Abstract: The particle breakage is satisfied with the fractal model and characteristized by the fractal dimension. The particle breakage of the bottom ash from municipal solid waste incineration(MSWI) is conducted, and the fractal dimension of particle breakage is analysized statistically. The evolution of the fractal dimension of particle breakage with the failure stress and breakage energy is studied based on the data collected in the literature. The value of the fractal dimension changes with the failure stress and breakage energy, and is gone by the name of the quasi fractal dimension. The quasi fractal dimension increases with the increases in the failure stress and breakage energy, and trends to a constant value 2.60 or so. This limit value of the fractal dimension is called as the intrinsic fractal dimension. Relation of the quasi fractal dimension to the failure stress and breakage energy is proposed based on the Weibull statistics.