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Materials Notebook: The Nuclear Asphalt Content Gauge for Measuring Asphalt Content in Mixes

Prepared by
Kevin Black
Materials Branch
Construction and Maintenance Division

May 1994

Introduction

Ninety-three percent of the 2.1 million miles of paved road in the U.S. are asphalt. Accurate monitoring of the asphalt cement content is important to insure that the mix design tolerance is met. Too low a percentage of asphalt can result in raveling, segregation, and insufficient compaction. Too high of an asphalt content can result in bleeding, shoving and rutting.

Asphalt concrete mixes are composite materials consisting of aggregate, asphalt, air, and other components which collectively develop structural characteristics capable of supporting highway traffic. One of the critical factors in the design of these mixes is the proportion in which the asphalt cement component exists. Many tests are used to evaluate the properties of mix designs such as voids (air content), asphalt cement content, gradation, voids in mineral aggregate (VMA), stiffness, and others to insure the quality of the mix design.

There are three major methods for determining asphalt content:

  • solvent extraction
  • nuclear asphalt content gauge
  • metering methods (automatic recordation, tank stabs)

These methods can generally be divided into direct tests and indirect tests. Direct tests measure the actual property of interest in a sample, in this case, the asphalt cement content. They are destructive or degradative since they determine the amount of asphalt by decomposing the mix into its individual components. They are usually very accurate but are time-consuming and use hazardous solvents. It is the environmental hazards and restrictions associated with these chemicals which is prompting additional interest in other analysis methods.

Indirect tests usually measure some other property which can be correlated with the desired property. They typically reduce the time needed to get an answer and often are used when actual property measurements are difficult or costly to make. In the case of asphalt cement content, an important difference between direct and indirect methods is that the extraction test allows gradation and asphalt cement content to be determined from the same sample, whereas the indirect tests only provide the asphalt content. Gradation tests must be performed separately such as through sampling of the conveyor feed belt. Although two separate indirect tests are required to replace the one extraction method, they yield similar accuracy, are faster to perform, and have minimal effect on the environment.

This paper discusses one specific indirect test, the nuclear test, in an effort to provide accurate information on its abilities and its limitations and to encourage its use. For more information about asphalt content determination, reference should be made to the Federal Highway Administration publication Asphalt Content Determination Manual [1].

Background

Asphalt cement content is an important component of flexible pavement design. Improper mix designs and amounts of asphalt cement are a major cause of premature failure of pavement structures. If cement contents are too low, a pavement will crack; if the content is too high, rutting and shoving will result. The influence that asphalt content has on mix design can be illustrated by the Marshall asphalt test property curves shown in Figure 1.

The direct tests for determining asphalt content are classified as chemical techniques and are commonly known as solvent extraction methods. The solvent extraction methods are further subdivided into the centrifuge method, the reflux method and the vacuum method. In these tests, asphalt cement content is determined using solvents such as methylene chloride, trichloroethylene or 1,1,1 trichloroethane to separate the asphalt cement from the aggregate. These chemicals are volatile organic compounds (VOC) which create health, environmental and disposal problems. All of these methods are being reevaluated by various States because of environmental and health concerns and because greater restrictions are being placed on their use.

For the past 15 years the highway community has been evaluating the use of indirect test methods because they do not present the environmental and health concerns attributable to the solvent extraction methods. Indirect tests for determining asphalt mix properties include metering methods and the nuclear method. Automatic recordation is the accurate measuring of the amount of asphalt cement used in the batching process and can be measured in the following three ways:

  • meter readings (instantaneous value for part of a batch)
  • weigh bucket readings (average of total batch)
  • AC storage tank volume readings (average of many batches)

The assumption is made that the amount of asphalt cement measured using one of these techniques (essentially by weight or volume) was properly blended with the aggregate to produce the required mix design. These methods have been in use for over 25 years but still are not fully supported by all users because it is not clear that all the asphalt added coated the aggregate properly. The testing frequency may also be considered insufficient to catch variations in production.

The nuclear asphalt content gauge is an indirect test that determines the amount of asphalt by measuring the amount of hydrogen in the mix. This method has been gaining increasing support as States become more confident with its operation.

Table 1 lists a comparison of the advantages and disadvantages of the current methods used in asphalt content determination.

Theory

The standard method of determining asphalt content can be shown using a phase diagram representing weight-volume relationships as depicted in Figure 2(a). This illustrates the components comprising an asphalt mix such as the aggregate, asphalt, filler and water. Direct measurement methods such as the extraction method compute the asphalt cement content based on the ratio of the mass (weight) of asphalt to the mass of the sample. This is expressed in the relationship:

Asphalt Content Weight of asphalt (coated and absorbed)

Dry Weight of Sample

In conventional extraction methods, the asphalt mix is physically separated into its components of aggregates and asphalt thus permitting computation of the asphalt cement contribution. More specifically, the calculation is made based on the initial mass of the sample, W1, the water in the sample, W2, the mineral filler in the sample, W3, and the aggregate, W4. This relationship can be found in AASHTO T-164 and is in the form:

Asphalt Content (%) = W1 - W2 - W3 - W4 X 100

W1 - W2

This is the traditional method and represents a macroscopic evaluation of the asphalt contribution to a mix.

The nuclear method represents a microscopic analysis with the measurements based on the actual number of hydrogen atoms contained within the mix. Its principle of operation is the same as that used for moisture content determinations in nuclear moisture-density gauges employed in construction. Neutrons are transmitted into the asphalt mix and their movement through the material is influenced by the hydrogen composing or surrounding the aggregate. Usually the source of hydrogen is water, for example, when making moisture determinations on soils. In asphalt content evaluations, the source of the hydrogen is predominantly the asphalt cement but can also be water in the mix and hydrogen contained within minerals in the aggregate. A conceptual view of this can be seen in Figure 2(b).

During the calibration process, samples of the material are tested to establish a relationship between counts and asphalt content. The nuclear gauge "counts" the neutrons influenced by the hydrogen as they pass through the sample establishing the hydrogen versus neutron count relationship depicted in Figure 3. Correlating these counts to asphalt contents using mathematical regression techniques then permits the evaluation of asphalt content for any sample having the same mix design. This is the basis by which the nuclear asphalt content gauge relates the hydrogen content, gauge counts, and the asphalt cement content.

Equipment

Currently there are three gauges on the market for determining the asphalt content. Two are made by Troxler Corporation, Models 3241-C and 3242, and one by CPN, Inc., Model AC-2. The other nuclear density gauge manufacturers, Seaman and Humboldt, do not currently offer asphalt content gauges.

These gauges consist of a control unit, sample chamber, and specimen pan. Within the control unit are the electronics including a microprocessor programmed to compute the asphalt content based on the theory described above. The sample chamber contains the nuclear source and the detector tubes and is where the sample pan containing the uncompacted sample is exposed to the neutron source. Figure 4 illustrates the typical gauge components.

One gauge manufacturer has developed a compact accessory tray which permits asphalt content to be determined on a compacted laboratory specimen (Marshall, Hveem, Gyratory) rather than uncompacted material. Another optional feature is a means for transferring the calibration from one gauge to another. These additional features may reduce chances for certain errors but they do not necessarily provide faster or more consistent results.

Operation

Asphalt content is determined at the producer's lab for quality control and at the owner's lab (usually a State Department of Transportation) as a means of quality assurance. Typically samples will be taken randomly over either some time or quantity (weight, volume) interval at the HMA plant and placed in the gauge to determine the percentage of asphalt. Proper operation of the instrument requires the examination of the environment around the instrument, calibration, and monitoring of the results. It also requires that samples be prepared in a prescribed manner. Specific information regarding correct procedures for sample preparation and calibration can be found in gauge operation manuals.

Sample Preparation

The procedure for performing the test is described by AASHTO T-287 and ASTM D 4125 and must be adhered to for accuracy. In addition to these tests, the moisture content must also be evaluated using AASHTO T-110 to insure that moisture makes no contribution to the hydrogen count. Each State DOT must make certain that the tests are followed as prescribed to insure repeatability of the results.

The material can either be heated to remove moisture by drying using AASHTO T-255 or extracted using AASHTO T-110. Drying can be done using a microwave oven if the aggregate is not highly absorptive. The length of time for heating will vary but should not exceed 30 minutes. The sample temperature should not be allowed to go higher than 110 C in accordance with AASHTO T 287. Determination of the moisture content by extraction will yield a percentage that can then be subtracted from the asphalt content reading to provide a corrected asphalt content.

The sample size may vary according to the gauge but generally the sample should fill the test pan as illustrated in Figure 4. Typically the amount of material required is about 7000 grams. Since the volume is constant owing to the pan's size, the mass should be very close to the manufacturer's recommended mass to insure that the proper compacted density is achieved for each sample. Consistent preparation of samples with respect to mass, density, and temperature is essential to insure accuracy and repeatability.

Gauge Environment

In operating the gauge, the influence of the environment surrounding the equipment must be minimized. This requires the operator to evaluate the potential sources of error and measure the daily "background" count. Care must be taken to keep the hydrogen environment as consistent as possible. The time necessary to perform this depends on the particular gauge being used.

Standard Counts

After evaluating the environment surrounding the gauge, the gauge must also be checked for the stability of the electronics to insure that they are not causing the counts to vary. Each gauge manufacturer has a procedure for establishing a "standard" count and has determined an acceptable range over which this count may vary for a particular instrument. If the gauge indicates a standard (background) count outside of this range, it must not be used. Problems with the electronics may be the reason for this variation.

Calibration of Gauge

Calibration is conducted using the aggregate and asphalt that will be used in a specific mix design. Each calibration is only valid for the one mix design on which it was made. Changes in mix design, sources of aggregate or sources of asphalt cement will require recalibration of the instrument. The importance of proper calibration cannot be overstated. If the gauge is not calibrated using the procedures described in the operator's manual, the measured asphalt content will not be accurate.

To perform the calibration, a sample weighing about 7000 grams is placed in the specimen pan and screeded flush with the top of the specimen pan flange as illustrated in Figure 4. In Figure 4, the "desired" placement is to be flush with the flange, however, this figure has been exaggerated to illustrate the difference between proper and improper placement techniques. Screeding will result in loosely compacting the material in the pan which is acceptable. Care should be taken not to compact the sample further.

The material is then placed in the sample chamber where it is exposed to the neutron source. The operator performs the calibration using a minimum of three tests, each one at a known and different asphalt content. The asphalt contents should be at 1 percent below the mix design target, one at the design asphalt content and one which is 1 percent above the target. Each sample should be tested for a 16 minute count to obtain the maximum precision. From this count versus asphalt content data, the gauge uses a regression analysis to determine the equation of the curve best describing that material. The results of this are illustrated in Figure 3(b). The relationship is then stored in memory and used to compute the asphalt content of other samples tested. More specific instructions can be found in the gauge operator's manuals or in AASHTO T-287 or ASTM D 4125 which outline the calibration procedure.

It should be noted that a "blank" sample (dry, hot aggregate, without asphalt) must be placed in the gauge and measured. This will establish a base line for the aggregate and can be helpful if questionable readings are obtained during the testing process.

Operation of Gauge

The gauge is used by selecting about 7000 grams of representative asphalt material according to AASHTO T 168. The sample is then placed in a specimen pan, loosely compacted and screeded off so that it is flush with the top of the pan. Improper placement in the pan or screeding may be a source of error that should be considered, therefore care should be taken to insure that this is done properly.

The operator places the sample in the specimen chamber and begins the test. The gauge permits the operator to select the amount of time for each test from 1 to 16 minutes. It is recommended that the time selected be 16 minutes to achieve the greatest accuracy. After running a test, the operator then records the asphalt content.

AASHTO T-110 should be used to determine the moisture in the mix. This value must be subtracted from the value provided by the gauge to provide accurate asphalt amounts.

Maintenance of Gauge

Properly maintained instruments are essential to assure high levels of accuracy. Part of this maintenance may involve the neutron source. In the case of gauges using a Californium-252 neutron source, the source has a short half-life of 2.65 years and therefore must be replaced periodically. Gauges using Americium-Beryllium sources have much longer half-lives (up to 458 years) and would not need to have their sources replace. Typical gauge lifetimes are based on the mechanical life of the instrument (about 15 years). The operating manual should provides all necessary maintenance information.

Test Results

The nuclear asphalt content gauge can be used for evaluating the asphalt cement content in many types of bituminous mixtures including:

  • hot mix (surface and binder)
  • recycled asphalt pavement (RAP)
  • surface treatments
  • material containing asphalt additives and modifiers

Several States have undertaken testing programs [1] to validate the use of the nuclear gauge in asphalt content determinations. Most tests have been very positive by indicating a good correlation with extraction tests. Results from three States(1) are included in Figure 5 to illustrate the level of agreement. Based on these and other continuing test programs, States are beginning to accept the results from nuclear asphalt content gauges for determining asphalt content of binder and surface mixes. Table 2 contains a list of States and their method for measuring asphalt cement.(2)

Testing has been undertaken on asphalt cements containing additives and certain treatments, however, additional tests are still required before complete acceptance of the gauge's use on these products is realized. Proper calibration procedures are needed (just as for bituminous mixes) to account for variations in material properties and proportions. Other material additives requiring further evaluation include mixes containing polymers and anti-strip agents.

Sources of Error

Variations resulting from material supply sources, aggregate types, temperature, moisture and the working environment are compensated for during the calibration process. Calibration permits the hydrogen counts to be related to the asphalt content for all samples from a given mix design and supply. Since the number of hydrogen atoms for any fixed quantity of bituminous cement will vary slightly, the calibration process must account for the influence this factor has on the measurement. The variations that occur in aggregate (such as specific gravity and chemical composition) require the gauge to be recalibrated for each new mix design to insure accuracy. Temperature must be monitored to control variations and moisture content must be measured to account for its influence on the hydrogen count. The gauge working environment should be surveyed to avoid contributions found near the gauge as is shown in Figure 6.

All approaches to the analysis of some property have constraints that must be considered before the investigation is undertaken. Failure to do so will result in inaccurate readings. Determining the likely sources of error for asphalt content has resulted in the identification of the following areas:

  1. Accuracy problems related to the sample's physical and chemical properties due to:
    1. physically bound moisture in aggregate pores
    2. physically bound moisture in mix
    3. chemically bound hydrogen in the aggregate (types of aggregate such as those that contain mica minerals)
    4. sources and grades of asphalt cement (including different sources for the same grade)
    5. additives such as hydrated lime and amine-based antistripping additives
  2. Accuracy problems related to testing procedures due to:
    1. insufficient drying of the mixture sample
    2. temperature of field samples differing significantly from the calibration temperature.
    3. variations of sample density from pan to pan
    4. varying degree of precision resulting from the various count intervals (1,4,8, or 16 minutes) at which the sample is measured
    5. failure to recalibrate when the mix design changes (or when the source of the aggregate or asphalt cement changes)
    6. electronic drift during a day's operation (not detected because of failure to periodically monitor the stability of the instrument)
    7. incorrect or inconsistent practices by technicians
    8. improper sample preparation such as overcompaction
    9. failure to note sources (and changes in sources) of hydrogen around gauge (such as water pipes, water coolers, oil tanks, paper products) which can cause the instrument readings to drift (see Figure 6)
    10. failure to follow procedures outlined in AASHTO T-287 and ASTM D 4125

The first group of problems listed above usually result from calibration errors or from changes in material supplies; the second set generally can be attributed to operator error. Although the problems identified represent most of the likely sources of error associated with the use of the nuclear asphalt content gauge, there may be other factors that can influence the results. The greatest care should be taken to make certain that the areas discussed above are considered to avoid known sources of potential error.

Physically bound hydrogen such as water in the mixture or water in the pores of the aggregate can be corrected for by heating the sample to drive off the water. This procedure is noted in AASHTO T-287 for calibration and testing. Samples should be monitored during production as a check against moisture content variations. Although the calibration is performed using dry aggregate, aggregate stockpiles may be watered permitting moist samples into the plant. If the moisture content is found to vary, this variation must be subtracted from the apparent asphalt content indicated during calibration. For other problems where elimination of the source of error is not possible, the cause of the variation should be isolated so that its influence can be determined in relative proportion and then subtracted out.

These problems can all be eliminated or compensated for if proper instruction is provided to the technician. Improper operation of the gauge can occur when an operator is either ignorant of the factors which contribute to erroneous measurements or fails to follow the prescribed practices for using the gauge. As an example, corrective measures may only require moving a gauge to a relatively isolated area a few meters from any object known to have a high hydrogen content.

Many of the items listed as contributing to inaccuracies in the asphalt content gauge also cause errors in nuclear moisture-density gauges. Since most States use moisture-density gauges, operators should already be familiar with many of the listed causes. Figure 6 illustrates some of these potential sources of error.

Safety

In discussing nuclear gauge safety, it is important to note the radiation terminology associated with use of the instrument. These terms are not normally used and the new metric terms and values are even less well understood. There are two types of measurements that are associated with nuclear gauges. One represents the "exposure" levels of radiation which gauge operators are exposed and the other type is used to express the "power" of the radiation source.

U.S. units are still the "official" method for reporting radiation exposure levels under guidelines established by the Nuclear Regulatory Commission (NRC). One reason for this is that the SI terms "appear" to reduce the "risk" involved in using the gauges even though the risk is low irregardless of the units used in reporting. But because the metric units have much lower numerical values it is a concern that the perception of a lower risk could occur resulting in a reduction to the adherence of safe operating procedures. Therefore the units described in the tables are in U.S. units. If SI units are desired, conversions can be made using units found in most operator manuals. The commonly used U.S. units for exposure levels are the rem and millirem.

The millirem represents the amount of radiation absorbed by the body and is the unit used in reporting exposure levels which are found on the radiation badges or dosimeters worn by gauge operators. These units represent the measurement of radiation absorbed rather than the amount emitted. Table 3 provides some millirem numbers used to define safe exposure limits(3). For reference purposes, one chest x-ray which is typically given in medical examinations, is 40 millirem and typical exposure levels for nuclear gauge operators is between 100 and 200 millirem of radiation exposure over a year. As a comparison, Table 4 also includes information on the exposure limits for the solvents commonly used in asphalt extraction tests(4). Information about typical exposure levels to workers using chlorinated solvents is not well documented and would require each laboratory to conduct its own test to determine these values.

Nuclear gauges have been used in the highway industry for decades with no documented evidence of either environmental or health problems. Safety courses are given to all users and radiation exposure histories should be continually monitored.

The becquerel is the unit used for representing the "power" of radioactive source and used to measure its output. It is the unit specified on the instrument and required by law to be displayed by regulations relating to its transportation. Since it is not a term associated with safety, it is not under the regulations of the NRC and therefore is expressed as an SI unit. Americium 241:Beryllium and Californium-252 sources are typically used in nuclear asphalt content gauges.

Licensing

State DOT's are required to maintain strict accounting methods for gauge ownership, training, use, maintenance and disposal under Nuclear Regulatory Commission (NRC) guidelines. States are usually licensed by the NRC although some State governments, known as Agreement States, have been given the authority by the NRC to regulate control of nuclear gauges and other sources of low-level radiation within their States. Licensing programs generally consist of the following:

  • radiation safety program
  • personnel monitoring using a dosimeter, TLD
  • (Thermoluminescent Dosimeter film badges)
  • security
  • storage
  • periodic leak testing
  • training

Some gauges use a Californium-252 isotope emitting low amounts of radiation and have other design features that remove the requirement for a license. Only one gauge manufacturer currently makes this type of gauge.

Economics

Although the primary reason for promoting the use of the nuclear gauge is environmental, there are also economic incentives. Several factors must be considered when doing the economic analysis. These include:

  • size of the project (number of tests to be performed)
  • material costs (including equipment)
  • labor costs

Some projects may be too small for the gauge to be cost-effective because of the time required for calibration . Calibration can require hours and must be done for each new mix (i.e. for base, binder, and surface)(5). Most jobs require many tests and as can be seen in Table 5, the cost [2] of using the nuclear gauge becomes attractive as the number of tests required increases(6). If a mix will be in production more than one day, the use of the nuclear asphalt content gauge can almost always be justified. For fewer than three tests per mix type, it probably would never be cost-effective to use nuclear gauges.

New nuclear gauges currently cost between $5000 and $6000 while extraction equipment typically will cost $1500 or more. Although initial costs tend to favor the extraction method, the greatest costs associated with extraction procedures are those for the purchase and disposal of chemicals for each test. For a laboratory conducting a significant number of tests, the "per test" cost for nuclear gauge testing is considerably lower than for extraction tests. Some values supporting this can be found in Table 6 [1].

A benefit that the chemical methods offer is that, once they have been completed, a gradation analysis can be performed quickly and inexpensively. Automatic recordation, which may be used in conjunction with the nuclear asphalt content gauge test, can not be used to provide gradation control. Some studies, however, indicate more asphalt control testing is needed rather than gradation testing.

Summary

This discussion has centered around the nuclear gauge for determining the asphalt content of bituminous mixes. It has shown that this method is both accurate and cost effective. Since environmental concerns are making chemical methods increasingly costly, the use of the nuclear asphalt content gauge should be encouraged.

Over the next few years, three solvents that have traditionally been used in extraction tests are going to come under additional regulation. Trichloroethane is being phased out and will no longer be manufactured after 1996. Methylene chloride and trichloroethylene are also having additional restrictions place on their use. Biodegradable solvents are an option, however, many of these still have shortcomings due to safety (flammability) and longer testing times. The changes that are occurring require that State highway agencies adopt new methods capable of replacing chemical tests that are both environmentally clean and can be performed quickly.

Some extractions must still be incorporated into the testing plan to provide a check on nuclear methods, to monitor the asphalt content in recycled asphalt pavement (RAP), as an option for jobs too small to warrant nuclear asphalt content gauge use, and as a means of providing gradation control. Eventually, however, biodegradable solvents or other methods of performing these tests and checks are likely to replace the hazardous chemicals used today.

References

  1. Asphalt Content Determination Manual, FHWA-IP-90-008, S.H. Carpenter, et al., ERES Consultants, Inc., 1990.
  2. Current Industry Practices and Procedures for determining Asphalt Cement Content in Hot Mix Asphalt, James Warren, et al., National Asphalt Paving Association, 1991.

Bibliography

  • Asphalt Content Determination Technique on Conventional and Dryer-Drum Mixed Asphalt Concrete, C.R. Farr, K.A. Millions, and K.O. Anderson, 1976.
  • Nuclear Asphalt Content Determination, H.L. Walters, Colorado Department of Highways (not published).
  • Report on the Use of the Troxler 104 Probe and the 115 Gauge for Asphalt Content Determination, Peter Todor, Florida State Road Department, 1966.
  • Development of Rapid Test Method for Asphalt Content Determination in Hot Mix Paving Mixtures, FHWA/IN/JHRP-84/3, Jorge Javier Martinez Chavez, Joint Highway Research Project, Indiana Department of Highways, 1984.
  • Nuclear Asphalt Content Gauge Study, Louis John Wagner, Maryland Department of Transportation, 1988.
  • Determination of Asphalt Content and Characteristics of Bituminous Paving Mixtures, John F. Adams, Iowa Department of Transportation, 1988.
  • Evaluation of Nuclear Asphalt Content Gauge, Missouri Department of Transportation, 1989.
  • Nuclear Method for Determination of Asphalt Content Corrected for Moisture in Bituminous Mixture, D.W. Christensen and J.P. Tarris, Pennsylvania Transportation Institute, 1989.
  • Asphalt Content Determination Manual, FHWA-IP-90-008, S.H. Carpenter, A.L. Mueller and M.B. Stanley, ERES Consultants, Inc., 1990.
  • Gradation Analysis of Cold Feed and Extracted Bituminous Mix Samples, Iowa Department of Transportation, Final Report for MLR 88-2, 1988.
  • Precision and Accuracy of Nuclear Asphalt Content Gauges in Determining Asphalt Content in Asphalt Concrete Pavements, Anthony
  • J. George, et al., Oregon Department of Transportation, 1988.
  • Current Industry Practices and Procedures for Determining Asphalt Cement Content in Hot Mix Asphalt, James M. Warren, et al., National Asphalt Pavement Association, 1991.
  • Kevin Black is a highway engineer in the Materials Branch of the Construction and Maintenance Division. He developed this article as a supplement to the Materials Notebook which is distributed to FHWA field offices for providing guidance on issues relating to construction materials.

Footnotes

  1. Results from unpublished tests conducted by VA, NC, and MN.
  2. Information obtained from the Asphalt Content Determination Manual [1] and from Troxler Electronic Laboratories.
  3. Values in the Table were taken from the Troxler 3400 Series Instruction Manual.
  4. Values in the Table were taken from "Pocket Guide to Hazardous Materials", a publication of the National Institute for Occupational Safety and Health.
  5. Taken from "Current Industry Practices and Procedures for Determining Asphalt Cement Content in Hot Mix Asphalt", NAPA, 1991.
  6. The figures do not include the cost of the equipment or of performing gradations.
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Updated: 04/07/2011
 

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