# QUALITY CONTROL

## Reliability of Data

In a previous entry I showed that the basic concepts of quality control, which depends upon the laws of probability (statistics), are surprisingly simple. All that we are trying to do is measure lengths of lines. The equations used to calculate the mean and standard deviation are those that describe only two lines so that no matter how many samples are tested, the calculations of those parameters result in just those two lines which are independent of each other. While “n” data points occupy “n” dimensions, the mean and standard deviation occupy only two. We can use the standard deviation as the ruler to measure the lengths of interest.

What makes things difficult is the fuzziness of those lines. In quality control the first thing we want to determine is the length of the distance from the measured length (sample mean) to some desired length. To do that we use a ruler in which the standard deviation is set to be one. For convenience, and because the standard deviation is defined as the second moment around the mean, the targeted mean is subtracted from the data points so that the resulting length of the data vector is reduced to the difference between the sample mean and the target. That length is then divided by the standard deviation. The resulting length is then measured not in inches or millimeters but rather in units of the standard deviation ruler. As an example, assume that 100 was the target value, the measured mean was 85 and the standard deviation was 10. We are not interested in what the actual measured mean is, but rather how close it is to the target, based upon the standard deviation ruler:

1. (100-85)/10 = a distance of 1.5 SD units. In some cases the measurement is not from the desired target, but to upper and lower limits.

However, the mean value is fuzzy and the standard deviation may or may not be fuzzy. The data generated in calculating the mean make up a random variable (X= (x1, x2, —, xn)) in vector space. How fuzzy it is depends upon the length of the SD, and the type of distribution. While there are many distributions, if the SD is not fuzzy, what is called the normal distribution is often used. Because of the uncertainty in the mean, the distribution function tells us the chances of the mean actually being somewhere else.  In example 1 with only the mean being fuzzy, and using the normal distribution, we can say that there is a 6.68% chance that the true mean of the data is the desired mean.

Unfortunately, the SD often is fuzzy too and is thus also a random variable. The square of the SD is called the variance, and has its own distribution function called the chi squared distribution. While the normal distribution is independent of the number of data points defining the random variable, the form of the chi squared distribution depends upon the degrees of freedom. The chi square distribution with one degree of freedom is the square of the normal distribution. That distribution may be used to determine whether two measured standard deviations are really the same.

How the fuzziness or uncertainty is handled will be covered later. Although the mathematics gets more complex, especially when multivariate sets of data must be considered, the goal is still to simply measure lengths with a specific ruler.

By bobdunning

# UNRELIABILITY OF PG GRADING SYSTEM

## Superiority of the AR Grading System

PG Grading. There is an astounding number of PG grades, 7, and up to 6 subgrades within each grade, based upon low temperature properties. If there was consistency within the grades it might make sense, but we have regressed even back beyond the AC grading system. These grades were set up primarily to control tenderness and rutting even while leaving the gradation specification so open that gradations that would allow grievous rutting are included. The equivalent PG grade is based upon the Dynamic Shear test of G*/sinδ of 1.00 kPa at 64° C with no maximum. For a sinδ of 1.00 (close to that of unmodified asphalt) the viscosity is G*· sinδ or 1000 poises. The G*/sinδ value from the RTFO test would be 2.20 kPa min or 2200 poises with sinδ = 1.00 and again there is no maximum. Sinδ for modified asphalts is less than one thus that drops the specification minimum viscosity below that of non-modified asphalt.` In other words, for the asphalt as placed in the pavement, the AR 4000 specification is 3000-5000 poises at 60° C. For the PG 64-XX , the-in place viscosity at 64° C can vary from somewhat less than 2200 poises to as high as one wishes.

Philosophical Inconsistency of the PG Grading System. I am only addressing the grading system, not the value of the low temperature specification. I am not suggesting that there is anything wrong with the use of the DSR, as it is a handy tool. I am suggesting that the grading should have been based upon the consistency of the RTFO residue whether viscosity tubes are used or the DSR. The value of the DSR data is that we can get information about the effect of polymer modification from the phase angle, sigma (δ).

We have shown above that the range of the allowed viscosity from the RTFO test of any particular PG grade is greater than that of any previous grading system even though there is are 7 specific grades in order to control rutting. The implication is that controlling rutting requires fine tuning. Yet, at the same time there is a movement to use warm mixes, one of the benefits of which is that the asphalt will have a considerably lower viscosity than the intention of the grade.

Controlling Rutting. The prime control of tenderness and rutting should be with aggregate gradation.  As long as the gradation specification allows badly oversanded mixes, rutting will be a problem.

Robert L. Dunning, chemistdunning@gmail.com, www.petroleumsciences.com

By bobdunning

# REDUCING HOT MIXED ASPHALT COSTS

## Controlling Voids in Mineral Aggregate (VMA)

Considerable effort is being made to reduce costs and amount of hydrocarbons that go into hot mixed asphalt (HMA) pavements. One such effort is to find ways to mix and compact at a lower temperature thus reducing the amount of fuel required. However, saving fuel can also be obtained by reducing the amount of asphalt used as asphalt can also be sold as a component of heavy fuel oil or cracked to make diesel, gasoline etc.

Mix Design.

Irrespective of the type of mix design or the amount of modification of the asphalt, the basic properties for an acceptable product remains the same. If we get down to basics, we want the gradation to be such that it inhibits rutting, want the gradation in the # 30 sieve size to be such that there isn’t a lack of material in that area and want the composition of the binder to be such that the film thickness is somewhere between 7 and 10 microns (based upon our experience. Idaho specifies 6 microns as a minimum) and, for example for a ½” nominal design, an effective asphalt content of 4-5%.

Trade off between % Asphalt and VMA. As the VMA increases, the % asphalt  required increases at a rate of about 0.25% per each percent of increased VMA, the exact amount depending on the actual specific gravities of the aggregate and asphalt. For a 400 ton an hour plant, the reduction of the VMA of 1% would reduce the asphalt by one ton per hour or a savings of \$500/hour if asphalt is \$500/ton.

Silliness of the “Forbidden Zone”. Some Superpave gradation specifications have a “forbidden zone” for the gradation through which the gradation must not go. It is supposed to be on the maximum density line (on the 0.45 power gradation curve) of the aggregate; however, in addition to being silly, it doesn’t even fall on the actual maximum density curve for the job mix formula.

Effect of RAP on VMA. With the introduction of SUPERPAVE the VMA, which used to be 13% if one was used, was increased to 14%. We were having problems in being able to make the 14% with granite aggregate, and found that we had to control this by blowing out -#200 material. On one project I used a factorial experimental design to aid in adjusting the gradation with considerable success. This allows evaluating the effect of numerous variables on mix properties. Of course saving money by reducing the VMA was not an option. With the introduction of RAP, however, the VMAs rose by as much as 2%, requiring as much as 0.5% more total asphalt (including that in the RAP).

Reducing VMA to Reduce Cost

A number of years ago I did a Gram-Schmidt orthogonalization on gradation data. I found that there were only three truly independent variables, one of which was the % -#200 material. By using three independent aggregate criteria and % asphalt as a fourth variable we should be able to determine what changes should be made in the mix to minimize the VMA within the specification criteria, thus minimizing cost. I would suggest the use of a 24 factorial design with triplicate centerpoint to find the most economical gradation. The following would be for a ½” nominal mix design. For variables I would use: 1) the % of the gradation between the ½” and the #4 screens; 2) the % of the gradation between the #4 and #30; 3) the  % -#200; and 4) the % asphalt. We have found that a Hveem compaction at the recommended compaction temperatures for a 75 gyration Superpave design give the same results as the gyratory compaction. We would suggest that this be done, therefore, with the Hveem compactor as it uses only 1/4th as much aggregate and asphalt as does the 6” gyratory design however gyratory compaction could be used. The advantage of the Hveem is we can also get as a bonus the stability. I would stipulate that one of the boundary limits would be that no gradation point should be above a line on the gradation curve (0.45 power graph) from the % passing through the first sieve that retains aggregate (1/2”) to the % passing of the #200 sieve. This would provide the information needed to minimize the VMA within the specification. The results could provide the starting gradation and asphalt needed for a gyratory design.

Decreasing the VMA from 16.5 to 14.5% for 100,000 tons of mix would save \$ 250,000 of \$500/ ton asphalt.

Petroleum Sciences, Inc. has the equipment and mathematical knowledge (as there is considerable mathematics involved) to provide a service should a contractor wish to reduce costs. We can set up the experiment to be done in the contractors own facility and then evaluate the results or do the complete project in our facilities.

Robert L. Dunning, www.petroleumsciences.com, chemistdunning@gmail.com