Necessary and sufficient conditions for reaching and maintaining critical state

• Published in: International journal for numerical and analytical methods in geomechanics 2019-08, Vol.43 (12), p.2041-2055
• Main Authors: Theocharis, Alexandros I., Vairaktaris, Emmanouil, Dafalias, Yannis F., Papadimitriou, Achilleas G.
• Format: Article
• Language: English
• Subjects: Abandonment; anisotropic critical state theory; Anisotropy; Contraction; critical state; Dilatancy; Discrete element method; discrete‐element modeling; fabric; Fabrics; Mathematical analysis; Mechanics; Plastic deformation; Qualitative analysis; Rotation; Strain; Strain rate; Tensors; Void ratio
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2943

Summary According to classical critical state theory (CST) of granular mechanics, two analytical conditions on the ratio of stress invariants and the void ratio are postulated to be necessary and sufficient for reaching and maintaining critical state (CS). The present work investigates the sufficiency of these two conditions based on the results of a virtual three‐dimensional discrete element method experiment, which imposes continuous rotation of the principal axes of stress with fixed stress principal values at CS. Even though the fixity of the stress principal values satisfies the two analytical CST conditions at the initiation of rotation, contraction and abandonment of CS occur, which proves that these conditions may be necessary but are not sufficient to maintain CS. But if fixity of stress and strain rate directions in regard to the sample is considered at CS, the two analytical conditions of CST remain both necessary and sufficient. The recently proposed anisotropic critical state theory (ACST) turned this qualitative requirement of fixity into an analytical condition related to the CS value of a fabric anisotropy variable A defined in terms of an evolving fabric tensor and the plastic strain rate direction, thus, enhancing the two CST conditions by a third. In this way, the three analytical conditions of ACST become both necessary and sufficient for reaching and maintaining CS. In addition, the use of A explains the observed results by relating the stress‐strain response, in particular the dilatancy, to the evolution of fabric by means of the relevant equations of ACST.