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OCR for page 11

11
Experimental Design and · Repeatability calculations: For each material and operator,
Statistical Analysis the average of replicates is given by Equation 1, and the
variation in measurements is calculated by Equation 2.
This section documents the experimental evaluation of the
test methods. The evaluation covered the repeatability, repro-
n
ducibility, accuracy, cost, and operational characteristics. The x ij
first three characteristics were evaluated through statistical xi =
j =1
(1)
analysis of the characteristics of a wide range of aggregates n
from different sources with various characteristics. The accu-
2
n 2
x if - nx i
racy analysis was conducted for the parameters employed in
the test methods, and for the test methods themselves includ-
j =1
Si =
2
(2)
ing the hardware components. The information that pertains (n - 1)
to cost and operational characteristics was collected from
vendors, researchers, and operators who have dealt with these Where n is the number of measurements by an operator for
systems. one material and x is the average of the measurements of
i
As indicated earlier, some of the selected methods have 2
operator i, and S i is the variance for operator i. Table 7 shows
been in practice for years and they are usually performed the arrangement of variation data within and between operators
using standard procedures. However, for the methods that have for one single material using one test method. The repeatability
been developed recently, the manufacturer's or the developer's of a test method is evaluated for each aggregate material and
instructions were followed to perform the testing. It was nec- all operators by Equation 3:
essary in some cases to perform the standard tests with minor
p
modifications in order to conduct the tests on the selected
s 2
i
aggregate sizes. A summary of aggregate sizes and parameters 2
Sm ( pooled ) = i =1
(3)
obtained from each of the selected test methods is shown in p
Table 6. Descriptions of the testing procedures and modi-
fications, if any, and aggregate properties are provided in where p = 3 is the number of operators.
Appendix D. · Reproducibility Calculations: The average of measure-
ments made by all operators for a singe material is given by
Equation 4 and the variation between operators is given by
Evaluation of Repeatability and Equation 5.
Reproducibility
Repeatability and reproducibility of test methods were
xm =
x i
(4)
evaluated through measuring the characteristics of aggregate p
samples several times by single and multiple operators. The
operators were uniformly trained on the application of the test
x - p( x ) 2 2
methods and were provided with the same set of instructional s 2
= i m
(5)
guidelines.
xm
( p - 1)
One coarse aggregate size (12.5 - 9.5 mm [1/2 - 3/8 ]),
and one fine aggregate size (2.36 - 1.18 mm [sieve #8 - #16]) Variations between operators are calculated by:
were used for the repeatability analysis. Each of the operators
measured the properties of these aggregate sizes three times. SL2 = Sx2 - [ Sm
m
2
( pooled ) n]
m
(6)
Reproducibility was assessed by measuring the shape char-
acteristics (as applicable to the test method, see Table 6) for
Then, reproducibility of a test method is given by:
aggregate sizes listed in Table 4 by each of the three opera-
tors. All operators conducted measurements using the same
samples.
2
SR = SL2 + Sm
2
( pooled )
m
(7)
Standard deviation and coefficient of variation were used
to quantify repeatability and reproducibility. Analysis of vari- Repeatability and reproducibility of the test method on all
ance (ANOVA) was used in the statistical analysis according aggregates were estimated by pooling standard deviations and
to the ASTM procedures (ASTM E 177, ASTM C 802, and coefficients of variations over all materials according to the
ASTM C 670). The repeatability and reproducibility statistical guidelines of ASTM C 802. Because each of the selected test
parameters were calculated for each test method as follows: methods measures aggregate characteristics using different

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12
Table 6. Aggregate size and characteristics measured using
the test methods.
Aggregate Size Characteristics
Test
C C C F F F Shape Angularity Texture
1 2 3 1 2 3 (Abbreviation) (Abbreviation) (Abbreviation)
Uncompacted % Loose
Void Content of Uncompacted
X X
Fine Aggregates Void Content
AASHTO T 304 (UCVCF)
Uncompacted
% Loose
Void Content of
Uncompacted
Coarse X X
Void Content
Aggregates
(UCVCC)
AASHTO TP 56
Compacted Max Shear
Aggregate X X X Resistance
Resistance CAR (CAR)
Percentage of
Fractured
Particles in % of Fractured
X X X
Coarse Faces (PFF)
Aggregate
ASTM D 5821
Flat and
Elongated Coarse Flat Elongated
X X X
Aggregates Ratio (FER)
ASTM D 4791
Multiple Ratio Dimensional
X X X
Shape Analysis Ratio (MRA)
Flat Ratio (VDG-
40 FLAT) &
VDG-40
X X X X Slenderness ratio
Videograder
(VDG-40
SLEND)
Buffalo Wire Roundness Roundness
Works PSSDA- X X X (PSSDA-Large (PSSDA-Large
Large ROUND) ROUND)
Buffalo Wire Roundness Roundness
Works PSSDA- X X X (PSSDA-Small (PSSDA-Small
Small ROUND) ROUND)
Sphericity
(CAMSPHT),
Symmetry
(CAMSYMM), Convexity
Camsizer X X X X X
Ratio of Length (CAMCONV)
to Breadth
(CAML/B)
Minimum
Dimensional Average Curve
WipShape X X X
Ratio (WSFER) Radius
(WSMACR)
University of
Illinois Surface
Flat Elongated Angularity
Aggregate Image X X X X Texture Index
Ratio (UIFER) Index (UIAI)
Analyzer (UISTI)
(UIAIA)
Gradient
Angularity
Sphericity
Index
Aggregate (AIMSSPH) Texture Index
(AIMSGRAD),
Imaging System X X X X X X & (Wavelet)
Radius
(AIMS) Form 2-D Index (AIMSTXTR)
Angularity
(AIMSFORM)
Index
(AIMSRAD)
Aggregate sizes:
C1 = 25.4 19.0 mm (1 3/4"); C2 = 12.5 9.5 mm (1/2 3/8"); C3 = 9.5 4.75 mm (3/8" #4); F1 = 4.75
2.36 mm (#4 #8); F2 = 2.36 1.18 mm (#8 #16); F3 = 0.6 0.3 mm (#30 #60).