Finite difference approach for consolidation with variable compressibility and permeability

The linear and elastic consolidation theory developed by Terzaghi is commonly used for evaluation of consolidation characteristics of fine-grained soils. As several simplifying assumptions have been made in the derivation of Terzaghi’s theory, the application of this theory in many practical problems, especially those involving soft clays, may lead to significant errors. In particular the assumption of constant value for coefficient of consolidation, Cv, during consolidation process is one of the major limitations in Terzaghi’s theory. In addition, the coefficient of consolidation is determined based on several empirical relationships and also using graphical procedures with empirical nature. In this paper a one-dimensional non-linear partial differential equation is derived for prediction of consolidation characteristics of soft clays considering variable values for Cv. A finite difference approach is used for the solution of the developed non-linear equation. Two coefficients (Cn and α) are introduced to describe changes in soil characteristic and take into consideration the changes in Cv during consolidation. The proposed approach in this study determines the relation between average degree of consolidation, U, and real time, t, directly without using the concept of time factor and coefficient of consolidation. It has been found that based on different values of α, consolidation can take place faster, slower, or as fast as that predicted by Terzaghi’s theory. It has also been shown that the predicted relation between average degree of consolidation, U, and time, t (based on numerical solution of the non-linear equation) is in good agreement with those obtained directly from consolidation tests. Based on the results obtained from the numerical solution, a direct and mathematical closed-form equation has been developed for prediction of relation between average degree of consolidation and real time.