Unsteady, nonuniform landslide motion: 2. Linearized theory and the kinematics of transient response

Unsteady, nonuniform landslide motion is caused by temporal and spatial variations in driving and resisting forces. Common sources of these variations include stream undercutting of landslide toes, episodic headscarp slumping, and ground-water potentiometric fluctuations. A linear theory for the kinematics of unsteady, nonuniform landslide motion is developed here by analyzing the behavior of small perturbations about a datum state of steady landslide shear flow. The analysis indicates that local perturbations in landslide sediment flux exhibit advective-diffusive behavior that is controlled largely by a single dimensionless parameter, here called the landslide Peclet number. Explication of the physical meaning of this parameter shows that motion of landslide sediment-flux perturbations is dominated by slow advection if the landslide material behavior is primarily viscous and by rapid diffusion if the behavior is more rigidly plastic. Landslides that deform along thin plastic slip zones are thus inferred to respond relatively rapidly and globally to transient perturbations. Landslides that deform in thick zones of creeping flow, in contrast, are inferred to respond over periods as long as many tens of years, with zones of perturbed sediment flux that translate downslope as weakly diffusive kinematic waves. Many landslides probably fall between these two extremes in their style of response. The measured response of a large California landslide to transient toe undercutting by an adjacent stream helps corroborate the theoretical results.