Analytical Solutions of Linear Finite-Strain One-Dimensional Consolidation

Abstract

Numerical solutions of linear finite-strain one-dimensional consolidation of both initially unconsolidated and initially fully consolidated soil layers with both one-way and two-way drainage have been available for some time. However, no solutions of the limiting cases for initially unconsolidated soil have been available. Nor, except for the limiting cases corresponding to small-strain consolidation of initially fully consolidated layers, has the accuracy of these solutions and the solution charts based on them been evaluated. Analytical counterparts of the earlier numerical solutions and solution charts, analytical solutions of the limiting cases for initially unconsolidated soil, and analytical solutions of the small-strain Terzaghi equation expressed in material coordinates are presented in this paper. The analytical solutions clarify aspects of the numerical solutions, improve marginally the accuracy of the solution charts, and enable the latter to be easily replicated and extended. They may also be applied to the validation of numerical solutions of nonlinear finite-strain consolidation.