Criticality of the "critical state" of granular media: Dilatancy angle in the Tetris model

The dilatancy angle describes the propensity of a granular medium to dilate under an applied shear. Using a simple spin model (the Tetris model) which accounts for geometrical "frustration" effects, we study such a dilatancy angle as a function of density. An exact mapping can be drawn with a direct ed percolation process which proves that there exists a critical density rh o(c) above which the system expands and below which it contracts under shea r. When applied to packings constructed by a random deposition under gravit y, the dilatancy angle is shown to be strongly anisotropic, and it constitu tes an efficient tool to characterize the texture of the medium.