Seawater glistens through a crack in the earth in the Egyptian desert.
Seawater glistens through a fracture in the earth in the Egyptian desert. Photo by Dreamstime.com
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Hebrew University
Prof. Jay Fineberg: The mathematics of crack propagation fit friction like a glove. Photo by Hebrew University

Sometimes minor earthquakes can cause massive damage. In Iran, for instance, a 2003 quake registering 6.6 killed 50,000 people. Now a paradigm-changing study on the mechanism of friction by physicists in Jerusalem leaps for the first time beyond theory of the great Leonardo da Vinci himself, among other things shedding light on why even relatively mild shudders of the earth can be so deadly.

Prof. Jay Fineberg at the Hebrew University of Jerusalem's Racah Institute of Physics had been thinking about earthquakes and concluded the way friction behaves sometimes didn't make sense. Something in the 500-year old theory was lacking.

Just ask any parent with kids: Friction (scraped knees) and fractures (broken elbows) are very different. Since da Vinci, physicists had also treated friction and fracture separately. But armed with superfast imaging technology, Fineberg and graduate student Ilya Svetlizky demonstrated that overcoming the one is a function of the other.

The da Vinci puzzle

What is friction? Put a block on the table. Now try to push it. You'll have to apply force to overcome the force keeping the block in place.

The force resisting the relative motion of two surfaces is friction.

"Da Vinci was the first scientist, that I know of at least, who found a quantitative way to describe friction," says Fineberg. But the great Italian visionary's paradigm couldn't explain why this description actually worked.

The heavier a block, the harder you have to push: the threshold force is proportional to the block's weight. (This proportionality is called the "friction coefficient," says Fineberg.) But one might think that the greater the surface area in contact between the block and table, the more resistance there would be, and the harder one would have to push.

Not so. Whether you put the block on a long, thin side or a wide side, the force needed to make the thing move stays the same, says Fineberg.

Why doesn't the area of contact surfaces affect the required force to get the blocks moving? The answer lay in the way the release from friction begins, Fineberg and Svetlizky explain in their ground-breaking Nature article, “Classical shear cracks drive the onset of dry frictional motion." 

All surfaces, even glass, are bumpy at the nanometric scale. "An interface is basically bumps sitting on other bumps. It's the ensemble of bumps supporting the weight of the block that creates the resistance to motion," Fineberg says. "The standard explanation for the da Vinci paradigm was that if you put enough shear force on your block, the contacts between the bumps would give up simultaneously and the thing would move."

Not so: what actually happens is much the same mechanism as your kid breaking his arm. It starts with one weak point.

You are the weakest link

To test their theory, Fineberg and Svetlizky devised a new way to observe "the real honest to God area of contact: to film this interface at unprecedented speed – a million times a second, while at the same time we pulled and prodded and whatnot. And, by God, we see that a crack develops, it propagates across the interface like a wave, sometimes approaching or even passing the speed of sound."

It isn't that the whole block starts moving at once. A flaw in the contacting bumpy surfaces breaks, starting a rapid shear crack that propagates at kilometers per second, leading the two entire surfaces to spring apart and start to move.

"The mathematics of crack propagation fit friction like a glove," says the professor gleefully. "You might not notice it while pushing your cup of coffee across the table but that's what's happening."

Thus seemingly identical blocks may require different forces to move them. "Materials are much less strong in general than their theoretical strength. Take a piece of paper. You can't pull it apart. But now make a small crack - a tear - in the paper – and you can break it easily.

"This is the essence of the mathematical description of how things break – the existence of a crack focuses energy to the crack’s tip – thereby breaking material like a chain of dominos," Fineberg explains.

Why one quake destroys

With their discovery, they kind of rediscovered the wheel regarding earthquakes, Fineberg laughs.

Much was known about faults and how deep actual breaks happen, sometimes hundreds of kilometers below the surface. Almost nothing is known about the actual dynamics of plate movement down there. But the conditions can be recreated in the lab.

What recreations teach is that a house will crumble even if the temblor itself is low in magnitude – but propagates fast. The house gets hit by a shockwave. If the same amount of energy is released slowly, you might even not notice it. The damage is caused by the shaking, which is happening far away from the quake itself, says Fineberg, and delivers the coup de grace: "The mathematics of crack propagation explain what's happening to that house. We're giving a precise description of how and why things are moving and damage occurs."

The fresh understanding of quake mechanisms could lead to better predictions and risk evaluation, he hopes. And meanwhile, man can now understand important processes usually hidden kilometers down below.