Aplicação da Teoria do Caos a diferentes geometrias de taludes mistos

Abstract

Mass movements are natural phenomena that frequently occur on slopes, especially in mountainous and densely populated regions, exhibiting destructive behaviour, with loss of life and destruction of materials. Therefore, the in-depth study of slope stability in geotechnical materials is extremely important in geotechnical engineering. The intricate nature of these phenomena makes it extremely difficult to predict and apply conventional models and analyses. The Mathematical Theory of Chaos has emerged as a promising tool for understanding the supposedly unpredictable and sometimes illogical behaviour of certain physical phenomena, characterized by the interaction of many agents in a cooperative process in which the behaviour of the whole is not reduced to that of its constituent parts. This leads to pronounced non-linearities and sensitivity to initial conditions, which makes the search for analytical (closed) mathematical solutions difficult, if not impossible. This work aims to deepen the application of Chaos Theory to mass movements on rocky slopes with mixed surfaces (concave and convex), with the aim of analyzing the stability and fall of irregular geometry blocks, 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 concave and convex regions in the constitution of the profile of natural slopes has a marked influence on the response of rock blocks located downhill. In more detail, convex regions close to where the blocks are launched (top of the slope) give rise to evolution dynamics that are 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 consisting of a linear combination of the Gaussian and extended q-exponential distributions.