MODEL OF GEOMEDIA CONTAINING DEFECTS: COLLECTIVE EFFECTS OF DEFECTS EVOLUTION DURING FORMATION OF POTENTIAL EARTHQUAKE FOCI - I. A. Panteleev; O. A. Plekhov; O. B. Naimark (Геодинамика и тектонофизика, 2015)
This paper describes the statistical thermo-dynamical evolution of an ensemble of defects in the geomedium in the field of externally applied stresses. The authors introduce ‘tensor structural’ variables associated with two specific types of defects, fractures and localized shear faults (Fig. 1). Based on the procedure for averaging of the structural variables by statistical ensembles of defects, a self-consistency equation is developed; it determines the dependence of the macroscopic tensor of defects-induced strain on values of external stresses, the original pattern and interaction of defects. In the dimensionless case, the equation contains only the parameter of structural scaling, i.e. the ratio of specific structural scales, including the size of defects and an average distance between the defects.The self-consistency equation yields three typical responds of the geomedium containing defects to the increasing external stress (Fig. 2). The responses are determined from values of the structural scaling parameter. The concept of non-equilibrium free energy for a medium containing defects, given similar to the Ginzburg-Landau decomposition, allowed to construct evolutionary equations for the introduced parameters of order (deformation due to defects, and the structural scaling parameter) and to explore their solutions (Fig. 3).It is shown that the first response corresponds to stable quasi-plastic deformation of the geomedium, which occurs in regularly located areas characterized by the absence of collective orientation effects. Reducing the structural scaling parameter leads to the second response characterized by the occurrence of an area of meta-stability in the behavior of the medium containing defects, when, at a certain critical stress, the orientation transition takes place in the ensemble of interacting defects, which is accompanied by an abrupt increase of deformation (Fig. 2). Under the given observation/averaging scale, this transition is manifested by localized cataclastic deformation (i.e. a set of weak earthquakes), which migrates in space at a velocity several orders of magnitude lower than the speed of sound, as a ‘slow’ deformation wave (Fig. 3). Further reduction of the structural scaling parameter leads to degeneracy of the orientation meta-stability and formation of localized dissipative defect structures in the medium. Once the critical stress is reached, such structures develop in the blow-up regime, i.e. the mode of avalanche-unstable growth of defects in the localized area that is shrinking eventually. At the scale of observation, this process is manifested as brittle fracturing that causes formation of a deformation zone, which size is proportional to the scale of observation, and corresponds to occurrence of a strong earthquake.On the basis of the proposed model showing the behavior of the geomedium containing defects in the field of external stresses, it is possible to describe main ways of stress relaxation in the rock massives – brittle large-scale destruction and cataclastic deformation as consequences of the collective behavior of defects, which is determined by the structural scaling parameter.Results of this study may prove useful for estimation of critical stresses and assessment of the geomedium status in seismically active regions and be viewed as model representations of the physical hypothesis about the uniform nature of development of discontinuities/defects in a wide range of spatial scales.