Four grade-scaling methods including scalping method

equivalent substitution method

similar grading method and hybrid method are adopted to model the site gradation of soil materials according to the code. 15 test gradations of coarse-grained materials from an engineering site have been simulated by using these grading scale methods

and the corresponding maximum particle diameters are 60 mm

40 mm

20 mm. The maximum dry density tests have also been conducted on the samples with test gradations and prototype gradation. The relationships among fractal dimension

grading scale methods and maximum dry density have been discussed by introducing the fractal dimension of particle diameters. It is found that the fractal dimension is a comprehensive evaluation index which can accurately reflects the test gradations by different grading scale methods. In addition

the grading scale methods significantly influence the maximum dry density

and the maximum dry density value of samples by the similar gradation methods is closest to that of prototype gradation

and the biggest disparity exists between equivalent substitution gradation method and prototype gradation. There exists a better linear normalization relationship between the fractal dimensions and the maximum dry density. Based on the normalization law

the maximum dry density of sample with prototype gradation could be calculated accurately.