Lawrence Livermore National Laboratory

Eric B. Herbold


Three main tasks were defined at the onset of this project: (1) conduct novel experiments on granular materials using three-dimensional x-ray diffraction and x-ray computed tomography; (2) study grain strains, force networks, local failure processes, and the consequent changes in material length scales, anisotropy, and strength; and (3) assess and improve Lawrence Livermore National Laboratory's computational modeling capabilities for geological material.

The first task required the design and construction of one compression load frame and the modification of an existing apparatus for small-scale granular material experiments. One of these load frames (built by Lund University in Sweden) was modified for uniaxial and triaxial experiments with ultrasound capabilities. The second load frame was built at Livermore for uniaxial compression experiments with enhanced ultrasound capabilities (including pulse shaping). Six other experiments were conducted at x-ray synchrotron sources in the United States, France, and Sweden.

The second task focused on data reduction and detailed analysis. These high-quality datasets enabled numerous detailed investigations into the contact, deformation, motion, and fracture of single grains within granular ensembles, the results of which comprise a body of work that is the first of its kind. The final experimental campaign produced data using diffraction contrast tomography on granular materials that resulted in the first-ever three-dimensional strain mapping for a single grain within a granular material under load.

The third task was to assess and improve Livermore's modeling capabilities for geological materials. The original idea for this task was to use discrete element methods to improve the contact physics model based on datasets compiled during this project. One such contact method was developed. However, the data processing of contact dissipation mechanisms was conducted too late in the project to calibrate and compare the results of contact modeling.

The field of granular mechanics has benefitted from this project by the dissemination of novel datasets and analytical results published in world-class journals and other venues. Ongoing efforts to calibrate discrete element methods models based on data is of great interest to the pharmaceutical and additive manufacturing communities because data combining grain stresses, grain contact locations, and grain contact histories have not been measured experimentally until now.

Figure 1.
Schematic diagram of the project's concept. Novel experiments and analyses were conducted to study the physics of force chains and mechanical failure in granular materials to enhance existing numerical models.

We used recently developed techniques in x-ray imaging and numerical data inversion to study failure in granular materials with unprecedented detail, thus enhancing the Laboratory's core capabilities in computer-based modeling. We combined three-dimensional x-ray diffraction and x-ray computed tomography to measure in situ the strains and kinematics of thousands of grains being loaded to the point of mechanical failure. These measurements, combined with novel data inversion techniques, allowed us to determine inter-particle force development during loading, unloading, and mechanical failure. The measurements were conducted at three separate synchrotron x-ray facilities: the Advanced Photon Source at Argonne National Laboratory (Lemont, IL), the European Synchrotron Radiation Facility (ESRF, Grenoble, France), and the Cornell High-Energy Synchrotron Source (Ithaca, NY).

The experimental data we gathered were used to answer the following questions: (1) Under what force and strain conditions do granular and amorphous materials mechanically fail? (2) How does failure affect force chains (and vice versa), as well as material length scales, anisotropy, and strength? (3) How well do Livermore's existing numerical models predict these processes? The answers provide new insight into the multiscale nature of failure processes in granular materials, and the datasets are informative enough not only for use in calibrating Livermore's existing constitutive models, but also to provide data for the next generation of models.

Impact on Mission

This research supports the DOE goal to deliver the scientific discoveries and tools that transform our understanding of nature and strengthen the connection between advances in fundamental science and technology innovation. It also enhances the Laboratory's core competencies in advanced materials and manufacturing, as well as high-performance computing, simulation, and data science. The analytical results of this project are relevant to the fields of basic geoscience in that the response of granular material under load is important to geophysicists investigating the phenomenon of fault gouge in earthquake zones. Ongoing efforts to calibrate grain models of different soil types is important to many other projects at Livermore. Furthermore, our analyses of datasets provided new information about intra-grain contact history that will have implications across multiple scientific disciplines, specifically those interested in grain contact physics. Ongoing research will continue to improve ultrasonic measurements to obtain dispersion and attenuation measurements for granular materials under load.


During this project, six separate experimental campaigns were conducted, and the analyses of their results are in progress. Novel analytical approaches were developed to interpret focused investigations into the relative motion of particles in contact. Several publications have supported previous theoretical and numerical findings regarding the distribution of normal force within granular materials under compressive load. We also investigated grain fracture and particle rotation and related these findings to topological information. Results exceeded expectations and are proving to be of interest to academia and industry alike.


Berthier, L., et al. 2011. "Dynamical Heterogeneities in Glasses, Colloids, and Granular Media." OUP Oxford. doi: 10.1093/acprof:oso/9780199691470.001.0001.

Jaeger, H. M., et al. 1996. "Granular Liquids, Solids and Gases." Reviews of Modern Physics 68(4): 1259. doi: 10.1103/RevModPhys.68.1259.

Trepat, X., et al. 2009. "Physical Forces During Collective Cell Migration." Nature Physics 5(6): 426–430. doi: 10.1038/nphys1269.

Zhang, H. and H. Makse. 2005 "Jamming Transition in Emulsions and Granular Materials." Physical Review E 72(1): 011301. doi: 10.1103/PhysRevE.72.011301.

Publications and Presentations

Hurley, R. C., et al. 2018. "Investigating Continuum Properties of Granular Materials Using Discrete Experiments and Simulations." APS March Meeting, Los Angeles, CA, March 2018. LLNL-ABS-763293.

——— . 2018. "Characterization of Crystal Structure, Kinematics, Stresses, and Rotations in Angular Granular Quartz During Compaction." Journal of Applied Crystallography 51(4): 1021–1034. LLNL-JRNL-740711.

——— . 2017. "Linking Initial Microstructure and Local Response During Quasi-Static Granular Compaction." Physical Review E, 96(1): 012905. LLNL-JRNL-725572.

——— . 2017. "Multi-Scale Mechanics of Granular Solids from Grain-Resolved X-ray Measurements." Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences, 473(2207): 0491. LLNL-JRNL-719225.

——— . 2017. "Understanding Mechanics and Stress Transmission in Granular Solids by Combining 3DXRD and XRCT." CHESS Users' Meeting, Ithaca, NY, 2017. LLNL-PRES-732616.