Mars Rover Drilling for 2020 Sample Return

Collaborator: Dr. Robert C. Anderson, NASA Jet Propulsion Laboratory
Project Sponsor: Keck Institute for Space Studies

The Mars Science Laboratory rover is currently drilling into rocks on Mars to create powder that can be scooped up and passed into her onboard instruments for analysis. In 2020 we plan to send another rover to Mars, but this rover will be drilling to collect intact cylindrical core samples of rock, and storing them in a special container so they can be returned to earth at a later date.

For mission success in 2020, we need to learn all we can from MSL’s current drilling operations, and also conduct experiments on Earth to understand exactly how the different drilling process to be used in 2020 might affect the delicate signs of life and other valuable science assets contained within the core samples. We are developing models of this new drilling process to ensure our 2020 drilling operations preserve the precious science content of the rock samples they produce.

Microscopic Origins of Friction in Granular Shear Flows

Project Sponsor: AFOSR

We have developed a new energy-based relationship between macroscopic friction and microscopic energy dissipation in granular shear flows. This relationship illustrates that macroscopic friction can be understood as the sum of average internal energy dissipation per unit volume within grains and average energy dissipation per unit volume of grain sliding. This relationship offers deeper insight into the microscopic origin of friction by going beyond currently existing fabric-based theories and empirical friction laws.

The energy-based friction relationship has been used to study the microscopic origin of friction in dense granular flows, an important regime of flow marking the transition between quasi-static deformations and rapid gas-like flows. Dense granular flows feature dramatic rate-strengthening of friction and have posed a major challenge to experimentalists, theorists, and modelers for the past decade. The energy-based friction approach allows us to determine, as a function of material properties, the precise tradeoff between average internal dissipation and surface sliding dissipation, visualizing for the first time the energetic origin of rate- strengthening behavior in granular shear flows.

The energy-based friction law offers the opportunity to gain a deeper insight into grain-scale or meso-scale behavior during macroscopic shear as well as the role of mesoscopic energy fluctuations in macroscopic response.

Granular Element Method for Measuring Dynamic Force Transmission in Opaque Granular Materials

Project Sponsor: AFOSR

We have developed the first numerical method for inferring dynamic inter-particle forces in opaque granular materials. The method, called the Granular Element Method (GEM), provides a new tool to quantitatively study the relationship between the transient or steady-state grain-scale response and macroscopic dynamic behavior of an opaque granular material. Previously, experimental measurements were restricted to the use of photoelastic materials in quasi-static settings.

GEM relies on experimental measurements of grain locations and intra-grain strain fields during  quasi-static or dynamic tests, and a numerical procedure incorporating momentum balance equations, stress relations, and multi-objective optimization technique. To obtain these experimental measurements, digital image correlation (DIC), X-ray computed tomography (XRCT) and 3D X-ray diffraction (3DXRD) provide state-of-the-art capabilities when paired with suitable post-processing algorithms.

GEM can be used to study contemporary issues involving granular materials, including the relationship between force transmission and macroscopic stresses, waves, and shocks. GEM will provide a new path forward for experimental dynamic characterization of these complex materials.

Dynamic Liquefaction

A mathematical criterion based on bifurcation theory and isotropic elastoplasticity has been developed to predict the onset of liquefaction instability in fully saturated porous media under static and dynamic loading conditions. The proposed liquefaction criterion is general, and can be applied to any elastoplastic constitutive model. Since the liquefaction criterion is only as accurate as the underlying constitutive model utilized, the modified Manzari-Dafalias plasticity model was chosen for its accuracy, relative simplicity and elegance. Moreover, an implicit return mapping algorithm has been developed for the numerical implementation of the Manzari Dafalias model, and a consistent tangent operator has been derived to obtain optimal convergence with finite elements. The accuracy of the implementation has been benchmarked against laboratory experiments under static and cyclic conditions and also with qualitative boundary value problems. The framework is expected to serve as a tool to enable prediction of liquefaction occurrence in the field under general static and dynamic conditions. Further, the methodology can help advance our understanding of the phenomenon in the field as it can clearly differentiate between unstable behavior, such as flow liquefaction, and material failure, such as cyclic mobility.




Characterizing Granular Materials using Level Sets

This work is focused on using level-sets to characterize the geometry and behavior of granular materials.  We are interested in using the level-set evolution method on high resolution x-ray CT scans of samples to obtain level sets of individual grains, and then using these level-sets to model grain behavior and kinematics through a method similar to DEM, which is in development.

Micro-Orogin of Macro Strength

This work attempts to develop an analytical study about the behavior of arbitrary shaped and sized non-cohesive two-dimensional granular materials. Several mechanical properties and relations are unraveled by connecting micro and macro scales in a explicit fashion that, at the same time, provides the basis for an analytical-theoretical multi-scale framework.

Furthermore, this work is based on three main ideas that are developed and connected progressively; namely, the obtention of explicit expressions that enable us to relate micro- scale parameters, such as contact forces and fabric, to stress and strain as a macro (continuum) physical properties. Then, with these powerful tools, physical connections and relations between the mentioned micro-parameters and macro-constitutive parameters as friction angle, dilatancy, vorticity, and critical state are established.

A Simple Device for In-Situ Direct Shear and Sinkage Tests

This work introduces a simple device designed to perform in-situ direct shear and sinkage tests on granular materials as sand, clays, or regolith. It consists of a box nested within a larger box. Both have open bottoms, allowing them to be lowered into the material. Afterwards, two rotating plates on opposite sides of the outer box will rotate outwards in order to clear regolith on either side, providing room for the inner box to move relative to the plates and perform a shear test without the resistance of the surrounding soil. From this test, Coulomb parameters, including cohesion and internal friction angle, as well as, Bekker parameters can be infferred. This device has been designed for a laboratory setting, but with few modifications, could be put on the underside of a rover for use in a remote location. The goal behind this work is to ultimately create a compact, but accurate measuring tool to put onto a rover or any kind of exploratory vehicle to test for regolith properties of celestial bodies.

Computational Discrete Mechanics

Project Sponsor: National Science Foundation

We developed the Granular Element Method (GEM),the next-generation discrete element method (DEM) based on Non-Uniform Rational Basis Splines (NURBS). GEM aims to improve the representation of particle morphology in computations and ease the transition from binary images to discrete models.

GEM allows for the representation of particle morphological features,
namely, sphericity and angularity, to their fullest extent, with local contact rolling resistance and interlocking emanating directly from grain geometry. By allowing for arbitrary particle shapes, modeling flexibility is significantly enhanced, to a level that is comparable with isogeometric methods. As such, the transition from image data to particle shapes is greatly streamlined. More importantly, increased macroscopic strength in granular packings comprising of non-convex angular particles is fully captured.

GEM is the first step towards constructing a new discrete element strategy that eliminates the shape deficiency that has plagued classical DEM for a long time and at the same time, maintaining a level of implementation simplicity that is comparable to classical DEM. With the above developments, GEM provides a long-awaited path forward towards a simple and predictive discrete analysis method.

Investigating the Life Cycle of Laboratory Avalanches

The aim of this research is to gain a better understanding of the physics encoded in granular avalanches. It has been observed that the inclination angle of particles during an avalanche is consistently higher than the angle of repose for granular materials.

The life cycle of an avalanche is studied here by running rotating drum experiments. The objectives of this experimental campaign are threefold. First, we investigate the evolution of the angle of inclination of the flowing layer, i.e. the life cycle of the avalanche. Second, we measure the kinematics of the particles that conform the flowing layer of the granular assembly at different stages of the development of the avalanche. Third, we study the evolution of dilatancy from computed average strains of representative groups of particles within the flowing layer.

Experiments are performed on a 300 millimeters diameter rotating drum containing 1 millimeter steel beads. The dry frictional monodisperse assembly is subjected to shear stresses imposed by the rotation of the drum. Subsequently, particle movements are captured by high-speed imaging and Digitial Image Correlation (DIC) is used to analyze the images and measure the kinematics of the grains. Finally, particle kinematics obtained from the experiments is used within a multiscale model to explain the cycle of an avalanche as observed in drum experiments. (Avalanches.avi)

Mechanics of Origin of Liquefaction

Project Sponsor: THOR

The 1964 Niigata earthquake, and more recently the 2011 Christchurch earthquake brought to the world’s attention the devastating effects of liquefaction. Despite it’s potential to cause enormous destruction to life and property, the physics underlying liquefaction is still very poorly understood. Even though the behavior of granular materials is fundamentally encoded at the grain-scale, liquefaction is still understood as an empirical macroscopic phenomenon. This work strives to bridge that gap by studying the mechanics behind the origin of this phenomenon. We study static liquefaction in loose sands as observed in triaxial tests. By analyzing the macro and micro-mechanics at play in the lead up to liquefaction in a triaxial test, we hope to gain a deeper insight into liquefaction, which could potentially transform our understanding of liquefaction as a truly multiscale phenomenon.

Inferring Thermal and Mechanical Properties of Celestial Bodies Regolith Using (Simple) Low-Tech Tools

This program aims to develop and test new tools and algorithms for in-situ characterization of thermal and mechanical properties of regolith on celestial bodies such as asteroids, planets, and moons. The new tools and algorithms will be used onboard a landing vehicle to assess properties of regolith including friction angle, dilatancy, thermal conductivity, and specific heat. The primary objective will be to obtain as many engineering and scientific properties with simple low-tech tools such as wheels, masses, awls, small shovels, and soldering irons. These tools and related post-processing algorithms will provide clues about the nature of fundamental morphological processes on celestial bodies by providing crucial mechanical properties. The goal of this project has also a significant impact on mission cost and success, where minimizing energy, eliminating high-tech equipment failure, and optimizing functionality and data extraction are the key issues to tackle and overcome.

Lead Student - Alex Jerves
Caltech Faculty Mentor - José Andrade
JPL Research Mentor - Robert C. Anderson

A Simple Device for In-Situ Direct Shear and Sinkage Tests (2.5 MB pdf)

Video 1 and Video 2

Multiscale Method for Granular Media

Collaborator: Professor Ted Belytschko, Northwestern University
Project Sponsor: AFOSR

A predictive multiscale framework has been developed for modeling the behavior of granular materials. The method is particularly attractive due to its simplicity and ability to exploit the existing finite element and computational inelasticity technologies. Furthermore, this semi-concurrent multiscale method extracts two key material parameters from the granular structure: dilatancy and frictional resistance. The evolution of these material parameters is upscaled into classical plasticity models, effectively bypassing phenomenological hardening laws. The predictiveness of the method has been  demonstrated by comparing its performance with experimental results and direct numerical simulations under homogeneous and inhomogeneous conditions.

As the numerical scheme for the multiscale method, a semi-implicit return mapping algorithm is developed for integrating generic nonsmooth elastoplastic models. The semi-implicit nature of the algorithm stems from 'freezing' the plastic internal variables at their previous state, followed by implicitly integrating the stresses and plastic multiplier. The plastic internal variables are incrementally updated once convergence is achieved (a posteriori). This method is able to integrate nonsmooth (C0) evolution laws that may not be integrable using implicit methods. Though accuracy of the proposed algorithm is step size-dependent, its simplicity and its remarkable ability to handle nonsmooth relations make the method promising and computationally appealing.





Multi-scale Random Fields in Geomechanics

Collaborator: Professor Jack W. Baker, Stanford University
Project Sponsor: NSF

In this research, the multi-scale nature of soil behavior is explicitly accounted for by obtaining the mechanical response of geosystems using an accurate multi-scale hierarchical computational framework. It is well known that the behavior of particulate media, such as sands, is encoded at the granular-scale and hence methods for up-scaling such behavior across relevant scales of interest—from granular-scale (~1mm) to field-scale (>1m)—are needed to attain a more accurate prediction of soil behavior. Multi-scale analysis is especially important under extreme conditions such as strain localization, penetration or liquefaction, where the classical constitutive description may no longer apply. Several unanswered questions illustrate the importance of studying such phenomena: What material parameterizations are most appropriate at various scales? What are the relevant scales needed for an accurate material description? What are the impacts of uncertainties and inhomogeneities on field-scale behavior? A probabilistic framework across multiple scales is needed to answer these questions and to consistently compute the behavior of the material across scales.

In an unprecedented fashion, probabilistic models for soil porosity are developed at multiple scales, using experimental results from X-Ray computed tomography to study spatial correlation down to the millimeter scale. From a computational standpoint, the multi-scale framework is demonstrated using well-established models for sands. In this hierarchical approach, a more accurate material description—at finer scales—is pursued only in the presence of strong inhomogeneities, either material or imposed (e.g. by deformations). The hierarchical approach is based on passing the macroscopic deformation down to the finer scale(s) and then returning more accurate, averaged stresses. Monte Carlo simulation is used to generate material properties in a hierarchical manner, so that fine scale material data can be obtained whenever necessary, conditional upon previously simulated coarse scale data. These modeling approaches will be developed and then used in several parametric and validation studies to bring insight to practical problems where multi-scale effects are important. Multi-scale modeling opens the door to develop design-specific engineering systems with desirable qualities or properties, and will allow scientists and engineers to better understand the role of finer scales on the behavior of complex geotechnical systems.

Discrete Element Modeling of the Nanostructure of Cement Paste

At the nano scale, cement paste is believed to be composed of tiny basic units of calcium-silicate-hydrate (C-S-H) colloids with a characteristic length of 5 nm.  These units cannot be directly seen in a microscope, but a vast array of experimental information about its properties have been determined using experimental methods such as gas adsorption, small-angle neutron scattering, calorimetry, electron microscopy, and nanoindentation.  Using indirect information about specific surface area, density, elastic modulus, and nucleation and growth mechanisms, a discrete element model of over 4 million particles with Hertzian contacts is being developed. These particles, believed to act as a granular material, have granular properties such as friction and cohesion along with the Van der Waals forces that take effect at the nano scale.

Currently, nanoindentation simulations on the model are being used to test predictions of properties such as indentation modulus, packing density, stress distributions, etc.  The goal is therefore to use the nanostructure of C-S-H to predict bulk properties in cement paste, such as shrinkage and creep.  By accurately predicting such properties, we hope to use the model to gain a greater understanding of macro-level characteristics with a long-term goal of developing new types of cementitious materials.

Partially Saturated Media

Thus far, a new constitutive relationship for drying of porous materials has been developed and shown to greatly improve the strain predictions in cement- and glass-based porous media.  Examining the implications of these results with respect to the classic expression of the effective stress in partially saturated media, largely unchanged in its form since the publication in the early 1960s, is an ongoing topic of interest. Efforts to incorporate the aforementioned material-point laws into an efficient FEM framework and thus to apply the results to the more complex boundary-value problems is also under way.

Constitutive laws that are based more on the physical mechanisms and less on the phenomenological attributes provide better predictions of material response and at the same time require less parameter calibration. One current topic being explored is an application of this maxim to materials whose pore spaces contain two or more fluids, i.e. partially saturated materials.

Liquefaction of Sands

The onset of liquefaction can be predicted by constitutive modeling via calculation of a critical plastic modulus.  The method has already been shown to accurately reproduce static liquefaction as observed in triaxial tests on loose sands.  This research is currently being expanded to predict potentially unstable regions of slopes using finite element methods.  Soon, the constitutive model will be enhanced to allow for the prediction of liquefaction caused by cyclic loading.

Micromechanics of Granular Media

A quantitative methodology has been developed that regularizes the numerical calibration procedure for explicit DEM schemes to achieve solution convergence and quasi-static states. One ongoing topic is to investigate the microscopic failure mechanism for granular materials using relevant numerical tools. Also, efforts are being made to develop a multi-scale framework that bridges microscopic models with traditional macroscopic models to capture granular material behaviors under dramatically different conditions spanning homogeneity to discontinuity.