Modeling of Compressible Self-Organized Granular Media under Static Load

摘要

A simple continual model of granular medium, based on original hypotheses, is built. It describes the matter under active quasi-static compression with taking into account the effects of both compaction and self-organization. The analysis of the hypotheses has given the model's constitutive relations. Thus, an exponential dependence for the porosity from the average stress and a linear relationship between the principal stresses are set. The analysis of the constitutive relations at the same time has given need for existence of two new constants. One of them characterizes particular material's compliance to compaction, its value should be determined from experiment. The other new constant is a macroscopic characteristic of the matter's mesoscopic state, its range of values has been determined and ensures for the internal consistency of the model as well as the accord with the mechanics general laws. Such applied questions as compacting granular media under their own weight and the Lamé problem for them are solved in the elementary functions. The proposed Lamé problem's solution eliminates singularity at the origin. The derived theoretical predictions are in good agreement with available experimental data. The latter include data on a natural carbonates deposit at depth up to 5.5 km, snow drifts at depth up to 10 m, and nano-sized powders in capsules of 10 mm radius under the GPa order pressure.