Mechanics of Granular Materials: Experimentation and Simulations for Determining the Compressive and Shear Behaviors of Sand at Granular and Meso Scales

Abstract

We present the results of experiments conducted to study the compressive and shear behavior of sand. Static and dynamic studies on the compression of sand grains were conducted. Nanoindentation was performed on single grains on sand of different sizes in order to determine the elastic and fracture properties of individual sand grains. Finite Element method (FEM) was used to solve the inverse problem so as to obtain the material properties from the load-displacement curves obtained from nanoindentation experiments. We also report the results of quasi-static compression tests conducted on sand held in a passive confinement. An in-house built compression fixture enabled the compression of sand grains up to axial stresses as high as 3 GPa. The results of tests conducted to study the dynamic behavior of ensemble to sand grains to compressive loading are also presented. Dynamic compression tests at strain rates of ∼700 s −1 were performed using a split Hopkinson pressure bar (SHPB). Characterization of sand grains based on initial packaging density, moisture content and different confinement materials were performed. In-situ quasi-static compression of sand grains along with X-ray micro-computed tomography was performed. Images from the tomographs were combined with the axial stress-strain data to explain various phenomenon such as re-arrangement and eventual fracture of grains during compression. Results obtained from various experiments performed in the course of this study would serve to validate the analytical models on mechanical behavior of sand. IntroductionGranular or particulate materials are ensembles of discrete macroscopic particles that respond to external forces only via inter-particle contact forces. They resemble solids as they behave rigidly under compression due to grain interlocking. Due to discrete and unbonded nature of the grains, they cannot withstand any load under tension. When the interlocking between the grains collapse, they lose resistance to shear loading and exhibit flow behavior similar to that of a viscous fluid. The solid-liquid transitional behavior of 2 the granular materials can be observed in grains stored in silos to landslides. They resemble liquids by assuming the shape of the container that they are stored and resemble gases as they lack intergranular cohesion. Jaeger et al. describe granular materials as "unusual" solids, liquids or gases [31]. They describe granular materials as a unique state of matter. The study of granular materials is currently active in various fields of engineering and sciences; including physics, geophysics, mechanics, and pharmaceuticals. Sand is a granular material found abundantly in nature. It has a hard structure with particle size varying between 7.5 µm and 4.75 mm. It primarily consists of silica (SiO 2 ) while other constituents, such as magnetite, gypsum, chlorite are present in minor quantities and vary from one geographic location to the other. Sand is usually described by their composition, morphology (shape), size, color, and text...