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.

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.

A significant'size effect' is observed in tensile strength of solid particles, such as ice, rock, ceramics and concrete: the tensile strength is not independent of the fragment size, but decreases with increasing size. The Weibull statistical theory was universally used to calculate the size effect observed in solid particles. Recent developments in fractal theory suggest that fractals may provide a more realistic representation of solid particles. In this paper, the scaling phenomenon of ice mechanics is explained using the fractal model for ice particle fragmentation. The Weibull statistics is modified using the fractal crushing of ice, and is compared with the conventional one. Goodness-of-fit statistics show that the modified Weibull statistics fits the experimental data of ice much better than the conventional one. The modified Weibull statistics has only one parameter, the fractal dimension of the fragment size distribution, which has a general value of 2.50 for the ice fragmentations.