A Nonlinear Catastrophe Model of Instability of Planar-slip Slope and Chaotic Dynamical Mechanisms of Its Evolutionary Process

This paper presents a nonlinear cusp catastrophe model of landslides and discusses the conditions leading to rapid-moving and slow-moving landslides. It is assumed that the sliding surface of the landslides is planar and is a combination of two media: one is elasto-brittle and the other is strain-softening. It is found that the instability of the slope relies mainly on the ratio of the sti€ness of the elasto-brittle medium to the sti€ness at the turning point of the con-stitutive curve of the strain-softening medium. A nonlinear dynamical model, which is derived by analyzing the catastrophe model and considering external environmental factors, is used to reveal the complicated mechanisms of the evolutionary process of the slope under environmental in¯uence and to explore the condition of the occurrence of chaos and the route leading to chaos. The present analysis shows that, when the nonlinear role of the slope itself is equivalent to the environmental response capability, a chaotic phenomenon can occur and the route leading to chaos is realized by bifurcation of period-doublings.