## 2 Materials and Methodology
### Geometric Characteristic Evaluating Methods  
#### 2.2.1 Indirect Methods  
The indirect tests are normally inexpensive and easy to conduct, and numerous methods and parameters have been proposed to evaluate the geometric characteristic of FAs. In this research, three commonly used indirect methods were adopted which are uncompact void content test, flow time test and ASTM D3398 test, respectively.  
(a) Uncompact void content test  
The uncompact void content test estimates the geometric characteristic of FA by measuring the loose uncompacted void content of fine aggregate particles. It provides an indication of the aggregate's  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Type** & **Origin** & **Fineness Modulus** & **Apparent Relative Density** & **Lithology** \\ \hline
1 & Natural sand & Heilongjiang & 2.9 & 2.618 & Siliceous \\
2 & Stone chips & Jilin & 2.6 & 2.740 & Limestone \\
3 & Stone chips & Jilin & 2.4 & 2.747 & Limestone \\
4 & Stone chips & Shandong & 2.7 & 2.861 & Limestone \\
5 & Stone chips & Heilongjiang & 2.9 & 2.708 & Andesite \\
6 & Stone chips & Gansu & 3.4 & 2.730 & - \\
7 & Machine-made sand & Gansu & 3.0 & 2.642 & Granite \\
8 & Machine-made sand & Jilin & 3.2 & 2.742 & Limestone \\
9 & Machine-made sand & Jilin & 2.8 & 2.755 & Limestone \\
10 & Machine-made sand & Shandong & 3.0 & 2.844 & Basalt \\
11 & Machine-made sand & Heilongjiang & 2.5 & 2.778 & Basalt \\
12 & Machine-made sand & Heilongjiang & 3.2 & 2.826 & Basalt \\
13 & Machine-made sand & Heilongjiang & 4.2 & 2.822 & Basalt \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic technical properties of the 13 fine aggregates (FAs).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No.** & **Particle Size/mm** & **4.75** & **2.36** & **1.18** & **0.6** & **0.3** & **0.15** & **0.075** \\ \hline
1 & 100.0 & 89.5 & 72.9 & 42.6 & 9.4 & 2.3 & 0.6 \\
2 & 100.0 & 87.9  
angularity, spherical shape, and surface texture compared to other fine aggregates tested in the same grading. The uncompact void content \(U\) can be calculated by:  
\[U=\left(1-\frac{\gamma^{\prime}a}{\gamma_{b}}\right)\times 100 \tag{2}\]  
It has been reported that a higher U can be observed in FA particles with less spherical particles and higher value of cubic aggregate, and vice versa.  
(b) Flow time test  
The flow time test is an indirect measurement of FA geometric characteristic by measuring the time required for a defined volume of aggregate passing through a standardized funnel. The test funnel has two standard diameters which are 12 mm and 16 mm. The 12 mm diameter funnel applies to FA with the particle size range of 0.075-2.36 mm while the 16 mm diameter funnel for FA with the particle size range of 0.075-4.75 mm. For the flow time test, a greater value of flow time \(T\) represents greater friction angle, fewer spherical particles, and coarser angularity.  
(c) ASTM D3398 test  
In the ASTM D3398 test method, the indicator average particle index \(I_{a}\) was proposed to evaluate the particle shape and texture characteristics of aggregates for each size fraction. The indicator particle index \(I\) was proposed to evaluate the particle shape and texture characteristics of graded aggregates. The average particle index \(I_{a}\) and particle index \(I\) can be obtained by:  
\[I_{a}=1.25\times q_{10}-0.25\times q_{50}-32 \tag{3}\]  
\[I=\sum_{i=1}^{n}(P_{i}\times I_{ai}/100) \tag{4}\]  
in which  
\[q_{10}=\left[1-m_{10}/sv\right]\times 100 \tag{5}\]  
\[q_{50}=\left[1-m_{50}/sv\right]\times 100 \tag{6}\]  
The particle index \(I\) is a quantitative measure of the aggregate form and texture characteristics that may affect the performance of road and paving mixtures and the greater value indicates fewer spherical particles and coarser angularity.