Granular materials exhibit a complex plastic behavior which can be observed under non-radial loading (Mehrabadi et al. 1982, Hicher 2000, Sun and Sundaresan 2011). For example, starting with a steady quasi-static flow, a long transient occurs when the direction of loading is changed. During such a transient, the packing fraction increases whereas the shear strength declines, but they both retrieve their steadystate values in the new direction after a sufficiently long shearing. In response to low-amplitude cyclic shearing, the packing fraction continues to increase, and hence the system is irreversibly driven away from the steady state (Garcia-Rojo et al. 2005).While such intricate flow properties can in principle be traced back to the frictional contact interactions of the particles and their displacements, proposing a theoretical model thoroughly based on the particle-scale dynamics and granular texture remains a challenging issue.