José E. Andrade

Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations

Tomographic images taken inside and outside a compaction band in a field specimen of Aztec sandstone are analyzed by using numerical methods such as graph theory, level sets, and hybrid lattice Boltzmann/finite element techniques. The results reveal approximately an order of magnitude permeability reduction within the compaction band. This is less than the several orders of magnitude reduction measured from hydraulic experiments on compaction bands formed in laboratory experiments and about one order of magnitude less than inferences from two-dimensional images of Aztec sandstone. Geometrical analysis concludes that the elimination of connected pore space and increased tortuosities due to the porosity decrease are the major factors contributing to the permeability reduction. In addition, the multiscale flow simulations also indicate that permeability is fairly isotropic inside and outside the compaction band.

Image-Based Modeling of Granular Porous Media

We propose a new method of modeling granular media that utilizes a single two- or three-dimensional image and is formulated based on a Markov process. The process is mapped onto one that minimizes the difference between the image and a stochastic realization of the granular medium and utilizes a novel approach to remove possible unphysical discontinuities in the realization. Quantitative comparison between the morphological properties of the realizations and representative examples indicates excellent agreement.

Quantifying Interparticle Forces and Heterogeneity in 3D Granular Materials

Interparticle forces in granular materials are intimately linked to mechanical properties and are known to self-organize into heterogeneous structures, or force chains, under external load. Despite progress in understanding the statistics and spatial distribution of interparticle forces in recent decades, a systematic method for measuring forces in opaque, three-dimensional (3D), frictional, stiff granular media has yet to emerge. In this Letter, we present results from an experiment that combines 3D x-ray diffraction, x-ray tomography, and a numerical force inference technique to quantify interparticle forces and their heterogeneity in an assembly of quartz grains undergoing a one-dimensional compression cycle. Forces exhibit an exponential decay above the mean and partition into strong and weak networks. We find a surprising inverse relationship between macroscopic load and the heterogeneity of interparticle forces, despite the clear emergence of two force chains that span the system.

Force chains as the link between particle and bulk friction angles in granular material

From sediment transport in rivers to landslides, predictions of granular motion rely on a Mohr-Coulomb failure criterion parameterized by a friction angle. Measured friction angles are generally large for single grains, smaller for large numbers of grains, and no theory exists for intermediate numbers of grains. We propose that a continuum of friction angles exists between single-grain and bulk friction angles due to grain-to-grain force chains. Physical experiments, probabilistic modeling, and discrete element modeling demonstrate that friction angles decrease by up to 15° as the number of potentially mobile grains increases from 1 to ~20. Decreased stability occurs as longer force chains more effectively dislodge downslope “keystone” grains, implying that bulk friction angles are set by the statistics of single-grain friction angles. Both angles are distinct from and generally larger than grain contact-point friction, with implications for a variety of sediment transport processes involving small clusters of grains.

Liquefaction Mapping in Finite-Element Simulations

Recent criteria have been developed to describe the onset of static liquefaction in constitutive models. This paper expands the theory to a finite-element framework in order to predict potentially unstable regions in granular soils at the engineering scale. Example simulations are presented for two plane strain tests and a submarine slope to demonstrate the applicability of a proposed liquefaction criterion to boundary value problems. In addition, loading rate and mesh size effects on the liquefaction prediction are examined. The methodology presented herein shows promise as a means of predicting soil liquefaction based on solid mechanical theory rather than empiricism.

Direct Modeling of Granular Materials

Granular packing is one of the long-standing problems that have been studied for decades. Most of the current methods are trying to infer some statistical properties to describe and then regenerate a granular medium. These techniques, however, remain at the lower orders and cannot extract very complex information and, thus, they produce unrealistic models that are physically unlikely. The texture of the generated particles using these techniques are mostly different from the real sharpness of granular materials. In this paper, a new technique for direct modeling of granular materials (DGM) based on using high-order statistics is introduced that can extract more information and, finally generate very accurate models. This method, indeed, does not employ any particle descriptor and uses the existing 2D/3D images directly. The results indicate a very good agreement between the simulated and original data. The computational cost of this method is very low.

Capturing the effective permeability of field compaction band using hybrid lattice Boltzmann/Finite element simulations

As observed in reconstructed 3D images of the field compaction bands (Lenoir et al 2010), their formation may cause a significant reduction in porosity and permeability. This paper describes essential a lattice Boltzmann/finite element model that may be advantageous for calculating effective permeability of compaction bands from obscured structure in a cost-efficient way. The pressing issues include the homogenization technique and the scale effect of the effective permeability.

Measuring Force-Chains in Opaque Granular Matter Under Shear

Microstructural information, such as inter-particle forces and particle kinematics, plays a key role in understanding the continuum behavior of complex granular structure. Although micromechanical techniques have provided tremendous insights, they still lack quantitative accuracy and, associated with this, capacity to predict macroscopic behavior. We report here a set of experiments performed on a novel mechanical device in which we have successfully extracted particle-scale kinematics and inter-particle forces in a two-dimensional idealized granular assembly. This mechanical device allows a specimen composed of a two-dimensional analogue granular assembly to be subjected to quasi-static shear conditions over large deformation. Digital Image Correlation (DIC) is employed to measure particle kinematics. The inter-particle forces are inferred using the Granular Element Method (GEM), provided that average particle strains are measured and that the location of the contact points in the array is known. DIC combined with GEM allow us to observe and assess the force distribution in the complex granular assembly. These results represent an important step in our understanding of the micromechanical response of a complex granular assembly to applied macroscopic strains and stresses.

Grain-Scale Measurements During Low Velocity Impact in Granular Media

This chapter will explore the connection between macroscopic and microscopic behavior during low velocity impact into granular media. We will discuss important grain-scale quantities, their use in understanding macroscopic penetration behavior, and numerical and experimental measurement techniques for obtaining them. A new experimental technique for measuring interparticle forces in opaque granular materials will be introduced. Examples of this technique applied to low velocity impact into granular media will be presented and discussed.

Particulate Study of Drained Diffuse Instability in Granular Material

Conventionally, the definition of instability is considered to be shear failure. However, there is substantial evidence that instabilities can also occur in a diffuse (homogeneous) manner without the apparent presence of a shear band under both undrained and drained conditions. Compared to undrained diffuse instability, drained diffuse instability of granular soil is less studied and is not yet well understood. This paper presents a discrete element method (DEM) study of drained diffuse instability of a granular soil. Instability and loss of controllability were observed well below the failure line when the DEM specimens were subjected to a constant shear-drained (CSD) stress path, which coincides with experimental and continuum numerical findings in the literature. The preliminary micro-scale examination includes the monitoring of coordination number evolution along CSD stress path. This study shows DEM modeling can well reproduce drained diffuse instability in granular materials and can be used to further investigate the mechanics of this phenomenon from a micro-scale perspective.