Implementation of the non-associated elastoplastic MSDPᵤ model in FLAC3D and application for stress analysis of backfilled stopes

The multiaxial Mises-Schleicher and Drucker-Prager unified (MSDPᵤ) criterion has been shown to exhibit several specific features compared to other yield and failure criteria, including a nonlinear mean stress dependency, influence of the Lode angle, use of independent uniaxial compressive and tensile strength values and absence of an apex (singularity) on the envelope surface in the negative stress quadrant. However, MSDPᵤ has been seldom used in practice to solve geotechnical and geomechanical engineering problems mainly because it had not yet been fully implemented into three-dimensional (3D) numerical codes. To fill this gap, a 3D elastoplastic MSDPᵤ formulation is developed and implemented into FLAC3D. The proposed MSDPᵤ elastic-perfectly plastic (EPP) constitutive model is then validated against existing analytical solutions developed for calculating the stress and displacement distributions around cylindrical openings. The FLAC3D MSDPᵤ-EPP model is then applied to evaluate the vertical and horizontal stress distributions in a three-dimensional vertical backfilled stope. The numerical results obtained with the MSDPᵤ-EPP model are compared with those obtained with the Mohr-Coulomb EPP model, to highlight key features of the new formulation.