Investigation of correlation structures and weak stationarity using the CPT soil behavior classification index

Weak stationarity or second-order statistical homogeneity is a prerequisite for geotechnical variability analyses. Non-parametric tests developed from independent data have been used in the geotechnical literature to assess weak stationarity. However, the underlying independence assumption contradicts the well known observation that spatially varying soil properties are correlated. This paper compares the assessment of weak stationarity using the classical non-parametric Kendall’s tau test and a modified Bartlett statistic procedure that explicitly includes the correlation structure in the rejection criterion. The relationship between weakly stationary layers and physically homogeneous layers [as defined by Robertson (1990)’s classification chart] is studied. Because cone penetration test soundings are nearly continuous and carry low measurement errors, they are most useful for such a statistical study. To derive sufficiently general conclusions, 70 normalized cone tip resistance profiles from a wide variety of soil types classified as distinct zones in Robertson (1990)’s chart (clays, silt mixtures, sand mixtures, sands) were used in this study.