Stabilizing Stick-Slip Friction

Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slow rupture modes which forces a transition to fast rupture, providing a possible mechanism for observed remote triggering of earthquakes. Such manipulation of collective modes may be generally relevant to extended nonlinear systems driven near to criticality.

Figure 1

Schematic views of the experimental system (a) and model (b). Typical stick-slip motion in experiments (c) and model (d) with no modulation of $F_s$. Parameter values used in the model: $F_N=4000\mathrm{N}$, $K_d=4\times {10}^7\mathrm{N}/\mathrm{m}$, $M=11.5\mathrm{kg}$, $V_0={10}^{-4}\mathrm{m}/\mathrm{s}$, $K={10}^8\mathrm{N}/\mathrm{m}$, ${\tau }_r=0.005\mathrm{s}$, $N_S=20$, $N=70$, $\gamma =6462{\mathrm{s}}^{-1}$, $f_s=1.37\mathrm{N}$, $\Delta f_s=6.9\times {10}^{-3}\mathrm{N}$, $k=⟨k_i⟩=5\times {10}^6\mathrm{N}/\mathrm{m}$, $\Delta =1\mu \mathrm{m}$.

Figure 2

Histograms of $\tau$ in experiments (left panels) and the model (right panels), when (a),(d) no external control is imposed, and for small-amplitude sinusoidal perturbations with external frequencies of 2 Hz (b), 1 Hz (c), 29 Hz (e), 58 Hz (f). The red dashed curve in (d) is a histogram calculated for identical surface contacts, when the system’s nonlinearity is the only source of stochasticity. The model parameter values used are as in Fig. 1.

Figure 3

Once phase locking occurs, $\tau$ becomes an integer multiple, $n$, of the forcing period, $T$. (a) A typical experiment for large $n$ and $T\ll {\tau }_0$ (${\tau }_0$ is the, unperturbed, mean stick-slip interval). Stick-slip intervals, $\tau$, as a function of $T$ for experiments (b) and the model (c) over a broad range of loading conditions. The data all fall on well-defined lines of $\tau =nT$ for different integer values of $n$. Examples are highlighted by solid lines. Plots of $\varphi$ vs $\eta$ for experiments (d) and the model (e). Experiments: $1<V_0<200\mu \mathrm{m}/\mathrm{s}$, $2<\Delta <100\mu \mathrm{m}$, $0.1<2\pi /T<500\mathrm{Hz}$. Phase locking is seen by the data clustering above a well-defined “backbone.” At low values of $\eta =(2\pi \Delta )/(T{V}_0)$ (shaded region), no phase locking occurs and $-\pi <\varphi <\pi$ occur with equal probability. As $\eta$ is increased, correlated events appear with the initial phase of $-\pi$ for small $\eta$ and saturate to zero for $\eta \gg 1$. Red curves in (d) and (e) correspond to ${\varphi }_{\min }\approx -2(\pi /\eta {)}^{1/2}$. Blue dots are averaged values of $\varphi$ for given values of $\eta$.

Figure 4

Space-time maps of the measured real contact area (a),(c) and fraction of attached contacts in the model (b),(d) when no control is applied (left panels) and in the presence of oscillatory perturbations (right panels). Hotter (colder) colors indicate increased (decreased) contact area in (a),(c). (b),(d) The bars to the right of the maps set up a correspondence between the colors and the percent of detached contacts.