3D Microstructure Simulation of Reactive Aggregate in Concrete from 2D Images as the Basis for ASR Simulation
Abstract
:1. Introduction
2. Research Significance
3. Material and Experimental Methods
3.1. Materials
3.2. Methods
3.2.1. Optical Petrography
3.2.2. Scanning Electron Microscope
3.2.3. X-ray Diffraction
3.2.4. Mercury Intrusion Porosimetry
4. Framework Development of 3D Microstructure Simulation
4.1. Thin Section Petrography and the 2D Microstructure Features from SEM-BSE
4.2. Thresholding & Binarization
4.3. 3D Simulation
4.3.1. Representative Image Selection
- Firstly, the normalized histograms of pore fraction and the quartz fraction from all of the 90 binarized images were drawn as shown in Figure 8. In Figure 8, the fraction distribution is divided into 10 bins represented by the blue bar. The x-axis is the pore or quartz fraction. The y-axis represents the probability distribution of the pore or quartz fraction within 90 binarized images.
- Based on the histogram, the lognormal distributions were fitted for the pore and quartz fractions, respectively. Equation (1) is the lognormal probability density function.Three representative statistical variables (the mode, the mean, and the median with their definition shown below Table 2) of the pore and quartz fraction calculated from the fitted lognormal distribution and images are shown in Table 2. The differences of these variables of pore fractions between the fitted curve and original data from 2D images are very small, except the mode pore fraction of the fitted curve is around 1% lower than the original one. The differences of these variables of quartz fraction between the fitted curve and raw data are also small, mainly below 2%, except that the median quartz fraction of the fitted curve is 4% higher than that of the original data. Generally speaking, the fitted lognormal distribution of the pore and quartz fraction can represent the true distributions pore and quartz fractions in the selected 90 images.
- Finally, representative fractions were selected through the probability density function curve. In total, 10 representative images were selected: Five images with quartz fractions of (6.58%, 10.44%, 20.68%, 32.58%, 41.23%) and another five images with a pore fractions of (0.66%, 2.18%, 3.26%, 4.3%, and 8.0%) as indicated by the x-axis values of the red solid circles in Figure 8a,b, respectively. These five fractions are representative not only because they cover the whole fraction distribution span of silica or pores, but also capture the main characteristics of the fraction distribution, such as the global maximum fraction value.
4.3.2. Simulation Method
5. Experimental Corroboration of the Simulated 3D Microstructure
5.1. Visual Checking
5.2. Numerical Checking
5.3. Quartz Fraction from Model and XRD
5.3.1. Quantitative Results from XRD
5.3.2. Upscale from Microscale to Mesoscale
5.3.3. Quartz Fraction Comparison
5.4. Pore Fraction from Model, SEM and MIP
6. Application of the Model
7. Conclusions
- (1).
- Suitable experimental methods should be chosen to obtain 2D images of the aggregate with a clear outline between particles, considering the particle sizes of the target phase, and suitable binarization methods should be chosen to segment the target phase from the images.
- (2).
- The pore and silica fraction distributions on the 2D SEM-BSE images of the limestone can be fitted by a lognormal distribution, which can be used to select representative images for 3D microstructure simulations.
- (3).
- The simulated microstructures of the siliceous limestone are able to retain the visual characteristics, such as the particle shape and spatial scattering, as well as the statistical characteristics of the air void and quartz silica, such as the fraction, characteristic particle size, and the specific surface area of the parent limestone. However, the pore information below the simulation voxel size (1 m) is lost during the simulation.
- (4).
- The simulated microstructures can be used to assemble the aggregate at a mesoscale embedded in mortar following the obtained lognormal distribution. The average air void and silica fraction show good consistency with the XRD and MIP results.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Properties | The Limestone |
---|---|
Surface-dried saturation density (gcm) | 2.69 |
Oven-dried density (gcm) | 2.67 |
Bulk density (gcm) | 2.71 |
Water absorption after 24 h (%) | 0.51 |
Specific gravity | 2.69 |
Phases | Data Resources | Mean Fraction , % | Median Fraction , % | Mode Fraction , % |
---|---|---|---|---|
Pore | Image analysis | 3.94 | 3.41 | 3.60 |
Fitted lognormal function | 3.76 | 3.32 | 2.58 | |
Quartz | Image analysis | 19 | 19.27 | 11.4 |
Fitted lognormal function | 17.03 | 15.05 | 11.35 |
Calcite, % | Dolomite, % | Fluorite, % | Quartz, % | |||||
---|---|---|---|---|---|---|---|---|
Mass | Volume | Mass | Volume | Mass | Volume | Mass | Volume | |
Sample 1 | 68.60 | 78.26 | 4.19 | 6.84 | 2.46 | 2.54 | 11.36 | 12.37 |
Sample 2 | 70.66 | 78.34 | 7.13 | 5.53 | 2.40 | 2.44 | 10.80 | 13.69 |
Sample 3 | 71.13 | 79.51 | 5.8 | 4.19 | 3.32 | 2.71 | 12.02 | 13.58 |
Average 1 | 70.13 | 78.70 | 5.71 | 5.52 | 2.39 | 2.56 | 11.39 | 13.21 |
Average 2 | 86.79 | 13.21 |
Microstructure ID | Pore & Quartz Fraction, % | Volume Fraction , % | Cube Pore Fraction , % | Cube Quartz Fraction , % | Cube Others Fraction , % |
---|---|---|---|---|---|
1 | (0.11 6.48) | 1.65 | 0.65 | 13.93 | 85.43 |
2 | (0.51 10.41) | 20.33 | |||
3 | (0.83 20.51) | 6.05 | |||
4 | (1.45 32.42) | 1.24 | |||
5 | (2.77 40.91) | 0.78 |
Sample ID | Total Pore Fraction, % | Pore Fraction over 1 m, % |
---|---|---|
1 | 0.23 | 0.17 |
2 | 0.55 | 0.49 |
3 | 0.37 | 0.37 |
4 | 0.79 | 0.79 |
5 | 0.25 | 0.09 |
6 | 2.56 | 2.35 |
Average | 0.8 | 0.7 |
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Qiu, X.; Chen, J.; Deprez, M.; Cnudde, V.; Ye, G.; De Schutter, G. 3D Microstructure Simulation of Reactive Aggregate in Concrete from 2D Images as the Basis for ASR Simulation. Materials 2021, 14, 2908. https://doi.org/10.3390/ma14112908
Qiu X, Chen J, Deprez M, Cnudde V, Ye G, De Schutter G. 3D Microstructure Simulation of Reactive Aggregate in Concrete from 2D Images as the Basis for ASR Simulation. Materials. 2021; 14(11):2908. https://doi.org/10.3390/ma14112908
Chicago/Turabian StyleQiu, Xiujiao, Jiayi Chen, Maxim Deprez, Veerle Cnudde, Guang Ye, and Geert De Schutter. 2021. "3D Microstructure Simulation of Reactive Aggregate in Concrete from 2D Images as the Basis for ASR Simulation" Materials 14, no. 11: 2908. https://doi.org/10.3390/ma14112908