A quasi-static inertia number taking soil compaction into account is proposed, specifically, from the perspective of granular physics. In analyzing classical triaxial test data of soil, the scaling law of quasi-statically deforming grains at the critical state is explored; a simple linear relationship is found between the coefficient of friction and the quasi-static inertia number. The proposed scaling law describes quantitatively the influence of initial compaction, shear rate, confining pressure, and particle size on the frictional strength of granular soils when they reach the critical state. The quasi-static inertia number proposed is employed to describe the scaling of volumetric behavior of granular soils undergoing quasi-static deformation. The difference between the particle volume fraction at the critical state and that at the initial compacted state is also found to be linearly correlated with the quasi-static inertia number, for soil at the critical state.
 

granular material,soil,dynamics,critical state