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

TL;DR

The paper tackles swelling in clay-sulfate rocks by marrying physics-based hydro-mechanical finite element modeling with a constrained CatBoost surrogate, optimized through Bayesian methods. A synthetic dataset derived from a coupled Richards' equation–deformation model in OpenGeoSys informs the ML training, with penalties enforcing physical plausibility on porosity, saturation, and displacement. Monte Carlo simulations quantify uncertainty, and results show the ML surrogate achieving near-FEM accuracy with substantially reduced computation time, enabling rapid risk assessment and site-specific design decisions. This hybrid approach offers a scalable, efficient tool for managing hydro-mechanical swelling challenges in geology, with potential extensions to PINNs for broader applicability.

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.

Figures (11)

• Figure 1: A schematic view of the numerical model illustrating the flow and mechanical boundary conditions during (a) the leakage period and (b) the mitigation period.
• Figure 2: Histograms showing the distribution of porosity, saturation, and displacement values for the entire dataset.
• Figure 3: The evolution of MSE, penalty term, and penalized MSE during hyperparameter tuning of the porosity model. Iteration 124 corresponds to the optimized parameter set.
• Figure 4: The evolution of MSE, penalty term, and penalized MSE during hyperparameter tuning of the saturation model. Iteration 77 corresponds to the optimized parameter set.
• Figure 5: The evolution of MSE, penalty term, and penalized MSE during hyperparameter tuning of the displacement model. Iteration 104 corresponds to the optimized parameter set.