The uncertainty of the consolidation coefficient is the fundamental reason for the limitation of the traditional consolidation theoretical calculation, which ignores the variation of permeability coefficient K and porosity ratio E with the consolidation state and time during the consolidation. In this paper, the porosity time-history is derived on the basis of five commonly used prediction models of permeability coefficient in engineering, having the relationship between consolidation degree and unconfined compression. Thus, the calculation formula of permeability coefficient related to both time and consolidation stress is constructed. Here the one-dimensional consolidation theory is modified by substituting the permeability coefficient formula into the Terzaghi one-dimensional consolidation equation and considering the consolidation state as well as consolidation stress and time variation. The comparations with the literatures and engineering cases confirm the necessity of the time effect on the porosity. The change of consolidation coefficient Cv cannot be ignored when suffering a larger overlying load. The new version of Terzaghi one-dimensional consolidation equation is much more anastomotic with the engineering practice which provides a more accurate calculation method for predicting foundation consolidation.