Abstract: We compare the probability density functions of normal forces in dry and wet granular systems from 3D simulations by molecular dynamics and contact dynamics methods. While the strong forces are characterized by a decreasing exponential distribution, we show that in the range of weak forces the force distribution in a dry granular packing is sensitive to the anisotropy of the packing and the shape of the particles. By means of a model of capillary cohesion, implemented as a force law expressing the capillary force as a function of water volume and the distance between particles, we find that distributions are exponential for both compressive and tensile forces. The particle pressures are shown to form a bi- percolating structure.

Abstract: We analyze the dynamics of a 3D granular packing composed of particles of irregular polyhedral shape confined inside a rectangular box with a retaining wall sub jected to horizontal harmonic forcing. The simulations are performed by means of the contact dynamics method for a broad set of loading parameters. We explore the vibrational dynamics of the packing, the evolution of solid fraction and the scaling of dy- namics with the loading parameters. We show that the motion of the retaining wall is strongly anharmonic as a result of jamming and grain rearrangements. It is found that the mean particle displacement scales with inverse square of frequency, the inverse of the force amplitude and the square of gravity. The short- time compaction rate grows in proportion to frequency up to a characteristic frequency, corresponding to collective particle rearrangements between equilibrium states, and then it declines in inverse proportion to frequency.

Abstract: We perform a detailed analysis of the contact force network in a dense confined packing of pentagonal particles simulated by means of the contact dynamics method. The effect of particle shape is evidenced by comparing the data from pentagon packing and from a packing with identical characteristics, except for the circular shape of the particles. A counterintuitive finding of this work is that, under steady shearing, the pentagon packing develops a lower structural anisotropy than the disk packing. We show that this weakness is compensated by a higher force anisotropy, leading to enhanced shear strength of the pentagon packing. We revisit �strong� and �weak� force networks in the pentagon packing, but our simulation data also provide evidence for a large class of �very weak� forces carried mainly by vertex-to-edge contacts. The strong force chains are mostly composed of edge-to-edge contacts with a marked zigzag aspect and a decreasing exponential probability distribution as in a disk packing.

Abstract: By means of two-dimensional contact dynamics simulations, we analyze the vibrational dynamics of a confined granular layer in response to harmonic forcing. We use irregular polygonal grains allowing for strong variability of solid fraction. The system involves a jammed state separating passive (loading) and active (unloading) states. We show that an approximate expression of the packing resistance force as a function of the displacement of the free retaining wall from the jamming position provides a good description of the dynamics. We study in detail the scaling of displacements and velocities with loading parameters. In particular, we find that, for a wide range of frequencies, the data collapse by scaling the displacements with the inverse square of frequency, the inverse of the force amplitude, and the square of gravity. Interestingly, compaction occurs during the extension of the packing, followed by decompaction in the contraction phase. We show that the mean compaction rate increases linearly with frequency up to a characteristic frequency and then it declines in inverse proportion to frequency. The characteristic frequency is interpreted in terms of the time required for the relaxation of the packing through collective grain rearrangements between two equilibrium states.

Abstract: The tamping operation on railway ballast is an example where the vibrations are used to restore the initial geometry of the track distorted as a result of ballast settlement. By means of tree-dimensional contact dynamics simulations, we analyze the vibrational dynamics of a confined granular layer in response to harmonic forcing. The sample is composed of polyedric grains with a shape derived from digitalized ballast. The system involves a jammed state separating passive (loading) and active (unloading) states. We show that an approximate expression of the packing resistance force as a function of the displacement of the free retaining wall from the jamming position provides a good description of the dynamics. We study in detail the scaling of displacements and velocities with loading parameters. In particular, we find that, for a wide range of frequencies, the data collapse by scaling the displacements with the inverse square of frequency, the inverse of the force amplitude and the square of gravity. We show that the mean compaction rate increases linearly with frequency up to a characteristic frequency of 10 Hz and then it declines in inverse proportion to frequency.

Abstract: Dans un milieu granulaire, les efforts de cisaillement sont entie�rement transmis par l'interme�diaire d�un re�seau « fort » de contacts, assiste� par un ensemble de contacts appartenant a� un re�seau « faible ». Cette organisation non triviale des forces a toujours e�te� e�tablie uniquement pour un milieu granulaire compose� de grains isome�triques comme les disques ou sphe�res. L�objectif du travail propose� est de mettre en e�vidence, par des simulations nume�riques, l�influence de la forme des grains sur le comportement tant macroscopique que microscopique (la texture) d�un milieu granulaire soumis a� un effort de cisaillement. Nous allons nous focaliser sur des grains de forme pentagonale simule�s a� l�aide de la me�thode de Dynamique des Contacts. Nous avons re�alise� des simulations de compression biaxiale de syste�mes compose�s de particules pentagonales et circulaires posse�dant la me�me distribution granulome�trique. La re�sistance au cisaillement est plus e�leve�e pour les pentagones. Un re�sultat contre- intuitif de cette e�tude est l�observation d�une anisotropie structurale plus faible du syste�me de pentagones par rapport aux disques. Nous montrons que la re�sistance au cisaillement plus e�leve�e des pentagones est due a� une anisotropie plus importante des forces qui rattrape ainsi la faiblesse de l�anisotropie structurale. Nous retrouvons, pour ce syste�me, le me�me comportement en re�seaux « faible » et « fort » que pour les disques. Mais les simulations montrent sans ambigui�te� l�existence d�une classe de forces « tre�s faibles » porte�es principalement par des contacts face-sommet. Par ailleurs, le re�seau « fort » est essentiellement constitue� de contacts face-face qui forment des chai�nes de forces en zig-zag.

Abstract: We analyze the contact and force networks in a dense confined packing of pen- tagonal particles simulated by means of the contact dynamics method. The particle shape effect is evidenced by comparing the data from pentagon pack- ing and from a packing with identical characteristics except for the circular shape of the particles. A surprising observation is that the pentagon packing develops a lower structural anisotropy than the disk packing. We show in this work that this weakness is compensated by a higher force anisotropy that leads to enhanced shear strength of the pentagon packing. With the polyg- onal shape of the particles, the strong force chains are mostly composed of edge- edge-to-edge contacts with a marked zig-zag aspect.

Abstract: The present PhD work deals with numerical modelling of the tamping process on railway ballast, which is a common operation in order to restore the level of the rail tracks following differential settlement under dynamic loading, in view of micromechanical analysis of physical phenomena invol- ved in different phases of this process. A discrete element model is developped in the framework of the contact dynamics method that allows us to simulate a full cycle of the process consisting of introducing vibrating metallic arms into the ballast, compressing the ballast under the sliders and pulling out the arms. These simulations take into account the polyhedral shape of the grains which is an important element for realistic simulations of ballast. A detailed investigation of the quasistatic rheology of granular materials with polyhedral particle shapes was performed allowing us to evidence the micrormechanical origins of the shear strength of these materials closely related to the facetedness of the particles. The vibrational dynamics of the grains was studied in interaction with a vibrating intruder and under the action of horizontal vibrations of a retaining wall. A scaling of the dynamics as a function of loading parameters is proposed by dimensional analysis and validated by simulations, as well as a characteristic frequency for optimal compaction of the material. Finally, on the basis of these investigations and parametric studies, concrete recommendations are proposed in order to improve the performance of the tamping process.