PINN-based approach to the nonlinear large-strain consolidation under time-dependent drainage boundary

The theory of large-strain consolidation of high compressibility soft soil under time-dependent drainage at the boundaries involves complex material and geometric nonlinearities. Existing analytical solutions are applicable to specific working conditions only and are not suitable for general evolving compression and permeability laws. A Physics Informed Neural Network (PINN) is here introduced to solve the Partial Differential Equation (PDE) governing the nonlinear large-strain consolidation induced by a loading applied on the top of the soft soil layer, under exponentially time-growing drainage boundaries. To describe the nonlinearities linked to the mechanical behavior and the permeability of the soil, double logarithmic models are employed. To avoid issues related to the length and timescales governing the problem, a scaling transformation of the entire solution is also exploited. The effectiveness of the proposed PINN-based approach is reported via a comparison with available analytical solutions. After this preliminary assessment, the effects on the consolidation process of drainage, initial stress, nonlinear mechanical and permeability properties of the soil are analyzed. The PINN based approach is reported to significantly reduce the difficulty in solving the nonlinear consolidation problem characterized by large strains and overcome the deficiency of existing methods to provide exact solutions only for some specific cases.