The Wedge-shaped And Conical Particles Heap Stress Depression Study

Macroscopic mechanical behavior of granular material is more complex than the our familiar Newtonian fluid and solid Hook, of which the nonlinear extent, the type and intensity of dissipation mechanisms, uncertainty of boundary conditions, are all far more complex than the latter. Even for a simple sandpile, how to analysis its stress distribution of is yet an unsolved question up to now.There are mainly two trains of thoughts on the calculation of the stress distribution in the static granular material. One is disposed to believe the granular material is essentially indeterminacy, so there is no a universal theory can be used for the stress distribution analysis. But for a particular geometry, like a sandpile on a table, a constitutive relation (or stress-relation) between different components of the stress tensor exist. The constitutive relation is not a universal theory equation, of which the expression is not only related with the geometry of the sample in considering, but also related with the prepared history of the sandpile. The other thought of solving the stress problem is regarding the static granular material as elastic rigid material, so once the boundary condition is given, the stress distribution in it is fixed and the stress can be calculated from a suitable elastic energy using the typical method of the elastic theory. It means that, in the elastic theory framework, we can get a series of general complete equations for granular material of arbitrary geometry and preparation history, meanwhile the constitutive relation in different condition is just the approximate particular solution of this group of equations.Several stress-relation models have been suggested in physical literature, including the famous fixed principle axe model and recently proposed tangential stress model. By calculating the degree of they compliance with the elastic equations, a quantitative study of the relation between the stress-relation and elastic approach is carried, and on this basis, we compare and discuss the rationality degree of these stress-relations. The result shows that a good agreement between the models and elastic theory can be seen well inside the pile, while remarkable deviation occurs as free boundary of pile side is approached. The deviation can be however improved by decreasing strength of tangential stress near the boundary. In addition, a qualitative study using the tangential stress model is carried for examing the link between the spatial similarity of stress (or the Radical Stress Field scaling short for RSF scaling) and the "pressure dip" under a sandpile. The result shows that the RSF scaling is associated with dip observed in distribution of normal stress: when the "up" of the shear stress intensity is greater than "lower" to a larger degree, the more notable of dip appear.