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E-1 Phase I Experiment ............................................................ E-1 Phase II Experiment ......................................................... E-10 Phase I Experiment The objective of the statistical analysis for Phase I was to identify factors with significant effects on resilient modulus (MR) stiffness of short-term aged asphalt mixtures. The factors of interest were: 1. WMA technology (HMA vs. WMA) 2. Production temperature (high temperature vs. control temperature) 3. Plant type (DMP vs. BMP) 4. Recycled materials (no RAP/RAS vs. RAP/RAS) 5. Aggregate absorption (low absorption vs. high absorption) 6. Binder source (Binder 1 vs. Binder 2) In addition to the aforementioned factors, the informa- tion on field site (Connecticut, Florida, Indiana, Iowa, New Mexico, South Dakota, Texas I, Texas II, Wyoming), specimen type (plant-mixed, plant-compacted [PMPC]; laboratory- mixed, laboratory compacted [LMLC]; cores at construction [Cores@Const]), nominal maximum aggregate size (NMAS; 9.5 mm, 12.5 mm, 19 mm), and air-void (AV) content (3.6 to 11.2 percent) was also available and incorporated into the analyses. Six separate experiments and analyses were per- formed to assess the effects of each of the six factors of inter- est listed above. WMA Technology (HMA vs. WMA) There were 343 non-missing (correct and recorded) MR stiffness measurements obtained from eight different field sites (Connecticut, Florida, Indiana, Iowa, New Mexico, South Dakota, Texas I, Wyoming), three specimen types, and two levels of WMA technology in the data for this analysis. Other relevant variables for the analysis were NMAS and AV. The analysis of covariance (ANCOVA) having WMA technology and specimen type as main effects along with a two-way inter- action effect between them (specimen type*WMA technol- ogy), NMAS and AV as covariates, and field site as a random effect was fitted to the data. Table E-1 contains the analysis outputs obtained by the restricted maximum likelihood (REML) method implemented in the JMP statistical package (SAS product). It can be observed from Table E-1 (see Fixed Effects Tests) that the effects of speci- men type, WMA technology, specimen type*WMA technology, and AV were statistically significant at a = 0.05, while the effect of NMAS was not. When there is a significant interaction effect, the effect of each factor involved in the interaction needs to be assessed conditional on the levels of the other factor because the effect might be different for each level of the other factor. Therefore, the effect of WMA technology was assessed for each level of specimen type. Figure E-1 contains the interaction plot for WMA technology and specimen type. An interaction plot is a graph of predicted mean responses (least squares means, which will be explained later) that are connected line segments. The y-axis is the predicted mean response, and the x-axis dis- plays the levels of one of the factors (here WMA technology). Separate line segments are drawn for each level of the other factor (specimen type). It can be observed from the plot that except for Cores@Const, the predicted MR stiffness was lower for WMA than for HMA. For Cores@Const, the predicted MR did not seem to be different. Table E-2 contains the analysis output obtained by the REML method implemented in JMP. Table E-2 presents the predicted values (least squares [LS] means) for MR stiffness for each level of significant factors along with their standard errors. When there are multiple factors in the model, it is not fair to make comparisons between raw cell means in data because raw cell means do not compensate for other factors in the model. The LS means are the predicted values of the A P P E N D I X E Statistical Analysis
E-2 Production Temperature (High vs. Control) There were 117 non-missing (correct and recorded) MR stiffness measurements obtained from two different field sites (Iowa, Wyoming), three specimen types, two levels of WMA technology, and two levels of production temperature in the data for this analysis. Another relevant variable that could be included in the analysis was AV content. The value of NMAS was held constant at 12.5 mm for all of the MR stiffness mea- surements in the data, so it was excluded from the analysis. The ANCOVA model including production temperature, WMA technology, and specimen type as main effects along with all possible two-way interactions, AV as a covariate, and field site as a random effect was first fitted to the data, but none of the two-way interaction effects were statistically signifi- cant. Thus, two-way interaction effects were removed from the model, and the ANCOVA model with production tempera- ture, WMA technology and specimen type as main effects, AV as a covariate, and field site as a random effect was fit- ted again to the data. Table E-4 contains the analysis output obtained by the REML method implemented in JMP. It can be observed from Table E-4 (see Fixed Effects Tests) that the effects of specimen type and WMA technology were statis- tically significant at a = 0.05, while the effect of production temperature and AV were not. Plant Type (BMP vs. DMP) There were 83 non-missing (correct and recorded) MR stiff- ness measurements obtained from two different field sites (Indiana, Texas II), three specimen types, and two levels of plant type (DMP vs. BMP) in the data for this analysis. Another relevant variable that was included in the analysis was AV. The value of NMAS was held constant at 9.5 mm for all of the MR stiffness measurements in the data, so it was excluded from the analysis. The ANCOVA model including plant type and response (MR stiffness) for each level of a factor that have been adjusted for the other factors in the model. Note that the âLeast Sq Meanâ denotes the least squares means for MR stiff- ness. The predicted values (LS means) and the corresponding standard errors for MR stiffness for each factor-level combi- nation of WMA technology and specimen type are presented in Table E-2. For specimen type*WMA technology, a multiple comparison procedure (Tukeyâs honest significant difference [HSD]) was also carried out to test which of those factor levels were statistically different. It can be seen that the dif- ference between HMA and WMA was statistically significant for PMPC while not for LMLC and Cores@Const. The ANCOVA model without the two-way interaction effect term (specimen type*WMA technology), but with WMA technology and specimen type as main effects, NMAS and AV as covariates, and field site as a random effect, was also fitted to the same data for comparison purposes. Note that this model is meaningful if the two-way interaction effect presented in Table E-2 can be considered to be practi- cally insignificant. Table E-3 contains the analysis outputs. Again, it can be observed from Table E-3 that the effects of specimen type, WMA technology, and AV were statistically significant at a = 0.05, while the effect of NMAS was not. Response MR Stiffness (ksi) Summary of Fit RSquare 0.770825 RSquare Adj 0.765336 Root Mean Square Error 111.2762 Mean of Response 435.519 Observations (or Sum Wgts) 343 Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F Specimen Type 2 2 329 12.7708 <0.0001* WMA Technology 1 1 329.2 15.4774 0.0001* NMAS (mm) 2 2 4.98 0.4257 0.6750 AV (%) 1 1 329.4 22.1249 <0.0001* Specimen Type*WMA Technology 2 2 329 4.9565 0.0076* _________________________________________________________________________________________________ Table E-1. Analysis results of the effect of WMA technology based on the ANCOVA model with main effects and a two-way interaction effect. Figure E-1. Least squares means or interaction plot for specimen type*WMA technology.
E-3 Effect Details Specimen Type Least Squares Means Table Level Least Sq Mean Std Error Cores@Const. 598.85750 222.91111 LMLC 659.23066 222.81605 PMPC 677.15810 222.80865 WMA Technology Least Squares Means Table Level Least Sq Mean Std Error HMA 669.82037 222.74650 WMA 620.34380 222.75855 NMAS (mm) Least Squares Means Table Level Least Sq Mean Std Error 9.5 645.08209 222.66375 12.5 419.98336 99.67253 19 456.93319 157.55805 Specimen Type*WMA Technology Least Squares Means Table Level Least Sq Mean Std Error Cores@Const., HMA 599.59226 223.18301 Cores@Const., WMA 598.12274 223.17083 LMLC, HMA 684.67667 223.12468 LMLC, WMA 633.78465 223.01576 PMPC, HMA 725.19219 223.10975 PMPC, WMA 629.12402 223.00803 LS Means Differences Tukey HSD α = 0.050 Level Least Sq Mean PMPC, HMA A 725.19219 LMLC, HMA A B 684.67667 LMLC, WMA B C 633.78465 PMPC, WMA B C 629.12402 Cores@Const., HMA C 599.59226 Cores@Const., WMA C 598.12274 Levels not connected by same letter are significantly different. ___________________________________________________________________________________________________ Table E-2. Effect details for model in Table E-1. Response MR Stiffness (ksi) Summary of Fit RSquare 0.763931 RSquare Adj 0.759715 Root Mean Square Error 112.5958 Mean of Response 435.519 Observations (or Sum Wgts) 343 Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F Specimen Type 2 2 331 11.1538 <0.0001* WMA Technology 1 1 331.2 15.7227 <0.0001* NMAS (mm) 2 2 4.979 0.4185 0.6792 AV (%) 1 1 331.4 18.5589 <0.0001* Effect Details Specimen Type Least Squares Means Table Level Least Sq Mean Std Error Cores@Const. 600.08926 223.27652 LMLC 658.35884 223.17444 PMPC 673.17074 223.16766 Table E-3. Analysis results of the effect of WMA technology based on the model with main effects only. (continued on next page)
E-4 LS Means Differences Tukey HSD α = 0.050 Level Least Sq Mean PMPC A 673.17074 LMLC A 658.35884 Cores@Const. B 600.08926 Levels not connected by same letter are significantly different. WMA Technology Least Squares Means Table Level Least Sq Mean Std Error HMA 669.09403 223.10848 WMA 618.65186 223.12016 NMAS (mm) Least Squares Means Table Level Least Sq Mean Std Error 9.5 643.87295 223.02364 12.5 420.33217 99.83569 19 458.19937 157.81461 _________________________________________________________________________________________________ Table E-3. (Continued). Response MR Stiffness (ksi) Summary of Fit RSquare 0.336584 RSquare Adj 0.30587 Root Mean Square Error 82.03103 Mean of Response 260.1842 Observations (or Sum Wgts) 114 Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F Specimen Type 2 2 107.4 9.4183 0.0002* WMA Technology 1 1 106.2 4.4461 0.0373* Production Temperature 1 1 107.5 0.0071 0.9329 AV (%) 1 1 107.7 3.3372 0.0705 Effect Details Specimen Type Least Squares Means Table Level Least Sq Mean Std Error Cores@Const. 210.45968 23.428893 LMLC 305.14533 22.979005 PMPC 267.66671 23.042212 LS Means Differences Tukey HSD α = 0.050 Level Least Sq Mean LMLC A 305.14533 PMPC A 267.66671 Cores@Const. B 210.45968 Levels not connected by same letter are significantly different. WMA Technology Least Squares Means Table Level Least Sq Mean Std Error HMA 279.41688 22.815326 WMA 242.76426 20.164048 Production Temperature Least Squares Means Table Level Least Sq Mean Std Error Control Temperature 261.74940 20.787180 High Temperature 260.43174 21.583983 _________________________________________________________________________________________________ Table E-4. Analysis results of the effect of production temperature.
E-5 specimen type as main effects, plant type*specimen type as a two-way interaction effect, AV as a covariate, and field site as a random effect was first fitted to the data. However, the two- way interaction effect plant type*specimen type was not sta- tistically significant, and the ANCOVA model with plant type and specimen type as main effects, AV as a covariate, and field site as a random effect was fitted again to the data. Table E-5 contains the analysis outputs obtained by the REML method implemented in JMP. It can be observed from Table E-5 (see Fixed Effects Tests) that the effects of specimen type and AV were statistically significant at a = 0.05, while the effect of plant type was not. Inclusion of Recycled Materials (RAP/RAS vs. No RAP/RAS) There were 79 non-missing MR stiffness measurements obtained from two different field sites (Texas I, New Mexico), three specimen types, two levels of WMA technology, and two levels of recycled materials (no RAP/RAS vs. RAP/RAS) in the data for this analysis. The other relevant variable that was included in the analysis was AV. The value of NMAS was held constant at 19 mm for all of the MR stiffness measurements in the data and was excluded from this analysis. The ANCOVA model including recycled materials, specimen type, and WMA technology as main effects along with all possible two-way interaction effects among them, AV as a covariate, and field site as a random effect was first fitted to the data. Because the WMA technology*recycled materials interaction effect was not statistically significant at a = 0.05, it was removed, and the ANCOVA model with recycled materials, specimen type, and WMA technology as main effects, specimen type*WMA technology and specimen type*recycled materials as two-way interactions, AV as a covariate, and field site as a random effect was fitted again to the data. Table E-6 contains the analysis output obtained by the REML method implemented in JMP. It can be observed from Table E-6 (see Fixed Effects Tests) that the effects of speci- men type, WMA technology, recycled materials, specimen type*WMA technology, and specimen type*recycled materials were statistically significant at a = 0.05, while the effect of AV was not. Table E-6 also presents the predicted values (least squares means) for MR stiffness for each level of sig- nificant factors along with their standard errors. For speci- men type*WMA technology and specimen type*recycled materials, a multiple comparison procedure (Tukeyâs HSD) was also carried out to test which of those factor levels were statistically different. It can be seen that for this dataset the difference between HMA and WMA was statistically signifi- cant for Cores@Const and PMPC but not for LMLC (Fig- ure E-2a). It can also be observed from the interaction plot and Tukeyâs HSD test result that the difference between no RAP/RAS and RAP/RAS was statistically significant for each of Cores@Const, LMLC, and PMPC although the amount of Response MR Stiffness (ksi) Summary of Fit RSquare 0.79484 RSquare Adj 0.784319 Root Mean Square Error 64.00318 Mean of Response 576.9036 Observations (or Sum Wgts) 83 Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F Specimen Type 2 2 77.02 34.5118 <0.0001* Plant Type 1 1 77.01 0.3386 0.5623 AV (%) 1 1 77.06 19.5165 <0.0001* Effect Details Specimen Type Least Squares Means Table Level Least Sq Mean Std Error Cores@Const. 487.23342 69.019735 LMLC 552.51341 68.516970 PMPC 662.81736 68.683869 Plant Type Least Square Means Table Level Least Sq Mean Std Error BMP 563.30111 68.075887 DMP 571.74168 68.038493 _________________________________________________________________________________________________ Table E-5. Analysis results of the effect of plant type.
E-6 Response MR Stiffness (ksi) Summary of Fit RSquare 0.738961 RSquare Adj 0.704913 Root Mean Square Error 96.6455 Mean of Response 473.443 Observations (or Sum Wgts) 79 Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F Specimen Type 2 2 68 9.1956 0.0003* WMA Technology 1 1 68.07 33.9737 <0.0001* Recycled Materials 1 1 68.34 132.8675 <0.0001* AV (%) 1 1 68.03 0.8223 0.3677 Specimen Type*WMA Technology 2 2 68 3.1880 0.0475* Specimen Type*Recycled Materials 2 2 68 9.4862 0.0002* Effect Details Specimen Type Least Squares Means Table Level Least Sq Mean Std Error Cores@Const. 503.05058 85.383434 LMLC 395.63973 85.251826 PMPC 487.16675 85.259816 WMA Technology Least Squares Means Table Level Least Sq Mean Std Error HMA 528.38576 84.750304 WMA 395.51894 84.505516 Recycled Materials Least Squares Means Table Level Least Sq Mean Std Error No RAP/RAS 324.35229 84.888197 RAP/RAS 599.55241 84.516152 Specimen Type*WMA Technology Least Squares Means Table Level Least Sq Mean Std Error Cores@Const., HMA 600.34646 88.702788 Cores@Const., WMA 405.75470 87.615965 LMLC, HMA 423.06789 87.716629 LMLC, WMA 368.21156 86.931067 PMPC, HMA 561.74294 87.675827 PMPC, WMA 412.59056 87.029846 LS Means Differences Tukey HSD α = 0.050 Level Least Sq Mean Cores@Const., HMA A 600.34646 PMPC, HMA A 561.74294 LMLC, HMA B 423.06789 PMPC, WMA B 412.59056 Cores@Const., WMA B 405.75470 LMLC, WMA B 368.21156 Levels not connected by same letter are significantly different. Specimen Type*Recycled Materials Least Squares Means Table Level Least Sq Mean Std Error Cores@Const., No RAP/RAS 307.57200 87.934962 Cores@Const., RAP/RAS 698.52915 87.629086 LMLC, No RAP/RAS 318.03673 87.970726 LMLC, RAP/RAS 473.24272 86.911187 PMPC, No RAP/RAS 347.44813 88.040685 PMPC, RAP/RAS 626.88537 86.917262 Table E-6. Analysis results of the effect of recycled materials.
E-7 difference varied with specimen type (Figure E-2b). It can be concluded that, in general, mixtures with RAP/RAS had sta- tistically higher MR stiffness than mixtures with no RAP/RAS. Aggregate Absorption (High- vs. Low-Absorptive Aggregate) There were 119 non-missing MR stiffness measurements obtained from two different field sites (Iowa, Florida), three specimen types, two levels of WMA technology, and two levels of aggregate absorption (low absorption vs. high absorption) in the data for this analysis. Another relevant variable that was included in the analysis was AV. The value of NMAS was held constant at 12.5 mm for all of the MR stiffness measurements in the data and was excluded from this analysis. The ANCOVA model including aggregate absorption, specimen type, and WMA technology as main effects, AV as a covariate, and field site as a random effect was fitted to these data. Table E-7 contains the analysis output obtained by the REML method implemented in JMP. It can be observed from Table E-7 (see Fixed Effects Tests) that the effects of specimen type, WMA technology, and aggregate absorption were statistically sig- nificant at a = 0.05, while the effect of AV was not. Table E-7 also presents the predicted values (least squares means) for MR stiffness for each level of significant factors along with their standard errors. Binder Source (Binder A vs. Binder V) There were 35 non-missing MR stiffness measurements obtained from three specimen types and two levels of binder source (Binder 1 vs. Binder 2) in the data for this analysis. The other relevant variable included in the analysis was AV. The value of NMAS was held constant at 9.5 mm and the field site was Texas II for all of the MR stiffness measurements in the data. The ANCOVA model including binder source and specimen type as main effects and AV as a covariate was fit- ted to these data. Originally, a model including a two-way interaction, binder source*specimen type, was fitted, but the interaction was not statistically significant. Table E-8 contains the analysis outputs obtained by the REML method imple- mented in JMP. It can be observed from Table E-8 that the effects of binder source, specimen type, and AV were all sta- tistically significant at a = 0.05. Table E-8 also presents the predicted values for MR stiffness for each level of significant factors. Specifically, Binder A yielded significantly higher MR stiffness than Binder V. Specimen Type In addition to the analyses for the identification of signifi- cant factors, the analysis of the effect of specimen type on MR stiffness was also conducted to determine if equivalent mixture stiffness is achieved by PMPC specimens and LMLC specimens as well as by cores at construction and LMLC specimens. LS Means Differences Tukey HSD α = 0.050 Level Least Sq Mean Cores@Const., RAP/RAS A 698.52915 PMPC, RAP/RAS A 626.88537 LMLC, RAP/RAS B 473.24272 PMPC, No RAP/RAS C 347.44813 LMLC, No RAP/RAS C 318.03673 Cores@Const., No RAP/RAS C 307.57200 Levels not connected by same letter are significantly different. _________________________________________________________________________________________________ Table E-6. (Continued). (a) Specimen type*WMA technology (b) Specimen type*recycled materials Figure E-2. Least squares means or interaction plots.
E-8 Response MR Stiffness (ksi) Summary of Fit RSquare 0.906554 RSquare Adj 0.902419 Root Mean Square Error 75.768 Mean of Response 442.0672 Observations (or Sum Wgts) 119 Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F Specimen Type 2 2 112 54.9220 <0.0001* WMA Technology 1 1 112 9.7778 0.0023* Aggregate Absorption 1 1 112 63.5877 <0.0001* AV (%) 1 1 112 0.1203 0.7293 Effect Details Specimen Type Least Squares Means Table Level Least Sq Mean Std Error Cores@Const. 358.61853 207.00726 LMLC 561.80383 206.93033 PMPC 526.57987 206.93214 WMA Technology Least Squares Means Table Level Least Sq Mean Std Error HMA 504.09964 206.78238 WMA 460.56851 206.77821 Aggregate Absorption Least Squares Means Table Level Least Sq Mean Std Error High Absorption 425.22727 206.78724 Low Absorption 539.44088 206.78706 _________________________________________________________________________________________________ Table E-7. Analysis results of the effect of aggregate absorption. Response MR Stiffness (ksi) Summary of Fit RSquare 0.911424 RSquare Adj 0.899613 Root Mean Square Error 35.99742 Mean of Response 503.3714 Observations (or Sum Wgts) 35 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 4 400005.74 100001 77.1726 Error 30 38874.43 1296 Prob > F C. Total 34 438880.17 <0.0001* Lack of Fit Source DF Sum of Squares Mean Square F Ratio Lack of Fit 15 27284.935 1819.00 2.3543 Pure Error 15 11589.500 772.63 Prob > F Total Error 30 38874.435 0.0540 Max RSq Effect Tests Source Nparm DF Sum of Squares F Ratio Prob > F Specimen Type 2 2 226092.08 87.2394 <0.0001* Binder Source 1 1 80832.73 62.3799 <0.0001* AV (%) 1 1 16571.39 12.7884 0.0012* Effect Details Specimen Type Least Squares Means Table Level Least Sq Mean Std Error Mean Cores@Const. 427.14738 11.302509 411.250 LMLC 470.13260 10.641587 478.333 PMPC 627.21056 11.136625 631.182 Table E-8. Analysis results of the effect of binder source.
E-9 There were 378 non-missing MR stiffness measurements obtained from nine field sites, three specimen types, and three levels of NMAS (9.5 mm, 12.5 mm, 19 mm) in the data for this analysis. Another relevant variable that was included in the analysis was AV. The ANCOVA model including specimen type as a main effect, NMAS and AV as covariates, and field site as a random effect was fitted to the data. Table E-9 contains the analysis output obtained by the REML method implemented in JMP. It can be observed from Fixed Effects Tests that the effects of specimen type and AV were statistically significant at a = 0.05, while the effect of NMAS was not. It also appears that higher values of AV are associated with lower values of MR stiff- ness (see âParameter Estimatesâ where the coefficient for AV is negative), as expected. Table E-9 also presents the predicted Binder Source Least Squares Means Table Level Least Sq Mean Std Error Mean Binder 1 (Binder A) 556.83935 8.8053350 553.000 Binder 2 (Binder V) 459.48767 8.5257073 456.500 _________________________________________________________________________________________________ Table E-8. (Continued). Response MR Stiffness (ksi) Summary of Fit RSquare 0.747895 RSquare Adj 0.744507 Root Mean Square Error 112.459 Mean of Response 441.8016 Observations (or Sum Wgts) 378 Parameter Estimates Term Estimate Std Error DFDen t Ratio Prob>|t| Intercept 795.80309 156.8864 7.24 5.07 0.0013* Specimen Type [Cores@Const.] â45.92381 8.992407 366.1 â5.11 <0.0001* Specimen Type [LMLC] 9.4336149 8.301336 366 1.14 0.2565 NMAS (mm) [12.5â9.5] â163.0417 176.9445 5.979 â0.92 0.3925 NMAS (mm) [19â12.5] 40.390787 176.9656 5.982 0.23 0.8271 AV (%) â30.53477 6.363505 366.5 â4.80 <0.0001* Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F Specimen Type 2 2 366 14.6422 <0.0001* NMAS (mm) 2 2 5.981 0.4252 0.6720 AV (%) 1 1 366.5 23.0248 <0.0001* Effect Details Specimen Type Least Squares Means Table Level Least Sq Mean Std Error Cores@Const. 530.99022 149.83759 LMLC 586.34765 149.73227 PMPC 613.40423 149.74051 LS Means Differences Tukey HSD α = 0.050 Level Least Sq Mean PMPC A 613.40423 LMLC A 586.34765 Cores@Const. B 530.99022 Levels not connected by same letter are significantly different. NMAS (mm) Least Squares Means Table Level Least Sq Mean Std Error 9.5 576.91403 149.52323 12.5 413.87236 94.60771 19 454.26315 149.56134 _________________________________________________________________________________________________ Table E-9. Analysis results of the effect of specimen type.
E-10 values for MR stiffness for each level of factors. For specimen type, a multiple comparison procedure (Tukeyâs HSD) was also carried out to test which levels were statistically different. It can be observed from âLS Means Differences Tukey HSDâ that PMPC and LMLC lead to significantly higher MR stiffness than Cores@Const while PMPC and LMLC are not statistically dif- ferent from each other at a = 0.05. Phase II Experiment The objective of the statistical analysis for Phase II was to identify factors with significant effects on MR ratio of long- term aged asphalt mixtures. The factors of interest were: 1. WMA technology (HMA vs. WMA) 2. Production temperature (high temperature vs. control temperature) 3. Plant type (DMP vs. BMP) 4. Recycled materials (no RAP/RAS vs. RAP/RAS) 5. Aggregate absorption (low absorption vs. high absorption) In addition to the aforementioned factors, the informa- tion on field site (Florida, Indiana, Iowa, New Mexico, South Dakota, Texas I, Wyoming) and aging level (Lab LTOA 1, Lab LTOA 2, Field Aging 1, Field Aging 2, and Field Aging 3âwhere each of three field aging levels are nested within the field site) was also available and incorporated into the analyses. Five sep- arate experiments and analyses were performed to assess the effects of each of the five factors of interest listed above. WMA Technology (HMA vs. WMA) There were 105 non-missing MR stiffness ratio measure- ments obtained from seven different field sites (Florida, Indiana, Iowa, New Mexico, South Dakota, Texas I, and Wyo- ming) and two levels of WMA technology in the data for this analysis. Another variable included in the analysis was aging level. Analysis of variance (ANOVA) having WMA technol- ogy and aging level as main effects along with a two-way interaction effect between them, and field site as a random effect was fitted to the data. However, the two-way interac- tion effect WMA technology*aging level was not statistically significant, and the ANOVA model with WMA technology and aging level as main effects and field site as a random effect was fitted again to the data. Table E-10 contains the analysis outputs obtained by the REML method implemented in the Response MR Stiffness Ratio Summary of Fit RSquare 0.722275 RSquare Adj 0.68605 Root Mean Square Error 0.241657 Mean of Response 1.603867 Observations (or Sum Wgts) 105 Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F WMA Technology 1 1 86.53 9.2668 0.0031* Aging Level 11 11 89.51 11.1913 <0.0001* Effect Details WMA Technology Least Squares Means Table Level Least Sq Mean Std Error HMA 1.5874780 0.09972780 WMA 1.7371166 0.09737346 Aging Level Least Squares Means Table Level Least Sq Mean Std Error Field Aging 1_FL 1.9166531 0.16887818 Field Aging 1_IA 1.4450960 0.13757681 Field Aging 1_IN 1.6608835 0.16887818 Field Aging 1_NM 1.0857561 0.16887818 Field Aging 1_SD 1.5925310 0.16888933 Field Aging 1_TX I 1.5054495 0.16476408 Field Aging 1_WY 0.8898908 0.16010955 Field Aging 2_FL 2.0004031 0.16887818 Field Aging 2_TX I 2.0336069 0.18696559 Field Aging 3_TX I 2.5919403 0.18696559 Lab LTOA 1 1.4584678 0.09949980 Lab LTOA 2 1.7668895 0.09927131 _________________________________________________________________________________________________ Table E-10. Analysis results of the effect of WMA technology.
E-11 JMP statistical package. It can be observed from Table E-10 (see Fixed Effects Tests) that the effects of WMA technology and aging level were statistically significant at a = 0.05. Table E-10 also presents the predicted values for MR stiffness for each level of factors (see âLeast Squares Means Tableâ). It can be seen that WMA led to a higher predicted MR ratio value than HMA. Also, in general, the predicted MR ratio seemed to increase as aging level increased. Production Temperature (High vs. Control) There were 36 non-missing MR stiffness ratio measure- ments obtained from two different field sites (Iowa, Wyoming) and two levels of production temperature in the data for this analysis. Other relevant variables included in the analysis were WMA technology and aging level. The ANOVA model includ- ing production temperature, WMA technology, and aging level as main effects along with all possible two-way interactions and field site as a random effect was first fitted to the data, but none of the two-way interaction effects were statistically significant. Thus, two-way interaction effects were removed from the model, and the ANOVA model with main effects, production temperature, WMA technology and aging level, as fixed effects and field site as a random effect was fitted again to the data. Table E-11 contains the analysis output obtained by the REML method implemented in JMP. It can be observed from Table E-11 (see âFixed Effects Testsâ) that the effect of the fac- tor of interest, production temperature, was not statistically significant at a = 0.05. Plant Type (BMP vs. DMP) There were 12 non-missing MR stiffness measurements obtained from one field site (Indiana) and two levels of plant type in the data for this analysis. Other relevant variables that could be included in the analysis were aging level and WMA technology. The ANOVA model including plant type, aging level, and WMA technology as main effects along with all pos- sible two-way interactions among them was first fitted to the data. However, none of the two-way interaction effects were statistically significant, and the ANOVA model with main effects only was fitted again to the data. Table E-12 contains the analysis outputs obtained by the REML method implemented Response MR Stiffness Ratio Summary of Fit RSquare 0.683867 RSquare Adj 0.631178 Root Mean Square Error 0.206745 Mean of Response 1.400333 Observations (or Sum Wgts) 36 Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F Production Temperature 1 1 29 2.3413 0.1368 Aging Level 3 3 19.74 15.1443 <0.0001* WMA Technology 1 1 29.84 3.8217 0.0600 Effect Details Production Temperature Least Squares Means Table Level Least Sq Mean Std Error Control Temperature 1.2538520 0.05916754 High Temperature 1.3619241 0.06452429 Aging Level Least Squares Means Table Level Least Sq Mean Std Error Field Aging 1_IA 1.3328748 0.11401034 Field Aging 1_WY 0.8594769 0.12539081 Lab LTOA 1 1.3461258 0.07461122 Lab LTOA 2 1.6930748 0.07322558 WMA Technology Least Squares Means Table Level Least Sq Mean Std Error HMA 1.2328373 0.07171734 WMA 1.3829388 0.05453665 _________________________________________________________________________________________________ Table E-11. Analysis results of the effect of production temperature.
E-12 in JMP. It can be observed from Table E-12 (see âFixed Effects Testsâ) that none of the factor effects (as well as the factor of interest plant type) were statistically significant at a = 0.05. Inclusion of Recycled Material (RAP/RAS vs. No RAP/RAS) There were 17 non-missing MR stiffness ratio measure- ments obtained from two different field sites (Texas I, New Mexico), and two levels of recycled materials (no RAP/RAS vs. RAP/RAS) in the data for this analysis. Other relevant factors included in the analysis were aging level and WMA technol- ogy. Because field site was confounded with aging level for this dataset, field site could not be included as a random effect in the model in this case. The ANOVA model including recycled materials, aging level, and WMA technology as main effects along with all possible two-way interaction effects among them was first fitted to the data. Because none of the two-way interaction effects was statistically significant at a = 0.05, the ANOVA model including main effects only was used. Table E-13 contains the analysis output obtained by JMP. It can be observed from Table E-13 (see âFixed Effects Testsâ) that the effects of recycled materials, aging level, and WMA technology were all statistically significant at a = 0.05. Table E-13 also presents the predicted values (least squares means) for MR ratio for each level of factors along with their standard errors. From this set of results, it can be concluded that mixtures with no RAP/RAS have a higher MR ratio com- pared to mixtures with RAP/RAS. Aggregate Absorption (High- vs. Low-Absorptive Aggregate) There were 39 non-missing MR stiffness ratio measure- ments obtained from two different field sites (Iowa, Flor- ida) and two levels of aggregate absorption in the data for this analysis. Other relevant factors that were included in the analysis were aging level and WMA technology. The ANOVA model including aggregate absorption, aging level, and WMA technology as main effects along with all possible Response MR Stiffness Ratio Summary of Fit RSquare 0.528446 RSquare Adj 0.258987 Root Mean Square Error 0.131003 Mean of Response 1.446583 Observations (or Sum Wgts) 12 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 4 0.13462633 0.033657 1.9611 Error 7 0.12013258 0.017162 Prob > F C. Total 11 0.25475892 0.2052 Effect Tests Source Nparm DF Sum of Squares F Ratio Prob > F Plant Type 1 1 0.00156408 0.0911 0.7715 Aging Level 2 2 0.12721017 3.7062 0.0798 WMA Technology 1 1 0.00585208 0.3410 0.5776 Effect Details Plant Type Least Squares Means Table Level Least Sq Mean Std Error Mean BMP 1.4351667 0.05348177 1.43517 DMP 1.4580000 0.05348177 1.45800 Aging Level Least Squares Means Table Level Least Sq Mean Std Error Mean Field Aging 1_IN 1.4935000 0.06550152 1.49350 Lab LTOA 1 1.3037500 0.06550152 1.30375 Lab LTOA 2 1.5425000 0.06550152 1.54250 WMA Technology Least Squares Means Table Level Least Sq Mean Std Error Mean HMA 1.4245000 0.05348177 1.42450 WMA 1.4686667 0.05348177 1.46867 _________________________________________________________________________________________________ Table E-12. Analysis results of the effect of plant type.
E-13 two-way interaction effects among them, and field site as a random effect was first fitted to these data. Because the WMA technology*aging level interaction effect was not statistically significant at a = 0.05, it was removed, and the ANOVA model with aggregate absorption, aging level, and WMA technology as main effects, aging level*aggregate absorption and WMA technology*aggregate absorption as two-way interaction effects, and field site as a random effect was fitted again to the data. Table E-14 contains the analysis output obtained by the REML method implemented in JMP. It can be observed from Table E-14 (see âFixed Effects Testsâ) that the effects of aggregate absorption, aging level, aging level*aggregate absorption, and WMA technology* aggregate absorption were statistically sig- nificant at a = 0.05. Table E-14 also presents the predicted values (least squares means) for MR ratio for each level of factors along with their standard errors. For WMA technology*aggregate absorption and aggregate aging level*absorption, a multiple comparison procedure (Tukeyâs HSD) was also carried out to test which of those factor levels are statistically different. It can be seen that for this dataset the difference between high absorption and low absorption was statistically significant for WMA but not for HMA (see âLS Means Differences Tukey HSDâ for WMA technology*aggregate absorption and Fig- ure E-3a). It can also be observed from the interaction plot (Figure E-3b) and Tukeyâs HSD test result that, although high absorption leads to higher MR ratio for each level of aging, in general (except for Field Aging 1_IA), the difference between high absorption and low absorption was statistically significant only for Lab LTOA 2. Response MR Stiffness Ratio Summary of Fit RSquare 0.832989 RSquare Adj 0.757074 Root Mean Square Error 0.214076 Mean of Response 1.789824 Observations (or Sum Wgts) 17 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 5 2.5143317 0.502866 10.9728 Error 11 0.5041147 0.045829 Prob > F C. Total 16 3.0184465 0.0006* Lack of Fit Source DF Sum of Squares Mean Square F Ratio Lack of Fit 7 0.38521025 0.055030 1.8512 Pure Error 4 0.11890450 0.029726 Prob > F Total Error 11 0.50411475 0.2880 Max RSq Effect Tests Source Nparm DF Sum of Squares F Ratio Prob > F Recycled Materials 1 1 0.8570860 18.7020 0.0012* Aging Level 3 3 1.7065448 12.4125 0.0007* WMA Technology 1 1 0.8227346 17.9524 0.0014* Effect Details Recycled Materials Least Squares Means Table Level Least Sq Mean Std Error Mean No RAP/RAS 2.1391094 0.09578452 1.94733 RAP/RAS 1.6087969 0.06723247 1.70391 Aging Level Least Squares Means Table Level Least Sq Mean Std Error Mean Field Aging 1_NM 1.6020781 0.11134181 1.46950 Field Aging 1_TX I 1.5340781 0.09763560 1.63420 Lab LTOA 1 2.0215781 0.11134181 1.88900 Lab LTOA 2 2.3380781 0.11134181 2.20550 WMA Technology Least Squares Means Table Level Least Sq Mean Std Error Mean HMA 1.6385000 0.07568736 1.63850 WMA 2.1094063 0.08138591 1.92433 _________________________________________________________________________________________________ Table E-13. Analysis results of the effect of recycled materials.
E-14 Response MR Stiffness Ratio Summary of Fit RSquare 0.764182 RSquare Adj 0.668108 Root Mean Square Error 0.155178 Mean of Response 1.454256 Observations (or Sum Wgts) 39 Fixed Effect Tests Source Nparm DF DFDen F Ratio Prob > F Aggregate Absorption 1 1 26 12.9133 0.0013* Aging Level 4 4 26.41 10.7705 <0.0001* WMA Technology 1 1 26.01 2.8022 0.1061 Aging Level*Aggregate Absorption 4 4 26 3.0540 0.0345* WMA Technology*Aggregate Absorption 1 1 26.01 5.0244 0.0337* Effect Details Aggregate Absorption Least Squares Means Table Level Least Sq Mean Std Error High Absorption 1.6080909 0.09268907 Low Absorption 1.4084768 0.09291451 Aging Level Least Squares Means Table Level Least Sq Mean Std Error Field Aging 1_FL 1.7168638 0.12146761 Field Aging 1_IA 1.2385112 0.10837145 Field Aging 2_FL 1.8006138 0.12146761 Lab LTOA 1 1.2523017 0.09692408 Lab LTOA 2 1.5331287 0.09618523 WMA Technology Least Squares Means Table Level Least Sq Mean Std Error HMA 1.4665357 0.09216360 WMA 1.5500320 0.09182246 Aging Level*Aggregate Absorption Least Squares Means Table Level Least Sq Mean Std Error Field Aging 1_FL, High Absorption 1.8803638 0.14413327 Field Aging 1_FL, Low Absorption 1.5533638 0.14413327 Field Aging 1_IA, High Absorption 1.2031362 0.12146761 Field Aging 1_IA, Low Absorption 1.2738862 0.12146761 Field Aging 2_FL, High Absorption 1.9583638 0.14413327 Field Aging 2_FL, Low Absorption 1.6428638 0.14413327 Lab LTOA 1, High Absorption 1.2865454 0.10610500 Lab LTOA 1, Low Absorption 1.2180580 0.10948715 Lab LTOA 2, High Absorption 1.7120454 0.10610500 Lab LTOA 2, Low Absorption 1.3542121 0.10610500 LS Means Differences Tukey HSD α = 0.050 Level Least Sq Mean Field Aging 2_FL, High Absorption A 1.9583638 Field Aging 1_FL, High Absorption A 1.8803638 Lab LTOA 2, High Absorption A 1.7120454 Field Aging 2_FL, Low Absorption A B 1.6428638 Field Aging 1_FL, Low Absorption A B 1.5533638 Lab LTOA 2, Low Absorption B 1.3542121 Lab LTOA 1, High Absorption B 1.2865454 Field Aging 1_IA, Low Absorption B 1.2738862 Lab LTOA 1, Low Absorption B 1.2180580 Field Aging 1_IA, High Absorption B 1.2031362 Levels not connected by same letter are significantly different. Table E-14. Analysis results of the effect of aggregate absorption.
E-15 (a) Aging level*aggregate absorption (b) WMA technology*aggregate absorption Figure E-3. Least squares means or interaction plots. WMA Technology*Aggregate Absorption Least Squares Means Table Level Least Sq Mean Std Error HMA, High Absorption 1.5104409 0.09897104 HMA, Low Absorption 1.4226305 0.10016495 WMA, High Absorption 1.7057409 0.09897104 WMA, Low Absorption 1.3943230 0.09899987 LS Means Differences Tukey HSD α=0.050 Level Least Sq Mean WMA, High Absorption A 1.7057409 HMA, High Absorption B 1.5104409 HMA, Low Absorption B 1.4226305 WMA, Low Absorption B 1.3943230 Levels not connected by same letter are significantly different. _________________________________________________________________________________________________________ Table E-14. (Continued).
