## 4 Verification and Evaluation of the Method on Target Particle Statistics Based on Digital Images
### Sand, Test Step, and Calibration  
Quartz sand with a specific gravity of \(G_{\mathrm{s}}\) = 2.69 and maximum and minimum dry densities of 1.84 g/cm\({}^{3}\) and 1.53 g/cm\({}^{3}\) was used; the particle size distribution of sand used in the validation test was as follows: particle size 2-3 mm accounted for 14.09%, particle size 1-2 mm accounted for 29.99%, particle size 0.5-1 mm accounted for 48.15%, particle size 0.25-0.5 mm accounted for 6.92%, and particle size 0.075-0.25 mm accounted for 0.85%. The corresponding maximum and minimum porosities were 0.419 and 0.315, respectively. Sand particles with particle sizes of 2-3 mm were selected as target particles, with a mass percentage of \(b=14.09\%\), and they were dyed black and then remixed with uniform stirring to make test objects containing black target particles. They were scattered in an acrylic soil box with transparent walls and internal dimensions of \(L\times B\times H^{\prime}\) = 29 cm \(\times\) 19 cm \(\times\) 9 cm. A Nikon D810 camera with about 36.35 million effective pixels and a manual focus was used.  
The test steps were as follows:  
1. The average pixel point of target particles (particles dyed black) was calibrated while determining the shooting distance and the focal length of the camera.  
2. We mixed the target particles with unstained particles of other sizes and mixed them evenly as much as possible to prepare the sand sample.  
3. We weighed a sample with a mass of \(m_{\mathrm{s}}\) (unit: g) and then layered it into a soil box. After leveling the surface of the sand, we measured the stacking height \(h\) in cm units to obtain the volume \(V_{\mathrm{s}}\) of the sand. We calculated the corresponding porosity according to the following equation and recorded it.  
\[n=1-\frac{m_{s}}{LBlG_{\mathrm{s}}\rho_{w}}\]  
In the formula, \(\rho_{w}\) is the density of water, taken as 1.0 g/cm\({}^{3}\).  
4. We took clear photos in the direction perpendicular to the height and length plane of the box. Digital images were taken at the same focal length and shooting distance as the calibration in step 1, and we recorded the name of the photo corresponding to the porosity.  
5. We gently tapped the wall of the soil box to slowly compact the sand and then tested the stacking height h of the sand, substituted it into the formula to recalculate the porosity, and recorded it. The soil box was vibrated to compact the sand, the height of the sand was measured, and the porosity was calculated.  
6. We repeated steps 2 and 3 above until the sand no longer solidified when the wall of the soil box was lightly tapped.  
7. Using the processing method established in Section 3, we processed the corresponding porosity photos to obtain the observed porosity. This article conducted a total of 4 sets of 21 working conditions tests, and the porosity of each set of sand was measured as shown in Table 1.  
When calibrating the average pixel of target particles, the photographed subjects were 699 target particle, which rarely touched each other on white paper, and the obtained average pixel of target particles was 604 with a standard deviation of 158; the pixels' range used in the program was (440,770).