A one-dimensional vertical two-phase flow model for sedimentation-consolidation process is presented. The model is based on solving the continuity and momentum equations for both fluid and solid phases. In the non-cohesive case, the momentum transfer between the two phases is reduced to the drag force around a single particle modified to take the hindrance effects into account. In the cohesive case, Darcy-Gersevanov's law is used for the closure of the momentum transfer between the two phases and the concept of "effective stress" is introduced to take into account the bed structuring. These closure laws are validated against high resolution experimental data in terms of settling curves and concentration profiles. The reliability of the model is illustrated from an analysis of the momentum balances at different stages during the process. Finally, the proposed closure laws and numerical algorithms are shown to be able to quantitatively reproduce sedimentation of non-cohesive and sedimentation- consolidation of cohesive sediments, including mud.