Adopting the non-Darcy flow presented by Hansbo and considering the nonlinear compression and permeability characteristics of soils, the one-dimensional nonlinear consolidation problem of soft clays is investigated by means of a continuous drainage boundary. The numerical solutions of average consolidation degrees defined by settlement and excess pore water pressure are derived by using the finite difference method, and the correctness of these solutions is verified by comparing them with existing analytical and numerical solutions. Based on the proposed solutions, a parametric study is conducted to study the influence of interface parameter, non-Darcy flow parameter and soil nonlinearity on the consolidation behavior of soft clays. The results show that the solutions based on the continuous drainage boundary can be degenerated into the solutions based on the Terzaghi drainage boundary if the interface parameter is taken as a reasonable value. The soil consolidation behavior considering both non-Darcy seepage and nonlinear characteristics of soil is very complex.

Based on the soil nonlinearity assumptions proposed by Mesri, the one-dimensional nonlinear consolidation of double-layered soil is investigated. To better align with engineering reality, a continuous drainage boundary is introduced, bolstering the reliability of the derived solution through comparison against existing findings. Subsequently, the consolidation behavior of double-layered soil is analyzed for the soil permeability, compressibility, nonlinear parameters, and interface parameters. The outcomes elicit a positive correlation between the consolidation rate of the double-layered soil and both the ratio of permeability coefficient from the lower to upper soil layers and the value of the interface parameter. Furthermore, it is observed that a lower compressibility coefficient ratio between the lower and upper soil layers, along with a reduced ratio of compression index to penetration index, both contribute to an increased consolidation rate within the context of double-layered soil. The one-dimensional nonlinear consolidation of double-layered soil is intricate, intertwined with the relative permeability and compressibility of soil layers, and the influence of nonlinear parameters and drainage boundary configuration. Integrating these factors is crucial for analyzing the consolidation traits of double-layered soil, leading to a more precise portrayal of the consolidation behavior of coastal soft soils.

Conventionally, drainage boundaries are often assumed to be either perfectly permeable or completely impermeable. However, a more realistic approach considers continuous drainage boundaries. In this context, an analytical solution for double drainage consolidation in vertical drains is derived. The proposed method is evaluated against existing solutions and finite element simulations. The study investigates the impact of drainage capacity, soil nonlinearity, smear effect, and well resistance. The results show that the continuous drainage boundary parameters (i.e., b and c) significantly affect the distribution of excess pore water pressure and the consolidation rate. Increasing b and c allows realistic modeling of drainage capacity variations from impermeable to permeable boundaries. Notably, when b ≠ c, the maximum excess pore water pressure plane shifts from the mid-height of the foundation soil, diverging from conventional consolidation theory. Soil nonlinearity (C_c/C_k) and boundary permeability (b and c) jointly affect consolidation. Higher C_c/C_k values correlate with more detrimental consolidation effects. Minimizing disturbance around vertical drains during construction is crucial due to well resistance and smear zone effects, which can significantly slow down consolidation. This study provides an analytical solution considering soil nonlinearity for predicting consolidation in actual engineering scenarios involving vertical drainage trenches.

Rheology has a significant impact on the long-term consolidation behaviors of clays. The rheological consolidation theory plays a vital role in the prediction of deformation of the clays. In this study, the fractional derivative-based Kelvin model (FKM) and the fractional derivative-based Merchant model (FMM) are used to simulate the rheological characteristics of clays, and the continuous drainage boundary condition is adopted to consider the temporal continuity of the pore-water pressure at the boundary. Based on this, a one-dimensional consolidation model for the clays subjected to a time-dependent load is established, and then the semi-analytical solutions of the excess pore-water pressure (EPP), the settlement and the degree of consolidation are derived. Two sets of rheological parameters are back-calculated using the nonlinear fitting methods. The influences of the fractional order, viscosity coefficient and interface parameter on the rheological consolidation behaviors are investigated in depth through systematic parametric studies.