We analyze the consolidation of freshly deposited cohesive and non-cohesive sediment by means of particle-resolved direct Navier-Stokes simulations based on the Immersed Boundary Method. The computational model is parameterized by material properties and does not involve any arbitrary calibrations. We obtain the stress balance of the fluid-particle mixture from first principles and link it to the classical effective stress concept. The detailed datasets obtained from our simulations allow us to evaluate all terms of the derived stress balance. We compare the settling of cohesive sediment to its non-cohesive counterpart, which corresponds to the settling of the individual primary particles. The simulation results yield a complete parameterization of the Gibson equation, which has been the method of choice to analyze self-weight consolidation.