Developing Conceptual and Empirical Models for Well- and Gap-Graded Soil Particle Size Distribution (PSD) Curve

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 (R-adjusted(2)), coefficient of determination (R-2), and corrected Akaike's information criterion (AICc). The RMSE,R(adjusted)(2)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 ofR(adjusted)(2), 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.