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Publication Number: FHWARD98171 Date: FEBRUARY 1999 
Introduction 

Variation exists in all material and constructionrelated acceptance quality characteristics (AQC’s). The implementation of performancerelated specifications (PRS) requires considerable knowledge about the variability of these AQC’s. The goal of this specific investigation was to establish the "typical" variability associated with the AQC’s included in the PRS for concrete pavements. The information obtained from this study will provide guidance to agencies when selecting PRS target asdesigned variabilities.
A comprehensive literature search was conducted (described in appendix C) to identify previous studies where variations of concrete pavement AQC’s were reported and documented in an unbiased manner. The information was evaluated so that those AQC’s for which variability was not welldocumented could be targeted for field testing and evaluation. In order to establish additional information on typical levels of variation, a field testing program was developed for the identified AQC’s. Using the work plan developed for this investigation, data were collected from actual field construction projects. The specific AQC variabilities investigated during this research project include:
All testing was performed in accordance with standards developed by the American Society for Testing and Materials (ASTM). The information collected and analyzed during this research will help identify allowable tolerances for each of the investigated AQC’s. These tolerances are based on the observed variability limits contractors are currently able to achieve. The identified AQC tolerances may then be used by agencies to select appropriate AQC target standard deviations.
A detailed discussion of the field/laboratory investigations (including projects studied, sampling and testing procedures, data analysis procedures, and a summary of results for each of the targeted AQC’s) is provided in the following sections.
Discussion of Variance 
Because the PRS approach determines the performance of a pavement on a lot basis, the most important variability of interest for the procedure is the overall withinlot variability. The procedure assumes that the pavement lot quality is represented by AQC's that are normally distributed. Each AQC is measured by testing randomly selected samples located within the pavement lot. Each sample is the mean of all replicate test values obtained at the randomly selected sample location. All samples representing a given lot are assumed to estimate a distribution of the AQC. For each AQC, the value targeted during construction of the lot (specified by the governing agency) is the mean of the distribution. The tolerance value for each AQC (minimum acceptable value without penalty) allowed by the governing agency was determined during this investigation as the currently achievable withinlot variability. For each AQC studied in this investigation, the total withinlot variability was calculated as the standard deviation of all samples collected within the lot. If replicate values were used to represent the samples, the total withinlot variability was calculated using equation 10.
s_{TOTAL WITHINLOT} = s_{MEASURED WITHINLOT} * n^{0.5} (10)
where
s_{TOTAL WITHINLOT} = The total withinlot standard deviation for the AQC (materials/process and testing).
s_{MEASURED WITHINLOT} = The standard deviation between all representative samples in the lot. Each sample is the mean of all replicate test values obtained at the sample location.
n = Number of replicate test values obtained at each AQC sample location.
For each AQC required by the governing agency, the withinlot variability is an estimate of the total variability of the AQC over the entire lot. This total withinlot variability is comprised of testing variation and materials/process variation. The testing variation, or withintest variability, is a measure of the repeatability of a particular testing method. This variability is calculated as the standard deviation of the test values representing a sample for a random sample location. As long as the standard deviation is independent of the mean, it can be used to represent the variability of the AQC being evaluated. The materials/process variability represents the variation due to actual AQC pointtopoint material differences and process control. It is the difference between the total withinlot variability and the withintest variability.
The relationship of the components of variance is shown in equation 11.
s^{2}_{TOTAL WITHINLOT} = s^{2}_{WITHINTEST} + s^{2}_{MATERIALS/PROCESS} (11)
where
s^{2}_{TOTAL WITHINLOT} = The total withinlot variance for the AQC.
s^{2}_{WITHINTEST} = The estimated variance of the testing method (testing repeatability).
s^{2}_{MATERIALS/PROCESS} = The estimated variance of the materials and process (material variance).
Calculating Equivalent Variability
When implementing a PRS, it is important that the selected AQC target variabilities correspond with the sampling and testing methods being used during construction. Each of the AQC variabilities recommended in this report represents the variability associated with evaluating individual samples (comprised of one actual test value) within a given lot. If an agency elects to collect replicate test values to represent a sample (for example, three cast cylinders from the same sample location tested for 3day compressive strength), the variability must be adjusted using equation 12.
s_{TARGET} = s_{RECOMMENDED} / n^{0.5} (12)
where
s_{TARGET} = The targeted withinlot standard deviation for the AQC.
s_{RECOMMENDED} = The recommended withinlot standard deviation for the AQC (materials/process and testing).
n = Number of replicate test values obtained at each AQC sample location.
Identification of Field Projects 
To evaluate the variability of construction parameters achievable by the contractor, testing was performed on field construction projects during the 1995 and 1996 construction seasons. The project team established criteria for the field sites as follows:
The established criteria for the field studies limited the search to northern midwestern States. SHA’s were contacted and a testing schedule was planned. As projects were let, close contact with field engineers was required to schedule beneficial field visits to the projects. When possible, the field evaluations were conducted once the contractor had established a smooth, troublefree paving operation. It was desirable to work with several SHA's to collect data for this investigation. The construction projects selected for evaluation in this study were performed in Illinois, Iowa, Michigan, Minnesota, Nebraska, Ohio, and Wisconsin. A list of the specific projects, along with the construction parameters evaluated, is shown in table 45.
Project 
Project Type 
Acceptance Quality Characteristic 


3day Cyl. Compressive  3day Core Compressive  14day Cyl. Compressive  28day Cyl. Compressive  28day Core Compressive  3day Cyl. Splitting Tensile  3day Beam Flexural  14day Beam Flexural  28day Beam Flexural  Predicted 28day Flexural  Slab Thickness by Coring  Slab Thickness by GPR  Plastic—Before Paver  Plastic—After Paver  Hardened Linear Traverse  Joint Sawcut Depth  Consolidation Around Dowels  Longitudinal Tie Bar Depth  Initial Smoothness  
Rochelle, IL—IL Route 38 
New Construction 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 

Shawano, WI—Route 29 East 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 

St. Johns, MI—Route 27 North 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 

Ottumwa, IA—Route 23 South 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 
Ö 

Omaha, NE—I80 East & West 
Ö 

Ontario, Canada—Hwy 115 
Ö 
Ö 

Mankato, MN—U.S. 169 
Ö 
Ö 
Ö 
Ö 

Bellefontaine, OH—U.S. 33 
Ö 
Ö 
Ö 
Ö 
Ö 

Des Plaines, IL—Route 58 West 
Doweled Joint Patching 
Ö 
Ö 
Ö 

Benton Harbor, MI—I94 West 
Ö 
Ö 
Ö 

Philo, IL—Route 130 South 
Ö 
Ö 
Ö 
The typical field concrete strength variability was evaluated for use in both Level 1 and Level 2 PRS programs. Both PRS levels require strength to be inputted into the distress indicator models as a 28day flexural strength (thirdpoint loading). For a Level 1 PRS, this required strength value is typically determined directly using 28day flexural strength data from beams cast in the field and cured under standard laboratory conditions. The Level 2 PRS, however, is being investigated to evaluate the possibility of providing the contractor with a quicker indication of the 28day flexural strength results so that he may make material or method adjustments sooner. Therefore, methods used to estimate the 28day flexural strength based on early age flexural, compressive, or splittensile strength tests were also investigated. Historical Concrete Strength Data As discussed previously, the variance in any AQC is comprised of two sources. The first source of variance is "withintest" variance, commonly expressed as the standard deviation between test values obtained from the same sample location. The withintest standard deviation indicates the amount of variation among strength tests from the same batch of concrete and is an indicator of the quality of specimen fabrication, handling, curing, and testing procedures (overall testing repeatability). Flexural strength tests for almost 200 laboratory mixes conducted during the expansion of the Atlanta International Airport in the 1970's, and numerous mixes reported in other research studies, indicated average withintest standard deviations of 0.23 MPa and 0.27 MPa, respectively.^{(18)} The withintest standard deviations for the laboratory data were independent of flexural strength. The analysis of field data from the Atlanta International Airport projects indicated average withintest standard deviations ranging from 0.21 to 0.28 MPa with an overall weighted average of 0.24 MPa. The overall average is very close to the 0.23 MPa determined from laboratory mixes.^{(18)} Average withintest standard deviation for the field data was only slightly dependent on flexural strength. The second source of variance is the "materials/process" variance. This variance cannot be physically measured without incorporating "withintest" variance. Therefore, the total variance, commonly expressed as the "betweentest" standard deviation, is measured. The betweentest standard deviation indicates the variance between different batches of the same concrete materials (attributed to material and production quality control), as well as the testing repeatability described above. The average betweentest standard deviation for laboratory mixes reported for the Atlanta International Airport, and numerous mixes reported in other research studies, was 0.19 MPa.^{(18)} As with the withintest standard deviation, the betweentest standard deviation for the laboratory data was generally independent of flexural strength. The analysis of field data from the Atlanta International Airport projects indicated average 7day betweentest standard deviations ranging from 0.17 to 0.33 MPa, with an overall weighted average of 0.29 MPa. The standard deviations at 28 days ranged from 0.18 to 0.36 MPa, with an overall weighted average of 0.24 MPa. The overall average is very close to those determined from laboratory mixes.^{(18)} The average betweentest standard deviation for the field data was only slightly dependent on flexural strength. Theoretically, the betweentest (or total withinlot) variance should be greater than the withintest variance as shown by equation 11. However, often the computed betweentest standard deviation is less than the calculated withintest standard deviation. For the Atlanta International Airport study of concrete flexural strength data, Greer attributed this observation to the use of averages for the betweentest calculations and suggested that it indicated that a significant portion of the variation in flexural strength tests is the result of inherent variations in the test procedure.^{(18)} Within and betweentest standard deviations were examined in the laboratory in a previous PRS study.^{(1)} The flexural strength withintest standard deviation ranged from 0.02 to 0.31 MPa and averaged 0.16 MPa at 7 days for 18 different mixes. At 14 days, the withintest standard deviation ranged from 0.06 to 0.35 MPa and averaged 0.18 MPa. At 28 days, the withintest standard deviation ranged from 0.03 to 0.57 MPa and averaged 0.23 MPa at 28 days. On average, the standard deviation slightly increased from 7 to 28 days. Betweentest standard deviations for nine replicated mixes were 0.15, 0.18, and 0.25 MPa at 7, 14, and 28 days, respectively. Similar to other studies reported, the betweentest and withintest standard deviations are nearly identical. As with the withintest standard deviation, the betweentest standard deviation slightly increased with age. This conclusion differs from other studies that have concluded that standard deviations of flexural strength are generally independent of age. The standard deviation of interest in the PRS is the betweentest standard deviation because all samples within each lot are assumed to come from the same population. The literature study indicates that the average betweentest standard deviation determined from different laboratory studies ranges from 0.15 to 0.26 MPa and is not significantly influenced by strength magnitude (age). Based on the Atlanta International Airport field study, the average betweentest standard deviation ranged from 0.24 MPa at 28 days to 0.29 MPa at 7 days.^{(18)} As reported in the previous PRS research, a recommended reasonable betweentest standard deviation for use in the PRS (when flexural strength is directly measured) is 0.24 to 0.28 MPa. Field Investigation of the Typical Concrete Strength WithinLot Standard Deviation To verify the recommended variability of 28day concrete flexural strength for a Level 1 PRS, 152 x 152 x 533mm beams were molded in the field and transported to the laboratory curing room for a standard 28day lab moist cure (temperature of 23 °C and 100percent humidity). The 28day flexural strength results were directly evaluated for the total withinlot standard deviations after verifying that the standard deviation was independent of the mean. For all the lots evaluated, the total withinlot standard deviations were summarized and the average value was reported as the recommended target standard deviation to be used for a Level 1 PRS. For a Level 2 PRS, the research team investigated the ability to predict the 28day flexural strength from earlier age strength data using maturity concepts. With the additional error involved with using early age flexural, compressive, or splitting tensile strength data and indirectly projecting a 28day flexural strength, the possibility for greater variability was investigated. Early age fieldcast beam, core, and cylinder specimens were used with laboratorydeveloped interstrength relationships to predict the 28day flexural strength. The predictions were compared with actual fieldcast beams tested at 28 days to determine the accuracy of the prediction models. The variability of the predicted flexural strength data was then calculated as described above for the most accurate prediction model. Field Sampling and Testing Procedures For all the projects shown in table 45, fresh concrete was sampled at the paver in accordance with ASTM D 172, Standard Practice for Sampling Freshly Mixed Concrete. In general, concrete was sampled from the discharged material in front of the paver and transported by wheelbarrow to the casting location. Specimens were cast in accordance with ASTM C 31, Standard Practice for Making and Curing Concrete Test Specimens in the Field. After casting, the samples were kept shaded in a lowtraffic area and cured using wet burlap. The burlap was kept moist by occasional wetting until the specimens could be transported and placed in a standard laboratory curing room until testing. During transport to the laboratory facilities, the samples were packed in wet sand or water tanks. In addition to freshly cast specimens, cores were removed from each project in accordance with ASTM C 42, Standard Test Method for Obtaining and Testing Drilled Cores and Sawed Beams of Concrete. After removal, the cores were treated in the same manner as the freshly cast specimens until testing. All strength testing was performed in the laboratory in accordance with the following ASTM specifications:
Predicting 28day Flexural Strengths Based on Early Age Concrete Testing In order to predict the 28day flexural strength from early age strength data, the concept of concrete maturity was used in conjunction with laboratory strength development and interstrength relationship curves. Throughout the sampling and testing at each site, concrete temperatures were monitored using thermocouples embedded at the approximate center of a cylinder and a beam from each sampling location. A combination of temperature recorders and maturity meters were used to monitor the maturity of the concrete specimens in accordance with ASTM C 1074, Standard Practice for Estimating Concrete Strength by the Maturity Method. The method describes two alternative functions for computing the maturity of the concrete from a measured temperature history. The traditional NurseSaul function is used to calculate a temperaturetime factor, such as °CHrs, to represent the maturity of concrete and the Arrhenius function computes an Equivalent Age (Eq. Hr. at 20 °C) for the monitored concrete. Previous PRS research showed that when the maturity is calculated within laboratorymaintained temperature conditions, both methods result in equal accuracy.^{(3)} However, the Arrhenius equation can better represent the effects of temperature on strength development when wide temperature ranges are expected.^{(56)} Since relatively large temperature fluctuations were recorded for the projects included in this study, the Arrhenius maturity method was chosen. Maturity, rather than age, is used to estimate the inplace strength because of the effect of curing temperature on the strength development of concrete. For example, the 3day strength of fieldcured concrete may not equal the 3day strength of laboratorycured concrete from the same mix. Using maturity instead of age considers the effect of different curing temperatures, which results in more accurate estimations of inplace strength. To minimize errors in calculating the maturity of the field specimens, during transport to the laboratory facilities, the samples were packed in wet sand or water tanks and the temperatures were continuously recorded. Once in the lab, prior to testing, the samples were kept in a moistcuring room where the temperature and humidity are maintained at 23 °C and 100 percent, respectively. To predict the 28day flexural strength at a significantly earlier age, the method of developing mixspecific strength interrelationships outlined in previous PRS research should be used.^{(1)} Strength development and interstrength relationship curves (specific to the chosen concrete mix) are developed in the laboratory prior to construction. This can easily be incorporated in the initial stages of a project by the testing laboratory contracted to develop the concrete mixture design. After obtaining adequate amounts of the coarse and fine aggregates, cement, flyash, and admixtures to be used for the production of the field trial concrete pavement, concrete beam and cylinder specimens are cast in the laboratory in accordance with ASTM C 192, Standard Practice for Making and Curing Concrete Test Specimens in the Laboratory. The maturity of the samples is measured over the curing period and samples are tested for flexural strength (thirdpoint loading) and compressive strength or splitting tensile strength (depending on the chosen strength testing type) at incremental ages of strength development. The number of testing ages should be sufficient to enable the user to predict strength from maturity. As a minimum, it is recommended that tests be conducted at strength development ages of 1, 3, 5, 7, 14, and 28 days. If possible, it is also recommended that testing ages be extended past 28 days to ensure that the field maturity at the time of coring falls within the range from which the maturity prediction equation was developed. Equations representing the strength development (maturity) and interstrength relationship curves are derived from the average strength test data. Simple regression equations are recommended for predicting strength as a function of Arrhenius maturity. For the regression analysis, dependent and independent variables are used directly and transformed using square root, logarithmic, and inverse transformations. In general, the equation with the highest R^{2} represents the best interstrength model; however, the derived curve should be plotted against the average strengths to evaluate the accuracy in predicting the desired 28day strength. Since predicting early age strength values is of less interest, sometimes a curve with a slightly lower R^{2} provides greater accuracy in predicting the 28day strength. After the equations are derived, they can be used to predict 28day flexural strengths based on early age field strength data. An example of this procedure is illustrated graphically in this section. Figures 39 and 40 show hypothetical laboratory strength development and interstrength curves (where compressive strength is the chosen strength type). Early age field test data can be plotted on the laboratory strength curve according to the measured field maturity, as shown in figure 41. Invariably, there will be a strength difference between the plotted field data point and the laboratorydeveloped strength curve. This difference is used to adjust the laboratory 28day compressive strength from the derived curve equation to a predicted field 28day compressive strength, as shown in figure 42. Once the 28day field compressive strength has been extrapolated, the interstrength relationship between compressive and flexural strength can be used to predict the field flexural strength. This step is shown graphically in figure 43.
Concrete Strength Field Data Collection For two of the new construction projects (Shawano, WI, and St. Johns, MI), the total withinlot variability was evaluated by sampling four cylinders each from five different trucks. Two of the four cylinders from each truck were used to establish 3day compressive strength, and the remaining two were used to establish 3day splitting tensile strength (in accordance with ASTM standards). These early age cylinder strengths were used in conjunction with the laboratorydeveloped strength curves to predict the 28day flexural strength of the sublots. Two beams were also cast from each of the five trucks. The beams were tested for 28day flexural strength. These actual 28day flexural strengths served two purposes in the study. First, the data were used to evaluate the typical variability in 28day flexural strength currently achievable in the field for use in a Level 1 PRS. Second, the data were used to evaluate the accuracy of the predictions obtained from the early age cylinder strength data. The results are presented in the following section. The Ottumwa, IA, project (also used as the original shadow field trial under this research project) was divided into three lots. Lot 1 was subdivided into three sublots, and Lots 2 and 3 were each divided into four sublots. From each sublot, the material from two trucks was sampled at two different longitudinal sampling locations. For the purpose of evaluating the total withinlot concrete strength standard deviation, the average strengths at each longitudinal sampling location in a lot (regardless of sublot divisions) were used to calculate the total withinlot standard deviation. Therefore, for this investigation, Lot 1 was comprised of six representative samples and Lots 2 and 3 each had eight representative samples. At each sampling location, six cylinders and six beams were cast. As in Shawano and St. Johns, two cylinders from each truck were used to establish the 3day compressive strength for that sample. However, additional cylinders were cast to determine the 14 and 28day compressive strength (two cylinders each) variation. Also, while a 3day early prediction model is preferred, a 14day prediction model was investigated to quantify the increase in accuracy in predicting the 28day flexural strength. The six beams per truck were used to evaluate the variability in flexural strength at 3, 14, and 28 days, as well as to provide a comparison for determining the accuracy of the 28day prediction models. In addition, two cores were removed from each sublot (one from each longitudinal sampling location) to evaluate the feasibility of predicting the 28day flexural strength from 3day core compressive strength. Maturity meters were left in the field to monitor thermocouple trees embedded in the pavement. Thermocouples monitored the temperature at the middle of the pavement slab. Two additional cores were removed from each sublot (one from each longitudinal sampling location) to measure the 28day in situ core compressive strength of the pavement. The withinlot variability of the core compressive strength data was evaluated. As shown in table 45, additional 28day strength data were collected from other projects evaluated during this investigation. Both 28day cylinder and core compressive strength data were obtained from the Rochelle, IL; Mankato, MN; and Bellefontaine, OH, projects. The data were included in the variability study as a point of interest because they were readily available; however, since flexural strengths were not measured at these projects, the collected strength data were not included in the study used to determine typical flexural strength standard deviations. Summary of Concrete Strength Variation Results Collection of Strength Variability Data Under the current PRS approach, the agency may base performance on any combination of the available AQC’s (concrete strength, slab thickness, entrained air content, initial smoothness, and percent consolidation around dowels). The PRS computer software, PaveSpec 2.0, is used to simulate the expected performance and associated lifecycle costs (LCC’s) for the pavement. Therefore, the PRS approach requires accurate, achievable target standard deviations for each of the chosen AQC’s. Current distress indicator prediction models (used to evaluate the fatigue performance of the concrete pavement) require knowledge of the 28day flexural strength. The standard deviation of this flexural strength is, therefore, important when calculating the LCC of a particular pavement lot. The most direct method for measuring the 28day concrete flexural strength is from beam specimens cast in the field. The specimens are labcured for a 28day period and tested in accordance with ASTM C 78 to obtain the 28day thirdpoint modulus of rupture. Thus, the asconstructed mean and standard deviation of the 28day flexural strength can be obtained directly. The field sampling and test methods are already being performed by SHA's to evaluate newly constructed pavements. Therefore, one objective of the current research project was to determine a recommended asdesigned target standard deviation for 28day beam flexural strength testing. For each of the construction project lots investigated, 28day flexural strengths were directly measured and evaluated to determine the representative total withinlot standard deviation (as described in the section Discussion of Variance). The variability of flexural strength was also evaluated at 3 and 14 days. In addition to the investigation of flexural strength, the variability of 3, 14, and 28day cylinder and core compressive strengths was evaluated. The variability of 3day splitting tensile strength was determined based on data collected from two projects (Shawano, WI, and St. Johns, MI). For each strength type (compressive, splitting tensile, and flexural), the data were summarized into the age/sample categories (e.g., 3day core, 14day beam) shown in table 46. For each category, lot statistics, including the total withinlot standard deviation, were summarized. The overall goal of the investigation was to recommend a target asdesigned variability for input into the PaveSpec 2.0 program. Therefore, for each strength category, the standard deviations computed for each investigated lot were assumed to be normally distributed. The mean standard deviation was then determined to be the recommended target standard deviation. The results are shown in table 47. Table 46. Summary of the measured total withinlot concrete strength variations.
Currently, there is a move toward computing concrete strength pay factors based on 28day flexural strengths predicted from early age concrete strength data. Eventually, it is envisioned that the predictions will be made from in situ (and even nondestructive) testing procedures. However, current research efforts focus on basing the predictions on early age strength data obtained using conventional sampling and testing methods. Curves representing the laboratory strength development and interstrength relationships for each of the three construction projects evaluated (Shawano, WI; St. Johns, MI; and Ottumwa, IA) are shown in figures 44 through 57. Also shown in the figures are the field sample test results for each project. The interstrength relationship curves were developed by plotting different strength measurements (flexural versus compressive or flexural versus splitting tensile) over equivalent maturity intervals. For the Shawano and St. Johns projects, interstrength relationships were plotted over equivalent time intervals. Based on the results of these two projects and because the Ottumwa project was also being investigated as the original field trial, it was necessary to omit the evaluation of the accuracy of the splitting tensile strength prediction for this project. Linear regression equations for the bestfitting curves through the data points were also developed, as shown in table 48.
Table 48. Strength development and interstrength relationship regression equations.
Once the strength and maturity standards were developed in the laboratory, they were used in the field to predict the 28day flexural strength for input into the PaveSpec 2.0 program. For the Shawano and St. Johns projects, the flexural strength was predicted from 3day compressive and 3day splitting tensile strength test data. Figures 58 and 59 show the predicted versus measured 28day flexural strength data for these respective prediction models. In the compressive strength model, the measured 3day cylinder strengths were first extrapolated to 28day cylinder strengths using maturity concepts, and then converted to 28day flexural strengths using the laboratory interstrength relationships provided in figures 44 through 53. For the splitting tensile strength model, a better prediction was achieved by first converting the 3day cylinder strengths to 3day flexural strengths, and then extrapolating to a 28day flexural strength using maturity concepts. The accuracy of these two prediction procedures was evaluated by comparing the standard deviations of the differences between predicted and measured values. The core compressive strength model, with a standard deviation of 0.13 MPa, resulted in a higher prediction accuracy than the cylinder splitting tensile strength model, with a standard deviation of 0.36 MPa. Based on these results, attention was focused on compressive strength as the early age strength predictor for the Ottumwa project. Also, because this investigation was being used to evaluate the feasibility of accurately predicting the 28day flexural strength at an acceptable earlier age, it was decided that two sampling ages would be attempted from which predictions would be made. It makes sense that the closer the sampling gets to the 28day age, the more accurate the prediction should be. Therefore, it was decided to attempt predictions from 3 and 14day compressive and flexural strengths. While the splitting tensile strength predictor was not evaluated for the Ottumwa project, early age beams were tested to evaluate the possibility of eliminating the error involved in converting from compressive to flexural strength.
The average predicted 28day flexural strengths (for all of the different investigated prediction methods) are plotted versus the average measured 28day flexural strengths in figures 60 through 66. Also, the average percent errors, and the standard deviations of the differences between predicted and measured values for each prediction model evaluated, are summarized in table 49. As shown in table 49, the most accurate prediction of 28day flexural strength was based on the 28day compressive strength estimated from a 3day cylinder compressive strength (this method had the lowest average prediction error of 2.32 percent). It is believed, based on data collected during this and previous PRS studies, that the core compressive strength also accurately predicts the 28day flexural strength. While the core prediction models slightly overpredicted the 28day beam flexural strengths (as shown in figure 63), the cores were not necessarily removed from the same batch of concrete from which the beams and cylinders were sampled. After the concrete was sampled for the fabrication of beams and cylinders, the paver blended several batches (or loads) transversely across the pavement width. This incorporates any material variability into the core prediction model. However, based on the study of coretocylinder strength ratios (discussed in appendix E), the core models probably predict the flexural strength of the blended batches as accurately as the cylinder models predict the flexural strength of the same batch of concrete.
Table 49. Summary of accuracy indicators for the 28day flexural strength prediction models.
A brief evaluation of the American Concrete Institute (ACI) conversion equation was also performed. Simply converting a 28day compressive strength to a 28day flexural strength using the mixspecific relationships developed in the laboratory resulted in a conversion error of 4.2 percent. For comparison, using the compressiveto flexural strength conversion suggested by ACI 318 (MR = 7.5 * [f'c]^{0.5}), the conversion error was 16 percent.^{(57)} The 7.5 multiplier does not accurately convert compressive to flexural strength for all data sets. The multiplier was backcalculated using measured compressive and flexural strength data from specimens sampled from the same batch of concrete during the Ottumwa field investigation. The most accurate multiplier to use in the square root conversion equation is 9.00, as recommended by the Portland Cement Association in the publication Slab Thickness Design for Industrial Concrete Floors on Grade.^{(58)} It was found that for samples cured for at least 4 days, age had little effect on the multiplier. Calculated multipliers for beams and cylinders cast in Ottumwa at ages 4, 14, and 28 days were 9.14, 9.11, and 8.94, respectively. Using 9.00 as the multiplier in the equation reduces the error in the 28day conversion to 2.6 percent. While this prediction error is better than that produced using the mixspecific relationship developed for the project, the mixspecific relationship included data at 1 and 3 days. At very early ages, the data seem to indicate a trend toward a somewhat lower multiplier. Figure 67 contains a plot of the backcalculated multipliers versus testing age for each of the three investigated projects. Using the multiplier backcalculated from early age strength data resulted in an average prediction error of 11 percent.
For a total of 30 sampling locations, the 3day cylinder compressive strength translation method (3day cylinder f'c ® 28day f'c ® 28day MR) predicted the 28day flexural strength with the greatest accuracy. While it was anticipated that better predictions would result from 14day compressive strength or early age flexural strength (eliminating strength conversion error) data, increased variability in the data inhibits the accuracy of these prediction models. Further work is needed to investigate these discrepancies; however, predictions made from 3day cylinder compressive strength samples would give the contractor earlier feedback so that alterations could be made as quickly as possible. Using the most accurate translation method (3day cylinder f'c ® 28day f'c ® 28day MR), the resulting 28day flexural strengths were evaluated to recommend a target standard deviation for use in the PRS method. The 28day flexural strength standard deviations (using the 3day cylinder f'c ® 28day f'c ® 28day MR translation method) are presented in table 50 for different numbers of replicate specimens per sampling location. (Note: The recommended 28day flexural strength standard deviations shown in table 50 are approximately equal to those presented in table 47.) Table 50. Recommended concrete strength target standard deviations.

Few reports were found in the literature review that specifically addressed the variation of slab thickness. One report that compiled the results from several field studies did recommend that a pointtopoint standard deviation of 8 mm be used in design.^{(8)} For the current research study, the investigation of slab thickness variation consisted of examining cores removed from new pavement and rehabilitation construction projects. Also, because the industry is shifting toward nondestructive testing techniques, thickness data were obtained using GPR equipment. The standard deviations of withinlot GPR thickness measurements were also determined. Field Investigation of the Typical Slab Thickness WithinLot Standard Deviation For each of the project sites investigated during this study, a significant number of cores were removed to evaluate characteristics such as hardened entrained air content, concrete strength, and percent consolidation around dowel bars. Fulldepth cores were removed for these cases, so an evaluation of the slab thickness withinlot variation was completed using the measured thickness of each of these cores. Additional data were obtained from an historical project in Ontario, Canada (Highway 115), and other research projects (as shown in table 45).^{(34)} For three of the investigated projects (Rochelle, IL; Mankato, MN; and Bellefontaine, OH), thickness was also determined using GPR. Radar traverses were made at distances of 0.46, 1.37, 2.29, and 3.20 m from the centerline of the pavement. Thickness was evaluated at 3.05m intervals along these traverses for each sublot. Summary of Slab Thickness Variation Results The slab thickness variability evaluated for all projects is summarized by lot in tables 51 and 52 for drilled core and GPR data, respectively. Recommended average withinlot standard deviations are computed using an analysis of variance of the standard deviations obtained from each lot studied. As shown in table 51, for drilled cores without replicates (n = 1), the recommended mean withinlot standard deviation was computed to be 8.03 mm. This standard deviation matches the previous recommendation by Darter for portland cement concrete (PCC) pavement design, as well as values published by Yoder and Witczak for new highway construction.^{(8,59)} Table 53 presents a comparison of the average standard deviations determined under this investigation with typical ranges given by Yoder and Witczak for various pavement thicknesses. Table 51. Summary of withinlot slab thickness standard deviations based on drilled core data.
Table 53. Comparison of average slab thickness standard deviations for different design thicknesses.
The data obtained by the GPR surveys yield a slightly higher average withinlot standard deviation of 9.5 mm. The higher variability recommended for the GPR as compared to drilled cores is probably due to a significantly higher number of thickness readings within each lot. Thickness variation is a function of the grade control, base preparation and protection, and elevation control lines for the paver. For the new highway projects studied, these factors are generally tightly controlled by the contractor. For smaller projects, such as city streets, the factors affecting slab thickness may not be controlled as carefully. This may lead to greater variation, as suggested by Yoder and Witczak, who report a typical city street standard deviation range of 14 to 22 mm.^{(59)}
In situ entrained air content and associated air void system parameters can affect concrete durability. A model (developed from laboratory test data) for determining the percentage of joints exhibiting spalling/scaling as a function of air void system parameters was established in the preceding PRS study.^{(3)} Two alternatives were recommended for incorporating in situ properties: incorporating air content measured directly from concrete in the plastic state using an air pressure meter, or using air void system parameters measured from linear traverse testing of cores. Commonly, when the air content exceeds minimum recommended percentages, the remaining air void system parameters also exceed recommended minimum standards. Historical Entrained Air Content Data Very little historical data were readily available on the typical withinlot standard deviation of in situ air void system parameters (air content, void spacing factor, specific surface, voids per mm). However, one interesting source of data on the variation of air content was the American Association of State Highway Officials (AASHO) Road Test, in which cores were retrieved and tested for entrained air content. Hardened and plastic concrete air content data from the Road Test are illustrated in figure 68.^{(60)} Plastic concrete air content data obtained from the Illinois Department of Transportation (IDOT) database are summarized in table 27 (in appendix C). Overall standard deviations from both data sources ranged from 0.32 to 1.13 percent. Although some studies have reported inconsistencies between plastic and hardened air contents, on average, there was not a significant difference in standard deviations measured for these data sets. Average standard deviations measured in the plastic and hardened state were 0.52 and 0.57 percent, respectively. The weighted average for the data was 0.54 percent. There is no significant trend between standard deviation and average air content, suggesting that air content variability can be represented by the standard deviation, rather than by the coefficient of variation.
The air content variations determined in the AASHO and IDOT research were computed from a significant number of tests. Presumably, the data cover multiple sublots placed on multiple paving days. However, using the weighted average of 0.54 percent may not be realistic for use in a PRS where smaller lots (comprised of a maximum of one day’s production) are of interest. Inherent multiday material or batching variability is included in the 0.54 percent weighted average. For the PRS, the variation of interest is the withinlot standard deviation. Field Investigation of the Typical Entrained Air Content WithinLot Standard Deviation Plastic and hardened air content testing was conducted at new pavement construction projects in order to evaluate the standard deviation of entrained air content representative of individual lots (considered to be one day of paving). Fresh concrete retrieved from before and after the paver was tested at each of the three projects where flexural strength standard deviation was determined. Cores were removed from locations where before and afterpaver plastic air contents were measured. The cores were used to determine the hardened air content properties of the concrete (via linear traverse testing). Field Sampling and Testing Procedures To evaluate the variation in the measurement of plastic air content, fresh concrete was sampled at the paver in accordance with ASTM D 172, Standard Practice for Sampling Freshly Mixed Concrete. Concrete was sampled from the discharged material in front of the paver (at each randomly selected longitudinal sampling location) and transported by wheelbarrow to the testing location. The air content of the concrete was measured in accordance with ASTM C 231, Standard Test Method for Air Content of Freshly Mixed Concrete by the Pressure Method. When possible, a sample of concrete was removed from the same location after the paver had distributed, vibrated, and finished the plastic concrete. In general, due to safety concerns (as well as to protect the slipformed edge), the contractor would not allow research personnel to retrieve the concrete from behind the paver. However, the finishers retrieved the samples by shovel from approximately 0.61 m from the pavement edge. The void left in the finished pavement was replaced with fresh concrete and finished by hand. Because the samples were retrieved from the wheelpath where smoothness was measured, the contractor would not allow an equal number of tests to be performed after the paver. However, enough data were collected so that significant conclusions could be drawn. The literature review indicated that several studies report a significant difference between air contents measured in the plastic and hardened states. In general, no data were reported on the variability between the plastic and hardened states. Nagi and Whiting investigated possible factors that may affect the discrepancies in entrained air content measurements.^{(25)} Based on their research, it was concluded that, although discrepancies almost always exist, they are not consistent, and if the testing is performed in accordance with ASTM procedures, the discrepancies should be minimal. To evaluate any differences between the measurement of plastic and hardened air content, cores were sampled at selected plastic concrete points for comparison. Hardened air void system parameters were established in accordance with ASTM C 457, Standard Test Method for Microscopical Determination of Parameters of the Air Void System in Hardened Concrete. The linear traverse data were also used to establish the typical withinlot standard deviation of hardened concrete air void system parameters for possible use in the PRS approach. Summary of Entrained Air Content Results Entrained Air Content Standard Deviation The typical plastic entrained air content withinlot standard deviations were computed and summarized in table 54. The table includes the results of data obtained from concrete sampled before and after the paver. As with the withinlot concrete strength standard deviations, each entrained air content withinlot standard deviation is computed using all of the representative sample values obtained from the lot. The recommended typical standard deviations are also given as a function of the number of replicate tests used (as discussed previously).
When the plastic air content was measured on concrete sampled from behind the paver, the recommended standard deviation was 0.78 percent. In this study, no replicate measurements were taken on concrete sampled after the paver. Very little published information exists on the variation of hardened air void system parameters (measured using the linear traverse technique on cores removed from the pavement). Therefore, as part of the field investigation, cores were removed from a number of projects to evaluate the variation of each air void system parameter. The resulting recommended total withinlot standard deviations for entrained air content, void spacing factor, specific surface, and voids per mm are presented in tables 55 through 58. Table 59 contains an overall summary of the withinlot standard deviation information (using all of the data collected from all projects) for each air void system parameter.
Table 58. Summary of withinlot voids per mm standard deviations (linear traverse testing data).
A particularly interesting result of the entrained air content variation research is the relationship between plastic entrained air content measurements taken before and after the paver. The plastic entrained air content was measured before and after the paver at 50 sampling locations. The results indicate that, on average, the consolidation and finishing action of the paver reduces the entrained air content of the plastic concrete by approximately 0.7 percent when measured using an air pressure meter (see figure 69).
Plastic versus Hardened Entrained Air Content Relationship Another interesting result of the entrained air content variability research involved the relationship between plastic and hardened entrained air contents of material taken from approximately the same location. Cores were removed for linear traverse analyses from 26 locations where the plastic concrete air content was measured before the paver. Unfortunately, the plastic concrete was only sampled after the paver from 16 of these locations. The collected data are plotted in figure 70.
According to this data, measuring the entrained air content by linear traverse yields a measurably higher value than that obtained using a plastic concrete pressure meter. On average, the difference for the projects evaluated was 2.4 and 1.4 percent greater than plastic concrete sampled before and after the paver, respectively. This result agrees with previous research which concluded that the hardened entrained air content was 2.0 percent higher than the plastic entrained air content.^{(61)} Mielenz attributed the difference to the dissolution of air from small bubbles and its release into larger bubbles. Various hypotheses have attempted to explain this observation, including an inability of the pressure meter to measure very small entrained air bubbles, addition of retempering water after plastic air tests have been completed, and the use of particularly sensitive airentraining admixtures. However, Nagi and Whiting performed extensive testing and concluded that retempering and admixture type have little effect on the discrepancy between plastic and hardened air contents.^{(25)} In a paper published in the ACI Journal in 1983, Burg stated that the air content of hardened concrete should be higher than that of fresh concrete.^{(62)} Burg hypothesized that:
Numerous studies of initial smoothness measuring error and variability were cited in the literature. The construction process, concrete temperatures, curing procedures, subgrade and pavement stiffness, and rainfall can lead to differences in initial pavement smoothness. Variation sources include betweenpath, betweendevice, betweenoperator, withindevice (repeatability), and withinoperator (repeatability). Under the PRS approach, it is assumed that one device and one operator are used to establish sublot initial smoothness within each wheelpath. The total withinlot variation of interest in a PRS would, therefore, include variation expected from testing different wheelpaths, withindevice repeatability, withinoperator repeatability, and the actual variation of the pavement smoothness. One study examined withindevice repeatability using four different profilographs and four different operators.^{(30)} Tests were conducted for two different initial smoothness levels. All four devices were repeatable within 24 mm/km and 32 mm/km on the smoother and rougher wheelpaths, respectively. The replicate root mean square calculated for the smoother wheelpath was 8 mm/km; and for the rougher wheelpath, it was 10 mm/km. Initial smoothness of concrete pavements is generally assessed using a Californiatype profilograph. Because of its widespread use and acceptance, the Californiatype profilograph is recommended for use in the PRS. However, it is important to recognize that there are both manual and automated versions of the Californiatype profilograph, and the characteristics and variability of each are different. The withintest variability of noncomputerized (manual) profilographs is a function of the pavement smoothness. Variability increases as smoothness decreases. This increase is attributed to increased subjectivity associated with more active output traces. For new construction, the standard deviation of noncomputerized profilographs generally ranges from about 8 mm/km to about 32 mm/km. An approximate rule of thumb is that the variability is generally about 1/10 of the recorded profile index. For example, if the profile index is 158 mm/km, the corresponding standard deviation is 16 mm/km. Withinoperator variability associated with manual trace interpretation and reduction was also determined. Eight traces were interpreted two times by four different operators. The replicate root mean square calculated for the four operators was 21 mm/km. The variability of computerized (automated) profilographs does not vary as much with pavement smoothness, presumably because of the more uniform and consistent application of interpretation rules. Generally, the variability of the initial smoothness from computerized systems is between 16 and 32 mm/km. The variation of interest for the PRS is the withinlot standard deviation of initial pavement smoothness measurements (profile indices). As with the other AQC’s studied, this total variability includes withintest (device and operator repeatability) and materials/process (actual deviations in smoothness) variabilities. The overall variability for use in the PRS was calculated as the standard deviation of all representative sample smoothness values recorded within the lot. If replicate measurements are collected (repeated profilometer trace location, such as a wheelpath), the replicate values are averaged into a representative sample value. Additional initial smoothness data (measured with a California profilograph) were obtained for all of the PRS shadow field trial projects, as well as those archived projects used in the comparison of actual to PRS pay adjustments (see chapter 5 of volume II). Data were also included from one additional project used in a recent NCHRP study on pavement smoothness.^{(63)} Data were collected for a total of 11 projects made up of 52 separate lots. The data for 6 projects (33 lots) were reduced using a 5.1mm blanking band, while the remaining 4 projects (19 lots) were reduced using a 0.0mm blanking band. The data are analyzed separately for each blanking band setting. Summary of the Initial Smoothness Variation Results A summary of the collected initial smoothness data reduced using a 5.1mm blanking band is presented in table 60; table 61 contains a summary of the collected initial smoothness data reduced using a 0.0mm blanking band. Plots showing the distribution of computed withinlot standard deviations for the data reduced using both blanking bands are presented in figures 71 and 72. The recommended average target withinlot standard deviation (for initial profile indices reduced using a 5.1mm blanking band) was computed to be 27.1 mm/km, while the recommended value for the 0.0mm blanking band data was 49.9 mm/km.

A recent study sponsored by the Ontario Ministry of Transportation measured the depth of sawing on 40 cores taken across the longitudinal joint.^{(34)} Sawcut depth ranged from 33 to 67 mm, with a standard deviation of 9 mm. The average and specified sawcut depths were 54 mm and 66 mm, respectively. Sawcut depth data for one project using an abrasive sawblade were also reported in a recent FHWA study of sawcutting.^{(35)} Sawcut depth for 22 transverse joints averaged 91 mm, with a standard deviation of 8 mm. For the 22 longitudinal joints measured, sawcut depth averaged 94 mm, with a standard deviation of 6 mm. Factors influencing sawcut depth variability include blade type and the operator’s experience. In general, two types of sawblades are used to cut joints in PCC pavements—abrasive and diamondimpregnated. Abrasive blades tend to wear as the saw progresses along the pavement. An experienced operator will pay attention to the wearing of the blade and make adjustments in the saw as necessary. If the operator lacks experience, the blade will gradually wear and the joint depth becomes shallower as the saw progresses along the pavement. Diamondimpregnated blades don’t wear as the abrasive blades do; however, operator inexperience may affect the initially established blade depth, or allow the saw to rise, as opposed to cutting the full depth intended. Sawcuts deeper than the target depth may result in loss of load transfer at nondoweled transverse joints. It is assumed that sawcut depth does not significantly affect the performance of doweled pavements, since the deflectionreducing benefits of dowel bars are much greater than the contribution from aggregate interlock. Field Investigation of the Typical Sawcut Depth WithinLot Standard Deviation Sawcut depths were recorded on four new construction projects, as shown in table 45. The data from the Ontario study were also included in this investigation.^{(34)} At the new construction projects, the joint depth was measured directly using a thin steel rule. The withinlot sawcut variation was evaluated for both transverse and longitudinal joints. For transverse joints, the sawcut depth was measured along the joint at 0.30m intervals and between joints as measured at the outside edge, midtruck lane, pavement centerline, midpass lane, interior edge, and interior wheelpaths. To determine the longitudinal joint depth variation, readings were made approximately 0.30 m from every transverse joint in the lot. For some projects, additional joint depths were measured at the midpoint between transverse joints. Summary of Sawcut Depth Variation Results The collected sawcut depth data are summarized in table 62. All the joints were cut using diamondimpregnated sawblades except for the Ottumwa, IA, transverse joints. The average withinlot transverse joint sawcut depth standard deviation measured 6 mm, but the Ottumwa withinlot transverse joint depth standard deviation averaged 8 mm, and the longitudinal joint depth standard deviation for Ottumwa was 6 mm. A relative increase in standard deviation is likely to occur for those projects in which joints are cut using abrasive sawblades. For both transverse and longitudinal joint sawcut depths, recommended typical standard deviations were computed assuming that the withinlot standard deviations for each lot studied were normally distributed. Table 62. Summary of withinlot sawcut joint depth standard deviations.
Very little data were found in the literature regarding the withinlot variation of percent consolidation around dowels. In the previous PRS study, reduction factors of 94, 97, and 100 percent were derived to apply to 28day flexural strength predictions from early age in situ cores.^{(3)} The research team suggested that the performance of doweled joints is dependent on the consolidation level around the dowel bars. It is possible the dowel basket assemblies interfere with the consolidation of the concrete below dowel bars, where the bearing stress will be affected. To incorporate an alteration into the current joint faulting model to account for the consolidation around dowel bars, the variation of consolidation level at doweled joints was evaluated at three doweled joint patching projects (Benton Harbor, MI; Des Plaines, IL; Philo, IL) and one new construction project (Ottumwa, IA). Field Investigation of the Percent Consolidation Around Dowels WithinLot Standard Deviation To evaluate in situ consolidation level variability, core densities were measured. For each project, several joints exhibiting varying degrees of deterioration were selected as part of the study. Cores were drilled through dowel bars, between dowel bars, and away from the joint to evaluate relative densities. Cores drilled through dowel bars were separated into concrete samples from above and below the dowel. To account for a portion of the permeable voids, sample densities were measured in a procedure similar to ASTM C 642, Standard Test Method for Specific Gravity, Absorption, and Voids in Hardened Concrete. The weight of the "asreceived" sample immersed in water was recorded quickly so as not to allow water to penetrate all permeable voids on the sides of the core sample. The sample was then weighed in wet and ovendried states. Equation 13 was used to determine the density of the concrete samples:
where
The consolidation of concrete removed from around dowel basket assemblies (above, below, and between dowel bars) was determined as the ratio of the density of the concrete sample to a fully consolidated sample. From all the cores removed away from joints within the lot being evaluated (including cores for thickness, concrete strength, and entrained air content), the core with the highest density was assumed to be 100percent consolidated. The doweled joint core densities (above, below, and between dowels) were then compared to the 100percent consolidated density to determine the relative consolidation levels. This procedure incorporates overconsolidation effects when vibration time is extended over basket assemblies or when vibrators contact dowels for longerthannormal periods. Summary of Percent Consolidation Around Dowels Variation Results The percent consolidation around dowels is summarized in table 63. As shown for the lots included in this investigation, the withinlot standard deviations are generally low, ranging between 0.61 and 2.07 percent. Table 63 also presents recommended target consolidation levels for below, above, and between dowels. A model was developed that relates the consolidation of concrete below dowel bars to the percentage of load transfer. While the data correlate well, future studies on consolidation should measure the concrete density by coating the specimen with paraffin prior to immersion in water. This step will increase the accuracy of the density measurement by accounting for the permeable voids in the concrete sample. Table 63. Summary of withinlot percent consolidation around dowels standard deviations.
Deviation of the Bar Placement from Slab MidDepthNo information on tie bar depth variability was found in the literature review. Tie bars placed too close to the pavement surface can lead to longitudinal joint spalling from load or corrosion. Tie bar placement problems can also influence the stress transfer effectiveness of tied lanes and concrete shoulders, reducing flexural stresses and increasing fatigue life. No performance models incorporating the effects of tie bar depth or alignment magnitudes of load transfer were identified in the literature survey. The research team proposed evaluation of tie bar depth on multilane projects using GPR to determine whether a longitudinal joint spalling model incorporating the effects of tie bar depth could be developed. Other factors, such as load transfer, tie bar size and spacing, deicer chemicals, lane width, climate, subbase, and subgrade were proposed to be included in the model. The research team also theorized that tie bars placed too high or too low result in a loss of load transfer along the longitudinal joint. A loss of load transfer across the longitudinal joint would cause an increase in the edge stress within the pavement and increased edge stress would directly affect the development of transverse fatigue cracking. The effects of loss of load transfer on the resultant edge stress could then be directly incorporated into the existing transverse cracking (fatigue) distress indicator model. To determine whether it was feasible to develop the relationship, the variation of tie bar depth deviation (from slab middepth) was first evaluated. The performance of tied shoulders varies depending on whether shoulders are constructed as part of the mainline pavement, constructed separately from the mainline pavement, or added as a tied concrete shoulder retrofit. While differences are recognized, the research team proposed evaluation of new pavement construction where tie bars were installed by the paver as part of the mainline section. This method of constructing tied joints should result in the greatest variability, as the tie bar inserter on the paver may release the bars at various depths. Other methods of constructing tied joints, such as inserting bent tie bars in the edge of slipformed pavement or drilling and installing tie bars for retrofit projects, generally utilize equipment or procedures that place the tie bars at a constant depth along the mainline pavement edge. Two projects (Ottumwa, IA, and Omaha, NE) were evaluated to investigate the variation in deviation of tie bar placement from slab middepth. Load transfer was also measured at one of these projects (Omaha, NE) to determine whether it was feasible to continue with the development of a model incorporating the effect of tie bar depth on the load transfer efficiency of the longitudinal joint. Using GPR, several sections within the project limits were identified with a range of tie bar depths. Stress transfer efficiency was measured directly using a fallingweight deflectometer (FWD), and the effective stress transfer efficiency was computed. Summary of the Deviation of Tie Bar Placement From Slab MidDepth Variation Results The statistical information reduced for the evaluated lots is presented in table 64. The measured withinlot variation shown in the table was calculated as the standard deviation of all tie bar depths (deviation from middepth) recorded for each lot. Each tie bar depthdeviation measurement was considered a sample. No replicate measurements were recorded. The average withinlot standard deviation of the deviation of tie bars from slab middepth (for all of the investigated lots) was 9 mm. The standard deviation of tie bar depthdeviation was significantly larger for the Ottumwa, IA, project (15 mm) than for the Omaha, NE, project (4 mm). Still, an average standard deviation of 15 mm does not represent poor control by the contractor. At the Ottumwa project, it was very rare to find tie bars placed more than 25 mm from the middepth of the 279mmthick pavement. Also, while the standard deviation of the tie bar depth deviations was small at the Omaha project, the average overall depth of tie bar placement was 110 mm for the 356mmthick pavement. Therefore, for the Omaha project, the tie bars were consistently placed nearly 76 mm above the theoretical slab middepth. Table 64. Summary of withinlot tie bar deviation from middepth standard deviations.
The recommended tie bar depthdeviation standard deviation was calculated in the same manner as the previously discussed AQC’s. The measured tie bar depthdeviation samples were assumed to be normally distributed within each investigated lot. The recommended average standard deviation for the case without replicates (n = 1) was found to be 8.8 mm (as shown in table 64).
