Failure behavior of single sand grains: Theory versus experiment

Abstract

[1] 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.

Deformation bands in porous carbonate grainstones: Field and laboratory observations

“…6a, 7a and 8c, d) in agreement with the previous scanning electron microscope analyses of Tondi et al (2006). Further detailed FESEM analyses within a CSB with negligible amount of cataclasis, allowed us to documented tiny (>100 mm, not discernible under optical microscope) Hertzian cracks (Zhang et al, 1990;Brzesowsky et al, 2011) at the grain contacts (Fig. 8 aeb).…”

“…As shown in Fig. 18, at low confining pressures, the cracks form either at the grain contacts (Hertzian cracks, Zhang et al, 1990;Brzesowsky et al, 2011) or, alternatively, in the proximity of slip surface (Wing cracks, Ashby and Sammis, 1990). These two typologies of cracks are characterized by different preferential orientation of propagation with respected to s 1 .…”

“…In laboratory CSBs, randomly distributed grain crushing starts from Hertzian cracks (Zhang et al, 1990;and Brzesowsky et al, 2011) at the grain contacts, this process enhances the reduction of intergranular pore sizes by means of infilling of fine material and particulate flow (Fig. 20).…”

An approach to enhance efficiency of DEM modelling of soils with crushable grains

“…Alonso et al, 2012). On the other hand, the experimental evidence is ambiguous: some studies (Tsoungui et al, 1999b;McDowell & Amon, 2000;Lobo-Guerrero & Vallejo, 2006) have found that the same value of the Weibull modulus is able to fit both the variability at a given scale and the variability across scales, yet others (Jansen & Stoyan, 2000;Lim et al, 2004;Brzesowsky et al, 2011) obtain the opposite result.…”

Validation of the log e–log σ normal compression law using particle strength data

“…b in equation (2)), this is not always accompanied by any normal compression results (e.g. Bolton et al, 1991;Lobo-Guerrero & Vallejo, 2006;Brzesowsky et al, 2011).…”