1. RATIONAL BAILEY RATIOS AND DOMINANT AGGREGATE SIZE RANGE POROSITY CORRELATED WITH RUTTING AND MIXTURE STRENGTH PARAMETERS
Emile HORAK*,1 , Haissam SEBAALY*, James MAINA*,2 & Sudhir VARMA*
*Engineering /Technical staff of ANAS SpA, Doha, Qatar
1 Kubu Consultancy and NCE, Centurion, South Africa
2Department of Civil Engineering, University of Pretoria, South Africa

2. Presentation Outline Recap of Bailey method (Rational approach)
Recap of DASR method
Porosity as link to Binary Aggregate Packing methodology
Rational Bailey ratios correlated to Binary Packing principles
Reworked data sets to correlate with Rational Bailey ratios
Correlation results with rut, elastic modulus and ITS
Basics of Binary Aggregate Packing explained
Use of Binary Aggregate Packing ratios to monitor porosity and thus permeability (Reworked data sets)

3. Nominal Maximum Particle (Aggregate) Size (NMPS) as per Superpave definition,
Half Size (HS), where HS = 0.5 x NMPS,
Primary Control Sieve (PCS), where PCS = 0.22 x NMPS,
Secondary Control Sieve (SCS), where SCS = 0.22 x PCS, and
Tertiary Control Sieve (TCS), where TCS = 0.22 x SCS.

4. Three level aggregate fraction ranges proposed
Bailey control sieves and fraction ranges
Three level aggregate fraction ranges proposed

5. DASR Porosity as per Kim et al. (2006)
𝜼 𝑫𝑨𝑺𝑹 = 𝑽 𝑽(𝑫𝑨𝑺𝑹 𝑽 𝑻(𝑫𝑨𝑺𝑹 = 𝑽 𝑰𝑪𝑨𝑮𝑮 + 𝐕𝐌𝐀 𝑽 𝑻𝑴 − 𝑽 𝑨𝑮𝑮 > 𝐃𝐀𝐒𝐑
Where: 𝜼 𝑫𝑨𝑺𝑹 = 𝑫𝑨𝑺𝑹 𝒑𝒐𝒓𝒐𝒔𝒊𝒕𝒚
V Interstitial volume = Volume of IC aggregates plus VMA, thus inclusive of bitumen binder volume;
VAGG>DASR = Volume of particles bigger than DASR;
VTM = Total volume of mix;
VT(DASR) = Total volume available for DASR particles;
VV(DASR) = Volume of voids within DASR;
VICAGG = Volume of IC aggregates;
VMA = Voids in mineral aggregate;
VICAGG = Volume of IC aggregates.

6. Single fraction Porosity as per Denneman et al. (2007)
ƞ= 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑉𝑜𝑖𝑑𝑠 𝑇𝑜𝑡𝑎𝑙 𝑉𝑜𝑙𝑢𝑚𝑒 = 𝑉 𝑉 𝑉 𝑇
𝛈(𝟒.𝟕𝟓−𝟐.𝟑𝟔) = 𝐏𝐏𝟐.𝟑𝟔 𝟏𝟎𝟎 𝐕𝐓𝐌−𝐕𝐌𝐀 +𝑽𝑴𝑨 𝐏𝐏𝟒.𝟕𝟓 𝟏𝟎𝟎 𝐕𝐓𝐌−𝐕𝐌𝐀 +𝑽𝑴𝑨
η ( ) = Porosity of a typical fraction passing 4.75mm sieve and retained on 2.36mm sieve
PP2.36 = Percentage particles passing 2.36 sieve
PP4.75 = Percentage particles passing 4.75 sieve
VMA = Voids in Mineral Aggregate
VTM = Total volume of mix

7. = %𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫𝐬 %𝐎𝐯𝐞𝐫𝐬𝐢𝐳𝐞
New and proposed Bailey ratios subscribe to the DASR rule of porosity in that the Numerator and denominator are aggregate fractions that do not overlap and ratio are thus contiguous
Matrix
Level
Gradation Ratios (See gradation in Figure 1 with associated indications for proper reference)
Explanation of new and proposed Bailey ratios and parameters
Macro
𝐂𝐂= (%𝟏𝟎𝟎−%𝐍𝐌𝐏𝐒) %𝟏𝟎𝟎
= %𝐎𝐯𝐞𝐫𝐬𝐢𝐳𝐞 %𝟏𝟎𝟎
New Bailey Ratio (Al Mosawe et al, 2015). This is the oversize or coarse of coarse ratio of % in the grading typically larger than the NMPS as described.
𝐈 𝐎 = ( %𝐍𝐌𝐏𝐒−%𝐇𝐒 ) (%𝟏𝟎𝟎−%𝐍𝐌𝐏𝐒)
= %𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫𝐬 %𝐎𝐯𝐞𝐫𝐬𝐢𝐳𝐞
Proposed New Bailey Ratio (Extending the Al Mosawe et al, 2015 approach). This can be called the interceptor to oversize (large) aggregate ratio. This is actually a ratio that bridges the macro and midi ranges.

8. Matrix
Level
Gradation Ratios (See gradation in Figure 1 with associated indications for proper reference)
Explanation of new and proposed Bailey ratios and parameters
Midi
𝑪 𝒇 𝑭 𝒄 = (%𝐏𝐂𝐒−%𝐒𝐂𝐒) (%𝐇𝐒−%𝐏𝐂𝐒)
= %𝐂𝐨𝐚𝐫𝐬𝐞 𝐩𝐨𝐫𝐭𝐢𝐨𝐧 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬 %𝐏𝐥𝐮𝐠𝐠𝐞𝐫𝐬
New Al Mosawe et al ( 2015)
Plugger stability ratio.
𝑭 𝑪 = (%𝐏𝐂𝐒) (%𝐍𝐌𝐏𝐒− %𝐏𝐂𝐒)
= %𝐅𝐢𝐧𝐞𝐬 %(𝐏𝐥𝐮𝐠𝐠𝐞𝐫+𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫)
New Al Mosawe et al ( 2015).
True midi range ratio
𝐏 𝐈 = (%𝐇𝐒− %𝐏𝐂𝐒 ) (%𝐍𝐌𝐏𝐒−%𝐇𝐒)
= %𝐏𝐥𝐮𝐠𝐠𝐞𝐫𝐬 %𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫𝐬
The pluggers fill the interceptor voids
Act as the main structural element of the middle (midi) portion of the aggregate matrix.
The ‘crux’ of the overall aggregate skeleton.

9. Matrix
Level
Gradation Ratios (See gradation in Figure 1 with associated indications for proper reference)
Explanation of new and proposed Bailey ratios and parameters
Micro
𝑭𝑨 𝒄𝒎 = (%𝐒𝐂𝐒−%𝐓𝐂𝐒) (%𝐏𝐂𝐒−%𝐒𝐂𝐒)
= %𝐌𝐞𝐝𝐢𝐮𝐦 𝐟𝐢𝐧𝐞 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬 %𝐂𝐨𝐚𝐫𝐬𝐞 𝐟𝐢𝐧𝐞𝐬
Provide an indication of the stability of the coarse range of the fine portion (typically fine sand range) in support of the whole fines range of the aggregate.
𝑭𝑨 𝒎𝒇 = (%𝐓𝐂𝐒−%𝐅𝐢𝐥𝐥𝐞𝐫 (%𝐒𝐂𝐒−%𝐓𝐂𝐒 )
= %𝐅𝐢𝐧𝐞 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬 %𝐌𝐞𝐝𝐢𝐮𝐦 𝐟𝐢𝐧𝐞 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬
Give an indication of the finer portion of the fines (without the filler component) versus the overall fines portion.
The Mastic Control Ratio.

10. Additional perspective of Binary Aggregate Packing Concepts
Fine fraction
Coarse fraction
This ratio is the same as the basis of the Bailey method (Fine/Coarse) diameter ratio
This ratio (Coarse/Fine) is the inverse of Bailey method (Fine/Coarse) by volume or by mass of fractions
The Furnas principles applied to a binary combination of coarse and fine aggregates (Olard 2015)

11. Visualization of three tiered aggregate fraction packing into the voids
(Zoomed in)
Macro level stone skeleton
Midi level stone skeleton
Micro level stone skeleton
This “unpacking” of the aggregate grading in three levels enables the visualization to understand the relevance and application of Binary Aggregate Packing principles

12. Macro Fine/Large ratios Bailey original
Large/Fine ratios To suit Binary Packing
Matrix
Level
Original rational Bailey ratios
Proposed Revised rational Bailey ratios in line with binary aggregate fraction packing principles
Macro
𝑰 𝑶 = ( %𝐍𝐌𝐏𝐒−%𝐇𝐒 ) (%𝟏𝟎𝟎−%𝐍𝐌𝐏𝐒)
= %𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫𝐬 %𝐎𝐯𝐞𝐫𝐬𝐢𝐳𝐞
𝑶 𝑰 = (%𝟏𝟎𝟎−%𝐍𝐌𝐏𝐒) ( %𝐍𝐌𝐏𝐒−%𝐇𝐒 )
= %𝐎𝐯𝐞𝐫𝐬𝐢𝐳𝐞 %𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫𝐬
𝐂𝐀= (% 𝐇𝐒−%𝐏𝐂𝐒) (% 𝟏𝟎𝟎−%𝐇𝐒)
= % 𝐏𝐥𝐮𝐠𝐠𝐞𝐫𝐬 % 𝐀𝐥𝐥 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫𝐬 & 𝐥𝐚𝐫𝐠𝐞𝐫
CAr = 1/CA
= (% 𝟏𝟎𝟎−%𝐇𝐒) (%𝐇𝐒−%𝐏𝐂𝐒)
= % 𝐀𝐥𝐥 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫𝐬 & 𝐥𝐚𝐫𝐠𝐞𝐫 % 𝐏𝐥𝐮𝐠𝐠𝐞𝐫𝐬

13. Matrix
Level
Original rational Bailey ratios
Proposed Revised rational Bailey ratios in line with binary aggregate fraction packing principles
Midi
𝑪 𝒇 𝑭 𝒄 = (%𝐏𝐂𝐒−%𝐒𝐂𝐒) %𝐇𝐒−%𝐏𝐂𝐒
= %𝐂𝐨𝐚𝐫𝐬𝐞 𝐩𝐨𝐫𝐭𝐢𝐨𝐧 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬 %𝐏𝐥𝐮𝐠𝐠𝐞𝐫𝐬
𝑭 𝒄 𝑪 𝒇 = (%𝐇𝐒−%𝐏𝐂𝐒) %𝐏𝐂𝐒−%𝐒𝐂𝐒
%𝐏𝐥𝐮𝐠𝐠𝐞𝐫𝐬 % 𝐂𝐨𝐚𝐫𝐬𝐞 𝐩𝐨𝐫𝐭𝐢𝐨𝐧 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬
𝑭 𝑪 = (%𝐏𝐂𝐒) (%𝐍𝐌𝐏𝐒− %𝐏𝐂𝐒)
= %𝐅𝐢𝐧𝐞𝐬 % 𝐏𝐥𝐮𝐠𝐠𝐞𝐫+𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫
𝑪 𝑭 = (%𝐍𝐌𝐏𝐒− %𝐏𝐂𝐒) %𝐏𝐂𝐒)
= % 𝐏𝐥𝐮𝐠𝐠𝐞𝐫+𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫 %𝐅𝐢𝐧𝐞𝐬
𝐏 𝐈 = (%𝐇𝐒− %𝐏𝐂𝐒 ) (%𝐍𝐌𝐏𝐒−%𝐇𝐒)
= %𝐏𝐥𝐮𝐠𝐠𝐞𝐫𝐬 %𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫𝐬
𝐈 𝐏 = (%𝐍𝐌𝐏𝐒−%𝐇𝐒 ) (%𝐇𝐒− %𝐏𝐂𝐒)
= %𝐈𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐨𝐫𝐬 %𝐏𝐥𝐮𝐠𝐠𝐞𝐫𝐬

14. Matrix Level Micro Original rational Bailey ratios
Proposed Revised rational Bailey ratios in line with binary aggregate fraction packing principles
Micro
𝑭𝑨 𝒄𝒎 = (%𝐒𝐂𝐒−%𝐓𝐂𝐒) (%𝐏𝐂𝐒−%𝐒𝐂𝐒)
= %𝐌𝐞𝐝𝐢𝐮𝐦 𝐟𝐢𝐧𝐞 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬 %𝐂𝐨𝐚𝐫𝐬𝐞 𝐟𝐢𝐧𝐞𝐬
𝑭𝑨 𝒓𝒄𝒎 = (%𝐏𝐂𝐒− %𝐒𝐂𝐒) (%𝐒𝐂𝐒−%𝐓𝐂𝐒)
= %𝐂𝐨𝐚𝐫𝐬𝐞 𝐟𝐢𝐧𝐞𝐬 %𝐌𝐞𝐝𝐢𝐮𝐦 𝐟𝐢𝐧𝐞 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬
𝑭𝑨 𝒎𝒇 = (%𝐓𝐂𝐒−%𝐅𝐢𝐥𝐥𝐞𝐫 (%𝐒𝐂𝐒−%𝐓𝐂𝐒 )
= %𝐅𝐢𝐧𝐞 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬 %𝐌𝐞𝐝𝐢𝐮𝐦 𝐟𝐢𝐧𝐞 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬
𝑭𝑨 𝒓𝒎𝒇 = (%𝐒𝐂𝐒−%𝐓𝐂𝐒 ) (%𝐓𝐂𝐒−%𝐅𝐢𝐥𝐥𝐞𝐫)
= %𝐌𝐞𝐝𝐢𝐮𝐦 𝐟𝐢𝐧𝐞 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬 % 𝐅𝐢𝐧𝐞 𝐨𝐟 𝐟𝐢𝐧𝐞𝐬

15. Al-Shamsi PhD data set was reworked to correlate various rational Bailey ratios and elastic moduli based on the Al_Mosawe et al correlation
Not a significant independent variable

16. Not a significant independent variable

17. independent variable in a narrow band

18. independent variable significant but in a narrow band

19. Not a significant independent variable

20. Not a significant independent variable

21. Independent variable significant but in narrow band

22. Independent variable significant but in narrow band

23. Independent variable significant but in narrow band

24. Trend the same Modulus and Indirect Tensile Strength Values
The data set of Al Shamsi (2006)
Trend the same

25. Independent variable significant but in narrow band

26. Independent variable significant but in narrow band

29. Concluding remarks
1. Bailey ratios and DASR porosities - Pluggers (between the PCS and HS) and Interceptors (between the HS and NMPS) best correlation with rut.
2. Structural strength at Midi range of the aggregate skeleton subsets - Rationale of the modulus values which Al-Mosawe et al. (2015) also found.
3.Elastic modulus derived Al-Mosawe et al. (2015) equation correlated with ITS values determined in the original data set.
4. ITS values correlate with Bailey ratios and DASR porosity values - Micro level subset of the aggregate skeleton subset. Logical as tensile strength - strongly linked to the mastic portion of the HMA/WMA.

30. 5. Equivalent Film Thickness (EFT) is correlated with ITS-adhesion and cohesion component is linked with the effective bitumen mastic portion represented by the EFT.
6. Bailey ratios limit permeability -confirm that the mixes are low to medium permeability. Concerns about the actual permeability measurement technique.
7. Scattergram correlations identified and confirmed the ratios and parameters that would contribute to rut resistance and strength in the aggregate skeleton as well as limiting permeability
8. Rut and permeability - better controlled via the Bailey ratios and porosity principles of the DASR method- improving aspects of the aggregate grading by monitoring it.

32. The knowledge that the revised Bailey and DASR methods subscribe to the same fundamental basis is good, but is it wise to link this with the Binary Aggregate Packing ? How to make the connection?

35. Visualization of three tiered aggregate fraction packing into the voids
(Zoomed in)
Macro level stone skeleton
Midi level stone skeleton
Micro level stone skeleton
This “unpacking” of the aggregate grading in three levels enables the visualization to understand the relevance and application of Binary Aggregate Packing principles

36. Olard (2015)

37. Macadam pavement layers are classical Binary packing mechanisms and therefore the superior bearing capacity

38. Note:
1. Coarse/large aggregate
2. Medium sized aggregate
3. Fine aggregate
Wall effect: When medium sized particles (2) are adjacent to the large or coarse aggregate (1) margins and thus the packing density of medium aggregates are disturbed. The increased voids between the medium particles and the wall (coarse aggregate) is thus the wall effect.
Loosening effect: When a fine particle (3) is in the matrix of medium (2) and coarse particles (1) and the small particle (3) is too large to fit into the interstices of the medium aggregate it disturbs the packing density of medium sized particles.

39. Monitoring permeability of asphalt via the Binary Aggregate Packing Principles

41. Knop and Peled, 2016

42. Mota et al. (2013 The Binary Packing link with Permeability
Wall effect on permeability
Wall effect and disruptor effect on permeability

43. Coarse % in binary combination threshold point is 60%
Note: e = porosity
p = proportion of coarse to fine material
Void index or porosity variation in the case of a binary aggregate mixture with a significantly low diameter ratio value. (Olard et al. 2010)

44. Good performing data set reworked porosity and coarse to fine proportion
Poor performing data set reworked porosity and coarse to fine proportion
When the coarse/fine or coarse fraction in the binary combination approaches 60% the porosity value becomes important as it then has a higher chance of being interconnected

45. Previous studies have shown permeability is influenced strongest by the porosity of the finer portion
All cases where high coarse portion in the mix also means interconnected of voids are more possible and therefore also high permeability
Case where high porosity is not supported by high coarse portion in the mix: thus voids are not interconnected and thus low permeability

46. Suggested criteria for Bailey ratios and DASR fraction porosity ranges
Skeleton level
Bailey Ratios
Suggested range
DASR descriptor
Macro CA
>0.5
Large Aggregate
>0.65
I/O
>6
Interceptor
<0.75
Midi
P/I
Interceptors + pluggers
>0.52
Cf/FC
<1.05
Pluggers
>0.7
F/C
<0.9
Coarse of fines
0.65
Micro
FAcm
<0.37
Fine of fines
FAmf
>0.37
Fine to filler
<0.6

47. Monitoring permeability of asphalt via the Binary Aggregate Packing Principles

48. Large aggregate is more prone to cause the wall effect
On a relative scale this is the most probable cause of permeability increase at larger NMPS in the HMA

49. Note: e = porosity
p = proportion of coarse to fine material
Void index or porosity variation in the case of a binary aggregate mixture with a significantly low diameter ratio value. (Olard et al. 2010)

50. Conclusions
Deconstruction or dismantling of the aggregate matrix in Macro, Midi and Mini aggregate structures resembles the Binary Aggregate Packing approach
Binary packing makes use of the Fine/Coarse diameter ratio similar as the Bailey method to relate to porosity and also similar to the DASR method
The Binary Packing also makes use of Coarse/Fine mass ratio of retained aggregate grading ration or % coarse in the binary ratio. This is the inverse of the Bailey method

51. Conclusions (Cont)
Binary Aggregate Packing approach show that the 60% coarse in the combination of coarse and fine fractions is a threshold value for porosity
This 60% threshold value also correlate with permeability and filter media results based on interconnected voids
The Binary Packing clearly illustrate that the “wall effect” and the “Loosening effects” have a “dilation point around this 60% threshold value

52. Conclusions (Cont)
Reworked data sets with actual permeability measurements explain the aggregate packing efficiency very logically in terms of coarse/fine sieve size retained mass ratios and the combined porosity as per the Binary Aggregate Packing approach
It is possible to relate the coarse/fine ratios by mass to the structural aspects as well as its impact on permeability at that subset level.
Permeability is primarily influenced by the void infill at the midi and micro subset levels. The coarse/fine mass ratio of the medium to fine portions of the fines (SCS to TCS or revised rational Bailey ratio FArcm ) clearly gives a good explanation of the effect of coarse/fine ratios on porosity restriction.

53. Conclusions (Cont)
The Binary Packing ratios at these various levels (Macro, Midi and Mini) offer a logical explanation why, at the same porosity level, the higher coarse/fine mass ratios may increase the probability of interconnected voids due to the wall effect and the loosening effect.
Interconnectedness and not merely values of porosity or void content is the main requirement for permeability for flow of water through the voids.

55. Attrition, segregation and abrasion observed at 100 gyrations in the gyratory shear compactor (GC) (Olard)