System size effects on the mechanical response of cohesive-frictional granular ensembles

Shear resistance in granular ensembles is a result of interparticle interaction and friction. However, even the presence of small amounts of cohesion between the particles changes the landscape of the mechanical response considerably. Very often such cohesive frictional (c-φ) granular ensembles are encountered in nature as well as while handling and storage of granular materials in the pharmaceutical, construction and mining industries. Modeling of these c-φ materials, especially in engineering applications have relied on the oft-made assumption of a "continua" and have utilized the popular tenets of continuum plasticity theory. We present an experimental investigation on the fundamental mechanics of c-φ materials specifically; we investigate if there exists a system size effect and any additional length scales beyond the continuum length scale on their mechanical response. For this purpose, we conduct a series of 1-D compression (UC) tests on cylindrical specimens reconstituted in the laboratory with a range of model particle-binder combinations such as sandcement, sand-epoxy, and glass ballotini-epoxy mixtures. Specimens are reconstituted to various diameters ranging from 10 mm to 150 mm (with an aspect ratio of 2) to a predefined packing fraction. In addition to the effect of the type of binder (cement, epoxy) and system size, the mean particle size is also varied from 0.5 to 2.5 mm. The peak strength of these materials is significant as it signals the initiation of the cohesive-bond breaking and onset of mobilization of the inter particle frictional resistance. For these model systems, the peak strength is a strong function of the system size of the ensemble as well as the mean particle size. This intriguing observation is counter to the traditional notion of a continuum plastic typical granular ensemble. Microstructure studies in a computed-tomograph have revealed the existence of a web patterned 'entangled-chain' like structure, we argue that this ushers an additional length scale as well as presents a system size effect.