Effect of the loading condition on the statistics of crackling noise accompanying the failure of porous rocks

We test the hypothesis that loading conditions affect the statistical features of crackling noise accompanying the failure of porous rocks by performing discrete element simulations of the tensile failure of numerical rock samples and comparing the results to those of compressive simulations of the same specimens. Cylindrical samples are constructed by sedimenting randomly sized spherical particles connected by beam elements representing the cementation of granules. Under a slowly increasing tensile load, the cohesive contacts between particles break in bursts whose size fluctuates over a broad range. Close to failure breaking avalanches are found to localize on a highly stressed region where the catastrophic avalanche starts and the specimen falls apart into two pieces along a spanning crack. The fracture plane has a random position and orientation falling most likely close to the center of the specimen perpendicular to the load direction. In spite of the strongly different strengths and spatial structure of damage of tensile and compressive failure of numerical rocks, our calculations revealed that the size, energy, and duration of crackling avalanches, and the waiting time between consecutive events all obey scale free statistics with power law exponents which agree within the error bars in the two loading cases.

Methods
The primary data files were obtained from our simulation program which generates the breaking process of numerical porous rock samples under slowly increasing elongation. The raw data obtained from discrete element simulations are further processed by a data evaluation program which identifies crackling avalanches, determines their characteristic quantities along with the probability distributions of the quantities of interest.  To further analyse the data we used two main freely available open source program packages:

the GLE Graphics program package was used to carry out the data analysis and the graphical representation of the numerical results. GLE is available under the link: https://glx.sourceforge.io/index.html

To generate snapshots of the simulations, the povray package was used which is available under the link: http://www.povray.org/