Envision a substantial book placed on a surface. When you attempt to softly nudge the book across the surface with the tip of your finger, it might initially seem to stay still—it requires considerably more strength to commence sliding noticeably. Likewise, if you gradually begin elevating the surface, the book still seems to be at rest, adhering to the surface through friction until the angle of the lift reaches a certain critical point and the book unexpectedly glides down. This shift from seemingly motionless to rapid movement under significant forces is evident in seismic events and landslides.
Friction among two sliding surfaces has traditionally been described using a straightforward formula known as Coulomb’s law. However, Caltech scholars have shown that Coulomb’s law is inadequate for accurately depicting reality, asserting that surfaces under shear and pressure, despite appearing still, are perpetually sliding at rates undetectable by the human eye.
These recent findings, announced in a paper published online on March 12 in the journal Nature, deliver a more detailed comprehension of the mechanics behind earthquakes and landslides, carrying significant consequences for engineering material interfaces.
This research is a joint effort between the 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 touch, whether it be a book and a table, or two plates of the Earth’s crust pressed together and sheared along a fault line, Coulomb’s law indicates that a specific amount, known as the “coefficient of static friction,” must be surpassed before the contacting surfaces begin to slide. In simpler terms, Coulomb’s law posits that the two compressed surfaces remain entirely still unless sufficient shear force—a force parallel to the surface—is applied.
Although Coulomb’s model may seem logical, for many years, experts in rock mechanics and fault analysis have recognized that it may not tell the whole story. These researchers have proposed more intricate equations referred to as rate-and-state laws, where friction is contingent on the sliding speed and the changing states of the sliding surfaces. Rate-and-state laws forecast that a static friction coefficient does not exist and that shear movement happens under all shear forces—thus, for instance, even the slightest push of a hefty book with a fingertip will result in the book sliding a minuscule, imperceptible distance.
In the new publication, the team presents the first conclusive evidence that motion occurs even at shear forces lower than those suggested by the apparent static friction coefficient, corroborating the rate-and-state laws. In laboratory tests, the researchers employed an optical technique known as digital image correlation (DIC) and a camera focused on two surfaces in contact. They discovered that, under shear, the surfaces slid against each other at a speed as low as 10-12 meters per second, or 0.000000000001 meters per second. At this speed, a small fraction of a millimeter of slip could build up over the span of a year.
The surfaces in contact were constructed from a type of plastic that mimics the behavior of sliding rock interfaces responding to shear forces in comparable ways. This investigation continues Caltech’s tradition of recreating and examining surrogate earthquake processes in a laboratory, which has been facilitated by the 30-year-old Caltech “seismological wind tunnel,” a facility at the Graduate Aerospace Laboratories (GALCIT) established by Rosakis (a former director of GALCIT) and seismologist Hiroo Kanamori, the John E. and Hazel S. Smits Professor of Geophysics, Emeritus, and past director of Caltech’s Seismological Laboratory. This facility is dedicated to creating experimental analogues of the physical processes involved in earthquake ruptures.
“In the words of the ancient Greek philosopher Heraclitus, everything flows; everything moves, nothing is ever at rest,” Rosakis states. “Experts have long suspected the absence of a static friction coefficient, but now we have definitively demonstrated this using optical micro-measurements of unprecedented precision directly at the interface to verify the advanced friction laws and to advocate their application in other domains.”
Moreover, the researchers found that when two materials remain in contact for a prolonged period, referred to as “hold time,” they tend to “adhere” more than if they had merely come in contact. This evolving adhesion is termed “healing,” whereby microscopic contact areas locally strengthen and expand over time, enhancing the interface’s resistance to sliding. In the paper, the team also measured healing by assessing how it reduces the microscopic sliding that happens under minimal forces.
“One might question why measuring such tiny sliding velocities is significant; after all, they nearly equate to zero as the static friction coefficient would imply,” Lapusta remarks. “The significance lies not only in confirming rate-and-state friction but also in quantifying the healing of the interface. Rate-and-state friction laws predict that healing will manifest as a reduction in sliding velocities, precisely what we measure, thus allowing us to quantify healing. This, in turn, enables us to forecast how the interface will withstand a sliding occurrence, such as an earthquake rupture traveling along a fault.”
Indeed, the team discovered that the friction between the surfaces during rapid sliding would be considerably higher—approximately 20 percent greater—for interfaces that had been in contact for a year as opposed to five minutes, for instance.
“Numerous earthquake and landslide modellers continue to utilize simpler friction laws, which do not account for the effects of healing,” asserts study lead author Krittanon (Pond) Sirorattanakul (PhD ’24), now a researcher at Chevron. “We hope our findings will motivate the community to acknowledge the significance of healing in these investigations.”
Aside from facilitating enhanced modeling of earthquakes and faults, the discoveries have considerable implications for the design and management of frictional experiments. “Our team has occasionally encountered issues with the reproducibility of earthquake ruptures in the laboratory,” Rosakis elaborates. “Now we understand that if you organize your experiment and then take a lunch interval, those surfaces are healing during that time, leading your earthquake rupture results to 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 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, currently an associate professor at École Centrale Nantes, France, who has been a long-term 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.