Christiane Stidham with funding from the U.S. Geological Survey. The model contains representations of large sedimentary basins (such as the San Pablo Basin, Santa Clara Valley, and Livermore Valley), deep crustal and mantle structures, near-surface alluvium and very low-velocity bay mud, high-velocity zones (such as Mt. Diablo), and seismic velocity contrasts across major faults in the region.
E3D has many advanced computational enhancements that allow it to run approximately a hundred times faster than other computational codes. In addition, it has been implemented on a variety of high-performance computers, including massively parallel processors.
E3D's simulations of the Hayward fault represent the largest seismic simulation done anywhere in the world, with 45 million nodes of calculations. These three-dimensional calculations model the response of an entire seismogenic zone at the resolution needed to assess ground motion effects and the resulting earthquake hazards (see figure above).
The Bay Bridge in an Earthquake
The ground motion predictions from E3D are fed into SUSPNDRS, the code for simulating long-span bridge dynamics. A bridge's numerous interacting parts and connections can act and react differently to each other, resulting in structural changes and effects that are out of proportion to their causes.
SUSPNDRS, a finite-element code developed by Livermore's David McCallen and UC Berkeley's Abolhassan Astaneh-Asl, incorporates algorithms that accommodate the nonlinearities in bridge geometry and material properties. The code also uses an efficient bridge model that represents the bridge structure through five components (towers, deck system, cable system, deck impacts, and piers) with reduced degrees of freedom to save computational time without sacrificing essential bridge dynamics. SUSPNDRS efficiently performs calculations in three dimensions in a matter of three to four hours instead of the days or weeks required for such calculations in the past.
One unique feature of SUSPNDRS is the way its calculations are sequenced. By having the code emulate the construction sequence of the bridge components, McCallen and Astaneh-Asl could make the model calculations match actual forces and loads in key elements of the structure. They referred to construction drawings and historical construction documents to make their code calculations approximate the order of construction: towers erected, cables spun into place, stiffening trusses for the deck lifted segmentally into place, deck steel added, and finally the deck joints rigidly connected. The specific construction sequence has a significant effect on the final bridge deck member forces, so the computational model must reflect the same physical forces.
The figure also shows the bridge model where responses were simulated. The simulation results are now being validated. One validation method compares SUSPNDRS results with the first ambient measurements of bridge vibrations, collected in the 1930s with a vibrometer and documented in the Bulletin of the Seismological Society of America.
As bridge simulations progress, the work will focus on three seismic safety issues specific to long-span bridges: (1) the effect of a series of seismic waves on the bridge structure if, instead of propagating singly, they combine into one large-amplitude wave; (2) the effects caused by waves arriving at different times at different points of a structure; and (3) permanent ground deformations occurring near the ruptured fault that would affect the nearby bridge structure. Because few measurements exist of this important near-field phenomenon, large-scale simulations are providing new understanding for seismologists and engineers.
The long-term results of this campus-laboratory collaboration will enhance seismic safety in California. In the interim, the Bay Bridge results may benefit retrofit efforts for one of the Bay Area's most important long-span bridges.
--Gloria Wilt |
