Improved mathematical models for particle-size distribution data representation of tropical weathered residual soils

Abstract

There is a need for accurate and cost-effective methods to estimate unsaturated soil property functions. Prior studies have suggested that particle-size distribution data of soils is central and helpful in this regard. This study proposes two improved mathematical models to describe and represent the varied particle-size distribution (PSD) data for tropically weathered residual (TWR) soils. The theoretical analysis and the comparative study of four existing models have indicated that they demand further improvement to handle the PSD of TWR soils. In particular the fixing of curve fitting parameters to the existing models M. Fredlund (2009) [19] result in a wide scatter of the parameters though the impact on the shape of the PSD curve is not significantly visible.

Aiming to improve the existing models, this study, thus proposes unimodal and bimodal models capable of fitting the PSD data of TWR soils more accurately. The new unimodal and bimodal curve fitting models are shown to give an extremely good fit to unimodal and bimodal data. Compared with the other models studied, the new models show a better fit to the soil data analyzed and are highly efficient. The fitting statistics and the range of the optimized parameters are significantly improved. Furthermore, the models developed in this study are of a more general nature and appear to be applicable to a larger range of soil types than those previously published. The newly proposed models greatly simplify and provide reliable PSD data that may be used in physical based prediction of unsaturated soil property functions.

Keywords: Unimodal, Bimodal, Nonlinear Optimization, Curve Fitting