Triaxial shearing of an assembly of sand grains is numerically simulated using X-ray CT imaging and FEM concurrently. The actual morphology of particles, geometric contacts, and arrangement of solid, void phases are captured using X-ray CT imaging. A novel framework is introduced wherein a realistic assembly of sand grains is discretized using shell-based finite elements to solve the boundary value problem. The shell elements are based on Mindlin-Reissner flexural theory and corotational velocity strain formulation which are well suited for problems involving large rotation. This approach is computationally less expensive compared to the finite discrete element approach where sand grains are discretized using solid finite elements. The latex membrane is modeled as hyper-elastic material to provide a flexible boundary condition for applying confining pressure.
A vertical surface load acting on a half-space made of discrete and elastic particles is supported by a network of force chains that changes with the specific realization of the packing. These force chains can be transformed into equivalent stress fields, but the obtained values are usually different from those predicted by the unique solution of the corresponding boundary value problem. In this research the relationship between discrete and continuum approaches to Boussinesq-like problems is explored in the light of classical statistical mechanics. In the principal directions of the stress established by the continuum-based approach, the probability distribution functions of the extensive normal and shear stresses of particles are anticipated to be exponential and Laplace distributions, respectively. The extensive stress is the product of the volumetric average of the stress eld within a region by the volume of that region. The parameters locating and scaling these probability distribution functions (PDFs) are such that the expected values of the extensive stresses match the solution to the corresponding boundary value problem: zero extensive shear stress and extensive normal stresses equal to the principal ones. The continuum-based approach is still needed to know the expected values, but this research article presents a powerful method for quantifying their expected variability. The theory has been validated through massive numerical simulation with the discrete element method. These results could be of interest in highly fragmented, faulted or heterogeneous media or on small length scales (with particular applications for laboratory testing).
Combining the Cosserat continuum with Breakage mechanics in a consistent thermodynamic way, offers substantial benefits to our capacity to model granular physics by accounting for both the entire grain size distribution, and its evolution. We provide an upscaling procedure that introduces material parameters accounting for the contribution of an evolving internal length representing the statistics of the entire grain size distribution. Our model requires no additional calibration relative to the same model in the classical continuum and enables us to examine the effect of grain size polydispersity and grain breakage on the thickness of shear bands and on apparent softening. By implementing the model using the finite element method, we provide an explanation for the geological formation of double cataclastic shear bands in seismogenic faults.
Single Leighton Buzzard sand particles were compressed uniaxially and two primary breakage modes were proposed: splitting and explosive. In the splitting mode, the particle breaks into two or three large pieces without the creation of numerous small fragments. In terms of force-displacement curve, it tends to be almost linear while the crack initiates and propagates from the upper loading contact to the center of the particle (a shadow occurs and expands). At the failure point, the force-displacement curve drops abruptly and the particle splits into two parts that remain between the two platens with little movement after failure, giving a significant residual strength. In the explosive mode, the particle undergoes a dramatic and instantaneous blasting into a mass of tiny fragments. In this case, once the crack occurs, it propagates very quickly causing a catastrophic breakage within 0·04s. The explosive process is sudden and fierce so that the fragments fly too quickly even to be captured by the high-speed microscope camera and are out of focus in the frames. Particles fail in the explosive mode tend to have more rounded loading contacts and so are stronger with more deformation at failure than those failing in the splitting mode, leading to greater energy stored inside the particles. Other conclusions about the single-particle breakage behavior can be found in our paper
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