A key mechanism by which geophysical flows evolve is mass exchange with the underlying bed, either by entraining material from the bed, or by depositing material. Although it is known that some consequences of these mass exchange processes include changes in the volume, momentum and local rheology of the flow, the circumstances under which specific changes occur are not well-established. Given the enormous number of competing mechanisms present in geophysical flows, it is not surprising that the state of the art for modelling entrainment is essentially still empirical. In this study, we implement a Herschel-Bulkley (non-Newtonian) rheology into an existing open-source Smoothed Particle Hydrodynamics solver (DualSPHysics). This rheology can reasonably represent clay-rich flows, typical of those observed in the French Prealps. We hence undertake a highly-idealised, quantitative investigation of entrainment mechanisms for flows overriding non-fixed beds. For the beds, we vary the yield stress and the depth. Preliminary results reveal a rich variety of behaviours that can be obtained for different bed properties, including both acceleration and deceleration of the flow material. These mechanisms are reminiscent (but not identical) of observations from other studies where geo-materials were used.