Gradation-Based Framework for Asphalt Mixtures
Licentiate Thesis
Bernardita Lira Miranda
KTH, Royal Institute of Technology
School of Architecture and Built Environment
Department of Transport Science
Division of Highway and Railway Engineering
SE-100 44 Stockholm
April 2012
TRITA-TSC-LIC 12-001
ISBN 978-91-85539-81-9
©Bernardita Lira
2012
Abstract
Asphalt mixture microstructure is formed by aggregates, bitumen binder and air voids.
Aggregates make for up to 90% of the mixtures volume and the structure formed by them
will depend mostly on their size distribution and shape. The study presented in this thesis
has as main objective to develop a framework that allows the characterization of asphalt
mixtures based on the aggregates gradation and its impact on pavement performance.
Moreover, the study aims to identify the range of aggregate sizes which form the load
carrying structure, called Primary Structure, and determine its quality.
The method has been developed as a numerical procedure based on packing theory of
spheres. Parameters like porosity, coordination number and disruption factor of the Primary
Structure; and a binder distribution parameter for the different sub-structures have been
used to evaluate the quality of the load carrying structure and predict the impact on several
failure modes. The distribution of bitumen binder has been derived from a geometrical
model which relates porosity of the mixture with film thickness of particles considering the
overlapping reduction as the film grows. The model obtained is a closer approximation to a
physical characteristic of the compacted mixture separated according to different elements
of the structure.
The framework has been evaluated on several field and laboratory mixtures and predictions
have been made about their rutting performance and moisture resistance. The calculated
parameters have compared favourably with the performances reported from the field and
laboratory testing. The developed gradation analysis framework has proven to be a tool to
identify those mixtures with a poor rutting performance based on the gradation of the
aggregates.
The Gradation - Based Framework has satisfactory distinguished between good and bad
performance of asphalt mixtures when related to permanent deformation and moisture
damage. The calculated parameters have allowed identifying and understanding the main
mechanisms and variables involved in permanent deformation and moisture damage of
asphalt mixtures. The developed model can be used as a tool to determine the optimal
gradation to assure good performance for hot mix asphalt pavements.
Keywords: Asphalt, aggregate gradation, packing theory, asphalt microstructure, porosity,
film thickness, rutting, moisture damage.
i
Acknowledgment
The work presented in this licentiate thesis has been carried out between June 2009 and
February 2012 at the division of Highway and Railway Engineering, School of Architecture
and the Built Environment at the Royal Institute of Technology, KTH.
I would like to express my gratitude to Trafikverket for the financial support to the project.
I would also like to thank my supervisors Professor Björn Birgisson and Dr. Denis Jelagin
for their guidance during this process. I am very grateful to Mr Måns Collin and Dr. Per
Redelius for all the great discussion that helped us understand and develop the final model.
I would like to thank my colleagues at the department which were always there to put a
smile in the difficult times. Also, nothing would have been possible without the invaluable
help of Mrs Agneta Arnius in all the administrative matters.
Finally, I would like to thank my husband Kristian for his support and patience and my
family in Chile that always believed in me.
Bernardita Lira
Stockholm, February 2012
iii
List of enclosed papers
I.
Lira, B., D. Jelagin, B. Birgisson, Gradation Based Framework for Asphalt Mixtures
Submitted to Journal of Materials and Structures, October 2011
II.
Lira, B., D. Jelagin, B. Birgisson, Binder Distribution Model for Asphalt Mixtures
Based on Packing of the Primary Structure
To be submitted to International Journal of Pavement Engineering
v
TABLE OF CONTENTS
Abstract
Keywords
Acknowledgements
List of enclosed papers
1. Introduction
2. Theoretical Model
3. Results
4. Discussion and Conclusions
5. Bibliography
Paper I. Gradation-Based Framework for Asphalt Mixtures. Lira, B., D. Jelagin, B.
Birgisson
Paper II. Binder Distribution Model for Asphalt Mixtures Based on Packing of the Primary
Structure. Lira, B., D. Jelagin, B. Birgisson
vii
1. Introduction
The impact of aggregate gradation on the performance of asphalt mixtures has been
extensively studied through the years. Several studies, e.g. (Kandhal, et al., 1998),
(Nukunya, et al., 2001), (Birgisson, et al., 2004) have shown that there is a relationship
between aggregate particles size distribution and the resistance to cracking, rutting, ageing
and moisture damage. Furthermore, the way that aggregate particles, bitumen binder and air
voids interact with each other will determine how a mixture will respond to different
loading conditions ( (Campen, et al., 1959), (Kumar & Goetz, 1977)). Through studying
and understanding these interactions future design can be optimized by combining the
available materials in the best possible way.
The objective of the present project is to develop a framework to characterize asphalt
mixtures based on their microstructure. Asphalt mixture microstructure is formed mostly by
aggregate particles and the structure that will be formed depends mainly on their size
distribution, shape and concentration. Bitumen binder will then flow around the particles
forming a film around them and binding all the components together. The framework aims
to describe different types of mixtures depending on how the aggregates group, how the
bitumen is distributed among them and the resulting size and location of the air voids. This
configuration will finally determine the type of response that an asphalt mixture will have
during loading.
Experimental studies on granular material (e.g. Cundall, et al. 1982) have shown the
existence of stress-transmitting paths enclosing virtually stress free regions (Jaeger and
Nagel 1992). In particulate materials then, the load is transferred through chains of particles
and other smaller particles play the secondary role of preventing the main chain from
buckling (e. g. Santamarina 2001). Based on the observations mentioned above two substructures within the aggregate particles have been defined: the Primary Structure, range of
sizes which due to their concentration provide the load bearing capacity of the mixture, and
the Secondary Structure, material smaller than the first one which provides stability to the
structure (Lira, et al., 2011). Packing theory for spherical particles has been used to identify
each sub-structure.
Results from field and laboratory mixtures have been used to validate the relationship
between the Primary Structure content and rutting performance. The model also proposes a
distribution system of the bitumen binder around the Primary and Secondary Structure. It is
shown that the thickness of the film around both structures has a great influence on not only
permanent deformation but also on the resistance for moisture damage on asphalt mixtures
(Lira, et al., 2012).
1
2. Theoretical Model
Mineral aggregates used for pavement construction are largely obtained from local
suppliers. A consequence of this is that certain regions will have better quality materials
than others. It is for this reason that is of key importance to understand the way aggregate
particles interact, and in that way give a tool to engineer mixtures to obtain the best
performance possible according to the available materials.
Aggregate´s physical characteristics, such as resistance to abrasion and strength, are
determined primarily by its mineral composition. However, the production process can
significantly improve the quality of the aggregate by elimination of weaker rock layers and
by the effect of crushing on the particle shape and gradation of the aggregate. Aggregate
gradation is the distribution of particle sizes expressed as a per cent of the total weight.
Gradation is determined by sieve analysis and is normally expressed as total per cent
passing various sieve sizes. Aggregate gradation is certainly one of the most important
properties of an HMA (hot mix asphalt) design. It affects almost all the important properties
of an asphalt mixture, including stiffness, stability, durability, permeability, workability,
fatigue resistance, friction, and resistance to moisture damage (Brown, et al., 2009).
Early studies have proposed that the best gradation for HMA is the one that gives the
densest packing, increasing stability through increased interparticle contact (Fuller &
Thompson, 1907) (Goode & Lufsey, 1962). However, there must be sufficient air void
space to allow enough bitumen binder to be incorporated to ensure durability and
workability, while still leaving some air voids in the mixture to avoid bleeding or rutting.
In 2006 a conceptual and theoretical approach to evaluate coarse aggregate structure based
on gradation was developed by (Roque, et al. 2006). The method identifies the load
carrying size range (DASR) in the mixtures and relates the quality of this structure to the
asphalt mixture performance. However, the DASR identification procedure is valid strictly
for gradations composed of discrete particle size with a size ratio 2:1.
Packing theory is a tool that allows the analysis of aggregate gradations based on the
geometrically systematic arrangement of uniform spheres. The term packing is applied to
any manner of arrangement of solid units in which each constituent unit is supported and
held in place in the earth´s gravitational field by tangent contact with its neighbour (Graton
& Fraser, 1935). From a two-dimensional geometric view there are two different types of
layers, a square and a rhombic layer, as shown in Figure 1. When combining those two
different layers in a three-dimensional space, six different arrangements are obtained. It can
be observed in Table 1 that only four are presented as some of the square arrangements are
repeated by the rhombic ones. By observing the values of porosities it can be determined
that the simple cubic packing is the loosest state and the rhombohedral packing is the
densest one.
2
Table 1. Properties of various packing arrangements
Tangent
neighbours
Volume of the
unit cell
Volume of unit
void
Porosity
Simple Cubic
6
8,00 R3
3,81 R3
47,67%
Orthorhombic
8
6,93 R3
2,74 R3
39,54%
Tetragonal –
sphenoidal
10
6,00 R3
1,81 R3
30,19%
Rhombohedral
12
5,66 R3
1,47 R3
25,95%
Figure 1. Types of layer. A) Square layer; B) rhombic layer (Graton & Fraser, 1935)
For an assemblage of equal-sized particles to be in contact with each other then they must
have porosity not higher than the loosest state given by packing theory. In order to transfer
load, stones need to form a continuous network, which means, the concentration of the load
carrying range has to be minimum around 45%. Concentration can be defined as follows:

Wretn
Wtot
[1]
where Wretn represents the weight of aggregate retained at sieve n and Wtot is the total weight
of aggregates. Based on standard practice is acceptable to assume that such a concentration
is not achieved by only one size material in a gradation. Packing theory can be used to
define the range of material where stone-to-stone contact is assured and a concentration
higher than 45% can be achieved. This analysis is done by checking the interaction between
consecutive sieve sizes and determining if their individual concentrations are enough to
assure contact between particles of both sizes.
For this analysis four initial assumptions are taken:


All particles are considered spherical.
The aggregate particles are uniformly distributed within the total volume.
3

The material retained at a certain sieve size presents a continuous size distribution
characterized by the parameter B. This means that the mean diameter ( Dn ) at a sieve
size can be described as presented in[2], where Dmin is the opening of the sieve and
Dmax is the opening of the previous sieve.
Dn  B  Dmin  Dmax 

[2]
The maximum concentration of spheres of two different sizes is equivalent to a
rhombohedral packing type ( Dmax&D  0, 74 ).
n
n1
The following model identifies three different groups within the mineral aggregates: the
Primary Structure, the Secondary Structure and the oversized material as shown in Figure 2.
The Primary Structure (PS) is a range of sizes in the gradation that due to its concentration
provides the load bearing capacity for the mix. The PS acts as a central core where all the
particles are connected with each other, and the more connections there are the stronger the
core is. The Secondary Structure (SS) is formed by the particles with a smaller size than the
PS. The SS fills in the voids between the PS particles and provides stability to the PS.
Finally, there are oversized particles which size is bigger than the PS and which do not
contribute to any load carrying. To determine the PS range the analysis must consider the
tightest and loosest case in which two consecutive sizes can have stone-to-stone contact,
which are represented in Figure 3.
100
90
80
60
50
40
30
20
Sieve size 0.45 [mm]
Figure 2. Gradation Analysis Framework
4
19.
0
12.
5
9.5
4.7
5
2.3
6
1.1
8
0
0.6
0
10
0.0
75
0.1
5
0.3
0
% Passing
70
Figure 3. Tightest (a.) and loosest (b.) configurations of the Primary Structure
For two consecutive sieve sizes with diameter Dn and Dn1 and concentrations n and n1
respectively, the average particle diameter ( Davg ) can be calculated as:
Davg 
Dn  n  Dn 1  n 1
n  n 1
[3]
The tightest case is built upon the addition of smaller spheres to one-sized un-compacted
bigger spheres. The bigger spheres will present a simple cubic configuration as shown on
Figure 3 previous the addition of smaller spheres. When these are added the porosity
decreases until a minimum representing a rhombohedral packing, assuring the contact
between the smaller spheres and the surrounding bigger ones. Numerically this can be
expressed as:
Davg 
Dn  0,52  Dn1  0, 22
 0, 703  Dn  0, 297  Dn 1
0, 74
[4]
In the loosest case the bigger spheres have no contact with each other, allowing the smaller
spheres to be positioned in between them. To assure contact between both sized spheres
then the distance between the bigger spheres must not be bigger than the diameter of the
smaller spheres. This can be calculated by using the separation distance between the
surfaces of two neighbouring elements (Coussot, 2005) as described in[5].
1


3



max

h  2r 
 1
   



5
[5]
The solution for two contiguous sieve sizes can be calculated considering h  Dn1 ,
r  Dn / 2 , max  0,74 and φ as the volume fraction of the spheres belonging to the sieve
size “n”. This will give the following relation[6]:
1


Dn   0, 74  3 
Dn 1  2 

  1
2    



[6]
1
3
Dn 1  0, 74 

 1
Dn   
Taking into consideration different sieve systems it is possible to notice that the relationship
  Dn1 / Dn moves between γmax=0,77 and γmin=0,47 giving φ=0,13 and φ=0,23
respectively. Contact between particles will then be assured for a minimum concentration
of the biggest sphere of 0,23. This can be expressed as:
Davg 
Dn  0, 23  Dn 1  0,51
 0,311 Dn  0, 689  Dn 1
0, 74
[7]
Finally, interaction between two contiguous sieve sizes will occur if the average diameter
for the particles is within the following limits, as given by equation[8]. A summary of the
process to determine the Primary Structure is given in Figure 4.
0,311 Dn  0,689  Dn1  Davg  0,703  Dn  0, 297  Dn1
6
[8]
From Gradation: - sieve sizes D1 and D2
- per cent retained at each sieve φ1 and φ2
Calculation of the
Average Particle Size
𝐷1 𝜑1 + 𝐷2 𝜑2
𝐷𝑎𝑣𝑔 =
𝜑1 + 𝜑2
Calculation of the
Interaction Range Limits
𝑚𝑖𝑛 = 0,311 ∗ 𝐷1 + 0,689 ∗ 𝐷2
𝑚𝑎𝑥 = 0,703 ∗ 𝐷1 + 0,297 ∗ 𝐷2
Check Interaction
𝑚𝑖𝑛 ≤ 𝐷𝑎𝑣𝑔 ≤ 𝑚𝑎𝑥
YES
NO
D1 and D2 have not
enough interaction to
belong to the Primary
Structure
D1 and D2 do interact and the
might belong to the Primary
Structure
Continue the analysis with the next sieve sizes until Dlast
Figure 4. Primary Structure Identification
Porosity of the Primary Structure
The relation between performance of asphalt mixtures and gradation characteristics is
influenced by several aggregate properties, e.g. stone texture, shape and stiffness. In the
following framework only the influence of the whole structure formed by the stones is
considered, which is characterized by porosity of the assemblage and contact points due to
their contribution to shear resistance. The calculation of the Primary Structure Porosity is
based on the general definition of porosity as a measure of the void spaces in a material,
given as a fraction of the volume of voids over the total volume (VT). The volume of voids
for the Primary Structure is everything in the mixture that is not considered to be part of the
PS, and the total volume of the mixture is all except the volume of particles bigger than the
Primary Structure. In[9] VaSS is the volume of aggregate belonging to the Secondary
7
Structure, Vaoversized is the volume of aggregate bigger than the Primary Structure, Vbtot is
the total volume of bitumen binder, VbabsPS is the volume of bitumen binder absorbed by the
Primary Structure, and Vv is the total volume of voids.
 PS 
VV VaSS  Vbtot  Vv  VbabsPS

VT
VT  Vaoversized
[9]
Coordination number (m) is the average of contact points per particle and can be calculated
using the relationship in[10], where η is the porosity, based on packing theory:
m  2,827  1,069
[10]
Disruption Factor
The Disruption Factor (DF) is a parameter developed to evaluate the potential of the
Secondary Structure to disrupt the Primary Structure (Guarin 2009; Guarin, et al. 2011
under revision). The DF is calculated as following:
DF 
Vdp 
Volume of potentially disruptive particles Vdp
 PS
Volume of PS voids
Vv
Wdp
[11]
Gsb
The weight of potentially disruptive particles considers the material belonging to the SS
bigger than the average void size of the PS, which depends on the packing arrangement
(porosity) of the PS particles.
Rutting performance is related to the mixtures capacity to resist shear. An adequate amount
of Secondary Structure, specially the potentially disruptive particles, will benefit the
mixture in the load carrying capacity.
Bitumen Distribution Parameter (t)
The developed framework proposes a solution to calculate the coating thickness of
aggregates in a hierarchical order according to particle size and the packing configuration
of the Primary Structure.
In the following model particles with size below the last sieve size (fines) and the bitumen
binder are considered to form a composite material called mastic. This mastic is distributed
around the Secondary Structure with a certain thickness (tSS). If this film is too thin then the
particles of the Secondary Structure will act as a granular material instead of a composite
8
one, leading to a brittle response under loading. The mixture of mastic and Secondary
Structure will then flow around the Primary Structure, coating it with a certain thickness
(tPS). The thickness of this second coating will depend on the packing configuration of the
Primary Structure and the per cent of air voids in the mixture, as the coat will represent the
distance between the air void and the aggregate-binder interface.
The relationship between film thickness and porosity developed by (Cooke & Rowe, 1999)
has been used to determine tSS and tPS. This relationship considers the different packing
arrangements that a set of spherical particles can present, and the change in porosity when
varying the film thickness taking into consideration the overlapping of the film as it grows.
The particles belonging to the Secondary Structure are always considered to be packed in
the densest possible way (φ=0,74), as their porosities are very low as calculated according
to[12]. However, the porosities of the Primary Structure will vary from the tightest case to
very loose; giving a dependency of the film thickness on the packing arrangement.
SS 
Vv
V f  V tot  V eff
 SS a f b tot v eff
VT Va  Va  Vb  Vv
[12]
Once calculated  SS and  (the porosity used to determine the PS coating thickness is the
one of the whole mixture and not PS ), the graph presented in Figure 5 is used to estimate a
dimensionless parameter 2 Lt / d p which represents the thickness of the film ( Lt ) related to
the particles diameter ( d p ). The diameter of the particle will be the weighted average size
of the sub-structure used.
0.5
Simple Cubic
Orthorhombic
Tetragonal
Rhombohedral
Porosity, 
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
Dimensionless parameter, 2Lt/dp
0.6
0.7
Figure 5. Relation between porosity and film thickness as developed by (Cooke & Rowe,
1999)
9
In Figure 5 only the theoretical packing arrangements are defined, but as the coordination
number for different mixtures is the average of contact points per volume, then
interpolation has to be done between the theoretical curves. In the case of having a mixture
with a coordination number less than 6 (simple cubic), then the distance between coated
particles must be taken into account for the final coating thickness. For cases with m<6 the
coating thickness (t) is calculated as following:
tm6  tm 6
1


 dp
   0,4764  3


 tm 6   
  1
2
1


PS 





[13]
In [13] tm=6 is the film thickness calculated assuming a simple cubic packing and dp is the
particles diameter.
3. Results
To validate the framework several field mixtures with known rutting performance have
been analysed, these mixtures are:


WesTrack road test facility [35, 36, 37, 38, 39, 54, 55, 56] in Nevada (USA) placed and
tested by the Federal Highway Administration (FHWA, 1998);
NCAT’s test track [E2, E3, E4, E8, E9, N5, N6, N7, and N8] in Alabama (USA) placed
and tested at National Centre for Asphalt Technology (Powell, 2001).
Also, laboratory mixtures tested for rutting and moisture damage have been analysed.
These mixtures are:



Limestone [FL] and granite [GA] mixtures [ICf, ICgood, ICc, IC-48], specially
designed to analyse the effect of material smaller than the load bearing range size on
rutting performance. This mixtures were tested with the asphalt pavement analyser
(APA) (Guarin, et al., 2011);
Laboratory based oolitic limestone mixtures [C3, C4/F3, C5, F2, F4, F5, F6] of varying
gradations design for studying shear instability for different compactive methods with
APA (Birgisson, et al., 2004);
Limestone and granite mixtures [C1, C2, C3, F1, F2, F3/C4], designed to study the
relationship between moisture damage, air void distribution and material surface
properties (Birgisson, et al., 2005).
Performance of an asphalt mix can be evaluated by checking individual failure modes. Two
of the most common failure cases are rutting and moisture damage. When the thickness of
the mastic surrounding the Secondary Structure is too low, then the particles are not bonded
10
Rut Depth[mm] per million ESALs
20
WesTrack
NCAT E
NCAT N
15
10
5
0
40
50
60
70
% of PS over the total mix volume
Rut Depth[mm] per million ESALs
Rut Depth[mm] per million ESALs
Rut Depth[mm] per million ESALs
to each other producing a brittle response to loading. This reduces significantly the capacity
of a mixture to resist permanent deformation. In the case of the Primary Structure, low
coating thickness affects the durability of the mixture by increasing the possibility of rutting
due to densification from the traffic. However, low thickness around the PS means
interconnected air voids which help the drainage of moisture trapped in the mix. In the
opposite case, when the coating thickness around the PS is too thick there is a risk of losing
the contact points between the PS particles, affecting the general load bearing capacity of
the mixture.
20
WesTrack
NCAT E
NCAT N
15
10
5
0
0
0.2
0.4
tSS [mm]
0.6
0.8
20
WesTrack
NCAT E
NCAT N
15
10
5
0
0
1
2
3
Disruption Factor
4
5
20
WesTrack
NCAT E
NCAT N
15
10
5
0
0.5
1
1.5
2
tPS [mm]
Figure 6. Results for Field Mixtures
Figure 6 presents the results for WesTrack and NCAT mixtures. It is possible to observe
how the framework is capable to identify those mixtures with rutting problems isolating
them to the extremes. High content of material acting as the load bearer structure produces
mixtures that suffer high permanent deformation. This is due to lack of supporting material
providing stability under loading. The Disruption Factor shows this effect as mixtures with
poor rutting performance have a higher potential to have their PS disrupted. Furthermore,
these “bad” mixtures also present low film thickness around both structures. Low thickness
11
around the SS shows a lack of bond between the supporting material, and low thickness
around the PS shows lack of supporting material in general.
10
8
8
6
4
Granite (G)
Limestone (G)
Limestone (B)
2
0
20
APA Rut [mm]
APA Rut [mm]
10
6
4
0
30
40
50
60
% of PS over the total mix volume
10
10
8
8
6
4
Granite (G)
Limestone (G)
Limestone (B)
2
0
0.08
0.1
0.12
Granite (G)
Limestone (G)
Limestone (B)
2
APA Rut [mm]
APA Rut [mm]
Figure 7 shows the results for laboratory mixtures tested with the Asphalt Pavement
Analyser (APA). As it can be observed in the left upper plot there is no clear tendency for
the material from (Guarin, et al., 2011), however the limestone mixtures from (Birgisson, et
al., 2004) show that there is a minimum rutting depth for mixtures with a PS content around
45 – 50% and it increases towards the extremes. Once again, it can be observed in the
Disruption Factor results that the rutting depth increases for DF>1.
0
0.5
1
Disruption Factor
6
4
Granite (G)
Limestone (G)
Limestone (B)
2
0
0.5
0.14
tSS [mm]
1.5
1
1.5
2
tPS [mm]
Figure 7. Results for Laboratory mixtures with APA test
In (Birgisson, et al., 2005) two groups of aggregates were used: oolitic limestone that in the
past has not shown significant stripping potential and crushed Georgia granite that has
shown potential to stripping. All mixtures were made up of four components: coarse
aggregate, fine aggregate, screenings and mineral filler. They were blended together in
different proportions providing six HMA mixtures for each mineral aggregate type which
were volumetrically equivalent to each other. The mixtures were designed according to the
SuperPave volumetric mix design method and all specimens were compacted on the IPC
Servopac SuperPave gyratoric compactor to 7-8% air voids.
12
Average Void Diameter [mm]
Average Void Diameter [mm]
Using digital images from X-ray Computed Tomographic imaging the air void size
distribution and number of air voids was determined for each specimen. In Figure 8 the
relation between air void size and thickness of film around the Primary and Secondary
Structures is presented. It can be observed that the higher tSS then the particles are better
“glued” together making the air voids bigger but fewer. The opposite trend is observed with
tPS as the space in between the particles will clearly decrease with thicker film around them.
Limestone
Granite
1.6
1.4
1.2
1
0.8
0.09
0.1
0.11
0.12
0.13
0.14
0.15
Limestone
Granite
1.6
1.4
1.2
1
0.8
0.4
0.6
tSS [mm]
0.8
1
1.2
tPS [mm]
Figure 8. Correlation between air void size and binder distribution
The granite mixtures were tested with the Hamburg Wheel Tracking Device to determine
their natural resistance too moisture damage. The test specifications determine that the test
is continued until either rut of 12,5 mm depth is measured or the number of loading cycles
reaches 20000. The number of cycles to strip, Ns, is defined as the loading cycle where the
rate of permanent displacement measured during the test markedly increases.
2.2
x 10
4
2.2
4
2
N of cycles to strip
N of cycles to strip
2
x 10
1.8
1.6
1.4
1.2
1
1.8
1.6
1.4
1.2
1
0.8
0.08
0.1
0.12
tSS [mm]
0.14
0.16
0.8
0.4
0.6
0.8
1
tPS [mm]
Figure 9. Hamburg wheel Device test results for granite mixtures
13
1.2
1.4
The results given in Figure 9 show the number of cycles to strip related to the thickness
around Primary and Secondary Structure. It can be observed that for a low value of tSS
mixtures strip very fast as the stones have no protection against moisture, and for a ticker
coating around the SS the air pockets are smaller but more numerous. In this case the
thickness of the PS is also high and the more air voids there are the bigger the surface are
exposed to water. It is possible to observe that there is an optimum tSS for which the
resistance to stripping is highest. At this level the stones in the SS are protected against
moisture and at the same time they leave enough open channels for the water to drain as tPS
is low.
1.2
1.2
Limestone
Granite
0.8
1
ERc/ERu
ERc/ERu
1
0.6
0.4
0.2
0.08
Limestone
Granite
0.8
0.6
0.4
0.1
0.12
tSS [mm]
0.14
0.2
0.4
0.16
0.6
0.8
1
tPS [mm]
1.2
1.4
Figure 10. Moisture analysis for limestone and granite mixtures
Figure 10 presents the energy ratio results of limestone and granite mixtures. Energy ratio is
a parameter that measures the fracture resistance of mixtures based on the dissipated creep
strain energy, forming a basis for a performance-based fracture criterion for flexible
pavements (Birgisson, et al., 2005). Since it is known that the fracture resistance of a
mixture is strongly affected by moisture damage, by evaluating the energy ratio of the
conditioned and the unconditioned samples a measure of the moisture damage is given.
According to the given definition, moisture damage decreases with higher ERc/ERu. The
influence of the film thickness around the PS is very well captured by the limestones, as
lower films means bigger air voids providing a proper drainage for the water trapped in the
structure as well as there is less mixtures exposed to the moisture. It can be noticed in this
type of testing that granite mixtures do not present such a clear response as in the Hamburg
Wheel Tracking Device. This is due to the conditioning of the samples, as for energy ratio
testing the samples are forced into saturation creating conditions which are unreal to certain
types of minerals, like granites, provoking a general failure of the samples.
14
4. Discussion and Conclusions
The following thesis presents a framework developed to characterize asphalt mixtures
based on the aggregates gradation and the structure formed by them. The framework
identifies the range of material which forms the Primary Structure and is the main load
bearing assembly. The amount of material belonging to the Primary Structure may
influence the load response of a mixture and can be characterized by its porosity and
coordination number according to packing theory of spheres. Particles that are smaller than
the Primary Structure are called the Secondary Structure and they provide stability to the
main network by keeping it in place, while particles that are bigger than the Primary
Structure are just considered to be floating in the mixture as their concentration is not
enough to influence the load carrying ability of the mixture.
A complete characterization of asphalt’s microstructure is achieved by determining the way
that the bitumen binder is distributed and how this affects the size and distribution of the air
voids. For this purpose a hierarchical distribution system has been developed which
assumes the following sequence: bitumen binder and fines creates mastic which covers the
particles of the Secondary Structure; this composite is then the material that coats the
Primary Structure. Both thicknesses have been calculated using a previous relationship
based on packing of the particles and the overlapping of the film as it grows. This method
has given a geometrical solution to binder distribution for each sub-structure, which
increases the understanding of asphalt mixture microstructure.
The framework has been validated by taking mixtures with known field rutting
performance and laboratory mixtures that have been tested for both rutting and moisture
damage. The range for Primary and Secondary Structure as well as porosity of the Primary
Structure, coordination number and the binder distribution parameter for each structure
have been calculated for each one of the mixtures. Results obtained show a favourable
relation between the per cent of material that the Primary Structure represents of the whole
mixture and the resistance to rutting, suggesting that there might be an optimum of material
that would give a minimum permanent deformation. Film thickness of the Primary
Structure has shown to be a key parameter to prevent moisture damage, as it is directly
related to the size of the air voids and the protection of the aggregate/mastic interface.
The developed framework is a tool to engineer mixtures and optimize the use of available
materials. The advantages of the model is its flexibility for any type of sieve system used
and its ability to include different size distribution within a sieve size, reducing the
limitations from previously developed models. The assumption of having aggregates as
spherical particles has shown, even though a very rough approximation, to give a good corelation to performance on asphalt mixtures. It is still desirable to include the influence of
aggregates shape and texture, and the differences on mixture response depending on the
mineral composition of the aggregates. Packing theory has proven that independent of the
15
shape of the particles the concept of contact points and porosity can be used to describe the
structure formed by the aggregates. The biggest potential of the developed framework can
be seen from the simulation side, as it works as a tool to reduce the number of variables in
asphalt microstructure.
The Gradation - Based Framework has satisfactory distinguished between good and bad
performance of asphalt mixtures when related to permanent deformation and moisture
damage. Further work is needed to calibrate the model based on x-ray tomography or
similar tools, to determine the range of validity of the formulations and to identify the
critical ranges for Primary Structure content and coating thickness for optimal performance
and more durable asphalt pavements. The developed model can be used as a tool to
determine the optimal gradation to assure good performance for hot mix asphalt pavements.
16
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