Nonlocal approach to the analysis of the stress distribution in granular systems. I. Theoretical framework

A theoretical framework for the analysis of the stress distribution in granular materials is presented. It makes use of a transformation of the vertical spatial coordinate into a formal time variable and the subsequent study of a generally non-Markoffian, i.e., memory-possessing (nonlocal) propagation equation. Previous treatments are obtained as particular cases corresponding to, respectively, wavelike and diffusive limits of the general evolution. Calculations are presented for stress propagation in bounded and unbounded media. They can be used to obtain desired features such as a prescribed stress distribution within the compact.