A Fractal Prediction Model for the Volume Change of Unsaturated Bentonite

Unsaturated, densely compacted bentonite blocks, employed as the primary buffering material for high-level radioactive waste disposal, undergo long-term volumetric deformation upon contact with groundwater. Accurately predicting these volumetric deformations is critical for the safety assessment of deep geological repositories. This study proposes a modified effective stress model (σ′) based on the fractal characteristics of bentonite microstructure under unsaturated conditions, incorporating suction as a key parameter to quantify the volumetric behavior of unsaturated bentonite. Volume variations in densely compacted Gaomiaozi bentonite samples subjected to controlled suction conditions were experimentally determined using vapor equilibrium and osmotic technique approaches. The reliability of the proposed unsaturated effective stress was verified by the experimental data from this study as well as existing literature. The results demonstrated that the unsaturated deformation of the same bentonite could be consistently represented by a unified e–σ′ curve under various combinations of suction and vertical stress. The void ratio e exhibited strong correspondence with effective stress σ′, indicating the reasonableness of the proposed effective stress.