# Quantitative Description for Sand Void Fabric with the Principle of Stereology
## 5 Image Analysis of Void Fabric
### Parallel Scan Line Analysis Method  
According to the principle of stereology, the scan line is the key to the test of void fabric. The void is the sum of all pixels with a value 0 in a binary image. Porosity is the ratio of the voids to the total pixels of the scan line, this definition is different from the soil mechanics, while their spatial distribution is the same and can be interchangeable.  
In the image analysis, the scan line and the image processing diagram of specimens are operated with \"&\", and the intersection image of the scan line and void is obtained, then void data is extracted. Figure 4 shows the calculation results of image analysis with parallel scan lines. Figure 4 is the diagram of the scan line (60\({}^{\circ}\)). Figure 4 is the binary image. Figure 4 is the result measured by the 60\({}^{\circ}\) scan line and Figure 4 is the result measured by the 30\({}^{\circ}\) scan line. The number of scan lines is 180.The scan line is drawn by AutoCAD. Figure 4,d show that the calculated image will better describe the void distribution.  
Figure 3: The general procedures to determine void fabric tensor in an image analyzer.  
Before test verification, the influence of scan line density and angle needs to be analyzed. Two examples are designed for the same image. One is to analyze the image with different scan line densities and the same angle. The other is to analyze the image with different scan lines at the same density and different angles. Figure 5 shows the influence of scan line density on test results, and the relationship between porosity and scan line density is obtained by increasing the number of scan lines with a fixed angle of the scan line. The images adopt three orthogonal planes of sand specimens from [PERSON] et al. (2016).  
As is presented in Figure 5, the fewer the number of test lines, the greater the impact on the porosity. However, as the number of scan lines increases, the fluctuation tends to be stable and nearly constant. When the number of scan lines is more than 100, the porosity fluctuation is ignored. Therefore 230 scan lines were used in this test. Figure 6 shows the relationship between the angle of parallel scan lines and porosity. The angle of the scan lines varied from 0\({}^{\circ}\) to 180\({}^{\circ}\) with an angle interval of 10\({}^{\circ}\). Figure 6a shows that the porosity varies little with the angle of the scan line and is close to a constant value.  
Figure 4: The procedures to determine voids with the parallel scan line. (**a**) The diagram of the scan line (60\({}^{\circ}\)). (**b**) Binary images. (**c**) Analysis of image (60\({}^{\circ}\)). (**d**) Analysis of image (30\({}^{\circ}\)).  
Figure 5: Scan line density vs. porosity.  
Figure 6b intuitively shows that the plane porosity measured by parallel scan lines is an invariant, which cannot reflect the plane distribution of voids.  
To sum up, the average porosity fluctuated greatly when the number of scan lines was small, but after reaching a certain number, the value tends to be constant. The average porosity is a scalar, which is independent of the direction. Thus, parallel scan lines can measure the average porosity, but cannot measure the distribution of voids.