Calculation Method for Grading Size and Grading Bounding Box of Virtual Aggregate Based on DEM

The grading size, which can be defined as the side length of the smallest square hole through which an aggregate with irregular shape can directly pass, is an important morphology parameter and can be used to calculate the gradation of mixture material. The grading bounding box, which can be defined as the circumscribed cuboid with central axis length being the grading size, is an important visual tool for observing the size and direction of the aggregate. Virtual test to calculate the grading size of a virtual aggregate is environmentally friendly and efficient, but the result provided by current research is imprecise and the grading bounding box is also rarely mentioned. In this paper, the multilevel complete projection algorithm is proposed to precisely calculate the grading size of a virtual aggregate. The whole process of the algorithm can be expressed by formula after the operation of sphere discretization by converting the virtual aggregate shell into the discrete aggregate. Then, the discrete aggregate is projected onto a complete series of the plane to form several 2D figures, and then, each 2D figure is projected onto a complete series of the orthogonal axis to form orthogonal segments. The grading size can finally be obtained by comparing the length of the above orthogonal segments based on the key central axis length principle. The influencing factors of computational accuracy and efficiency are considered in the algorithm. Finally, the grading bounding box can be built by using the Rodrigues transformation according to the information obtained from the above algorithm.