Exact solution of Terzaghi's consolidation equation and extension to two/three-dimensional cases (3th versione)

TL;DR

This paper presents an exact, non-linear solution to Terzaghi's consolidation equation that aligns with both theoretical principles and experimental data, extending it to multi-dimensional cases with practical application examples.

Contribution

It introduces a mathematically rigorous non-linear solution to Terzaghi's equation and extends it to 2D and 3D cases using a transversally isotropic soil model.

Findings

The proposed solution aligns with experimental results.

Extension to multi-dimensional consolidation models.

Application examples demonstrate improved accuracy.

Abstract

Terzaghi's one-dimensional consolidation equation simulates the visco-elastic behaviour of soils depending on the loads applied as it happens, for example, when foundation are laid and start carrying the weight of the structure. Its application is traditionally based on Taylor's solution that approximates experimental results by introducing non-theoretical variables that, however, contradict the actual behaviou of soils. After careful examination of the theoretical and experimental aspects connected with consolidation, the proposal of this research is a solution consisting in a non-linear equation that can be considered correct as it meets both mathematical and experimental requirements. The solution proposed is extended to include differential equations relating to two/three dimensional consolidation by adopting a transversally isotropic model more consistent with the inner structure of soils. Finally, this essay is complete with application examples that give more reliable results than the traditional solution. Future developments are also highlighted considering that the uniqueness theorem has not been proven yet.