Trembling dice

Virtual earthquakes compute probable damage to a highway network

Earthquakes can strike anywhere in the U.S., and there is always a chance that a quake will topple a bridge pier, shake open a gaping rupture in a road or make the earth flow like liquid out from under a highway. A transportation agency needs to know what the risk really is and how it might be cost-effectively reduced. REDARS (for Risks from Earthquake DAmage to Roadway Systems) is software being designed to offer seismic risk analysis.
REDARS can simulate damage to highway systems, including bridges and roadways, and how the damage might affect traffic flow. The simulations yield information about potential bridge damage, geographic areas where infrastructure is more likely to sustain serious damage and potential traffic congestion caused by the damage. Transportation managers can use information from the simulation before an earthquake to devise measures to strengthen bridges, control traffic and prevent economic losses. After an earthquake, transportation managers can use the simulation to help identify traffic control and bridge repair measures that will mitigate losses and get traffic flowing normally as soon as possible.
REDARS is being produced under a program called Seismic Vulnerability of the Highway System. The program is sponsored by the Federal Highway Administration and administered by the Multidisciplinary Center for Earthquake Engineering Research at the University at Buffalo, State University of New York, Buffalo, N.Y. (http://mceer.buffalo.edu).
“I think REDARS will be useful to transportation agencies nationwide who face earthquake risks to their highway system and can possibly use this software to help plan seismic improvements to their system,” Stuart D. Werner, a principal at Seismic Systems & Engineering Consultants, Oakland, Calif., and team leader of the REDARS project, told Roads & Bridges.
An early version of REDARS was used to demonstrate the requirements and capabilities of the software by estimating seismic risk in Shelby County, Tenn.
Why Shelby County? “We wanted to choose a roadway system that was compact, moderate in size, had some interesting earthquake hazard risk implications to it and also was located outside of California in order to demonstrate REDARS’ applicability in other parts of the country,” Werner said.
Shelby County has several major infrastructural features, such as the city of Memphis. Two bridges over the Mississippi River along I-40 and I-55 are critical to interstate travel.
Earthquakes that might affect Shelby County occur infrequently. But when they do occur, such as the 1811-12 New Madrid earthquakes, they tend to have severe consequences. Much of the existing highway infrastructure in the Midwest (and the East where damaging earthquakes also have occurred) have been built with limited seismic protection.
And earthquakes in the Midwest and East are felt over a much larger area, according to Werner. “The seismic waves tend to attenuate, or reduce, much slower in the Midwestern or Eastern United States than they do in California.”

Probable quake

REDARS takes various characteristics of the roadway network as input parameters: locations and capacities of the roads; soil conditions; locations and structural characteristics of the bridges; and traffic demands.
For a given earthquake, REDARS first uses seismic models to estimate ground shaking and permanent ground displacement from liquefaction or rupture. Then REDARS estimates damage to each bridge by applying either simplified default models of bridge fragility that are built into the software or by importing a more detailed fragility model derived from a separate analysis of the specific bridge. The models also are used to estimate damage to related components, such as approach fills and tunnels.
Once the damage is estimated, REDARS uses default or user-specified repair models to estimate a repair cost and a repair time for each component and then to estimate traffic flows and travel times.
In the final step of the analysis, the program estimates the cost of repairing the highway system and the economic losses from delays in travel caused by earthquake damage.
In a probabilistic simulation like REDARS, the software generates many events and performs a statistical analysis of the results. For the Shelby County demonstration, REDARS used a “walk-through” period of 50,000 years. For each year of the walk-through, regional earthquake models developed by the U.S. Geological Survey are randomly sampled to predict whether an earthquake will occur in that year. At the end, the combined results of the earthquakes are used to develop probabilistic estimates of losses resulting from earthquake damage.
Random sampling for Shelby County resulted in 2,321 earthquakes during the walk-through with magnitudes ranging from 5.0 to 8.0 on the Richter scale.

It pays to have confidence

The goal of conducting a long walk-through period, or running multiple simulations, is to build up enough statistics to yield what the statisticians call good confidence levels and limits (CLLs). The Shelby County demonstration yielded 95% confidence that the true value of the average annual loss was within ±12.6% of the computed average annual loss. That was considered acceptable.
Since the Shelby County experiment, the REDARS group has incorporated more advanced statistical analysis methods into the software. The new methods reduce the walk-through period needed to achieve the desired CLLs.
Another upgrade since the Shelby County simulations is the inclusion of a variable-demand traffic model that estimates how trip demands and travel times will vary with traffic congestion after an earthquake. The early REDARS evaluated how traffic flow would change depending on congestion, but did not account for the fact that, as damage and congestion increases, fewer potential travelers will choose to travel. Use of the variable-demand model will improve REDARS’ estimates of travel times and economic losses.
REDARS is scheduled to be available as public-domain software by the end of next year. Between now and then, Werner and his colleagues will be programming and testing the software. As the release date nears, they plan to run another demonstration on an actual highway network to show the software’s applicability for potential users.
Werner will present a paper on the subject of the REDARS software at the 13th World Conference on Earthquake Engineering in Vancouver, British Columbia, Aug. 1-6. His co-authors on the paper are his co-workers and fellow contributors to REDARS: Craig E. Taylor, Natural Hazards Management Inc., Torrance, Calif.; Sungbin Cho, Charles K. Huyck and Ronald T. Eguchi, ImageCat Inc., Long Beach, Calif.; Jean-Paul Lavoie and Chip Eitzel, Geodesy, San Francisco; and James E. Moore II, the University of Southern California, Los Angeles.
“I like to look at REDARS as a decision-guidance tool where one can first look at the highway network as is, with no seismic improvement,” said Werner, “and then proceed with this risk analysis and estimate potential risks and losses due to earthquake damage to the as-is system. Then one can ask, ‘What if we strengthen certain bridges in the highway network?’ This will have a certain initial design/construction cost associated with it. Next, the REDARS risk analysis can be repeated using a model that now includes these strengthened bridges in order to determine how much the risks and losses are reduced as a result of these bridge improvements.”
The transportation agency can run several simulations with different seismic improvement options and see which one would be most cost-effective. It can investigate where a new roadway would be least likely to suffer earthquake damage while increasing system redundancy and traffic capacity. The agency can plan how to reroute traffic after a quake, possibly converting some two-way routes to one-way routes, for example, to improve overall traffic flow or improve access to a medical center, airport or other emergency-response facility.
By studying the effects of virtual earthquakes in REDARS, agencies around the country have a better chance to minimize damage when a real earthquake hits.

Allen Zehyer is Associate Editor for Roads & Bridges.

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