Mechanical model of evolution of granular matter force chains

Granular models are key for understanding many phenomena in seismology, geophysics and geotechniques. Investigations of granular matters have shown that the scale of activated force chains decreases and a transition from solid-like behavior to liquid-like behavior occurs with the increase of shearing rate, and that at a low shearing rate viscosity is almost inversely proportional to maximal sliding velocity. At present, mechanical models describing the aforementioned behavior of granular matter are still lacking. Here we proposed a mechanical model of granular matter with internal length scale, reflecting the fact that the loading of granular matter is caused by shearing, and the stress relaxation is caused by shear band propagation. In combination with the constancy of shear band propagation speed, relationship between the length of activated force chains and shearing rate is obtained, the inverse proportionality of viscosity to shearing rate is interpreted, and the solid-to-liquid behavior transition shearing rate is predicted very well. This model can provide an effective approach to describe force chain evolution and the transition of granular matter from solid-like behavior to liquid-like behavior.