A multiple separation-of-variables method for 2D consolidation of anisotropic soils under multidirectional drainage constraints and non-uniform loading

Addressing the persistent challenge of non-uniform consolidation in coastal soft soils under complex drainage and loading conditions, this study presents a two-dimensional (2D) analytical model utilising the multiple separation of variables and superposition principles. The model effectively captures the coupling between multi-directional semi-permeable boundaries, soil anisotropy, and non-uniform loadings. Unlike conventional methods relying on integral transforms, this approach avoids convergence and numerical inversion issues. Its accuracy and reliability are demonstrated through comprehensive verification with experimental, analytical, and numerical benchmarks. Results indicate that vertical drainage systems, while accelerating overall pore water pressure dissipation, induce more intricate seepage patterns that exacerbate consolidation non-uniformity during the initial stages compared to horizontal drainage. Critically, this study reveals that strategically optimised non-uniform loading serves as a proactive mechanism to actively homogenise the spatial consolidation field, bypassing the need for structural modifications to existing drainage configurations. These findings elucidate the complex coupling mechanisms inherent in soil consolidation and provide a robust theoretical-to-practical bridge for mitigating consolidation nonuniformity in critical soft-soil infrastructure.