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.

Particle breakage can be quite considerable even at low-stress levels, and it has a significant influence on the stress dilatancy of rockfill materials. In order to reasonably quantify the energy consumed by particle breakage, which has yet to be satisfactorily addressed, a function of friction ratio relating to the distortional strain and critical state stress ratio is proposed in this paper. The friction ratio references the widely accepted evolution rule of particle breakage and the new calculated energy consumption by particle breakage is proved to result in a reasonable distribution against increasing strain. Then, the rate of energy consumption per unit volume of aggregates is certified and suggested to be a linear relationship with the proposed friction ratio. Additionally, a stress dilatancy relationship for rockfill materials, based on modified Rowe's dilatancy law, is derived and verified by successfully predicting the stress dilatancy of drained rockfill triaxial specimens. It is believed to be an effective stress dilatancy for the study of elastoplastic constitutive model of rockfill materials.

The optimal gradation for coarse-grained soil used in earth-rockfill dams is an essential design index when determining the compactability of coarse-grained soil. With the optimal gradation, coarse-grained soil can be rolled to the maximum of dry densities among all gradations under the same compaction effort. Accordingly, this research introduced a gradation equation with the gradation parameters b and m and the maximum particle size d_max to establish a quantitative description of the gradation curve. From the results of the maximum dry density tests, the maximum dry density ρ_max is found to show a parabolic curve relationship with a parameter called gradation area S, which is defined as the area surrounded by the gradation curve. If the maximum particle size is a constant, the optimal gradation area, S₀, has the same value for coarse-grained soils with different shapes or different parent rocks, whereas S₀ linearly decreases with the increase in ln d_max. Furthermore, if d_max is known, the optimal gradation area S₀ can be evaluated by the proposed linear equation. Findings support a feasible method for designing the optimal gradation distribution in laboratory tests and in-situ.