New Gradation Equation and Applicability for Particle-Size Distributions of Various Soils

A new gradation equation that can describe the particle-size distribution curves of soils with continuous gradation is presented. The results obtained for a large amount of test data from soil gradations prove that the equation is applicable over a wide range of soils, including rockfill, gravel, sand, and clay. Three parameter determination methods are proposed, with the optimization method yielding the best results. The possible values of the parameters m and b in the proposed equation were intensively investigated, and the suggested ranges of the parameters were found to be b<1 and m>0. However, for most soils, these parameters have values of -4<b<1 and 0<m<12. The study of the features of the gradation equation and the resulting curves in P-logd coordinates revealed that the parameter b determines the gradation curve shape. If b 0.5, the gradation curve is hyperbolic, and if 0.5<b<1, the curve is sigmoidal. The parameter m determines the gradation curve slope, which increases with increasing m. Several soil gradations used in earth-rockfill dams worldwide were investigated to summarize the gradation characteristics, and the results revealed that the values of the parameters b and m for the rockfill fall within a narrow range. The proposed equation is more convenient for expressing the soil gradation and makes it possible to quantitatively describe the relationship between the mechanical properties of the rockfill and the gradation.