Abstract: When the compacted bentonite is inundated in distilled water, the effective stress on montmorillonite particles is equal to the external load applied; in salt solution, the effective stress incorporates the osmotic stress due to the osmotic suction of pore water. In addition, the relationship between void ratio em and the effective stress p of montmorillonite in compacted bentonite is found to satisfy a fractal relationship, which can be used to calculate the swelling deformation. Base on the dispersion and fractal characteristics of bentonite particles in salt solution, the expression of osmotic stress is derived, and the formula for effective stress on bentonite particles is developed. The swelling deformations of GMZ01 and MX-80 bentonites are calculated by incorporating the fractal model into the effective stress. Comparison of the experimental results available in the literature and the estimated value shows a good consistence. It is shown that the swelling deformation of bentonite can be expressed by a unified curve of em-p in distilled water or salt solution with different concentrations, implying that the proposed effective stress represents the actual force condition. The fractal model offers a good approach to expressing the swelling characteristics in salt solution.

Key words: bentonite, swelling deformation, surface fractal dimension, fractal method, salt solution, effective stress