Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback
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Abstract
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.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback |
| Series title | SIAM Journal on Applied Mathematics |
| DOI | 10.1137/07070704X |
| Volume | 69 |
| Issue | 3 |
| Year Published | 2008 |
| Language | English |
| Publisher | SIAM |
| Contributing office(s) | Volcano Hazards Program, Volcano Science Center |
| Description | 18 p. |
| First page | 769 |
| Last page | 786 |
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