Analysis of IT CY Stiffness Modulus of Foamed Bitumen Asphalt Concrete Compacted at 95°C Procedia Engineering 172 ( 2017 ) 550 – 559 1877 7058 © 2017 The Authors Published by Elsevier Ltd This is an o[.]
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 172 (2017) 550 – 559 Modern Building Materials, Structures and Techniques, MBMST 2016 Analysis of IT-CY stiffness modulus of foamed bitumen asphalt concrete compacted at 95ºC Anna Chomicz-Kowalskaa*, Władysław Gardziejczykb, Mateusz M Iwańskia a Department of Transportation Engineering, Faculty of Civil Engineering and Architecture, Kielce University of Technology, Al Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland Department of Transportation Engineering, Faculty of Civil and Environmental Engineering, Białystok University of Technology, Ul Wiejska 45A, 15-351 Białystok, Poland Abstract This study is to compare the results of temperature sensitivity tests of foamed bitumen asphalt concrete (AC 8) compacted at 95ºC with that of the reference mixture compacted at the conventional temperature of 140ºC The tests and subsequent analysis confirm the advantageous effects the modification of bitumen 50/70 with 2.5% Fischer-Tropsch (FT) synthetic wax has on the characteristics of asphalt concrete The characteristics investigated in this study included the air void content and moisture resistance of the specimens in one freezing cycle test (ITSR) Additionally, the relationships between air void content and stiffness moduli were investigated The analysis of temperature sensitivity was conducted based on the measured indirect tensile stiffness modulus, Sm, (IT-CY) at -10ºC, 0ºC, 10ºC and 25ºC The parameters of the asphalt concrete compacted at 95ºC made with FT wax modified foamed bitumen (FT=2.5%) are comparable to those of the reference mixture compacted at 45ºC © 2017 2016The TheAuthors Authors Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd This (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of MBMST 2016 Peer-review under responsibility of the organizing committee of MBMST 2016 Keywords: Half-Warm Mix Asphalt (HWMA); foamed bitumen; stiffness modulus (Sm); Fischer-Tropsch (FT) synthetic wax; asphalt concrete (AC) Introduction Hot mix asphalt technologies (HMA) are the most commonly used technologies in Poland for the production of asphalt mixtures intended for the structural layers of roads The HMA mixtures are produced with aggregate and bitumen heated to high temperatures above 150ºC The production and placement processes consume large amounts * Corresponding author E-mail address: akowalska@tu.kielce.pl 1877-7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of MBMST 2016 doi:10.1016/j.proeng.2017.02.065 Anna Chomicz-Kowalska et al / Procedia Engineering 172 (2017) 550 – 559 of energy and emit large amounts of greenhouse gases with a negative effect on the environment The idea of reducing energy use and limiting emissions in road construction industry has been a subject of interest for many years now by many researchers [4,14,18,19] More than a dozen years ago, the technology called warm mix asphalt (WMA) was introduced to Polish road building industry The WMA mixture production temperature is in the range between 100ºC and 140ºC The lowered processing temperature results from the use of chemical additions or from the reduction in binder viscosity with organic modifiers, such as synthetic waxes derived from the Fischer-Tropsch (FT) process The FT wax significantly affects bitumen rheological properties by increasing the viscosity of the binder below 100ºC, thus increasing its softening point, and by rapidly decreasing the binder viscosity below 100ºC, which allows the asphalt compaction temperature to be reduced by about 30ºC [1] Another option used to reduce the temperature of asphalt production and placement is the modification of the technological process through the foaming of bitumen in the presence of water or through the addition of zeolite Jenkins and his research team [2] developed a new process of asphalt mixture production, half warm mix asphalt (HWMA) with foamed bitumen, in which the processing temperature is below 100ºC Compared with WMA, the technology of foaming with the use of water does not need chemical additions [3] Chemical additions are recommended only when the binder foaming potential is low Analysis of low temperature mixture sensitivity to temperature changes under dynamic loading is an important issue The results of the analysis can be used for comparative evaluation of the resultant mixture relative to the conventional technology Foamed HWMA implementation in Poland will contribute to the protection of the environment by a marked reduction in harmful emissions and non-renewable energy consumption [3,4,5] Tested materials and methodology 2.1 Experimental program The tests aimed at determining temperature sensitivity, that is, the dynamics of stiffness modulus changes with the temperature change in HWMA mixtures with foamed bitumen, and at making direct comparison to the traditional HMA technology The following parameters were determined according to the Technical Guidelines [6], and the EN 13108-1:2008 standard for the analysis of the effect of AC production technology: x air void content (Vm, %) to EN 12697-8:2005, x moisture resistance with one freezing cycle according to Testing Instruction attached as Schedule to WT-2 2010 [6] and according to EN 12697-12, on the basis of the assessment of the indirect tensile strength for a set of wet specimens (ITSw, kPa) and a set of dry specimens (ITSd, kPa) and the indirect tensile strength ratio (ITSR=ITSw / ITSd·100, %), x indirect tensile stiffness modulus, Sm, (IT-CY) at -10ºC, 0ºC, 10ºC and 25ºC according to EN 12697-26 (Annex C) To establish the values of Vm and Sm, the samples were compacted in the Marshall compaction apparatus with the use of 75 impact blows per side To determine the indirect tensile strength and calculate the ITSRs, the samples were compacted with 35 impact blows per side All parameters were measured on samples, which satisfied the assumed requirements with respect to physical and geometric characteristics 2.2 Materials and mix design procedure The mixture design was based on the national requirements [6] for AC mixtures intended for wearing courses under traffic load between KR1 and KR4 (20 year design pavement life of 0.03x10 < ESAL100 kN ≤ 7.30x106 in accordance with the Polish standard [7]) The composition and grading of the designed asphalt concrete mixture are presented in Fig and summarized in Table Laboratory tests involved producing the HMA mixture with bitumen 50/70 (Mix A), HWMA mixtures with foamed bitumen made of bitumen 50/70 (Mix B) and with bitumen 50/70 modified before foaming with FT wax in the amount of 2.5% by mass of the binder (Mix C) The FT processed synthetic wax used in the mixtures is an odourless, milk-white granular material of the congealing temperature in the range from 70 to 100ºC [14] The optimum foaming water amount 551 552 Anna Chomicz-Kowalska et al / Procedia Engineering 172 (2017) 550 – 559 added to produce the bitumen foam was 2.5% for bitumen 50/70 and 2.0% for the bitumen with the FT wax The application of the viscosity-lowering agent (FT wax) before foaming decreased the amount of foaming water with the level of foaming parameters (expansion and half-life) maintained at the same level Too large amounts of water applied to the binder affect the temperature of the bitumen foam and cause fast reduction in its stability (i.e., shortened half life) Positive influence of the synthetic wax on the results of bitumen 50/70 basic tests and on physical properties of the bitumen foam is described in detail in [8,9] The samples made from the reference mixture (Mix A) were compacted at 140ºC, whereas Mix B and Mix C samples were compacted at 95ºC The asphalt mix production temperature was 10ºC and 20ºC higher than the compaction temperatures of HWMA and HMA, respectively In HWMA mixture, the dynamics of the temperature drop relative to the HMA mixture temperature is lower, which is the result of the smaller temperature difference between the asphalt mixture and the ambient This agrees with the solution to the heat flow differential equation [13] and that is why the difference between the mixing and compaction temperatures for Mixes B and C was smaller Table Composition of asphalt concrete mixtures Materials Mineral mixture (% m/m) Bituminous mixture (% m/m) Filler (limestone aggregate) 7.0 6.6 Crushed fine continuously graded aggregate 0/2 mm (limestone) 37.0 34.8 Coarse aggregate 2/5 mm (gabbro) 16.0 15.1 Coarse aggregate 4/8 mm (gabbro) 40.0 37.7 Paving bitumen 50/70 - 5.8 Fig Composition and grading of AC mixture with marked limiting points Results and Discussion 3.1 Physical and mechanical parameters The results from the tests of conventional HMA and foamed HWMA mixtures are compiled in Table Table Results for HMA and foamed HWMA AC mixtures Feature Required values [6] Mix A Mean Std Dev Mix B Mean Std Dev Mean Std Dev Vm (% v/v) 2÷4 2.11 0.154 3.38 0.239 2.29 0.257 ITSd (kPa) - 1052.35 75.578 844.70 73.023 1144.85 33.265 ITSw (kPa) - 1024.01 51.272 727.62 48.982 1069.51 36,079 ITSR (%) ≥ 90 97.3 86.1 Mix C 93.4 Analysis of these results indicates that all mixtures investigated satisfied the requirements with regard to Vm and ITSR Note that one freezing cycle is used to determine ITSR, as in Finland, while in other CEN (European Committee for Standardisation) member countries, even with similar climate to that in Poland (Slovakia, Germany), the freezing cycle is not used for calculating this parameter [15] According to [16,17], in our climatic conditions the number of freeze-thaw cycles should be increased to properly evaluate the adverse effect of moisture and frost on the sensitivity of the asphalt, and hence on the road surface durability The highest average air void content was observed in foamed Anna Chomicz-Kowalska et al / Procedia Engineering 172 (2017) 550 – 559 HWMA Mix B based on neat binder 50/70 The increased amount of air voids was one of the reasons why the ITSR was lower than desired (ITSR=86.1% < 90% according to [6]) Comparable levels of Vm were recorded for Mix A and Mix C, with a difference of only 0.2% The low content of air voids in the specimens formed from Mix C had a positive effect on the water resistance factor (ITSR=93.4%), the value of which was about 7% higher compared with Mix B without the FT wax Moisture sensitivity of asphalt concrete mixtures is a crucial parameter for the durability of asphalt layers in Poland’s climate where pavements experience frequent soaking and multiple freeze-thaw cycles Improved workability and compactability, hence moisture resistance, of the low temperature asphalt concrete (Mix C) was due to the use of FT wax, the presence of which lowered the viscosity and improved the foamability of the 50/70 binder (foam volume increased as did its half life [8, 9]) At service temperatures, FT wax changes the structure of bitumen and asphalt mixture This leads to the increase in viscosity and stiffness, thus improving the rut resistance of the pavement 3.2 Stiffness modulus of foamed bitumen asphalt concrete produced in HMA and HWMA technologies The stiffness modulus of the asphalt concrete mixtures was determined based on the test conducted on cylindrical specimens (IT-CY) The test is non-destructive and provides early information about the behaviour, that is, stiffness, of the asphalt mixture under dynamic loading The tests for the indirect tensile stiffness modulus were carried out in the Universal Testing Machine (UTM-25) under the following conditions: x x x x x test temperature: 10ºC, 0ºC, 10ºC, 25ºC; rise time: 124±4 ms; deformation level: μm; number of loadings: Poisson ratios values (were taken depending on the test temperature): υ=0.25 for -10ºC and 0ºC, υ=0.30 for 10ºC and υ=0.30 for 25ºC The results from the stiffness modulus measurements in indirect tensile testing of AC mixtures in terms of the technology and test temperature used are compiled in Table 3, together with the results of the statistical analysis The graphical interpretation of the relationships above is presented in Figs and Each result for the nine specimens and for each mixture (A, B and C) was the mean value from two measurements obtained before and after turning the specimen by 90º±10º around the horizontal axis, in compliance with EN 1269726, which was in the range of +10% to -20% from the mean value recorded from the first measurement For the results obtained, the arithmetic mean was calculated along with standard deviation, coefficient of variability and minimum and maximum values The normal distribution of the variables was verified with the Shapiro-Wilk normality test The value of p=0.05 was taken as the critical level of significance The assessment of the degree to which the distribution of the variables agreed with the normal distribution was based on the calculated values of skewness and kurtosis, which will be explained later in this article, and used while selecting a significance test in order to evaluate the effect of the selected factors on the Sm value The analysis of the measurement results (indirect tensile stiffness moduli) indicates that the stiffness of Mix B and Mix C, compacted at the same temperature (95ºC), differed significantly independently of the test temperature The presence of FT wax in Mix C has a considerable effect on the increase in the stiffness, leading to similar values of the variable relative to that of the reference mixture, Mix A, compacted at much higher temperature (140ºC) High values of the variable for Mix C in the full range of test temperatures (from -10ºC to 25ºC) are attributable to the presence of the 2.5% synthetic wax, the application of which [8] reduced penetration at 25ºC from 65.9 to 44.3 (0.1mm) and increased the softening temperature by about 13ºC (from 50.4ºC to 63.3ºC) Therefore, this relationship can be expected to hold at higher service temperatures (e.g., during the rutting test at 60ºC) given the effects of the wax modification The presence of the FT wax at processing temperatures reduces the viscosity of the binder thus improving workability and compactability of the asphalt mixture, and at service temperatures it has a significant effect on changes in the structure of the binder and the resultant material by increasing the pavement stiffness and resistance to permanent deformation [8] 553 554 Anna Chomicz-Kowalska et al / Procedia Engineering 172 (2017) 550 – 559 Table Breakdown table of descriptive statistic (N=108) Variable Type of the mix Means N Std Dev Minimum Maximum Coef Var Sm(-10ºC) (MPa) Mix A 25401.1 464.0720 24813 26006 1.826975 0.061755 -1.93698 Mix B 22241.8 554.4634 21410 22909 2.492892 -0.315922 -1.24507 Mix C 25484.3 950.8758 24706 26768 3.731217 0.760626 -1.75316 Mix A 18495.8 318.7557 18001 18909 1.723397 -0.290343 -1.07702 Mix B 15043.6 396.1698 14525 15654 2.633485 0.478011 -1.03970 Mix C 17708.1 314.1618 17207 18091 1.774112 -0.414781 -1.13503 Mix A 9276.6 402.8431 8775 9926 4.342593 0.290182 -1.26042 Mix B 7537.3 552.9338 6876 8271 7.335934 0.145505 -1.91304 Mix C 9538.1 320.7201 9031 9949 3.362511 -0.415528 -1.24061 Mix A 2640.6 123.3097 2467 2792 4.669839 -0.172067 -1.25383 Mix B 1774.7 136.7708 1600 1991 7.706844 0.154675 -1.17571 Mix C 2545.8 137.0874 2350 2725 5.384891 -0.031990 -1.55738 Sm(0ºC) (MPa) Sm(10ºC) (MPa) Sm(25ºC) (MPa) a) b) c) d) Skewness Kurtosis Fig Stiffness moduli of AC mixtures at different measurement temperature: -10ºC (a), 0ºC (b), 10ºC (c), 25ºC (d) 555 Anna Chomicz-Kowalska et al / Procedia Engineering 172 (2017) 550 – 559 3.3 Evaluation of the significance of compaction temperature effect on S m Another element in these considerations was the inference about the significance of the differences between the mean values of independent variables Sm(-10ºC), Sm(0ºC), Sm(10ºC) and Sm(25ºC), in three groups (i.e., Mix A, B and C) in terms of the production technique and stiffness modulus measurement temperature The significance evaluation was also conducted for Vm, which will be used in further analyses for finding relationships between selected parameters of asphalt concrete mixtures The assumption about normal distribution of variable Sm was satisfied in most cases, as was the assumption of the homogeneity of variance checked with Levene’s test for three unrelated groups (Mix A, Mix B, Mix C) Therefore, and due to harmonised calculations, the parametric F test was used for the related samples (with repeated measurements) In the case of variable Vm, both assumptions were satisfied and the F test was also used, here for unrelated samples Calculated values of skewness and kurtosis (Table 3) confirmed a minor deviation from the normal distribution; their absolute values did not exceed the limiting value taken to be [12] Furthermore, Lindman [10] and Box and Anderson [11] demonstrated that statistic F is totally immune to violation of parametric assumptions of normality of distribution and equality of variance, which made it possible to use it for the analysis of the results The results of the calculations conducted to determine the significance of the effect of Type of the mix factor on Vm and Type of the mix and Test temperature factors on Sm, are compiled in Table and Table Figure illustrates the dynamics of changes in indirect tensile stiffness moduli in terms of test temperature for HMA and foamed HWMA concrete (without and with the addition of FT wax) Table Results of analysis of variance (One-way ANOVA) for Vm Effect Univariate Tests of Significance SS Degr of Freedom MS F p-value Intercept 181.4815 181.4815 3712.121 < 0.0001 Type of the mix 8.4652 4.2326 86.576 < 0.0001 Error 1.1733 24 0.0489 Table Results of analysis of variance (Two-way ANOVA) for Sm Effect Repeated Measures Analysis of Variance SS Intercept 1.864905E+10 Degr of Freedom MS F p-value 1.864905E+10 33250.45 < 0.0001 Type of the mix (TM) 1.204208E+08 6.021040E+07 107.35 < 0.0001 Temperature of the test (TT) 7.501274E+09 2.500425E+09 31031.34 < 0.0001 TM*TT 2.535030E+07 4.225050E+06 52.43 < 0.0001 Error 5.801572E+06 72 8.057739E+04 Results of the statistical analysis confirmed that the asphalt concrete mixtures varied significantly with respect to air void content (p-value < 0.0001) As for Sm, both test temperature and mixture type had a significant impact on the values obtained for the parameter tested, because the p-value was lower than the assumed level of significance (α=0.05) 556 Anna Chomicz-Kowalska et al / Procedia Engineering 172 (2017) 550 – 559 Fig Dependence of stiffness moduli changes in indirect tensile test (Sm) on test temperature for HMA and foamed HWMA mixtures The relationships obtained (Fig 3) revealed high effectiveness of the FT wax at lower temperatures of asphalt concrete production The plot of the linear function for the conventional HMA mixture and that compacted at 95ºC with the addition of synthetic wax (Mix C), being nearly identical, allows the inference about similar behaviour of both mixtures under loading at variable temperatures The Mix B, which is a HWMA mixture based on the neat 50/70 binder had a significantly lower values of stiffness modulus within the full range of test temperatures Too high an air void content, hence lowered stiffness, may result in susceptibility to compaction under traffic in the summer season, that is, to permanent deformation (rutting) in the pavement Mathematical dependencies in the form of linear functions explain to a degree higher than 99% the variability of the results (R 2>0.99) The highest, often 4-fold increase in stiffness for the three types of mixtures was recorded at the temperature reduced from 25ºC to 10ºC, while the lowest increase (1.5-fold) was recorded when the temperature was reduced from 0ºC to -10ºC For temperatures in the range 0ºC to 10ºC, an average two-fold increase in the value of Sm was observed with test temperature reduction The results of the F test allowed concurrent comparison of several means, but they did not indicate which group means differ from other group means If the differences between the means turn out to be significant, as was the case, than the test only shows that at least one mean differs from the others Therefore, to estimate detailed significance of the differences between the groups and to determine which particular means differ from each other, the post-hoc comparison was used (Table 6, 7) Table Results from the multiple comparison tests for Vm Duncan test; Variable: Vm (%); M – mean value Marked differences are significant at p < 0.05000 Factor: Type of the mix Mix A Mix A Mix B 0.000065 Mix C 0.101150 Mix B Mix C 0.000065 0.101150 0.000152 0.000152 Table Results from the multiple comparison tests for Sm Duncan test; Variable: Sm (MPa); M – mean value Marked differences are significant at p < 0.05000 -10ºC 0ºC Factors: TT and TM Mix A Mix B Mix C Mix A Mix A 0.000110 0.808198 0.000053 10ºC 25ºC Mix B Mix C Mix A Mix B Mix C Mix A Mix B Mix C 0.000029 0.000047 0.000020 0.000017 0.000024 0.000017 0.000017 0.000018 557 Anna Chomicz-Kowalska et al / Procedia Engineering 172 (2017) 550 – 559 -10ºC 0ºC 10ºC 25ºC Mix B 0.000110 Mix C 0.808198 0.000053 Mix A 0.000053 0.000110 0.000047 Mix B 0.000029 0.000047 0.000024 0.000053 Mix C 0.000047 0.000053 0.000029 0.023442 0.000110 Mix A 0.000020 0.000024 0.000017 0.000029 0.000053 0.000047 Mix B 0.000017 0.000020 0.000017 0.000024 0.000047 0.000029 0.000111 Mix C 0.000024 0.000029 0.000020 0.000047 0.000110 0.000053 0.445995 0.000053 Mix A 0.000017 0.000017 0.000018 0.000020 0.000029 0.000024 0.000053 0.000110 0.000047 Mix B 0.000017 0.000018 0.000011 0.000017 0.000020 0.000017 0.000029 0.000047 0.000024 0.017270 Mix C 0.000018 0.000017 0.000017 0.000017 0.000024 0.000020 0.000047 0.000053 0.000029 0.782198 0.000053 0.000110 0.000047 0.000053 0.000024 0.000020 0.000029 0.000017 0.000018 0.000017 0.000047 0.000024 0.000029 0.000017 0.000017 0.000020 0.000018 0.000011 0.000017 0.000053 0.023442 0.000029 0.000024 0.000047 0.000020 0.000017 0.000017 0.000110 0.000053 0.000047 0.000110 0.000029 0.000020 0.000024 0.000047 0.000029 0.000053 0.000024 0.000017 0.000020 0.000111 0.445995 0.000053 0.000029 0.000047 0.000053 0.000110 0.000047 0.000053 0.000047 0.000024 0.000029 0.017270 0.782198 0.026383 0.026383 It is evident from Table that in the Duncan post-hoc test the p-values above the assumed significance level were obtained from pair comparison for Mix A and Mix C for stiffness moduli at test temperatures of -10ºC (pvalue=0.808198), 10ºC (p-value=0.445995) and 25ºC (p-value=0.782198) This relationship occurred also in the case of Vm, where no statistically significant differences between Mix A and Mix C were observed (p-value=0.101150) This finding supports previous results indicating that the AC mixture with FT wax-modified bitumen compacted at 95ºC (Mix C) does not differ significantly from the conventional hot mixture (Mix A) in terms of compactability and mechanical parameters The remaining comparisons were significant at the adopted level of α=0.05 3.4 Correlation between Vm and Sm of asphalt concrete produced in HMA and HWMA technologies The last stage of the analysis was to find correlations between particular parameters To this end, the analysis of correlation and regression was used The correlation and in the next step regression analysis are statistical tools for accurate quantification of the degree to which the investigated characteristics are associated The strength and direction of the relationship between the measured characteristics were described by the Pearson coefficients of linear correlation (r) The significance of this factor was evaluated The correlation coefficient takes values from interval If the coefficient takes negative values, then the relationship between the tested variables is inverse; when these values are positive, then the association between the variables is direct, which means that the values of the dependent variable increase with increasing value of the independent variable The relationship between the air void content in the asphalt mixtures and indirect tensile stiffness moduli at various temperatures can be used to assess the sensitivity of low temperature mixtures (HWMA mixtures with foamed bitumen) under dynamic loading to temperature changes It can also be used to compare the quality of the mixture against the conventional hot mixture in terms of its compactability, water and frost resistance, stiffness and susceptibility to rutting Table compiles the calculation results of correlation coefficients Table Correlation matrix of the parameters of AC produced in HMA and foamed HWMA technologies Color map of correlations (Sm vs Vm) r >= -1 -0.80 -0.60 -0.40 -0.20 Variable Vm (Mix A) Sm -10ºC -0.803391 0.20 0.40 0.60 0.80 Vm (Mix B) -0.891402 Vm (Mix C) -0.749758 0ºC -0.751275 -0.833511 -0.873834 10ºC -0.813716 -0.853406 -0.872487 25ºC -0.774869 -0.892246 -0.880270 The results indicate that the variable Vm for Mix B shows the strongest correlation with characteristic Sm in the full test temperature range The weakest correlation is demonstrated by variable Vm for the Mix C with characteristic Sm(10ºC) A strong negative correlation (|r| > 0.7) exists for all mixtures On this basis, regression function is developed, defined as an analytical method for assigning mean values of dependent variable to the particular values of the independent variable: y=ax+b, where a tells us by how many units, on average, the value of the dependent variable will increase/decrease when the value of the independent variable increases by unit 558 Anna Chomicz-Kowalska et al / Procedia Engineering 172 (2017) 550 – 559 Previous analyses (item 3.3), which revealed the lack of significant differences between the air void content and indirect tensile stiffness moduli in the case of the comparison of mixtures A and C, allow developing one function describing the relations between these parameters The fit of the model to the empirical data was evaluated through the analysis of the coefficient of determination R2 The mechanism of associations between the selected parameters (Vm and Sm(25ºC)) is presented in the form of regression equations, as graphically illustrated in Fig Table summarizes the values of the estimated structural parameters of the regression function The accuracy of the proposed models was assessed a) b) Fig Relationship between Sm(25ºC) and Vm for Mix A and Mix C (a) and for Mix B (b) Table Results from the regression analysis for Mix A and Mix C (a) and for Mix B (b) a) b) Regression Summary for Dependent Variable: Sm(25ºC) for Mix A & C 2 R = 0.9754 R2 = 0.9513 Adjusted R2 = 0.9444 R = 0.9523 R = 0.9068 Adjusted R = 0.9010 F (1,16) = 155.74 p < 0.0001 Std.Error of estimate: 42.651 ` N=18 b* Intercept Vm Std.Err of b* b Std.Err of b t(16) 3855.864 101.6789 37.9220 -0.952280 0.076307 -573.953 45.9912 Regression Summary for Dependent Variable: Sm(25ºC) for Mix B F (1,7) = 136.79 p < 0.0001 Std.Error of estimate: 32.260 p-value N=9 < 0.0001 Intercept -12.4796 < 0.0001 Vm b* Std.Err of b* b Std.Err of b t(7) 3662.927 161.8047 22.6380 -0.975356 0.083393 -559.024 47.7968 p-value < 0.0001 -11.6959 0.000008 The results presented in Fig and Table indicate that there is a negative association between the indirect tensile stiffness modulus and the content of air voids in the specimens The estimated models have a high adjustment coefficient (R2) and allow explaining more than 90% of the results variability for the mixtures A and C, independent from the production technology An average difference between the observed values of the response variable (Sm) and the theoretical values (standard error of the estimate) was 42.651 for the hot mixture and for the HWMA mixtures with foamed bitumen, Mix A and Mix C (Table 9a), and 32.260 for Mix B (Table 9b) These results are suggestive of a slightly stronger impact of the air void content on the stiffness modulus in mixtures A and C tested at 25ºC (Fig 4a) than in Mix B (higher slope of the regression line) Conclusions Based on the results of the laboratory tests, the following findings are offered: x The modification of bitumen 50/70 with 2.5% FT wax brought advantageous changes in the HWMA mixture, resulting in physical and mechanical parameters comparable with the reference AC hot mixture; Anna Chomicz-Kowalska et al / Procedia Engineering 172 (2017) 550 – 559 x The use of synthetic wax markedly improved workability and compactability of HWMA AC as a result of reduced viscosity and improved foamability, with a positive effect on the lowering of air void content in the specimens and increasing the water resistance of the mixture (ITSR); x The analysis of variance (One/Two-way ANOVA) revealed significant differences between Mix B compacted at 95ºC without the synthetic wax and mixtures A and C; x The Pearson analysis of correlation showed a strong negative association (|r|>0.7) between the compaction level (Vm) of the mixtures and the stiffness moduli (Sm), which can be used for initial assessment of the resistance of low temperature mixtures to water and rutting; x The effectiveness of the synthetic wax was confirmed in the analysis of asphalt concrete compactability and stiffness, conducted with the use of statistical tools (Duncan post-hoc test) to corroborate the fact of obtaining similar properties of the mixture compacted at 95ºC (Mix C) relative to the conventional hot mixture (Mix A) References [1] M Iwański, G Mazurek, Optimization of the Synthetic Wax Content on Example of Bitumen 35/50, Procedia Engineering 57 (2013) 414-423 [2] K.J 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Verification of the criteria for evaluation of water and frost resistance of asphalt concrete, Road Mater Pavement Des., 9(1) (2008) 135-162 [17] P Jaskuła, J Judycki, Durability of asphalt concrete. .. demonstrated that statistic F is totally immune to violation of parametric assumptions of normality of distribution and equality of variance, which made it possible to use it for the analysis of the