The Slippery Rules of Mudslides

Oso, Washington 5 days after the landslide — The U.S. Geological Survey captured the upper parts of the landslide in Oso, Washington in an aerial survey taken five days after the natural disaster.

(Image credit: Jonathan Godt, USGS)

This Behind the Scenes article was provided to Live Science in partnership with the National Science Foundation.

Mudslides. Landslides. Volcanic debris flows. Avalanches. Falling rocks . . .

They may bury and destroy homes, roads and even towns with little or no warning. Recently, we've had dramatic reminders of the unpredictability and variability of these types of natural disasters: a mudslide in Oso, Wash. , that killed 41 people, an avalanche on Mt. Everest that killed 13 experienced Sherpas, and a non-fatal, but destructive, relatively slow-moving landslide that occurred in mid-April in Jackson, Wyoming.

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Adults may remember simple math story problems from elementary school, such as, "If an avalanche flow is moving at a rate of 50 meters per second, how long will it take to swallow up a village located 30 kilometers away?" Unfortunately, for geologists and others researching mudslides, landslides, volcanic debris flows, avalanches and rock falls, the particulars make the solution far from simple algebra.

After all, earthen, volcanic and snowy materials — all of which can move quickly downhill — do so at varying rates depending on their composition, the composition of the geological features over which they flow and the weather. Though it may be challenging to model the way rocks, ice, lava and volcanic gases are likely to move and where they are likely to go post-volcano or during a particularly wet spring, the results of such analyses may ultimately support policymaking, urban planning, insurance risk assessment and most importantly public safety.

"You see these wonderful volcanic eruptions with the plumes, but gravity currents are going down the mountain even as all this stuff is going up into the air," Pitman said. "It can be very deadly. And depending on the mountain — if there's snow on the mountain — then you have this muddy sort of muck, so it can go even faster downhill." (Volcanic flows and mudslides are examples of what geoscientists call gravity currents.)

According to the Centers for Disease Control and Prevention, landslides and debris flows result in 25 to 50 deaths each year in the United States. The U.S. Geological Survey (USGS) reports that "all 50 states and the U.S. territories experience landslides and other ground-failure problems," including 36 states with "moderate to highly severe landslide hazards," which include the Appalachian and Rocky mountains, Pacific Coast regions and Puerto Rico. USGS notes that areas denuded because of wildfires or overdevelopment are particularly vulnerable to the whims of what's termed generally as "ground failures."

Pitman has spent the past 13 years studying the flows of the Soufrière Hills volcano on Montserrat, the Colima volcano west of Mexico City, and the Ruapehu volcano in New Zealand, among other sites. Working with an engineer whose expertise is in high performance computing, statisticians, and several geologists, Pitman studies geophysical mass flows, specifically volcanic avalanches and pyroclastic (hot gas and rock) flows, which are "dry" flows.

"We started modeling volcanic flows as dry volcanic flows, so the equation described the material as each particle frictionally sliding over the next particle," Pitman said. "However, we knew it wasn't only solid particles. There could be air or water too, so we developed another model. This naturally makes the analysis harder. In mudslides, you have to factor in mud, which is a viscoplastic fluid—partly like a fluid but also able to deform like a plastic material and never rebound. In wet or dry materials, you can make some reasonable predictions because flow is more or less the same. It is much harder to do that with mud."

We might be inclined to think that lava flows are far more complicated to model because of the issues of heat and explosive force, says Michael Steuerwalt, a National Science Foundation Division of Mathematical Sciences program director. However, a mix of dramatically different particle sizes and shapes — which range from dirt grains to people, cars, houses, boulders and trees — can considerably complicate a slide model.

The Belham Valley of Montserrat is overrun by lahars — volcanic flows that stayed higher up the mountainside and washed down due to intense rains. In 2011, E. Bruce Pitman joined engineers, statisticians and geoscientists who in 2011 were studying 15 years of eruptions there. Pitman is actually standing on the first floor’s roof. Mudslides decimated the house 10 years prior.

"If you're trying to deduce, for example, where under this mudslide is the house that used to be way up there (along with its inhabitants), then the model is very complicated indeed," Steuerwalt said. "Math won't solve this problem alone, either. But with topographic data, soil data and predictions of precipitation, one could make assessments of where not to build and estimates of risk. This really is an opportunity for mathematicians coupled not only with statisticians, but also with geographers, geoscientists and engineers."

The researchers depicted in Behind the Scenes articles have been supported by the National Science Foundation, the federal agency charged with funding basic research and education across all fields of science and engineering. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. See the Behind the Scenes Archive.

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