Despite the landslides and, in particular, rock slides are well investigated and classified, several aspects are still not clear. For example, in spite of self-stabilizing nature of rotational slides there are several cases where these landslides occurred with extreme speed. Given these observational data which expose significant potential for environmental damage, we developed a new analytical model which incorporates post-failure strain-softening into elasto-plastic and visco-ferma rheology for the gouge shear layer. The strain-softening behavior itself is necessary but not sufficient for the transition from smooth creeping movement to the rapid "slide-quake" rock avalanche. The model shows that despite gravitational self-stabilization of rotational landslide, the rapid slide instability is possible, and provides condition for initiation of rapid slide. A precursor of rapid slide is formulated for the strain rate as a function of increasing gravitational load (either due to precipitation or additional debris load). In a simple case of linear dependence of the load as a function of time, the strain-rate increases as a power function of temporal proximity τ = 1/(tc -t)1/2 while approaching the time of rapid slide, tc,. The model, presented in this paper, is developed predominantly for the case of rotational instability (or rotational slump) but the strain vs. time precursor is valid for translational instabilities as well. The developed approach is sufficiently general, and as an example, is applied to a physically similar case of fault gouge instability caused by fluid injection.

1. Introduction

Landslides and faults instabilities pose a significant environmental hazard. Most landslides and tectonic faults shear within a shear zone or gouge, which consists of clay and granular material (Schulz et al, 2018). The system of displacements inside the shear zone is generally quite non-homogeneous. There is a high number of degrees of freedom for local displacements in the shear zone. However, the landslide instability is characterized by collective, long-range-correlated slip, when different parts of the shear zone are shifting in concert. It brings a hopeful consideration that there is a single dominant collective mode, responsible for the transition from the slow creep to rapid slide, similarly to long-range correlations near phase transitions in statistical systems.

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