Three-Dimensional Consolidation of Saturated Soil with Distributed Drainage Boundaries

Most existing studies on saturated soil consolidation with distributed drainage boundaries are confined to two-dimensional analyses, and their corresponding semianalytical solutions require presetting intermediate variables for boundary transformation and iterative solving. This paper presents a novel semianalytical solution for solving three-dimensional (3D) consolidation problems with distributed drainage boundaries. The method first transforms the consolidation governing equation into the Laplace domain and employs the Fourier cosine series expansion with its orthogonal property to directly address the distributed drainage boundary condition. Subsequently, a system of linear algebraic equations with respect to the solution coefficients is constructed and solved by applying matrix decomposition techniques. More intuitive expressions for excess pore pressure (EPP), average drainage velocity, and average consolidation in the Laplace domain are quickly derived. The time domain solution is ultimately obtained through a numerical inverse Laplace transform. Theoretical verification demonstrates that when the top surface is either fully drained or fully undrained, the solution reduces exactly to Terzaghi’s classical one-dimensional consolidation theory. Numerical simulations further validate the accuracy and reliability of the proposed method for complex 3D consolidation problems. Additionally, the influence of drainage parameters on consolidation behavior, drainage velocity, and the dissipation rate of EPP is systematically evaluated.