Avalanche mixing and the simultaneous collapse of two media under uniaxial stress

Avalanches in coal and sandstone samples under common uniaxial stress serve as a model for mixing of avalanche exponents in ceramics, multiferroics, and alloys. The two media are sandwiched together and subjected to common uniaxial stress using high- and low-stress compression. Each medium collapses individually through avalanches that often coincide with secondary avalanches into the other medium. The total avalanche time sequence allows a detailed investigation of the mixing by superposition and delayed coincidence. Correlations can be described by an inter-media Båth's law.

Figure 1

(a) Experimental arrangement for high-stress measurements. (b) Energies of AE hits, detected by the transducers attached to coal and sandstone as indicated by color, as a function of time. In this experiment, there are 1001 events in coal and 4875 events in sandstone. The shadow areas indicate time intervals from 790 to 1100 s and from 1460 to 1635 s.

Figure 2

(a) Log-log histogram of energy distributions and (b) ML analysis of the power-law exponent as a function as a moving threshold for sandwiches of sandstone and coal. Setup A indicates lower-stress measurements and Setup B indicates higher-stress measurements.

Figure 3

ML analysis of the power-law exponent as a function of a moving threshold for coal samples. Setup A indicates lower-stress measurements and Setup B indicates higher-stress measurements.

Figure 4

ML analysis of the power-law exponent as a function of a moving threshold for sandstone samples. The plateau is not flat but shows a slope indicating a possible exponential cutoff to the power-law distribution [46]. Setup A indicates lower-stress measurements and Setup B indicates higher-stress measurements.

Figure 5

(a) Complete sequence of energies of AE signals recorded during collapsing of sandstone (blue circles) and coal (red circles) in interval 1 [see Fig. 1]. (b),(c) Enlarged views. “Events pairs” are indicated by the dashed ellipse. The time intervals for each event pair correspond to the transmission time from the source in sandstone to the detector attached to coal. (d)–(f) AE hit energy sequences in interval 2 [see Fig. 1]. Here the coal collapse dominates. Event pairs are equally common in intervals where coal appears as the AE generating medium and subsequent, delayed AE signals appear in sandstone.

Figure 6

(a) Two-layer arrangement with coal as the upper layer and sandstone as the lower level. Acoustic waves travel between the layers. The delay time is given by the travel time between the two layers. The delay time is defined as $\mathrm{\Delta }t$. (b) Bath's law for event in the same and mixed media. Most magnitudes approach values between 1 and 1.2 for large main shocks. Only main shocks in sandstone generate aftershocks in coal with a relative magnitude approaching 3. (c) Delay time for main shocks and their largest aftershocks.

Figure 7

Probability distribution functions of the interevent time ratio $R$ for two event regimes and S, C, and “events pair.” AE data in sandstone and coal are shown in blue and red. Black circles indicate pair events. The insets show an enlarged view near the origin with strong indication for delay mechanisms for short-time ratios.