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17 achieved during testing conducted by previous researchers, Mortar Pull-Out Testing for such as in the NASPA-funded work, which was performed Correlation Round of Evaluation under ram displacement-rate control. The mortar pull-out test As mentioned, the sample sources used for the Correlation was conducted with load-rate control instead of displacement- Round of testing were selected by Bruce Russell of OSU. rate control because load rate, which may influence the results Mortar pull-out data were provided for each of the sources. of the physical tests on structural materials, is independent of The reported NASPA pull-out forces represent the average the stiffness of the testing frame. It is desirable that the test load at 0.1-in. slip for multiple (5 to 12) specimens, all tested method be universally applicable, and so should not be influ- on the same day with the same batch of mortar. Per the pro- enced by the load frame. tocol outlined by Chandran (2006), the mortar pull-out force was measured on strands embedded in 5-in. diameter by 18-in. Hydrocal Pull-Out Test long cylinders (with 16 in. of strand in direct contact with mortar). These mortar pull-out tests were conducted under A range of Hydrocal-based mixtures was evaluated as displacement-rate control, with an additional criterion for possible surrogate materials for use in a pull-out test. The load rate. For comparison with mortar pull-out test results final mixture used in this testing contained Hydrocal White for the Screening Round of testing, the loads at 0.1-in. slip (a material similar to plaster of Paris made by United States provided from OSU were converted to average bond stresses Gypsum), Ottawa graded sand (ASTM C778), calcium hy- at 0.1-in. slip. droxide flakes, USG Retarder for Lime-Based Plasters, and water. This formulation of Hydrocal is almost pure plaster of Paris and was chosen because it is produced at only one Statistical Evaluation of Results manufacturing facility from consistent raw materials. Also, like cement, it is a calcium compound (plaster of Paris is A large experimental program was conducted to support hemihydrated calcium sulfate). Calcium hydroxide flakes the evaluation of the various proposed test methods for strand were added to simulate the alkalinity of concrete, and the bond that were intended for use as part of a QC program. Hydrocal was combined with sand and plaster retarder These were classified as performance-based (i.e., mechanical) to limit the heat production generated during the rapid tests and surface and chemical tests. The correlation between plaster hydration. bond and the methods that fall under each of these classifica- In this test, each prestressing strand is embedded 12 in. in tions was evaluated differently based on the strand sources a 3-in. diameter steel cylinder filled with the Hydrocal mortar that were collected for testing and the data quantifying bond (gypsum/lime plaster, sand, and water). Six cylinders are tested performance that were available. The evaluation of correlations for each source of strand. The required mortar strength at time between the various pull-out testing methods and the bond of the test is 3000 to 4000 psi. The test is conducted similarly were based on bond performance as measured with transfer to the mortar pull-out test. The bond stress at 0.1-in. slip and length tests. The correlations between the surface and chemi- the average maximum bond stress for each strand tested are cal test methods were evaluated based on the results of pull-out reported and averaged. tests from concrete in the Screening Round and based on the results of pull-out tests from mortar in the Correlation Round. Statistical analyses have been performed with two objectives: Interpretation of Historic and Recent (1) to determine and quantify the relationship between the Concrete Pull-Out Test Results chemical and surface test results and bond performance, and The "first observable slip" and "0.1-in. slip" are measured (2) to allow the determination of acceptance thresholds for in different ways, yet are considered to be close in value to the chemical and surface test results that can predict, with a one another. This was verified during the current test pro- given level of confidence, that adequate bond performance gram, which showed that the first observed slip at the live can be achieved. The first objective was achieved based on end of the strand occurred at generally the same time at standard linear regression techniques, while the second objec- which 0.1-in. of end slip was measured in the pull-out test. tive requires the determination of prediction intervals. A more This similarity is significant because the stress at 0.1-in. end extensive discussion of both of these analysis methods is given slip was not determined during the historic concrete pull-out in Appendix B. tests conducted on the historic samples that were included in the screening testing program. However, because of the Regression similarity, when evaluating the correlation between bond performance and the screening test results, both the "first To provide a quantitative measure of the goodness-of-fit to observable slip" and "0.1-in. slip" characterizations of bond aid in the evaluation of these methods, a linear regression has are used together. been performed, and the coefficient of determination (R2) was

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18 determined for the relationship between each proposed test QC test results or uncertainty in the regression model. Instead, method and the bond quality measure. No physical basis for what is needed to interpret and practically apply a given QC a linear relationship between these measures of bond is known; test result is the computation of a lower bound on the interval however, the linear relationship was assumed as the simplest that, with a given confidence, includes the pull-out stress for model relating the parameters. The R2 is a measure of the ad- a strand sample with that QC test result. This type of interval equacy of a regression model (i.e., it describes the amount of is known as a one-sided prediction interval and is a standard variability in the data explained by the regression model). The part of regression theory and practice. closer the R2 is to 100%, the more completely the model de- The prediction interval concept is a necessary part of the scribes the relationship between the test method results and development of acceptance/rejection thresholds for the rec- the basis for evaluation. ommended QC test methods, since, to conservatively ensure To further evaluate the validity of these methods, the signif- that a specified pull-out bond stress is achieved, the threshold icance of the linear models developed based on these data was on the QC test must be chosen as the value where the prediction evaluated by the calculation of P-values for the coefficients interval lower bound is equal to the pull-out stress threshold. (slope) from the linear models. The coefficient from the linear The regression model gives an estimate of the average pull-out model is judged to be significant when there is a sufficiently high stress if the pull-out test was actually conducted repeatedly on confidence that it is not equal to zero. If this is the case, the re- the same source of strand. For a given measurement of the lationship represented by the model is statistically significant predictor, half of the actual pull-out test results would be ex- and the results of the surface tests are meaningful in the predic- pected to fall above this average and half would fall below. tion of the pull-out test result. A 95% confidence level is com- The distribution of individual pull-out observations about monly used to evaluate significance. The level of confidence of that average pull-out stress is the basis for the prediction in- significance on the coefficient is given by (1 - P-value) 100%, terval, which is calculated based on the variability in the data so a P-value < 0.05 implies that the confidence interval does not used for the regression. include zero with higher than 95% confidence. This concept is demonstrated graphically in Figure 3, which For the contact angle and organic residue extraction test shows the prediction interval lower bound plotted along with methods, coefficients of determination have been calculated the regression line, and data for the mortar pull-out plotted using only data from sources identified in the FTIR analyses as versus the change in corrosion potential. If a specified thresh- carrying only stearate-based lubricants. This was done to elim- old on mortar pull-out is defined as 0.313 ksi, the threshold inate the potentially confounding influences of non-stearate- on the corrosion potential is the value where the pull-out based lubricants. Analyzing these data in this manner has a threshold and the curve delineating the lower bound of the practical motivation, since such models could be useful in a prediction interval intersect, shown by the red lines in the plot. production setting where the lubricant in use is known to be In this case, the threshold would be approximately -0.175 V. stearate-based only. If a multiple-predictor regression model is used for predic- In addition to the regression with a single predictor, re- tion of the pull-out stress, the prediction interval is still needed. gression analyses were also performed based on selected com- Determining the prediction interval for models based on mul- binations of the surface and chemical test results to see if the tiple predictors is possible; however, it is more complicated and pull-out performance could be better predicted using more can not be shown graphically. The predicted pull-out stress is than one predictor variable. When regression was performed not uniquely determined by a single combination of predic- with multiple predictors, the R2 adjusted was calculated and tors, but can be found based on numerous combinations of used to interpret how well the model fits the data. The R2 ad- those predictors. However, the prediction interval for the justed is the most appropriate measure of goodness-of-fit pull-out stress will be different depending on the specific com- for multiple-predictor regression. Since adding predictors bination of predictors used. That means that when multiple re- makes the model more flexible and thus better able to fit the gression is used to improve the predictive ability of the model, data, the R2 adjusted measure includes a penalty for additional a single threshold can not be defined. Instead, for a specific set predictors in the model. of predictors, a new prediction interval must be calculated based on the set of data used to develop the regression model. The lower bound of the newly calculated prediction interval Prediction Intervals must then be compared with the specified pull-out threshold. The models generated by the regression analysis allow for the prediction of the pull-out stress based on results obtained Computational Tool with the surface and chemical QC test methods. However, the prediction formulas give the average estimated pull-out stress, To facilitate the implementation of the prediction interval but do not account for variation that is bound to occur in the concept, a computational tool in the form of a Microsoft