This paper deals with the one-dimensional consolidation of saturated fine soils, described as a discontinuum process. The theory is based on two foundations: the ideal space-time structure of matter and the principle of the mean value. The canonical domain of influence of each node is made of two vertical nodes, and only one antecedent node, in regard of the time irreversibility, yielding a parabolic differential equation, whose coefficient of dissipation depends only on the space-time structure of the soil. For the one-dimensional consolidation problem, the best suitable variable is a statistical estimator, that satisfies the boundary and initial conditions of the oedometer test. Of all dependent quantities involved in a consolidation process, only the excess pore water pressure and the settlement are taking into account, assuming to be linearly and logarithmically related to the estimator, in order to find the degree of consolidation. As a result, it is found that Terzaghi´s, and Davis and Raymond´s equations are particular cases of the equations thus obtained. Also, the comparison with the experimental data reported by several authors leads to the conclusion that, in general terms, the best fit for the excess pore pressure dissipation corresponds to the logarithmic discontinuum process.