The Discrete Particle And Coupled Discrete-Continuum Models And Numerical Methods For Granular Materials

Granular material is one kind of matter, which exists most widely in nature and is comprehensively applied to engineering practices. However, the physical properties of granular material are so complicated that it still remains as one among a few most less-understood materials. In the recent years, the researches on mechanical behavior of granular materials and the developments in mechanics of granular materials have attracted comprehensive attentions in many scientific and engineering fields.A final goal in the study of the mechanics of granular materials is to formulate their macro-behavior in terms of micro-quantities. The discrete element method (DEM) based on the discrete particle model (DPM) has been widely accepted as a useful tool in numerical simulation of mechanical behavior of granular materials owing to its easy to determine physical quantities at grain level. The calculation of contact forces between particles is the core part of DEM, however, a universally accepted view on the mechanism of relative movement between two typical particles in contact, especially for the sliding and rolling movement in tangential direction, has not been achieved. One of the objectives of this thesis is to propose a discrete particle model for granular materials. Each grain in the particulate system under consideration is assumed as rigid and circular. Starting with kinematical analysis of relative movements of two typical grains with different radius in contact, measurements to describe both the relative rolling and sliding motions, including the translational and angular velocities (displacements), are defined. Further, Both the rolling and sliding friction tangential forces, and the rolling friction resistance moment, which are constitutively related to the defined relative motion measurements respectively, are formulated and integrated into the framework of dynamic model of DEM. In view of the fact that the rolling resistance mechanism described in currently available models in the literature is inadequate in both physical and numerical aspects, the proposed model is thus focused on an adequate description of the rolling resistance mechanism. Moreover, the definitions of nominal effective and volumetric strains are proposed on the formalism of the continuum theory to illustrate the movements of each particle relating to its surrounding particles in a particulate system.The crushable soil possesses special characters in mechanical and engineering properties. The studies on crushing mechanism of soil granules and its engineering effects are strongly related to safety and work in order to be ensured for engineering constructions with large scales. Meanwhile, the particle crushing at micro-scale directly influences upon macroscopic nonlinear behavior of granular materials, studies on particle crushing possess a scientific significance in advancing the theory of soil mechanics. In addition, the studies will be also beneficial to improve the granulation technology. Based on the proposed conventional discrete particle model, a hierarchical multi-scale model for granular materials, in which basic particles and particle clusters are defined for simulation of particle crushing in different scales, is presented in this thesis. The particle crushing probability in the model is derived on the basis of the Weibull distribution formula in the frame of statistical fracture mechanics with the nominal particle stress concept. With the de-cluster mechanism of the particle clusters the proposed model can be used to simulate particle crushing phenomenon in failure analysis of granular materials.At present, the discrete element methods are mostly concerned with single-phase granular materials or dry granular materials. However, it is well known that the addition of liquid to a dry granular medium, even in small quantity, can modify in a significant way its behavior when compared to the dry state. Moreover, with deep and intensive investigations on dry granular medium by means of DEM, the numerical simulation for wet granular materials based on DEM has been paid more attentions in recent years. In the frame of discrete particle model for modeling of granular materials, there exist two main types of mathematical models for modelling interstitial liquid, i.e. the discrete (liquid-bridge)and continuum models. The liquid-bridge model is mainly used for low moisture content, i.e. the pendular and funicular state of interstitial liquid, which exists as liquid-bridges around the contacts between solid particles and exerts the adhesion and suction effects at liquid-air interfaces. Although the fluid phase in a porous medium is inherently discrete at the microscopic level and the discrete (i.e. the liquid-bridge) model takes into account the effect of capillary liquid surrounding the contacts between solid particles on inter-particle adhesion, it is noticed that the discrete models for interstitial liquid are not able to model the fluid transport within a porous medium and can be only used in the case of low liquid content. On the other hand, with an increasing degree of liquid saturation in the medium, the capillary and droplet states of interstitial liquid develop and the voids are fully or nearly saturated with liquid. In such cases, the liquid-bridge model is no longer valid. To model fluid flow through a porous medium and its interaction with the solid grains of the medium, a continuum model should be employed. In this thesis, a coupled discrete particle-continuum model for wet granular materials is developed. The motion of the interstitial fluid phase and its interaction with the solid phase are described by means of the two parallel continuum schemes govemed by the averaged incompressible N-S equations and Darcy's law respectively. In light of SPH approach, the characteristic based SPH method is presented for numerical modelling of pore fluid flow. A numerical Solution procedure based on DEM and characteristic based SPH for saturated granular materials is formulated. Furthermore, as the passive air phase assumption is introduced, the change of water content in unsaturated granular materials can be simulated. In addition, based on the concepts of continuum theory the relation between the voidage variation and volumetric stain is discussed, the equation to determine the pore water pressure depending on volumetric strain and dilation (or contraction) of particulate assemblage are given.The main work of the present thesis can be summarized as follows. A discrete particle model for granular materials in which the rolling mechanism is particularly emphasized is first developed. With introduction of the concepts of basic grain and the cluster into the model, a hierarchical discrete particle model capable of modeling particle crushing phenomenon is formulated. To model the coupled response of discrete solid particles with pore fluid a discrete particle-continuum model for wet granular materials is further developed, in which the solid phase is modelled by the discrete particle model while the interstitial liquid is modelled by the two continuum schemes based on the averaged incompressible N-S equations or the Darcy's law respectively. Finally a numerical solution procedure on the basis of the DEM and characteristic based SPH is developed.For "self-completeness" of present thesis, fundamental concepts of both granular material and mechanics of granular material are briefly introduced; differences and relations between rigid-particle models and soft-particle models are discussed. In addition, most comprehensively used constitutive models for displacement-force relation at contacts and the boundary condition presentations in common use for granular assemblages are summarized.