Sedimentation in a suspension and self-weight consolidation of the resulting deposit can be described by a general unifying theory, which is composed of the elements of the theories employed by geotechnical and chemical engineers. Concentration profiles can be obtained as the solution of the mass balance equation of the solid phase, which expresses that a concentration variation is caused by a net sediment flux (the product of sediment concentration and velocity). The particle velocity is obtained from the particle force balance equation, the generalized Darcy-Gersevanov equation, which also includes thermodynamic forces. Effects of differential settling due to polydispersity and upward drag by displaced water can be incorporated by adding a diffusive flux. Segregation in graded sediment can be simulated by solving the mass balance equations of different particle size fractions separately. The equations are expressed in terms of sediment volume fraction. The present formulation is shown to be consistent with the Gibson equation.