Is the friction angle the maximum slope of a free surface of a non cohesive material?

Starting from a symmetric triangular pile with a horizontal basis and rotating the basis in the vertical plane, we have determined the evolution of the stress distribution as a function of the basis inclination using Finite Elements method with an elastic-perfectly plastic constitutive model, defined by its friction angle, without cohesion. It is found that when the yield function is the Drucker-Prager one, stress distribution satisfying equilibrium can be found even when one of the free-surface slopes is larger than the friction angle. This means that piles with a slope larger than the friction angle can be (at least) marginally stable and that slope rotation is not always a destabilising perturbation direction. On the contrary, it is found that the slope cannot overpass the friction angle when a Mohr-Coulomb yield function is used. Theoretical explanation of these facts is given which enlightens the role plaid by the intermediate principal stress in both cases of the Mohr-Coulomb criterion and of the Drucker-Prager one. It is then argued that the Mohr-Coulomb criterion assumes a spontaneous symmetry breaking, as soon as the two smallest principal stresses are different ; this is not physical most likely; so this criterion shall be replaced by a Drucker-Prager criterion in the vicinity of the equality, which leads to the previous anomalous behaviour ; so these numerical computations enlighten the avalanche process: they show that no dynamical angle larger than the static one is needed to understand avalanching. It is in agreement with previous experimental results. Furthermore, these results show that the maximum angle of repose can be modified using cyclic rotations; we propose a procedure that allows to achieve a maximum angle of repose to be equal to the friction angle .Comment: 21 pages + 1 page, 12 figure

Experimental Proof of the Existence of a Bifurcation Process During the undrained test in Clay

Recent papers, based on a new simple incremental modelling which assumes an "isotropic" response, predicts that the trajectory followed during an undrained compression test exhibits a bifurcation process when the stress field arrives at q=M'p', where q stands for the deviatoric stress, p' for the mean stress and M' is a coefficient describing friction. This indicates a discontinuous change of solution when arriving at q=M'p'. This paper looks at experimental data on dense sample obtained at p'=constant, and it shows that the trajectory (p'=constant, v=constant) does continue to exist at and beyond the q=M'p' plane. So, this demonstrates the validity of the analysis which uses the bifurcation theory and this strengthens the proposed modelling. Indeed, this demonstrates the reality of the bifurcation process during undrained compression. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.FnComment: 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

Experimental Test of the validity of "Isotropic" Approximation for the Mechanical Behaviour of Clay

Experimental data from axially symmetric compression test at constant mean pressure p on kaolinite clay are used to study the validity of an "isotropic" modelling as a function of the overconsolidation ratio (OCR).The isotropic assumption is found to be quite good for 2<OCR<3 and/or in the range of small deformation for OCR>4. For very large OCR (OCR >10), anisotropic response is observed at few percents of axial deformation. Relation with anisotropic distribution of local forces is made. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.FnComment: 6 pages + 1 page, 1 figur

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

Experimental Stick-Slip Behaviour in Triaxial Test on Granular Matter

This paper is concerned with the quasi-static rheology of packings of glass spheres of diameter d (d=0.2mm, 0.7mm or 3mm). Stick-slip behaviour is observed on small spheres, i.e d=0.2mm & 0.7mm ; one observes also in this case a weakening of the rheology as the rate of deformation increases, and the larger the rate the larger the weakening; this generates macroscopic instabilities and stick-slip. Statistics of stick-slip events have been determined, which show that the larger the sample the more regular (i.e. "periodic") the sick-slip, the faster the strain rate the less periodic the events. One concludes that this stick-slip is generated at the macroscopic level and comes from the macroscopic rhelogical law. However when sample is small, local fluctuations perturb the macroscopic events and trigger them erratically. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.FnComment: 7 pages + 1 page, 5 figure

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

Cyclic Maxwell Demon in granular gas using 2 kinds of spheres with different masses

The problem of Maxwell's demon in granular gas is revisited in the case of a mixture of two particle species. The phase space is found to be 2d. Existence of cyclic orbits, with periodic segregation, is demonstrated by investigating the case of 2 kinds of particles with identical parameters but different masses. At large excitation equi-partition shall be obtained, but convergence towards the steady state is found in spiral. The spiral convergence is imposed due to the rule of kinetic-energy transfer between the two species. It results that the most probable scenario is that the steady state breaks into cyclic orbit at lower amplitude of vibration below a bifurcation threshold. The nature of the bifurcation is not known; it can be critical, subcritical, hypercritical or can exhibit a tri-critical point as varying the control parameters. No conclusion is obtained at very low vibration amplitude: it is guessed two scenarii under further cooling which generates Maxwell's demon and segregation..Comment: Poudres et Grains 200

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

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