Nonlinear Evolutionary Mechanisms of Instability of Plane-Shear Slope: Catastrophe, Bifurcation, Chaos and Physical Prediction

A cusp catastrophe model is presented and the necessary and sufficient conditions leading to landslides are discussed. The sliding surface is assumed to be planar and is a combination of two media: medium 1 is elastic-brittle or strain-hardening and medium 2 is strain-softening. The shear stress-strain constitutive model for the strain-softening medium is described by the Weibull’s distribution law. This paper is a generalization and extension of the paper by Qin et al. (2001b), in which the shear stress-strain constitutive model for medium 2 was described by a negative exponent distribution; a special case of the Weibull’s distribution law. It is found that the instability of the slope relies mainly on both the stiffness ratio of the media and the homogeneity index and that a new role of water is to enlarge the material homogeneity or brittleness and hence to reduce the stiffness ratio. A nonlinear dynamic model (also called a physical forecasting model), which is derived by considering the time-dependent behavior of the strain-softening medium, is used to study the time prediction of landslides. An algorithm of inversion on the nonlinear dynamic model is suggested for seeking the precursory abnormality and abstracting mechanical parameters from the observed series of a landslide. A case study of the Jimingsi landslide is analysed and its nonlinear dynamic model is established from the observation series of this landslide using the suggested model and the algorithm of inversion. It is found that the catastrophic characteristic index jDj shows a quick rise till reaching an extremely high peak value after the slope evolves into the tertiary creep, and subsequently approaches a zero value prior to instability, which can be regarded as an important precursory abnormality index. By taking into account the evolutionary characteristic of the slope being in the secondary creep, a simplified nonlinear dynamic model is proposed for studying the properties of bifurcation and chaos. It is shown that the emergence of chaos depends on the mechanical parameters of the sliding-surface media.