Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback


Journal Article

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. © 2008 Society for Industrial and Applied Mathematics.

Full Text

Duke Authors

Cited Authors

  • Schaeffer, DG; Iverson, RM

Published Date

  • December 1, 2008

Published In

Volume / Issue

  • 69 / 3

Start / End Page

  • 769 - 786

International Standard Serial Number (ISSN)

  • 0036-1399

Digital Object Identifier (DOI)

  • 10.1137/07070704X

Citation Source

  • Scopus