Modeling One-Dimensional Consolidation Problems Using Physics-Informed Neural Networks with Domain Decomposition

Soil consolidation modeling is essential for estimating settlement and pore-water pressure dissipation, but analytical solutions are limited for layered soils with complex drainage and interface conditions. This study evaluates physics-informed neural networks (PINNs) for one-dimensional consolidation of saturated soils and extends them to a domain-decomposed XPINN framework for two-layered soils. Governing equations, boundary conditions, interface-continuity constraints, and synthetic measurement data are embedded in the loss function. Layer-wise locally adaptive activation functions (L-LAAF) and residual-based adaptive resampling (RAR) are used to improve training stability. For homogeneous soil, the PINN accurately reproduces the analytical solution, although conventional finite difference methods remain more efficient for simple single-query forward analysis. For heterogeneous soil, the full XPINN model achieves a relative L₂ error of 0.0173 ± 0.0058, whereas removing RAR, L-LAAF, or domain decomposition increases the error to 0.0578 ± 0.0555, 0.1488 ± 0.0378, and 0.1673 ± 0.0104, respectively. In inverse tests using synthetic noisy measurements, denser and lower-noise observations improve the identification of unknown drainage coefficients. The framework provides a meshless and continuous representation for forward and inverse layered consolidation problems, but validation with laboratory or field data remains necessary.