Long-Term Pavement Performance Pavement Loading User Guide (LTPP PLUG)

PART II - GUIDELINES FOR DEVELOPING AXLE LOADING DEFAULTS

INTRODUCTION

Although the SPS TPF data provide an improved set of traffic loading defaults compared with the original MEPDG defaults because they were collected with better calibrated WIM equipment, the SPS TPF data, by necessity, represent national conditions. Unfortunately, many truck characteristics differ markedly from State to State. Consequently, if a State operates well-calibrated WIM scales, summarizing the data obtained from those scales can provide default truck characteristic data that are more accurate for designs in that State than if national defaults are used. Therefore, States are encouraged to develop and apply their own NALS and other truck characteristics when their WIM data have been carefully checked for quality assurance (QA) and found to be accurate.

Analysis of WIM data from the LTPP program indicates that axle loading distributions vary among different axle types, different truck types (vehicle classes), and different roadways. Differences in axle load spectra between different axle types can, in part, be attributed to a variety of factors related to different truck configurations, including differences in:

• Axle configuration.
• The legal axle load limits that apply to single, tandem, tridem, and quad axles.
• Truck body structure needed to carry different commodities (e.g., flatbeds versus tanks versus basic cargo boxes).
• Vehicle length and the number of units (single unit versus multiple units) pulled by the truck's power unit.
• The purpose of an axle (steering or load-carrying axle).

Even for the same vehicle class and axle type, axle weights vary based on local conditions for reasons such as:

• Differences in truck size and weight laws between States.
• Presence and effectiveness of weight enforcement activities.
• Dominant commodities carried by specific classes of trucks on each road (e.g., a standard five-axle tractor semitrailer weighs much more when carrying a full load of wood chips than it does carrying a full load of computer parts shipped with large amounts of padding).
• Number of roadway lanes (outer lanes typically are loaded more heavily than inner lanes on multilane roads).

In addition, the percentage of trucks carrying full or partial loads versus those returning empty to a terminal is a function of the type of trucking movement, the type of commodity hauled, and the location of the road segment being analyzed. Factors that can significantly affect the percentage of loaded trucks observed include:

• Percentage of long haul trucking movements occurring versus the percentage of local delivery movements.
• Proximity of the roadway to urban areas (roads in or near urban areas are more likely to see partial or empty loads).
• Nature of the commodities hauled on the road (e.g., most trucks carrying natural resources operate loaded in one direction and empty in the other).
• Lane of traffic monitored (heavier trucks are more frequently in the outside lanes).

Local site conditions are more likely to have a significant effect on load spectra for locations that have a high percentage of local traffic and a low percentage of through traffic (i.e., traffic that is generated from far away, especially when that through traffic must cross State boundaries).

HOW TO CAPTURE DIFFERENCES IN AXLE LOADING IN DEFAULTS

The key to successful development of NALS defaults is an understanding of differences in loading conditions within the road network for which defaults are being developed. This guide emphasizes the need to identify different trucking patterns and collect data on those patterns to develop an understanding of the NALS associated with those patterns. State agency personnel need to work with their freight community to accomplish this task. Once loading conditions are identified, the number of WIM sites that should be used to develop a default NALS could be determined based on observed variability in loading data.

This guide does not prescribe the number of WIM sites that should be used to develop a default NALS. This information can be found in the FHWA's Traffic Monitoring Guide and NCHRP Reports 538, Traffic Data Collection, Analysis, and Forecasting for Mechanistic Pavement Design, and 509, Equipment for Traffic Load Data.^(3,5,6) In general, it is advisable to use all available WIM sites in development of the defaults, provided that these sites have data that satisfy the data selection criteria described in the following section.

At the same time, to keep this data analysis task manageable, those developing and applying the default NALS should focus on the truck and loading patterns that will significantly affect the outcome of the pavement analysis - in other words, the dominant vehicle classes. For example, if one type of truck carries a highly variable load (axles on these trucks can be very heavy or not too heavy), but only 1 of 1,000,000 trucks is of that truck type, then it is not necessary to spend much time or effort understanding when and where this specific truck type occurs, or what it weighs when it is observed. On the other hand, if 9 of 10 heavy trucks are of a specific type in a given State, understanding the differences in load carried by these trucks, and being able to correctly select the loading condition occurring on specific road segments, is very important. Alternatively, if a specific truck type never carries heavy weights, it is not important to understand the variation in that type of truck's weights, even if the percentage of variation is large. (That is, the analyst does care whether truck axles vary from 2,000 to 4,000 lb, even though that is a 100-percent variation, because neither of these axles will cause significant pavement damage.) In both the case of the "rare truck type" and the case of the "very light truck type," significant amounts of variability are acceptable simply because the effects of that variability will have little effect on the pavement analysis.

For the majority of the LTPP sites (and the majority of U.S. primary roads), Class 9 is the dominant heavy vehicle type and is responsible for a very high percentage of the traffic load applied to pavements. Therefore, when developing and applying NALS, a special effort should be made to identify different loading conditions for Class 9 vehicles. While Class 5 vehicles are frequently dominant in terms of truck volume, they normally are not heavy enough to make a significant contribution to total traffic loading and thus may be excluded from determination of the dominant heavy vehicle classes (unless local knowledge exists of heavier-than-usual Class 5 vehicles at the site).

Finally, it is advised that when NALS are developed, they should be accompanied by descriptive information about the loading conditions to help users correctly identify the NALS that should be applied for any given analysis. In this guide, these descriptions begin with the identification of the "typical" loading condition. This represents the most commonly observed loading condition. This designation serves as a useful starting point in selecting a NALS. Alternative NALS are then defined as lighter or heavier than the default, meaning that trucks exhibiting these alternative patterns will cause less or more pavement damage than trucks exhibiting the pattern most commonly observed. These designations are meant to help analysts select the appropriate NALS and understand whether the NALS they are using will provide a particularly conservative design.

It is also recommended to use all available loading information (both quantitative and qualitative) when assigning the available default loading conditions to specific pavement analysis sections.

APPROACH FOR DEVELOPMENT OF AXLE LOADING DEFAULTS

Two types of NALS defaults are frequently used with MEPDG applications. Each of these types of defaults should be computed at the State level whenever possible:

• Tier 1, or global, defaults representing statewide or nationwide default loading conditions.
• Tier 2, or alternate, defaults representing specific loading conditions. These defaults are developed from, and assigned to, groups of roads that have common loading conditions for specific truck class-truck weight road groups.

As described in Part I, Tier 1 NALS defaults are used for sites that have no information regarding expected traffic loading patterns on a specific pavement analysis segment. These defaults represent an average traffic loading condition observed at all sites used in the development of the default. The benefit of Tier 2 defaults is that they provide multiple choices for selecting traffic loading conditions for different truck classes and axle types. Appropriate selection of these defaults requires some knowledge about the expected traffic loading condition at the pavement design site.

In some cases, Tier 2 roads can be grouped and/or identified based on regional trucking patterns that affect the nature of truck loads carried on those roads. For example, a "regional pattern" might be based primarily on the commodity routinely carried on the road (coal, cut trees, specific agricultural products), or "regional" may simply refer to roads that are or are not in proximity to large metropolitan areas (rural versus urban). Some truck weight road groups and regional designations may only apply to specific classes of trucks. For example, the "coal region" in a midwestern State may only apply to Class 7 and Class 10 trucks, because other truck classes (e.g., Class 9) may not be involved in the specific commodity movements identified by the group or regional designation. This also means that more than one "truck weight group" may need to be applied for any given pavement analysis to reflect the different loading patterns applied by different classes of trucks.

In addition, the availability of Tier 2 defaults allows easy testing of the sensitivity of the pavement analysis outcomes to differences in NALS inputs. That is, the user can perform two different runs, one using the selected NALS and one using a heavier NALS. The differences in the analysis outcomes provide the analyst with considerable insight into the consequences of using different NALS for pavement design.

The development of MEPDG traffic-loading defaults starts with the selection of WIM sites that satisfy specific data selection criteria, followed by the development of representative NALS for each of the sites with data that meet those criteria. Then, NALS from selected individual sites (or all the sites, in the case of global defaults) are averaged to compute Tier 1 default NALS or grouped in clusters with similar loading characteristics and averaged for each cluster group. Based on this approach, the methodology for development of the MEPDG traffic loading defaults includes the following sequence of tasks:

• QA testing of available WIM data and selection of sites.
• Development of site-specific representative NALS for all selected WIM sites.
• Development of one set of global defaults using data for all selected WIM sites (Tier 1).
• Development of supplemental sets of NALS using subsets of data for sites with similar loading conditions (Tier 2).

Guidelines to accomplish these tasks are described in the following sections.

DATA SELECTION AND DEVELOPMENT OF RANALS FOR INDIVIDUAL SITES

MEPDG NALS are produced by vehicle class and axle type for a typical day of a month. Each NALS represents the expected frequency with which an axle within each specified load range will be encountered for that vehicle type and class of axle.

Because seasonal changes in axle load frequency distributions are not uniform across different States and are likely to be observed only on the roads that carry a large percentage of seasonally affected loads, national default NALS values are developed to represent axle load frequency distributions for a typical day of the year. These distributions are called "representative annual normalized axle load spectra," or RANALS. If truck loads change seasonally owing to truck volume changes, monthly adjustment coefficients are used to adjust truck volumes between different months. If a State has a group of roads subject to seasonal changes in load distribution frequencies, default NALS should be developed to represent each month or season in the year.

Data Selection Criteria for Development of Site-Specific Representative NALS

These guidelines address WIM data requirements to develop representative site-specific NALS for computation of the default NALS. To take full advantage of the available WIM data, the data selection criteria focus on maximizing the use of available data without compromising the quality of MEPDG defaults. WIM data selection criteria address the following data selection categories:

• Data availability: maximized use of available data that satisfy data quality criterion.
• Data quality: identification and utilization of reliable, high-quality axle loading data.
• Data reasonableness: identification of data that are not only accurate but also represent typical/expected conditions for a given site or a group of sites that have similar traffic-loading patterns.

The following conservative minimum data availability criteria were identified to remove any potential day-of-the-week (DOW) and monthly bias from the computation of RANALS for individual WIM sites:

• Availability of at least 1 of each 7 DOW per month to avoid potential DOW bias. Days do not need to be consecutive.
• Availability of at least 1 of each 12 calendar months to avoid potential seasonal bias. Months do not need to be consecutive or from the same calendar year.

These minimums were developed through a number of statistical analyses designed to evaluate the reliability of computed NALS using different data quality and availability scenarios.

When more than 7 DOWs per month or more than 12 calendar months of acceptable quality data are available, all available data for that site should be used in the computation of site-specific RANALS. If less than these minimums are present, the lack of data may create bias in the RANALS such that they underestimate the effects of loading patterns missing from the data. For example, if no data are present from the spring months owing to equipment failure, and loads are lighter in the spring months than during the rest of the year owing to spring thaw load restrictions, the RANALS will overestimate the average loading condition. Similarly, in urban areas, weekend loads may be heavier than weekday loads as the percentage of through traffic to local traffic increases.

The following acceptable data quality criteria were identified for RANALS to be used in the LTPP project:

• Data should be from a WIM site conforming to ASTM (ASTM International, formerly American Society for Testing and Materials) 1318 specification for Type I WIM system accuracy and performance requirements specified in the LTPP SPS Field Operation Guide.^(7,8)
• Selected data must pass quality review using LTPP QC procedures for the SPS TPF study and be identified as Level E data in the LTPP database.⁽⁹⁾

States developing NALS default tables for their own use are encouraged to follow these same data quality standards but are not expected to follow LTPP reporting requirements. It is also advisable to limit the maximum acceptable bias in axle weight measurements to less than 5 percent to avoid significant differences in MEPDG outcomes owing to bias in axle weight data.

In addition to the basic quality of the data and the number of days for which data are available at each site, data from specific sites should be evaluated for reasonableness for inclusion in default NALS used to represent the traffic load expected to occur on other roads in a State. In some circumstances, data may be valid but (1) are atypical because of atypical conditions that occurred at a site (for example, a 6-month-long, temporary load restriction imposed during bridge construction downstream of the data collection site); (2) truck volumes for a particular vehicle class are so low, given a specific truck class distribution at the site, that data are not sufficient to produce a representative axle load spectrum for some vehicle classes; or (3) the loading pattern observed at a site is significantly different from other sites owing to unique truck traffic generators in the vicinity of the site.

In the first two conditions, data for vehicle classes affected by the loading restriction are not suitable for use in default RANALS. In the first case, the data are not representative of "normally observed" loading conditions. In the second case, the very low frequency of vehicles makes the values in the RANALS unstable statistically. When averaged with other RANALS, these few axles have too much impact on the NALS for any group in which they are placed. For example, if only four axles are measured at a site and two fall into one load range in the NALS, that load range contains 50 percent of all axles in the RANALS for that site. When averaged with any other set of RANALS, the 50-percent value badly biases the computation of the average percentage of axles that fall into that load range.

In the third case, the RANALS should not be included in a load group with data from other sites. Instead, it should be treated as a "special case." This means that a "special case" description of why it is unique should be developed for that condition so that it can be used in pavement analysis when other pavements also experience that condition.

All of these data would be useful for site-specific MEPDG analysis but should not be used for creation of generalized defaults, which are designed to represent typical traffic loading conditions for sites without site-specific axle load spectra.

Procedure for Development of RANALS Estimates

The following procedure describes the steps for developing RANALS using daily axle load spectra stored in a format consistent with LTPP LTAS DD_AX tables:

1. Identify all sites for which the available data meet the selection criteria of having data for at least 7 DOWs, for each calendar month, and at least 12 calendar months. These data must have passed the LTPP SPS TPF QC checks for data and performance of the WIM equipment. They must also pass the data reasonableness checks described in the LTPP report MEPDG Traffic Loading Defaults Derived from LTPP Transportation Pooled Fund Study.⁽¹⁰⁾
2. Extract daily axle load spectra from the LTPP LTAS DD_AX tables for all years and months from all sites that were identified in the previous step, where the resulting data are expressed as daily axle load counts by weight bin.
3. For each site, compute axle load spectra representing the typical day of the month for each month, by year, axle type, and vehicle class (classes 4 through 13). The daily axle load spectra should be averaged first by DOW and then across DOWs to produce an unbiased monthly axle load spectra (as representative loading for a day of the month for a given year) for each vehicle class, axle type, month, and year.
4. For each site, year, month, axle type, and vehicle class, normalize the axle load spectra representing the typical day of the month to obtain monthly NALS.
5. For each site, axle type, vehicle class, and calendar month (January through December), compute average monthly NALS (as representative loading for a day of the month) by averaging data across all available years. This will result in 12 representative monthly NALS for each calendar month, axle type, and vehicle class for each site.
6. For each site, axle type, and vehicle class, average the 12 monthly NALS. This will result in one RANALS representing the typical day of the year for each axle type and vehicle class for each site.

Each set of RANALS includes a normalized axle load spectrum for each vehicle class (for classes 4 through 13) and each axle type (single, tandem, tridem, and quad as applicable) representing the expected axle loading distribution for a typical day of the year for that site.

DEVELOPMENT OF GLOBAL NALS DEFAULTS (TIER 1)

Overview

The purpose of the global NALS defaults is to serve as input to the MEPDG when very little or no information about existing or expected future traffic loading patterns is available for a design site. Global NALS defaults follow the exact format of the original MEPDG defaults and can be implemented easily. These defaults are based on averaging RANALS from all the WIM sites that have sufficient data.

Procedure for Development of Global NALS Defaults (Tier 1)

This procedure is based on averaging RANALS from the WIM sites that have sufficient data. To avoid biasing NALS as a result of unstable load spectra distributions caused by very low axle counts (which are considered insufficient to define a load spectra frequency distribution for a given class and axle), if a site has fewer than 100 axles and/or an APC of less than 0.01, that site should not be included in the computation of global NALS defaults for that vehicle class and axle type.

The computational steps and data availability criteria are presented below:

1. Obtain RANALS for all sites that satisfy the data selection criteria presented in this guide.
2. For each vehicle class and axle type, exclude from further computations RANALS that are based on very low axle counts, using the following criteria:
   • RANALS that are based on very low axle counts (fewer than 100 axles and/or axles per class less than 0.01).
   • RANALS representing highly unusual or unique loading conditions that are not likely to be encountered on road classes where global defaults will be used.
3. For each vehicle class and axle type, average the available RANALS.
4. Save the results in a table format provided in the LTPP PLUG database (see appendix B).

DEVELOPMENT OF ALTERNATE NALS DEFAULTS REPRESENTING ALTERNATIVE AXLE LOADING CONDITIONS (TIER 2)

This section provides guidelines for States to use their own WIM data to develop NALS representing different loading conditions within the State for use with the MEPDG and DARWin-ME software. NALS representing different loading conditions within the State's road network provide flexibility to MEPDG users in the selection of axle loading defaults so that they can more accurately describe their local loading conditions.

Tier 2 NALS are designed to be used independently to specify different truck loading conditions by class and axle type. For example, a pavement designer may select a "heavy" axle load spectrum for Class 9 vehicles but a "light" load spectrum for Class 6 vehicles because those loading conditions are appropriate for the truck traffic using the roadway they are designing.

Methodology for Grouping WIM Sites With Similar Loading Conditions

To create Tier 2 NALS, the site-specific RANALS should be grouped in clusters based on similarities in the axle loading conditions. For each cluster, alternative default NALS should be computed for each vehicle class and axle type in such a way that there is a high probability that the use of these alternative NALS will result in a significant differences in the expected pavement life or design thickness predictions.

The grouping of site-specific NALS into Tier 2 defaults should be done separately for each class and axle type. That is, just because tandem axles for Class 9 trucks from sites 1 and 2 are shown to belong to the same Tier 2 NALS does not mean that tandem axles for Class 10 trucks from those same two sites should also be placed together in a default NALS.

The recommended way to create Tier 2 NALS is to use the hierarchical clustering technique, available in most statistical software packages, to group RANALS from State WIM sites that have similar pavement damaging potential. Step-by-step instructions are given below. The methodology and detailed analysis behind this procedure are presented in chapters 8 through 10 of the LTPP report, MEPDG Traffic Loading Defaults Derived from LTPP Transportation Pooled Fund Study. ⁽¹⁰⁾

Procedure for Development of NALS Defaults Representing Different Loading Conditions

The procedures described below are based on the methodology described in the LTPP report, MEPDG Traffic Loading Defaults Derived from LTPP Transportation Pooled Fund Study.⁽¹⁰⁾ Other mechanisms to group load spectra into "similar" groups are also possible. The steps required to create Tier 2 NALS are as follows:

1. Ensure that the WIM data used to compute State-specific defaults come from data collection equipment that is calibrated and functioning properly.
2. Develop RANALS for each site.
3. Using the RANALS, compute an RPPIF summary statistic associated with each load spectrum that takes into account both the pavement damage potential of different axle load weights and the frequency of the application of those loads (i.e., the fraction of loads of a given magnitude in the axle load spectra).
4. Determine the importance of each vehicle class and axle type based on the frequency with which specific classes of vehicles are observed and the loading characteristics of those vehicles (i.e., identify types of trucks that cause heavy damage to the pavement because of their weight and volume).
5. Determine the sensitivity of the MEPDG to the variation inherent in the truck fleets observed by the agency, given the pavement design philosophy of the agency, and establish maximum RPPIF differences for cluster analysis.
6. Perform a cluster analysis of the RPPIFs (by vehicle class and type of axle) using the output of the sensitivity of the MEPDG as a guide for determining when to stop the clustering process.

The first two steps above were discussed as part of constructing the Tier 1 default NALS. Each of the remaining steps is described below.

Step 3: Compute RPPIF Statistics Using RANALS

The RPPIF summary statistics were used in the creation of the new national default NALS based on SPS TPF data. The intent of the RPPIF is to allow simple summary comparisons of the size of different loading conditions by providing a single statistic associated with each load spectrum. RPPIF is computed by taking into account both the pavement damage potential of different axle load weights and the frequency of the application of those loads (i.e., the fraction of loads of a given magnitude in the axle load spectra). It is computed using the W-factors shown in table 18. These factors provide a generic measure of the relative pavement damaging potential caused by axles of specific weights and configurations, as determined through MEPDG analysis in the report, MEPDG Traffic Loading Defaults Derived from LTPP Transportation Pooled Fund Study.⁽¹⁰⁾

The RPPIF statistic is used to identify axle loading conditions within each vehicle class and axle type that are likely to produce significantly different MEPDG outcomes. States wishing to group "similar" RANALS using other criteria are welcome to do so.

To compute the RPPIF statistics, use the equation shown in figure 1. Start with the RANALS computed for each vehicle class and axle type. For each of those RANALS, multiply the load frequency corresponding to each load bin in those load spectra by the corresponding W-factor from table 18. Sum these values across all load bins (i = 1 to n) for that load spectra.

Figure 1. Equation. Computation of RPPIF statistics

Where:
RPPIF_jk = relative pavement performance impact factor for axle type j and vehicle class k
i = load bin
j = the type of axle
k = the class of vehicle
W_ij = the impact factor for load range i, for axle type j from table 18
F_ijk = the fraction of axles in load range i, for axle type j, and vehicle class k

Table 18. Pavement performance impact factors, Wij

Step 4: Determine the Importance of Specific Vehicle Classes and Axle Types

If the criteria used for the creation of the national Tier 2 NALS are acceptable (see step 6), simply skip to step 6 and use the criteria presented in table 20, along with State-specific RANALS, to develop State-specific Tier 2 NALS. If State-specific traffic attributes and design criteria/performance models are to be used, then steps 4 and 5 must be followed to develop a State-specific criteria table that replaces table 20 in step 6.

Because of their complexity, this guide only summarizes steps 4 and 5. They are discussed in greater detail in chapter 9 of the LTPP report, MEPDG Traffic Loading Defaults Derived from LTPP Transportation Pooled Fund Study.⁽¹⁰⁾

In step 4, a State determines the truck volumes to test the sensitivity of the MEPDG pavement designs to State-specific loading conditions. The Tier 2 national defaults described in Part I of this guide are based on the truck volume patterns observed in the LTPP traffic database. As a result, they may or may not be representative of the kinds of trucks traveling on a given State's roads. For example, roads in the western States often have a much higher percentage of multi-trailer truck travel than roads in most eastern States. Consequently, the use of national averages tends to overestimate multi-trailer truck travel and importance to pavement performance in eastern States and underestimate their importance in western States. Similarly, in portions of some midwestern States (e.g., Ohio, Pennsylvania, and Kentucky), very heavy, multi-axle single-unit trucks (i.e., four, five, and six+ axle, single-unit trucks) are commonly found on roads that serve natural resource extraction industries (e.g., coal). The largest of these trucks is rarely found in many other States.

The primary purpose of step 4 is to determine the upper bounds of the volume of trucks occurring and the maximum percentage of all truck traffic that occurs in that class. These two factors are used to set up tests of the sensitivity of the MEPDG's outputs to different observed loading conditions for that class of trucks.

To obtain the maximum observed truck volumes per lane and the maximum observed truck percentages by class of truck, the agency should examine the data in its own historical traffic database. The intent is to find those traffic conditions that maximize the impact of each vehicle class on pavement design. That is, under what truck volume and vehicle class distribution conditions does a given vehicle class represent the largest percentage of the total truck load on roads found in the State? Identified maximum truck volume conditions (relative to other truck volumes) can then be used to determine how sensitive the MEPDG outcomes are to the possible changes in load observed in that class. Table 19 shows an example of the outcome of this data analysis task. The highlighted percentage values and average annual daily truck traffic (AADTT) values can then be taken into the MEPDG sensitivity tests.

Table 19. Example of traffic design conditions for each vehicle class

Step 5: Determine MEPDG Sensitivity

This task uses the RANALS obtained in step 2 and the traffic volume data developed in step 4 to test the sensitivity of the selected MEPDG designs to the loading conditions present in the State. States implementing this step should identify a set of typical pavement designs and pavement distress modes frequently observed in the State, determine pavement performance criteria for MEPDG design, and use locally calibrated pavement design models.

To test MEPDG sensitivity to a single class of trucks at a time, all traffic loading conditions other than the axle load spectra for the class being studied should be held constant for a selected pavement design. For each class of trucks being tested, the truck traffic volume and vehicle class distribution parameters should represent the case when the test truck class contributes the largest percentage of total load, compared with other vehicle classes, observed in that State (using the AADTT and the percentage shown in the State-specific version of table 19).

Different MEPDG runs are then performed for the class of vehicles being examined, with all inputs held constant, except that different RANALS are used as inputs. The RANALS developed in step 2 for that vehicle class are selected from the State's WIM data to represent the range of axle weight conditions those trucks are observed to carry in that State.

The output from the MEPDG is then used to determine the degree to which differences in observed axle loads for each vehicle class can change pavement analysis outcomes. When two RANALS for a given vehicle class produce "significantly different" pavement analysis results, the RPPIF values that represent those two RANALS can be compared. The difference in the RPPIF values between those two RANALS can be used to establish criteria for determining when two RANALS should be kept as part of two different Tier 2 NALS clusters. That is, if two RANALS produce significantly different pavement analysis outcomes, they are not "similar," and they should not be combined into the same group for computation of default NALS. The difference in their RPPIF values then becomes a measure that can be used to determine the size of required boundaries between Tier 2 NALS clusters.

Each State may select its own definition of "significantly different" MEPDG outcome. For example, a change in asphalt concrete or portland cement concrete thickness of ½ inch could be used as one measure of "significantly different." So when differences in load spectra do not produce a change in thickness equal to or greater than ½ inch, those load spectra are determined to be "similar." Another measure of significance could be a difference in predicted pavement service life greater than 20 percent.

By summarizing the RPPIF differences that resulted in significant differences in MEPDG outcomes for each class of truck, it is possible to produce a table such as table 20, shown in step 6 below. This table is then used as the criterion for when to stop the clustering process that produces Tier 2 NALS.

Step 6: Perform Cluster Analysis

The final step in the development of agency-specific default load spectra is the actual clustering of "similar" load spectra into a limited number of groups. This is best done with a statistical program such as SPSS, SAS, or similar programs.

The clustering of agency-supplied RPPIFs (computed in step 3 above for each site, vehicle class, and axle type) is controlled by the sensitivity of the pavement design process to traffic loadings. If State-specific sensitivity tests have been performed, use those results to control the clustering process. If no State-specific tests have been performed, use the values in table 20.

Table 20. Difference in RPPIF per axle likely to cause change in pavement performance

In the clustering process, the difference between the mean RPPIF for two nearest-neighbor clusters should not exceed the values in table 20. Thus, the cluster process should be stopped one step prior to the step when that distance is exceeded.

Once all clusters are identified, RANALS for the sites that belong to the same cluster should be averaged to compute default NALS representing that cluster group. This should be done for each vehicle class and axle type. For each computed average NALS, RPPIF and percentage heavy statistics should be computed and compared with the values in table 2 or a similar table defined by the agency. Based on these statistics, a name and/or code should be assigned to the NALS cluster, similar to the names/codes included in the first column of table 2. If more than one cluster is identified for the same loading category, then sequential codes should be assigned to these NALS. For example, if two NALS clusters for Class 9 tandems fall within the "heavy" (H) loading category, cluster codes H1 and H2 should be used. H1 should be used for the lighter of the two NALS and H2 for the heavier. A cluster that has a majority of sites for a given vehicle class and axle type should be selected as the default or "typical" cluster, and the letter code (T) should be added to the cluster code, for example, H1(T). All computed NALS should be saved to the database. Appendix B provides a data dictionary to facilitate appending State-defined Tier 2 NALS to the LTPP PLUG database.

DEVELOPMENT OF REPRESENTATIVE SITE-SPECIFIC AND DEFAULT AXLE-PER-CLASS COEFFICIENTS

Overview

The MEPDG requires users to specify the number of axles per truck type as a part of traffic inputs for pavement design and analysis. These values are used in the computation of total axle loading. These numbers are also called APC coefficients. The MEPDG procedure uses APC as a multiplier in the process of converting NALS to projected axle load spectra for use in pavement design.

APC values are required for each vehicle class and axle type. If a specific axle type is not used for a given vehicle class, then a zero value is entered as the APC for that axle type. One set of APCs is used per pavement design, representing the typical number of axles observed for each axle type for each vehicle class.

APCs are computed for each vehicle class and axle type by dividing axle load counts by vehicle volumes collected for the same periods of time and the same vehicle class. Because the MEPDG requires only one set of APCs per design, these values are computed based on the annual axle count and vehicle volume estimates.

Procedure to Develop Site-Specific and Default APC Coefficients

The following approach is recommended to compute a default set of APCs using the daily axle weight and vehicle volume data stored in database tables that are consistent with the LTAS DD_AX and DD_WT_CT tables:

1. Extract daily vehicle and axle count summaries from the LTPP LTAS DD_AX and DD_WT_CT tables for each site for the years and months that satisfy the data selection criteria of having data during at least 7 DOWs for each calendar month and at least 12 calendar months per site that pass the LTPP SPS TPF QC checks for data and WIM equipment.
2. Compute site-specific APC for each site (MEPDG Level 1 inputs) using the following procedure:
   1. Develop a list of all matching dates in the DD_AX and DD_WT_CT tables.
   2. For all matching dates, compute the total daily axle counts by class and axle type by summing axle counts reported in individual load bins. If no axle counts are found for a given axle type, vehicle class, year, month, and day while a non-zero volume is computed for the matching vehicle class, year, month, and day, enter 0 for the total axle counts for this axle type, vehicle class, month, and year.
   3. For all matching dates in DD_AX and DD_WT_CT tables, compute the total daily vehicle volumes by vehicle class for each month and year.
   4. For each day, month, and year that had non-zero total vehicle class volume, divide the total axle counts by the total vehicle volumes for each axle type and vehicle class. This step results in an APC for each axle type and vehicle class by day, month, and year.
   5. For each axle type and vehicle class, average the computed daily APC over all available days. This step results in site-specific APC for each axle type and vehicle class for a given site (MEPDG Level 1 inputs for individual site).
3. To compute a default APC based on all sites, average the site-specific APCs among all sites for each axle type and vehicle class. This step results in a global default APC for each axle type and vehicle class (MEPDG Level 3 input).

DEVELOPMENT OF DEFAULT AXLE SPACING AND WHEELBASE VALUES

Average Axle Spacing and Wheelbase for JPCP Model

Average axle spacing or wheelbase information is used for MEPDG applications involving the top-down slab cracking failure mode in JPCP. For this failure mode, the critical loading is caused by a combination of axles that place axle loads close to both ends of the same slab (in the direction of travel) at the same time. For JPCP designs with 15-ft-long slabs, axle spacings of between 12 and 15 ft would result in the axle loading positions most critical to development of top-down slab cracking. For JPCP with 20-ft joint spacings, the most critical axle spacings would be between 17 and 20 ft.

The current MEPDG top-down slab cracking model assumes that the majority of axle spacings that could induce top-down slab cracking are attributed to the wheelbase of the tractor (power) units in tractor-semitrailer combination trucks (FHWA classes 8 through 13). To account for these axles and axle spacings, the MEPDG directly considers the wheelbase of the tractor unit in the form of three inputs: the percentages of tractor units with short, medium, and long wheelbases. The MEPDG states that the percentage of trucks in each of these three categories should be based on the axle spacing distribution (or wheelbase) of truck tractors in Class 8 and above. The MEPDG recommends the following three-axle spacings or "tractor" wheelbase categories for analysis:

• Short - 12 ft.
• Medium - 15 ft.
• Long - 18 ft.

By default, the MEPDG software assumes an even distribution of short, medium, and long axle spacing occurrences: 33, 33, and 34 percent, respectively.

Axle spacing can be estimated based on a sample of per-vehicle records obtained for each of the LTPP WIM sites. One month of data for each WIM site is considered sufficient, unless it is a low truck volume site. This sample size is considered to be representative based on an evaluation of the consistency of the axle spacing measurements through the year.

Procedure to Compute Average Axle Spacing and Wheelbase

1. Extract axle spacing values from per-vehicle records by vehicle class for all the sites.
2. Filter records corresponding to the first axle spacing for classes 8 and above.
3. Determine ranges for short, medium, and long axle spacing relative to JPCP joint spacing values used by the agency, or use the MEPDG values of 12, 15, and 18 ft.
4. Compute percentages of the first axle spacing for classes 8 and above for each of the three categories referenced in step 3.

In addition, the MEPDG states that if other vehicles in the traffic stream have axle spacings in the range of the short, medium, and long spacing defined above, the frequency of those vehicles could be added to the axle spacing distribution of truck tractors. For example, if 10 percent of truck traffic is multiple trailers (Class 11 and above) that have trailer-to-trailer axle spacings in the "short" range, 10 percent should be added to the percentage of truck tractors with "short" axles. Thus, the sum of the percentages of trucks in the short, medium, and long categories can be greater than 100. "Short" spacing should not include multi-axle groups such as tandem, tridem, and quad in the computation.

Procedure to Compute Axle Spacing for Multi-Axle Groups

Axle spacing for multi-axle groups is the distance between the two consecutive axles of a tandem, tridem, or quad. Default axle spacing values can be computed based on averaging the values extracted from per-vehicle records for all the sites, using the following procedure:

1. Extract axle spacing values from per-vehicle records for all sites.
2. Filter records that have axle spacings of less than 8 ft for vehicle classes 4 through 13.
3. Review filtered records and identify multi-axle groups as follows:
   1. Mark two consecutive spacings of less than 8 ft each per record as tridem axles.
   2. Mark three consecutive spacing less than 8 ft each per record as quad axles.
   3. If there is only one spacing less than 8 ft in sequence per record, mark it as tandem axle.
4. Compute average axle spacing values among axles marked as tandem, tridem, and quad axles.

For tridem and quad axles, compute average axle-to-axle spacing.

USE OF AXLE LOADING DEFAULTS WITH DARWIN-ME

Currently, the DARWin-ME software contains the NALS defaults developed under NCHRP Project 1-37A. If the user wants to use NALS defaults generated based on SPS TPF data, there are four ways to enter these data into the Axle Distribution table in the DARWin-ME project file:

• Enter data manually.
• Import default NALS file in MEPDG (*.alf) format.
• Import default NALS file in an XML format.

The LTPP PLUG software provides the options of generating an axle load file in both the MEPDG (*.alf) format and the DARWin-ME XML formats for any of the default or site-specific NALS included in the LTPP PLUG database. Generated *.alf or XML files could be stored in a user-specified directory and uploaded in DARWin-ME using the data import option. *.alf files work with both NCHRP 1-37A and DARWin-ME software products.