A nonlinear Drucker–Prager and Matsuoka–Nakai unified failure criterion for geomaterials with separated stress invariants

A nonlinear Drucker–Prager and Matsuoka–Nakai unified (DPMNu) failure criterion for geomaterials is developed using the Haigh–Westergaard (HW) coordinates. This criterion ensures convenience in its application due to its simple formulation with separated HW invariants. Explicit formulations are presented to evaluate the material constants in the current criterion. In the meridian plane the criterion is expressed by a simple power function. The failure locus of this criterion in the deviatoric plane covers the various convex curves from a curved triangle of the Matsuoka–Nakai criterion to the circle of the Drucker–Prager criterion. The test results of a series of polyaxial strength tests on various geomaterials are compared with the predicted results by the current criterion. It shows that the nonlinear DPMNu criterion captures quite well the experimental trend and reasonably predicts the multiaxial strength of various geomaterials.

► Based on the nonlinear unified strength theory, we develop a new failure criterion for geomaterials.
► The exponent n and shape factor α control the nonlinear failure loci of various geomaterials.
► The Drucker–Prager criterion and Matsuoka–Nakai criterion are special cases of this criterion.
► The experimental trend can be captured quite well by this criterion in polyaxial strength tests.
► This criterion is convenient due to a simple and unified form with separated stress invariants.