Arching in confined dry granular materials
Departamento de Física, Facultad de Ciencias, UNAM - 04510 México, D. F., Mexico
2 Centro de Investigación en Energía, UNAM - 62580 Temixco, Mor., Mexico
Accepted: 28 October 1998
We discuss a simple model that applies to a random array of arbitrarily shaped grains, contained between rigid vertical walls, that predicts arching. That is, the pressure (or weight) of the column of grains saturates as its height increases. The average behavior of the model is solved through a discrete and a continuum analysis. We find a qualitative agreement with Janssen's phenomenological result for arching. The saturating pressure grows with N2, where N is the horizontal size of the system. Adjusting our numerical results to Janssen's model we find a relaxation depth that also grows with N2. The results of the average behavior allow us to measure fluctuations; the relative fluctuation of the pressure goes to zero as . The continuum analysis shows that the weight inside the column satisfies a diffusion equation with a source term and particular boundary conditions which leads to a complete solution. The first-order approximation is similar to Janssen's result.
PACS: 83.70.Fn – Granular solids / 46.10.+z – Mechanics of discrete systems / 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion
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