Statistical analysis of some correlations between compression index and Atterberg limits
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ORIGINAL ARTICLE
Statistical analysis of some correlations between compression index and Atterberg limits Giovanni Spagnoli1 · Satoru Shimobe2 Received: 27 June 2020 / Accepted: 6 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The relationship between the compression index and Atterberg limits (liquid limit, plastic limit, shrinkage limit) is wellknown. 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 ( RD ) and ranking index ( 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. Keywords Atterberg limit · Shrinkage index · Compression index · RMSE · Probabilistic analysis · Monte Carlo simulation List of symbols Cc Compression index CEC Cation exchange capacity COV Coefficient of variation ( 𝜎/𝜇) e Void ratio e0 Initial (in-situ) void ratio cv Coefficient of consolidation e0 Initial void ratio Gs Specific gravity IS Index of shrinkage IP Index of plasticity LL Liquid limit M Median n Data points (sample size) PL Plastic limit RD Ranking distance * Giovanni Spagnoli giovanni.spagnoli@mbcc‑group.com Satoru Shimobe shimobe.satoru@nihon‑u.ac.jp 1
MBCC Group, Dr‑Albert‑Frank‑Strasse 32, 83308 Trostberg, Germany
College of Science and Technology, Nihon University, Funabashi 274‑8501, Japan
2
RI Ranking index RP Plasticity ratio (PL/LL) RMSE Root mean square error SL Shrinkage limit SSA Specific surface area tX%,n−2 Student t value, relating to a confidence level of X% and a degree of freedom equal to n − 2 wn Natural water content 𝜇 Mean value 𝜎 Standard deviation
Introduction In soil mechanics, oedometer tests are used to determine the compressibility characteristics of fine-grained soils, which is one of the most important parameters required in the design of foundations. The compressibility characteristics of finegrained soils are mainly described by the compression index, Cc , which is the slope of the linear portion of the e – log 𝜎 ′ plot and is dimensionless, and by the coefficient of consolidation, cv , whose unit is m2/year (Craig 2004). The compression index is constant for a wide range of pressure changes on any particular soil, and it provides a convenient
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