Fully coupled physics-informed neural networks for hydro-mechanical analysis of saturated poroelastic media

A physics-informed neural networks (PINNs) framework is presented for the fully coupled hydro-mechanical analysis of saturated poroelastic materials. Continuous-time PINNs are developed that simultaneously solve the coupled momentum balance and mass conservation equations with no training data or spatial and time discretisation. The framework is validated against three benchmark hydro-mechanical problems with known analytical solutions: one-dimensional Terzaghi’s consolidation (linear and nonlinear elasticity, with a stress-dependent bulk modulus), De Leeuw’s cylindrical problem, and Cryer’s spherical problem. A key contribution is the implementation of a simultaneous optimisation strategy to capture the strong coupling between the mechanical and hydraulic fields, enabling accurate modelling of the Mandel–Cryer effect. Parametric studies are presented to demonstrate the robustness of the proposed approach across varying Poisson’s ratios and fluid bulk moduli.