Abstract: The critical state theory of soil describes the correspondence between effective stress, shear strength, and soil density. Numerous soil mechanics experiments have also revealed a correlation between soil strength and loading rate. Considering that granular matter is the actual media of natural soil, this paper proposes a quasi-static inertia number, i.e., Q=Φ0(ln(I)+α), for granular soil considering particle volume fraction. Based on the classical triaxial test data of soil, the scaling law of quasi-static deforming sand in critical state from the perspective of granular physics is explored, a simple linear relationship i.e., μ=ξQ, is found between the friction coefficient and the quasi-static particle inertia number. The newly established scaling law can quantitatively describe the influence of volume fraction, shear rate, confining pressure, and particle size on the frictional properties of sand when reaching the critical state. In addition, to quantify the volumetric deformation law of sand under quasi-static shear, we obtain a correlation between the particle volume fraction Φ at the critical state and the quasi-static inertia number Q. In attempt to characterize the scaling law of the three-dimensional stress state, a new dimensionless number (i.e., the intermediate principal stress number) is defined in this paper to reveal the influence of intermediate principal stress on frictional properties. Thus, the scaling law is extended.