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The Density Functions of Pore-Size and Particle-Size Distribution Established by Using Fractal Theory and their Applications

Based on the Sierpinski carpet and Menger sponge models, the density functions of pore-size and particle-size distribution are put forward. Using the proposed density functions, expressions of soil porosity and grain mass are obtained. Using the expression of soil porosity, the porosity of soil sample is correctly predicted. The expression of grain mass is used to predict the mass of grains. The results show that the mass predictions of grains of size smaller than 0.002mm are very close to the measure results.