Synchronized oscillations and acoustic fluidization in confined granular materials

According to the acoustic fluidization hypothesis, elastic waves at a characteristic frequency form inside seismic faults even in the absence of an external perturbation. These waves are able to generate a normal stress which contrasts the confining pressure and promotes failure. Here, we study the mechanisms responsible for this wave activation via numerical simulations of a granular fault model. We observe the particles belonging to the percolating backbone, which sustains the stress, to perform synchronized oscillations over ellipticlike trajectories in the fault plane. These oscillations occur at the characteristic frequency of acoustic fluidization. As the applied shear stress increases, these oscillations become perpendicular to the fault plane just before the system fails, opposing the confining pressure, consistently with the acoustic fluidization scenario. The same change of orientation can be induced by external perturbations at the acoustic fluidization frequency.

Figure 1

Upper panels: The evolution of the top-plate position along the direction of the applied drive ($x$ direction) exhibits stick-slip dynamics. The panels show four time intervals during which six slips of different sizes are observed at times indicated by the dashed vertical orange lines. The colored arrows show the times considered for the evaluation of $P\left(\theta \right)$ (Fig. 4). Central panels: The power spectral density $\widehat{C}(t,\omega )$ of the autocorrelation function $C(t,t^{\prime })$ as a function of time $t$ for different values of $j·d\omega$, with $d\omega =0.05\pi$ and $j=20$ (blue), 28 (red), 36 (purple). Values of $\widehat{C}(t,\omega )$ significantly different than 0 are only observed for $j=28$ corresponding to $\omega ={\omega }^{*}$. Lower panels: The standard deviation of the angle $\theta$ formed by the particle velocities with the $z$ axis as a function of time $t$.

Figure 2

Upper left panels: Time dependence of the $x$ (solid triangles) and $z$ coordinate (open squares) of the position of four nearest-neighbor particles at time $t_{s_1}-t=20$, far from the slip. The vertical scale of $x_4$ is 3000 times larger than the scale of $x_1,x_2,x_3$. Upper right panels: The position components $y_1,y_2,y_3$ and $z_1,z_2,z_3$ are plotted as a function of $x_1,x_2,x_3$, respectively, at time $t_{s_1}-t=20$. Each trajectory has been shifted to be all centered in $(0,0)$. The same symbols and colors as in the left panels. Lower panels: The same as the upper panels at time $t_{s_1}-t=5$, at the onset of the slip.

Figure 3

The map of the power spectral density ${\widehat{C}}_{x_i}\left(\omega \right)$ of particle position as a function of $\omega$, for all particles. The horizontal axis represents the particle index. The intensity of the power spectrum can be obtained from the color code.

Figure 4

Left panels: The distribution of the angle $\theta$ formed by the particle velocities with the $z$ axis in the unperturbed evolution. Each color corresponds to a different time $t$ indicated by the vertical arrows in the upper panels of Fig. 1. In the upper panel we consider the temporal interval $t\in [60,190]$ and in the lower panel the temporal interval $t\in [300,450]$. Right panels: The quantity $P\left(\theta \right)$ under a pressure perturbation evaluated at the same times, identified by the same color codes, of the left panels.