Imagine a heavy book resting on a table. If you try to gently push the book across the table with the tip of your finger, it may first appear to remain motionless-it needs a lot more force to start sliding visibly. Similarly, if you slowly start tilting the table upward, the book still appears to remain motionless, sticking to the table through friction until the table's tilt reaches some critical angle and the book suddenly slides down. This transition from apparent stillness to sudden movement under large forces is seen in earthquakes and landslides.
Friction between two sliding interfaces historically has been modeled with a simple expression called Coulomb's law. Now, Caltech researchers have demonstrated that Coulomb's law is insufficient for describing reality, and that interfaces subjected to shear and pressure, though they may appear motionless, are, in fact, always sliding at rates imperceptible to the human eye.
These new observations, reported in a paper appearing online on March 12 in the journal Nature, provide a more precise understanding of the mechanics of earthquakes and landslides, and have major implications for the engineering of materials interfaces.
The work is a collaboration between the research teams of Ares Rosakis , the Theodore von Kármán Professor of Aeronautics and Mechanical Engineering, and Nadia Lapusta , the Lawrence A. Hanson, Jr., Professor of Mechanical Engineering and Geophysics.
When two surfaces are in contact, whether they are a book and a table or two plates of the Earth's crust pressed and sheared along a fault, Coulomb's law indicates that there is a certain quantity, called the "coefficient of static friction," that must be overcome before the interfacing surfaces start sliding. In other words, Coulomb's law states that the two compressed interfaces are completely motionless unless enough shear force-a force parallel to the direction of the interface-is applied.
Coulomb's model may seem intuitive, but, for decades, researchers who study rock mechanics and faults have known that it may not be the full story. These scientists have introduced more detailed equations, called rate-and-state laws, in which friction depends on the sliding rate and the evolving states of the sliding interfaces. Rate-and-state laws predict that there is no static friction coefficient and that shear movement occurs under all shear forces-so, for example, even the slightest pushing of a heavy book with the tip of your finger will cause the book to slide some tiny, imperceptible amount.
In the new paper, the team presents the first direct proof that motion is happening even at shear forces lower than those implied by the apparent static friction coefficient, validating the rate-and-state laws. In laboratory studies, the team used an optical method called digital image correlation (DIC) and a camera trained on two surfaces in contact. They determined that, under shear, the surfaces slid over each other at a rate as small as 10-12 meters per second, or 0.000000000001 meters per second. At this rate, a fraction of a millimeter of slip would accumulate in one year.
The contacting surfaces were made of a kind of plastic that emulates the sliding rock interfaces responding to shear forces in analogous ways. This study extends Caltech's practice of re-creating and studying surrogate earthquake processes in the laboratory, research enabled by the 30-year-old Caltech "seismological wind tunnel," a facility at the Graduate Aerospace Laboratories (GALCIT) created by Rosakis (a former GALCIT director) and seismologist Hiroo Kanamori , the John E. and Hazel S. Smits Professor of Geophysics, Emeritus, and former director of Caltech's Seismological Laboratory. The facility is devoted to the creation of experimental analogues of the physical processes involved in earthquake rupture.
"In the words of ancient Greek natural philosopher Heraclitus, everything flows; everything moves, nothing is ever stationary," Rosakis says. "Specialists have suspected that there is no static friction coefficient, but now we have conclusively proven this by using optical micro-measurements of unprecedented accuracy directly at the interface to validate the advanced friction laws and to promote their use in other fields."
Additionally, the researchers found that when two objects have been held in contact for an extended period of time, called "hold time," they tend to "stick" together more so than if they had just come into contact. This evolving adhesion is a phenomenon called "healing," in which microscopic contact areas locally strengthen and increase over time, making the interface more resistant to sliding. In the paper, the team also quantified healing by measuring how it slows down the microscopic sliding that occurs under small forces.
"One may wonder why measuring such minute sliding rates are important; after all, they are close to zero as the concept of the static friction coefficient would predict," Lapusta says. "The importance is not just in validating rate-and-state friction but also in quantifying the interface healing. Rate-and-state friction laws predict that the healing should manifest itself in the decrease of sliding rates, which is exactly what we measure, enabling us to quantify healing. This, in turn, allows us to predict how the interface would resist a sliding event, such as an earthquake rupture propagating along a fault."
Indeed, the team found that the friction between the interfaces during rapid sliding would be significantly larger-around 20 percent larger-for interfaces that had been in contact for a year versus five minutes, for example.
"Many modelers of earthquakes and landslides still use a simpler friction law, which does not incorporate the effects of healing," says study first author Krittanon (Pond) Sirorattanakul (PhD '24), now a researcher at Chevron. "We hope that our work will encourage the community to recognize the importance of healing in these studies."
In addition to enabling better modeling of earthquakes and faults, the findings have major implications for the design and control of frictional experiments. "Our team has had occasional problems with reproducibility of earthquake ruptures in the lab," Rosakis explains. "Now we know that if you set up your experiment, then take a lunch break, those surfaces are healing during that time, and your earthquake rupture results will be significantly different!"
The paper is titled "Sliding and healing of frictional interfaces that appear stationary." In addition to Sirorattanakul, Lapusta, and Rosakis, co-authors also include former graduate student Stacy Larochelle (PhD '22), now a postdoctoral research scientist at Columbia University's Lamont-Doherty Earth Observatory; and Vito Rubino, a former research scientist in aerospace at Caltech, now an associate professor at École Centrale Nantes, France, who is a longtime collaborator of Rosakis and Lapusta. Funding was provided by the National Science Foundation (NSF)-IUCRC Center for Geomechanics and Mitigation of Geohazards (GMG) at Caltech, the NSF, and the US Geological Survey.
