Failure behavior of single sand grains: Theory versus experiment

Grain-scale brittle fracture and grain rearrangement play an important role in controlling the compaction behavior of reservoir rocks during the early stages of burial. Therefore, the understanding of single-grain failure is important. We performed constant displacement rate crushing tests carried out on selected, well-rounded, single sand grains and on randomly sampled grains from different grain size (d) batches of pure quartz sand. Applying a Hertzian fracture mechanics model for grain crushing, the critical load at failure (F-c) data obtained for the selected grains were converted into an accurate estimate of the size of flaws associated with failure (c(f)). Similarly, the distributed F-c data obtained from the different batch samples were converted into distributions of grain failure stress. Weibull weakest link theory could not explain the observed grain failure behavior. On the contrary, the Hertzian grain failure criterion enabled the conversion of the distributed F-c data, for the batch samples, into distributions of c(f), assuming spherical grains, or of "effective" radius of curvature (r(g)), characterizing contact surface asperities in the case of nonspherical grains. In contrast to the model of Zhang et al. (1990), our work shows that there is no clear physical basis for a grain size dependence of c(f). However, since roundness data for dune sands exhibit a similar relation between r(g) and d, as seen in our grain size batches, it is inferred that the Hertzian fracture mechanics model assuming nonspherical grains with a distributed r(g) is the most physically reasonable model for grain failure.