Granular Stress Research Articles

Modeling of the interaction of rigid wheels with dry granular media

We analyze the capabilities of various recently developed techniques, namely granular Resistive Force Theory (RFT) and continuum plasticity implemented with the Material Point Method (MPM), in capturing dynamics of wheel-dry granular media interactions. We compare results to more conventionally accepted methods of modeling wheel locomotion. While RFT is an empirical force model for arbitrarily-shaped bodies moving through granular media, MPM-based continuum modeling allows the simulation of full granular flow and stress fields. RFT allows for rapid evaluation of interaction forces on arbitrary shaped intruders based on a local surface stress formulation depending on depth, orientation, and movement of surface elements. We perform forced-slip experiments for three different wheel types and three different granular materials, and results are compared with RFT, continuum modeling, and a traditional terramechanics semi-empirical method. Results show that for the range of inputs considered, RFT can be reliably used to predict rigid wheel granular media interactions with accuracy exceeding that of traditional terramechanics methodology in several circumstances. Results also indicate that plasticity-based continuum modeling provides an accurate tool for wheel-soil interaction while providing more information to study the physical processes giving rise to resistive stresses in granular media.

A rapid granular chute avalanche impinging on a small fixed obstacle: DEM modeling, experimental validation and exploration of granular stress

• A DEM model is used to study the flow characteristics of a rapid granular avalanche subject to an obstacle. • The free flow shows slightly anisotropic stress state, whereas the disturbed flow shows strongly anisotropic stress state. • A shear band develops at a distance of roughly twice the particle diameter above the basal surface. • A stronger shear band forms in the upstream region near the obstacle due to granular jamming. • On the centerline of the chute, the principal direction of the normal stresses is nearly parallel to the flow direction. Granular flows are constrained by applied stresses. When a granular flow moves rapidly and impinges on an obstacle, the stress is significantly increased along the contact force networks. Granular stresses are still incompletely understood. The aim of this study is to investigate a rapid avalanche of spherical glass beads in an inclined chute with a small fixed semi-cylindrical obstacle by using particle image velocimetry (PIV) technique and discrete element method (DEM). The proposed DEM model produces good agreement with the corresponding avalanche experiment in terms of the velocity profiles. The validated DEM results are then used to explore the internal flow characteristics of a granular avalanche that are not directly observable in experiments, such as the solid fraction, the average coordination number and the granular stress. Rectangular measurement cells, similar to representative volume elements, are developed to determine the spatial variation in stresses for the granular avalanche. The internal flow characteristics of a rapid granular avalanche with and without obstacles are compared. For the unobstructed flow, the normal and shear stresses decrease in the downstream direction because the solid fraction and the average coordination number decrease, resulting from the gravitational acceleration. On the other hand, granular jamming forms in front of the semi-cylindrical obstacle and results in a significant increase in the normal and shear stresses. The unobstructed flow shows slightly anisotropic stress states, giving an earth pressure coefficient of approximately 1.0, whereas the disturbed flow exhibits strongly anisotropic stress states. The simulation results show that the corresponding earth pressure coefficient can be much higher than unity and increases to a maximum value of roughly 5.0. A shear band develops at a distance of roughly twice the particle diameter above the basal surface and a stronger shear band forms in the upstream vicinity of the obstacle.

On the mechanics of granular shear: The effect of normal stress and layer thickness on stick-slip properties

Seismic stress drop is one of the most important earthquake source parameters, playing a key role in elastic energy release and in scaling relations for seismic moment and fault length. While stress drop does not scale systematically with earthquake size, it varies greatly within seismic catalogs and there is much broad interest in understanding how such variations relate to fault zone properties. Here, we address connections between stress drop and fault zone properties via laboratory experiments that investigate the role of normal stress and layer thickness during frictional sliding. We sheared granular layers at normal stresses from 4 to 22 MPa and document both elastic and inelastic processes that couple with layer dilation to determine the granular fragility and stress drop during stick-slip failure. Stick-slip stress drop scales directly with fault normal stress and inversely with layer thickness. Thicker layers exhibit, greater dilation during shear loading, however shear driven dilatant volume strain is independent of layer thickness. We posit that force chains form rapidly after a dynamic slip event and that bulk inelastic creep occurs via formation and destruction of force chains, interparticle slip, and rolling. Stick-slip recurrence time and stress drop vary with fault normal stress and stiffness, which increases with shear strain, consistent with a model in which stiffness increases as porosity decreases and fault zone density increases. We propose a micromechanical model that accounts for force chains and spectator regions where granular processes are dominated by inelastic slip. We document the role of elastic and inelastic processes during three stages of the stick-slip cycle and show how these change systematically as a function of normal stress and layer thickness. Our work shows that dilation during shear loading contributes to frictional strength via volume strain and that apparent friction scales inversely with the granular thinning ratio.

Universal friction law at granular solid-gas transition explains scaling of sediment transport load with excess fluid shear stress

A key interest in geomorphology is to predict how the shear stress $\tau$ exerted by a turbulent flow of air or liquid onto an erodible sediment bed affects the transport load $M\tilde g$ (i.e., the submerged weight of transported nonsuspended sediment per unit area) and its average velocity when exceeding the sediment transport threshold $\tau_t$. Most transport rate predictions in the literature are based on the scaling $M\tilde g\propto\tau-\tau_t$, the physical origin of which, however, has remained controversial. Here we test the universality and study the origin of this scaling law using particle-scale simulations of nonsuspended sediment transport driven by a large range of Newtonian fluids. We find that the scaling coefficient is a universal approximate constant and can be understood as an inverse granular friction coefficient (i.e., the ratio between granular shear stress and normal-bed pressure) evaluated at the base of the transport layer (i.e., the effective elevation of energetic particle-bed rebounds). Usually, the granular flow at this base is gaslike and rapidly turns into the solidlike granular bed underneath: a liquidlike regime does not necessarily exist, which is accentuated by a nonlocal granular flow rheology in both the transport layer and bed. Hence, this transition fundamentally differs from the solid-liquid transition (i.e., yielding) in dense granular flows even though both transitions are described by a friction law. Combining this result with recent insights into the nature of $\tau_t$, we conclude that the transport load scaling is a signature of a steady rebound state and unrelated to entrainment of bed sediment.

Development of a mathematical model for submarine granular flows

An Eulerian-Eulerian two-phase model based on a collisional-frictional law for the granular stress is proposed for the description of underwater granular flows and is applied to the collapses of immersed granular columns, which can be viewed as an idealized physical model of submarine landslides. In the mathematical model, the kinetic theory for dry granular flows is extended to take into account the particle-fluid interaction when formulating the collisional stress in the granular material, while the frictional stress is modeled based on an existing relation obtained by statistically averaging the individual contact forces among cohesionless particles. The drag force and the virtual-mass force are considered to represent the inter-phase interaction. The two-phase model is then employed to simulate the laboratory experiments of the collapses of granular columns immersed in an ambient liquid with an emphasis on the effect of the initial packing condition of the granular particles. It has been shown that the computed collapsing process of granular columns is in very good agreement with the experimental observations, and the proposed model can well capture the dynamic features of underwater granular flows. The effects of fluid pressure, drag force, and particle and fluid properties on the granular collapse are also discussed. It is demonstrated that the interstitial fluid flow plays a significant role in the collapsing process.

DEM study on the macro- and micro-responses of granular materials subjected to creep and stress relaxation

The behavior of a typical crushable granular material, i.e., rockfill, during creep and stress relaxation is studied using the discrete element method. Rockfill particles are modeled as breakable agglomerates with time-dependent bond strengths. Parameters are derived from experimental results and reasonable macro-responses are reproduced. The deviator stress level is found to have significant influence on the evolution of the agglomerate breakage number and mechanical coordination number during creep, whereas these two numbers increase slightly during stress relaxation in all situations. The relationship between the macro- and micro-responses is explored. The micro-mechanism of the observed nonisochronous phenomenon is also investigated.

Fractal dimension of roughness: Influence of grain size and granular class

The soil structure can be described as an assembly of elements of various sizes separated by a complex system of cracks and fractures, since the grains of the soil are differentiated by their shape, size and orientation. They are thus differently associated and related, their masses can form complex and irregular configurations which are in general extremely difficult to characterize in exact geometric terms. To understand the mechanical behavior of granular materials, it is then necessary to characterize the grains using the fractal dimension which is a characteristic that indicates the degree of irregularity and fragmentation of the latter.
 This experimental work consists in studying the influence of the parameters variation: granular class, grain size and normal stress applied during Casagrande's direct shear tests on the roughness fractal dimension calculated with the method of Box counting. The analysis of the results obtained at the end of a granulometric variation which caused a variation of the fractal dimension of grain roughness. This variation made it possible to analyze the level of fragmentation suffered by the sandstone grains during the various shear tests. This fragmentation produces fines that are the source of variations in the mechanical properties of the sandstone material.

Pattern formation of frictional fingers in a gravitational potential

Aligned finger structures, with a characteristic width, emerges during the slow drainage of a liquid/granular mixture in a tilted Hele-Shaw cell. A transition from vertical to horizontal alignment of the finger structures is observed as the tilting angle and the granular density are varied. An analytical model is presented, demonstrating that the alignment properties is the result of the competition between fluctuating granular stresses and the hydrostatic pressure. The dynamics is reproduced in simulations. We also show how the system explains patterns made during dyke formations.

Experimentally determined distribution of granular-flow characteristics in collisional bed load transport

A series of laboratory experiments on turbulent open-channel two-phase flow in a form of intense bed load transport is reported. Measurements in a laboratory tilting flume included camera based imaging techniques to identify the structure of the flow at the local level. Obtained experimental distributions of two-phase flow related parameters - granular velocity, concentration, and temperature - across a collisional transport layer are discussed. The results are analysed together with additional measured quantities (discharges of mixture and grains, flow depth, bed slope etc). Our major goal is to evaluate the distribution of granular stresses across the transport layer with a special attention paid to the interface between the transport layer and the bed. Furthermore, comparisons are discussed between the experimental results and predictions produced by suitable kinetic-theory based models.

Volcanic avalanche fault zone with pseudotachylite and gouge in French Massif Central

Structures and textures with sedimentological variations at different scales of the lithofacies assemblage help us to constrain the basal kinematic transition from non-depositional to depositional conditions during volcanic avalanche emplacement. In the well-exposed impact-sheared contact along volcanic avalanche fault zone in the French Massif Central, we observe how the granular textures of the pseudotachylite and fault gouge have recorded the propagation of shock wave with granular oscillatory stress. Sequential events of basal aggradation along avalanche fault zone have been established related to fractal D-values, temperature pressure regime and oscillatory stress during slow wave velocity.A typical lithofacies assemblage with a reverse grading shows the pseudotachylite and fault gouge. A cataclastic gradient is characterised by the fractal D-values from 2.7 in jigsaw breccias with pseudotachylite partial melt, to 2.6 in the polymodal gouge. Shock, brecciation and comminution produce cataclastic shear bands in the pseudotachylite and quartz microstructures along the basal contact of the volcanic debris-avalanche deposit. Gouge microstructures show granular segregation, cataclasis with antithetic rotational Riedel shear, and an arching effect between the Riedel shear bands. X-ray microtomography provided 3D microfabrics along the clastic vein in the sandy-gouge. From the available statistical dataset, a few equations have been developed implicating the same cataclastic origin with a co-genetic evolution of lithofacies.An impact wave during primary shear propagation may contribute to produce hydroclastic matrix, pseudotachylite partial melt and proximal gouge thixotropy with v~50m/s and a T<654°C. The interseismic period with oscillatory stress is related to crushed clasts and basaltic melt around ~800°C, Riedel shear bands with granular segregation along the fault gouge. The secondary shock by matrix-rich avalanche (ΔP=10GPa, T≥1000–1500°C) contributes to quartz microstructures along the avalanche basal contact and quartz spheroids in microscopic cataclastic shear bands. Decompression around 654–800°C is related to tertiary sub-vertical oscillations with a backward moving shock and antithetic rotational fault megablock. Semi-quantitative analyses of seismogenic fault basement contribute to establish the localised conditions related to sequential aggradation along volcanic avalanche fault zone.

A two-phase thermomechanical theory for granular suspensions

In this paper, a two-phase thermomechanical theory for granular suspensions is presented. Our approach is based on a mixture-theoretic formalism and is coupled with a nonlinear representation for the granular viscous stresses so as to capture the complex non-Newtonian behaviour of the suspensions of interest. This representation has a number of interesting properties: it is thermodynamically consistent, it is non-singular and vanishes at equilibrium and it predicts non-zero granular bulk viscosity and shear-rate-dependent normal viscous stresses. Another feature of the theory is that the resulting model incorporates a rate equation for the evolution of the volume fraction of the granular phase. As a result, the velocity fields of both the granular material and the carrier fluid are divergent even for constant-density flows. Further, in this article we present the incompressible limit of our model which is derived via low-Mach-number asymptotics. The reduced equations for the important special case of constant-density flows are also presented and discussed. Finally, we apply the proposed model to two test cases, namely, steady shear flow of a homogeneous suspension and fully developed pressure-driven channel flow, and compare its predictions with available experimental and numerical results.

On large deformation granular strain measures for generating stress–strain relations based upon three-dimensional discrete element simulations

Generating stress–strain relations based upon three-dimensional discrete element simulations, for hierarchical multiscale constitutive modeling of granular materials at finite strain, requires measures of stress and strain in the reference and current configurations. The Cauchy stress tensor calculated from interparticle forces and branch vectors resulting from discrete element simulations, is well-established, but the various finite strain definitions existing in the literature are not as well studied or accepted. Thus, the paper develops seven finite strain measures in three-dimensions (Cartesian coordinates assumed): two are calculated in the reference configuration, and five are calculated in the current configuration. In the process, a time-integrated deformation gradient is formulated, with which the Cauchy stress tensor can be mapped to either the Kirchhoff stress, first Piola–Kirchhoff stress, or second Piola–Kirchhoff stress. The difficulty in calculating strain measures for granular materials is the discrete particulate nature of the materials. In the paper, strain measures are motivated by the equivalent continuum method, but are extended to finite strain in three-dimensions. Simulations are conducted to test the finite strain measures, and it is found that these strain measures are independent of rigid body rotation of a particle assembly. Granular Cauchy stress is also calculated for these discrete element simulations to be able to plot stress–strain curves in the current configuration. Finally, two numerical examples with large deformation are simulated: (1) cavity expansion, and (2) pile penetration; and their results are analyzed.

Viscoplastic modeling of granular column collapse with pressure-dependent rheology

A mechanical and numerical model of dry granular flows is proposed that quantitatively reproduce laboratory experiments of granular column collapse over inclined planes. The rheological parameters are directly derived from the experiments. The so-called μ(I) rheology is reformulated in the framework of Drucker–Prager plasticity with the yield stress and viscosity η(‖D‖,p) depending on both the pressure p and the norm of the strain rate tensor ‖D‖.The granular domain, velocities, stress deviator and pressure fields are calculated using a finite element method based on an iterative decomposition–coordination formulation coupled with the augmented Lagrangian method.2-D simulations using this model well reproduce the dynamics and deposits of collapsing granular columns. The flow is essentially located in a surface layer behind the front, whereas it is distributed over the whole depth near the front where basal sliding occurs. The computed runout distances and slopes of the deposits agree very well with the values found in the experiments.Using an easily calculated order of magnitude approximation of the mean viscosity during the flow (η=1Pas here), we show that a Drucker–Prager rheology with a constant viscosity gives results very similar to the μ(I) rheology and agrees with experimental height profiles, while significantly reducing the computational cost. Within the range of viscosities 0.1<η<1Pas, the dynamics and deposits are very similar. The observed slumping behavior therefore appears to be mainly due to the flow/no-flow criterion and to the associated strain-independent part of the “flowing constitutive relation” (i.e. related to plastic effects). However, the results are very different when an unrealistically large value of viscosity (10Pas) is used.

Silo Collapse under Granular Discharge

We investigate, at a laboratory scale, the collapse of cylindrical shells of radius R and thickness t induced by a granular discharge. We measure the critical filling height for which the structure fails upon discharge. We observe that the silos sustain filling heights significantly above an estimation obtained by coupling standard shell-buckling and granular stress distribution theories. Two effects contribute to stabilize the structure: (i) below the critical filling height, a dynamical stabilization due to granular wall friction prevents the localized shell-buckling modes to grow irreversibly; (ii) above the critical filling height, collapse occurs before the downward sliding motion of the whole granular column sets in, such that only a partial friction mobilization is at play. However, we notice also that the critical filling height is reduced as the grain size d increases. The importance of grain size contribution is controlled by the ratio d/√[Rt]. We rationalize these antagonist effects with a novel fluid-structure theory both accounting for the actual status of granular friction at the wall and the inherent shell imperfections mediated by the grains. This theory yields new scaling predictions which are compared with the experimental results.

Sidewinding with minimal slip: snake and robot ascent of sandy slopes.

Limbless organisms such as snakes can navigate nearly all terrain. In particular, desert-dwelling sidewinder rattlesnakes (Crotalus cerastes) operate effectively on inclined granular media (such as sand dunes) that induce failure in field-tested limbless robots through slipping and pitching. Our laboratory experiments reveal that as granular incline angle increases, sidewinder rattlesnakes increase the length of their body in contact with the sand. Implementing this strategy in a physical robot model of the snake enables the device to ascend sandy slopes close to the angle of maximum slope stability. Plate drag experiments demonstrate that granular yield stresses decrease with increasing incline angle. Together, these three approaches demonstrate how sidewinding with contact-length control mitigates failure on granular media.

Effective stress in saturated soil: a granular solid hydrodynamics approach

Effective stress is one of the most fundamental concepts in soil mechanics. A comprehensive interpretation of its physical essence is important for a better understanding and prediction of the mechanical behaviour of the soil. The granular solid hydrodynamics approach is used in this study to establish a more generalised effective stress principle for saturated soils. In this approach, the stress formulation is theoretically derived from the constraints between conservation laws and thermodynamic principles, in which the energies in soils are quantitatively described by the classical non-equilibrium thermodynamics. Five physical mechanisms of the soil deformation, including the elastic potential, the elastic relaxation, the granular fluctuation, the viscosity and the effect of bound water, are taken into account in the derivation of the stress formulation. Consequently, the effective stress derived in this study is classified into four categories. The first is elastic effective stress that is determined by the elastic potential energy and is limited by a stress state boundary line. The second is granular effective stress that is relevant to the granular fluctuation and is very important to the unrecoverable soil deformation. The third is bound effective stress which is a result of defining the bound water as an independent phase of the soil system. It is an important driving force in the non-isothermal unrecoverable soil deformation induced by the conversion of bound water to free water. The last—viscous stress—is another important part of effective stress.

Initiation of immersed granular avalanches.

By means of coupled molecular dynamics-computational fluid dynamics simulations, we analyze the initiation of avalanches in a granular bed of spherical particles immersed in a viscous fluid and inclined above its angle of repose. In quantitative agreement with experiments, we find that the bed is unstable for a packing fraction below 0.59 but is stabilized above this packing fraction by negative excess pore pressure induced by the effect of dilatancy. From detailed numerical data, we explore the time evolution of shear strain, packing fraction, excess pore pressures, and granular microstructure in this creeplike pressure redistribution regime, and we show that they scale excellently with a characteristic time extracted from a model based on the balance of granular stresses in the presence of a negative excess pressure and its interplay with dilatancy. The cumulative shear strain at failure is found to be ≃ 0.2, in close agreement with the experiments, irrespective of the initial packing fraction and inclination angle. Remarkably, the avalanche is triggered when dilatancy vanishes instantly as a result of fluctuations while the average dilatancy is still positive (expanding bed) with a packing fraction that declines with the initial packing fraction. Another nontrivial feature of this creeplike regime is that, in contrast to dry granular materials, the internal friction angle of the bed at failure is independent of dilatancy but depends on the inclination angle, leading therefore to a nonlinear dependence of the excess pore pressure on the inclination angle. We show that this behavior may be described in terms of the contact network anisotropy, which increases with a nearly constant connectivity and levels off at a value (critical state) that increases with the inclination angle. These features suggest that the behavior of immersed granular materials is controlled not only directly by hydrodynamic forces acting on the particles but also by the influence of the fluid on the granular microstructure.

Trans- Granular Stress Corrosion in Partially Fabricated Austenitic Stainless Steel Items and their Re-Conditioning to make them Suitable for Balance Fabrication

Fabrication of various sub assemblies and items from imported austenitic stainless steel material of SA 240 - 304L (32 mm to 85 mm thick) was started in the year 1990 and work on these assemblies was stopped in 1993 due to unavoidable circumstances. Items and sub-assemblies were either in partially welded / machined or formed condition. Sub assemblies / items were stored in open yard for 13 years after applying plastic peal coating compound and covered with tarpaulin. The storage yard was near to the sea (roll on &amp; off Jetty) as well as next to petrochemical industries. Sub assemblies have seen different extreme weathers conditions, saline and corrosive atmosphere for all these years and during this storage time base material and welded joints were subjected to contamination.

Dip of the granular shear stress

Recent experiments reveal an unexpected dip of the shear stress as the shear rate increases, from the rate-independent regime to Bagnold flow. Employing granular solid hydrodynamics, it is shown that in uniform systems, such dips occur for given pressure or normal stress, but not for given density. If the shear rate is strongly nonuniform, enforcing a constant volume does not prevent the local density to vary, and a stress dip may still occur.

Performance evaluation of a complete Lagrangian KTGF approach for dilute granular flow modelling

Finely resolved gas–solid flow simulations were carried out using an improved Lagrangian method known as the dense discrete phase model (DDPM). The DDPM differs from the traditional Eulerian two fluid model (TFM) approach in that the solids phase is treated as discrete parcels of particles and not as a continuum. This method of particle tracking has several important fundamental advantages over standard Eulerian multifluid approaches including the much improved grid independence behaviour and easy inclusion of particle size distributions. Similarly to the TFM, particle collisions and uncorrelated translations are not simulated directly and still need to be modelled by means of the kinetic theory of granular flows (KTGF). This work presents two important improvements to the present state of development of the DDPM: the granular temperature was transported and the additional particle force due to the modelled granular shear stresses was included. The complete model compared well to control simulations carried out using the well-established TFM approach. The impact of the two modelling improvements was also investigated to find large effects, especially with regard to the granular temperature fields. Negligence of granular temperature transport reduced the total amount of granular temperature by a factor of fifteen, while negligence of the shear force resulted in a factor of three increase. It could therefore be concluded that the model improvements are indeed necessary to correctly capture the physics in the dilute riser flows simulated in the present study.