Statistical Prediction of Soil Atterberg Limits from Grain Size Distribution Alone Using Excel Solver

Abstract

Atterberg limits play a crucial role in soil investigations due to their ability to provide fundamental insights into the mechanical behavior of soils. The primary objective of this study was to derive empirical equations for determining the liquid limit (LL) and plastic limit (PL) of soils using only soil particle size distribution data. Microsoft Excel was used for statistical analysis, applying 10 different methodologies. The methodology integrated the clay fraction (CF) (<0.002 mm) as the main independent factor in all models. The only independent variable in model M1 is CF, while model M2 includes sand and silt, in addition to clay fractions, as independent factors. In the analytical process, the number of independent variables progressively increased from model M1 to model M10, systematically enhancing the predictive capacity of the models. Using this methodology, two robust equations were developed in model M6, which are capable of determining LL and PL, with R-squared values reaching the value 1.0 and an RMSE of approximately zero; however, it is important to note that while an RMSE of zero does indicate an R-squared of 1.0, an R-squared of 1.0 does not necessarily imply a zero RMSE.  The results of this study show that full grain size analysis data alone may effectively predict LL and PL, negating the need for additional physical or chemical characteristics of the soil.