Open Access

ARTICLE

Multi-Phase Fluid Transport in Expansive Soils: A Fractal-Constrained Physics-Informed Neural Network Framework for Permeability and Capillary Flow Characterization

Shaohui Wang^1,2,*, Minpo Jung^1,*, Zongzheng Jiao¹, Yanmei Xu³

1 Department of Computer Information Engineering, Youngsan University, Yangsan-si, Republic of Korea
2 Department of Building and Building Materials, Guangxi Polytechnic Vocational Technical School, Nanning, China
3 School of Civil Engineering, Guangxi Vocational Institute of Technology, Chongzuo, China

* Corresponding Authors: Shaohui Wang. Email: ; Minpo Jung. Email:

(This article belongs to the Special Issue: High-Order Computing and Deep Reinforcement Learning for Multiphase Interfacial Flows)

Fluid Dynamics & Materials Processing 2026, 22(9), 1 https://doi.org/10.32604/fdmp.2026.085897

Received 20 May 2026; Accepted 07 September 2026; Issue published 28 September 2026

Abstract

This paper develops a Fractal-Constrained Physics-Informed Neural Network (FC-PINN) framework to reinterpret mercury intrusion porosimetry (MIP) data from a fluid-mechanics perspective and to infer multiphase flow parameters and predict permeability in compacted expansive clay. The approach exploits the physical equivalence between mercury intrusion and water–air displacement in unsaturated soils, both of which are governed by the Laplace–Washburn relationship, while incorporating the steady-state Richards equation into the neural-network loss function as a physical constraint. Compacted expansive clay specimens with three void ratios (e = 1.4, 1.5, and 1.6) are considered, and surface fractal dimensions (Ds = 2.47–2.55) are determined using four established fractal models. The results show that increasing void ratio enhances pore-structure complexity and inter-aggregate pore connectivity, leading to an approximately four-fold increase in saturated permeability, from 3.18 × 10⁻⁹ to 1.31 × 10⁻⁸ m/s. Compared with conventional curve-fitting methods, the FC-PINN reduces the Root Mean Square Error (RMSE) by 31% to 0.0198, achieving R² > 0.995, while reducing the prediction error in the engineering-critical intermediate saturation range (Sw = 0.3–0.7) by 42%. The results demonstrate that incorporating fractal pore-structure information and governing physical laws enables the FC-PINN to move beyond empirical curve fitting towards a physically interpretable description of fluid transport. The framework provides a means of linking pore-scale topology to macroscopic hydraulic properties and offers physically consistent parameters for slope seepage analysis and rainfall-induced landslide early-warning applications.

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Keywords

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