A Numerical Study on the Effect of Initial Void Ratio and Areal Extent of Heterogeneity on Instability Onset in Granular Media

Abstract

The present study numerically explores the coupled biaxial undrained instability analysis of Hostun RF sand with varying initial void ratio (e₀) for a given confining pressure (σ′_c). A transient analysis of 100 mm × 100 mm sand specimen has been carried out with the implementation of a generalized 3D nonassociative elastoplastic material model. Finite element analysis has been performed in ABAQUS v6.14 and the constitutive model has been incorporated by scripting a user-defined material model subroutine (UMAT). The standard custom for instability analysis involves introduction of some form of heterogeneity within the material domain (perturbation) and probing its response against the prescribed boundary conditions. Mesh sensitivity of instability onset has been explored in the current context numerically while material imperfection has been introduced in terms of e₀. The coupled analysis allowed local fluid motion within the material continuum, while the undrained boundary condition was imposed globally. Instability onset gets delayed as e₀ is decreased (relatively denser specimens) for a given σ′_c with distinct signatures of dilative and contractive zones existing adjacent to each other (for specimens with e₀ < critical void ratio (e_c)) for a particular perturbation magnitude. Influence of spatial extent of heterogeneity for a given perturbation intensity and σ′_c also showed some effect in lowering down the instability onset strain to some degree and ceased to display significant impact on further increase in the areal extent of material imperfection.