The dispersal and sedimentation of particles (tephra) from volcanic plumes and clouds represents a significant threat for various public and economic sectors of society. Despite the advances in computational capabilities, some associated fundamental aspects remain unconstrained with large consequences on our predictive capacities. In particular, particle sedimentation and associated tephra deposits are largely controlled by size-selective processes (i.e. particle aggregation and settling-driven gravitational instabilities), whose effects might be often misinterpreted and wrongly described given that they both affect the same grainsize population (i.e. fine ash) in a similar manner (i.e. increasing settling velocity and sedimentation rate). Neglecting the description of these size-selective processes could potentially lead to an overestimation of ash concentration in the far field and an underestimation of ash load in proximal area. Settling-driven gravitational instabilities remain largely unconstrained, and no Volcanic Ash Transport and Dispersal Model exists that describes them. We developed a single-phase 3D model for the description of settling-driven gravitational instabilities supported by validation with both field and experimental investigations with and without horizontal shear. The model also integrate the aggregation process in order to investigate the combination with settling-driven gravitational instabilities.