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.

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.

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.