A particle-breakage critical state model for rockfill material

Particle breakage has a significant influence on the stress-strain and strength behavior of rockfill material. A breakage critical state theory (BCST) was proposed to describe the evolution of particle breakage. The breakage critical state line in the breakage critical state theory was correlated with the breakage factor, which was fundamentally different from that of the original critical state theory. A simple elastoplastic constitutive model was developed for rockfill in the frame of BCST. An associated flow rule was adopted in this model. Isotropic, contractive and distortional hardening rules were suggested in view of the particle breakage. It was observed that the proposed model could well represent the complex deformation behaviors of rockfill material, such as the strain hardening, post-peak strain softening, volumetric contraction, volumetric expansion, and particle breakage under different initial confining pressures

Fractional order modelling of the cumulative deformation of granular soils under cyclic loading

To model the cumulative deformation of granular soils under cyclic loading, a mathematical model was proposed. The power law connection between the shear strain and loading cycle was represented by using fractional derivative approach. The volumetric strain was characterized by a modified cyclic flow rule which considered the effect of particle breakage. All model parameters were obtained by the cyclic and static triaxial tests. Predictions of the test results were provided to validate the proposed model. Comparison with an existing cumulative model was also made to show the advantage of the proposed model

Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail. Then a modified elasto-plastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of factional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential considering particle breakage is used. Test results of several types of granular soils are used to validate the model performance

Compressibility dependence on grain size distribution and relative density in sands

A framework of continuum breakage mechanics was used to investigate the dependence of compressibility on grain size distribution (GSD) as well as relative density of sand. Compressibility dependence on GSD was considered by employing a GSD index and relative density dependence was reflected by varying the plastic-breakage coupling angle. Simulations of the experimental results including isotropic compression and one-dimensional compression of sands with different relative densities and GSDs revealed that sand compressibility increased with the increasing GSD index and plastic-breakage coupling angle. The coupling angle decreased with increasing relative density, indicating that grains would break more in sand with comparatively high relative density