An unconventional subdivision of volumetric strains, the newly formulated frictional and critical frictional states and some of energetic and stress condition assumptions result in new stress-plastic dilatancy relationships. These new stress-plastic dilatancy relationships are functions of the deformation mode and drainage conditions. The critical frictional state presented in this paper is a special case of the classical critical state.

Different forms of the stress-dilatancy relations obtained based on the frictional theory for the triaxial condition are presented. The analysed test data show that the shear resistance of many soils is purely frictional. The angle Φ⁰ represents the resistance of the soil as a combined effect of sliding and particle rolling on the macro-scale during shear at the critical frictional state. The stress-plastic dilatancy relations differ not only for triaxial compression and extension but also for drained and undrained conditions. The experiment investigated shows the correctness of the frictional state theory in the triaxial condition.

The validation of the general stress-dilatancy relationship is shown based on biaxial compression test data presented in the literature under drained and undrained conditions. Rowe’s and Bolton’s relationships can be treated as simplified forms of the general stress-dilatancy relationship. The stress ratio values are a function of not only the dilatancy but also the intermediate principal stress, the non-coaxiality angle defined by Gutierrez and Ishihara and the stress-strain path. For many granular soils, the critical frictional state angle of the shearing resistance Φ^o = Φ′_cv and parameters α and β are functions of the drainage condition, the stress level and the stress and strain paths.

This paper validates the frictional state theory using published experimental data from simple, direct and ring shear tests. Simple shear is treated as a special case of plane strain conditions. In order to define complete stress and strain, additional assumptions are made: in the direct shear and ring shear tests, simple shear is assumed to occur in the shear band. For Φ^o = Φ′_cv = Φ′_r, the stress-dilatancy relationship obtained from the frictional state theory is similar to the relationships proposed by Taylor and Bolton. Further experiments, especially those that use a hollow cylindrical shear apparatus, are necessary to fully validate the frictional state theory in simple shear conditions.

The strength of sand is usually characterized by the maximum value of the secant friction angle. The friction angle is a function of deformation mode, density, and stress level and is strongly correlated with dilatancy at failure. Most often, the friction angle is evaluated from results of conventional compression tests, and correlation between the friction angle of sand at triaxial compression and triaxial extension and plane strain conditions is a vital problem of soil mechanics. These correlations can be obtained from laboratory test results. The failure criteria for sand presented in literature also give the possibility of finding correlations between friction angles for different deformation modes. The general stress-dilatancy relationship obtained from the frictional state concept, with some additional assumptions, gives the possibility of finding theoretical relationships between the friction angle of sand at triaxial compression and triaxial extension and plane strain conditions. The theoretically obtained relationships presented in the paper are fully consistent with theoretical and experimental findings of soil mechanics.

In this study, the results of triaxial compression tests of some naturally and artificially bonded soils presented in the literature were analysed. It was shown that the three characteristic stages of plastic flow during shear can be identified. In all stages, the stress–dilatancy behaviour could be approximated by the general linear stress–dilatancy equation of the Frictional State Concept. For many shear tests, the failure states and newly defined dilatant failure states are not identical. The points representing dilatant failure states lie on a straight line, for which the position and slope in the η-D plane depend on the soil type and the amount of cement admixture. This line defines the critical frictional state angle, and its slope for bonded soils is greater than for unbonded soils.