Three Comments on "A Simple Incremental Modelling of Granular-Media Mechanics"

Using the recent incremental modelling, it is shown that the trajectory of a sample in the phase space of soil mechanics in the vicinity of the critical state is not governed by the rigidity matrix, but by its variations. The characteristics are used to predict that pseudo Young modulus tends to 0 as B -M-1 tends to 0, i.e. near the critical point, where B is the vertical-to-lateral-stress ratio during an axi-symmetric test. An attempt to understand and predict unstable behaviours is done using the same modelling. Compatibility of this modelling with results on soil liquefaction is emphasised.Comment: 6 pages, 1 figur

On the complexity/criticality of Jamming during the discharge of granular matter from a silo

This paper is aimed at pursuing a recent discussion about the comparison between Self-Organised Criticality, the jamming process and the percolation theory in the problem of a silo discharge [I. Zuriguel, A. Garcimartin, D. Maza, L.A.Pugnaloni, J.M.Pastor, "Jamming during the discharge of granular matter from a silo", Phys.Rev.E 71, 051303 (2005)]. Statistics of blocking a silo is investigated from different models: percolation, self organised criticality..Comment: Poudres & Grains 200

Are Temperature and other Thermodynamics Variables efficient Concepts for describing Granular Gases and/or Flows ?

Granular flows and vibro-fluidised granular gases have been extensively studied recently; most of the theoretical analyses and the experimental descriptions use temperature and other thermodynamics concepts. However, taking the very simple case of a vibro-fluidised gas made of identical particles, we show the lack of efficiency of such concepts for the understanding of the physics of such systems. This results from both (i) the fact that the vibrator does not transmit the same amount of energy to each particle, but an amount which depends on its mass and/or its size and (ii) from the fact that it is a strongly dissipative medium. We conclude that most experimental device works rather as velostat as a thermostat. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.FnComment: 7 pages + 1 page, 0 Figur

Comparison between Classical-Gas behaviours and Granular-Gas ones in micro-gravity

Recent vibration experiments in microgravity are re-examined. We show that they demonstrate that "granular-gas" state exists only in the Knudsen regime, that its excitation is "supersonic" and that the probability density function of the pressure of the gas scales as (Af) to the power 3/2, with A and f being the excitation amplitude and frequency. This paper pursues the description of the experimental results. Then, it compares these ones to what can be predicted from few simple modelling, which are (i) the classical-gas theory and (ii) the thermodynamics of a single particle in a 1d box. The anomalous scaling of pressure fluctuations (Af) to the 3/2 is explained by the crossover from the regime of a single collision during the sampling time, which imposes p scales as_ (Af) at small speed, to a multiple collision imposing p scales as_(Af)_ . Air effect and effect of g-jitter are discussed and quantified. Influence of grain-grain collisions is described on the distribution of speed. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.FnComment: 23 pages +2 page+ 1 page; 5 figure

New corner stones in dissipative granular gases

Theory of granular dissipative gas is discussed based on Boltzmann's equation and in view of recent experimental results in micro-gravity during few CNES and ESA campaigns [9,11]. It is recalled that the Boltzmann's distribution is a steady solution only when collisions are elastic; hence it is not applicable in the case of dissipative granular gas. The first experimental case concerns non-interacting balls in a vibrated cylindrical box, which proves that rotation-induced dissipation has important consequence: it reduces the efficient phase space dimension of this billiard-like system from 13-d to 1-d, since the motion is 1d and quasi-periodic for large enough forcing; the result remains valid with 2 balls. The second experiment concern the dynamics of interacting particles in the case of a small number (N= 12,24,36,48) of grains: The typical speed of a balls is found to vary linearly with the piston speed, but decreases when the number of balls N increases. The distribution of waiting times T1 between successive ball-gauge collisions follows an exponential distribution experimentally, i.e. P(T1)= exp(-T1/To), proving uncorrelated motions of balls. The amplitude I of the ball-gauge impacts is found to decrease exponentially p(I)=exp(-I/Io).This is temptatively explained using a model "a la Boltzmann" associated with the notion of "velostat", and a second model is proposed based on dissipation. Experiments show the coupling between rotation and translation during collisions cannot be neglected, because it generates efficient dissipation.Comment: 46 pages + 1 page, 12 Figure

How to Fit simply Soil Mechanics Behaviour with Incremental Modelling and to Describe Drained Cyclic Behaviours

It has been proposed recently a new incremental modelling to describe the mechanics of soil. It is based on two parameters called the pseudo Young modulus E=1/Co and the pseudo Poisson coefficient n, which both evolve during compression. Evolution of n is known since it shall fit the Rowe's law of dilatancy, but Co has to be evaluated from experiment. In this paper we proposed a way to evaluate the Co variation from other mechanical modelling. The way cyclic behaviour of drained sample can be modelled is also described.Comment: 9 pages + 1 page, 2 Figure

On Jaky constant of oedometers, Rowe's relation and incremental modeling

It is recalled that stress-strain incremental modelling is a common feature of most theoretical description of the mechanical behaviour of granular material. An other commonly accepted characteristics of the mechanical behaviour of granular material is the Rowe's relation which links the dilatancy K to the ratio B of vertical to lateral stress during a test at constant lateral stress, i.e. B=(1+M)(1+K). We combine these two features and extract an incremental pseudo-Poisson coefficient which varies with the stress ratio . We solve the oedometric-test case, starting from isotropic sample and stress, for which the vertical stress is increased continuously. It is found that the stress ratio B evolves towards an asymptotic value ko which depends on the friction angle only. It is shown that this asymptotic value ko compares well with the experimental fit known as the Jaky constant.Comment: 9 pages, 1 figur

1-d granular gas with little dissipation in 0-g : A comment on "Resonance oscillations in Granular gases"

It is demonstrated that recent results on 1d granular gas in a container with a vibrating piston, which was modelled by a shock wave propagation, can be understood with a modelling using ideas coming from the "thermodynamics of a single particle". Defining e as the square root of the energetic-restitution coefficient of a single collision, and N as the total number of grains, the mean loss during a round trip of the momentum is calculated in the limit N(1-e)<<1. It is also demonstrated that the system cannot propagate sound waves nor shock waves in the limit of N(1-e)<<1 and that hydrodynamics equations cannot be defined when N(1-e)<<1. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.FnComment: 10 pages + 1 page, 1 figur

Trajectories of loose sand samples in the Phase Space of Soil Mechanics

In general, the evolution of soil submitted to simple stress-strain paths is characterised using the 3d phase space (v,p',q) i.e. (specific volume, mean intergranular pressure, deviatoric stress q. When uniaxial compressions is performed at constant lateral pressure p' or at constant mean pressure p', one finds that all trajectories end up at a line of attracting point called the critical-state line via the surface of Roscoe or of Hvorslev depending if the initial volume is the loosest possible one (at a given p') or densest. Trajectories of weakly dense samples are not often reported in this phase space. We find here that they shall present some sigmoid shape as it can be found from soil mechanics argument. This seems to indicate that Roscoe's surface shall exhibit a singularity at the critical point.Comment: 4 pages + 1 page, 1 Figur

Limits of isotropic plastic deformation of Bangkok clay

A model assuming incremental plastic isotropic response has been recently proposed to model the deformation of isotropic packing of grains, in the small-strain range. It is used here on over-consolidated remould clay, to interpret the small-strain range behaviour obtained in [1,2] on Bangkok clay. The data published in [1,2] at constant volume are also used here to measure the size of the domain of validity in the (q/(M'p), p/po) plane, where po is the over-consolidation isotropic pressure, p is the mean stress and q the deviatoric stress, q . So, it is shown that the model works also for clay. This enlarges the application domain of model [3,4] to soft clay with OCR larger than 1.2 to 1.5. Pacs # : 45.70.-n ; 62.20.Fe ; 83.80.Fg, 83.80.HjComment: 4 pages + 1 page, 1 figur