Inversion of Fractal Dimension Parameters for the Pore Structure of Swelling Soils Based on PINNs

Swelling soil landslides pose severe challenges in geotechnical engineering due to non-linear deformation and strength degradation. Accurate characterisation of pore structure parameters remains the core difficulty. This study proposes a Physics-Informed Neural Network (PINNs) framework that utilises Mercury Intrusion Porosimetry (MIP) data to simultaneously invert three key physical parameters: pore fractal dimension (Ds), surface tension (γ), and contact angle (θ). By embedding the Washburn equation and fractal pore theory into the neural network loss function, the framework achieves high-precision inversion without requiring complete prior information. Validated on three expansive soil samples, the inverted Ds values were 2.47, 2.53, and 2.58, showing excellent agreement with classical models (R² > 0.99) and an average relative error below 2.3%. The inverted γ ranged from 0.476 to 0.480 N/m and θ from 142.3° to 144.2°, both satisfying physical plausibility requirements. Five-fold cross-validation confirmed the absence of overfitting (ΔR² < 0.001). Sensitivity analysis identified Ds as the dominant parameter controlling pore volume distribution; Ds exceeding 2.55 indicates elevated landslide susceptibility. This framework provides a rapid, automated approach for extracting pore structure parameters, offering parametric support for preliminary risk assessment of expansive soil slopes.