ON THE INFLUENCE OF VISCOSITY ON THE DEVELOPMENT OF INSTABILITY IN ANOMALOUSLY STRATIFIED GEOSYSTEMS

Abstract

The paper investigates the question of the influence of viscosity on the rate of development of instability in heavy viscoelastic geosystems with an anomalous density distribution over depth. Geomaterials are considered as incompressible, and the Maxwell model of viscoelasticity (that makes it possible to adequately describe the dynamics of geosystems even in the case of huge viscosity of geomaterials) is adopted for them. Along with viscoelastic systems, the elastic comparison systems are considered, which are characterized by the same anomalous stratification and the same values of shear stiffnesses as the viscoelastic systems studied. Bilateral estimates for the increment of growth of the fastest mode of loss of stability (the “main increment of growth”) are obtained, which are valid for any viscosity. It has been found that the main growth increment always exceeds the main growth increment for the unstable elastic comparison system, which is determined by the inertial properties of the latter together with the degree of supercriticality of the parameters characterizing its unstable equilibrium state. As viscosity increases, the main growth increment for the viscoelastic system tends from above to the corresponding increment for the unstable elastic comparison system. In the case of stability of elastic comparison systems, the corresponding viscoelastic systems are unstable, but the rate of development of their instability is very low due to the great viscosity of geomaterials. Precisely and only in the case of stability of comparison systems, the viscosity slows down this rate, and for geosystems with extremely great viscosity, the manifestation of their instability during real observation times is very small. The analysis carried out confirms the fact that the study of stability and instability of elastic comparison systems can serve as a methodological basis for studying stability and instability of viscoelastic geosystems.