This paper provides a micro-mechanical commentary on the macroscopic behaviour observed in DEM simulations of the compression of individual crushable grains, and of triaxial tests on assemblies of both crushable and uncrushable grains. A fragmentation ratio is defined to describe the bond breakage processes, and the significance of other micro-mechanical parameters such as sliding contacts ratio, average coordination number, deviator fabric, and internal energies per unit volume is discussed. Three different modes of grain damage were observed: asperity breakage, internal shear cracking, and internal tensile cracking leading to fast fracture. Energy balances both for the compression of a single grain, and for triaxial tests on assemblies of grains, showed that the loss of elastic energy due to bond breakage was a negligible fraction of the significantly enhanced dissipation encountered with crushable materials. This extra dissipation was associated with frictional sliding triggered by the creation of new degrees of freedom among the breaking fragments. Different modes of grain breakage were found to be representative of different regions of soil states of stress defined with respect to the virgin compression line. The secondary role of elastic grain deformability, increasing coordination number but reducing dilatancy, has also been demonstrated.

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Cheng and co-workers showed how to make numerical simulations of crushable soils by the discrete element method (DEM). Stress-path tests on triaxial elements comprising crushable agglomerates have now been simulated. The plastic behaviour of this numerically generated soil closely resembles that of real sand. Crushing in the aggregate begins at stresses less than one tenth of the characteristic strength of single grains. The yield surfaces of isotropic ‘lightly overconsolidated’ DEM simulations are also contours of breakage, and are elliptical on Cambridge-style (q, p′) plots and symmetrical about the p′ axis. The points of maximum deviator stress at yield lie along lines of stress ratio My = ±0·8, but the plastic strain increments at yield are non-associated, giving more contraction than normality would allow. Significantly, therefore, the stress ratio My was found not to coincide with critical states. All stress-path simulations yielding with q/p′ > My were found to satisfy the requirements of stress–dilatancy theory. In particular, their yielding was best described using a unique Mohr–Coulomb angle of internal friction ϕ, correlated with dilatancy rate. Points of zero dilation were found within this regime, providing a critical-state friction angle ϕcrit = 42° for these very ‘rough’ agglomerates. They also coincided with the location of a critical-state line on an e–log p′ plot. The peak angle (ϕpeak) developed in a variety of tests showed a unique correlation, reducing by progressive grain crushing as log σ′1 increased. As macroscopic stress levels approached the characteristic crushing strength of grains, it was impossible even to mobilise ϕ = ϕcrit, owing to large strains and high degress of breakage.

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