DOI: 10.5061/dryad.mcvdnck95
title: Loading-dependent microscale measures control bulk properties in granular material: an experimental test of the Stress-Force-Fabric relation

description: The bulk behaviour of granular materials is tied to its mesoscale and
 particle-scale features: strength properties arise from the buildup of
 various anisotropic structures at the particle-scale induced by grain
 connectivity, force transmission, and frictional mobilization. More
 fundamentally, these anisotropic structures work collectively to define
 features like the bulk friction coefficient and the stress tensor at the
 macroscale and can be explained by the Stress-Force-Fabric (SFF)
 relationship stemming from the microscale arrangement of the forces and
 fabric. Although the SFF relation has been extensively verified by
 discrete numerical simulations, a laboratory realization has remained
 elusive due to the challenge of measuring both normal and frictional
 contact forces. In this study, we analyze experiments performed on a
 photoelastic granular system under four different loading conditions:
 uniaxial compression, isotropic compression,  pure shear, and
 annular shear. During these experiments, we record particle locations,
 contacts, and normal and frictional forces to measure the particle-scale
 response to progressing strain. We experimentally assess the
 Stress-Force-Fabric (SFF) relation across multiple loading conditions in a
 2D photoelastic granular system. We track microscale measures like the
 packing fraction, average coordination number, and average normal force,
 along with anisotropic distributions of contacts and forces. We then
 connect these particle-scale anisotropies to bulk behavior using the SFF
 relation, which provides compact expressions for both the stress tensor
 and the bulk friction coefficient in terms of fabric and force
 anisotropies. Our results demonstrate that these expressions accurately
 capture the bulk stress and friction across different loading histories,
 validating the predictive power of the SFF framework. Additionally, we
 test the assumption that contact and force anisotropies contribute equally
 to load transmission in our granular packings and show that this
 assumption is sufficient at large strain values and can be applied to
 areas like rock mechanics, soft colloids, or cellular tissue where force
 information is inaccessible.
description: Photoelastic granular images were taken using colour images and
 analysed using the PhotoElastic Grain
 Solver algorithm to determing the particle positions and contact
 forces. <br><br>Four distinct loading histories are recorded,
 packings in a rectangular chamber are subject to pure shear, isotropic
 compression and uniaxial compression, where particles in an annular
 chamber are annular shear. <br><br>Each loading history has a
 number of datasets, in which are the particle positions, adjacency matrix
 and in the case of the rectangular chambers are the valid images. See
 README for a further description
description: # Loading-dependent microscale measures control bulk properties in
 granular material: an experimental test of the Stress-Force-Fabric
 relation Dataset DOI: [10.5061/dryad.mcvdnck95](10.5061/dryad.mcvdnck95)
 ## Description of the data and file structure This repository contains
 three folders corresponding to the data (at different stages of
 processing) for three cartesian loading schemes for photoelastic particles
 on an airtable. ### Files and variables #### File: figure2.zip
 **Description:** The data in this folder contains three files
 corresponding to the angular distributions of the contact, normal forces
 and tangential forces that are plotted in figure2 of the paper.
 **Ec(theta).txt** columns correspond: -angle: angle corresponding to
 \theta as defined in the text. Units radians -eps = 0.xx : column labels
 indicate the strain step at which each distribution is measured columns
 beyond the first angle column corresponds to $E^c(\theta)$, the contact
 probability density. **Fn(theta).txt** columns correspond: -angle: angle
 corresponding to \theta as defined in the text. Units radians -eps = 0.xx
 : column labels indicate the strain step at which each distribution is
 measured columns beyond the first angle column corresponds to
 $ Dataset -&gt; Adjacency list,
 particle positions, image values (for IsotropicCompression, PureShear and
 Uniaxial Compression). A conversion file for the Daniels lab use is also
 included with the filename dryad2eno.txt **centers_tracked.txt** The
 format is :frame number, particleID, x, y, r, edge. Frame number
 corresponds to the relevant image, particleID is the unique particle
 number, x, y are the coordinates in pixels, r is the radius of the
 particle in pixels and edge is a binary flag whether the particle is at an
 edge or not. Pixel to meter conversion is 0.00019853 m/pixel
 **Adjacency_list.txt** The format is: frame number, particleID1,
 particleID2, tangential force, normal force Frame number corresponds to
 the relevant image, particleID is the unique particle number for each in
 contact. The normal and tangential forces correspond to the force from
 particle 1 to particle 2. **image_segments.txt** This format is :frame 1,
 frame 2 Where the first frame indicates the starting frame for the
 relevant loading (where the forces start) and the second is where the
 loading ends. **dryad2eno.txt** A file for the Daniels lab to use to match
 this dataset to the data stored on the lab server, eno. It matches the
 name of the data set presented here to the name of the data as stored on
 the server.