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.



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



There are a lot of risks in construction. One problem is that once something is built it is around a long time. Consider asphalt. If it is a component of heavy fuel oil, it is purchased and used in a short time. If there are problems, they are obvious, almost immediately found and taken care of. If the asphalt is used in pavements, on the other hand, it is around for years, and can be subjected to tort suites throughout its lifetime. One area where legal actions have been used extensively is with gated communities. What happens is that a team of attorneys and civil engineers contact the managers of gated communities and arrange to inspect the facilities, even after many years from construction, then sue all the contractors for one problem or another, real or imaginary. What is supposed to take place is that all of the contractors are expected to bring their insurance agent to a meeting and settle, then the attorneys and gated community share in the settlement. The attorneys can get real testy if the contractors don’t immediately capitulate.

I have had experience as a consultant on the side of a paving contractor, in which we demonstrated that one does not have to submit to such extortion.

It was very interesting with the projects with which I was involved that the engineering consultants on the attorney’s team did not even know the vocabulary of the field of asphalt technology nor were they to truly able to identify causes of stress or determine which contractor was at fault. In one case they were complaining that a product that had been applied years before had been out of specification. Unfortunately they were comparing that product to a specification of a completely different product but didn’t know enough about asphalt products to be able to recognize their error. Once I finally got that across to the attorney in a deposition, he immediately shut down the deposition.

The lesson to the contractor is to confront the attorneys with personnel who are truly experts in the field; not those with only limited academic training, but those with true experience with the field. While there can be problems that have occurred during construction that need to be addressed, problems of aging and lack of maintenance are not the contractor’s problem no matter how strong attorneys and unknowledgeable “experts” may make demands.

The lesson for the managers of gated communities is to engage someone who has real practical knowledge in the various areas of technology without the intervention of attorneys. It is very important that a maintenance program includes sealing the pavements to prevent oxidation and water damage which can greatly affect the life of a pavement.

In other areas of construction damage can be avoided. As an example, waterproofing stucco walls with certain excellent products can avoid water damage and mold problems.

And finally, a lesson for those writing the specification for asphalt paving in gated communities is to be sure that the paving specification requires that the paving mix be tested for water resistance.

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