Scaling laws for quasi-statically deforming granular soil at critical state

To enhance our understanding of soil behavior at critical states, considering that natural soil is composed of granular matter, a quasi-static inertia number taking soil compaction into account is proposed. 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 proposed number. This 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 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. Graphic abstract