Towards Reliable Barrier Systems: A Constrained XGBoost Model Coupled with Gray Wolf Optimization for Maximum Swelling Pressure of Bentonite

Bentonite and bentonite mixtures are used as buffer material for deep geological radioactive waste repositories. The proper determination of bentonite maximum swelling pressure is important as it influences the long-term stability and sealing characteristics of the barrier system. We developed a constrained machine learning model based on extreme gradient boosting (XGBoost) algorithm tuned with grey wolf optimization (GWO) to determine the maximum swelling pressure of bentonite and bentonite mixtures. We integrated a penalty term into the XGBoost algorithm's loss function to constrain the model during the training phase ensuring meaningful predictions. To this end, we compiled a dataset containing 305 experimental data of bentonite maximum swelling pressure and other relevant soil properties including montmorillonite content, liquid limit, plastic limit, plasticity index, initial water content, and soil dry density to develop the model. The performance of the hybrid GWO-XGBoost model was benchmarked against feed-forward and cascade-forward neural network models. The GWO-XGBoost model showed a better performance in estimating the experimental values comparing to the other models, thereby demonstrating its effectiveness and reliability in determining the maximum swelling pressure of bentonite and bentonite mixtures.