Using copulas to characterise the dependency of GCL shear strengths

Abstract

ABSTRACT: The sensitivity of landfill design to shear strength variability is controlled by the measured internal shear strength of the geosynthetic clay liner and the interface shear strength between the geosynthetic clay liner and the geomembrane. Based on the Mohr–Coulomb criterion, the measured shear strength values (including the internal and interface shear strength values) depend on the cohesion and friction angle. Here, a novel and efficient mathematical tool for analysing the properties of the bivariate and the correlated geosynthetic shear strength was constructed. The arbitrary marginal probability density distribution of the componential shear strength was organised as a bivariate joint distribution with a copula function to characterise the dependency between the different shear strengths. Generally, a copula-based method provides a simple and powerful framework for modelling interdependence among variables. Thus, the construction of copulas as an alternative to correlation coefficients is addressed. In addition, the shear strength marginal distributions were described by a non-normal distribution, which was identified by the Akaike information criterion. The dependency of these margins is implemented from several empirical copulas, which were chosen from the most frequently used Elliptical and Archimedean families. The simulated correlated material properties that were generated by the copula-based sampling method were used as input values to calculate the performance of a landfill lining problem. Moreover, the computed reliability indexes were compared with the reliability indexes that were obtained by the first-order second moment method. In addition, a sensitivity study with various correlation coefficients was conducted to determine the influence of the correlation measurements on the reliability index.