Developing conceptual and empirical models for well- and gap-graded soil particle size distribution (PSD) curve

ABSTRACT

Most of the previously introduced soil particle size distribution (PSD) models have at least one limitation. To overcome the limitations of the PSD models, two conceptual soil PSD models (unimodal- and bimodal-exponential), and one empirical model were suggested to represent PSD curve and evaluated based on the root mean square error (RMSE), adjusted coefficient of determination (R²_adjusted), coefficient of determination (R²), and corrected Akaike’s information criterion (AICc). The RMSE, R²_adjusted and AICc were 0.068, 0.969, and −29.6; 0.073, 0.955 and −3.5; and 0.102, 0.905, and −13.9 for unimodal-exponential, bimodal-exponential and empirical models, respectively. Therefore, the unimodal and bimodal-exponential models were flexible over the entire range of soil PSD. The results were compared with those of 35 PSD models investigated in the previous studies. The results showed the superiority of the conceptual models and only eight percent of the models had an accuracy similar to the conceptual models. Therefore, fewer parameters (three, five and two parameters for unimodal-exponential, bimodal-exponential and empirical models, respectively), easy fitting procedure and high accuracy in terms of R²_adjusted, RMSE and AICc criteria are considered as the most important advantages of the proposed models to describe the soil PSD from 0 to 0.002 m.

KEYWORDS:

• Particle size distribution
• conceptual models
• empirical model

Acknowledgments

This work was funded by the Bu-Ali Sina University, Hamedan, Iran. The authors are deeply grateful to anonymous reviewers and the editor for their helpful comments on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Bu-Ali Sina University, Hamedan, Iran.