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.



Resisting Failure if Treated with Care


A pavement is about 93-96% rock, by weight, however it seems that there is a strong belief that by properly modifying the asphalt all problems can be solved. Asphalt or more properly, asphalts have served us well, even before modification. The properties of asphalts are primarily determined by their crude sources, however blending crudes or asphalts can at times produce an asphalt that performs better than either of the components. Modifying asphalts can also enhance their properties. However, it is important that we keep in mind that its performance depends to a great extent to its ability to flow, and its ability to suppress hardening as time goes.

Rutting is Not an Asphalt Failure. Asphalt is a liquid whose job is to flow in response to stress. If a pavement ruts, it is either ground by studded tires, or the aggregate size or the gradation is improper. If the stress is greater than the aggregate can handle, rutting occurs with the asphalt doing what it is designed to do, flow. Modifying the asphalt can affect how fast the flow occurs, however it is the aggregate properties that affect the rutting.

Many Aggregates Prefer Water to Asphalt. Asphalt doesn’t work well if it can’t stick to aggregate. Water can interfere with adhesion. One cause can be in the asphalt itself. If it is produced from crude oil that had been treated with caustic soda, it will contain soaps that will make the asphalt itself water sensitive. That has been solved by lime treating the crude. Antistrips are used to aid adhesion; however it has been shown that with some antistrips the effect wears off which allows water to lift the asphalt off of the rocks. There is one antistrip that combines chemically to aggregate and provides long term durability.

Non-load Associated Cracking Occurs when the Asphalt Cannot Relax Stresses. The fluidity of the asphalt is essential to prevent cracking. Trying to make the asphalt stronger only makes the matter worse as its maximum tensile strength is about 1000 psi. Portland cement cannot defeat thermal stress so don’t expect asphalt to do so. The solution is to have a binder that can relax stresses faster than they build up.

Pavement Slippage. Slippage occurs when of tack coats and primes are not used properly.

Fatigue Failure. There are suggestions that asphalt could be modified to increase its stiffness so that the pavement thickness could be reduced. Again it must be remembered that it is the aggregate that carries the load, in compression, not the asphalt. However fatigue failure occurs in tension, and again the tensile strength of asphalt is much less than that of aggregate. The pavement is stretched underneath the wheel path, and between the wheel paths. However, tensile failure is often really crack propagation, thus additives that stop crack propagation such as tire buffings may be of value.

chemistdunning@gmail.com, http://www.petroleumsciences.com


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




Tort or Penalties Called for, or the Result of Natural Aging

Once a pavement is laid it is expected to last a long time. However over time distress will occur at which time there can be a blame game, especially if tort lawyers get involved. Unfortunately the attorneys may team up with “experts” who have only limited understanding of pavement technology and absolutely no understanding of multivariate statistics upon which are based possible penalties where data collected during construction would suggest there would be future distress.

In a construction contract there are various contractors involved. One contractor may prepare the subgrade and base while another would lay the pavement. The design engineer may not have built in sufficient strength into the pavement or paid attention to the properties of the paving material with respect to the expected traffic. Also, whether the location is in a city or on a highway will affect judgments. Following are a few types of distress:

Residential Streets.

  1. There is a sunken “bird bath” in the street. There were separate contractors for the subgrade, base and pavement. There were alligator cracking in the sunken area. The thickness of the pavement is the design thickness. Who’s at fault and what can be done? Usually the paving contractor will be blamed; however the actual problem is an area in the subgrade that was not properly compacted. The pavement has to follow the consolidation that occurs in the subgrade thus the cracking comes from stretching the pavement as it sinks and is not the fault of the paving contractor. To repair it the section may be removed and reconstructed. If the pavement is to be slurry sealed, leveling can be done by the slurry seal contractor.
  2.  There is loss of matrix, called raveling, in the pavement in areas of continuing flowing water. Wet asphalt pavements are weaker than dry ones. This usually occurs on corners where there is shear stress from the tires. The source of the water needs to be identified and stopped. There are asphalt paving mixes designed for hydraulic structures, however a pavement in a street is not one of them. Another cause is the lack of use of additives to the asphalt that address the loss of wet strength. A discussion of such additives is outside of my goal at this time however it will be addressed later.



Main Streets and Highways

  1. Longitudinal Crack in the Wheel Path. This usually starts in the right wheel path and later occurs in the left wheel path. This is caused by lack of structural strength. It can be accelerated by lack of proper compaction or lack of anti stripping additives in the asphalt. It isn’t unusual for an agency to mill off two inches and repave. That is like blowing in the wind, as the lack of structural strength continues, and the cracks will soon reappear. The lack of structural strength and stripping are design problems, not construction.
  2. Damaged from Studded Tires. In areas in which studded tires are used there will be ruts, whether the pavement in asphalt concrete or portland cement concrete. The width between ruts will be consistent to that of passenger tires. That problem still lacks a solution. Some say that such rutting is caused by trucks, but that is not true for ruts described above. Rutting caused by trucks is a mix design problem that is solvable. In that case the width between ruts is that of truck tires, and the effect of the duals is obvious. This is not caused by poor construction techniques.
  3. Traffic Cause Ruts. There is a considerable effort to solve rutting by changing the binder. Adjusting the binder can affect the rate of rutting; however the true solution to rutting is to make sure that the coarse aggregate particles can interlock. Yet the specifications generally allow over-sanded mixes in which a sand asphalt matrix is supposed to stop rutting. I would suggest that both the design engineer and the supplier of the (hot mixed asphalt) HMA are equally at fault. The design engineer specified gradation limits that allow oversanded mixes, and the HMA supplier crushed and blended to a gradation that would cause ruts when in the pavement.
  4. Block (Thermal) Cracking. Often called transverse cracking, however it really occurs in blocks if the pavement is wide enough. This cracking occurs when the asphalt in the pavement is too hard to relax thermal stress fast enough. Public agencies or other owners are at fault for not sealing the pavements, which reduces the hardening rate of the asphalt.
  5. Water Damage. If the aggregate would prefer being wetted by water rather than asphalt, the asphalt will at least get weak, and probably strip off. The result is raveling. While there are additives to asphalt that helps in this area, there are data that shows that some of the more popular antistrips may lose their ability to prevent stripping over time. Once the pavement loses it strength, fatigue cracking may also be prevalent. The fault here is the design specification that does not specify proper antistrips.

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