Exact Solution to Terzaghi's Consolidation Equation

TL;DR

This paper derives an exact solution to Terzaghi's consolidation equation, providing a more precise method to calculate soil consolidation times without relying on Taylor's approximate solution.

Contribution

The paper introduces a nonlinear exact solution based on elastic wave properties, improving the accuracy of consolidation analysis over traditional approximate methods.

Findings

Decay times can be accurately calculated using the exact solution.

The exact solution aligns with approximate methods, removing the need for additional parameters.

Application demonstrates improved precision in modeling pore pressure dissipation.

Abstract

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 Delta u(z,t100) = 0. Finally, decay times match the approximate solution eliminating in fact the introduction of Taylor's additional parameters.