Simplified Relationships for Particle-Size Distribution and Permeation Groutability Limits for Soils

The particle-size distribution of soil with mean particle size and fines content are used not only in soil classifications but also in a number of other soil property relationships. In this study, two simple relationships (hyperbolic $\left[\text{tan}h\left(x\right)\right]$ and $S$ -curve) were investigated to represent the particle size distribution of soils. The parameters of the hyperbolic model were correlated to various soil parameters such as the mean particle size, particle size range, and fines content. There was no direct correlation between Fredlund (four-parameter model) and $S$ -curve model parameters and the soil parameters. The predictions of the two (hyperbolic) and three ( $S$ -curve) parameter models were compared to the four-parameter model (unimodal) using limited soil data from the literature and the agreements were good. The hyperbolic model was used to map the Unified Soil Classification System. A recent study had quantified the relationship between the grouting pressure and the fines content in nonplastic soils. Also in the current practice, upper and lower particle-size distribution limits are used in determining the groutability of soils. In this study, the relationship between grouting pressure and fines contents of the soil was generalized using the hyperbolic particle-size distribution model and verified with a groutability study using an acrylamide grout. Based on limited data in the literature, the groutability of soils was defined using a new set of parameters, grouting pressure, fines content, and mean particle size diameter of the soil.