The Longitudinal Stress and Strain-rate Gradients in Ice Masses

Abstract

AbstractThe fundamental equation for the longitudinal stress and strain-rate gradient For ice masses with small slope (Budd, (1968)) has been derived exactly for any slope by Nye (1969) who shows that by using a variable longitudinal axis inclination, parallel to the surface, this equation takes on its simplest form. However for the integration of this equation along the ice mass to obtain stress and strain-rates it is necessary to use a fixed axis direction. Here the equation is derived generally for a longitudinal axis of arbitrary inclination, from which the relation between the expressions for the fundamental equation with respect to any longitudinal axis inclination such as parallel to the surface, parallel to the base or horizontal is readily discerned.An expression for the longitudinal strain-rate is derived to obtain the flow law from longitudinal stress and strain-rate measurements. A single “generalized viscosity function” is introduced to avoid the complication of both the power flow-law parameters varying with stress.