A large direct shear apparatus was used to test coarse granular soil. In shear tests with a small shear box, deformation in shear band is homogeneous and stress–dilatancy relationships at pre-peak and post-peak phases of shearing are similar. However, in tests with a large shear box, the pre-peak and post-peak stress–dilatancy relationships are different. Using frictional state theory, it has been shown that the stress–dilatancy relationship for the large shear box is different from that for the small one conventionally used in direct shear tests, which suggests higher non-homogeneity deformation in the shear band in a large shear box in comparison to that in a small one. Parameter α of frictional state theory equals zero for the small and large shear boxes at failure. Parameter β = 1.4 for the small shear box and is a function of initial moisture and compaction for the large shear box. Average values of β range between 2.27 and 2.52 for dry coarse granular soil and between 2.17 and 2.30 for wet one. The value of critical frictional state angle Φ°= 41.2° of tested coarse granular soil is independent of soil moisture and compaction. The influence of the box’s size on stress–dilatancy relationship has also been observed in the previous studies.

Analyzing the results of triaxial compression tests under drained conditions for Erksak sand published in the literature, the stress–dilatancy relationships were described using the frictional state concept. At all phases of shearing, the linear stress ratio–plastic dilatancy relationship can be expressed by the critical frictional state angle and two parameters of the frictional state concept. At failure, dense sand exhibits purely frictional behavior (α = 0, β = 1) and the stress ratio–dilatancy relationship may be correctly described by the Rowe, Bolton, and frictional state concept relationships. Very loose Erksak sand sheared under drained triaxial compression at the ultimate state reaches a stable condition, but the reached stress ratio is significantly smaller than the one at a critical state.

Knowledge of the mechanical behaviour of ballast is very important for designing a railway track, especially for high-speed lines. The monotonic drained triaxial tests of scaled and fouled ballast presented in literature were analysed using the Frictional State Theory. The stress–plastic dilatancy relationship shows that four characteristic stages of shearing may be specified. The influence of stress level and water content may be quantified by the use of the Frictional State Theory.

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.

This paper analyses the stress–strain behaviour of fibre-reinforced sand using the results obtained by drained triaxial compression tests presented in the literature. The general stress–plastic dilatancy equation of the Frictional State Concept has been used to describe the behaviour of fibre-reinforced sand for different shear phases. The behaviour of pure sand is taken as a reference for the behaviour of sand with added fibres. It is shown that the characteristic shear phases can only be determined when the $\eta -D^p$ relationships are used, which are very rarely demonstrated in the results of shear tests presented in the literature. It has been shown that tensile strains must occur in order to achieve the strengthening effect of fibre reinforcement. A reduction in the stiffness of the fibre–sand composite is observed in the absence of tensile strains below certain threshold values.