Approximate Analytical Solutions for One-Dimensional Consolidation of a Clay Layer with Variable Compressibility and Permeability under a Ramp Loading

There are no analytical solutions concerning the consolidation of a clay layer subjected to a ramp load with consideration of the variation of the consolidation coefficient and the nonlinearity of compressibility and permeability of the clay layer. Based on the assumption that the initial effective stress of the clay layer remains constant with depth, an analytical solution for one-dimensional consolidation of a clay layer with variable compressibility and permeability under a ramp load is derived in this study. The solution is validated against the results of the finite-difference method for the same problem. With the proposed solution, the influence of the ratio (C-c/C-k) of the compressibility index (C-c) to the permeability index (C-k) and the final external load (q(u)) on the consolidation of clay layer is studied. The results show that C-c/C-k and q(u) have significant influence on the behavior of nonlinear consolidation. Both the dissipation rate of the excess pore-water pressure and the average consolidation rate of the clay layer decrease when C-c/C-k increases. When C-c/C-k<1, the average degree of consolidation represented by the settlement at the same time increases as the final external load (q(u)) increases. When C-c/C-k>1, however, the average degree of consolidation represented by the settlement at the same time decreases when q(u) increases. The loading rate has a great influence on the dissipation of excess pore-water pressure, and the rate of nonlinear consolidation decreases when T-vc increases.