Analogy to the chaos theory applied to the study of rockfalls

Abstract

Chaos Theory is a mathematical theory devoted to study dynamic systems presenting very peculiar characteristics -sensitivity to initial conditions, positive or close to zero Lyapunov exponents, statistics governed by gaussian or non-gaussian distributions, among otherswhich make them, in the long run, unpredictable in time and space. This article aims at applying Chaos Theory to rockfall phenomenon. More precisely, the fall of unstable rock blocks was simulated through the RocFall 6.0 program by four preliminary case studies, having different rock slope geometry, different heights of the fall and blocks with different size and shapes. Moreover, the trajectories and reaches of gneissic rock blocks in a section of a phacoidal augen gneiss slope located in Morro do Cantagalo, in the city of Rio de Janeiro, were also simulated from the perspective of Chaos Theory. More precisely, the results suggest that the statistics of the number of fallen blocks at each end point of the trajectories located downstream of the respective slopes can be described by distributions derived from Chaos Theory. In addition, weakly or strongly chaotic behavior seems to be very specially associated with the concavity or convexity of the slopes.