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Publication Number: FHWA-RD-98-155
Date: FEBRUARY 1999

Volume 1: Practical Guide, Final Report and Appendix A

 
 

Introduction   

When developing a PRS for use in the field, the agency must make some important pay adjustment-related decisions. One of these decisions involves deciding whether to use Level 1 or Level 2 pay adjustment procedures. If the agency chooses to accept as-constructed pavement using Level 1 pay adjustment procedures, an appropriate lot composite pay factor (CPF) equation must be determined. Finally, the agency must determine how pay factors are to be limited when making final contractor pay adjustments. This chapter is designed to provide the agency with the information required to make these decisions.

 
 

Selecting a Pay Adjustment  Procedure (Level 1 or Level 2)   

The current revised PRS prototype specification allows the agency to choose from two different pay adjustment procedures (representing the two different PRS implementation levels). Level 1 is offered as a simplified (and, therefore, more immediately implementable) method of estimating the results obtained from Level 2. Table 9 reiterates some of the main differences between the two PRS implementation levels.

Table 9. Key differences between PRS Level 1 and Level 2 pay adjustment procedures.

Characteristic

Level 1

Level 2

Primary Method of Acceptance Testing

Current acceptance tests used by the agency.

In situ acceptance testing is recommended.

Included Acceptance AQC's

Only those AQC's (of the available five) historically measured by the agency for acceptance.

Any or all of the five AQC's available for inclusion in the PRS.

Preconstruction Output

Individual pay factor charts for each AQC. Each is developed assuming that the other AQC's are held constant at their target values.

One simulated overall as-designed lot LCC (reflecting the interactions between AQC's).

Overall Lot Pay Factor Method

Determined as a simple mathematical function of the individual AQC pay factors (CPF equation). This CPF estimates the pay factor obtained from the Level 2 direct simulation.

Determined directly through simulation of all AQC's. The closest simulation of actual field conditions.

It is strongly recommended that an agency gain experience with the current PRS approach using Level 1. Although the Level 1 pay factor is only an estimate of the computed Level 2 pay factor, at this time, the Level 1 approach is by far the most practical of the two approaches as it provides important preconstruction output desired by both the agency and the contractor. After gaining experience with the Level 1 approach, an agency may begin using the Level 2 approach or a combination of Level 1 and Level 2.

Defining a Level 1 Composite Pay Factor Equation

It is recommended that the governing CPF equation be a simple mathematical relationship of the independently determined AQC pay factors. A number of different simple equation forms are currently used by agencies to determine CPF equations. These same concepts may be used to determine CPF's using the Level 1 PRS approach. Four specific CPF equation forms are discussed in more detail in the following sections.

Weighted Average

The weighted average CPF method involves multiplying each calculated individual AQC pay factor by agency-chosen AQC weighting factors. Each of the AQC weighting factors is "determined through empirical observation or other engineering considerations," as stated in the AASHTO Implementation Manual for Quality Assurance.(28) Using this method, the resulting lot CPF is determined using equation 18.

CPFLOT  = å(PFn*Wn) / å(Wn)                                      (18)

  where

CPFLOT  = Calculated Level 1 lot CPF.

n  = Total number of AQC's included in the Level 1 specification (e.g., if the agency chooses to only include concrete strength and slab thickness, then n =2).

PFn  = Independently determined Level 1 pay factors for each of the n AQC's included in the Level 1 specification.

Wn  = Respective weighting factors for each of the n AQC's included in the Level 1 specification.

An example illustrating the weighted average method is as follows:

CPFLOT  = [å(PFn* Wn) / å(Wn)]

              = [543.5 / 5.3]

              = 102.5 percent

Table 10. Example calculations demonstrating the weighted average CPF method.

AQC

AQC number (n)

Individual AQC PF (PFn)

AQC PF Weighting Factor (Wn)

PFn* Wn

Concrete Strength

1

106.5

1.3

138.5

Slab Thickness

2

102.3

1.5

153.5

Entrained Air Content

3

98.5

1.0

98.5

Initial Smoothness

4

102.0

1.5

153.0

å(Wn) = 5.3

å(PFn*Wn) = 543.5

Note: PF = pay factor.

Simple Average Method

The simple average CPF method involves computing the average of the calculated individual AQC pay factors. The resulting lot CPF equation is computed using equation 19.

CPFLOT  = å(PFn) / n                                           (19)

  where

CPFLOT  = Calculated Level 1 lot CPF.

n  = Total number of AQC's included in the Level 1 specification.

PFn  = Independently determined Level 1 pay factors for each of the n AQC's included in the Level 1 specification.

An example illustrating the simple average method is as follows:

CPFLOT  = å(106.5 + 102.3 + 98.5 + 102.0) / 4
(409.3) / 4

=  102.3 percent

Summation Method

The summation CPF method involves summing the individual AQC pay adjustments (difference between the computed AQC pay factor and 100 percent). The resulting lot CPF equation is computed using equation 20.

CPFLOT  = å(PFn – 100) + 100                                     (20)

where

CPFLOT  = Calculated Level 1 lot CPF.

n  = Total number of AQC's included in the Level 1 specification.

PFn  = Independently determined Level 1 pay factors for each of the n AQC's included in the Level 1 specification.

An example illustrating the summation method is as follows:

CPFLOT  = å(PFn – 100) + 100
(106.5 – 100) + (102.3 – 100) + (98.5 –100) + (102.0 – 100) + 100

=  6.5 + 2.3 – 1.5 + 2.0 + 100

=  109.3 percent

Product Method

The product CPF method involves multiplying the individual AQC pay factors (expressed as decimals, e.g., 103 percent = 1.03). The resulting lot CPF equation is expressed in equation 21.

CPFLOT  = (PF1 * PF2* ………*PFn) /(100)n-1                    (21)

where

n  = Total number of AQC's included in the Level 1 specification.

PF1 to PFn  = 1 to n independently determined Level 1 AQC pay factors.

An example illustrating the product method is as follows:

CPFLOT  = (PF1 * PF2* ………*PFn) /(100)n-1
(106.5 * 102.3 * 98.5 * 102.0) /1003

=  109.5 percent.

Selecting an Appropriate CPF Method

The goal is to determine the overall lot CPF that represents the performance that actually occurs over time. The Level 2 PRS simulation gives the best available estimate of the true pay factor. Of the four CPF methods presented in this section, the product method has typically been found to most closely approximate this Level 2 pay factor. However, agencies are encouraged to choose an appropriate CPF method after conducting comparisons of the available CPF methods using the sensitivity analysis portion of the PaveSpec 2.0 software.

 

 

Selecting Pay Factor Limits   

Although the agency indirectly limits pay factors by defining appropriate MQL's for the quality of each AQC (see the section titled Retesting Procedures in chapter 5), an agency should also apply direct limits to the calculated individual AQC pay factors, the overall lot pay factor, or both. This pay factor limiting process is

Let's use the product method for illustration purposes. For the chosen example, all five AQC's are included in the specification. The assumed AQC pay factors for use in the example consist of the following:

The CPF for the lot (without applying any pay factor limits) is calculated as the following, using equation 21:

CPFLOT  = (PF1 * PF2* ………*PFn) /(100)n-1
(108.5 * 105.3 * 99.5 * 96.4 * 102.4) /1004

=  112.2 percent

The following sections show the different methods by which this calculated CPF of 112.2 percent may be limited.

Limiting the Overall Lot CPF

The agency may choose to limit the overall lot pay factor to an agency-chosen subjective value. For our example, let's assume the agency feels that it cannot pay more than 106 percent of the bid price due to budgetary limits. Therefore, the calculated lot CPF of 112.2 percent would be limited to the agency-chosen 106-percent value. For this case, the contractor would then receive a 6-percent incentive payment for the project.

Limiting Individual AQC Pay Factors

Another approach for limiting pay factors for budgetary purposes is to apply limits to the individual AQC pay factors. For our example, let's assume that each of the individual AQC pay factors is limited to 103 percent. Table 11 shows a comparison of the individual AQC pay factors and resulting overall lot CPF's for both cases of with and without applied AQC limits.

Table 11. Example of limiting individual AQC pay factors
(CPF calculated using the product method).

AQC

Individual AQC Pay Factors

Without Limits

All Limited to 103%

Concrete Strength

108.5

103.0

Slab Thickness

105.3

103.0

Entrained Air Content

99.5

99.5

Initial Smoothness

96.4

96.4

Percent Consolidation

102.4

102.4

Calculated Lot CPF

112.2

104.2

Using the 103-percent individual AQC limits, the overall lot CPF is then calculated to be 104.2 percent. For this case, the contractor would then receive a 4.2-percent incentive payment for the project.

 


The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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