Persistence of crack accumulation in rocks under load, and a concentration-based rock-failure criterion

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Current descriptions of the kinetics of crack (joint) accumulation during the failure process are based on Markovian kinetic equations, and the process is thus treated as a random process with independent increments. But until recently there had been no experimental test of the validity of this assumption, which was thus essentially unproven. The fractal approach has been coming into increasing use in the physics of failure. In this paper the authors attempt to construct a simple model of an intermittent random process of damage accumulation, characterized by an arbitrary Hurst index that in the limit H = 1/2 becomes a Poisson event stream with independent increments.

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The authors construct 3D probabilistic cellular automata to model accumulation of elementary damages and evolution of their cluster structure. Kinetic dependences of number of the clusters and evolution of time correlation functions are studied for the number of clusters and number of elementary damages. It is proved that intersection of the time autocorrelation function of a random process “number of impulses of emission” with the local minimum in the field of negative correlation can be interpreted as a sign of transition of a loaded material to a stage immediately preceding irreversible failure.
The behavior of the Hurst rescaled range during evolution of a system of elementary damages is investigated in simulation by the probabilistic cellular automation. It is established that the processes of the damage accumulation and the damage clustering evolution are the persistent random processes. The curves of the rescaled range statistics of the number of elementary damages have two marked linear segments, the second segment beginning at the times that are larger than 70% of the time of failure. It is possible to interpret this second segment appearance as a sign of the system transiting to the final stage of destruction.
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