On the similarity of shear deformation of a granular massif and a fragmented medium in the seismically active area

Abstract

In recent research, the dynamics of the medium located in the seismic region at the boundary of tectonic plates is considered as the behavior of a complex open system that is in a state of self-organized criticality. Such an approach results from the very laws of earthquake generation and the complex structure of these areas. The network of faults and cracks makes seismic zones significantly heterogeneous and fragmented. Therefore, discrete models are increasingly used to model the dynamics of these media. The basis for comparing the model and the full-scale object serves the statistical regularities of their dynamic deformation. Relying on this concept, in the paper it is modeled the shear dynamics of a granular massif composed of identical cubic granules and is compared system’s statistical characteristics with the similar characteristics obtained for the earthquake generation zone. Shear deformation is carried out by means of the box consisting of two parts — movable and immovable ones. The movable part possesses the cover which receives kinetic energy from the granular massif in the process of shear deformation. For numerical simulations of the shear dynamics, the discrete element method is applied. The numerical calculations result in the distribution of cover’s kinetic energy jumps simulating the perturbations transmitted from the granular system to an external medium. It turned out that the distribution for these perturbations is the power dependence with an exponent that is inherent in earthquakes (Gutenberg-Richter law). Before and after large perturbations it is observed the swarms of smaller perturbations which are the analogues of foreshocks and aftershocks. The distributions of element’s velocity fluctuations and the correlation of velocity fluctuations are calculated as well. It is revealed the similarity of distributions for velocity fluctuations in the model massif and in the seismically active region of California, which includes the San Andreas fault. Moreover, the similarity of corresponding correlation functions is shown. They both are the functions of the stretched exponent. The obtained result indicates that shear processes in granular massifs and natural seismic processes in the San Andreas Fault are statistically similar.