The application of the consolidation equation is based on Taylor's approximate solution alone. The existence of the exact solution emerged from the analysis of the logical structure of d’Alambert's, Fourier' and Laplace's differential equations. This led to a nonlinear equation -based on the properties of elastic waves and elastic functions - which is able to simulate excess pore pressure transmission in the soil. The research is completed with the application of the solution obtained, thereby discovering that consolidation decay times may be calculated both 

through the construction of dissipation curves and through he analytical research of the time value satisfying the condition Δu(z,t100) = 0. Finally, decay times match the approximate solution eliminating in fact the introduction of Taylor's additional parameters.