APPLICATION OF CHAOS THEORY TO DIFFERENT MIXED SLOPE GEOMETRIES

Abstract

Mass movements are natural phenomena that frequently occur on slopes, especially in mountainous and densely populated regions, exhibiting destructive behaviors, with the loss of life and destruction of material goods. Therefore, the in-depth study of slope stability is extremely important in geotechnical engineering. The intricate nature of these phenomena makes it extremely difficult to predict them and to apply conventional models and analyses. The Mathematical Chaos Theory emerges as a promising tool to understand the supposedly unpredictable and sometimes illogical behavior of certain physical phenomena, characterized by the interaction of many agents, in a cooperative process, in which the behavior of the whole is not reduced to that of its constituent parts. This leads to marked nonlinearities and sensitivity to initial conditions, which makes the search for (closed) mathematical analytical solutions difficult, if not impossible. This work aims to deepen the application of Chaos Theory to mass movements on rock slopes of mixed surfaces (concave and convex), aiming at the analysis of the stability and fall of blocks of irregular geometry, their dynamic evolution, sensitivity to initial conditions, among other related aspects, in the wake of the research inaugurated by Ignácio (2019). The results of this research showed that the relative arrangement of the concave and convex regions in the constitution of the profile of natural slopes has a marked influence on the response of the rock blocks located downhill. In more detail, convex regions close to the release of the blocks (top of the slope) give rise to evolution dynamics adequately described by non-Gaussian statistics (extended q-exponentials). On the other hand, in the situation where those convex regions are closer to the base level of the natural slopes, their dynamics are more appropriately described by a statistical distribution constituted by the linear combination of the Gaussian and extended q-exponential distributions.