Thesis: Vertical sealing systems for deep geological nuclear waste disposals are one of the key elements for long-term waste containment since they constitute the main potential pathway between the storage facility and the biosphere. Swelling clay mixtures are strong candidates as sealing materials due to their low permeability in unsaturated and saturated conditions as well as their swelling potential. The present thesis evaluates and connects the hydro-mechanical processes in these clay mixtures occurring at the sub-millimeter and meter scales by developing a set of novel conceptual models discretized with the discrete element and finite volume methods. At the sub-millimeter scale, the present work investigates the evolution of water and gas permeabilities as a result of crack developments in partially saturated compacted clay. X-ray CT scan imagery is used to inform the initial porosity field, and directional water/gas permeabilities are collected for all saturation levels. This microscopic permeability data is upscaled to the laboratory scale, where a mixed packing of spherical compacted clay pellets and clay powder is modeled using a custom-built mass transport framework. The framework governs the transport of mass between clay-powder-filled voids and compacted clay pellets. Such a model enables an assessment of permeability evolution at the meter scale with respect to saturation levels, as well as the heterogeneous development of swelling pressures. Finally, the thesis also contains a demonstration of the computational and numerical stability constraints associated with combining the discrete element and finite volume method. Further, a variety of acceleration techniques are proposed and ultimately used within the frameworks presented. The thesis concludes with a variety of non-intuitive results for permeability evolutions at partially saturated conditions for both the sub-millimeter and meter scales.