Nonlinear consolidation scenarios, based on potential type constitutive dependences—like those proposed by Juárez-Badillo—and eliminating the more restrictive hypothesis of 1+e and d z constant, were characterized by the nondimensionalization process of the governing equations, providing the independent dimensionless groups that rule the main unknowns of interest. From these, universal curves have been depicted for both the characteristic time and the average degree of consolidation. The solutions were verified by numerical simulations and successfully compared in a case study, showing the simplicity of use of the curves and the high reliability of the solutions they provide.