Abstract: A linear relationship between the maximum swelling deformation and the effective stress of bentonite under double logarithmic coordinates is derived based on the fractal theory. The effective stress of bentonite is related to the osmotic suction of concentration solution. However, the osmotic suction must be obtained through complicated tests, and it brings the difficulty to the practical application in projects. Based on the modified Debye-Huckel formula, the osmotic coefficients of CaCl₂, NaCl, NaNO₃ and Ca(NO₃)₂ solutions in different concentrations are obtained, and are proved to be reliable through other literatures. Then, the effective stress can be obtained by using the calculated osmotic suction. The maximum swelling deformations of the same kind of bentonite with different concentrations or different kinds of solutions have a unique linear relationship with the effective stress in log-log coordinates, which conforms to the theoretical formula.