Gibson's equation is widely used to describe the behaviour of consolidating soft mud soils. This equation needs to be supplied with constitutive relationships, which relate effective stress and permeability to a quantity describing the soil density (mass concentration or void ratio for instance). In this paper, a method to determine the constitutive relationships is presented. This method requires recording the height of the interface between the clear water and the mud deposit. The results compare well with the ones obtained following the conventional method, which requires pore water pressure and density measurements.