Novel Semianalytical Solution for Three-Dimensional Consolidation of Multilayered Saturated Soils with Distributed Drainage Boundaries

This study develops a novel semianalytical solution to the three-dimensional (3D) consolidation problem of multilayered saturated soils with distributed drainage boundaries. The method integrates the piecewise-defined distributed drainage boundary conditions into a unified mathematical expression by introducing an indicator function. Subsequently, the Laplace transform is applied to process the governing equation in the time domain, and the Fourier cosine series expansion and its orthogonality are utilized to directly treat the distributed drainage boundary. Thus, a linear system with respect to the solution coefficients is derived, avoiding the complex iterative process used in previous studies. By using matrix operation techniques, analytical expressions for excess pore pressure (EPP), average drainage velocity, and average degree of consolidation are obtained in the Laplace domain. The time domain solutions are then obtained using numerical inverse Laplace transforms. The accuracy and effectiveness of the proposed solution are verified through rigorous theoretical reduction analysis and comparisons with finite-element simulation results. Parametric analysis indicates that compared to fully permeable conditions, the distributed drainage boundary extends the seepage path and delays the consolidation rate in the early stage. Increasing the pave rate, thickness–width ratio, anisotropy coefficient, and relative permeability, as well as reducing relative compressibility, can effectively accelerate the consolidation process and weaken the stratification phenomenon of EPP. Furthermore, due to the drainage boundary being located at the top surface, the parameters of the upper soil layer typically have a more significant influence on the overall consolidation behavior. These findings can provide theoretical guidance for the optimal design of distributed drainage systems.