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11 Rut Resistance research is done on performance modeling of HMA pave- ments. Furthermore, some researchers and engineers may A very good relationship has been found between mixture prefer other approaches to estimating characteristic temper- rut resistance and mixture resistivity. Resistivity indicates the atures for rutting in HMA pavements. resistance to binder flow exhibited by a particular aggregate An important practical question in applying Equation 1 is structure. It is analogous to electrical resistivity, defined as "a how to estimate the specific surface of the aggregate. In analyz- materials opposition to the flow of electrical current." Resis- ing a wide range of aggregate gradation data, it was found that tivity can also be thought of as the inverse of the coefficient of for routine purposes the aggregate specific surface can be accu- permeability for a granular material. It increases with increas- rately estimated by summing the percent passing the 75-, 150-, ing binder viscosity, increasing aggregate specific surface and and 300-m sieves and dividing the total by 5. The sum of the decreasing VMA. Because HMA is almost always designed at percent passing the 75-, 150-, and 300-m sieves is called the close to 4% air voids, VMA will normally be proportional to fineness modulus, 300-m basis, abbreviated as FM300. The rela- VBE so that resistivity is closely but indirectly related to tionship between this parameter and aggregate specific surface apparent film thickness; mixtures with thin binder film thick- was evaluated using data from eight projects, as shown in Fig- ness will generally exhibit high resistivity values. Resistivity ure 1; the data used in this analysis was as reported for NCHRP can be calculated using the following formula: Project 9-9, the NCAT Test Track, Pooled Fund Study 176, the * Sa2Gsb 2 Florida permeability study, MnRoad, FHWA's Accelerated P= (1) Loading Facility (ALF) rutting study, WesTrack, and data from 4.9VMA 3 NCHRP Projects 9-25 and 9-31 (2, 3, 5, 6, 2931). This was the where best and one of the simplest methods found for relating aggre- P = resistivity, s/nm; gate gradation to aggregate specific surface and is well suited for |*| = binder viscosity at the temperature of interest, Pa-s; routine use in mix design work and HMA specifications. Spe- Sa = aggregate specific surface, m2/kg; cific surface can be estimated reasonably accurately simply by Gsb = aggregate bulk specific gravity; and dividing FM300 by 5. The r2 for this relationship is 90%, while the VMA = voids in the mineral aggregate, volume %. 95% prediction limit for new observations (including in Figure 1) is about ± 0.8. It should be emphasized that Equation 1 is not an empiri- The current method of controlling aggregate specific sur- cal relationship developed during NCHRP Projects 9-25 and face involves establishing limits on the amount of aggregate 9-31 for characterizing the rut resistance of HMA. Instead, it passing the 75-m sieve and controlling the dust-to-binder is the inverse of an existing equation for estimating the per- ratio. To compare this approach with FM300, Figure 2 shows the meability of a granular material (28). Therefore, the choice of same data set used in Figure 1, but in this case the horizontal variables, the values of the exponents, and the value of the axis is the percent finer than 75 m. The r2 value in this case is constant 4.9 are not of the authors' choosing--they result only 76%, and the 95% prediction limit increases to ±1.3. directly from Winterkorn's formula for permeability and Clearly there is a relationship between the specific surface of a reflect on a fundamental level the factors governing fluid flow given aggregate and its mineral filler content, but this rela- through porous media. tionship is only moderately strong. FM300 appears to be a sig- Because of the extreme influence of temperature on the nificantly more accurate approach and is also more flexible in flow properties of asphalt, care must be taken in selecting the temperature at which viscosity is determined when calculat- ing resistivity for HMA. For laboratory tests, the viscosity 12 NCHRP 9-9 Agg. Spec. Surf., m /kg NCAT Track should be determined at the same temperature at which the 10 S a = 0.203FM 300 2 P.F. 176 HMA is being characterized. For field rutting, the situation is 8 FL/Perm. more complicated. The value used should be some tempera- 6 MN/Road ture estimated to be characteristic of the overall potential for 9-25/31 4 permanent deformation in the given climate. For example, ALF 2 within the current Superpave system, the critical temperature WesTrack for rutting used in selecting PG binders is the yearly, 7-day- 0 Fit 0 20 40 60 95 % P.L. average, maximum pavement temperature, measured 50 mm 95 % P. L. below the pavement surface. This is the temperature used in FM300 this research in calculating resistivity for field projects. How- Figure 1. Estimated Aggregate Specific Surface as a ever, it should be kept in mind that the manner of calculating Function of FM300 P75 P150 P300 (r2 90%; Plot the critical rutting temperature will likely evolve as further Includes 95% Prediction Limits for New Observations).
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12 12 NCHRP 9-9 ing the asphalt content ± 0.5% from the design value. The rela- Agg. Spec. Surf., m /kg 10 NCAT Track tionship in Figure 3 is quite good although it appears that the 2 P.F. 176 MPSS values at a given level of Ndesign × resistivity are somewhat 8 FL/Perm. higher for mixtures containing limestone aggregate compared 6 MN/Road with the gravel and granite aggregates. One possible explana- 4 9-25/31 tion for this is that the limestone aggregate, being relatively S a = 2.05 + 0.623P 75 ALF 2 soft, breaks down during the RSCH test more than do the WesTrack 0 Fit harder aggregates. As discussed below, limited calibration of 0 5 10 15 95 % P.L. the resistivity equation suggests that this is not a serious prob- P75, % 95 % P.L. lem in applying this approach to field-rutting data. The resistivity approach to estimating mixture rut resist- Figure 2. Estimated Aggregate Specific Surface as a ance was verified by using field-rut data from the MnRoad, Function of Material Finer than 75 m (r2 76%; Plot NCAT, and WesTrack project (2, 5, 6). It must be emphasized Includes 95% Prediction Limits for New Observations). that this calibration was performed using a substantial set of existing field data and not the limited laboratory data col- that it will allow producers with materials deficient in mineral lected during NCHRP Projects 9-25 and 9-31. The data used filler to provide additional surface area by increasing the in calibrating the rutting model is summarized in Tables 1 amount of material in the 75- to 300-m size range. Some and 2. In calculating resistivity, the 7-day average high pave- engineers may object to the use of FM300 because it appears ment temperature at a depth of 50 mm was used. Further- possible to meet requirements stated in this manner using more, the amount of binder age hardening was estimated aggregate with little or no mineral filler; however, it should be using a modification of Mirza and Witczak's global aging remembered that current Superpave requirements have clear model (discussed below). A statistical analysis of this data minimum and maximum values on the amount of material resulted in the following semi-empirical equation: finer than 75 m. Figure 3 is a plot showing maximum permanent shear RR = 224 P -1.08 N eq -0.650 RD -18.6 (2) strain (MPSS) determined using the RSCH test as a function of Ndesign × resistivity. Multiplying resistivity by Ndesign is neces- where sary to account for differences in compaction energy, which RR = Rutting rate, mm rutting/m thickness/ESALs1/3 can increase resistance to permanent deformation independ- (equivalent single axle loads); ent of mixture composition. RSCH tests were performed at P = Resistivity, in s/nm; 54 °C and 60 °C, and the HMA tested incorporated a range of Neq = Ndesign or number of blows with Marshall com- asphalt binders; the viscosity values used in calculating resis- paction hammer; and tivity were determined for each binder at the temperature for RD = Relative field density = (100% - in-place voids)/ the corresponding RSCH test. The specimens tested represent (100% - design voids). a wide range of mix composition and Ndesign levels. Addition- ally, air void contents were varied for these mixtures by alter- The relationship between this function and the observed rutting rate is shown in Figure 4. The r2 value for this model was 89%, which is very good considering that this model 10 KY Limestone includes data from three widely different climates and uses PA Gravel PA Limestone only laboratory mix data and in-place air voids to predict the 8 CA Granite rutting rate. The 90% prediction limits shown in Figure 4 cor- RSCH MPSS, % respond closely to plus or minus a factor of 2.0 in the esti- 6 Limestone Fit mated rut depth. Thus, if the estimated rut depth found with 4 Gravel/Granite Fit Equation 2 were 8 mm, the 90% prediction limits would be 2 4 to 16 mm. The 90% confidence level was chosen because for R = 81% 2 rutting, only the upper confidence level is of practical inter- 2 R = 88% est, so this corresponds to a 95% one-sided prediction limit 0 for design purposes. Although a factor of 2 might seem large 0 5000 10000 15000 for a confidence limit, this is equivalent to a factor of safety of N x Resistivity, s/nm 2, which is common in much practical engineering work. Figure 3. RSCH Permanent Shear Strain as a It should be emphasized that Ndesign in Equation 2 refers to Function of Gyrations Resistivity. the number of gyrations (or Marshall blows) required to
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13 Table 1. Properties of mixtures used in calibration of rutting model. Mix Design Ndesign Method or Aggregate Aggregate Binder Modifier Section Blows Aggregate Type NMAS Gradation Grade Type mm NCAT Test Track Mixtures N1 Superpave 100 Slag/Limestone 12.5 ARZ PG 76-22 SBS N2 Superpave 100 Slag/Limestone 12.5 ARZ PG 76-22 SBS N3 Superpave 100 Slag/Limestone 12.5 ARZ PG 67-22 N/A N4 Superpave 100 Slag/Limestone 12.5 ARZ PG 67-22 N/A N5 Superpave 100 Slag/Limestone 12.5 BRZ PG 67-22 N/A N6 Superpave 100 Slag/Limestone 12.5 BRZ PG 67-22 N/A N7 Superpave 100 Slag/Limestone 12.5 BRZ PG 76-22 SBR N8 Superpave 100 Slag/Limestone 12.5 BRZ PG 76-22 SBR N9 Superpave 100 Slag/Limestone 12.5 BRZ PG 76-22 SBS N10 Superpave 100 Slag/Limestone 12.5 BRZ PG 76-22 SBS N11 Superpave 100 Granite 12.5 TRZ PG 76-22 SBS N12 SMA 50 Granite 12.5 SMA PG 76-22 SBS N13 SMA 50 Gravel 12.5 SMA PG 76-22 SBS S1 Superpave 100 Granite 12.5 BRZ PG 76-22 SBS S2 Superpave 100 Gravel 9.5 BRZ PG 76-22 SBS S3 Superpave 100 Limestone/Gravel 9.5 BRZ PG 76-22 SBS S4 Superpave 100 Limestone 12.5 ARZ PG 76-22 SBS S5 Superpave 100 Gravel 12.5 TRZ PG 76-22 SBS S6 Superpave 100 Limestone/RAP 12.5 ARZ PG 67-22 N/A S7 Superpave 100 Limestone/RAP 12.5 BRZ PG 67-22 N/A S8 Superpave 100 Marble/Schist 12.5 BRZ PG 67-22 N/A S9 Superpave 100 Granite 12.5 BRZ PG 76-22 SBS S10 Superpave 100 Granite 9.5 ARZ PG 67-22 N/A S11 Superpave 100 Marble/Schist 12.5 BRZ PG 76-22 SBS S13 Superpave 100 Granite 12.5 ARZ PG 76-22 SB MnRoad Mixtures 1 Marshall 75 Gravel/Granite 12.5 ARZ PG 58-28 N/A 2 Marshall 35 Gravel/Granite 12.5 ARZ PG 58-28 N/A 3 Marshall 50 Gravel/Granite 12.5 ARZ PG 58-28 N/A 4 Superpave 100 Gravel/Granite 12.5 ARZ PG 64-22 N/A 14 Marshall 75 Gravel/Granite 12.5 ARZ PG 58-28 N/A 15 Marshall 75 Gravel/Granite 12.5 ARZ PG 58-28 N/A 16 Superpave 100 Gravel/Granite 12.5 ARZ PG 64-22 N/A 17 Marshall 75 Gravel/Granite 12.5 ARZ PG 58-28 N/A 18 Marshall 50 Gravel/Granite 12.5 ARZ PG 58-28 N/A 19 Marshall 35 Gravel/Granite 12.5 ARZ PG 58-28 N/A 20 Marshall 35 Gravel/Granite 12.5 ARZ PG 58-28 N/A 21 Marshall 50 Gravel/Granite 12.5 ARZ PG 58-28 N/A 22 Marshall 75 Gravel/Granite 12.5 ARZ PG 58-28 N/A 23 Marshall 50 Gravel/Granite 12.5 ARZ PG 58-28 N/A WesTrack Mixtures 35 Superpave 96 Andesite 19.0 BRZ PG 64-22 N/A 38 Superpave 96 Andesite 19.0 BRZ PG 64-22 N/A 39 Superpave 96 Andesite 19.0 BRZ PG 64-22 N/A 54 Superpave 96 Andesite 19.0 BRZ PG 64-22 N/A Notes: SMA = stone matrix asphalt; RAP = recycled asphalt pavement; ARZ = above restricted zone; BRZ = below restricted zone; TRZ = through restricted zone; SBS = styrene-butadiene-styrene rubber; SBR = styrene-butadiene rubber; SB = styrene-butadiene compact the specimen during quality-control (QC) testing, should also be noted that using as-designed data when apply- corresponding to Ndesign for the job mix formula (JMF). The ing Equation 2 to field data will often result in poor predic- air void content at Ndesign will, in this case, often deviate from tions of rutting rate because HMA mixes as-placed often vary 4.0%; however, changes in air void content and VMA are substantially from their as-designed characteristics. If an esti- accounted for in Equation 2 in the resistivity term, which mate is needed of the effect of deviations during production should also be calculated using QC data when possible. It from as-designed characteristics, rutting should be calculated
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14 Table 2. Summary of factors and levels included in calibration of rutting model. Factors Types/Levels Sections/mixtures 43 U.S. climates Southeastern (Alabama), Northcentral (Minnesota), Intermountain (Nevada) Aggregate type Andesite, granite, gravel, limestone, marble, schist, slag Mix design methods Superpave--29 (96 and 100 gyration), Marshall--12 (35, 50 and 75 blows), SMA--2 (50 gyration) Aggregate NMAS 36 mixtures 12.5-mm, 3 mixtures 9.5-mm, 4 mixtures 19.0-mm Aggregate gradation 22 mixtures ARZ, 17 BRZ, 2 TRZ, 2 SMA PG grades PG 58-28, PG 64-22, PG 67-22, PG 76-22 Modified/unmodified binders 15 mixtures modified, 28 unmodified Modifier types SBS, SBR FM300 (QC) Min. 21.6, Max. 42.8, Avg. 29.4 VMA (QC) Min. 10.9 %, Max. 16.3 %, Avg. 14.6 % VTM (QC) Min. 1.9 %, Max. 7.4 %, Avg. 3.7 % VTM (In-Place) Min. 3.3 %, Max. 8.2 %, Avg. 6.2 % Notes: SMA = stone matrix asphalt; ARZ = above restricted zone; BRZ = below restricted zone; TRZ = through restricted zone; SBS = styrene-butadiene-styrene rubber; SBR = styrene-butadiene rubber using both as-designed and as-produced data (using field air decreases rutting rate by 18%. This might at first seem counter- voids in each case to calculate relative density). The difference intuitive, but by increasing the design air void level while main- between these rutting rates will then provide an estimate of taining the in-place air void content, the energy of compaction the effect on rutting rate of deviations from the mix design. required to construct the pavement is increased significantly. A series of simple plots can be constructed using Equations Conversely, decreasing air voids under constant in-place air 1 and 2 to illustrate the specific effect of changing VMA, design voids decreases the energy required for field compaction. air voids, and aggregate fineness on rutting rate. These plots Figure 6 shows the effect of in-place air voids on rutting rate were constructed assuming typical values for Superpave mix- at a constant design air void content of 4%. Each 1% decrease tures for |*|, aggregate specific surface and Ndesign - 5,000 Pa-s, in in-place air voids decreases the rutting rate by about 18%. 4.8 m2/kg and 75 gyrations, respectively. Figure 5 shows esti- Note that the magnitude of the effect of changes in design air mated rutting rate (mm/m/ESALs1/3) as a function of design void content and in-place air void content appear to be nearly VMA and design air void content for a constant in-place air identical. In fact, if in-place air void content is allowed to vary void content of 7%. As VMA increases, rut resistance decreases; with design air voids (i.e., in-place air voids of 8% for 5% the estimated rutting rate decreases by about 20% for each 1% design air voids, in-place air voids of 6% for design air voids decrease in VMA. Each 1% increase in design air voids of 3%), the factors nearly offset each other and there is little net change in rut resistance. As will be emphasized repeatedly in this report, in order to develop efficient HMA mix designs 2.5 1/3 Rut Rate, mm/m/ESALS 2.0 NCAT 1.5 (1/3) MN/Road 1.5 Rut Rate, mm/m/ESALs 3% design / 7% in-place WesTrack 1.0 4% design / 7% in-place 1.0 5% design / 7% in-place 0.5 0.0 0.5 0 2,000 4,000 6,000 8,000 1.08 0.65 18.6 P N RD 0.0 Figure 4. Relationship Between Field Rutting 12 13 14 15 16 17 18 Rate and Proposed Function of Resistivity, Design VMA, Vol. % Ndesign and Air Voids; the Heavy Center Line Represents the Rutting Rate Predicted Using Figure 5. Effect of Design VMA and Air Voids on Equation 2 While the Thinner Lines Represent Rut Resistance of Superpave Mixtures at a Constant 90% Prediction Limits for New Observations. In-Place Air Void Content of 7%.
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15 1.5 Project, and the WesTrack project. The aggregate fineness has Rut Rate, mm/m/ESALs(1/3) 4% design / 8% in-place a very large effect on rut resistance; changing the value of 4% design / 7% in-place FM300 from 20 to 30 decreases the rutting rate by more than a 1.0 4% design / 6% in-place factor of 2; increasing FM300 from 30 to 40 further decreases the rutting rate by a factor of about 1.9. It can be concluded 0.5 that aggregate fineness, as indicated by FM300, should be care- fully controlled in order to better design Superpave mixtures for specific levels of rut resistance. Because rut resistance 0.0 depends on both VMA and aggregate specific surface (as indi- 12 13 14 15 16 17 18 cated in this case by FM300), these factors should ideally be Design VMA, Vol. % controlled simultaneously. As discussed later in this report, Figure 6. Effect of VMA and In-Place Air Voids on control of aggregate specific surface also helps to limit mix- Rut Resistance of Superpave Mixtures at a Con- ture permeability. The main practical problem is how to stant Design Air Void Content of 4%. establish such control without being unduly restrictive in the requirements for VMA and aggregate gradation. in the laboratory and then to effectively control these mixtures In order to put the previous analysis into perspective, Fig- in the field, it is essential to understand how changes in design ure 8 was constructed, which shows the relationship between air void content effect performance. If in-place air voids are rutting rate, asphalt binder grade, and Ndesign. Binder PG grade, assumed to be independent of design air voids, increasing like FM300, is a very important factor in determining mixture design air void content will improve performance because greater compaction energy is required to reach the target value rutting rate; in this analysis, increasing the binder grade from for in-place voids. Under these conditions, decreasing design a PG 58-28 to a PG 64-22 increases the rutting rate by a factor air void content will reduce performance because less com- of 2.6. Increasing the binder grade from a PG 64-22 to a PG paction energy is then required to reach the target in-place air 70-22 increases the allowable traffic by a factor of 2.4. The void level. However, if in-place air voids more or less follow effect of compaction is not nearly as large as that of binder changes in design air voids, there will be little effect on per- grade. Increasing Ndesign from 50 to 75 reduces the estimated formance as a result of changing design air voids. It should be rutting rate by 23%. Increasing Ndesign again from 75 to 100 fur- noted (as discussed later in this chapter) that changes in in- ther decreases rutting rate by 17%, while again increasing place air void level also significantly affect permeability. Engi- Ndesign from 100 to 125 decreases rutting rate by 14%. neers contemplating changes in design air void content should In summary, the effects of changing various aspects of mix- carefully and realistically consider the ways in which such ture composition on rutting resistance (mm/m/ESALs1/3) are changes will affect pavement performance. as follows: Figure 7 is similar to the previous two plots and shows the effect of VMA and aggregate fineness, as indicated by FM300. · Decrease VMA 1%, increase design VTM 1%, or decrease This value was allowed to vary from 20% to 40%, which is a field VTM 1%: decrease rutting rate by about 20%. typical range for Superpave mixtures based upon quality con- · Increase in aggregate fineness by 10 as indicated by FM300: trol gradation data from the NCAT Test Track, the MnRoad decrease rutting rate by a factor of about 2. 1.5 1.5 Rut Rate, mm/m/ESALs(1/3) Rut Rate, mm/m/ESALs(1/3) FM-300 = 20 PG 58-28 FM-300 = 30 PG 64-22 1.0 FM-300 = 40 1.0 PG 70-22 0.5 0.5 0.0 0.0 12 13 14 15 16 17 18 25 50 75 100 125 150 Design VMA, Vol. % Ndesign Figure 7. Effect of Aggregate Fineness and Design Figure 8. Effect of Binder Grade and Ndesign on Rut VMA on Rut Resistance of Superpave Mixtures at a Resistance of Superpave Mixtures (Design Air Voids Constant In-Place Air Void Content of 7%. 4%, In-Place Air Voids 7%).
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16 · Increase of one level in high-temperature PG-grade: extreme caution should be used in applying this model to decrease rutting rate by a factor of about 2.5. mixtures containing poor quality aggregates. Aggregate gra- · Increase Ndesign by one level: decrease rutting rate by about dations included in the mixtures upon which Equation 2 were 15% to 25%. based included mostly coarse gradations, with significant numbers of fine and dense gradations, and a few gap-graded Several comments should be made concerning this analy- materials (SMA mixtures). However, no open-graded sis. First, although the model used in this analysis was based mixtures were included in these data. Therefore, Equation 2 on a substantial data set, further refinement of the model should also not be applied to open-graded friction course using an even wider range of data is needed before it can be mixtures until its accuracy for such materials has been used with confidence for a wide range of conditions. Of par- verified. ticular concern are the specific effects of mineral filler and A second important limitation to the proposed model for polymer modification on rut resistance; the data set used in rut resistance involves the behavior of mixtures at very low calibration of the resistivity model included mixtures made air void contents. It is well known that at in-place air void using a large number of modified binders, but these mixtures contents below about 2% to 3%, many HMA pavements will also tended to be those with the highest specific surface. exhibit a sudden and dramatic decrease in rut resistance. Therefore, there is some confounding of these effects. As part This is attributable to excessive asphalt binder content, of NCHRP Project 9-33, the rutting/resistivity model is being which prevents aggregate particles from developing the re-evaluated and refined; preliminary results indicate that the internal friction needed for good rut resistance. For this rea- general form of the model is correct, as are most of the trends son, it is generally accepted that air void contents below predicted by the model. Specific exponents in the final model about 3% should be avoided when designing HMA mixes. will be somewhat different from those given in Equation 2. This phenomenon is not directly addressed in the resistivity For example, initial analysis suggests that the exponent to equation (Equation 1) or the associated equation for rutting Ndesign in Equation 2 should be -.949 rather than -0.595. Most rate (Equation 2). Therefore, the proposed approach to importantly, it appears that, all else being equal, many accounting for the effect of mixture composition on rut mixtures made using polymer modified binders will exhibit resistance should not be applied to mixtures with very low substantially better rut resistance than predicted on the basis air void contents. Based upon the range of air void contents of resistivity alone (32). included in this analysis, the proposed equations should not It must be emphasized that the various factors affecting rut be applied to mixtures designed at air void contents below resistance are additive and that although some may seem rel- about 3%, or to field produced mixtures with air void con- atively insignificant, if these act together in the same way the tents in QC testing below about 2.5%, or to pavements with results can be quite large. Engineers contemplating modifica- in-place air void contents below about 4%. This qualifica- tion in current Superpave requirements (or specifications for tion does not mean that the model is not accurate for these other HMA types) must consider not only the effect of a par- conditions--only that its accuracy has not been evaluated ticular change in a given characteristic, but also the combined for such circumstances. effects of all other such changes. Although these caveats to the proposed rutting model are Although aggregate angularity and gradation do not substantial, in essence the proposed model should be valid appear in either the resistivity equation or the related equa- for mixtures meeting or nearly meeting current require- tion for rutting rate, Equation 2 does include terms for both ments for Superpave mixtures, heavy-duty Marshall mix design compaction level and field compaction, which is designs, and SMA mixtures. As discussed in Chapter 3, it accounted for through relative density--that is, field density/ appears that the overall level of rut resistance in the vast air voids compared with design density/air voids. As aggregate majority of HMA designed using the Superpave system is quality decreases--that is, as an aggregate becomes less angu- adequate. However, some agencies have noted a decrease in lar and/or cubical and/or resistant to crushing--Ndesign (i.e., fatigue resistance and an increase in permeability with the gyrations required to reach 4% air voids) will decrease, which widespread adoption of Superpave mix design require- will cause the rutting rate estimated using Equation 2 to ments, and some have increased minimum VMA require- increase. Thus, the proposed approach for accounting for the ments to improve fatigue resistance of these materials. The affect of mixture composition on rut resistance indirectly findings above suggest that aggregate specific surface should includes the effect of aggregate angularity and gradation be increased along with VMA in order to maintain good rut through inclusion of terms for laboratory and field com- resistance. As discussed below, this will have the added ben- paction effort. Because the proposed relationship for rut efit of helping to limit HMA permeability. This and other resistance was based on mixtures that were mostly made with ramifications of the findings presented above are discussed cubical, well-crushed aggregates with little or no natural sand, in greater detail in Chapter 3.