Constitutive modelling of sand: a progressive calibration procedure accounting for intrinsic and stress-induced anisotropy

The recently developed constitutive model for sand, designated as Ta-Ger sand (as described by the present authors in another recent paper), is reformulated to account for intrinsic and stress-induced anisotropy. The model combines features of bounding surface plasticity and Bouc–Wen type hysteresis, and incorporates Rowe's dilatancy theory and the critical state concept. A physically motivated calibration methodology is developed with the aim to reduce the number of internal model parameters by expressing them as functions of four state variables: (a) Bolton's relative density index, I_r, for measuring the ‘distance’ between the current stress state and the critical state; (b) cumulative absolute deviatoric strain increment for controlling the evolution in stress space of the bounding and phase transformation lines; (c) principal stress rotation angle; and (d) intermediate stress ratio accounting for stress-induced anisotropy. The calibration procedure is step-by-step validated against experimental data for various drained and undrained loading paths (including triaxial compression and extension, plane-strain compression and direct simple shear) and initial states (relative density and pressure). Three different types of sand are examined to account for diverse behaviour, even for the same initial states and applied stress paths, due to intrinsic anisotropy attributed to fabric effects (e.g. grain size, shape and packing).