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33 Table 35. Priority vectors of test methods measuring coarse aggregate shape with respect to characteristics. Priority Vectors for Test Methods with Respect to Characteristics Reproducibility Interpret Data Repeatability Applicability Ease of Use Portability Readiness Accuracy Cost Test Method FER 0.143 0.019 0.041 0.496 0.328 0.408 0.356 0.270 0.180 MRA 0.143 0.183 0.213 0.244 0.125 0.213 0.158 0.270 0.180 VDG-40 0.143 0.183 0.213 0.052 0.125 0.076 0.158 0.105 0.180 Camsizer 0.143 0.183 0.213 0.052 0.125 0.076 0.158 0.105 0.066 WipShape 0.143 0.066 0.019 0.052 0.125 0.076 0.057 0.105 0.180 UIAIA 0.143 0.183 0.088 0.052 0.046 0.076 0.057 0.105 0.034 AIMS 0.143 0.183 0.213 0.052 0.125 0.076 0.057 0.105 0.180 PSSDA- 0.143 0.183 0.088 0.052 0.046 0.076 0.057 0.105 0.180 Large ratio (FER, MRA, VDG-40 Videograder, Camsizer, Wip- X-Ray Computed Tomography of Shape, UIAIA, AIMS, and Buffalo Wire Works [PSSDA- Aggregates Large]). The criterion that was used in the coarse aggregate texture example was used here. Therefore, the priority list Traprock, limestone, and crushed river gravel aggregates for all the characteristics in the second level and the result- were analyzed in this part of the study. Particles smaller than ing priority vector presented in Table 35 will apply for this 12.5 mm (1/2 in.) but larger than 9.5 mm (3/8 in.) were placed example. in a plastic sample container 100 mm (4 in.) in diameter and The results presented in Table 36 show that, when all char- 150 mm (6 in.) in height that was then filled with wax to acteristics are considered, the MRA has the highest rank among eliminate any disturbance to the particle arrangement during all methods. The method's high accuracy, ease of use, and low scanning. X-ray computed tomography (CT)--a nondestruc- cost contributes to this ranking. It is expected that the imag- tive technique to image the interior of the sample--was used ing methods will become more practical and easy to use after to produce images (examples are shown in Figure 9) that being in practice for some time and thus only repeatability, were analyzed to quantify the characteristics of the granular reproducibility, accuracy, and applicability should be consid- materials. ered in comparing test methods. The 3-D shape of particles was quantified based on measure- The weighting factors assigned to the accuracy catego- ments conducted on 3-D X-ray CT images using the Spherical ries can influence the ranking of test methods. For exam- Harmonic Series (SHS) presented by Garboczi (22). ple, the threshold for the highest accuracy category is 0.7 The results of the X-ray CT images analysis are shown in (Table 26). If the analysis is conducted for an R2 of 0.69 Figure 10 and summarized in Table 37. These results show (instead of 0.7) for the highest accuracy level, a somewhat gravel to be the most spherical material and that traprock has different ranking will result (as shown in the last column of the highest angularity and texture, followed by limestone and Table 36). then gravel. Table 36. Overall ranking of test methods for measuring coarse aggregate shape. Only Repeatability, Only Repeatability, Test Method All Characteristics Considered Reproducibility, Accuracy, and Reproducibility, Accuracy, and Applicability Considered Applicability Considered* FER 0.15 0.06 0.06 MRA 0.20 0.15 0.15 VDG-40 0.18 0.15 0.15 Camsizer 0.15 0.13 0.13 WipShape 0.08 0.06 0.06 UIAIA 0.08 0.06 0.13 AIMS 0.17 0.15 0.15 PSSDA-Large 0.11 0.09 0.09 *Using different values for accuracy categories.

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34 100 Percentage of Particles, % 90 Gravel Limestone 80 Traprock 70 60 50 (a) 40 30 20 10 0 0 0.2 0.4 0.6 0.8 1 (a) Gravel Sphericity Index 100 Percentage of Particles, % 90 80 Gravel 70 Limestone 60 Traprock 50 40 (b) 30 20 10 0 0 0.05 0.1 0.15 0.2 (b) Limestone Form, SHS Signature 100 Percentage of Particles, % 90 80 Gravel 70 Limestone 60 Traprock 50 40 (c) 30 20 10 0 (c) Traprock 0 0.01 0.02 0.03 Angularity, SHS Signature Figure 9. Examples of X-ray CT images. These 2-D images are 1024 1024 pixels in size, with each pixel representing a physical distance of about 100 Percentage of Particles, % 0.1 mm. The slice-to-slice resolution in the out of 90 plane direction was 0.8 mm per voxel length. The 80 images to the left were obtained using X-ray CT; 70 and the images to the right were thresholded to 60 highlight aggregate particles. 50 (d) 40 30 The SHS based on the images supplied by 3-D imaging 20 Gravel Limestone techniques (such as X-ray CT) can be used to reconstruct the 10 Traprock 3-D particle profiles. These reconstructed profiles can be 0 used in simulation programs that incorporate real 3-D particle 0 0.0002 0.0004 0.0006 representations (22, 23). Figure 11 shows 3-D reconstructed Texture, SHS Signature profiles of gravel, limestone, and traprock materials. These Figure 10. Results of the analysis of images profiles show some digital layering resulting from the relatively obtained using X-ray CT. low resolution used to capture the X-ray CT images (0.8 mm/

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35 Table 37. Summary of the statistical analysis of X-ray CT images. Statistical Mean* St. Dev.** Analysis Distribution Method TR. LS. GR. TR. LS. GR. Model Sphericity Normal 0.61 0.61 0.65 0.16 0.17 0.16 Index Shape, SHS -1.11 -1.21 -1.30 LogNormal 0.26 0.28 0.36 Signature (0.0773) (0.0610) (0.0496) Angularity, -1.98 -2.06 -2.33 LogNormal 0.26 0.27 0.46 SHS Signature (0.0106) (0.00868) (0.00466) Texture, SHS -3.64 -3.66 -3.76 LogNormal 0.22 0.21 0.24 Signature (2.2910-4) (2.1710-4) (1.7610-4) *The mean values for the LogNormal models are provided for the log scale and between brackets for the arithmetic scale. **The standard deviation values for the LogNormal model are provided for the log scale. slice). However, the reconstructed profiles show the smooth- Analysis of X-ray CT images was capable of discriminating ness of the gravel particles. among the angularity and texture of the different aggregates. The findings of the X-ray CT of aggregate shape analysis 3-D X-ray CT stores the 3-D shapes in a computer for fur- are summarized as follows: ther computer simulations. The image processing techniques used in separating the SHS analysis indicated that traprock had the highest angu- particles in X-ray CT require substantial manual manip- larity and texture, followed by limestone, and then gravel. ulation of images. These segmentation techniques could (a) Gravel (b) Limestone (c) Traprock Figure 11. Reconstruction of three-dimensional profiles of particles using spherical harmonic series.