A Semianalytical Solution for Plane-Strain Consolidation of Saturated Soil with a Distributed Drainage Boundary

This paper presents a novel semianalytical solution for plane-strain consolidation of saturated soil with a distributed drainage boundary, offering an economically feasible alternative to the traditional fully permeable boundary. The method employs the Laplace transform to convert the consolidation problem into a transform domain, where the distributed drainage boundary is directly handled using Fourier cosine series expansion and its orthogonality properties. A system of linear equations involving solution coefficients was constructed and solved, and then the solutions of excess pore-water pressure, average consolidation degree, and average drainage velocity were obtained through the inverse Laplace transform. A convergence analysis was performed to optimize the computational efficiency of the algorithm and determine the required number of series terms. The results indicate that increasing the pave rate, thickness-to-width ratio, and anisotropy coefficient significantly enhances the stability of the algorithm and decreases dependency on series terms in computations. For general engineering problems, 40 series terms are sufficient to achieve the required accuracy in calculating the average degree of consolidation. The validity of the proposed solution was confirmed through comparisons with existing literature and finite-element simulations, and it simplified the classical Terzaghi one-dimensional consolidation solution under fully paved conditions. Furthermore, the effects of drainage parameters on the distribution characteristics of excess pore-water pressure and consolidation rate were systematically evaluated using several specific examples. These findings provide valuable guidance for the design of distributed drainage systems.