Materials and Structures DOI 10.1617/s11527-015-0658-7
ORIGINAL ARTICLE
Identification of dominant parameters for stripping potential in warm mix asphalt using response surface methodology A. Khodaii . E. S. Mousavi . M. Khedmati . A. Iranitalab
Received: 27 March 2015 / Accepted: 22 June 2015 Ó RILEM 2015
Abstract In this study, response surface methodology was utilized for creating a continuous response function and optimization of effective variables to improve the tensile strength ratio, as an indicator of stripping potential, using factorial experiment with center composite design. The polynomial regression model equations were proposed based on the regression coefficients calculated for the indirect tensile strength in dry and saturated condition as well as tensile strength ratio. Statistical analyses indicated that all first and second orders plus interactive terms were statistically significant with 90 % confidence level except for interactive terms of bitumen–Sasobit content in tensile strength ratio, and grading-Sasobit
content in dry indirect tensile strength. Furthermore, it was found that all first, second and interactive terms were statistically significant for saturated indirect tensile strength.
A. Khodaii (&) Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran e-mail:
[email protected];
[email protected]
International concerns of environmental considerations, air quality, fuel crisis and global warming has increased the popularity and usage of warm mix asphalt (WMA) as a substitute for hot mix asphalt (HMA). WMA technology facilitates lower mixing, hauling and laying temperature by decreasing asphalt viscosity and increasing the workability of mixture and hence requiring significantly lower heating energy [9]. The use of warm mixture reduces energy consumption, lowers emissions and odors or greenhouse gases from plants, making better working conditions at both plants and paving sites [9, 22, 24, 30, 32]. Researchers identified as many as fifteen WMA technologies currently available. The eight most common of them are: Synthetic Zeolite, Double Barrel GreenÒ, Low Energy Asphalt, WAM Foam,
E. S. Mousavi Durham School of Architectural Engineering and Construction Management, University of NebraskaLincoln, Lincoln, USA e-mail:
[email protected] M. Khedmati A. Iranitalab Department of Civil Engineering, University of NebraskaLincoln, Lincoln, USA e-mail:
[email protected];
[email protected] A. Iranitalab e-mail:
[email protected];
[email protected]
Keywords Stripping potential Response surface methodology Grading Bitumen content Lime content Sasobit content Warm mix asphalt
1 Introduction 1.1 Background
Materials and Structures
EvothermÒ, RedisetTM WMX, REVIXTM, and SasobitÒ. The first four technologies are foaming based WMA, and the second four are based on chemical or organic additive(s) [9]. These technologies facilitate the decrease in mixing and compaction temperature. Typically mixing temperature used in WMA production is in the range of 100–140 °C compared to the mixing temperatures of 150–180 °C for HMA [17, 30, 36]. Using WMA with lower temperature may lead to an increase in stripping potential of this kind of mixture. In fact decreasing production temperature can cause adhesion failure as moisture may remain in the aggregate. In mixing temperatures of WMA, the aggregates are incompletely dried out as a result many researchers have suggested the use of dry sources [9]. Among many anti-stripping agents that have been used including liquid anti- stripping, hydrated lime and many other commercially available products, hydrated lime is most popular. Researchers believe that after the aggregate and bitumen source, hydrated lime has the most influence on moisture resistance increase [25, 33–35, 37, 38]. It has also been shown that hydrated lime improves rutting and fatigue resistance in WMA [4, 31, 33–35, 38]. Various types of tests have been utilized to evaluate moisture sensitivity of asphalt mixtures, but it seems that there is no consensus among researchers on a single method for evaluating this distress. Although many test procedures are available to predict stripping potential of mixtures, such as Marshal, boiling test and indirect tensile test, some institutions and researchers are of the opinion that the latter is most effective in predicting this phenomenon [20, 31]. The stripping phenomenon has been extensively studied. Several factors have been identified to mitigate stripping. For any given mix temperature, the type and percentage of bitumen, anti-stripping agent, and warm additive, as well as the aggregate gradation and source, are the most contributing factors. Most researches, to date, when studying the stripping potential of WMA, studied the effects of one factor while keeping all other parameters constant. One of the shortcomings of such methodologies is that it cannot explore any possible interaction between the contributing factors. Whereas, these interactive effects are reported to be significant. Haghshenas et al. stated that in parametric studies, the interaction- and second order-terms are sufficiently large that they should not be neglected [11]. Therefore, to conduct a thorough study, the
design of experiment (DOE) must be meticulously selected. Experimental planning is an active, ongoing research area whose ultimate purpose is to guarantee unbiased findings from experimental observations. Several DOE methods such as 3n factorial, center composite design (CCD), Box and Behnken etc. have been developed and choosing a proper method is deeply dependent on the experiment setup, the number of sample points, and the data range [5–8, 16, 27]. Amongst various DOE methods, the response surface method (RSM) has attracted a growing attention in recent years [10, 12–15, 23, 28]. RSM is a collection of statistical and mathematical techniques that are based on an experimental design with the final goal of developing, improving, and optimizing a response variable using minimum experimental effort [11, 12, 19]. In this method, quality characteristic and input variables are called the response and the independent variables respectively. The RSM consists of experimental strategies for exploring independent variables, empirical statistical models for developing an appropriate approximate relationship between the yield and the process variables, and optimization methods for finding values for the process variables that produce desirable response values [5, 27]. In general, the response is a function (f) of the independent variables, perhaps very complicated, which is to be approximated normally by a polynomial function. First-order approximation models are likely to be appropriate when a small region of the independent variables is studied in a vicinity of little curvature in ‘‘f’’. Second-order modes however are more widely used mainly because it is more flexible, it is not too computationally intensive, and there is considerable practical experience indicating that second-order models work well in solving real response surface problems. The RSM is also capable of taking the interaction between the variables into account. The RSM method enables researchers to study problems with a large number of variables. Also, this method can approximate the response function using a few data points which makes the experiment process faster and cheaper. Above all, the RSM accommodates exploring higher terms such as the second-order and the interaction terms. Researchers have recently attempted to quantify simultaneous effects of various factors and their interaction on stripping potential using the RSM method. For instance, Kavussi et al.
Materials and Structures
studied the interactive effects of aggregate gradation and Sasobit content on the moisture susceptibility of WMA mixtures modified by two types of antistripping agent; hydrated lime [18] and Zycosoil [19]. The results revealed that the anti-stripping agents have the greatest effect on the tensile strength ratio (TSR), compared to aggregate gradation and Sasobit content. Furthermore, the influence of the aggregate gradation on decreasing TSR was much greater than that of the anti-stripping agents and Sasobit content. The aim of this study is to create a continuous mathematical model based on statistical concepts. The RSM is employed to assay the influence of percent passing sieve size 4.75 mm (PPSS 4.75 mm), lime content (LC), bitumen content (BC), Sasobit content (SaC) on the stripping potential of WMA and quantify their relative importance. A half fractional factorial CCD is selected as the design matrix since it allows the first order interaction between factors and provides second order polynomial models, which can be employed to predict optimum level of these parameters.
2 Materials and mix design 2.1 Materials Three grading levels of one aggregate type [1], containing 85, 70 and 55 % passing 4.75 mm sieve size were selected (Fig. 1). The grading levels were named as fine, medium and coarse grading. Tables 1 and 2 show physical properties of the aggregates used in this research. AC 60/70 penetration grade bitumen was used to prepare all mixes. Properties of the bitumen are presented in Table 3. Furthermore, hydrated lime was utilized as the anti-stripping and Sasobit as the warm additive. 2.2 Mix design One of the most widely used methods of bituminous mix design is the Marshall method. Stability and flow, together with density, voids and percentage of voids filled with binder are determined at varying binder contents to determine an ‘optimum’ value for stability. The optimum bitumen contents determined according to ASTM D1559 [2], were 6.1, 5.6 and 5.4 % for mixtures with fine, medium and coarse aggregate
grades, respectively. All WMA samples were manufactured at 130 °C.
3 Experimental methods 3.1 Indirect tensile strength test Modified Lottman test [3] aims to evaluate susceptibility characteristics of the mixture to water damage. The test is performed by compacting specimens to an air void level of 6–8 %. Three specimens were selected to be conditioned by saturation with water. These samples were vacuum saturated to a saturation level of 70–80 % before immersing in water. Then samples were submerged in water at 60 ± 1 °C for 24 h and then in water at 25 ± 1 °C for 2 h before testing. The specimens were then tested for indirect tensile strength by loading the specimens at a constant rate (50 mm/ min) and measuring the force required to break them. The tensile strength of the conditioned specimens were compared with the control specimens to determine the TSR. The TSR is calculated as follows: S2 Tensile strength ratio ðTSRÞ ¼ 100 ð1Þ S1 where S1 is a average indirect tensile strength of the dry subset, (kPa) and S2 is a average indirect tensile strength of the conditioned subset, (kPa). 3.2 Design of experiments To investigate the effects of pertinent parameters on WMA properties, the response surface methodology (RSM) was employed. A central composite design (CCD) was adopted in this research to study four factors at three levels. 28 experimental runs including four face centers were generated with four factors and three levels by the principle of RSM using MINITAB Release 15. The CCD design matrix employed includes different levels of factors (Table 4). A quadratic polynomial regression model proposed by Montgomery [27] as shown in Eq. 2 was chosen for predicting the response variable in terms of the four independent variables chosen for this study: Y ¼ b0 þ
4 X i¼1
b i Xi þ
4 X i¼1
bii Xi2 þ
3 X 4 X
bij Xi Xj
i¼1 j¼iþ1
ð2Þ
Materials and Structures
Fig. 1 Grading size distribution of the coarse, medium and fine aggregates
Table 1 Properties of the siliceous aggregate used Test
Standard
Values (%)
MS—2 specifications (%)
LA abrasion loss
AASHTO T96
19
\30
Crushed in one face
ASTM D5821
100
–
Fractured particles in two Face and more
ASTM D5821
93
90\
Coating of aggregate
AASHTO T182
97
95\ \25
Flakiness
BS-812
20
Sand equivalent
AASHTO T176
75
50\
Sodium sulphate soundness
AASHTO T104
2.90
\12
0.40
\8
Table 2 Engineering properties of aggregate used Fraction
Standard
Specific gravity Apparent
Absorption Bulk
Retained on 2.36 mm (no. 8)
AASHTO T85
2.62
2.52
1.58
Passed from 2.36 mm and retained on 0.075 mm
AASHTO T84
2.62
2.51
2.2
Passed from 0.075 mm (no. 200)
–
–
2.68
–
Bulk specific gravity on blended aggregate
–
–
2.53
–
Materials and Structures Table 3 Properties of bitumen used in the study
Test
Standard
AC 60/70
Ductility at 25 °C (cm)
ASTMD 113
100
Penetration at 25 °C, 100 g (0.1 mm)
ASTMD 5
61
Softening point (°C)
ASTMD 36
50.1
Specific gravity at 25 °C
ASTMD 70
1.016
Viscosity at (135 °C)-Pa.s
ASTM D4402
0.51
Table 4 Central composite design arrangement and responses for mixtures Run
Factors
Responses
Passing sieve size 4.75 mm (%)
LC (%)
BC (%)
SaC (%)
TSR (%)
ITSdry (kPa)
ITSsaturated (kPa)
1
55
0.0
4.5
0.5
45
613
274
2
85
0.0
4.5
0.5
28
412
115
3
55
3.0
4.5
0.5
66
708
470
4
85
3.0
4.5
0.5
63
693
439
5
55
0.0
6.5
0.5
43
626
268
6
85
0.0
6.5
0.5
40
426
172
7
55
3.0
6.5
0.5
70
705
496
8
85
3.0
6.5
0.5
78
690
536
9
55
0.0
4.5
2.5
49
440
217
10
85
0.0
4.5
2.5
46
433
199
11
55
3.0
4.5
2.5
56
462
260
12 13
85 55
3.0 0.0
4.5 6.5
2.5 2.5
61 49
641 576
393 284
14
85
0.0
6.5
2.5
56
570
317
15
55
3.0
6.5
2.5
66
581
383
16
85
3.0
6.5
2.5
78
761
593
17
55
1.5
5.5
1.5
81
502
409
18
85
1.5
5.5
1.5
82
491
405
19
70
0.0
5.5
1.5
67
571
383
20
70
3.0
5.5
1.5
85
714
605
21
70
1.5
4.5
1.5
66
672
441
22
70
1.5
6.5
1.5
71
739
526
23
70
1.5
5.5
0.5
88
731
641
24
70
1.5
5.5
2.5
89
698
622
25
70
1.5
5.5
1.5
85
654
557
26
70
1.5
5.5
1.5
87
647
560
27 28
70 70
1.5 1.5
5.5 5.5
1.5 1.5
89 87
639 650
569 563
PPSS percent passing sieve size 4.75 mm, LC lime content, BC bitumen content, SaC Sasobit content
In this equation Y is the response variables (i.e. ITSdry, ITSsat and TSR) and b0, bi, bii, and bij are constant coefficients of intercept, linear, quadratic and
interaction terms, respectively, and Xi and Xj represent the two independent variables (i.e. PPSS 4.75 mm, LC, BC, SaC). The experiments were carried out with
Materials and Structures
three replicates and conducted in a randomized order to avoid systematic bias. The statistical significance of the developed model as well as the effect of factors (linear, quadratic and interactive terms) were evaluated by analysis of variance (ANOVA).
4 Results and discussion 4.1 Model fitting In statistical significance testing, P value is the probability of obtaining a test statistic at the least extreme as the one that was actually observed. This is with the assumption that the null hypothesis is true and P value determines the appropriateness of rejecting the null hypothesis. The smaller the P value is, the smaller will be the probability that rejecting null hypothesis is a mistake. In the above hypothesis it is recommended that before conducting any analyses, the alpha level (i.e. significance of the test) should be determined. The commonly used value for this parameter lies between 0.05 and 0.1. If in a statistical testing, the P value is less than the assumed alpha, the null hypothesis is rejected. P value is calculated from the observed sample. It represents probability of incorrectly rejecting the null hypothesis (i.e. type 1 error). Table 4 lists the values of responses at each of the 28 combination of factorial levels generated by the principles of RSM. Low P values for the regression (P \ 0.1) and the fact that the lack of fit of the model is not significant (P [ 0.1) indicates the suitability of the model (Table 5). According to the results of Table 6, all the first order terms of independent parameters together with second order terms of PPSS 4.75 mm (X1), LC (X2), BC (X3) and SaC (X4) are significant at 90 % confidence level. In case of TSR interactive terms of X1X2, X1X3, X1X4, X2X3 and X2X4, in case of ITS dry interactive terms of X1X2, X1X4, X2X3, X2X4 and X3X4 and in case of ITSsat all interactive terms are significant at 90 % confidence level. Based on the regression coefficients calculated for the response shown in Table 4, the following polynomial regression model Eqs. (3), (4) and (5) are proposed:
TSR ¼ 86:53 þ 0:33X1 þ 11:15X2 þ 3:90X3 þ 1:63X4 4:34X12 10:41X22 17:92X33 þ 2:07X42 þ 2:35X1 X2 þ 2:58X1 X3 þ 2:18X1 X4 þ 1:52X2 X3 3:79X2 X4 ð3Þ ITSdry ¼ 653:22 5:33X1 þ 71:55X2 þ 33:33X3 24:55X4 160:54X12 14:54X22 þ 48:45X32 þ 57:45X42 þ 46:43X1 X2 þ 48:56X1 X4 4:18X2 X3 18:31X2 X4 þ 30:68X3 X4 ð4Þ ITSsat ¼ 560:64 þ 6X1 þ 108:11X2 þ 42:61X3 7:94X4 152:56X12 65:56X22 76:09X32 þ 71:93X42 þ 37X1 X2 þ 16:37X1 X3 þ 37:75X1 X4 þ 13:12X2 X3 31:25X2 X4 þ 20:87X3 X4 ð5Þ where X1 is a percent passing sieve size 4.75 mm (PPSS 4.75 mm), X2 is a lime content (LC), X3 is a bitumen content (BC), X4 is a Sasobit content (SaC). 4.2 Main effect plot Figure 2 is ‘‘Main Effects Plot’’, which is a plot of the mean values of the results obtained at each level of a factor. A main effects plot can be drawn for either the measured response data—the means of the response variable for each level of a factor—or predicted values for each level of a factor. Main effect plots show the relative strength of the effects across factors. It is worthy to note that these plots are used in conjunction with an analysis of variance and DOIs to examine the differences between mean levels for one or more factors [13, 26, 29]. A main effect is present when different levels of a factor affect the response differently. This graph plots the mean response for each factor connected by a line. Figure 2 shows that the influence of LC is more than the influence of BC, SaC and grading (PPSS 4.75 mm) on TSR when each parameter moves from its low level to its mid-level. A change in the BC from low level (4.5 %) to mid-level (5.5 %) results in an increase in the TSR value approximately from 52 to 83 % and in case of SaC varying from low to mid-level leads to a 22 % rise. But in case of LC, a change in the
Materials and Structures Table 5 ANOVA table for TSR, ITSdry and ITSsat values
DF
SS
MS
F values
P values
Total
27
8206.70
–
–
–
Regression
14
8163.71
583.12
175.93
0.000
Residual error
13
43.09
3.31
–
–
Lack of fit (model error)
10
35.30
3.53
1.36
0.446
Pure error (replicate error)
3
7.79
2.6
–
–
R2
99.45
–
–
–
–
TRS
ITSdry Total
27
301469
–
–
–
Regression
14
300950
21496.1
538.43
0.000
Residual error
13
519
39.9
–
–
Lack of fit (model error)
10
398
39.8
0.99
0.573
Pure error (replicate error)
3
121
40.3
–
–
R2
99.83
–
–
–
–
27
615963
–
–
–
ITSsat Total
DF degrees of freedom, SS sum of squares, MS mean square
Regression
14
615073
43933.8
641.84
0.000
Residual error
13
890
68.4
–
–
Lack of fit (model error)
10
811
81.1
3.09
0.192
Pure error (replicate error)
3
79
26.2
–
–
R2
99.86
–
–
–
–
LC from low level to mid-level leads to an increase in the TSR value from around 45–81 %. Then, TSR decreases when PPSS 4.75 mm, BC, LC and SaC move from their mid-level to high level. Variations in PPSS 4.75 mm from its low level (coarse grading) to mid-level (medium grading), and mid-level to high level (fine grading), leads to around 21 % increase and 22 % decrease, respectively, in this response. In addition, it can be concluded that the optimum grading appears to be around the mid-level of 70 in PPSS 4.75 mm. Hence, the maximum TSR value is achieved at this mid-level. 4.3 Effects of parameters: analysis of response surface Surface plots are commonly very helpful in deriving any possible relationships between variables. In a surface plot, the two predictor variables, are plotted in the x and y axis and the response is shown in the z direction by a smooth surface known as surface plot. To study the dependence of the response on the variables, contours and surface plots can be used in conjunction with the established polynomial
relationship between response and factors. To draw the surfaces plots, the mathematical fitted model and the best settings for all the remaining factors are used. If the interactions between variables are shown to be statistically significant, the surface plot gives a complete insight into the effect of a factor on the response [26, 29]. The curvature of the surface plot presented in Fig. 3 suggests that BC–PPSS 4.75 mm, LC–PPSS 4.75 mm, SaC–PPSS 4.75 mm, BC–LC and LC–SaC have interaction with each other in TSR. For instance, at constant LC (3 % of the mixture), an increase in the amount of PPSS 4.75 mm from low level to mid-level results in enhancement of TSR from almost 82–89 % and after that, the values of TSR decrease when PPSS 4.75 mm moves from mid-level to high level (Fig. 3a). Also, at a constant PPSS 4.75 mm (i.e. 85 %), TSR first increases to reach TSRmax (*83 %) and then decreases relative to LC (Fig. 3a). Related, at a constant BC (6 %) when PPSS 4.75 mm changes from low level (55 %) to mid-level (70 %), the values of TSR rises and then it decreases with increasing the amount of PPSS 4.75 mm from
Materials and Structures Table 6 Values of regression coefficients calculated Independent factor
Regression coefficient
T value
SE
P value
137.456
0.6295
0.000
TSR Constant Linear PPSS 4.75 mm
86.53 0.3369
0.785
0.4291
0.044
LC
11.1591
26.005
0.4291
0.000
BC
3.9074
9.106
0.4291
0.000
SaC
1.6381
3.817
1.1336
0.002
Quadratic PPSS 4.75 mm
-4.3441
-3.832
1.1336
0.002
LC
-10.4189
-9.191
1.1336
0.000
BC
-17.9223
-15.810
1.1336
0.000
2.0765
1.832
0.4551
0.090
2.3500
5.163
0.4551
0.000
PPSS 4.75 mm—BC
2.5844
5.678
0.4551
0.000
PPSS 4.75 mm—SaC
2.1823
4.795
0.4551
0.000
LC–BC
1.5214
3.343
0.4551
0.005
LC–SaC
-3.7959
-8.340
0.4551
0.000
BC–SaC ITSdry
0.4387
0.964
0.4551
0.353
2.185
0.000
SaC Interactive PPSS 4.75 mm—LC
Constant
653.228
298.981
PPSS 4.75 mm
-5.333
-3.581
1.489
0.003
LC
71.556
48.046
1.489
0.000
Linear
BC SaC
33.333
22.382
1.489
0.000
-24.556
-16.488
1.489
0.000
Quadratic -160.547
-40.808
3.934
0.000
LC
PPSS 4.75 mm
-14.547
-3.698
3.934
0.003
BC
48.453
12.316
3.934
0.000
SaC
57.453
14.603
3.934
0.000
PPSS 4.75 mm—LC
46.438
29.397
1.580
0.000
PPSS 4.75 mm—BC PPSS 4.75 mm—SaC
0.187 48.562
0.119 30.397
1.580 1.580
0.907 0.000
Interactive
LC–BC
-4.188
-2.651
1.580
0.020
LC–SaC
-18.312
-11.593
1.580
0.000
BC–SaC
30.688
19.427
1.580
0.000
560.641
195.974
2.861
0.000
ITSsat Constant Linear PPSS 4.75 mm LC
6.000
3.077
1.950
0.009
108.111
55.440
1.950
0.000
BC
42.611
21.851
1.950
0.000
SaC
-7.944
-4.074
1.950
0.001
Materials and Structures Table 6 continued Independent factor Quadratic PPSS 4.75 mm
Regression coefficient
T value
SE
P value
-152.569
-29.617
5.151
0.000
LC
-65.569
-12.728
5.151
0.000
BC
-76.069
-14.767
5.151
0.000
71.931
13.964
5.151
0.000
PPSS 4.75 mm—LC
37.000
17.889
2.068
0.000
PPSS 4.75 mm—BC
16.375
7.917
2.068
0.000
PPSS 4.75 mm—SaC
37.750
18.251
2.068
0.000
SaC Interactive
LC–BC
13.125
6.346
2.068
0.000
LC–SaC
-31.250
-15.109
2.068
0.000
BC–SaC
20.875
10.093
2.068
0.000
PPSS percent passing sieve size 4.75 mm, LC lime content, BC bitumen content, SaC Sasobit content
Fig. 2 Main effect plots of TSR versus PPSS 4.75 mm, LC, BC, SaC
mid-level to high level (Fig. 4b). In addition, TSR peaks for 6 % BC for a fine grading (e.g. PPSS 4.75 mm = 85 %). Similar analyses can be carried out for other parameters. It can be concluded that the maximum TSR occurs around mid-level of PPSS 4.75 mm (70 %) where the optimum grading exists. Also in around mid-level of LC (1.5 %) the maximum TSR is achieved, this is also confirmed by the results of other researches. Many researchers reported that 1–1.5 % lime content can control or prevent stripping phenomena [13, 18, 22, 25]. Like the surface plot, a contour plot can be used to illustrate the relationships between three variables on a
single plot. It takes two predictor variables (x and y) and uses the contour plot to show how they influence a response variable (z). A contour plot is like a topographical map in which x, y, and z values substitute for longitude, latitude, and elevation. Values for the predictor factors are plotted on the x and y axes, while contour lines and colored bands represent the values for the z factor (response). Contour lines connect points with the same response value. For example in Fig. 4a, the range where TSR is higher than 80 % is limited to the LC of around 1.3–3 % and PPSS 4.75 mm of around 58–85 %.
Materials and Structures
Fig. 3 Surface Plots of TSR for TSR versus a LC and PPSS 4.75 mm, b BC and PPSS 4.75 mm, c SaC and PPSS 4.75 mm, d LC and BC, e SaC and LC
Also, the range where TSR is higher than 85 % is limited to the BC of around 5.3–5.9 % and PPSS 4.75 mm of around 61–81 % (Fig. 4b).
5 Optimization of the process response One of the main objectives of RSM is to determine the optimum settings of the control variables that result in
a maximum (or a minimum) response over a certain region of interest. The derived models can be used for interpolation within the levels of the studied parameters to achieve the maximum (or a minimum) desired response [18, 21]. Based on the contemplated factors in this research, the aim would be to achieve a maximum for TSR. The maximum response was achieved under the following conditions:
Materials and Structures
Fig. 4 Contour Plots of TSR versus a LC and PPSS 4.75 mm, b BC and PPSS 4.75 mm, c SaC and PPSS 4.75 mm, d LC and BC, e SaC and LC
TSR ¼ 89 % 1; LC ¼ 1:5 %; BC ¼ 5:5 %; SaC ¼ 2:25 and PPSS 4:75 mm ¼ 70 %: Although the optimization indicates an amount of 2.25 % Sasobit, for practical purposes one can use lower Sasobit content if relatively lower TSR of say about 80 % is acceptable.
6 Conclusion The RSM was utilized to derive mathematical models for predicting stripping potential of warm mixed asphalt. From the experimental work and statistical analyses carried out, the following conclusions could be derived for the range of materials tested in this study:
Materials and Structures
1.
2.
3.
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Using the RSM based on CCD concepts could create a continuous response function of a number of involving parameters and their interactions with sufficient precision and smaller number of tests. Statistical analyses indicated that except interactive term of bitumen content–Sasobit content in case of TSR and percent passing sieve size 4.75 mm-Sasobit content in case of the indirect tensile strength (dry samples), all first- and second- order plus interactive terms were statistically significant at 90 % confidence level. Also, it could be derived that all terms were statistically significant at the same confidence level in the case of the indirect tensile strength (saturate samples). From derived mathematical models (i.e. ITSdry and ITSsat) it could be concluded that coefficient for the first degree term for lime content in the dry samples were smaller than the saturated samples. This could be an indication that in saturated specimens, hydrated lime may act both as filler and as an additive, causing a pronounced increase in indirect tensile strength properties of the samples. From main effect plots of the TSR it could be summarized that the influence of the lime content is more than that of bitumen content, Sasobit content and percent passing sieve size 4.75 mm on TSR when each parameter moves from its low level to mid-level. From main effect plots of the TSR, it could be summarized that the influence of percent passing sieve size 4.75 mm is less than that of bitumen content, Sasobit content and lime content on TSR when each parameter moves from its mid-level to high level. Using the RSM and its optimization process, the maximum value of TSR occurred in the following situation: Lime content ¼ 1:5 %; bitumen content ¼ 5:5 %; Sasobit content ¼ 2:25; and percent passing sieve size 4:75 mm ¼ 70 %:
Acknowledgments Authors would like to acknowledge Mr. H.F. Haghshenas for his discussion on statistical modeling.
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