## 2 Morphological Characteristic Evaluation
### Shape
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Shape Indexes** & **Equations \({}^{*}\)** & **Characteristics** & **Literatures** \\ \hline \hline \multicolumn{4}{c}{Roundness} & \multicolumn{1}{c}{\(4\frac{\pi A}{L^{2}}\)} & \multicolumn{1}{c}{Roundness was the inverse of the form} \\ \multicolumn{4}{c}{Roundness} & \multicolumn{1}{c}{\(4\frac{\pi A}{L^{2}}\)} & \multicolumn{1}{c}{factor. In early imaging techniques, it was} \\ \multicolumn{4}{c}{} & \multicolumn{1}{c}{used to calculate 2D features of} \\ \multicolumn{4}{c}{} & \multicolumn{1}{c}{particle shape.} \\ \multicolumn{4}{c}{Form index using} \\ \multicolumn{4}{c}{Fourier series} \\ \multicolumn{4}{c}{(FRFORM)} & \multicolumn{1}{c}{\(R(\theta)=a_{0}+\sum\limits_{m=1}^{\infty}\left[a_{m}\cos(m\theta)+b_{m}\sin(m \theta)\right]\)} & \multicolumn{1}{c}{Fourier series can be used to analyze the} \\ \multicolumn{4}{c}{form, angularity, and texture of} \\ \multicolumn{4}{c}{index(Fourier series)} & \multicolumn{1}{c}{\(\frac{1}{2}\sum\limits_{m=1}^{m=m_{1}}\left[\left(\frac{a_{m}}{a_{0}}\right)^{2}+ \left(\frac{b_{m}}{a_{0}}\right)^{2}\right]\)} & \multicolumn{1}{c}{aggregate shape.} \\ \multicolumn{4}{c}{Ratio of Breadth} & \multicolumn{1}{c}{\(\frac{\min(x_{t})}{\max(x_{t})}\)} & \multicolumn{1}{c}{Breadth to width ratio can be used to} \\ \multicolumn{4}{c}{} & \multicolumn{1}{c}{to Width} \\ \multicolumn{4}{c}{Symmetry} & \multicolumn{1}{c}{\(\frac{1}{2}\left[1+\min\left(\frac{n}{n_{t}}\right)\right]\)} & \multicolumn{1}{c}{Symmetry is a term that some imaging} \\ \multicolumn{4}{c}{} & \multicolumn{1}{c}{systems use to describe aggregate form.} \\ \multicolumn{4}{c}{Shape Factor was a typical index in a} \\ \multicolumn{4}{c}{} & \multicolumn{1}{c}{system that represented in terms of three} \\ \multicolumn{4}{c}{dimensions (longest, intermediate, and} \\ \multicolumn{4}{c}{shortest dimensions).} \\ \multicolumn{4}{c}{FER represents the ratio between the} \\ \multicolumn{4}{c}{longest dimension and the shortest} \\ \multicolumn{4}{c}{dimension of a particle.} \\ \multicolumn{4}{c}{} & \multicolumn{1}{c}{\(\frac{\text{{D}}_{\text{s}}}{\text{{D}}_{\text{t}}}\)} \\ \multicolumn{4}{c}{Sphericity is a 3D parameter, which can} \\ \multicolumn{4}{c}{characterize the aggregate morphology} \\ \multicolumn{4}{c}{more accurately.} \\ \hline \hline \multicolumn{4}{c}{\(\theta\)–directional angle; \(\Delta\theta\)—incremental difference in the angles; \(R_{\theta}\)—radius of the particle at angle \(\theta\); \(R_{\theta+A\theta}\)—radius of the particle at angle \(\theta+\Delta\theta\). \(D_{max}\)—the maximum length of the minimum extremal rectangle of the aggregate profile; \(D_{min}\)—minimum size of the minimum extremal rectangle. \(A\)—Area of the aggregate profile; \(A_{MER}\)—area of minimum circumscribed rectangle. \(L_{max}\)—major axis length of equivalent ellipse; \(L_{min}\)—minor axis length of equivalent ellipse. \(c\)—focal length of ellipse with same second moment; \(a\)—major axis of the ellipse. \(L\)—Circumference of the aggregate profile. \(m\)—frequency; \(a_{0}\)—average radius; \(a_{m}\), \(b_{m}\)—Fourier coefficients \(n_{1}\)—threshold frequencies separating shape and angularity, \(x_{t}\)—maximum chord; \(x_{t}\)—the Fret diameter, \(r_{1}\), \(r_{2}\)—the distances of the center of gravity to the edge in a given direction. \(D_{L}\)—length, longest dimension; \(D_{t}\)—width, intermediate dimension, the maximum dimension in the plane perpendicular to the length; \(D_{S}\)—thickness, shortest dimension.} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._of coarse aggregates and derived that small-size aggregates have a larger proportion of elongated particle number. From the above research, it can be seen that the 3D scanning technique can well-characterize the aggregate's shape. However, previous studies using 3D scanning technology have mainly focused on the shape, volume, and surface properties of aggregates from one or different quarries, with less research on the morphological decay pattern of aggregates during application.