The application of discrete element modelling to finite deformation problems in geomechanics

Discrete element methods are numerical methods that model granular materials by explicitly considering their true particulate nature. These methods can be used by geotechnical engineers to study the micro-mechanisms underlying the often complex response of soil. These methods are also an attractive alternative to more conventional continuum based approaches for modelling the localizations which occur in boundary deformation problems.; This work considers the development of discrete element methods as analytical tools for geotechnical engineers, and extends the earlier research of Thomas (1997). This earlier study considered two-dimensional discrete element models of granular materials. Real soils are three-dimensional. The capabilities of a pre-existing three-dimensional discrete element code were extended to enable simulation of conventional laboratory tests. A new three-dimensional particle called the overlapping sphere cluster was developed and shown to be better able to represent the actual shape of sand grains.; Another important element of this research is the critical examination of the discrete element methods themselves. Two (two-dimensional) prevalent discrete element approaches, the method of discontinuous deformation analysis (DDA) and the distinct element method (DEM), are critically compared and key insights regarding solution strategies, damping, and energy conservation are described. A new shear spring formulation for the discontinuous deformation analysis method is proposed and validated.; Granular materials are comprised of large numbers of particles that form a statically indeterminate system. Consequently, analytical validation of discrete element methods as tools to model soil behavior is not usually feasible. A database of high-quality physical test data (both two-dimensional and three-dimensional), which is suitable for validation of discrete element approaches, was created. It was found that minor variations in particle shape, size, and surface friction can lead to significant variations in the results of laboratory tests, especially if the particle response is highly constrained.; Geotechnical analyses are typically carried out using the continuum-based finite element method. Discrete element methods calculate contact forces and particle displacements, while continuum mechanics analyses consider stress and strain. In order to make discrete element methods more useful to engineers, homogenization techniques that translate the results of discrete element simulations into continuum mechanics terminology are required. Hence, new kinematic homogenization approaches that can be used to calculate strain values for both two- and three-dimensional simulations were developed. It is recommended that the results of particulate simulations employ the non-linear interpolation approach with particle rotation, which uses algorithms developed for the mesh free methods, as this approach better captures the development of localizations in particulate materials.