A ruptura em taludes como um fenômeno crítico auto-organizado

Abstract

This research aimed to show that slope instability can be considered as a self-organized critical phenomenon. In more detail, the time series of horizontal displacements of a set of points chosen close to and far from the slope instability region, in the analysis domain, invariably presented a power law evolution, exponents, in their majority, with similar values, and correlation coefficients very close to unity. This suggests the existence of a functional universality of the power law expression, relating to horizontal displacements close to failure, which would occur regardless of the geometry of the slope considered, the parameters adopted for the materials under analysis and the location of the points studied. On the other hand, the intrinsic time, which governs the phenomenon of slope failure, is not the usual time t, but that related to the slope failure time and the exponent of the power law mentioned above, and that studying this phenomenon for the time t usual is inaccurate. This made it possible to adopt a correct temporal measurement of this instability phenomenon, which translated into time series of horizontal displacements with very simple characteristics – inclined straight lines. The research also determined the largest effective Lyapunov exponents for each of the monitored points. The results showed an asymptotic tendency towards the null value of those exponents according to a power law with time, regardless of the selected points being subjected to different states of stress, deformation and displacement in the analysis domain.