Abstract
In micromechanics, the stress–force–fabric (SFF) relationship is referred to as an analytical expression linking the stress state of a granular material with microparameters on contact forces and material fabric. This paper employs the SFF relationship and discrete element modelling to investigate the micromechanics of fabric, force and strength anisotropies in two-dimensional granular materials. The development of the SFF relationship is briefly summarized while more attention is placed on the strength anisotropy and deformation non-coaxiality. Due to the presence of initial anisotropy, a granular material demonstrates a different behaviour when the loading direction relative to the direction of the material fabric varies. Specimens may go through various paths to reach the same critical state at which the fabric and force anisotropies are coaxial with the loading direction. The critical state of anisotropic granular material has been found to be independent of the initial fabric. The fabric anisotropy and the force anisotropy approach their critical magnitudes at the critical state. The particle-scale data obtained from discrete element simulations of anisotropic materials show that in monotonic loading, the principal force direction quickly becomes coaxial with the loading direction (i.e. the strain increment direction as applied). However, material fabric directions differ from the loading direction and they only tend to be coaxial at a very large shear strain. The degree of force anisotropy is in general larger than that of fabric anisotropy. In comparison with the limited variation in the degree of force anisotropy with varying loading directions, the fabric anisotropy adapts in a much slower pace and demonstrates wider disparity in the evolution in the magnitude of fabric anisotropy. The difference in the fabric anisotropy evolution has a more significant contribution to strength anisotropy than that of force anisotropy. There are two key parameters that control the degree of deformation non-coaxiality in granular materials subjected to monotonic shearing: the ratio between the degrees of fabric anisotropy and that of force anisotropy and the angle between the principal fabric direction and the applied loading direction.
Highlights
Granular materials have anisotropic structures either formed during natural geological processes or resulting from various in situ loading conditions
When the fabric anisotropy is much smaller than the force anisotropy, i.e. the ratio /B1f is small, the angle between the principal stress direction and the principal force direction is small with the maximum occurring around ψ − β1f /2 = 45◦
Despite the differences in the loading directions and the early evolutions, the two anisotropic specimens approached the same critical state characterized by macroscopically the critical stress ratio ηc = 0.85, and microscopically, the critical material fabric anisotropy c = 0.18 and the critical force anisotropy
Summary
Granular materials have anisotropic structures either formed during natural geological processes or resulting from various in situ loading conditions. Numerical simulations using discrete element methods [8] are reported and found in qualitative agreement with laboratory observations [22,31,41] Another interesting phenomenon associated with anisotropic soil behaviour is deformation non-coaxiality, which is defined as the non-coincidence between the principal stress directions and the principal strain increment directions [1,11,36,44,47]. In a study of the dependence of granular material behaviour on initial fabric and loading directions, Li and Yu [22] prepared and tested two anisotropic specimens consisting of non-spherical particles using a twodimensional commercial discrete element package, Particle Flow Code in Two Dimensions (PFC2D) [15]. Multiscale data obtained from Li and Yu [22] will be used here, where appropriate, to facilitate our discussion in this paper
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