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.

Great efforts have been made to determine the shear strength of unsaturated soils using both elaborate laboratory tests and empirical methods. However, elaborate laboratory tests are difficult and time consuming to perform, and the physical meaning of empirical parameters is not obvious in empirical methods. A simple method to determine the unsaturated shear strength is proposed based on a fractal model for the pore surface. The unsaturated shear strength can be easily estimated using the surface fractal dimension and air-entry value, which can be calculated from the soil-water characteristic curves. The unsaturated shear strength obtained from the proposed method is in satisfactory agreement with the experimental data found in the literature. The proposed method is critically examined and its advantages and limitations are also discussed.

The adsorption of contaminants is one of the key mechanisms governing the transport of contaminants in the clay liner at landfill sites. This study presents an investigation of some factors controlling the adsorption of potassium (K+) onto two soils, named Ariake clay and Akaboku soil. The KCl solution and multi-salt solution containing KCl, NaCl and CaCl2 were selected as the synthetic leachates. The results show that with the increase of the solid/solution ratio, the adsorbed amount of K+ decreased for both soils. This dependence of adsorption behavior on the solid/solution ratio was found more significant for the Ariake clay. Both soils arrived an equilibrium condition in short time less than the contact time prescribed by the ASTM and US EPA standard batch-type tests. It was observed that both soils adsorbed larger amount of K+ in the case of KCl solution condition than in the case of multi-salt condition.