Bentonite with a low hydraulic conductivity is often used as engineered barriers to prevent groundwater contamination by leachate from the nuclear waste. When bentonite is immersed into the water solution, swelling deformation and swelling pressure will occur to create a tight contact with confining rock. The swelling deformation and swelling pressure are proportional to the amount of water volume absorbed by bentonite. The water volume absorbed by bentonite is related to its surface fractality. The correlation of the normalized water volume by bentonite volume (Vw=Vm) to vertical overburden pressure (p) is obtained as Vw=Vm ¼ KpDs 3, which presents a method to determine the surface fractal dimension of bentonite using the swelling tests. The surface fractal dimensions (Ds) of Wyoming bentonite and Tsukinuno bentonite are 2.64, 2.65, respectively obtained from the swelling tests. The surface fractal dimension of bentonite can be used to estimate the maximum swelling strain and swelling pressure in the disposal system f nuclear waste.

Modelling flow and solute transport in unsaturated porous media on the basis of the Richards equation requires specifying values for unsaturated hydraulic conductivity and water potential as a function of saturation. The high cost and large spatial variability of measurements makes the prediction of these properties a viable alternative. Fractal approach seems to be a potentially useful tool to describe hierarchical systems and is suitable to model the structure and hydraulic properties of porous media. In this paper, the fractal model for the pore-size distribution of unsaturated soils is constructed. The soil-water characteristics, hydraulic conductivity and soil-water diffusivity of unsaturated soils are derived and expressed by only two parameters, the fractal dimension and the air-entry value, which can be evaluated from the fractal model for the pore-size distribution. The predictions of the soil-water characteristics, hydraulic conductivity and soil-water diffusivity of unsaturated soils are in good accord with the published experimental data. Correlation between the pore-size distribution and the grain-size distribution is also studied, and it is found that both the pore-size distribution and the grain-size distribution satisfy the fractal model and they have the same fractal dimension. The fractal dimension of the grain-size distribution can be used to determine the unsaturated hydraulic conductivity, instead of the fractal dimension of the pore-size distribution.

Soil surface area does not keep constant and varies with the yardstick. Experimental results show that the amount of molecules absorbed in the surface monolayers is a function of absorbate size. The surface topography of soils from a few up to as many as thousand angstroms is very well described by fractal dimension, Ds. The surface fractal dimension, Ds is usually used to measure the irregularities of soil surface. The surface fractal dimensions of kaolin, montmorillonite and other six soils are measured using the adsorption method. The surface fractal dimensions of kaolin and montmorillonite are examined by the values measured using the nitrogen/water isotherm adsorption. The relationship between the surface fractal dimension and the content of clay is also discussed in this paper.

A significant 'size effect' is observed in ice failure strength: the ice strength is not independent of ice fragment size, but decreases with increasing size. The fractal approach to the ice mechanics with a multiscale microstructure provides an elegant and unified explanation of the size effect on ice failure strength. Ice fragments are found to have a fractal size distribution, with a fractal dimension (D) close to 2.50 over a remarkably wide range of ice fragment size. The size effect on ice strength can be well predicted using the fractal dimension D=2.50 of the ice fragment size distribution.

The hydraulic conductivity of unsaturated soils with constant volume is a function of the saturation degree or matric suction, and can be obtained based on currently available procedures. However, each procedure has its limitations and consequently cares should be taken in the selection of a proper procedure. Fractal approach seems to be a potentially useful tool to describe hierarchical systems and is suitable to model the structure and hydraulic properties of porous media. In this paper, the soil-water characteristic curve and hydraulic conductivity function of unsaturated soils were derived from the fractal model for the pore-size distribution, and were expressed by only two independently physical parameters, the fractal dimension and the air-entry value. The predictions of the proposed soil-water characteristic curve and unsaturated hydraulic conductivity were in good accord with the published experimental data. Comparisons between the experimental results and the predictions of both the fractal model and the van Genuchten- Mualem model were performed, and it was found that the predictions of the fractal model were better than that of the van G-M model.