  We propose a model to describe the quasistatic shearing of dry granular
materials, which notably captures the differences in velocity profiles recently
observed in 2 and 3-D Couette flow experiments. In our scheme, the steady-state
flow is due to the intermittent motion of particle clusters moving together
with the wall. The motion of a cluster is associated with the transient
formation of a fracture inside the sheared pack. The model is based on the
existence of a persistence length for the fractures, which imposes a
self-similar structure on the clusters. Through a probabilistic approach, we
can evaluate the rate of appearance of a cluster of a given size and obtain a
prediction for the average velocity profiles. We also predict the existence of
large stress fluctuations at the moving wall, which characteristics are in good
agreement with experimental data.
