Micromechanical Exploration of the Lade-Duncan Yield Surface by the Discrete Element Method

The Lade-Duncan yield surface has long been known to outperform other yield criteria (e.g., Mohr-Coulomb, Drucker-Prager) for predicting macro-scale failure in non-cohesive granular (pressure-dependent) materials. Such yield criteria are critical for a wide variety of civil and infrastructure engineering applications, including the design and analysis of foundations and retaining walls for architectural, highway, and railway support structures. The Lade-Duncan yield surface has been repeatedly validated, not only by numerous experimental studies, but also by three-dimensional discrete element method numerical simulations performed on mono- and poly-disperse assemblies of spheres. However, a fully satisfying micromechanical explanation for the empirically-motivated Lade-Duncan yield criterion has never been offered. In particular, the increase in the macro-scale friction angle phi relative to the Mohr-Coulomb yield surface that occurs as the Lode angle of deviatoric stress moves from simple compression toward simple extension on the Pi-plane in principal stress space, which is characteristic of the Lade-Duncan yield surface, has never been given a rigorous micromechanics-based explanation. In this paper, we attempt to fill this "gap", by presenting a simple yet rigorous analysis of micro-scale inter-particle force-equilibrium, which, when combined with detailed 3D-DEM data obtained from simulations of cubical true-triaxial tests performed on mono- and poly-disperse spheres with a variety of micro-scale or inter-particle friction coefficients mu, provides a meaningful micromechanics-based explanation for the shape of the Lade-Duncan yield surface. In particular, we hypothesize that the Lade-Duncan yield criterion can be motivated directly from the continuum-mechanics-based spatially mobilized plane or Matsuoka-Nakai criterion in terms of the ratio of shear stress to normal stress on the spatially mobilized plane if the magnitude of the shear stress on the SMP is increased to account for deviations in the paths of sliding particles on the SMP.