To investigate the one-dimensional nonlinear consolidation characteristics of a double-layer foundation under multi-stage loading, a one-dimensional nonlinear consolidation equation for the double-layer foundation was established, and numerical solutions were obtained through the finite difference method. The accuracy of the proposed solution was validated by comparing it with existing analytical solutions and finite element analysis results. Based on these comparisons, the influence of nonlinear parameters, double-layer soil properties, and loading conditions on the consolidation behavior of the double-layer foundation was further examined. The results indicated that, under multi-stage linear loading conditions, an increase in the initial permeability coefficient ratio of the double-layer foundation resulted in a significant reduction in excess pore water pressure and an acceleration of consolidation. The compression index was found to predominantly affect the later stages of consolidation, with minimal impact on the early stages. The consolidation rate was observed to increase as the permeability coefficient ratio decreased. Despite notable differences in early consolidation behavior under varying loading conditions, the findings reveal that these discrepancies are alleviated in the later stages, ultimately resulting in no significant overall difference in the time required for the foundation to achieve complete consolidation.

Introduction Many theories of consolidation for soils have been proposed in the past, but most of them have ignored the structural characteristics of clay, yet the natural layered soils are widely distributed around the world.Methods A theoretical model is established to analyze the one-dimensional consolidation behavior of layered soils, in which a time-dependent drainage boundary and the structural characteristics of the soil are taken into account. Using the integral transform and characteristic function methods, the analytical solution is derived, the effectiveness of which is evaluated against the degradation of solutions and the numerical results calculated using the finite element method.Results and discussion Finally, the influences of interface parameter, soil permeability coefficient and soil compressibility on consolidation behaviors are discussed. Results show that in structured soils, early dissipation of excess pore water pressure and consolidation rates are predominantly influenced by interface parameters, permeability, and volume compression coefficients. Higher values of these parameters accelerate early stages of consolidation, which is especially evident in the upper soil layers. Over time, the distinct effects of interface and permeability coefficients on consolidation diminish. Higher volume compression coefficients, while initially beneficial, eventually slow down the consolidation process, indicating an interaction with the ongoing soil structural changes.

Laboratory one-dimensional consolidation tests were conducted to measure the variation trend of the soil pore pressure at the drainage boundary with time under different magnitudes of loads. Based on the test data, continuous drainage boundary interface parameters under arbitrary loads were inversely derived, the reasonableness of which was verified by comparing the theoretical values of the boundary pore pressure with the experimental results. Moreover, the one-dimensional consolidation model of the layered foundation was established with a continuous drainage boundary. The semianalytical solution of the corresponding model under an arbitrary load was given by using the boundary transformation method. A comparison with degraded results and the finite-element calculation results verified the correctness of the present solutions. Finally, the influences of the interface parameters and loading rate on the soil consolidation behavior were studied, where three different types of loads (i.e., linear, exponential, and simple harmonic) were considered. The results revealed that the consolidation rate reaches the peak value for the linear loading pattern when the loading is completed. Moreover, the exponential load used to describe the surcharge preloading method also positively influenced the theoretical analysis due to its concise expression form. When the simple harmonic load was applied, the excess pore-water pressure in the soil element presented stable periodic vibration after the first cyclic load. In addition, the loading rate and interface parameters exhibited different influences on the consolidation behaviors. The research results of this paper can provide a theoretical reference for the settlement calculation of subgrades during the construction and operation phases.

To comprehensively consider the impacts of stratification, residual pore water pressure, soil nonlinearity, and boundary permeability on consolidation settlement of soft soil foundations for accurate prediction, a continuous drainage boundary condition is proposed in this study that reflects the residual pore pressure under multistage loading, and a nonlinear elastic constitutive model based on the double logarithmic model is adopted to account for the nonlinear consolidation behaviour of soils. A UMAT subroutine is developed based on the proposed boundary condition and nonlinear elastic constitutive model. Subsequently, the developed subroutine is compared with the built-in linear elastic soil constitutive model in ABAQUS and engineering examples. The application of continuous drainage boundaries in stratified foundations is analysed, as well as the influence of factors such as the loading rate and soil nonlinearity on consolidation settlement. The results indicate that, compared to the built-in model, the subroutine developed in this study can be employed to more accurately calculate the nonlinear consolidation of multilayered foundations under multistage loading. By adjusting the loading rate parameter alpha k, consolidation under different loading conditions can be predicted. Additionally, the proposed boundary condition simplifies the calculations for soft soil foundations with sand layers, providing a novel computational approach for the design of construction loading schemes and long-term settlement predictions in soft soil foundations.