Three-Point Imaging Test for AASHTO Soil Classification Roman D. Hryciw and Yongsub Jung methods for the determination of grain size from images of contacting particle assemblies (as opposed to individual noncontacting particles) are necessary. The present paper discusses a simple procedure that uses grayscale images of contacting particles to rapidly obtain the volume fraction of soils in the four grain size ranges needed to fully classify AASHTO soils in the A-1 and A-3 groups—that is, soils with predominantly coarse-grained materials. However, soil classification in all other groups requires knowledge of the percentage passing the No. 200 sieve and separation of the minus No. 40 fraction for Atterberg limits testing. The proposed imaging method facilitates both tasks. The key to the method’s success is rapid segregation of the soil specimen by grain size before image collection. A rapid, digital image–based test has been developed for the classification of highway subgrade materials according to the AASHTO system. The test involves segregating particles in a sedimentation column, then determining the elevations at which 2.0-, 0.425-, and 0.075-mm grains (No. 10, No. 40, and No. 200 sieves, respectively) are found. If it is assumed that porosity variations throughout the column are insignificant, as established in previous studies, then the distances between these elevations translate to the percentages that pass through the various sieves. The method uses a previously developed calibration between an image wavelet decomposition index and the pixels per particle diameter. At a camera magnification of 32.5 pixels/mm, the entire grain size range from 2.0 to 0.075 mm is resolved. Thus, only a single fixed magnification lens is needed for the system. The accuracy of the new test is demonstrated by comparing the digital image–based results and conventional sieving for three soil specimens: well-graded sand, uniformly fine sand, and sandy silt. The advantages of the three-point imaging test for AASHTO soil classification over conventional sieving and hydrometer tests include reduced testing time, low noise, possibly lower equipment costs, and the elimination of airborne particles in the lab. WAVELET DECOMPOSITION Following Haralick et al. (4) and other early attempts (5–8) to use classic textural indices for soils, Shin and Hryciw (9) showed that the mathematical wavelet decomposition of grayscale images of relatively uniform soils yields a more robust index of grain size. Details of the wavelet decomposition are available elsewhere (e.g., 10, 11), as are the procedures adapted for developing the soil grain size index (7, 9). In short, the simple Harr wavelet transformation is performed on a 2-in. × 2-in. pixel image, where n is an integer (12). The original image is decomposed n times into n images of geometrically increasing pixel size; the number of pixels representing the image is therefore quartered with each decomposition. For each decomposition level, an “energy” is then computed that reflects the magnitude of the differences between average grayscale values of adjacent pixels at that level (9). A pixelized region with few grayscale differences at a particular decomposition level is considered to have a low energy. The highest energy is associated with the decomposition level at which the image pixel size approaches soil grain size. The energies computed at each decomposition level (eight levels for a 256- × 256-pixel image) are normalized by the total energy of the original image, as described by Shin and Hryciw (9) or Jung et al. (13). Normalized energy distributions are charted versus decomposition level in Figure 1 for various soil specimens whose uniform grain size is defined by the number of pixels per particle diameter (PPD). The PPD measure was first suggested by Ghalib et al. as a way to normalize image indices by the camera magnification (5). Figure 1 shows that as PPD increases, the energy curves shift to higher decomposition levels. Shin and Hryciw sought a single-index parameter that would relate a normalized energy curve to PPD (9). The first moment with respect to the ordinate in Figure 1 was ideal. It also can be thought of as the horizontal coordinate of the center of area (CA) under a normalized energy plot. The CA–PPD correlation will be valuable to AASHTO Both the AASHTO system for the classification of highway subgrade materials (AASHTO M145; ASTM D3282) and the Unified Soil Classification System (USCS; ASTM D2487) require sieving to determine the grain size of a coarse-grained soil fraction. Whereas the USCS often requires developing a complete distribution curve of grain size to determine the coefficients of uniformity (D60/D10) and gradation (D302/D60D10), the AASHTO system requires only knowledge of the percentages passing the No. 10, No. 40, and No. 200 sieves. Soil sieving is a noisy, dusty, and energy-intensive task; the equipment is expensive, and parts often need to be replaced—particularly the finer-meshed sieves. Image-based methods for determining grain size have been proposed. Hryciw et al. summarize the development of image-processing techniques used for this purpose (1). If the soil particles can be separated (noncontacting)—say, on a glass back-lit plate—then the grain size distribution can be assessed deterministically from images. For soils with a wide range of grain sizes, this task requires capturing images at several magnifications with statistical data reduction (2) or by mosaic imaging (3). However, no simple method for particle separation has been developed, and doing so manually—grain by grain—is an unappealing task. For this reason, Department of Civil and Environmental Engineering, University of Michigan, 2340 GG Brown, 2355 Hayward Street, Ann Arbor, MI 48109-2125. Corresponding author: R. D. Hryciw, firstname.lastname@example.org. Transportation Research Record: Journal of the Transportation Research Board, No. 2101, Transportation Research Board of the National Academies, Washington, D.C., 2009, pp. 27–33. DOI: 10.3141/2101-04 27 28 Transportation Research Record 2101 Normalized Energy (%) 40 PPD 0.9 1.8 3.1 4.4 6.4 12.0 20.9 32.3 35 30 25 20 15 Support tower Soil release chute Sedimentation column 10 Camera tower 5 0 0 1 2 3 4 5 Decomposition Level 6 7 8 Camera FIGURE 1 Normalized energy versus decomposition level for images of various PPD (1). Monitor soil classification because it spans almost three orders of magnitude of PPD (Figure 2). The PPD values used to develop Figure 2 were based on soil grain sizes obtained by conventional sieve analysis. PARTICLE SEGREGATION Unfortunately, the CA–PPD concept and calibration shown in Figure 2 has no application to soils with mixed grain sizes. The authors’ attempts to extend the CA parameter to mixed soils have been unsuccessful to date, and future successes are uncertain. Given that most coarse-grained soil specimens obtained by traditional sampling techniques contain a range of grain sizes, the particles would have to be segregated by size to use Figure 2. Sieving would achieve segregation but also would make image-processing techniques (and this paper) pointless. Therefore, a sedimentation column 5 cm × 5 cm × 122 cm was constructed to rapidly separate the grains by size (Figure 3). The column was extended to 244 cm to improve particle segregation. After sedimentation, which takes only a few minutes for soils without clay-sized particles, continuous images are collected along the length of the column. Because of the segregation, each image contains only soil grains of a relatively uniform size. Note that images are not collected during sedimentation. 6.0 No. 16-20 (1.19-0.85 mm) No. 20-40 (0.85-0.425 mm) No. 170-200 (0.088-0.075 mm) No. 200-270 (0.075-0.053 mm) No. 270-400 (0.053-0.038 mm) No. 40-50 (0.36 mm): multi-color No. 40-60 (0.33 mm): uniform color 5.5 Wavelet Index, CA 5.0 4.5 3.0 2.5 2.0 10 Pixels per Diameter, PPD FIGURE 2 Initially, it was feared that, because of self-weight consolidation and variable settlement velocities in accordance with Stokes’ law, the porosity would decrease with depth in the sedimented column. This situation would have necessitated various height-measurement corrections to produce a valid grain size distribution. Because porosity variations in the sedimented soil column fortunately were found to be insignificant in other experiments, each height increment in the soil column corresponds to a proportional percentage of soil solids (14). Percentages for AASHTO Soil Classification 3.5 1 Sedimentation column and camera system (14). SOIL CLASSIFICATION 4.0 0.1 FIGURE 3 Wavelet index (CA) versus PPD (1). 100 Image processing by wavelet decomposition lends itself particularly well to the AASHTO soil classification system because all of the images can be taken at a single fixed magnification of 32.5 pixels per image millimeter. At this resolution, the No. 10 sieve opening (2.00 mm) corresponds to PPD10 = 65.0, the No. 40 sieve opening (0.425 mm) corresponds to PPD40 = 13.8, and the No. 200 sieve opening (0.075 mm) corresponds to PPD200 = 2.4. From Figure 2, the corresponding CA values for PPD10, PPD40, and PPD200 are CA10 = 5.1, CA40 = 3.9, and CA200 = 2.9, respectively. These values are summarized in Table 1 for quick reference. Hryciw and Jung 29 the four soil sizes are easily computed. The results are in good agreement with those from sieving (Figure 5a). Under the AASHTO system, the soil would be classified as A-1-b; ASTM D3282 would describe it as “material consisting predominantly of coarse sand, either with or without a well-graded binder.” A second test was performed on a poorly graded sand (Figure 6). Again, the sieve- and image-based results show good agreement; the observed percentages of the various soil sizes are within approximately 2% of each other. Under the AASHTO system, the soil is classified as A-3. It typically is a fine beach sand or a fine desert-blown sand either without silty or clay fines or with a small amount of nonplastic silt. The soils used in Examples 1 and 2 were not used to develop the CA–PPD calibration in Figure 2. As such, the good agreements between sieve- and image-based grain size distributions reaffirm the CA–PPD calibration curve. TABLE 1 Pixels per Particle Diameter and Center of Area for Critical Sieve Openings Sieve # 10 40 200 Sieve Opening (mm) Pixels per Diameter (PPD) Wavelet Index (CA) 2.000 0.425 0.075 65.0 13.8 2.4 5.1 3.9 2.9 NOTE: Image resolution = 32.5 pixel/mm. Three-Point Imaging Test for AASHTO Soil Classification Unlike the USCS, which may require extending a grain size distribution curve above the No. 10 sieve and below the No. 200 sieve to compute the coefficients of uniformity and gradation, the AASHTO system requires only the percentages of soil in the four zones shown in Figure 4. Therefore, the only task for image processing is to locate the height in the sedimented soil column at which CA10 (5.1), CA40 (3.9), and CA200 (2.9) are found. The procedure can appropriately be called the three-point imaging (TPI) test for AASHTO soil classification. Examples of Soil Classification A well-graded sand with approximately 16% fines and 18% coarse sand and gravel was used to demonstrate the TPI test procedure. The sieve-based grain size distribution is shown in Figure 5a, and the distribution from the sedimented soil column is shown in Figure 5b. The soil column height can be expressed in image pixels or actual distance. Although the authors use image pixels as the unit of measure, units are easily converted to millimeters by dividing the pixels by the fixed image magnification (32.5 pixels/mm). CA10 was found at a height of 810 pixels (24.9 mm), CA40 at 2,080 pixels (64.0 mm), and CA200 at 3,490 pixels (107.4 mm) (Figure 5b). With an overall sedimented soil column height of 4,096 pixels, the percentages of Sedimented Soil Column CA200 One-Point Imaging Test for Fine-Grained Soils The key value for the classification of soils in AASHTO Groups A-2, A-4, A-5, A-6, and A-7 is the percentage passing the No. 200 sieve. If 35% or less of the material passes the No. 200 sieve, then the soil is in the broad A-2 grouping, which can be further refined into subgroups A-2-4, A-2-5, A-2-6, or A-2-7, depending on Atterberg limits. If 36% or more of the material passes the No. 200 sieve, then the soil is A-4, A-5, A-6, or A-7, depending on the Atterberg limits. As such, to make the “35% determination” by imaging, only the depth in the sedimentation column at which CA = 2.9 must be determined. If this depth is more than 35% of the distance from the surface, then the soil is a silt or clay. Depending on the Atterberg limits, the soil would be A-4, A-5, A-6, or A-7. If more than 10% of a soil passes the No. 200 sieve, then AASHTO soil classification calls for Atterberg limits tests to be performed on the soil fraction passing the No. 40 sieve. It requires splitting the original soil sample to perform both sedimentation imaging and Atterberg tests. Alternatively, soil may be recovered from the sedimented column to the depth of CA40 (3.9). As a practical matter, the authors recommend removing a bit more soil and washing it over a No. 40 sieve to collect soil for the Atterberg tests. AASHTO Soil Classification % Fines (silt and clay) CA Coarse Sand and Gravel CA10 % Fine Sand Medium Sand CA40 CA40 Fine Sand % Medium Sand CA200 Fines CA10 % Coarse Sand and Gravel PPD200 FIGURE 4 Soil regions by type, PPD, and CA for fixed magnification. PPD40 PPD10 PPD 30 Transportation Research Record 2101 Sieve # 10 100 # 40 # 200 18.1% Coarse Sand & Gravel 90 % Finer by Weight 80 81.9% 70 31.9% Medium Sand 60 50 50.0% 40 34.2% Fine Sand 30 20 10 15.8% Fines (Silt & Clay) 15.8% 0 10 1 0.1 0.01 Grain Size (mm) (a) Sieve # 200 # 40 # 10 4000 14.8% Fines (Silt & Clay) 3500 (3490) 34.4% Fine Sand Soil Column Height (pixel) 3000 2500 2000 (2080) 31.0% Medium Sand (810) 19.8% Coarse Sand & Gravel 1500 1000 500 0 2 3 4 CA 5 6 (b) FIGURE 5 Well-graded sand: (a) sieve-based grain size distribution and (b) CA versus soil column height. Test results on a sandy silt are shown in Figure 7. The height corresponding to CA200 (2.9) is 1,408 pixels. With a measured total specimen height of 4,040 pixels, the fines content is computed as 65.1%, in good agreement with the 63.6% observed by sieving. The soil is A-4, A-5, A-6, or A-7 depending on the Atterberg limits. Finally, CA at the highest elevation (finest grain size) is uncharacteristically high in Figures 5b and 7b. This apparent departure from the expected trend is caused by laboratory fluorescent light illumination from above and will be fixed by using a more uniform light source. DISCUSSION OF RESULTS The following discussion addresses two topics that explain and justify the use of a single camera magnification and a recommended PPD range of 2.4 to 65 for use in the TPI test. Hryciw and Jung 31 Sieve # 10 100 # 40 # 200 2.1% Coarse Sand & Gravel 97.9% 90 % Finer by Weight 80 39.6% Medium Sand 70 60 58.3% 50 40 56.2% Fine Sand 30 20 10 2.1% Fines (Silt & Clay) 2.1% 0 10 1 0.1 0.01 Grain Size (mm) (a) Sieve # 200 4000 # 10 # 40 (4066) 3500 54.5% Fine Sand Soil Column Height (pixel) 3000 2500 2000 (1850) 1500 42.3% Medium Sand 1000 3.2% Coarse Sand & Gravel 500 (130) 0 2 3 4 CA 5 6 (b) FIGURE 6 Poorly graded sand: (a) sieve-based grain size distribution and (b) CA versus soil column height. Single Versus Multiple Magnification TPI is ideal for classifying soil according to the AASHTO system (Figure 5b). The soil specimen used in the example was “engineered” to have a log-linear distribution of grain sizes by weight (Figure 5a); Figure 5b shows this log-linear distribution between the No. 10 and No. 200 sieves. Above the No. 10 and below the No. 200 sieve openings, the results depart somewhat from linearity. This result is to be expected because at low PPD values (less than about 1.0) and at high PPD values (greater than about 70), the data used to develop the calibration curve in Figure 2 show greater scatter. The problem arises at low PPD values because individual pixels contain information about more than one particle; thus, the grayscale information blurs. Meanwhile, at high PPD values, the wavelet indices may be more affected by the internal textures of particles than by distinctions in grayscales between particles. Also at high PPD values, 32 Transportation Research Record 2101 Sieve # 10 100 # 40 # 200 100% 90 36.4% Fine Sand % Finer by Weight 80 70 60 63.6% 50 63.6% Fines (Silt) 40 30 20 10 0 10 1 0.1 0.01 Grain Size (mm) (a) # 40 Sieve # 200 4000 3500 Soil Column Height (pixel) 3000 65.1% Fines (Silt) 2500 2000 1500 (1408) 1000 34.9% Fine Sand 500 (0) 0 2.5 3.0 3.5 4.0 CA (b) FIGURE 7 Sandy silt: (a) sieve-based grain size distribution and (b) CA versus soil column height. the number of particles per image becomes too small to be statistically accurate. The latter phenomenon is the cause of the premature peak in the CA plot at a height of about 650 pixels (Figure 5b); the two large particles responsible for this erratic high point are evident in the image. Both problems cited above can be overcome by using variable magnification so that all of the PPD values fall into the “sweet range” of about 2 to 60 on the calibration curve. While doable, this method introduces unnecessary complexity to the hardware requirements, data acquisition, and data reduction: a zooming lens would be needed; focal length and focusing would have to be adjusted during data acquisition; and in data reduction, Table 1 would require new values for each magnification. Fortuitously, none of these modifications are necessary because the actual size Hryciw and Jung distributions of grains larger than the No. 10 sieve opening and smaller than the No. 200 sieve opening are not needed for AASHTO classification. 33 ACKNOWLEDGMENT Partial funding for this study was provided by a grant from the National Science Foundation Geomechanics and Geotechnical Systems Program. Optimal PPD Range Close inspection of Figure 2 reveals that the absolute best CA–PPD correlations are in the PPD range of about 0.8 to about 30. This raises the question of why 2.4 ≤ PPD ≤ 65 is recommended. To achieve a PPD of 30 for a grain size of 2.0 mm (No. 10 sieve) and a corresponding PPD of 1.1 for a grain size of 0.075 (No. 200 sieve), a fixed image magnification of 15 pixels/mm would be required. In turn, a 17- × 17-mm field of view is required to procure the requisite 256- × 256-pixel image for eight-level wavelet decomposition. (In contrast, the recommended image magnification of 32.5 pixels/mm requires a field of view of only 8 mm × 8 mm.) A PPD range of 1.1 to 30 would necessitate more than double the dimensions of the field of view (more than quadruple the area) and would reduce the data points shown in Figures 5b, 6b, and 7b by more than 50%, resulting in an unacceptable loss in grain size resolution. Moreover, each individual image would contain a large grain size distribution. The upshot would be less-precise CA value locations corresponding to the No. 10, No. 40, and No. 200 sieve openings and correspondingly poorer soil classification. To rectify this situation, modifications to the test procedure would have to be considered, including the use of larger soil specimens or a smaller column cross-section. Unfortunately, such modifications create other problems, including poorer particle segregation during sedimentation. Fortunately, the excellent results and agreement shown between the TPI test using 2.4 ≤ PPD ≤ 65 and sieve analysis suggest that such test modifications are unnecessary. CONCLUSIONS A TPI test was proposed to rapidly classify soils according to the AASHTO system. A soil specimen is sedimented through a long vertical column to segregate grains by size. Continuous grayscale images of the sedimented soil are taken at a fixed resolution of 32.5 pixels/mm. At this resolution, the three critical grain sizes that separate coarse sands and gravels, medium sands, and fine sands (i.e., 2.00, 0.425, and 0.075 mm, respectively) correspond to PPD values of 65.0, 13.8, and 2.4, respectively. 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