  We present a framework for analyzing the rheology of dense driven granular
materials, based on a recent proposal of a stress-based ensemble. In this
ensemble fluctuations in a granular system near jamming are controlled by a
temperature-like parameter, the angoricity, which is conjugate to the stress of
the system. In this paper, we develop a model for slowly driven granular
materials based on the stress ensemble and the idea of a landscape in stress
space. The idea of an activated process driven by the angoricity has been shown
by Behringer et al (2008) to describe the logarithmic strengthening of granular
materials. Just as in the Soft Glassy Rheology (SGR) picture, our model
represents the evolution of a small patch of granular material (a mesoscopic
region) in a stress-based trap landscape. The angoricity plays the role of the
fluctuation temperature in SGR. We determine (a) the constitutive equation, (b)
the yield stress, and (c) the distribution of stress dissipated during granular
shearing experiments, and compare these predictions to experiments of Hartley &
Behringer (2003).
