Nonlinear consolidation of arbitrary layered soil with continuous drainage boundary: An approximate closed-form solution

Based on the double nonlinear consolidation constitutive associated with the compression and permeability coefficients, presented by Mesri and Rokhsar (1974), this paper derives an approximate closed-form solution for the one-dimensional nonlinear consolidation of the arbitrary layered soils incorporating the continuous drainage boundary condition. The approximate closed-form solution is obtained by the homogenization of the boundary conditions and eigenfunction method. A model test is conducted to justify the rationality of the approximation and the continuous drainage condition utilized in this study. The calculated results are also compared with those acquired from the simplified analytical solution and the finite difference method. A parametric study is conducted to investigate the influence of various parameters on the consolidation process. The most significant finding is that the influence of $N_{\text{q}}$ appears to be completely different for the cases when $C_{\text{c}}/C_{\text{k}}>1$ and $C_{\text{c}}/C_{\text{k}}<1$. When $C_{\text{c}}/C_{\text{k}}>1$, the increase of $N_{\text{q}}$ shows an adverse influence on the consolidation, whereas the influence becomes positive when $C_{\text{c}}/C_{\text{k}}<1$. The approximate solution derived herein offers a rigorous analytical approach for the double nonlinear consolidation problems of arbitrary layered soils, providing an effective benchmark for comparison and verification of future sophisticated numerical approaches.