Laboratory Studies of Granular Materials Under Shear: From Avalanches to Force Chains

Granular materials reveal their complexity and some of their unique features when subjected to shear deformation. They can dilate, behave like a solid or a fluid, and are known to carry external forces preferentially as force chains. In this dissertation, we employ laboratory experiments to study the complex behavior of granular materials under shear. We introduce a multiscale approach in which the underlying grain-scale mechanics are experimentally measured and homogenized to obtain enriched macroscopic quantities. First, we investigate granular avalanches spontaneously generated by a rotating drum. Measurements of grain kinematics are directly incorporated into a rate-dependent plasticity model that explains and reproduces the life cycle of laboratory avalanches. The results presented here feature dilatancy as the key material parameter governing the triggering of an avalanche. Second, we report a set of experiments performed on a custom-built mechanical device that allows a specimen composed of a two-dimensional analogue granular assembly to be subjected to quasi-static shear conditions. A numerical force inference technique, the Granular Element Method (GEM), provides direct observation and quantitative characterization of force chain structures in assemblies made of realistic grains. Equipped with a complete description of the grain-scale mechanics, we show that shear deformation creates geometrical (fabric) and mechanical (force) anisotropy. Finally, the influence of grain shape on grain-scale processes is studied. We find that grain interlocking is a prominent deformation mechanism for non-circular grains that ultimately promotes a significant increase in macroscopic shear strength. By seamlessly connecting grain-scale information to continuum scale experiments, this dissertation sheds light on the multiscale mechanical behavior of granular assemblies under shear.</p

A novel experimental device for investigating the multiscale behavior of granular materials under shear

In this paper, we report a set of experiments performed on a novel mechanical device that allows a specimen composed of a two-dimensional opaque granular assembly to be subjected to quasi-static shear conditions. A complete description of the grain-scale quantities that control the mechanical behavior of granular materials is extracted throughout the shear deformation. Geometrical arrangement, or fabric, is quantified by means of image processing, grain kinematics are obtained using Digital Image Correlation and contact forces are inferred using the Granular Element Method. Aiming to bridge the micro-macro divide, macroscopic average stresses for the granular assembly are calculated based on grain-scale fabric parameters and contact forces. The experimental procedure is detailed and validated using a simple uniaxial compression test. Macroscopic results of shear stress and volumetric strain exhibit typical features of the shear response of dense granular materials and indicate that critical state is achieved at large deformations. At the grain scale, attention is given to the evolution of fabric and contact forces as the granular assembly is sheared. The results show that shear deformation induces geometrical (fabric) and mechanical (force) anisotropy and that principal stresses and force orientation rotate simultaneously. At critical state, stress, force and fabric orientation reach the same value. By seamlessly connecting grain-scale information to continuum scale experiments, we shed light into the multiscale mechanical behavior of granular assemblies under shear loading

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

Capturing the inter-particle force distribution in granular material using LS-DEM

Particle shape, as one of the most important physical ingredients of granular materials, can greatly alter the characteristic of inter-particle force distribution which is of vital importance in understanding the mechanical behavior of granular materials. However, currently both experimental and numerical studies remain limited in this regard. In this paper, we for the first time validate the ability of the level set discrete element method (LS-DEM) on capturing the inter-particle force distribution among particles of arbitrary shape. We first present the technical detail of LS-DEM; we then apply LS-DEM to simulate experiments of shearing granular materials composed of arbitrarily shaped particles. The proposed approach directly links experimentally measured material properties to model parameters such as contact stiffness without any calibration. Our results show that LS-DEM is able to not only capture the macro scale response such as stress and deformation, but also to reproduce the particle scale contact information such as the distribution of contact force magnitude, contact orientation and contact friction mobilization. Our work demonstrates the promising potential of LS-DEM on studying the mechanics and physics of natural granular material and on aiding design granular particle shape for novel macro-scale mechanical property

Extracting inter-particle forces in opaque granular materials: Beyond photoelasticity

This paper presents the first example of inter-particle force inference in real granular materials using an improved version of the methodology known as the Granular Element Method (GEM). GEM combines experimental imaging techniques with equations governing particle behavior to allow force inference in cohesionless materials with grains of arbitrary shape, texture, and opacity. This novel capability serves as a useful tool for experimentally characterizing granular materials, and provides a new means for investigating force networks. In addition to an experimental example, this paper presents a precise mathematical formulation of the inverse problem involving the governing equations and illustrates solution strategies

Discrete element modeling of planetary ice analogs: mechanical behavior upon sintering

Potentially habitable icy Ocean Worlds, such as Enceladus and Europa, are scientifically compelling worlds in the solar system and high-priority exploration targets. Future robotic exploration of Enceladus and Europa by in-situ missions would require a detailed understanding of the surface material and of the complex lander-surface interactions during locomotion or sampling. To date, numerical modeling approaches that provide insights into the icy terrain's mechanical behavior have been lacking. In this work, we present a Discrete Element Model of porous planetary ice analogs that explicitly describes the microstructure and its evolution upon sintering. The model dimension is tuned following a Pareto-optimality analysis, the model parameters' influence on the sample strength is investigated using a sensitivity analysis, and the model parameters are calibrated to experiments using a probabilistic method. The results indicate that the friction coefficient and the cohesion energy density at the particle-scale govern the macroscopic properties of the porous ice. Our model reveals a good correspondence between the macroscopic and bond strength evolutions, suggesting that the strengthening of porous ice results from the development of a large-scale network due to inter-particle bonding. This work sheds light on the multi-scale nature of the mechanics of planetary ice analogs and points to the importance of understanding surface strength evolution upon sintering to design robust robotic systems. Graphic abstractISSN:1434-5021ISSN:1434-763

The InSight HP³ Penetrator (Mole) on Mars: Soil Properties Derived from the Penetration Attempts and Related Activities

The NASA InSight Lander on Mars includes the Heat Flow and Physical Properties Package HP3 to measure the surface heat flow of the planet. The package uses temperature sensors that would have been brought to the target depth of 3–5 m by a small penetrator, nicknamed the mole. The mole requiring friction on its hull to balance remaining recoil from its hammer mechanism did not penetrate to the targeted depth. Instead, by precessing about a point midway along its hull, it carved a 7 cm deep and 5–6 cm wide pit and reached a depth of initially 31 cm. The root cause of the failure – as was determined through an extensive, almost two years long campaign – was a lack of friction in an unexpectedly thick cohesive duricrust. During the campaign – described in detail in this paper – the mole penetrated further aided by friction applied using the scoop at the end of the robotic Instrument Deployment Arm and by direct support by the latter. The mole tip finally reached a depth of about 37 cm, bringing the mole back-end 1–2 cm below the surface. It reversed its downward motion twice during attempts to provide friction through pressure on the regolith instead of directly with the scoop to the mole hull. The penetration record of the mole was used to infer mechanical soil parameters such as the penetration resistance of the duricrust of 0.3–0.7 MPa and a penetration resistance of a deeper layer (> 30 cm depth) of 4.9±0.4 MPa. Using the mole’s thermal sensors, thermal conductivity and diffusivity were measured. Applying cone penetration theory, the resistance of the duricrust was used to estimate a cohesion of the latter of 2–15 kPa depending on the internal friction angle of the duricrust. Pushing the scoop with its blade into the surface and chopping off a piece of duricrust provided another estimate of the cohesion of 5.8 kPa. The hammerings of the mole were recorded by the seismometer SEIS and the signals were used to derive P-wave and S-wave velocities representative of the topmost tens of cm of the regolith. Together with the density provided by a thermal conductivity and diffusivity measurement using the mole’s thermal sensors, the elastic moduli were calculated from the seismic velocities. Using empirical correlations from terrestrial soil studies between the shear modulus and cohesion, the previous cohesion estimates were found to be consistent with the elastic moduli. The combined data were used to derive a model of the regolith that has an about 20 cm thick duricrust underneath a 1 cm thick unconsolidated layer of sand mixed with dust and above another 10 cm of unconsolidated sand. Underneath the latter, a layer more resistant to penetration and possibly containing debris from a small impact crater is inferred. The thermal conductivity increases from 14 mW/m K to 34 mW/m K through the 1 cm sand/dust layer, keeps the latter value in the duricrust and the sand layer underneath and then increases to 64 mW/m K in the sand/gravel layer below.ISSN:1572-9672ISSN:0038-630

The InSight HP³ Penetrator (Mole) on Mars: Soil Properties Derived From the Penetration Attempts and Related Activities

The NASA InSight Lander on Mars includes the Heat Flow and Physical Properties Package HP3 to measure the surface heat flow of the planet. The package uses temperature sensors that would have been brought to the target depth of 3--5 m by a small penetrator, nicknamed the mole. The mole requiring friction on its hull to balance remaining recoil from its hammer mechanism did not penetrate to the targeted depth. Instead, by precessing about a point midway along its hull, it carved a 7 cm deep and 5-6 cm wide pit and reached a depth of initially 31 cm. The root cause of the failure - as was determined through an extensive, almost two years long campaign - was a lack of friction in an unexpectedly thick cohesive duricrust. During the campaign -- described in detail in this paper -- the mole penetrated further aided by friction applied using the scoop at the end of the robotic Instrument Deployment Arm and by direct support by the latter. The mole finally reached a depth of 40 cm, bringing the mole body 1--2 cm below the surface. The penetration record of the mole and its thermal sensors were used to measure thermal and mechanical soil parameters such as the thermal conductivity and the penetration resistance of the duricrust and its cohesion. The hammerings of the mole were recorded by the seismometer SEIS and the signals could be used to derive a P-wave velocity and a S-wave velocity and elastic moduli representative of the topmost tens of cm of the regolith. The combined data were used to derive a model of the regolith that has an about 20 cm thick duricrust underneath a 1 cm thick unconsolidated layer of sand mixed with dust and above another 10 cm of unconsolidated sand. Underneath the latter, a layer more resistant to penetration and possibly consisting of debris from a small impact crater is inferred