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A numerical analysis of the micromechanical behaviour of a granular material is described using a new program MASOM based on Cundall's discrete element method. In the analysis the individual grains which make up the material are taken to be deformable 2D polygons of arbitrary size and shape. Contact forces between the grains are calculated according to Mindlin's solution for frictional contact between elastic bodies. The material in each grain is taken to be linear elastic but limited by the fracture strength of the material. Fracture is permitted along any one of a number of candidate fracture planes if an associated compressive load tending to split the gain reaches a critical level. Fragments of fractured grains are carried until they become too small to track using the explicit time integration algorithm used to advance the solution. The MASOM program is able to consider a number of different classes of elements and different types of contact between the various classes. Thus, in addition to the granular material the program can also model containers and loading devices. The program is used to simulate uniaxial and triaxial compression tests for geological materials. The results are shown to give results for stress‐strain and stress difference versus pressure which are in qualitative agreement with test data. The numerical results reveal a very complex micromechanical behaviour in granular materials, including highly variable and rather unstable load paths and a very inhomogeneous load distribution within a representative sample of the material. A video of the response of a typical frictional material to applied loads shows an interesting localized effect near sample boundaries involving crowding together of grains which cannot be observed using conventional static field plots.

A general overview is presented on applications of the discrete element method (DEM) to granular media. A literature survey is performed of static and dynamic simulations using random arrays of compliant particles, and forty‐two references published mostly in the last ten years are identified and categorized according to a number of relevant criteria. It is concluded that the interest in the use of the technique is rapidly increasing in the research and engineering community, with applications concentrated in soil mechanics, rock mechanics, grain flow and engineering problems. Additional studies and verifications of some numerical aspects of the DEM technique are suggested including parametric studies and comparisons. Program CONBAL‐2 (CONTACT + TRUBAL in 2D) developed by the authors based on TRUBAL created by Strack and Cundall, is described. CONBAL‐2 uses the complete Mindlin solution for the contact between two spheres and thus can be used for small strain and cyclic loading. The program is applied to study the cyclic response of uniform, medium dense to dense rounded quartz sand. Cyclic strain‐controlled loading at constant volume is applied to isotropically consolidated, random arrays of 531 spheres, using cyclic strains ranging from 10–4% to 10–1%. The calculated shear modulus, Gmax, constrained modulus, D, and Poisson's ratio at small strains are correlated with the confining pressure, the porosity of the array, and the coordination number. The calculated variations of secant modulus and damping ratio with cyclic strain compare favourably with the experimental results on sands compiled by Seed and Idriss. Finally, ‘pore water pressure buildup’ and cyclic stiffness degradation of the material with number of cycles is calculated at a cyclic strain of 10–1%, and the prediction is found to represent closely cyclic undrained experiments on sands. The existence of a threshold strain, yt ≈ 10–2%, found experimentally, is also predicted by the simulations.

Discrete element methods are numerical procedures for simulating the complete behaviour of systems of discrete, interacting bodies. Three important aspects of discrete element programs are examined: (1) the representation of contacts; (2) the representation of solid material; and (3) the scheme used to detect and revise the set of contacts. A proposal is made to define what constitutes a discrete element program, and four classes of such programs are described: the distinct element method, modal methods, discontinuous deformation analysis and the momentum‐exchange method. Several applications and examples are presented, and a list is given of suggestions for future developments.

The rigid spherical particle models proposed in the literature for modeling fracture in rock have some difficulties in reproducing both the observed macroscopic hard rock triaxial failure enveloped and compressive to tensile strength ratio. The purpose of this paper is to obtain a better agreement with the experimental behavior by presenting a 3D generalized rigid particle contact model based on a multiple contact point formulation, which allows moment transmission and includes in a straightforward manner the effect of friction at the contact level.

The explicit formulation of a generalized contact model is initially presented, then the proposed model is validated against known triaxial and Brazilian tests of Lac du Bonnet granite rock. The influence of moment transmission at the contact level, the number of contacts per particle and the contact friction coefficient are assessed.

The proposed contact model model, GCM‐3D, gives an excellent agreement with the Lac du Bonet granite rock, strength envelope and compressive to tensile strength ratio. It is shown that it is important to have a contact model that: defines inter‐particle interactions using a Delaunay edge criteria; includes in its formulation a contact friction coefficient; and incorporates moment transmission at the contact level.

The explicit formulation of a new generalized 3D contact model, GCM‐3D, is proposed. The most important features of the model, moment transmission through multiple point contacts, contact friction term contribution for the shear strength and contact activation criteria that lead to a best agreement with hard rock experimental values are introduced and discussed in an integrated manner for the first time. An important contribution for rock fracture modeling, the formulation here presented can be readily incorporated into commercial and open source software rigid particle models.

When simulating the behaviour of granular assemblies and multi‐body systems using a discrete element analysis, the shape representation of the bodies and the contact detection algorithm greatly influence the flexibility, accuracy and efficiency of the simulation. Several geometrical shape descriptors of two and three dimensional arbitrary rigid bodies are reviewed and a flexible 3‐D descriptor introduced. The aim is to identify appropriate shape descriptors which allow a variety of types of bodies to be investigated while ensuring accurate and efficient detection of inter‐particle contacts. Polygons/polyhedrons, and continuous and discrete function representations are examined. The investigation favours discrete representations due to their efficiency and flexibility, but illustrates the elegance and efficiency of using a continuous function representation, e.g. a superquadric, to generate the discrete representation and simplify the contact detection process.