Modelling dependence structures of soil shear strength data with bivariate copulas and applications to geotechnical reliability analysis

Accurate estimates of the dependence of soil shear strength parameters (including cohesion and friction angle) play a crucial role in decision making by civil engineers in terms of geotechnical engineering safety. With increased site-specific information comes the need for joint soil strength models to account for the correlation characteristics between shear strength properties. In this study, using 16 sets of soil shear strength observations (consisting of 391 samples) as examples, the suitability of the dependence structure for these experimental observations is firstly identified by a goodness-of-fit test based on the Bayesian Information Criterion (BIC) with the normal, Student's t, Clayton, Frank, Gumbel, and Plackett copulas. The dependence structure between shear strength components is found to be asymmetric in most cases. Secondly, a set of paired samples of shear strength simulated from the different bivariate copulas, which contributed to various dependencies, is implemented as input for two typical geotechnical probabilistic analyses, e.g., infinite slope stability against a single sliding plane and the bearing capacity of a shallow foundation. The impact of the different choices for these dependence structures on the resulting reliability index is discussed. In both illustrative examples, the normal copula leads to an overestimation of the reliability index, whereas the Gumbel copula yields the lowest reliability index. Conservative reliability indices are obtained when the joint behaviour of the soil shear strength follows a bivariate normal distribution.