An equation to represent grain-size distribution

Abstract

The grain-size distribution is commonly used for soil classification; however, there is also potential to use the grain-size distribution as a basis for estimating soil behaviour. For example, much emphasis has recently been placed on the estimation of the soil-water characteristic curve. Many methods proposed in the literature use the grain-size distribution as a starting point to estimate the soil-water characteristic curve. Two mathematical forms are presented to represent grain-size distribution curves, namely, a unimodal form and a bimodal form. The proposed equations provide methods for accurately representing uniform, well-graded soils, and gap-graded soils. The five-parameter unimodal equation provides a closer fit than previous two-parameter, log-normal equations used to fit uniform and well-graded soils. The unimodal equation also improves representation of the silt- and clay-sized portions of the grain-size distribution curve.Key words: grain-size distribution, sieve analysis, hydrometer analysis, soil classification, probability density function.

The best mathematical models describing particle size distribution of soils

“…Thus, it is concluded that accuracy of a model, doesn't always increase with over-parameterization. This result was different from Hwang (2004) one as well as Fredlund et al (2000), who reported that the performance of the Fredlund model would be All small letters are signs for significant difference at level 5 %. SD standard deviation, Ave average Fig.…”

“…So that, in Fig. 7, except sandy texture group, Fredlund model provided the best fitting ability in majority number of all soil samples and also, for loamy and clay texture groups, due to having further parameters than models that have fewer parameters such as lognormal likewise, the relative performance increased with increase of clay content (Fredlund et al 2000;Hwang 2004). Also, we can consider that Fredlund model is physical one.…”

“…In reality, the grain-size distribution is often nonsymmetric and can be better fit by a different type of equation. Second, a method for fitting soils that are bimodal or gap-graded is of value and the four parameter log-normal equations have not been found to be satisfactory for fitting these types of grain-size distribution (Fredlund et al 2000).…”

“…Modeling and mathematical explanation of PSD, in addition to above-mentioned issues, has some more benefits such: (a) classification of soils using the best fitting parameters, (b) facilitating the search for soils with similar characteristics in data bases (Fredlund et al 2000), (c) using for designing of drainage filters and (d) obtaining useful soil parameters such as effective diameter (d 10 ) and uniformity coefficient (Vipulanandan and Ozgurel 2009).…”

“…Soil PSD is often assumed log-normal (Campbell 1985;Shirazi and Boersma 1984), but, Buchan (1989) showed that in half part of soil texture triangular, hypothesis of being lognormal isn't valid, because, soil texture classes consist extensive range of particle size from \0.02 to 2 mm. Fredlund et al (2000) reported that main limitation of lognormal distribution model for PSD demonstration is its symmetry in logarithmic scale While, PSD of many soils don't show this symmetry.…”