Coupled models for total stress dissipation tests

TL;DR

This paper analyzes coupled consolidation models with different boundary conditions and embedding dimensions, providing analytical solutions and insights into total stress dissipation, especially for pile shaft conditions, and suggests a new evaluation approach.

Contribution

It unifies various coupled consolidation models into a single analytical framework and explores their stress dissipation behavior with practical implications.

Findings

Significant stress decrease in coupled 1 models at pile shaft

Zero stress drop in coupled 2 models

Convergence depends on initial conditions

Abstract

Two linear, point-symmetric, coupled consolidation model families with various embedding space dimension values (oedometer models - 1, spherical models - 3, cylindrical models - 2), differing in one boundary condition (coupled 1 - constant displacement, coupled 2 - constant stress) are analysed analytically and numerically. The method of the research is partly analytical, the models are unified into a single model with unique analytical solution, every model can be derived from this by inserting the proper boundary condition and embedding space dimension m. The constants of the solutions are determined and an approximate time factor and model law are derived for the m >1case which is identical to the one valid in the oedometer case. The convergence of the infinite series are examined in the function of the initial condition. Concerning the total stress at the pile shaft, significant decrease (with the value of the initial mean pore water pressure) is encountered for the coupled 1 consolidation models, zero stress drop is resulted by the coupled 2 models. The total stress dissipation test is suggested to be evaluated by the coupled 1 models with a time dependent constitutive law, eg., by adding a relaxation part-model. The rate of convergence is the smaller if the initial condition is the closer to the one of a zero solution (beyond the trivial one, a non-trivial zero solution exists for the coupled 1 model, at the Terzaghi initial condition).