Prediction and Uncertainty Analysis of Soil-Bentonite Permeability Using Monte Carlo Dropout and Bayesian Variational Inference

The soil-bentonite cutoff wall is a crucial engineering technique for controlling contaminant transport. The permeability of soil-bentonite is a key parameter of cutoff wall design, affected by multiple factors including the engineering properties of the base soil and bentonite, as well as consolidation stress. In engineering practice, a large number of permeability tests on mixtures with different proportions are often required to determine suitable mix ratios, which demands extensive empirical experience and involves considerable testing time. In this study, based on 160 sets of sample data from tests and literatures, a dropout neural network model was developed to predict the permeability of soil-bentonite mixtures, using eight factors as input features, including base soil gradation, bentonite free swelling index, content of bentonite and consolidation stress. Uncertainty analysis was then performed using two approaches: Monte Carlo dropout and Bayesian variational inference. Both methods demonstrate excellent permeability prediction performance. Monte Carlo dropout offers higher analysis efficiency, while Bayesian variational inference yields explicit posterior distributions of the network parameters. The feature importance analysis reveals that the free swelling index and content of bentonite exhibit stronger correlations with permeability, while consolidation stress exhibits a relatively weaker relationship. The proposed predictive frameworks offer quantitative guidance for soil–bentonite mixture design, reducing empirical experience and decreasing the amount of mixture testing.