Frictional Sliding of Rough Surfaces Using a Quasi-static Approach to the Maxwell-slip Model

The Maxwell-slip model consists of independent mass-spring units that are slipped by a driver over a rigid, flat, fixed substrate. In the present study, the model is interpreted as a multi-asperity model and is used to study both the friction force and the mechanisms involved in the sliding of a rough elastic surface. Coulomb friction law is assumed at the single mass-spring level. A beta probability distribution function is used to generate the initial block positions randomly. The standard deviation of the initial lateral position of the blocks is interpreted as the surface roughness. The results show that when the surface is rough enough, the sequential slip of the blocks induces a steady friction force. On the other hand, when the surface is smooth enough, the collective slip of the blocks induces stick-slip. The border between the two regimes of sliding is sharply delineated by a specific roughness value. A tribological implication is that a sufficiently rough surface may bring about steady sliding. A geophysical implication is that a geological fault segment that undergoes aseismic creep may have a rougher surface compared to its locked counterpart.

Critical zone of the branching crack model for earthquakes: Inherent randomness, earthquake predictability, and precursor modelling

The branching crack model for earthquakes was developed by Vere-Jones and Kagan in the 1970s and the 1980s, respectively. With some simple and rational assumptions, its simulation results explain the Gutenberg-Richter magnitude-frequency relationship and the Omori-Utsu aftershock decay formula. By introducing the concept of the critical zone, this model can be connected with the asperity model, the barrier model, and the nucleation model through a parameter – criticality. Particularly, the size of the critical zone determines the maximum magnitude of potential earthquakes and the source of their anomalies. The key to earthquake forecasting is to determine whether the concerned area is in a critical state and how large the critical zone is. We discuss what kinds of anomalies are meaningful as candidates of earthquake precursors. Finally, we outline modelling strategies for earthquake precursors with low probability gains that are due to the inherent randomness of earthquake source processes.

The Elastic Contact of Rough Spheres Investigated Using a Deterministic Multi-Asperity Model

In this paper, we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures. The deterministic analysis enables to capture both particular deformation modes of individual rough surfaces and also statistical deformation regimes, which involve averaging over a big number of roughness realizations. Two regimes of contact area growth were identified: the Hertzian regime at light loads at the scale of a single asperity, and the linear regime at higher loads involving multiple contacting asperities. The transition between the regimes occurs at the load which depends on the second and the fourth spectral moments. It is shown that at light indentation the radius of circumference delimiting the contact area is always considerably larger than Hertzian contact radius. Therefore, it suggests that there is no scale separation in contact problems at light loads. In particular, the geometrical shape cannot be considered separately from the surface roughness at least for approaching greater than one standard roughness deviation.