The compactness of waste residue soil significantly affects its mechanical properties

and it is particularly important to quantitatively analyze the influence of particle gradation on its dry density. The effect of particle size distribution on the dry density of waste slag soil was quantitatively studied by collecting waste slag soil formed by different slag forming methods and conducting particle size distribution and indoor relative density tests. The results show that slag material presents obvious fractal characteristics

with the main gradation curve types being concave and slow S-shaped. Based on the generalized Logistics function and the particle mass fractal model

a two-parameter particle size fractal grading equation is developed. This equation effectively describes the grading characteristics of the waste slag

with parameters a and b adjusting the slope and curvature of the curve. Using the particle size fractal grading equation

the area of the grading curve is integrated

and a prediction model for the extreme dry density of waste slag soil is established. The characteristics of the optimal gradation curve of the waste slag soil and the corresponding parameter range are determined. The research results offer a scientific basis for the stacking design

rolling construction and slope stability analysis of waste slag yards.