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Table 7. Arrangement of variation in measurements within
and between operators for one aggregate.
Data (replicates) Average Within Operator Variance
Operator
xij xi S i2
1 I II III x1 S12
2
2 I II III x2 S2
3 I II III x3 S 32
analysis parameters or indices with different scales, repeat- The results of this test were analyzed using the same specific
ability and reproducibility were assessed independently for gravity for each aggregate. The variability of the test results is
each parameter. The final results of repeatability and repro- mainly due to error in measuring the specific gravity. Therefore,
ducibility for all test methods are reported for each character- it is expected that the variability of the uncompacted void con-
istic and for coarse and fine aggregates separately in Tables 8 tent test would increase significantly when the variability in
and 9, respectively. The abbreviations of the parameters specific gravity measurements is considered.
provided in the manuals and standards of test methods are The image analysis methods had high variability when the
used here. percentage of particles with a dimensional ratio of 5:1 was
In interpreting the results, the following factors should be considered. This was mainly due to the small percentages of
taken into consideration: particles that exhibited this characteristic, such that any slight
variation in accounting for these particles was manifested as
(1) The methods differ significantly in the level of detail pro- high coefficient of variation. Therefore, the variability was
vided in the results. While the indirect methods provide evaluated based on the percentage of particles with a dimen-
only an average index, direct methods can provide the sional ratio smaller or larger than 3:1.
distribution of characteristics in an aggregate sample. This The image analysis methods (UIAIA, AIMS, Camsizer,
advantage of direct methods has not been considered PSSDA, WipShape) had low to medium variability in terms
because the calculations are based on average values in of angularity and texture measurements. The AIMS angular-
order to analyze all test methods using the same statisti- ity indices had low variability, while the texture indices had
cal methods. medium variability. As will be discussed later, automation of
(2) The test methods differ in the range of results. Some the AIMS top lighting intensity would reduce the variability.
methods have analysis parameters with narrow ranges
that make it difficult to distinguish between aggregates, Evaluation of Accuracy
while others have wide ranges. The accuracy of the test methods can be evaluated by
(3) Measurements from a test method were all conducted correlating the measurements from these tests with the mea-
using a single device and well-trained operators. surements obtained from standards or reference tests that are
(4) The high sensitivity of some test methods to variations considered to be accurate. The three dimensions of coarse par-
in aggregate characteristics, which is an advantage, ticles can be measured using a digital caliper--an accurate, but
can increase variation and reduce the repeatability and slow method. However, because test methods that are accepted
reproducibility. to be accurate in quantifying texture and angularity are not
available, the following approach was adopted to assess the
Considering all these factors, it is recommended to differ- accuracy of the test methods:
entiate among test methods based on the levels of variability
shown in Tables 8 and 9. · The accuracy was evaluated based on the procedure rec-
The percentage of fractured faces test had very high vari- ommended by standards and/or by the developers, and for
ability compared to all other test methods as also reported by the analysis methods (mathematical functions and indices)
Meininger (5) and Saeed et al. (2). According to the results in employed in the imaging-based systems. This approach
Table 9, the uncompacted void content test for fine aggregate allowed evaluation of the accuracy of the analysis methods
had low variability. Saeed et al. (2) rated this test as having a irrespective of the characteristics of the image acquisition
fair precision (ability to repeatedly provide correct results). setup.
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Table 8. Classification of coarse aggregate test methods based on repeatability and reproducibility.
Parameter Measured Parameter as Coefficient of Variation (CV)
Characteristics Test Method
Abbreviation Reported by Test Method Repeatability Reproducibility
Uncompacted Void Content
Percent Uncompacted
of Coarse Aggregate UCVCC L L
Voi d Content
0 Fractured Faces H H
Percent Fractured Faces PFF 1 Fractured Face M H
2 Fractured Faces M H
Camsizer CAMCONV Conv3 L L
Angularity Minimal Average
WipShape WSMACR L L
Curve Radius
University of Illinois
Aggregate Imaging System UIAI Angularity Index L L
UIAIA
Aggregate Imaging System AIMSGRAD Gradient Angularity L L
AIMS AIMSRAD Radius Angularity L L
Buffalo Wire Works PSSDA-Large
Average Roundness L L
PSSDA-Large ROUND
University of Illinois
Mean Surface Texture
Aggregate Imaging System UISTI L L
Index
UIAIA
Aggregate Imaging System
AIMSTXTR Texture Index M M
AIMS
Texture
Camsizer CAMCONV Conv3 L L
Uncompacted Void Content Percent Uncompacted
UCVCC L L
of Coarse Aggregate Voi d Content
Minimal Average
WipShape WSMACR L L
Curve Radius
CAMSPHT SPHT3 L L
Camsizer
CAMSYMM Symm3 L L
Aggregate Imaging System AIMSFORM Form 2-D L L
Shape/Parameter
AIMS AIMSSPH Sphericity L L
Buffalo Wire Works PSSDA-Small
Average Roundness L L
PSSDA-Large ROUND
Percent of Flat and
Flat and Elongated Ratio FER L H
Elongated Particles
15
Table 9. Classification of fine aggregate test methods based on repeatability and reproducibility.
Parameter Measured Parameter as Coefficient of Variation (CV)
Characteristics Test Method
Abbreviation Reported by Test Method Repeatability Reproducibility
Uncompacted Void Content Percent Uncompacted
UCVCF L L
of Fine Aggregates Voi d Content
Camsizer CAMCONV Conv3 L L
Aggregate Imaging System AIMSGRAD Gradient Angularity L L
AIMS AIMSRAD Radius Angularity L L
Angularity
Buffalo Wire Works PSSDA-Small
Average Roundness M M
PSSDA-Small ROUND
Compacted Aggregate
Resistance CAR Aggregate Resistance L L
CAR
CAMSPHT SPHT3 L L
Camsizer CAMSYMM Symm3 L L
CAML/B l/b3 L L
Shape Aggregate Imaging System
AIMSFORM Form 2-D L L
AIMS
Buffalo Wire Works PSSDA-Small
Average Roundness M M
PSSDA-Small ROUND
Low (L) CV<=10%, Medium (M) 10%
16
Table 11. Pearson and Spearman correlation
coefficients of Rittenhouse sphericity.
Pearson Spearman
Analysis Method
Correlation Correlation Applicability
Parameter
Coefficient Coefficient
AIMSGRAD 0.458 -0.54 N
AIMSRAD -0.868 -0.894 Y*
AIMSFORM -0.98 -0.991 Y*
FRFORM -0.918 -0.993 Y
FRANG -0.814 -0.99 Y*
FRTXTR -0.858 -0.999 Y*
UIFER -0.938 -0.993 Y
UIAI -0.388 -0.368 N
UISTI 0.273 0.425 N
ASPTPRO -0.938 -0.995 Y
FRCTLPRO 0.256 -0.322 N
ROUNDPRO -0.941 -0.996 Y*
* Method correlates with two characteristics.
where x and y represent two p-dimensional observations
(items) x = [x1, x2, . . . , xp] and y = [y1, y2, . . . , yp]. x represents
the values measured by the image analysis methods on the
(a) Rittenhouse (1943)
projections, and y represents the visual numbers assigned to
the projections in Figures 2a and 2b. The Spearman coefficient
is defined exactly as the Pearson coefficient in Equation 8, but
x and y represent the ranking of the image analysis results and
visual numbers, respectively, instead of the actual values. The
correlation results are shown in Tables 11 and 12. Examples
of the correlations of image analysis methods with angularity
visual numbers are shown in Figure 3.
Rittenhouse (13) and Krumbein (18) projections can be
used to identify analysis methods capable of capturing changes
in shape and angularity, respectively. The correlation results
shown in Tables 11 and 12 suggest that:
(b) Krumbein (1941) · The following methods can be used only to describe shape
Figure 2. Charts used by geologists in the past for without being affected by angularity of a particle: (a) Flat
visual evaluation of granular materials. Elongated Ratio used by University of Illinois test method
(UIFER), (b) Form Index measured using Fourier Series
observations of sediments and manual measurements of their
shape and angularity. Figure 2(a) was developed by Rittenhouse Table 12. Pearson and Spearman correlation
(13) based on an earlier version developed by Wadell (14, 15) coefficients of Krumbein roundness.
to measure 2-D shape; it is considered a standard and accurate Pearson Spearman
Analysis Method
method for evaluating shape (16, 17). Figure 2(b) was devel- Parameter
Correlation Correlation Applicability
oped by Krumbein (18) to evaluate angularity. Coefficient Coefficient
AIMSGRAD -0.886 -0.983 Y
Correlations between analysis method parameters and AIMSRAD -0.964 -0.967 Y*
visual numbers by Rittenhouse and Krumbein (Figure 2) AIMSFORM -0.958 -0.967 Y*
FRFORM -0.016 -0.033 N
were analyzed using the Pearson and Spearman coefficients. FRANG -0.908 -0.883 Y*
The Pearson coefficient (r) is defined as in Equation 8: FRTXTR -0.942 -0.967 Y*
UIFER 0.486 -0.317 N
UIAI -0.959 -0.983 Y
n
(x - x )( y i - y )
UISTI -0.957 -0.983 Y
i ASPTPRO -0.414 0.317 N
r= n
i =1
n
(8) FRCTLPRO -0.869 -0.867 Y
(x - x) ( y - y)
2 2 ROUNDPRO -0.959 -0.967 Y*
i i
i =1 i =1 * Method correlates with two characteristics.
17
700 Figure 2b as they might have been created to have the same
600
levels of surface irregularities at the angularity and texture
scales. In other words, there was no distinction between
500 angularity and texture in the projections in Figure 2b.
UIAI Value
400
Uniqueness of test methods. This task was performed to
R2 = 0.92
300 examine the uniqueness of the analysis methods in capturing
aggregate characteristics. A simple setup of a camera and a
200
microscope was used to capture images of 50 randomly selected
100
coarse particles (12.5 - 9.5 mm; 1/2 - 3/8 in.), and 50 fine par-
ticles (2.36 - 1.18 mm; sieve #8 #16) of each aggregate type at
0 specific resolution. The setup was equipped with top lighting
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
to capture gray images for texture analysis and a backlighting
Krumbein Visual Number
(a)
to capture black and white images for angularity analysis. The
resulting images were analyzed using standard image analysis
6000 techniques, some of which are employed in the imaging-based
tests evaluated in this study.
5000 Using the capabilities of SPSS software, the analysis results
from the 50 images of the coarse aggregate size of each aggre-
AIMSGRAD Value
4000
gate type were used to cluster the analysis methods. The analy-
sis methods were clustered on the basis of similarities or
3000
distances using Ward's Linkage method.
R2 = 0.94 Two types of similarities were used. The Pearson correlation
2000
coefficient, given by Equation 8, was used as a measure of
proximity when variables (analysis methods) were grouped,
1000
and the Euclidean distance, given by Equation 9, was used to
0
cluster aggregates.
0 0.2 0.4 0.6 0.8 1
p
d ( x, y ) = (x - yi )
Krumbein Visual Number 2
i (9)
(b) i =1
Figure 3. Examples of the correlations of image
where x and y represent two p-dimensional observations
analysis methods with visual numbers of angularity.
(items) x = [x1, x2, . . . , xp] and y = [y1, y2, . . . , yp].
Ward's Linkage method was applied with Pearson cor-
(FRFORM), and (c) Aspect Ratio measured using Image relation proximity measure to the analysis results to identify
Pro software (ASPTPRO). clusters of analysis methods. The results of the cluster analysis
· The following methods can be used to describe angularity are shown in Table 13. For each aggregate type, the test methods
without being affected by shape: (a) Gradient Angularity that have the same number (1, 2, 3, or 4) are more correlated
used in the Aggregate Imaging System AIMS (AIMSGRAD), with each other than with other test methods and are consid-
(b) Angularity Index used by the University of Illinois ered clustered. For example, the data from AIMSTXTR analy-
test method (UIAI), (c) Fractal technique used in Image sis of CA-1 is statistically different than the data from all the
Pro software (FRCTLPRO). other test methods, indicating that this analysis method cap-
· Roundness measured using Image Pro (ROUNDPRO), tures an aggregate characteristic different than what is captured
and Texture Index using Fourier (FRTXTR), Angularity by all the other methods. The percentage of aggregates that a
Index using Fourier (FRANG), Form Index Using AIMS test method is clustered with other test methods is shown in
(AIMSFORM), and Radius Angularity using AIMS Table 14. For example, the AIMSTXTR method is clustered
(AIMSRAD) have good correlation with Rittenhouse alone in 54 percent of aggregates, clustered with another method
sphericity numbers and Krumbein roundness numbers. in 31 percent of aggregates, and with two other methods in
This indicates that these methods are not as unique as the 9 percent of aggregates. The increase in percentage in the
other methods in distinguishing between angularity and cells toward the left of the table indicates an increase in the
shape of particles. The Angularity Index (UIAI) and Tex- uniqueness of the characteristic measured using this method.
ture Index (UISTI) have high correlations with each other. Based on the results in Tables 15 and 16, AIMSTXTR is the
This could be attributed to the nature of the projections in most unique among the texture parameters, AIMSGRAD and
18
Table 13. Clustering of analysis methods (4 clusters) based
on Pearson correlation.
Analysis Coarse Aggregate
Method 1 2 3 4 5 6 7 8 9 10 11 12 13
AIMSTXTR 1 1 1 1 1 1 1 1 1 1 1 1 1
AIMSGRAD 2 2 2 2 2 2 2 2 2 2 1 2 2
AIMSRAD 2 2 3 2 2 3 2 1 2 3 2 3 3
AIMSFORM 2 2 2 2 2 3 2 1 2 3 2 3 3
AIMSSPH 3 3 3 3 3 1 3 3 3 1 3 1 4
UIFER 4 4 4 4 4 4 4 3 4 4 4 4 1
UIAI 4 4 4 4 4 4 4 2 4 4 4 4 2
UISTI 4 4 4 4 4 4 4 2 4 4 4 4 1
FRFORM 2 2 2 2 2 3 2 1 2 3 2 3 3
FRANG 2 2 2 2 2 3 2 1 2 3 2 3 3
FRTXTR 2 2 2 2 2 3 2 4 2 3 2 3 3
ASPCTPRO 2 2 2 2 2 3 2 1 2 3 2 3 3
FRCTLPRO 2 2 3 2 2 3 3 1 2 3 2 3 3
ROUNDPRO 2 2 2 2 2 3 2 1 2 3 2 3 3
UIAI are the most unique among the angularity parameters, both aggregates CA-2 (crushed gravel) and CA-10 (granite)
and AIMSSPH is the most unique among the shape parameters. in the same texture cluster.
The UIAI and UISTI methods are clustered together for 12 of The results in Table 16 show that AIMSRAD, FRANG, and
the 13 aggregates. ROUNDPRO methods cluster the uncrushed (CA-1) and
Clustering of aggregates based on the results of analysis crushed gravel (CA-2) in the same group, indicating the
methods. Ward's Linkage method was used to cluster aggre- inability of these methods to distinguish the difference in
gates based on the angularity and texture measured using each angularity. Table 17 summarizes the characteristics of the
of the analysis methods; results are shown in Tables 15 and 16. analysis methods.
As shown in Table 15, both the FRTXTR and FRACTLPRO
texture parameters place aggregates CA-1 (uncrushed gravel)
Accuracy of Test Methods
and aggregates CA-9 and CA-10 (both are granite) in the same
cluster, indicating the inability of methods to detect significant A digital caliper was used to measure the three dimensions
differences between these aggregates. Similarly, UISTI places of 100 particles selected randomly from each of the aggregates
Table 14. Percentage of clustered aggregates
for each analysis method.
Number of Methods to Cluster With
Analysis Method 0 1 2 6 7 8
AIMSTXTR 54% 31% 8% 8% 8%
AIMSGRAD 23% 15% 8% 8% 8% 38%
AIMSRAD 8% 54% 38%
AIMSFORM 8% 54% 38%
AIMSSPH 54% 38% 8%
UIFER 8% 92%
UIAI 8% 92%
UISTI 100%
FRFORM 8% 54% 38%
FRANG 8% 54% 38%
FRTXTR 8% 8% 46% 38%
ASPCTPRO 8% 54% 38%
FRCTLPRO 8% 8% 46% 38%
ROUNDPRO 8% 54% 38%
19
Table 15. Coarse aggregates in texture classes with sizes passing a 12.5 mm (1/2 in.) sieve and retained on a
estimated using Ward's Linkage. 9.5 mm (3/8 in.) sieve. The percentage of particles with a longest
Method Class 1 Class 2 Class 3 Class 4
to shortest ratio dimension of 3:1 or more sphericity was
AIMSTXTR 1, 2, 12 3, 5, 10, 11, 13 4, 6, 7, 8 9 calculated; the results are shown in Table 18. The correlations
UISTI 1, 8 2, 3, 7, 10, 11, 13 4, 6, 9, 12 5
FRTXTR 1, 7, 9, 10, 12 2, 4 3, 5, 6, 11, 13 8
between the caliper measurements and results of test methods
FRACTLPRO 1, 4, 9, 10, 12 2, 3, 6, 11, 13 5, 7 8 were estimated in terms of the coefficient of multiple deter-
minations (R2). R2 is a statistic that measures how successful
the fit is in explaining the variation of the data. It is defined as
the ratio of the sum of squares of the regression (SSR) and the
Table 16. Coarse aggregates in angularity classes
estimated using Ward's Linkage. total sum of squares (also known as sum of squares about the
mean [SST]) and is expressed as
Method Class 1 Class 2 Class 3 Class 4
AIMSGRAD 1, 8 2, 4, 6, 7, 12 5, 9, 10 3, 11, 13 n
)
( y - y)
2
AIMSRAD 1, 2, 9 3, 4, 11, 13 5, 6, 7, 10, 12 8
UIAI 1 2, 6, 9 3, 4, 5, 7, 10, 8 SSR i
11, 12, 13 R =
2
= i =1
n
(10)
SST
( y - y)
2
FRANG 1, 2, 3, 6, 9, 4, 5, 7, 10 8 13 i
11, 12 i =1
FRACTLPRO 1, 4, 9, 10, 2, 3, 6, 11, 13 5, 7 8
12
ROUNDPRO 1, 2, 6, 12 3, 4, 5, 7, 9, 8 13 The MRA method had the highest correlation with the digi-
10, 11 tal caliper. The UIFER test method was not able to measure all
Table 17. Features of methods used in analyzing
aggregate images.
Analysis
Features
Method
· Capable of separating aggregates with different texture
AIMSTXTR characteristics.
· Most unique among the texture parameters.
· Capable of separating aggregates with different angularity
AIMSGRAD characteristics.
· Capable of separating angularity from shape.
· Captures angularity but it is not capable of separating 2-D shape from
AIMSRAD
angularity.
AIMSFORM · Captures 2-D shape but it is not capable of separating shape from
angularity.
AIMSSPH · Capable of separating aggregates with different characteristics.
· Captures unique characteristics of aggregates.
· Does not separate angularity from shape.
FRTXTR · Clusters aggregates with distinct characteristics. This can be
improved if different image resolutions are used.
· Does not separate angularity from shape.
FRANG · Clusters aggregates with distinct characteristics. This can be
improved if different image resolutions are used.
· Capable of separating shape from angularity.
FRFORM · Clusters aggregates with distinct characteristics. This can be
improved if different image resolutions are used.
Used by
University of · Capable of separating aggregates with different characteristics.
Illinois System · Capable of separating shape from angularity.
(UIFER)
· Capable of separating aggregates with different aggregate
UISTI characteristics.
· Clusters aggregates similar to UIAI. This can be improved if different
image resolutions are used.
ASPTPRO · Separates angularity from shape.
· Separates angularity from shape.
FRCTLPRO · Clusters aggregates with distinct characteristics in the same group.
This can be improved if different image resolutions are used.
· Separates angularity from shape.
ROUNDPRO · Clusters aggregates with distinct characteristics in the same group.
This can be improved if different image resolutions are used.
