Granular Dilatancy Research Articles

Granular dilatancy and non-local fluidity of partially molten rock

Partially molten rock is a densely packed, melt-saturated, granular medium, but it has seldom been considered in these terms. In this paper we extend the continuum theory of partially molten rock to incorporate the physics of granular media. Our formulation includes dilatancy in a viscous constitutive law and introduces a non-local fluidity. We analyse the resulting poro-viscous–granular theory in terms of two modes of liquid–solid segregation that are observed in published torsion experiments: localisation of liquid into high-porosity sheets and radially inward liquid flow. We show that the newly incorporated granular physics brings the theory into agreement with experiments. We discuss these results in the context of grain-scale physics across the nominal jamming fraction at the high homologous temperatures relevant in geological systems.

Impact Behavior of Dense Debris Flows Regulated by Pore‐Pressure Feedback

AbstractThe impact dynamics of dilute debris flows (typically volumetric solid fractions<50%) have been extensively investigated within the framework of hydraulics. For dense debris flows, the impact mechanisms have been poorly studied. From a geotechnical viewpoint, the feedback between granular dilatancy and pore‐pressure response may play an important role in the dense debris‐flow regime. In this study, the impact behavior of dense and dilute debris flows in an instrumented flume is analyzed. The basal stresses (normal/shear stresses, pore‐fluid pressure) and impact pressure on a rigid barrier are measured. A time‐dependent creeping mode is observed for the impact process of slow‐moving dense debris flows, which cannot be accurately estimated using current debris‐flow load models. At the grain scale, this macroscopic creeping mode is a result of the feedback between granular dilatancy and pore‐pressure response. This feedback can be further characterized by examining the timescales associated with pore‐pressure generation and dissipation. The regulation of pore‐pressure feedback on basal shear stress, impact load, and state of static deposit is revealed. Finally, a tentative phase diagram is proposed for dense and dilute debris‐flow impact. The proposed framework complements the theory for debris‐flow impact loads.

A two-fluid model for immersed granular avalanches with dilatancy effects

When a deposited layer of granular material fully immersed in a liquid is suddenly inclined above a certain critical angle, it starts to flow down the slope. The initial dynamics of these underwater avalanches strongly depends on the initial volume fraction. If the granular bed is initially loose, i.e. looser than the critical state, the avalanche is triggered almost instantaneously and exhibits a strong acceleration, whereas for an initially dense granular bed, i.e. denser than the critical state, the avalanche's mobility remains low for some time before it starts flowing normally. This behaviour can be explained by a combination of geometrical granular dilatancy and pore pressure feedback on the granular media. In this contribution, a continuum formulation is presented and implemented in a three-dimensional continuum numerical model. The originality of the present model is to incorporate dilatancy as an elasto-plastic normal stress or pressure and not as a modification of the friction coefficient. This allows an explanation of the two different behaviours of initially loose and dense underwater avalanches. It also highlights the contribution from each depth-resolved variable in the strongly coupled transition to a flowing avalanche. The model compares favourably with existing experiments for the initiation of underwater granular avalanches. Results reveal the interplay between shear-induced changes of the granular stress and fluid pressure in the dynamics of avalanches. The characteristic time of the triggering phase is nearly independent of the local rheological parameters, whereas the initial drop in pore pressure and the surface velocity at steady state still strongly depend on them. Finally, the multidimensional capabilities of the model are illustrated for the two-dimensional Hele-Shaw configuration and some of the observed differences between one-dimensional simulations and experiments are clarified.

Evidence of a non-local ø(I) response

Granular dilatancy has been previously characterised through a simple linear relationship between the packing fraction and dimensionless shear rate. However, this relationship was developed for granular flows in a simple shear cell geometry. Here we examine inertial volume changes in a shear cell with gravity, a vertical chute, and a pseudo-2D hopper. In so doing, we show that the packing fraction displays both a local and non-local response, analogous to what is typically observed for the stress ratio µ.

Dilatancy in dry granular flows with a compressible μ(I) rheology

Dilatancy plays a key role in mixtures of grains and fluid but is poorly investigated in dry granular flows. These flows may however dilate by more than 10% in granular column collapses. We investigate here dilatancy effects in dry flows with a shallow depth-averaged model designed to be further applied to simulate natural landslides. We use a compressible μ(I), ϕeq(I) rheology with a dilatancy law, where ϕeq(I) is the volume fraction at the equilibrium (i.e. critical) state and I the so-called inertial number. This law is obtained by simply removing the fluid phase in the solid/fluid model of our previous work (Bouchut et al., 2016) [7] and derived from critical state theory. A numerical method is proposed to solve the equations, that have however singularities that are rather difficult to handle.Simulations of granular collapses on horizontal and sloping beds show that the maximum height of the deposits changes as a function of the initial volume fraction with higher (lower) deposits for initially denser (looser) granular masses, as observed with Discrete Element simulations. The front position and the deposit shape behind it are on the contrary poorly affected by the initial volume fraction, as if the flow had almost forgotten its initial state. However subtle effects can be observed with the occurrence of low velocity regimes on steep slopes that strongly depend on the initial volume fraction. Simulations show complex compression/dilation effects during the flow, in particular with front dilation (compression) during the acceleration (deceleration) phases. These effects may dramatically change the effective friction that is observed to decrease at the front in some situations, while the μ(I) rheology without dilatancy would have predicted an increasing friction. The model predicts an increasing dilation of the mass for increasing slopes by up to 10% in the studied configurations, in agreement with laboratory experiments. Our results suggest that this compressible model contains key features to describe granular dilatancy.

Investigation of influence of an obstacle on granular flows by virtue of a depth-integrated theory

Understanding granular flows past an obstacle is very important to most possibly avoid damage to human properties and infrastructures. The present paper investigates the influence of an obstacle on dry and fluid-saturated granular flows to gain insights into physics behind them. To this end, we extend the existing depth-integrated theory by considering additional effects from the pore fluid pressure and the granular dilatancy. We revisit a large-scale experiment to validate the extended theory. The good agreement between numerical results and experimental data reveals that the granular dilatancy plays a crucial role in the mobility and peak depth. Furthermore, we investigate the influence of obstacles on dynamics of dry granular flows by comparing numerical results with experimental data. It is shown that shock waves, dead zones and vacuum (grain-free zone) well observed in the experiments can be captured. Additionally, a fluid-saturated granular flow past the same obstacle is numerically simulated to interpret the role of the interstitial fluid, especially the pore fluid pressure, in the fluid-granular mixture causing distinct dynamic behaviours from those of a dry granular flow. It is also found that the granular dilatancy has a significant influence on the pore fluid pressure which can mitigate the granular friction. This is consistent with many experimental observations. Additionally, it is demonstrated that the pore fluid pressure is prone to elevate in front of a cuboid dam (but not in front of a forward-facing tetrahedral wedge), which in turn mitigates the granular friction. The findings are helpful to understand complex behaviours encountered in geophysical flows and industrial processes.

Continuum modelling of primary and secondary granular flows in a torsional shear cell

In granular flows, the particles not only move along the principal streamlines but can also circulate perpendicularly to streamlines slowly in a vortex-like manner. Such behaviours have both scientific and practical significances, e.g. in convective mixing of particles, but their mechanisms are still under study. Previous experimental observations have stimulated two explanations for them: centrifugal force and volumetric dilatancy. Here a theoretical model is constructed to test these conjectures, which is based on the frictional plasticity and accounts for both dynamic effect and strain-dependent dilatancy. The simulation results show that, under the influence of gravity, the centrifugal force can indeed give rise to vortices in a Couette cell. In the absence of centrifugal force, granular vortices can still be observed depending on the shape of the yield surface. If the yield surface is a von Mises circle in the deviatoric plane, i.e. of Drucker-Prager type, no vortex is observed in continuum modelling. But for noncircular yield surfaces, a clear secondary flow is generated at some boundary conditions and increases in magnitude with the non-circularity of yield surface. Large granular dilatancy occurs in some regimes of high gradients, but altogether its influence on secondary flow is not critical. The role of boundary conditions is also discussed.

Modeling dynamic flows of grain–fluid mixtures by coupling the mixture theory with a dilatancy law

A depth-averaged two-velocity grain–fluid mixture model is proposed to describe flows of grain–fluid mixtures. Motivated by the experimental observations, the proposed model considers that the granular and the fluid phases are moving with different velocities, and the velocity difference between the granular phase and the fluid phase is coupled with the granular dilatancy that is described by a granular dilatancy law. The characteristics of flows allow to formulate a simpler depth-averaged PDE system. To scrutinize the proposed equations, an analysis for steady flows in rectangular channels is performed, which reproduces the cross-stream velocity profiles commonly observed in fields. Additionally, a uniform flow is investigated to illustrate the effects of the granular dilatancy on the velocities, flow depth, and volume fractions.

Discussion of “The relation between dilatancy, effective stress and dispersive pressure in granular avalanches” by P. Bartelt and O. Buser (DOI: 10.1007/s11440-016-0463-7)

A paper recently published by Bartelt and Buser (hereafter identified as “the authors”) aims to clarify relationships between granular dilatancy and dispersive pressure and to question the effective stress principle and its application to shallow granular avalanches (Bartelt and Buser in Act Geotech 11:549–557, 2). The paper also criticizes our own recent work, which utilizes the concepts of evolving dilatancy and effective stress to model the initiation and dynamics of water-saturated landslides and debris flows. Here we first explain why we largely agree with the authors’ views of dilatancy and dispersive pressure as they apply to depth-integrated granular avalanche models, and why we disagree with their views of effective stress and pore-fluid pressure. We conclude by explaining why the authors’ characterization of our recently developed D-Claw model is inaccurate.

Local rheology of suspensions and dry granular materials

The flow of dry and wet granular media is investigated in a Couette geometry using magnetic resonance imaging in order to test the applicability of the “fluidity model” for nonlocality in these materials. Local volume fraction measurements show that the systems become heterogeneous during flow. We find that the nonlocal rheology of suspensions can be correlated using the fluidity model, but the length scale that emerges is not a material property and the model cannot be used for predictive purposes. Rather, the suspension behavior is fully explained as a consequence of stress-driven particle migration and the resulting concentration gradient. The conclusion is less strong for the dry granular system, but it appears likely that the apparent nonlocal behavior is simply due to the formation of a shear band caused by granular dilatancy.

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis

To simulate debris-flow behaviour from initiation to deposition, we derive a depth-averaged, two-phase model that combines concepts of critical-state soil mechanics, grain-flow mechanics and fluid mechanics. The model's balance equations describe coupled evolution of the solid volume fraction, m , basal pore-fluid pressure, flow thickness and two components of flow velocity. Basal friction is evaluated using a generalized Coulomb rule, and fluid motion is evaluated in a frame of reference that translates with the velocity of the granular phase, v s . Source terms in each of the depth-averaged balance equations account for the influence of the granular dilation rate, defined as the depth integral of ∇⋅ v s . Calculation of the dilation rate involves the effects of an elastic compressibility and an inelastic dilatancy angle proportional to m − m eq , where m eq is the value of m in equilibrium with the ambient stress state and flow rate. Normalization of the model equations shows that predicted debris-flow behaviour depends principally on the initial value of m − m eq and on the ratio of two fundamental timescales. One of these timescales governs downslope debris-flow motion, and the other governs pore-pressure relaxation that modifies Coulomb friction and regulates evolution of m . A companion paper presents a suite of model predictions and tests.

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests

We evaluate a new depth-averaged mathematical model that is designed to simulate all stages of debris-flow motion, from initiation to deposition. A companion paper shows how the model's five governing equations describe simultaneous evolution of flow thickness, solid volume fraction, basal pore-fluid pressure and two components of flow momentum. Each equation contains a source term that represents the influence of state-dependent granular dilatancy. Here, we recapitulate the equations and analyse their eigenstructure to show that they form a hyperbolic system with desirable stability properties. To solve the equations, we use a shock-capturing numerical scheme with adaptive mesh refinement, implemented in an open-source software package we call D-Claw. As tests of D-Claw, we compare model output with results from two sets of large-scale debris-flow experiments. One set focuses on flow initiation from landslides triggered by rising pore-water pressures, and the other focuses on downstream flow dynamics, runout and deposition. D-Claw performs well in predicting evolution of flow speeds, thicknesses and basal pore-fluid pressures measured in each type of experiment. Computational results illustrate the critical role of dilatancy in linking coevolution of the solid volume fraction and pore-fluid pressure, which mediates basal Coulomb friction and thereby regulates debris-flow dynamics.

Evolution of elastic wave speed during shear‐induced damage and healing within laboratory fault zones

AbstractEarthquake faults fail and restrengthen repeatedly during the seismic cycle. Faults restrengthen via a set of processes known collectively as fault healing, which is well documented in the laboratory but less well understood in tectonic fault zones. Recent observations of fault zone wave speed following earthquakes suggest opportunities to connect laboratory and field observations of fault healing. However, existing laboratory data lack detail necessary to identify specific processes linking elastic wave speed to fault damage and healing. Here we document changes in elastic properties during laboratory seismic cycles, simulated via periods of nonshear and quasistatic fault slip. Experiments were conducted on brine‐saturated halite under conditions favoring pressure solution, analogous to healing processes within and at the base of the seismogenic zone. We find that elastic wave speed (V) and amplitude (A) correlate with porosity. For each percent of porosity lost during compaction, VP increases by ~3%, VS by ~2%, AP by ~10%, and AS by ~7%. Moreover, V and A decrease with granular dilation during fault slip. With increasing shear strain, fabric formation dominates the ultrasonic signals. We find that fault strength depends on fault porosity, making VP and VS potential proxies for fault strength evolution. Our data show that a 1% change in VP or VS results in a friction increase of 0.01 or 0.02, respectively. Within natural fault zones, advances in monitoring elastic wave speed may provide critical information on the evolution of fault strength and seismic hazard throughout the seismic cycle.

Impact-activated solidification of dense suspensions via dynamic jamming fronts

Although liquids typically flow around intruding objects, a counterintuitive phenomenon occurs in dense suspensions of micrometre-sized particles: they become liquid-like when perturbed lightly, but harden when driven strongly. Rheological experiments have investigated how such thickening arises under shear, and linked it to hydrodynamic interactions or granular dilation. However, neither of these mechanisms alone can explain the ability of suspensions to generate very large, positive normal stresses under impact. To illustrate the phenomenon, such stresses can be large enough to allow a person to run across a suspension without sinking, and far exceed the upper limit observed under shear or extension. Here we show that these stresses originate from an impact-generated solidification front that transforms an initially compressible particle matrix into a rapidly growing jammed region, ultimately leading to extraordinary amounts of momentum absorption. Using high-speed videography, embedded force sensing and X-ray imaging, we capture the detailed dynamics of this process as it decelerates a metal rod hitting a suspension of cornflour (cornstarch) in water. We develop a model for the dynamic solidification and its effect on the surrounding suspension that reproduces the observed behaviour quantitatively. Our findings suggest that prior interpretations of the impact resistance as dominated by shear thickening need to be revisited.

Cement-based mixes: Shearing properties and pore pressure

This study presents original results on the rheological measurement of concrete mixes. It focuses on how to determine their mechanical and physical behavior under shearing stress. More specifically, the influence of aggregate content on shearing properties is studied. A vane rheometer was developed to characterize fresh cement-based materials. In addition to the conventional concrete rheometer, a special hydraulic pressure transducer was fitted to the container to monitor the pore water pressure variation while shearing the material. Experiments on cement paste, mortar, and concrete bring a new approach to help us understand the behavior of fresh-state mixes. The results show 1) a correlation between water pore pressure and torque applied on the vane; 2) a critical sand volume fraction, ϕ c, as a limit between colloidal interaction behavior and frictional behavior in mortars; beyond this critical fraction, a leap in yield stress and a drop in pore pressure due to granular dilatancy are noticed; 3) the granular content clearly influences the increase in yield stress of the cement mixes: above ϕ c, this increase becomes negligible.

Particle Pressure in a Sheared Suspension: A Bridge from Osmosis to Granular Dilatancy

The normal stress exerted by particles in a sheared suspension is measured by analogy with a method used to measure osmotic pressure in solutions. Particles in a liquid are confined by a fine screen to a gap between two vertical concentric cylinders, the inner of which rotates. Pressure in the liquid is sensed either by a manometer or by a pressure transducer across the screen. The particles are large enough so that Brownian motion and equilibrium osmotic pressure are vanishingly small. The measured pressure yields the shear-induced particle pressure Pi, the nonequilibrium continuation of equilibrium osmotic pressure. For volume fractions 0.3< or =varphi< or =0.5, Pi is strongly dependent on varphi, and linear in shear rate. Comparisons of the measured particle pressure with modeling and simulation show good agreement.

Anisotropic model for granulated sea ice dynamics

A continuum model describing sea ice as a layer of granulated thick ice, consisting of many rigid, brittle floes, intersected by long and narrow regions of thinner ice, known as leads, is developed. We consider the evolution of mesoscale leads, formed under extension, whose lengths span many floes, so that the surrounding ice is treated as a granular plastic. The leads are sufficiently small with respect to basin scales of sea ice deformation that they may be modelled using a continuum approach. The model includes evolution equations for the orientational distribution of leads, their thickness and width expressed through second-rank tensors and terms requiring closures. The closing assumptions are constructed for the case of negligibly small lead ice thickness and the canonical deformation types of pure and simple shear, pure divergence and pure convergence. We present a new continuum-scale sea ice rheology that depends upon the isotropic, material rheology of sea ice, the orientational distribution of lead properties and the thick ice thickness. A new model of lead and thick ice interaction is presented that successfully describes a number of effects: (i) because of its brittle nature, thick ice does not thin under extension and (ii) the consideration of the thick sea ice as a granular material determines finite lead opening under pure shear, when granular dilation is unimportant.

Influence of particle characteristics on granular friction

We report on laboratory experiments designed to illuminate grain‐scale deformation mechanisms within fault gouge. We vary particle size distribution, grain and surface roughness, and gouge layer thickness to better understand how grain sliding, rolling, dilation, and compaction affect the strength and stability of granular fault gouge. The experiments employed the double direct shear testing geometry and were run at room temperature, controlled humidity, and shearing rates from 0.1 to 3000 μm/s. Experiments were carried out under constant normal stress of 5 and 10 MPa and thus within a nonfracture loading regime where sliding friction for smooth, spherical particles is measurably lower than for rough, angular particles. We compare results from shear between smooth boundaries, where we hypothesize that grain boundary sliding is the dominant deformation mechanism, and roughened surfaces, where rolling and granular dilation contribute to shear deformation. We find that particle angularity and bounding surface roughness increase the frictional strength within sheared layers, indicating differences in particle reorganization due to these factors. In gouge material composed of &lt;30% angular grains we observe repetitive stick‐slip sliding where stress drop decreases while preinstability creep increases with increasing gouge layer thickness. Our data show significant differences in stick‐slip characteristics as a function of gouge layer thickness and particle size, which we interpret in terms of the mechanics of grain bridges that support forces on the layers. We suggest that force chains exhibit qualitative differences as a function of grain angularity and bounding surface roughness.

Granular Dilatancy and the Plasticity of Glassy Lubricants

This note is concerned with various experimental observations of plastic-flow behavior in presumably glassy states of low-molecular-weight lubricants subject to high shear rates and confining pressures. It is proposed here that the nearly linear relation found between shear stress and presssure can be attributed to shear-induced volume change, qualitatively the same as that associated with Reynolds dilatancy and shear strength in a hypothetical frictionless granular material. Recent computer simulations of the latter lend quantitative support to this hypothesis.

SHEAR-FLOW AND MATERIAL INSTABILITIES IN PARTICULATE SUSPENSIONS AND GRANULAR MEDIA

ABSTRACT This article is a review of recent theoretical work on shear flow instabilities of particulate suspensions and dry granular medium. Attention is devoted largely to steady homogeneous unbounded simple shearing flows, as a generalization of the classical Kelvin problem for Newtonian fluids, with a view towards identifying material or constitutive instabilities arising from the coupling of stress to particulate concentration and temperature fields. After reviewing the most common constitutive models, a unified linear-stability treatment is given for suspensions and granular media, based on an assumed ‘short-memory’ response of stress and various fluxes to perturbations on materially steady and uniform base states. A two-dimensional stability analysis of inertialess suspension flow indicates the possibility of particle-depleted shear bands. A comprehensive three-dimensional analysis of rapid granular flow reveals transverse ‘layering and spanwise ’corrugations’ as possible modes of instability. The latter appear to result from a kind of material instability, although not the simple short-wavelength instability found for suspensions. Based on the current theoretical treatments, several new studies are recommended, including the effects of granular dilatancy and yield stress, three-dimensional disturbances in suspensions and the effects of gravity in granular now.