Radial periodic boundaries for axi-symmetric DEM simulations: development, implementation and validation.

The ability of discrete element modelling (DEM) to provide useful information on the micro-scale parameters that underlie the observed macro-scale response of soil is now well established. Notable examples include the work of Thornton (2000) and Cheng et al (2003). In geotechnical laboratory testing the need to maintain a small ratio for the particle dimensions to the sample dimension is well established. The same consideration should be made when simulating element tests using discrete element simulations. One option is to consider an ideal, boundary free simulation environment using a rectangular periodic cell (e.g. Thornton, 2000). However where this approach, the simulations cannot easily be directly compared with physical tests for validation purposes. Furthermore, as demonstrated by Cui and O’Sullivan (2005) DEM simulations can provide insight into the nonuniformities present in real physical tests when the test boundary conditions are included in the DEM model. One limitation associated with particulate DEM simulations is their computational cost. Each particle is modelled as a rigid body, or a number of rigid bodies bonded together. Consequently of the number of degrees of freedom associated with the simulation of even a conventional triaxial laboratory test can easily be in the order of 10 5 – 10 6 . The simulations are also dynamic, requiring the dynamic equilibrium of each particle to be considered at discrete points in time. The inherent non-linearity of the particulate systems considered and conditional numerical stability of the central difference time integration algorithm used in DEM limit the time step that can be used in the simulations, further adding to the computational cost. While there is potential to improve DEM simulation run-times by efficient coding, careful compiler selection and parallel processing, there is also merit in exploring the possibility to reduce the number of particles or degrees of freedom present in the system by taking advantage of symmetry considerations where possible.