A constitutive equation for mass-movement behavior

A phenomenological constitutive equation can serve as a basis for modeling and classifying mass-movement processes. The equation is derived using the principles of continuum mechanics and several simplifying assumptions about mass-movement behavior. These assumptions represent idealizations of field behavior, but they appear highly justifiable in light of the geomorphological insight that can be gained through modeling application of a mathematically tractable constitutive equation. The equation represents coupled pressure-dependent plastic yield and nonlinear viscous flow deformation components. The plastic yield component is a generalization of the Coulomb criterion to three-dimensional stress states, and the effect of pore-water pressures is accounted for by treating normal stresses as effective stresses. The nonlinear viscous flow component is a dimensionally homogeneous form of a three-dimensional power-law equation. Straightforward laboratory and field experiments can be used to estimate all plastic and viscous parameters in the constitutive equation. Reduction of the three-dimensional constitutive equation to two-and one-dimensional forms shows that it embodies, as special cases, many other constitutive models for mass movement. These include models of creeping, slumping, sliding, and flowing types of deformation. The equation may, therefore, serve as a conceptual basis for rheological classification of diverse mass-movement phenomena.