Unsteady, nonuniform landslide motion: 1. Theoretical dynamics and the steady datum state

Unsteady, nonuniform motion of persistently active landslides is a process of widespread importance. A general, three-dimensional theory aimed at elucidating this process is developed from physical principles and field measurements of landslide behavior. The theory employs a versatile constitutive model that represents landslides as deformable bodies composed of frictional, nonlinear viscoplastic material. The three-dimensional theory is reduced to a mathematically tracTable form by defining an ideal landslide datum state that consists of steady, unidirectional shear flow driven by ground-water seepage and gravitational forces. Solution of the datum-state equation of motion yields vertical landslide velocity profiles that can represent deformation styles ranging from shear-thickening viscoplastic flow to perfectly plastic frictional slip. This range of theoretical profiles encompasses the range of profiles measured in four persistently active northern California landslides. Also obtained from the datum-state equation of motion is an analytical solution for datum-state landslide sediment fluxes. An important feature of this solution is that it represents theoretical landslide sediment fluxes as a family of continuous-functions. The solution thus provides a mathematical basis for a general perturbation analysis of the kinematics of unsteady, nonuniform landslide motion, which will be presented in a companion paper in a subsequent issue of the Journal.