Persistence and intermittency in sliding of blocks

Abstract

An extensive Hurst analysis to quantify long-term statistical dependence is performed on time series associated with sliding of blocks on an inclined plane induced by small perturbations. The analysis reveals the existence of a fluctuation phenomenon exhibiting two phases, depending on the angle of inclination, both obeying a Hurst scaling . The first (second) phase has H = 0.70 (0.50) and refers to large (small) inclinations irrespective of the material of the block. These results indicate that sliding of blocks in the first regime exhibits persistence and indicate that there are long-term memory effects on the storage of shear stress at the block-plane interface. In the second regime, the long-term memory effects disappear and the sliding activity is intermittent; that is, it is distributed in bursts separated by variable periods of stasis.

Nontrivial temporal scaling in a Galilean stick-slip dynamics

“…It has to be emphasized that the geometric and statistic properties exhibited by the time series of sliding events are a consequence of the particular nature of the microscopic friction at the block−incline interface. No spatial and temporal correlations as shown here and as those reported in [6,7,8,20] are found in these series if the block is moved back to the top of the incline after each sliding event, which would mean removing the strong correlation between the configuration of the contacts at the interface and the past history of the block on the incline. Due to the very time-consuming nature of the experiments described in this paper, many aspects remain to be investigated in the future.…”

“…In the last few years, it has been shown that intermittent sliding or stick-slip dynamics of a rough solid nonrotating cylinder on a rough inclined groove submitted to small controlled perturbations is a fluctuation phenomenon characterized by nontrivial spatiotemporal scaling laws [6,7] and complex critical exponents [8] if the inclination is well below the angle of repose. In particular, the time series of intermittent slidings associated with the stick-slip motion of the cylinder on the incline were found to present many similarities to time series of earthquakes: The sliding distribution is described by the Gutenberg and Richter law n(s) ∼ s −0.5 , where n(s) is the number of events of size s, and the Omori law for the number of smaller events occurring at a time t after a large event, n(t) ∼ t −p , where the exponent p is an anomalous one, lying between 0.25 and 0.45, and may be a complex number.…”

Sliding susceptibility of a rough cylinder on a rough inclined perturbed surface

“…In principle, we expect in conformity with Eq. (6), that cylinder and chute rough surfaces with increasing values of D tend to be more tightly engaged as a consequence of the increment in the effective area for microscopic interactions. This effect materializes itself in a microscopic reduction in the number of allowed vibration modes of the cylinder, i.e.…”

Omori law for sliding of blocks on inclined rough surfaces

“…Recent experiments have shown that long sequences of slidings of cylindrical blocks occurring on a rough incline submitted to small controlled perturbations give origin to nontrivial scaling laws for the measured length and lifetime distributions of events [1][2][3]. These slidings of blocks occur as an energy dissipation process on the interface block-incline to which the elastic energy is continuously input, and as a consequence, some connection between this problem and the nonlinear dynamics of earthquakes could be hypothesizing.…”