STP 204-26 Standard Test Section: ASPHALT MIXES Procedures ManualSubject: CORRELATION OF NUCLEAR GAUGE DENSITY AND LABORATORY CORE DENSITY 1. SCOPE 1.1. Descriptio n of Test The standard test procedure is used to correlate the density results of asphalt concrete pavements obtained with a nuclear density gauge and with a laboratory test on a cored sample. 1.2. Applicatio n of Test This test is to be performed at the beginning of each paving contract for each lift, forevery change in lift thickness, for every change in the job mix formula and anytime there is a substantial change in the material of the underlying layers to calibrate the density-in- place by nuclear gauge (obtained by STP 204-6) with the density obtained from cored samples.2. APPARATUS AND MATERIALS 2.1. Equipment Required A calculator and the form “BASIC WORKSHEET FOR LINEAR RELATIONSHIPS BETWEEN TWO VARIABLES”. Alternatively a computer using Microsoft Windows, Microsoft Excel and a disk containing the Microsoft Excel Workbook“DENSCOR.XLS”. A printer for hard copy records. 2.2. Data Required Seven to ten random test locations where cores and nuclear density readings will be taken. The test locations are to be determined by STP 107. The core diameter is 150 mm. 3. PROCEDURE 3.1. Test Procedure Determine the sample locations using the procedure described in STP 107. Mark the core/nuclear gauge sample locations. Obtain density-in-place measurements with the nuclear gauge using the procedure Date: 2003 05 30 Page: 1 of 13
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Correlation of Nuclear Gauge Density and Laboratory Core Density Procedures
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7/31/2019 Correlation of Nuclear Gauge Density and Laboratory Core Density Procedures
Section: ASPHALT MIXES Subject: CORRELATION OF NUCLEAR GAUGE DENSITY
AND LABORATORY CORE DENSITY
described in STP 204-6. Record the density measurement for each sample location as Xi.
Obtain a core, in the exact same location as the nuclear gauge density readings were
taken, using the procedure described in STP 204-5. Number this core with the samenumber that was used to record the in-place-density with the nuclear gauge. Determine
the core density in the laboratory. Record the core density for each sample as Yi.
Enter the results of Xi and Yi on the form “BASIC WORKSHEET FOR LINEAR
RELATIONSHIPS BETWEEN TWO VARIABLES”.
Complete the calculations on the form to determine:
• Are any of the samples outliers that should not be used.
• The linear regression coefficients “a” and “b” for the equation “y = b X + a”.
• The regression coefficient ( r =S
S S
xy
xx yy
).
• The tstatistic ( tr (n - 2)
(1-r statistic
2=
)
).
Compare the value of the tstatistic to the value of t(0.975) obtained from the Student’s t
Distribution Table for n-2 degrees of freedom and a 97.5% probability level.
• If the tstatistic is larger than t(0.975), there is a 97.5% chance that the correlation
coefficient (r) is significantly different from 0 (a correlation coefficient (r) of 0
indicates a complete absence of correlation and a correlation coefficient (r) of 1 or -1 indicates perfect correlation). This means that there is a statistically valid
correlation.
• If the tstatistic is smaller than t(0.975), there is a 97.5% chance that the correlation
coefficient (r) is not significantly different from zero. This means that there is not
a statistically valid correlation. Two additional random sample locations should
be determined. Cores and nuclear density readings should be obtained. The
correlation procedure should be repeated with the additional samples included.
Plot the sample data and the regression equation on the Correlation Chart to ensure that
the regression line has a good fit to the data and that the data is in fact linear. Check the
value of the standard error Syx. It should be relatively small (less than 1%) compared tothe value of in-place-density by nuclear gauge.
Alternatively enter the values for Xi and Yi into the Microsoft Excel Workbook
“DENSCOR.XLS”. The program will check for outliers, calculate all of the coefficients
and check for statistical validity.
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7/31/2019 Correlation of Nuclear Gauge Density and Laboratory Core Density Procedures
Section: ASPHALT MIXES Subject: CORRELATION OF NUCLEAR GAUGE
DENSITY AND LABORATORY CORE DENSITY
is relatively small (< 1.0%) compared to the in-place nuclear density values of
2,200-2,360 kg/m3, so it should provide a good estimate of the core density.
4.1.15. Once the correlation has been completed the equation is used to adjust in-place-
density by nuclear gauge readings. If a nuclear density reading of 2,250.0 kg/m3
was obtained, the adjusted density would be computed using the equation:
Y = Adjusted Nuclear Density
= b (X) + a
= 0.7096 (X) + 621.904
= 0.7096 (2,250.0 kg/m3) + 621.904
= 2,218.5 kg/m3
The value of 2,218.5 kg/m3
would be used to determine acceptance.
4.2. Reporting Results
The Department will develop the regression equation to be used for correcting the
nuclear density gauge readings.
5. CALIBRATIONS, CORRECTIONS, REPEATABILITY
5.1. Tolerances and Repeatability
The correlation coefficient (r) is an index of the degree of correlation between the data.
The size of the correlation coefficient (r) is an indication of the degree of relationship
between two variables. A high value of the correlation coefficient (r), i.e. close to 1 or -1, merely indicates a close straight line relationship between the two variables. It does
not mean that one caused the other. Values of the correlation coefficient (r) equal to 1 or
-1 indicate perfect correlation and values of the correlation coefficient (r) equal to 0
indicate the complete absence of linear correlation.
If the relationship line is based on a relatively small number of points, in our case 7
points, the value of the correlation coefficient may be due to chance variations in
sampling and errors of measurement. The value of the regression coefficient should be
checked for statistical significance by computing the tstatistic. and comparing it with the t
value at a 97.5 % probability level (t(0.975)) (and the appropriate degrees of freedom). If
the tstatistic is greater than the value of t(0.975) then there is a 97.5% chance that the
correlation coefficient (r) is significantly different than 0 and there is a correlation
between the two variables.
The standard error of the estimate (Sy.x) gives an indication of the error associated with the
regression line. In the previous example, the standard error is 14.746 kg/m3. The value
of Sy.x is of practical importance because it gives an indication of the reliability of the
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7/31/2019 Correlation of Nuclear Gauge Density and Laboratory Core Density Procedures
Section: ASPHALT MIXES Subject: CORRELATION OF NUCLEAR GAUGE DENSITY
AND LABORATORY CORE DENSITY
equation. If the value of Sy.x is relatively small (<1.0%), compared to the values of the in-
place-density by nuclear gauge, and the regression coefficient is statistically significant,
the equation will provide a good estimate of the density that would have been obtained
by coring.
5.2. Sources of Error
Possible sources of error include those listed in STP 204-6 and STP 204-5.
6. ADDED INFORMATION
6.1. References
References are STP 204-5, STP 204-6 and the owner’s manual for the nuclear gauge.
6.2. Sample Retention
Samples should be retained according to the procedures laid out in STP 204-5.
Correlation worksheets and equations should be retained as part of the contract
documents.
6.3. Protection of Samples
The core samples should be protected according to the procedures set out in STP 204-5.
6.4. Proper Sample Identification
It is vital to ensure that the samples are identified so that the in-place-density by nuclear gauge corresponds to the laboratory core density for the same sample location.
6.5. Safety
The current safety regulations are to be followed as outlined in the Traffic control
Devices Manual For Work zones and the Safety Manual.
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7/31/2019 Correlation of Nuclear Gauge Density and Laboratory Core Density Procedures