Arching in confined dry granular materials

We discuss a simple model that applies to a random array of arbitrarily sha ped 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 dis crete and a continuum analysis. We find a qualitative agreement, with Janss en's phenomenological result for arching. The saturating pressure grows wit h N-2, where N is the horizontal size of the system. Adjusting our numerica l results to Janssen's model we find a relaxation depth that also grows wit h N-2. The results of the average behavior allow us to measure fluctuations ; the relative fluctuation of the pressure goes to zero as N-1/2 The contin uum 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.