A depth-averaged two-phase model is proposed for debris flows over fixed beds, explicitly incorporating interphase and particle-particle interactions, fluid and solid fluctuations and multi grain sizes. A first-order model based on the kinetic theory of granular flows is employed to determine the stresses due to solid fluctuations, while the turbulent kinetic energy - dissipation rate model is used to determine the stresses from fluid fluctuations. A well-balanced numerical algorithm is applied to solve the governing equations. The present model is benchmarked against USGS experimental debris flows over fixed beds. Incorporating the stresses due to fluid and solid fluctuations and properly estimating the bed shear stresses are shown to be crucial for reproducing the debris flows. Longitudinal particle segregation is resolved, demonstrating coarser sediments around the fronts and finer grains trailing the head. Based on extended modeling exercises, debris flow efficiency is shown to increase with initial volume, which is underpinned by observed datasets.