Fractal dimension, particle shape, and particle breakage analysis for calcareous sand

To explore the fractal dimension, particle shape, and particle breakage of calcareous sand (CS) under multi-level ending pressure, a series of one-dimensional compression experiments along with microscope image recognition tests were performed. Test results demonstrated that compression behavior of CS was similar to that of silt soil for the reason that considerable particle breakage occurred under high-stress level. In unloading process, rebound index of tested specimens was in the range of 0.0027–0.0052 which suggested that irrecoverable plastic deformation consists of the main part of compression. The shape index sphericity (SC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{C}$$\end{document}), aspect ratio (AR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{R}$$\end{document}), convexity (CX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{X}$$\end{document}), and overall regularity (OR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${O}_{R}$$\end{document}) increased as increasing axial stress or decreasing average grain size. Besides, there existed a turning point of axial stress of 3200 kPa; these shape indexes increased rapidly first and then approached to a stable value after that. At present study, the surface and mass fractal dimension of tested specimens were in the range of 1.12–1.93 and 2.14–2.92, respectively. Both fractal dimension and relative breakage ratio increased logarithmically as increasing axial stress from 0 to 6400 kPa. In addition, an increase in the average grain size led to an increase in the relative breakage ratio and a decrease in fractal dimension which indicated that larger particles are more easily broken for the reason that the stress concentration between granular grains. Furthermore, there existed approximate linear relations between surface or mass fractal dimension with relative breakage ratio which might be helpful to quantitate the particle breakage of granular materials.