Proportional paths, Barodesy, and granular solid hydrodynamics

Proportional paths as summed up by the Goldscheider Rule (GR)-stating that given a constant strain rate, the evolution of the stress maintains the ratios of its components-is a characteristics of elasto-plastic motion in granular media. Barodesy, a constitutive relation proposed recently by Kolymbas, is a model that, with GR as input, successfully accounts for data from soil mechanical experiments. Granular solid hydrodynamics (GSH), a theory derived from general principles of physics and two assumptions about the basic behavior of granular media, is constructed to qualitatively account for a wide range of observation - from elastic waves over elasto-plastic deformation to rapid dense flow. In this paper, showing the close resemblance of results from Barodesy and GSH, we further validate GSH and provide an understanding for GR.