The traditional view of tectonics is that the lithosphere comprises a strong brittle layer overlying a weak ductile layer, which gives rise to two forms of deformation: brittle fracture, accompanied by earth- quakes, in the upper layer, and aseismic ductile flow in the layer beneath Although this view is not incorrect, it is imprecise, and in ways that can lead to serious misunderstandings The term ductility, for example, can apply equally to two common rock deformation mechanisms: crystal plasticity, which occurs in rock above a critical temperature, and cataclastic flow, a type of granular deformation which can occur in poorly consolidated sediments Although both exhibit ductility, these two deformation mechanisms have very different rheologies Earthquakes, in turn, are associated with strength and brittleness—associations that are likewise sufficiently imprecise that, if taken much beyond the generality implied in the opening sentence, they can lead to serious misinterpretations about earthquake mechanics Lately, a newer, much more precise and predictive model for the earthquake mechanism has emerged, which has its roots in the observation that tectonic earthquakes seldom if ever occur by the sudden appearance and propagation of a new shear crack (or 'fault') Instead, they occur by sudden slippage along a pre-existing fault or plate interface They are therefore a frictional, rather than fracture, phenomenon, with brittle fracture playing a secondary role in the lengthening of faults 1 and frictional wear 2  This distinction was noted by several early workers 3 , but it was not until 1966 that Brace and Byerlee 4 pointed out that earthquakes must be the result of a stick-slip frictional instability Thus, the earthquake is the 'slip', and the 'stick' is the interseismic period of elastic strain accumula- tion Subsequently, a complete constitutive law for rock friction has been developed based on laboratory studies A surprising result is that a great many other aspects of earthquake phenomena also now seem to result from the nature of the friction on faults The properties traditionally thought to control these processes— strength, brittleness and ductility—are subsumed within the over- arching concept of frictional stability regimes Constitutive law of rock friction In the standard model of stick-slip friction it is assumed that sliding begins when the ratio of shear to normal stress on the surface reaches a value ms, the static friction coefficient Once sliding initiates, frictional resistance falls to a lower dynamic friction coefficient, md, and this weakening of sliding resistance may,

/pdf/earthquakes-and-friction-laws-22mbgrykdx.pdf

Earthquakes and friction laws

This paper reviews rock friction and the frictional properties of earthquake faults. The basis for rate- and state-dependent friction laws is reviewed. The friction state variable is discussed, including its interpretation as a measure of average asperity contact time and porosity within granular fault gouge. Data are summarized showing that friction evolves even during truly stationary contact, and the connection between modern friction laws and the concept of “static” friction is discussed. Measurements of frictional healing, as evidenced by increasing static friction during quasistationary contact, are reviewed, as are their implications for fault healing. Shear localization in fault gouge is discussed, and the relationship between microstructures and friction is reviewed. These data indicate differences in the behavior of bare rock surfaces as compared to shear within granular fault gouge that can be attributed to dilation within fault gouge. Physical models for the characteristic friction distance are discussed and related to the problem of scaling this parameter to seismic faults. Earthquake afterslip, its relation to laboratory friction data, and the inverse correlation between afterslip and shallow coseismic slip are discussed in the context of a model for afterslip. Recent observations of the absence of afterslip are predicted by the model.

/pdf/laboratory-derived-friction-laws-and-their-application-to-44s35v6won.pdf

Laboratory-derived friction laws and their application to seismic faulting

In this paper, new scaling properties for granular flows down rough inclined planes are presented. In the dense steady uniform flow regime, we have systematically measured the mean velocity of the flow as a function of the inclination of the surface θ and of the thickness h of the layer. The results obtained for different systems of beads corresponding to different surface roughness conditions are shown to collapse into a single curve when properly scaled. The scaling is based on the measurement of the minimum thickness hstop(θ) necessary to observe a steady uniform flow at inclination θ. From this experimental observation an empirical description for granular flows down inclined planes is proposed in terms of a dynamic friction coefficient.

Scaling laws in granular flows down rough inclined planes

We study the stability of steady sliding between elastically deformable continua using rate and state dependent friction laws That is done for both elastically identical and elastically dissimilar solids The focus is on linearized response to perturbations of steady-state sliding, and on studying how the positive direct effect (instantaneous increase or decrease of shear strength in response to a respective instantaneous increase or decrease of slip rate) of those laws allows the existence of a quasi-static range of response to perturbations at sufficiently low slip rate We discuss the physical basis of rate and state laws, including the likely basis for the direct effect in thermally activated processes allowing creep slippage at asperity contacts, and estimate activation parameters for quartzite and granite Also, a class of rate and state laws suitable for variable normal stress is presented As part of the work, we show that compromises from the rate and state framework for describing velocity-weakening friction lead to paradoxical results, like supersonic propagation of slip perturbations, or to ill-posedness, when applied to sliding between elastically deformable solids The case of sliding between elastically dissimilar solids has the inherently destabilizing feature that spatially inhomogeneous slip leads to an alteration of normal stress, hence of frictional resistance We show that the rate and state friction laws nevertheless lead to stability of response to sufficiently short wavelength perturbations, at very slow slip rates Further, for slow sliding between dissimilar solids, we show that there is a critical amplitude of velocity-strengthening above which there is stability to perturbations of all wavelengths

http://esag.harvard.edu/rice/197_Rice_Lap_Ranj_JMPS_01.pdf

Rate and state dependent friction and the stability of sliding between elastically deformable solids

The physics of sliding friction is gaining impulse from nanoscale and mesoscale experiments, simulations, and theoretical modeling This Colloquium reviews some recent developments in modeling and in atomistic simulation of friction, covering open-ended directions, unconventional nanofrictional systems, and unsolved problems

/pdf/colloquium-modeling-friction-from-nanoscale-to-mesoscale-2gi3akfv3u.pdf

Colloquium : Modeling friction: from nanoscale to mesoscale

We perform an extensive study of the dry-friction dynamics of a paper-on-paper system. We explore the dynamical phase diagram by systematically varying the relevant control parameters (driving velocity V, slider mass M, and loading machine stiffness k). A set of experimental results gives strong proof that the low-velocity dynamics is controlled by a creep process, in agreement with previous results from rock mechanics and metals [C. H. Scholz, The Mechanics of Earthquakes and Faulting (Cambridge University Press, Cambridge, 1990), Chap. 2 and references therein; E. Rabinowicz, Proc. Phys. Soc. 71, 668 (1958) and references therein]. At higher velocities, a crossover to inertial dynamics is observed. In each regime, when k is increased, the system bifurcates from periodic stick-slip to steady sliding: in the creep regime, the bifucation is a direct Hopf one; in the inertial regime it becomes subcritical. We identify, from comparison of the time dependence of the static friction coefficient ${\mathrm{\ensuremath{\mu}}}_{\mathit{s}}$(t) and of the velocity dependence of the stationary dynamic one, ${\mathrm{\ensuremath{\mu}}}_{\mathit{d}}$(V), a memory length of the order of 1 \ensuremath{\mu}m. The V dependence of ${\mathrm{\ensuremath{\mu}}}_{\mathit{d}}$(V) changes from V weakening to V strengthening at the creep-inertial crossover. We propose a heuristic model of low-velocity friction based on two main ingredients: (i) following and extending the ideas of Ruina [J. Geophys. Res. 88, 10 359 (1983)], we define a phenomenological contact age accounting for the renewal of physical contacts on the scale of the memory length, and (ii) we assume that the dynamics is controlled by the Brownian motion of an effective creeping volume in a pinning potential, the strength of which increases with age.The crossover from creep to inertial motion then naturally appears as the runaway threshold between thermally activated and free motion. The bifurcation analysis in the creep regime is compared in detail with experimental results, yielding a very satisfactory agreement. When confronted with rock mechanics results, this study strongly suggests that low-velocity creep is quite generic; further studies of this process should in particular bear on models of earthquake dynamics.

Creep, stick-slip, and dry-friction dynamics: Experiments and a heuristic model.

FRICTION between dry surfaces plays a role in solid dynamics over a wide range of length scales, from the mechanics of micromachines to earthquakes. Some common features of frictional dynamics have been observed for rather different materials, such as rock sliding on rock or metal on metal1,2. But there is still relatively little understanding of the way in which frictional motion varies generically with mechanical parameters. Here we present the results of experiments on frictional sliding of Bristol board, which show how the characteristics of frictional sliding depend on mass, driving velocity and stiffness of the driving spring constant. In general, there is a bifurcation from stick–slip to steady sliding with increasing velocity. The character of the frictional motion and of the associated bifurcation changes with velocity: at low speeds creep is dominant, which can be ascribed a characteristic length, whereas at high speeds the motion can be described as inertial, with a characteristic timescale. The kinetic friction coefficient decreases with increasing velocity in the former case, and increases with velocity in the latter. We anticipate that these results are likely to be generic.

Crossover from creep to inertial motion in friction dynamics

We perform an experimental study of the amplitude and frequency shift of the stick-slip (SS) oscillations of a paper-on-paper block and spring system close to the SS--steady-sliding Hopf bifurcation. The confrontation of the experimental results with a weakly nonlinear analytical analysis of the dynamics and with direct numerical calculations yields very satisfactory agreement with the model of creep-controlled dry friction proposed by Heslot et al. [Phys. Rev. E 49, 4973 (1994)].

Nonlinear analysis of the stick-slip bifurcation in the creep-controlled regime of dry friction.

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Creep, stick-slip, and dry-friction dynamics: Experiments and a heuristic model.

Crossover from creep to inertial motion in friction dynamics

Nonlinear analysis of the stick-slip bifurcation in the creep-controlled regime of dry friction.