Abstract: Natural rock and soil have complex mesostructure and composition characteristics, and it is difficult to model geotechnical mesostructure, which has specific particle size, aspect ratio, dip angle, and plane distribution characteristics. For this reason, a method is introduced to use four connected arcs to approximate the shape of an ellipse, combining with improved advancing front method. A highly dense ellipse packing allowing any size, aspect ratio, orientation angle, and spatial distribution is generated by this method. Based on the ellipse packing generated, a complex geotechnical mesostructure with imposed elliptical particle size, aspect ratio, dip, and plane distribution characteristics is generated. A comparison between the proposed method and two traditional methods (optimized dropping and rolling method (ODR) and advancing layer algorithm (ALA)) shows that the ellipse packing generated by the proposed method has a higher density and faster speed than that generated by ALA and ODR, with a packing efficiency of 500-600 s in the MATLAB environment. Compared with the size distribution generated by GBM in modeling mesostructure of rock and soil, the method proposed in this paper can consider four factors (i.e., particle, size, long-to-short axis ratio, dip angle, and plane distribution). The method can construct a convex-based structure equivalent to real rock and soil. Two application cases show that the method proposed in this paper can improve the modeling accuracy and efficiency from the current geotechnical model.

Key words: ellipse packing, Laguerre Voronoi, advancing front method, multi-factor, mesostructure