A finite element-based machine learning model for hydro-mechanical analysis of swelling behavior in clay-sulfate rocks

Abstract

The hydro-mechanical behavior of clay-sulfate rocks, especially their swelling properties, poses significant challenges in geotechnical engineering. This study presents a hybrid constrained machine learning (ML) model developed using the categorical boosting algorithm (CatBoost) tuned with a Bayesian optimization algorithm to predict and analyze the swelling behavior of these complex geological materials. Initially, a coupled hydro-mechanical model based on the Richards' equation coupled to a deformation process with linear kinematics implemented within the finite element framework OpenGeoSys was used to simulate the observed ground heave in Staufen, Germany, caused by water inflow into the clay-sulfate bearing Triassic Grabfeld Formation. A systematic parametric analysis using Gaussian distributions of key parameters, including Young's modulus, Poisson's ratio, maximum swelling pressure, permeability, and air entry pressure, was performed to construct a synthetic database. The ML model takes time, spatial coordinates, and these parameter values as inputs, while water saturation, porosity, and vertical displacement are outputs. In addition, penalty terms were incorporated into the CatBoost objective function to enforce physically meaningful predictions. Results show that the hybrid approach effectively captures the nonlinear and dynamic interactions that govern hydro-mechanical processes. The study demonstrates the ability of the model to predict the swelling behavior of clay-sulfate rocks, providing a robust tool for risk assessment and management in affected regions. The results highlight the potential of ML-driven models to address complex geotechnical challenges.