An official website of the United States government
Abstract The empirical constitutive modeling framework of rate‐ and state‐dependent friction (RSF) is commonly used to describe the time‐dependent frictional response of fault gouge to perturbations from steady sliding. In a previous study (Ferdowsi & Rubin, 2020), we found that a granular‐physics‐based model of a fault shear zone, with time‐independent properties at the contact scale, reproduces the phenomenology of laboratory rock and gouge friction experiments in velocity‐step and slide‐hold (SH) protocols. A few slide‐hold‐slide (SHS) simulations further suggested that the granular model might outperform current empirical RSF laws in describing laboratory data. Here, we explore the behavior of the same Discrete Element Method (DEM) model in SH and SHS protocols over a wide range of sliding velocities, hold durations, and system stiffnesses, and provide additional support for this view. We find that, similar to laboratory data, the rate of stress decay during SH simulations is in general agreement with the “Slip law” version of the RSF equations, using parameter values determined independently from velocity step tests. During reslides following long hold times, the model, similar to lab data, produces a nearly constant rate of frictional healing with log hold time, with that rate being in the range of ∼0.5 to 1 times the RSF “state evolution” parameterb. We also find that, as in laboratory experiments, the granular layer undergoes log‐time compaction during holds. This is consistent with the traditional understanding of state evolution under the Aging law, even though the associated stress decay is similar to that predicted by the Slip and not the Aging law.
more »
« less
Velocity-weakening and -strengthening friction at single and multiasperity contacts with calcite single crystals
Although earthquakes are one of the most notorious natural disasters, a full understanding of the underlying mechanisms is still lacking. Here, nanoscale friction measurements were performed by atomic force microscopy (AFM) on calcite single crystals with an oxidized silicon tip to investigate the influence of roughness, contact aging, and dry vs. aqueous environment. In dry environments, smooth and rough calcite surfaces yielding single- and multiasperity contacts, respectively, exhibit velocity-weakening ( β D ln V ) or neutral friction at slow sliding velocities and velocity-strengthening friction ( α D ln V ) at higher velocities, while the transition shifts to slower velocities with an increase in roughness. The origin of the velocity-weakening friction is determined to be contact aging resulting from atomic attrition of the crystalline surface. Friction measurements in aqueous environment show evidence of pressure solution at sufficiently slow sliding velocities, which not only significantly reduces friction on single-and multiasperity contacts but also, eliminates atomic attrition and thereby, velocity-weakening friction. Importantly, the friction scaling law evolves from logarithmic ( β D ln V ) into linear ( α P S V ), deviating from commonly accepted rate-and-state friction (RSF) laws; this behavior extends over a wider range of velocities with higher roughness. Above a transition velocity, the scaling law remains logarithmic ( α W ln V ). The friction rate parameters α D , β D , α P S , and α W decrease with load and depend on roughness in a nonmonotonic fashion, like the adhesion, suggesting the relevance of the contact area. The results also reveal that parameters and memory distance differ in dry and aqueous environments, with implications for the understanding of mechanisms underlying RSF laws and fault stability.
more »
« less
- Award ID(s):
- 1856525
- PAR ID:
- 10331144
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 119
- Issue:
- 22
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract This work examines the effect of environmental humidity on rate-and-state friction behavior of nanoscale silica-silica nanoscale contacts in an atomic force microscope, particularly, its effect on frictional ageing and velocity-weakening vs. strengthening friction from 10 nm/s to 100 μm/s sliding velocities. At extremely low humidities ($$\ll 1\% RH$$ ), ageing is nearly absent for up to 100 s of nominally stationary contact, and friction is strongly velocity-strengthening. This is consistent with dry interfacial friction, where thermal excitations help overcome static friction at low sliding velocities. At higher humidity levels (10–40% RH), ageing becomes pronounced and is accompanied by much higher kinetic friction and velocity-weakening behavior. This is attributed to water-catalyzed interfacial Si–O-Si bond formation. At the highest humidities examined (> 40% RH), ageing subsides, kinetic friction drops to low levels, and friction is velocity-strengthening again. These responses are attributed to intercalated water separating the interfaces, which precludes interfacial bonding. The trends in velocity-dependent friction are reproduced and explained using a computational multi-bond model. Our model explicitly simulates bond formation and bond-breaking, and the passivation and reactivation of reaction sites across the interface during sliding, where the activation energies for interfacial chemical reactions are dependent on humidity. These results provide potential insights into nanoscale mechanisms that may contribute to the humidity dependence observed in prior macroscale rock friction studies. They also provide a possible microphysical foundation to understand the role of water in interfacial systems with water-catalyzed bonding reactions, and demonstrate a profound change in the interfacial physics near and above saturated humidity conditions.more » « less
-
Multi-legged robots with six or more legs are not in common use, despite designs with superior stability, maneuverability, and a low number of actuators being available for over 20 years. This may be in part due to the difficulty in modeling multi-legged motion with slipping and producing reliable predictions of body velocity. Here, we present a detailed measurement of the foot contact forces in a hexapedal robot with multiple sliding contacts, and provide an algorithm for predicting these contact forces and the body velocity. The algorithm relies on the recently published observation that even while slipping, multi-legged robots are principally kinematic, and employ a friction law ansatz that allows us to compute the shape-change to body-velocity connection and the foot contact forces. This results in the ability to simulate motion plans for a large number of contacts, each potentially with slipping. Furthermore, in homogeneous environments, this kind of simulation can run in (parallel) logarithmic time of the planning horizon.more » « less
-
Lubricated sliding on soft elastic substrates occurs in a variety of natural and technological settings. It very often occurs in the iso-viscous elasto-hydrodynamic lubrication (EHL) regime ( e.g. , soft solid, low pressure). In this regime, for sliding of a smooth sphere on a soft solid, a “Hertz-like” effective contact region forms. Much of the fluid is squeezed out of the contact region although enough is retained to keep the solid surfaces fully separated. This is accompanied by complex deformation of the soft solid. The behavior of such soft lubricated contacts is controlled by a single dimensionless parameter 1/ β that can be interpreted as a normalized sliding velocity. Solving this fundamental soft-lubrication problem poses significant computational difficulty for large β , which is the limit relevant for soft solids. As a consequence, little is known about the structure of the flow field under soft lubrication in the intake and outlet regions. Here we present a new solution of this soft lubrication problem focusing on the “Hertz” limit. We develop a formulation in polar coordinates that handles difficult computational issues much better than previous methods. We study how hydrodynamic pressure, film thickness and hydrodynamic friction vary with β . Scaling laws for these relationships are given in closed form for a range of β not previously accessible theoretically but that is typical in applications. The computational method presented here can be used to study other soft lubrication problems.more » « less
-
Abstract Theory and experiments indicate that ice–bed separation during glacier slip over 2-D hard beds causes basal shear stress to reach a maximum at a particular slip velocity and decrease at higher velocities. We use the sliding theory of Lliboutry (1968) to explore how friction between debris particles in sliding ice and a rock bed affects this relationship between shear stress and slip velocity. Particle–bed contact forces and associated debris friction increase with increasing slip velocity, owing to increased rates of ice convergence with up-glacier facing surfaces. However, debris friction on diminished areas of the bed counteracts this effect as cavities grow. Thus, friction from debris alone increases only slightly with slip velocity, and for sediment particles larger than ~60 mm in diameter, debris friction peaks and decreases with increasing slip velocity. The effect on the sliding relationship is to steepen its rising limb and shift its shear stress peak to a slightly higher velocity. These results, which exclude the effect of debris friction on cavity size and debris concentrations above ~15%, indicate that the effect of debris in ice is to increase basal shear stress but not significantly change the form of the sliding relationship.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2112505119
