Nonlinear Evolutionary Mechanisms of Instability of Plane-Shear Slope: Catastrophe, Bifurcation, Chaos and Physical Prediction |
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Authors: | S Q Qin J J Jiao Z G Li |
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Institution: | (1) Engineering Geology and Applied Geophysics Department, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, P.R. China;(2) Department of Earth Sciences, The University of Hong Kong, Hong Kong, P.R. China |
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Abstract: | Summary. 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 |D| 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. |
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Keywords: | : Cusp catastrophe instability stiffness ratio homogeneity index chaos physical prediction |
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