Date of Award
Doctor of Philosophy (PhD)
The behavior of soils is fundamentally the combined interactions between billions and billions of individual particles and particle matrices. For computational tractability and despite this fact, many soil models assume the material is a continuum essentially averaging the inter-particle interactions to predict the behavior of the bulk material. In recent years, multiscale modeling techniques have been developed to reintroduce the effect of the grain-scale interactions to help model situations where the continuum assumption fails, such as shear band development in triaxial tests or soil disaggregation under blast loading. One of such multiscale models called hierarchical upscaling, or global-local analysis, model the problem domain using typical continuum-based approaches, but replace the continuum constitutive model with grain-scale models that represent the microstructure at the given point. The deformation of the material is solved via the continuum-scale boundary value problem, which is then passed to the grain-scale as boundary conditions on these representative volume elements (RVEs). The RVEs are then allowed to deform, and the resulting stress is passed back to the continuum scale.
Three hierarchical multiscale models were developed to model a series of experimental results on dry Colorado Mason Sand. In all three models, the grain-scale was modeled using the discrete element method through a code called ellip3D. Ellip3D models of dry Colorado Mason Sand were integrated with three continuum models: a one dimensional, finite strain finite element model with full dynamics (1D FEM-DEM model), a one dimensional material point method implementation (1D MPM-DEM model), and a two dimensional, small strain, axisymmetric finite element model (2Daxi FEM-DEM model). The one dimensional models were used to model a split Hopkinson pressure bar test and the two dimensional model was used to model two triaxial tests. With the inclusion of a particle fracture model, the results of the split Hopkinson pressure bar experiment were reasonably well replicated; however, the 2Daxi FEM-DEM model over-predicts the stress response of the triaxial tests. Regardless, to the author's knowledge, the results herein presented are the first attempt to directly compare FEM-DEM global-local analysis models to experimental data. Also, the MPM-DEM implementation is a novel extension of other FEM-DEM models to a meshfree numerical methods.
Jensen, Erik Wallace, "Hierarchical Multiscale Modeling to Inform Continuum Constitutive Models of Soils" (2017). Civil Engineering Graduate Theses & Dissertations. 99.