Richard M. Iverson David G. Schaeffer 2008 <p><span>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,&nbsp;</span><i>unlike stick-slip behavior in classical models</i><span>, 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.</span><br><br></p> application/pdf 10.1137/07070704X en SIAM Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback article