Amy L. Rechenmacher

Analysis of grain-scale measurements of sand using kinematical complex networks

Plastic deformation in a plane strain compression test of a dense sand specimen is studied using functional networks. Kinematical information for the deforming material is obtained using digital image correlation (DIC) and summarized by two types of complex network with different connectivity rules establishing links between the network nodes which represent the DIC observation sites. In the first, nodes are connected to a minimum fixed number of neighbors with similar kinematics such that the resulting network forms one connected component. In the second, nodes are connected to other nodes whose kinematical behavior lies within a fixed distance of each other in an observation space. The fixed radius is determined using optimization with a stopping criterion again with the resulting network forming one connected component. We find different network properties of each network provide useful information about plastic deformation and nonaffine kinematical processes emerging within the material. In particular, persistent shear bands and mesoscale structures within them (e.g. vortices) appear to be closely related to values of network properties including closeness centrality, clustering coefficients, k-cores and the boundaries of community structures determined using local modularity.

Towards a complete model of soil liquefaction: the importance of fluid flow and grain motion

When loosely packed water-saturated granular soils, for example sands, are subjected to strong earthquake shaking, they may liquefy, causing large deformations with great destructive power. The phenomenon is quite general and occurs in any fluid-saturated granular material and is a consequence of the transfer of stress from inter-grain contacts to water pressure. In modern geotechnical practice, soil liquefaction is commonly considered to be an ‘undrained’ phenomenon; pressure is thought to be generated because earthquake deformations are too quick to allow fluid flow, which enables water depressurization. Here, we show via a first principles analysis that liquefaction is not a strictly undrained process; and, in fact, it is the interplay between grain rearrangement, fluid migration and changes in permeability, which causes the loss of strength observed in so many destructive earthquake events around the world. The results call into question many of the common laboratory and field methods of evaluating the liquefaction resistance of soil and indicate new directions for the field, laboratory and scale-model study of this important phenomenon.

Image-based sensing of 3-D displacements for enhanced soil model calibration

Calibration of soil constitutive parameters is performed traditionally by analyzing results from triaxial experiments, which are equipped to measure only vertical stress and strain responses and average volumetric responses. Material response characterization thus is relegated to an overall, averaged sense. The 3-D image-based sensing technique of 3D Digital Image Correlation (3D-DIC) allows capturing spatio-temporal displacement processes over triaxial specimen surfaces. Utilizing stereo digital images, 3D-DIC captures hundreds of thousands of local displacement measurements over a specimen’s surface. This work introduces the exploratory data analysis of displacement field’s ensembles that are currently used for the probabilistic calibration of constitutive parameters.

Local Deformation Analysis of a Sand Specimen using 3D Digital Image Correlation for the Calibration of a Simple Elasto-Plastic Model

The use of Digital Image Correlation (DIC) technique has become increasingly popular for displacement measurements and for characterizing localized material deformation. In this study, a three-dimensional digital image correlation (3D DIC) analysis was performed to investigate the displacements on the surface of a dense sand specimen during a triaxial compression test (drained, vacuum consolidated). The deformation of a representative volume of the material captured by 3D DIC is used for the estimation of the kinematic and volumetric conditions of the specimen at different stages of deformation, combined with the readings of the global axial compression of the specimen, which allow for the characterization of the Mohr-Coulomb plasticity model with hardening and softening law. A 2D finite element model is developed for comparing the experimental results under displacement controlled loading conditions. A comparison between model predictions and the expected displacement fields show good agreement, as to reproduce accurately the overall mechanical behavior of a dense sand specimen and to take into account the influence of local effects in the mechanical parameters obtained by 3D DIC.

Vortex Structures inside Shear Bands in Sands

We show experimental evidence of vortices emanating from collapsed force chains in shear bands in real sands. Digital image correlation (DIC)-based local displacement analyses have been conducted on overlapping particle clusters to provide grain-scale displacement measurements of sand specimens undergoing plane strain compression. Spatially varying systematic patterns in kinematic data fields have been found within shear bands, defining a coordinated collapse event of the force chains that initially comprise the shear band upon formation. We have identified co-rotating vortices or circulation cells within the shear band by subtracting an overlaid linearly varying shear band displacement field from the observed non-homogeneous shear band displacement field. These vortex structures correlate precisely with previously observed kinematic patterns. We discuss the fate of these vortices and note differences in the vortex patterns observed in our sands from those observed by others in simulations on ideal granular materials.

Length Scales for Nonaffine Deformation in Localized, Granular Shear

We offer experimental observations of meso-scale deformation and kinematic activity within sheared granular layers to investigate the nature and spatial periodicity of nonaffine displacement fields within shear bands in a granular material. Prismatic specimens of sands and glass beads are subjected to plane strain deformation in which zero-strain conditions are enforced by translucent glass walls. We use the Digital Image Correlation (DIC) to track movements of small, overlapping particle clusters. By subtracting a superimposed first-order shear displacement field from the observed non-affine displacement fields, co-rotational vortices appear and coordinate with previously-observed kinematic patterns. We undertake a preliminary assessment of the spatial periodicity of such patterns to glimpse the nature of an underlying length scale for granular material deformation.

EXPERIMENTAL EVIDENCE OF STRUCTURAL DEVELOPMENT INSIDE SHEAR BANDS IN SANDS

We show experimental evidence of vortices emanating from collapsed force chains in shear bands in real sands. From digital image-based local displacement data, a systematic, spatial pattern in kinematic data fields appears at the softening-critical state transition. By subtracting a linear shear displacement field from the observed non-affine displacement field, vortices appear and coordinate with the observed kinematics. We note differences in the vortex patterns observed in our sands from those observed in simulations on “ideal” granular materials, and discuss the fate of these vortices.

VORTICES IN SHEAR BANDS IN SANDS

We show digital image-based experimental evidence of vortex structures within shear bands in sands deforming in plane strain compression. Spatially varying systematic patterns in kinematic data fields have been found within shear bands, defining a coordinated collapse event of the force chains that initially comprise the shear band upon formation. We have identified co-rotating vortices or “circulation cells” within the shear band by subtracting an overlaid linearly varying shear band displacement field from the observed nonhomogeneous shear band displacement field. These vortex structures correlate precisely with previously observed kinematic patterns.

Discovering Community Structures and Dynamical Networks from Grain-Scale Kinematics of Shear Bands in Sand

The quest to understand the connections between the triumvirate of structure, dynamics and function continues to drive the forefront of research in Complex Systems. Crucial to these explorations is the development of graph-theoretic techniques that: (i) can detect communities and associated boundaries in the underlying network or graph, which represents the interactions of constituent units, and (ii) quantify shortest paths and related network measures within this graph. We report on a new study using data from high resolution digital image correlation (DIC) measurements of grain-scale kinematics in sand under shear. Preliminary results show that the nodes of the network in the shear band region exhibit high closeness centrality – a network measure of how efficient a given node is in spreading information to all the other nodes in the graph. It is thus reasonable to expect that the most efficient routes for spread of kinematical information within this network are those from nodes that correspond to the grid points that lie along the shear band. We believe these studies will ultimately lead to an improved understanding of self-organization, the nature of energy flow and dynamics in the critical state regime in the presence of persistent shear bands.

Force Chain Lifetimes in Shear Bands in Sands

We present imaging‐based experimental data of the meso‐scale kinematics associated with force chain buildup and collapse within shear bands in sands. Dense sand specimens are subjected to plane strain compression in an apparatus in which the zero‐strain conditions are enforced by glass walls which permit imaging if in plane deformations. Grain‐scale displacements are quantified continuously through the experimental technique of Digital Image Correlation (DIC). We evaluate the meso‐scale kinematics within the shear bands, the patterns in which have been shown to be strongly indicative of force chain buildup and collapse. We follow the change in these kinematic patterns from global softening to critical state deformation, and discuss the implications of the observed microstructural changes with regard to the evolution in macroscopic response. The kinematics suggest the transition from softening to critical state to be defined microstructurally by a distinct collapse event of the force chains formed at shear...