Quantifying the non-normality of shear strength of geomaterials

Abstract

Geotechnical shear strength variables generally include the cohesion and angle of internal friction based upon the Mohr-Coulomb failure criterion. In this study, the non-normality of a univariate probability density function (PDF) and the bivariate probability density contour (PDC) of observed shear strength pairs is examined for 33 geomaterial types, comprising of soils (24 types), rocks (7 types), and geosynthetic clay liners (2 types), with sample sizes ranging from 14 to 97. After a detailed analysis on the graphic features of probability density and box-whisker plots of shear strength parameters, normality testing is further quantified by skewness, kurtosis, and energy statistic tests. In most cases (23/31), distributions of cohesion are positively skewed, as are distributions of friction angle (17/29), while the distribution of these parameters is mostly platykurtic (characterised by negative excess kurtosis). Bivariate energy statistic analyses of shear strength pairs indicate that, in ten cases, p-values are below .05, demonstrating that the joint distribution differs from the bivariate normal distribution, and these results are largely consistent with those achieved by the Shapiro-Wilk test. Moreover, a slope stability analysis with different joint distributions is used to assess the impact of marginal PDFs on the failure probability.

Keywords:

• Skewness
• kurtosis
• non-normality
• multivariate
• geomaterials

Acknowledgements

The author would like to thank Prof. Ping Lin at the University of Science and Technology Beijing for his valuable comments. The author wishes to thank colleagues who have generously made their source data publicly available. The contributors of the R project are greatly appreciated.