Formula for permeability coefficient of coarse-grained soil based on parameters of two-dimensional fractal gradation model

The coarse-grained soil is widely distributed in nature and used in engineering. The permeability is one of its key properties, and for the same type of coarse-grained soil, its permeability is almost determined by the grain-size distribution and the pore characteristics. In principle, its permeability coefficient can be calculated based on the grain-size distribution and the pore characteristic parameters. The two-dimensional fractal gradation model based on the fractal theory is used to quantitatively describe the continuous gradation and gap gradation of the coarse-grained soil so as to determine the applicability of the gradation model and obtain its parameters. Then, based on the parameters of the two-dimensional fractal gradation model and the Kozeny-Carman formula, a formula for calculating the permeability coefficient including grain-size distribution parameters and the porosity is established. After discussing the physical meaning of each item in the formula, the validation of the formula is verified by using the measured data in the existing researches. The results show that the two-dimensional gradation model can accurately and uniquely describe the grain size distribution of the coarse-grained soil. The established formula for calculating the permeability coefficient of the coarse-grained soil including grain-size distribution parameters and the porosity is reasonable, and it is suitable for calculating the permeability coefficient of continuously graded and gap-graded coarse-grained soil.