STEADY AND INTERMITTENT SLIPPING IN A MODEL OF LANDSLIDE MOTION REGULATED BY PORE-PRESSURE FEEDBACK

This paper studies a parsimonious model of landslide motion, which consists of the one-dimensional diffusion equation ( for pore pressure) coupled through a boundary condition to a first-order ODE ( Newton's second law). Velocity weakening of sliding friction gives rise to nonlinearity in the model. Analysis shows that solutions of the model equations exhibit a subcritical Hopf bifurcation in which stable, steady sliding can transition to cyclical, stick-slip motion. Numerical computations confirm the analytical predictions of the parameter values at which bifurcation occurs. The existence of stick-slip behavior in part of the parameter space is particularly noteworthy because, unlike stick-slip behavior in classical models, here it arises in the absence of a reversible (elastic) driving force. Instead, the driving force is static ( gravitational), mediated by the effects of pore-pressure diffusion on frictional resistance.