Photogrammetry-Based Volume Measurement Framework for the Particle Density Estimation of LECA
Abstract
:1. Introduction
- Laboratory testing: the presented framework is a cost-effective method for measuring the particle density of porous aggregates (they do not require that the grains be immersed in a fluid that can penetrate the pores hence bias the result);
- Calibration of numerical simulations: popular calibration techniques of DEM models require assumptions about particle shapes and intergranular porosity [9]. Usually, the bulk volume and mass of the granular sample can be easily measured. However, the result of intergranular porosity depends on the grains’ particle density, which has to be measured as well.
2. Materials and Methods
2.1. Material
2.2. Computed Tomography Measurements
2.3. Remarks on CT Volume Measurement
2.4. Photogrammetry Workflow
2.4.1. Sample and Scene Preparation
2.4.2. Image Acquisition
2.4.3. 3D Modeling and Postprocessing
2.4.4. Comparison of SfM and CT Models
2.4.5. Archimedes’ Method
3. Results and Discussion
4. Conclusions
- In the case of aggregates with open pores, such as LECA, the particle volume (envelope volume) estimation depends on the envelope definition;
- We proposed a procedure for the envelope computation that can be applied to 3D models obtained from CT and SfM measurements;
- We recommend applying the threshold () of 0.175 for the grain envelope computation if the method is used in order to assess the intergranular porosity of LECA;
- We compared the particle density of grains obtained by the different methods. The SfM approach underestimated the mean density by 0.33% (0.0016 g/cm3), while Archimedes’ method overestimated the density by 2.49% (0.0120 g/cm3). All three methods show sufficient accuracy for most engineering purposes. Nevertheless, the SfM is the most accurate;
- The shape reconstruction with the SfM approach is very accurate. For 95% of the grain surface, the error is no higher than 0.129 mm (in the case of irregularly shaped grains) and no higher than 0.073 mm (in the case of round grains).
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Parameter | Value |
---|---|
X-ray tube voltage | 80 kV |
X-ray tube current | 120 µA |
Integration time | 800 ms |
Detector gain | 8× |
Number of projections | 1500 |
Voxel size | 34 µm |
Focal spot control | YES–Frame interval 64 |
Noise reduction filter | Shepp Logan |
Grain | Computed Volume (mm3) | ||||||
---|---|---|---|---|---|---|---|
CT Model | SFM Model | ||||||
t = 0.050 | t = 0.075 | t = 0.100 | t = 0.125 | t = 0.150 | t = 0.175 | No Threshold | |
A1 | 1340.39 | 1346.89 | 1354.07 | 1362.07 | 1370.14 | 1381.08 | 1345.96 |
A2 | 2167.83 | 2177.34 | 2185.38 | 2191.19 | 2196.73 | 2202.93 | 2210.19 |
B1 | 1315.02 | 1318.21 | 1320.74 | 1323.69 | 1327.25 | 1331.44 | 1321.53 |
B2 | 1249.45 | 1255.90 | 1260.36 | 1264.08 | 1270.02 | 1275.76 | 1257.78 |
C1 | 774.25 | 779.20 | 784.81 | 789.74 | 793.94 | 798.85 | 784.93 |
C2 | 1409.53 | 1415.49 | 1417.71 | 1420.44 | 1424.19 | 1429.29 | 1426.71 |
Grain | Mass (g) | Density (g/cm3) | Error (%) | |||
---|---|---|---|---|---|---|
SfM | Archimedes’ | CT | SfM | Archimedes’ | ||
A1 | 0.66390 | 0.4883 | 0.4979 | 0.4807 | 1.59% | 3.59% |
A2 | 1.03283 | 0.4643 | 0.4814 | 0.4688 | −0.97% | 2.69% |
B1 | 0.57681 | 0.4350 | 0.4392 | 0.4332 | 0.40% | 1.39% |
B2 | 0.68286 | 0.5383 | 0.5449 | 0.5353 | 0.56% | 1.81% |
C1 | 0.36727 | 0.4624 | 0.4697 | 0.4597 | 0.58% | 2.16% |
C2 | 0.72321 | 0.5051 | 0.5228 | 0.5060 | −0.18% | 3.32% |
mean | 0.4822 | 0.4927 | 0.4806 | 0.33% | 2.49% |
Grain | Reconstruction Error (mm) | |||
---|---|---|---|---|
Max | Mean | RMS | 95th Percentile | |
A1 | 0.397 | 0.038 | 0.052 | 0.102 |
A2 | 0.485 | 0.048 | 0.067 | 0.129 |
B1 | 0.347 | 0.029 | 0.040 | 0.080 |
B2 | 0.448 | 0.038 | 0.053 | 0.105 |
C1 | 0.247 | 0.027 | 0.036 | 0.073 |
C2 | 0.210 | 0.021 | 0.030 | 0.065 |
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Brzeziński, K.; Duda, A.; Styk, A.; Kowaluk, T. Photogrammetry-Based Volume Measurement Framework for the Particle Density Estimation of LECA. Materials 2022, 15, 5388. https://doi.org/10.3390/ma15155388
Brzeziński K, Duda A, Styk A, Kowaluk T. Photogrammetry-Based Volume Measurement Framework for the Particle Density Estimation of LECA. Materials. 2022; 15(15):5388. https://doi.org/10.3390/ma15155388
Chicago/Turabian StyleBrzeziński, Karol, Adam Duda, Adam Styk, and Tomasz Kowaluk. 2022. "Photogrammetry-Based Volume Measurement Framework for the Particle Density Estimation of LECA" Materials 15, no. 15: 5388. https://doi.org/10.3390/ma15155388