Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/14199
Title: Onset of natural terrain landslides modelled by linear stability analysis of creeping slopes with a two-state variable friction law
Authors: Chau, KT 
Keywords: Creeping slopes
Friction law
Natural terrain landslides
Stability analysis
Issue Date: 1999
Publisher: John Wiley & Sons
Source: International journal for numerical and analytical methods in geomechanics, 1999, v. 23, no. 15, p. 1835-1855 How to cite?
Journal: International journal for numerical and analytical methods in geomechanics 
Abstract: 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 (τ) along the slip surface depends on the creeping velocity (V) as well as the two state variables (θ1 and θ2), which evolve with the ongoing slip. For translational slides, a system of three coupled non-linear first-order ordinary differential 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 classification 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. dτ(ss)/dV > 0, where τ(ss) is the steady-state 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.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 (τ) along the slip surface depends on the creeping velocity (V) as well as the two state variables (θ1 and θ2), which evolve with the ongoing slip. For translational slides, a system of three coupled non-linear first-order ordinary differential 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 classification 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. dτss/dV>0, where τss is the steady-state 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.
URI: http://hdl.handle.net/10397/14199
ISSN: 0363-9061
EISSN: 1096-9853
DOI: 10.1002/(SICI)1096-9853(19991225)23:15<1835
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