Gradation equation and compaction characteristics of continuously distributed coarse-grained soil

Based on the growth curve proposed by Morgan et al., a two-parameter gradation equation that can reflect the "upward convex" and "S-shaped" particle distributions of coarse-grained soil is proposed. When the shape parameter a goes to infinity, the gradation formula is transformed into a fractal distribution equation. On this basis, a method for determining the optimal compaction performance gradation by using the relative density test method is proposed. The suggested gradation equation has good applicability to the filling gradation of high-rockfill dams in Changheba, Dashixia and Lianghekou. Using these research results, the indoor relative density tests on Dashixia gravel material are conducted. The results show that: (1) For the coarse aggregates with gradation of d_max=60 mm and different distribution laws, with change of gradation parameters, the maximum and minimum dry densities both have extreme points or inflection points, and the corresponding critical P5 values are approximately 35% and remain basically unchanged. (2) The critical P5 value corresponds to the excellent compaction performance gradation. The test value of dry density obtained by the fractal distribution gradation is the largest. When the particle gradation is close to the fractal distribution, the compaction performance is satisfactory, and the critical P5 value corresponding to the fractal distribution gradation is the optimal compaction performance gradation. The rockfill of Changehe dam with fractal distribution has a higher filling density under the lower field compaction parameters, which proves the rationality of this conclusion. (3) According to the scale independence of the critical fractal dimension, the research results of the indoor optimal compaction performance can be conveniently extended to different maximum particle size gradations on site. The conclusion can be used for the gradation design and compaction performance evaluation of coarse-grained soil.