Volume 1: Practical Guide, Final Report and Appendix A

Introduction

After the agency has defined the specification and developed the corresponding project-specific preconstruction output, the agency may then use the developed specification for acceptance. PRS-related contractor pay adjustments are then determined based on the actual samples taken from the as-constructed pavement lot (in accordance with the agency-defined AQC acceptance sampling and testing plan). This chapter describes the procedures to be used by an agency to determine Level 1 or Level 2 pay adjustments for a given as-constructed pavement lot.

Step 1: Dividing the As-Constructed Pavement Lot into Sublots

To judge the quality of the as-constructed in-place pavement lot, the agency must conduct sampling and testing in accordance with the previously chosen acceptance sampling and testing plan. (Note: The defined acceptance sampling and testing plan is determined in accordance with the guidelines presented in the section titled Selecting an AQC Acceptance Sampling and Testing Plan, in chapter 5 of this volume.) As a first step in the sampling of the pavement, the pavement lot is divided into sublots. Prior to the placement of any paving for the given lot, the agency must estimate the starting and ending stations of all of the sublots expected to be paved within that lot. These specific stations are determined by assuming sublot lengths equal to the chosen target sublot length (the target sublot length is determined in accordance with the guidelines presented in the section titled Selecting an Appropriate Target Sublot Length, in chapter 5 of this volume). An appropriate number of expected sublots are defined so that sublots are defined well past the expected lot length (see the section titled Definition of Lots and Sublots in chapter 5 of this volume).

Step 2: Determining the As-Constructed Acceptance Sampling Locations

The estimated sublot starting and ending stations allow the agency to determine random sampling locations prior to the placement of any pavement within the lot. For each AQC, the appropriate number of random sampling locations per sublot is identified by the agency in accordance with the guidelines presented in the section titled Recommended Number of AQC Samples Per Sublot, in chapter 5 of this volume. (Note: The chosen AQC sample types determine what sampling locations are required.) Specific sample locations are, therefore, determined based on the agency-chosen sample specimen types and in accordance with the guidelines presented in the section titled Selection of Random Sampling Locations, in chapter 5 of this volume.

Step 3: Conducting Lot Acceptance Sampling and Testing

Once the paving begins for a given lot, the actual sublot lengths are determined in accordance with the guidelines presented in the section titled Determining Actual Sublot Lengths in the Field, in chapter 5 of this volume. The appropriate sample specimens are taken at the random sample locations identified in the previous step. If replicate samples are taken at a given sampling location (e.g., three cylinders molded from a batch of concrete taken from one randomly selected longitudinal sample location), the replicate sample specimen testing values are averaged to give one AQC testing value representing the sample location. These sample location representative testing values are used to define the quality of the pavement lot.

Step 4: Determining the Overall Lot Pay Factor

The procedures used to determine an overall lot pay factor differ for Level 1 and Level 2 specifications. The Level 1 overall lot pay factor is computed using a chosen composite pay factor equation, while the Level 2 pay factor is based on a direct comparison of the simulated as-designed LCC mean and the estimated as-constructed LCC. The details of both of these procedures are described separately below.

Level 1—Determining the Overall Level 1 Lot CPF

If the Level 1 procedure is used to calculate the pay adjustment, the following steps apply:

Summarizing the As-Constructed AQC Acceptance Data for the Lot

The first step in calculating a Level 1 lot pay adjustment requires that the measured as-constructed AQC acceptance data be summarized for the entire lot. Therefore, all of the representative testing values (representing every sample location within the lot—all sublots are included) are summarized into one lot mean and unbiased standard deviation for each AQC. These AQC lot means and unbiased standard deviations are then used in the developed individual AQC pay factor curves and equations.

Computing the Individual Pay Factors for Each AQC

Individual pay factors are determined independently for each AQC based on the respective lot means and unbiased standard deviations computed in the previous section. For each AQC, the representative lot mean and unbiased standard deviation is used in the following step-by-step procedure to determine individual AQC Level 1 pay factors:

1. Compute the representative as-constructed AQC lot mean and unbiased sample standard deviation.
   
   
2. Identify the two regression equations that surround the AQC lot unbiased standard deviation. For example, if the AQC lot unbiased standard deviation for strength is 0.48 MPa, and regression equations have been developed for the cases of 0.00, 0.45, and 0.90 MPa, then the two equations surrounding the AQC lot unbiased standard deviation would be those represented by the 0.45 and 0.90 MPa.
   
   If the AQC lot unbiased standard deviation exactly matches one of the standard deviations used in the development of the regression equations, then that matching regression equation is used in step b. If the AQC lot unbiased standard deviation is larger or smaller than any of the standard deviations used to simulate the individual AQC pay factor curves, the agency must choose one of the following methods for acceptance.
   
   
   1. Choose the simulated AQC pay factor curve closest to the AQC lot unbiased standard deviation—i.e., if the AQC lot unbiased standard deviation for strength is 1.00 MPa, and regression equations had been developed for the cases of 0, 0.45, and 0.90 MPa only, the agency could choose to estimate the corresponding pay factor using the pay factor equation representing the closest standard deviation. Therefore, since 1.00 MPa is closest to 0.90 MPa, the pay factor equation developed for the case of standard deviation equal to 0.90 MPa would be used.
      
      
   2. Resimulate a pay factor regression equation for the case of the AQC lot unbiased standard deviation—i.e., if the AQC lot unbiased standard deviation for strength is 1.00 MPa, and regression equations had been developed for the cases of 0, 0.45, and 0.90 MPa only, the agency could choose to resimulate a pay factor equation for the case where the standard deviation is equal to 1.00 MPa.
      
      
3. Use the computed AQC lot mean in the one or two pay factor regression equations (identified in step b) to compute respective pay factors. If only one governing pay factor equation is identified under step b, then the computed pay factor (using that single equation) represents the individual AQC pay factor for the lot. If two pay factors are computed (one each using the two surrounding pay factor regression equations), then the individual AQC pay factor representing the lot must be determined using the interpolation procedures outlined in step d.
   
   
4. Use the AQC lot unbiased standard deviation to interpolate between the independent pay factors determined using the two surrounding pay factor regression equations. The interpolated pay factor is then used to represent the individual AQC pay factor for the lot. The representative lot pay factor is then interpolated using equation 22.
   
   AQC-PF_LOT  = PF_HIGH + (PF_LOW– PF_HIGH) *[(SD_HIGH – SD_UNB)/(SD_HIGH – SD_LOW)] (22)

     where

   AQC-PF_LOT  = Representative individual AQC pay factor, percent.
   
   PF_HIGH  = Individual AQC pay factor (for measured AQC lot mean) determined using the pay factor equation based on the larger of the two surrounding standard deviation values, percent.
   
   PF_LOW  = Individual AQC pay factor (for measured AQC lot mean) determined using the pay factor equation based on the smaller of the two surroundingstandard deviation values, percent.
   
   SD_HIGH  = Larger of the two surrounding standard deviation values.
   
   SD_LOW  = Smaller of the two surrounding standard deviation values.
   
   SD_UNB  = Computed AQC lot unbiased sample standard deviation.
5. Any agency-identified pay factor limits may be applied to the Level 1 individual AQC pay factors. The limited pay factors, therefore, become the representative AQC pay factors used to compute the overall lot CPF. Individual AQC pay factor limits shall be selected in accordance with the guidelines presented in the section titled Selecting Pay Factor Limits, in chapter 6.

Finally, this procedure is repeated so that representative individual AQC pay factors are determined for each AQC included in the specification.

Computing the Level 1 Lot CPF

For Level 1, the overall lot CPF is calculated using the specific CPF equation determined by the agency in accordance with the guidelines presented in the section titled Defining a Level 1 Composite Pay Factor Equation, in chapter 6. Just as with the individual AQC pay factors, the agency has the option to apply pay factor limits to the computed lot CPF. The limited CPF, therefore, is the representative CPF used to compute the overall lot pay adjustment. Any such lot CPF pay factor limits shall be selected in accordance with the guidelines presented in the section titled Selecting Pay Factor Limits, in chapter 6.

Level 2—Determining the Overall Level 2 Lot Pay Factor

If the Level 2 procedure is used to calculate the pay adjustment, the following steps apply:

Summarizing the As-Constructed AQC Acceptance Data for Each Sublot

The first step in calculating the Level 2 lot pay adjustment requires that the measured as-constructed AQC representative testing values be summarized for each sublot independently. The means of these AQC testing values are computed for each sublot and are then used to define the as-constructed quality of the pavement lot in the PaveSpec 2.0 software. The future performance and corresponding lot LCC's (over the agency-chosen analysis period) related to the computed AQC sublot means are determined using the PaveSpec 2.0 software. The total PW value of the predicted lot LCC's (LCC_CON) is used as the overall measure of quality for the as-constructed lot. The overall Level 2 lot pay factor is then computed as a function of this LCC_CON, the simulated as-designed LCC (LCC_DES), and the actual contractor bid price (BID_CONTRACTOR) using equation 3 in chapter 3.

As with the Level 1 CPF, the agency has the option to apply pay factor limits to the computed overall Level 2 lot pay factor. The limited lot pay factor, therefore, is the representative pay factor used to compute the overall lot pay adjustment. Any such lot pay factor limits shall be selected in accordance with the guidelines presented in the section titled Selecting Pay Factor Limits, in chapter 6.

Step 5: Computing the Lot Pay Adjustment

The total payment to the contractor for the as-constructed lot may be determined using equation 23.

Contractor Lot Payment  = BID_CONTRACTOR * (PF_LOT / 100) * LOT_LENGTH (23)

  where

Contractor Lot Payment  = Adjusted payment paid to the contractor for the as-constructed lot, $.

BID_CONTRACTOR  = Actual contractor bid price, $/km.

PF_LOT  = Representative overall pay factor for the as-constructed lot, percent. (Note: This is either the Level 1 lot CPF, or the Level 2 overall lot pay factor. This pay factor will take into account any pay factor limits identified by the agency.)

LOT_LENGTH = Measured actual as-constructed lot length, km.