Failure processes of cemented granular materials

Abstract

The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here, we use a discrete element model (DEM) simulation, consisting of an assemblage of elastic particles connected by softer but breakable elastic bonds, to explore how this class of material deforms and fails under uniaxial compression. We are particularly interested in the connection between the microscopic interactions among the grains or particles and the macroscopic material response. To this end, the properties of the particles and the stiffness of the bonds are matched to experimental measurements of a cohesive granular media with tunable elasticity. The criterion for breaking a bond is also based on an explicit Griffith energy balance, with realistic surface energies. By varying the initial volume fraction of the particle assembles we show that this simple model reproduces a wide range of experimental behaviors, both in the elastic limit and beyond it. These include quantitative details of the distinct failure modes of shear-banding, ductile failure and compaction banding or anti-cracks, as well as the transitions between these modes. The present work, therefore, provides a unified framework for understanding the failure of porous materials such as sandstone, marble, powder aggregates, snow and foam.

Measuring and upscaling micromechanical interactions in a cohesive granular material

“…To link the microscopic and macroscopic length scales we use a discrete element model (DEM), developed by some of us to investigate the failure mechanisms of cohesive granulates, and which incorporates a Griffith-like energybased failure criterion for the bonds. 15 Both the experiments and model involve hard particles, connected by softer bridges, and in this limit we show that the bridge geometry is a key parameter in upscaling mechanical properties. The experimental observations will inform the parameters used in the model and we will then show that this approach can reproduce, both qualitatively and quantitatively, key features observed in the experiments, such as the results of uniaxial compression tests.…”

“…Even more challenging is the prediction of how, and when, such a system will fail, because of the importance of nonlinear effects such as force chains and strain localisation when approaching failure. 8,15,[26][27][28][29][30] Here, we pursue this goal of upscaling the micromechanical properties of a cohesive granular material. Experimentally, we imaged such materials using X-ray microtomography, and extracted the positions of the constituent beads along with statistical information about the bridge networks.…”

“…These measurements, combined with the micromechanical characterisation of single bridges (see Section 2), are then used as inputs for a minimal model of cohesive granular materials. 15 This model is thus constrained in all its parameters by observations at the microscopic scale. In Section 4, we will then simulate unconfined uniaxial testing of the modelled material, and find that the results compare favourably to in situ experimental compression tests.…”

“…To link the microscopic measurements to the bulk properties of a cohesive granular material, we used a discrete element model (DEM) that simulates the interactions between particles and their bonds. As the development of this model has been detailed elsewhere, 15 we focus only on its main features here, including the modifications made for this study.…”

“…Uniaxial compression tests are then simulated by keeping the top wall fixed and moving the lower one upwards at a constant speed. For example, sample A was compressed at 46.4 mm/s, corresponding to a speed of 10 −4 in the non-dimensionalised terms of the simulation, 15 and the same dimensionless speed was used for all simulations. This velocity is a compromise between requiring the dynamics to be slow enough to reproduce the quasi-static experiments, while keeping a reasonable computation time.…”