Yielding of granular materials

 This paper examines the yielding of brittle granular materials subjected to one-dimensional compression. For an aggregate of uniform grains, at low stresses there is negligible reduction in voids ratio, and at high stresses voids ratio reduces approximately logarithmically with stress as a distribution of particle sizes evolves. A suitable definition of yield would appear to be the point of maximum curvature on a plot of voids ratio against the logarithm of stress, corresponding to the onset of grain fracture. It is proposed that the yield stress is approximately proportional to the average or Weibull 37% tensile strength of the particles in the aggregate. One-dimensional compression tests were performed on aggregates of brittle breakfast cereals, (cornflakes, rice krispies) and pasta and compared with the results for a typical one-dimensional compression test on dense silica sand at much higher stress levels. In addition, the tensile strengths of 30 particles for each material were determined by compression between flat platens, and found to satisfy the Weibull distribution. It is found that if voids ratio is plotted against the logarithm of stress, then yield occurs at much lower stresses for the cereals and pasta than for the dense silica sand, typically by two orders of magnitude. However, if voids ratio is plotted against the logarithm of stress normalised by the Weibull 37% tensile strength of the constituent grains, then the yielding region for each material is approximately the same. This confirms the proposed definition of yield as suitable, and that the yield stress determined in this way is approximately proportional to the tensile strength of the grains. The constant of proportionality is in the range 0.1–0.3, and this is consistent with observed heterogeneous stress distributions in discrete element simulations.