Memory effects in geological faults linger on for years

Earthquakes occur when the frictional force between two tectonic plates is overcome. The plates slide against each other and eventually settle into their new positions. But that isn’t the end of the story. A recent report, about to be published in the journal Mechanics of Materials, uses computer simulations to examine the same effect on an everyday material such as Plexiglas. The findings show how a memory effect from earlier events influences the next generations of slides. Using numerical simulations, EPFL researcher Mathilde Radiguet has helped shed some light onto this mysterious facet of friction.

Solid surfaces slide against each other in a “stick-slip” motion that occurs when a solid block is pushed along a surface with a spring. Initially, the spring is relaxed, and friction at the interface between the surfaces makes them stick. Gradually compressing the spring increases the force acting on the block, until suddenly the friction force is overcome. The block slips forward, the spring relaxes, and the block sticks in a new position. Then the whole thing starts over.

But is that really all that happens? Researchers are only beginning to understand the complexity of the phenomena that occur leading up to each slip. One reason that they have remained elusive for so long is because it is extremely difficult to get detailed measurements on the stresses acting at each point of the interface in the lab.

From Plexiglas to Earthquakes
Earthquakes are Mathilde Radiguet’s real area of interest, but studying them in the field can be a headache. “If we wanted to measure the forces between two tectonic plates sliding against each other in the field, we would have to deploy sensors at the interface between two plates and patiently wait for the next earthquake,” she says. But the long recurrence times between quakes and the difficulty in deploying the sensors so far underground has long made such experiments difficult.

“Using simulations, we can study phenomena that are all but impossible to observe, even in the lab,” she explains. Because simulations give researchers access to all of the values that are computed, Radiguet was able analyze the stresses that build up at any point between the mobile plate and its base, and watch how they evolve between successive slips.

To make her research more relevant to seismological research, she decided to run her simulations using so-called viscoelastic materials. Rather than quickly bouncing back to their original shape when deformed, the viscoelastic materials she used in her simulations respond more slowly and in a time dependent way, storing some of the deformations and the stresses they give rise to, sometimes for minutes. Translated from laboratory to geological settings, these minutes can become years or even decades.

What she observed was that, when the top plate is pushed using a force that is just above the threshold that will make it slide, a portion of the surface close to where the force is applied detaches from the surface, causing stresses to accumulate at the far edge of the detached zone. When the force is increased, a second rupture initiates and propagates until it reaches the location where first rupture came to a halt. There, the stored stresses accelerate its propagation, which continues until it too comes to a halt in a new location.

The process continues in the same way: with increasing loading, the detached area propagates until they reach each previously established arrest position, where stresses are stored in the viscoelastic material’s “memory.” And at each boundary, the stored stresses cause the propagation of the rupture to accelerate again, and again.

Twenty to forty kilometers underground, geologists and geophysicists consider the hot, malleable bedrock to deform in a ductile manner, so that movements there do not lead to earthquakes. Closer to the surface, the bedrock is considered to deform elastically, and produce brittle ruptures, leading to the tremors experienced at the surface. It is likely, however, that within the brittle crust, the state of the bedrock is not purely elastic and that viscoelasticity is important. In future modeling studies Mathilde Radiguet will study the phenomena that occur in this intermediate state more directly, using parameters that more closely match the actual materials found in the bedrock.