A DEM-based framework to optimize the gradation of concrete aggregate using fractal approach

Several gradations of concrete with fractal dimension D = 2.0–2.9 (i.e., 2.0, 2.2, 2.4 2.6, 2.7, 2.8, 2.9) were designed based on particle size-mass distribution fractal model. The random polyhedral aggregate model was generated and then imported particle flow code, the discrete element method (DEM), to establish a multi-phase model considering mortar, aggregate, and interfacial transition zone (ITZ). On this basis, the relationship between fractal dimension D and macro-mechanical properties and microstructure of concrete was discussed, and the grading evaluation index was proposed based on fractal dimension D. The results show that the number of large-size aggregates decreases with increase in the fractal dimension, the compressive strength of concrete increases and reaches the maximum when the fractal dimension D = 2.7. Meanwhile, the fractal dimension affects the failure mode, as fractal dimension D increases, the total microcracks gradually increase, among which the ITZ microcracks increase mainly. Compared with the uncertainty of the non-uniformity coefficient and curvature coefficient, the fractal dimension can more accurately describe the aggregate grading characteristics. In addition, appropriate adjustments should be made to determine the range of fractal dimensions considering the differences between the aggregate filling.