Onset of natural terrain landslides modelled by linear stability analysis of creeping slopes with a two-state variable friction law
✍ Scribed by Chau, K. T.
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 204 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0363-9061
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✦ Synopsis
This paper further examines the possibility of modelling landslide as a consequence of the unstable slip in a steadily creeping slope when it is subject to perturbations, such as those induced by rainfall and earthquakes. In particular, the one-state variable friction law used in the landslide analysis by Chau is extended to a two-state variable friction law. According to this state variable friction law, the shear strength ( ) along the slip surface depends on the creeping velocity (<) as well as the two state variables ( and ), which evolve with the ongoing slip. For translational slides, a system of three coupled non-linear "rst-order ordinary di!erential equations is formulated, and a linear stability analysis is applied to study the stability in the neighbourhood of the equilibrium solution of the system. By employing the stability classi"cation of Reyn for three-dimensional space, it is found that equilibrium state (or critical point) of a slope may change from a &stable spiral' to a &saddle spiral with unstable plane focus' through a transitional state called &converging vortex spiral' (i.e. bifurcation occurs), as the non-linear parameters of the slip surface evolve with its environmental changes (such as those induced by rainfall or human activities). If the one-state variable friction law is used in landslide modelling, velocity strengthening (i.e. d /d<'0, where is the steadystate shear stress) in the laboratory always implies the stability of a creeping slope containing the same slip surface under gravitational pull. This conclusion, however, does not apply if a two-state variable friction law is employed to model the sliding along the slip surface. In particular, neither the region of stable creeping slopes in the non-linear parameter space can be inferred by that of velocity strengthening, nor the unstable region by that of velocity weakening.