Statistical analysis of some correlations between compression index and Atterberg limits

Abstract

The relationship between the compression index and Atterberg limits (liquid limit, plastic limit, shrinkage limit) is well-known. Several equations are found in literature for general correlations or more specifically for correlations considering the state of the soil (e.g. remolded or undisturbed). This paper evaluates different studies considering 250 data points, and relations among the compression index and the liquid limit, index of plasticity, index of shrinkage, soil activity and plasticity ratio are provided. These relations are validated against 12 independent data points. The objective of the research is not to provide a new relation, but it is rather to statistically evaluate the input data used to obtain the new relationships. Therefore, several statistical analyses considering the root mean square error (RMSE), a probabilistic analysis, ranking distance ( $$\mathrm{RD}$$ ) and ranking index ( $$\mathrm{RI}$$ ) are performed by taking into account the correlations obtained to quantify the accuracy of each correlation. A Monte Carlo simulation with 100,000 simulations showed that the type of correlation has an influence on the distribution output.