design of pavements incorporating grouted macadams
TRANSCRIPT
The design of pavements incorporating grouted macadams
Joel R. M. Oliveira1; Nick H. Thom2; Salah E. Zoorob3
Abstract: Grouted Macadam, a material that consists of a porous
asphalt skeleton with 25-35% voids, filled with a cementitious
grout, has traditionally been used as a specialist surfacing with
excellent resistance to both deformation and fuel spillage.
However, the actual engineering properties of the material have
rarely been investigated in depth and design of pavements
incorporating grouted macadam has relied heavily on past
experience. The purpose of this study was to assess the
consequences of applying analytical pavement design methods to
pavements incorporating grouted macadam layers. Two different
design methodologies were tested, 1- a conventional approach
based on the traditional fatigue criterion used for bituminous
materials and, 2- an iterative approach, which took realistic
1 PhD, Lecturer, Department of Civil Engineering, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal. E-mail: [email protected]. Telephone: +351253510200. Fax: +351253510217.2 PhD, Lecturer, Nottingham Transportation Engineering Centre, School of CivilEngineering, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. E-mail: [email protected] PhD, Senior Research Officer, Nottingham Transportation Engineering Centre, School of Civil Engineering, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. E-mail: [email protected].
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account of the actual damage accumulation within the material.
For both methodologies, a comparison was made between a grouted
macadam and a conventional bituminous mixture. The main
conclusion drawn from this study is that extended fatigue life
can be obtained from pavements incorporating grouted macadam
although this advantage will be overlooked if design is carried
out using the traditional fatigue failure criterion.
CE Database subject headings: grouted macadams, semi-flexible
materials, pavement design, fatigue performance.
2
1 Introduction
A conventional Grouted Macadam consists of a single-sized porous
asphalt skeleton (25-35% voids), filled with a highly flowable
cementitious grout. Grouted macadams have traditionally been used
as specialist surfacings, taking advantage of their excellent
resistance to both deformation and fuel spillage. However,
pavement layers incorporating these materials are rarely
‘designed’ and tend to be specified on the basis of successful
past performance. This has resulted in the use of different mix
designs in different countries (Oliveira et al., 2006a).
In order to address these issues, a full study of grouted macadam
behavior was conducted at the University of Nottingham (Oliveira,
2006) and this paper reports on some of the implications of that
study for pavement design. Two approaches will be evaluated and
compared. The first is a traditional analytical approach for
conventional asphalt pavements, basing pavement life on computed
tensile strain in the material and interpreting fatigue data in a
conventional way. The second, which is believed to be more
3
appropriate for grouted macadams, considers the actual process of
deterioration evident from the test data.
2 Design Parameters and Methodology
In accordance with the Highways Agency (2001, 2006), pavement
designs have been carried out for a reference temperature of
20 °C. In the present study, both stiffness and fatigue tests
were therefore carried out at 20 °C. Indirect Tensile Stiffness
Modulus (ITSM) and four-point bending tests carried out under the
same reference temperature and at similar loading rates by
Oliveira (2006) have shown similar stiffness results. An increase
in frequency (i.e., loading rate) led to increased stiffness,
confirming that a grouted macadam is fundamentally an asphaltic
material with a visco-elastic nature. The average stiffness
chosen for pavement design in this investigation (8000 MPa) was
obtained from tests carried out on a particular grouted macadam
mixture, based on a 10mm single-sized material with 4% of 200 pen
binder (including 0.15% fibers by mass of mixture), giving 25-30%
4
of grout-filled voids. Testing was at 10 Hz, since all the
fatigue tests and the corresponding fatigue lines were also
obtained for the same frequency. This frequency represents a
relatively slow traffic speed and is therefore a conservative
value for design. A similar value was also obtained from ITSM
tests at a loading frequency of approximately 5 Hz, carried out
at 20 °C on 2-year old laboratory specimens (Oliveira, 2006). The
results obtained by Oliveira (2006) also showed that the fatigue
life of grouted macadam was not significantly susceptible to
temperature variations between 0 and 20 °C.
Four pavement foundation classes were considered in this study
(Figure 1), as suggested by Nunn (2004) and adopted by the
Highways Agency (2006). The design characteristics of each
foundation class are shown in Table 1. Designs are based on
pavement response calculations carried out using a multilayer
linear elastic analysis computer program – BISAR 3.0 (Shell
International, 1998).
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3 The Traditional Analytical Approach
A key element in design against fatigue is the development of a
meaningful relationship between laboratory behavior and field
performance. Laboratory tests normally employ sinusoidal loading
and a fixed strain or stress amplitude during any one test, while
in practice load level is randomly distributed, there are rest
periods between pulses, and a lateral distribution of loads
across the pavement. To accommodate these effects, correction
factors (known as shift factors) are commonly applied. However,
determination of the correct shift factor is not straightforward,
since it depends on the type of test, mode of loading, testing
temperature and type of mixture (Shell, 1978; Rao Tangella et
al., 1990). In fact, shift factors for flexible pavements ranging
from 2 up to 440 have been suggested by different authors (Shell,
1978; Brown et al., 1985; Rao Tangella et al., 1990; Khweir and
Fordyce, 2003; Ekdahl and Nilsson, 2005).
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In this investigation, the relevant information was obtained by
conducting experiments to analyze the influence of rest periods
on the fatigue life of grouted macadam mixtures (Oliveira et al.,
2006b). This led to the recommendation of a shift factor of 45
(relative to strain-controlled four-point beam fatigue tests),
which included an extra factor of 1.1 for lateral load
distribution, as suggested by Brown et al. (1985). This was still
considered a conservative value, due to the unusual behavior of
grouted macadams in terms of crack propagation (Oliveira et al.,
2006b), highlighted in subsequent sections of this paper.
Fatigue designs for grouted macadam pavements were therefore
based on the laboratory results obtained by Oliveira (2006),
multiplied by a shift factor of 45, which resulted in Equation 1.
These were compared with designs for dense bituminous macadam
(DBM) pavements using the fatigue criterion specified by Powell
et al. (1984) and Nunn (2004), which was developed to represent
the field performance of asphalt mixtures in the UK (Equation 2).
(1)
7
(2)
where:
N = Number of equivalent standard axle loads (ESALs);
εt = Tensile strain induced at either the surface or underside of the
bituminous bound layers.
In order to minimize the number of variables in the study, a
layer of either grouted macadam or DBM 50 (DBM with 50pen grade
bitumen) directly overlying the foundation was used in the
calculations. As previously stated, four foundation classes were
considered and in each case, the required thickness of bound
material was obtained as a function of design traffic. The
mechanical properties of the materials used in the calculations
are summarized in Table 2, in accordance with Oliveira et
al. (2006a) and as specified in design standard HD26/06 (Highways
Agency, 2006). The thickness designs are presented in Figure 2.
A longer life is noted for grouted macadam pavements surfacing
when compared with DBM 50 pavements of similar thickness.
However, this extended fatigue life is principally due to the
8
higher stiffness modulus of the material, which reduces the
tensile strain level. It shows a degree of enhancement when using
grouted macadam, but it is the contention of this paper that it
significantly understates the actual enhancement expected,
because of the unusual manner in which grouted macadams undergo
deterioration. For this reason, a more detailed analysis has been
undertaken and this is presented in the next section.
4 Pavement design based on detailed fatigue behavior
The fatigue life data referred to in the previous section was
determined according to the traditional failure criterion (i.e.,
50% reduction in initial stiffness for controlled-strain tests).
However, analysis of the stiffness reduction curves generated
during fatigue tests led to the observation that curves for
grouted macadam have a particular shape, flatter than those for
normal asphalts. A more focused investigation was therefore
carried out with the objective of assessing the extended fatigue
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life of grouted macadams, with emphasis on performance beyond the
traditional 50% stiffness reduction normally considered.
4.1Laboratory testing program
In order to compare the fatigue performance of grouted macadams
with traditional bituminous materials, tests should be carried
out using the same testing equipment. Most of the laboratory
tests carried out on grouted macadams in this investigation were
performed using a four-point bending equipment developed by
Oliveira (2006, 2006a). Unfortunately, this equipment displayed
some limitations, in particular when testing mixtures susceptible
to permanent deformation during the course of a test. Grouted
macadam has negligible susceptibility to permanent deformation
and so was unaffected.
For this reason, a trapezoidal cantilever (also known as two-
point bending) test was chosen. The two-point bending test is one
of those specified in European Standards, EN 12697-24 (BSI,
2004), and it represents the bending of a pavement layer
10
reasonably realistically. The same equipment type has been widely
used to study the fatigue performance of asphalt mixtures by
other researchers (Rowe, 1993; Breysse et al., 2003; Bodin et
al., 2003; Breysse et al., 2004).
A series of tests was carried out on laboratory prepared
trapezoidal specimens to determine the fatigue performance of
both standard grouted macadam and 10 mm size DBM 50 mixtures. The
specimens were cut from slabs prepared in the laboratory
according to the procedure used by Oliveira (2006). Figure 3
represents schematically the trapezoidal specimen shape. The
temperature used in these tests was 20 °C. The tests were carried
out in displacement (strain) control mode at 10 Hz, the same test
conditions as those described in Oliveira et al. (2006a), using
the four-point bending equipment.
Strain controlled tests are normally stopped after the stiffness
modulus of the specimen has reduced to half of its initial value.
However, observations made by Oliveira (2006) on the shape of the
stiffness reduction curve for grouted macadams (Figure 4), using
11
the four-point bending test apparatus, suggested fatigue behavior
fundamentally different from that of conventional bituminous
mixtures, as represented in Figure 5 (Rowe, 1993; Kim et al.,
2003; Lundstrom et al., 2004). For this reason, fatigue tests
were extended beyond the normal 50% criterion and stopped only
when the stiffness modulus had reduced to 10% of its initial
value. This allowed an assessment of the full performance of the
mixtures during the tests.
4.2 Fatigue test results
The two-point bending fatigue test results obtained in this study
for the standard grouted macadam mixture can be compared with
those obtained by Oliveira et al. (2006a) for the same mixture,
using the four-point bending test apparatus. As can be seen in
Figure 6, the fatigue lives obtained for both test
configurations, using the same failure criterion (50% stiffness
reduction) are very close to each other and could almost be
considered as one common trend line.
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The results from two-point bending tests show a higher degree of
scatter when compared with four-point bending test results. The
reason for this may be related to the specimen dimensions, since
the thickness of trapezoidal specimens (25 mm) is only two and a
half times the nominal aggregate size used in the mixture
(10 mm), in contrast to the beam specimens used in four-point
bending tests, where the dimensions of the specimens (50×50 mm
cross-section) are five times the nominal aggregate size.
Therefore, in the trapezoidal specimens, local variability
(concentration of voids, bitumen or fibers) within the structure
of the mixture is more likely to influence the fatigue life of
the specimen than in the case of the beams.
Results from the two-point bending fatigue tests carried out on
the DBM 50 mixture are presented in Figure 7, together with the
fatigue line for the standard grouted macadam mixture, and again
based on a 50% stiffness reduction. Expressed in this way, the
DBM 50 appears to have a superior fatigue performance.
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However, Figures 8 and 9 reveal the full stiffness reduction
curves for the standard grouted macadam and DBM 50 mixtures,
respectively. Naturally, the strain level used in each individual
test influences the stiffness reduction rate and this inhibits
comparison of the data sets. Therefore, in order to analyze the
results without this strain level dependency, they were
normalized against the number of cycles necessary to reach the
50% stiffness reduction point (i.e., conventional failure). Thus,
for each data point, the ‘relative time’ was obtained by dividing
the actual number of cycles corresponding to that data point by
the number of cycles corresponding to 50% stiffness loss. These
normalized data sets can be observed in Figures 10 and 11, for
the grouted macadam and DBM 50 mixtures, respectively.
Although some scatter is evident in Figures 10 and 11, especially
at relative times greater than 1.0, it can be readily observed
that the two materials follow quite different trends. The rate of
stiffness reduction beyond 50% stiffness loss is dramatically
different for the two types of material. While the rate of
stiffness loss increases rapidly in the case of DBM 50, this does
14
not occur in the case of grouted macadam, where the rate tends to
decrease very gradually with time (i.e., number of cycles). This
suggests that grouted macadams may continue to perform
satisfactorily even beyond the conventional ‘failure point’,
whereas this is not the case for standard asphalt mixtures.
In order to facilitate use in pavement design, the results were
averaged, a best-fit trend line fitted, and equations defined.
Figures 12 and 13 show the trend lines obtained for each material
type. They are also plotted together in Figure 14 for direct
comparison. In Figure 14, the different behavior of the two
materials becomes even more evident.
The difference in fatigue behavior should logically have a
significant influence on the design of pavements. For this a new
approach has been developed and is discussed in the following
section.
4.3 Implications for pavement design
15
Fatigue life of bituminous materials is traditionally defined by
the number of load applications to which the materials can be
subjected before failure at a particular stress or strain level.
In standard calculations, the degradation of the material
properties is not taken into account, as the amplitude of dynamic
strain is considered constant throughout the pavement life.
However, such an assumption is not correct. As the material
properties, namely stiffness, decrease, the strain levels imposed
in the pavement increase, resulting in a gradually lower
resistance of the mixture to fatigue. In order to take full
account of the fatigue performance of both materials as they
become weaker by accumulation of damage, an iterative approach
was adopted. As before, four different foundation classes were
used, on top of which a single 40 mm grouted macadam or DBM 50
surface course was directly applied. Greater thicknesses would of
course be possible, but 40 mm is assumed here in order to
demonstrate the methodology. The pavement response under a
standard 40 kN load was calculated using multi-layer linear
elastic analysis for several levels of ‘degradation’, represented
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by several levels of stiffness reduction in the bound material
layer (either grouted macadam or DBM).
Since the rate of stiffness reduction with time or number of load
applications decreases during a typical strain controlled fatigue
test, different stiffness intervals were used in order to follow
the stiffness reduction curve reasonably closely. Thus, at the
beginning of the test, short intervals of ‘relative time’ were
taken, according to the interval of stiffness chosen. Figure 15
represents an example for the grouted macadam mixture. Within
each interval, the average stiffness value was used as the input
value for determination of the strain level in the pavement,
which was assumed constant during the interval.
For each strain level, the corresponding fatigue life was
estimated by referring to the traditional fatigue line of each
mixture, i.e., assuming constant strain until failure. However,
since only a portion of the fatigue life is consumed during each
interval, the cumulative fatigue life is calculated by adding the
lives consumed during all the intervals, as schematically
17
illustrated in Figure 16. This approach is known as “Miner’s
Law”.
According to this new approach, the fatigue life of any pavement,
calculated by summing the lives until 50% stiffness reduction
(the traditional failure criterion), will be lower than if
estimation is made based directly on the fatigue line using only
the initial strain value. This is because the new approach takes
the continuously decreasing stiffness into consideration. In
these example calculations, the number of load applications was
determined using the fatigue characteristic obtained directly
from laboratory tests, without taking any shift factor into
account, in order to isolate the effect of the differing
stiffness loss behavior. The results for the two materials are
given in Figure 17, in which it is evident that the standard
fatigue calculations slightly overestimate pavement life.
Although the pavement structures used in these examples may not
be totally realistic due to the high strain levels induced in the
surface course, a slightly increased fatigue life can also be
18
observed for grouted macadam pavements, regardless of the
approach used for fatigue life estimation. However, the
differences are small and reduce further with an increase in the
bearing capacity of the foundation, since the surface course then
has less influence on the overall behavior of the pavement, as
the overall strains are reduced (Figure 18).
However, a key point is that the traditional failure criterion
(i.e., 50% stiffness loss) does not represent the true fatigue
life of grouted macadam pavements due to the particular behavior
presented by this type of material. In fact, the main advantage
of grouted macadams is most noticeable after the stiffness
modulus of the mixture has reached 50% reduction from its initial
value. The new iterative approach to fatigue life calculation
allows this to be modeled and the result is shown in Figure 19.
In Figure 19 the cumulative number of cycles obtained for each
pavement with different foundation classes is extended until 90%
stiffness loss has occurred, and this highlights the extended
fatigue life of grouted macadam surface courses expected relative
19
to conventional asphalt mixtures. After a stiffness reduction of
approximately 40 to 50%, the DBM 50 mixture has little residual
life left, while the grouted macadam mixture continues to lose
stiffness approximately according to the logarithm of the
cumulative number of cycles. Figure 20 shows the increase in
tensile strain on the underside of the surface course with the
cumulative number of load applications, again demonstrating the
contrast in behavior type between grouted macadam and the
conventional mixture.
5 Summary and Conclusions
Analytical pavement design has traditionally been carried out
based on laboratory test results, to which shift factors are
generally applied to ‘convert’ the data from laboratory to field
conditions. In the last few decades, fatigue models have been
developed in this way and validated using feedback information
from the field. However, those models have not been tested to
assess their suitability to be applied to grouted macadam
mixtures. A comparative analysis has therefore been carried out
in this investigation using laboratory experimental results
20
obtained from both grouted macadam and conventional asphalt
mixtures in order to evaluate the appropriateness of such models
in the design of pavements incorporating grouted macadam layers.
In the present study, two different approaches were analyzed: a
traditional methodology, in which the fatigue life of the bound
layers was determined by converting laboratory test results into
field performance using shift factors; and an iterative approach,
where the response of the pavement was computed at several levels
of degradation. For the former, a grouted macadam shift factor
was suggested, based on the observed effect of rest periods on
the fatigue life of the mixture. The latter was carried out on a
purely comparative basis, using a traditional DBM 50 mixture as a
reference for each pavement structure studied, and took account
of the different stiffness reduction trends observed during
grouted macadam and DBM 50 fatigue tests. In this study, fatigue
tests were carried out beyond the traditional failure criterion
(50% of initial stiffness), where grouted macadam showed a
behavior notably different from a conventional asphalt.
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Although extended fatigue lives for pavements incorporating
grouted macadam layers were obtained in all calculations made in
the present study, the real advantage is overlooked by adopting
the traditional failure criterion (50% of initial stiffness). As
demonstrated in Section 4.1, the particular behavior of grouted
macadams beyond the traditional failure point extends the
predicted life of grouted macadam pavements considerably. The
iterative approach used in this investigation allows the lower
damage growth rate of grouted macadams under fatigue to be
modeled realistically. In fact, according to this analysis
approach, grouted macadams could theoretically have an
indeterminate fatigue life, provided that the support is properly
prepared.
References
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(2003). “Prediction of the Intrinsic Damage during Bituminous
22
Mixes Fatigue Tests.” 6th RILEM Symposium on Performance Testing and
Evaluation of Bituminous Materials, Zurich.
Breysse, D., De La Roche, C., Domec, V., and Chauvin, J. J.
(2003). “Influence of Rest Time on Recovery and Damage during
Fatigue Tests on Bituminous Composites.” 6th RILEM Symposium on
Performance Testing and Evaluation of Bituminous Materials, Zurich.
Breysse, D., Domec, V., Yotte, S., and De La Roche, C., (2004).
“Better Assessment of Bituminous Materials Lifetime Accounting
for the Rest Periods.” 5th RILEM International Conference on “Cracking in
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Analytical Design of Bituminous Pavements.” Proc. Institution of Civil
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Bituminous mixtures - Test methods for hot mix asphalt –
Resistance to fatigue.” British Standard Institution, London.
23
Ekdahl, P., and Nilsson, R. (2005). “How may the variation of
traffic loading effect measured asphalt strains and calculated
pavement service life?” 7th International Conference on the Bearing Capacity of
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- Pavement Design.” Design Manual for Roads and Bridges. London.
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- Pavement Design.” Design Manual for Roads and Bridges. London.
Khweir, K., and Fordyce, D. (2003). “Influence of layer bonding
on the prediction of pavement life.” Proc. Institution of Civil Engineers,
Transport 156, Issue TR2, 73-83.
Kim, Y. R., Little, D. N., and Lytton, R. L. (2003). “Fatigue and
Healing Characterization of Asphalt Mixtures. Journal of Materials in
Civil Engineering, Vol. 15, No. 1, ASCE, 75-83.
24
Lundstrom, R., Di Benedetto, H., and Isacsson, U. (2004).
“Influence of Asphalt Mixture Stiffness on Fatigue Failure.”
Journal of Materials in Civil Engineering, Vol. 16, No. 6, ASCE, 516-525.
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TRL Limited. Crowthorne.
Oliveira, J. R. M. (2006). “Grouted Macadam: Mechanical
Characterisation for Pavement Design.” PhD Thesis. University of
Nottingham. Nottingham.
Oliveira, J., Thom, N. H. and Zoorob, S. (2006a). “Fracture and
Fatigue Strength of Grouted Macadams.” Proceedings of the 10th
International Conference on Asphalt Pavements. Quebec.
Oliveira J. R. M., Pais, J. C., Thom, N. H., and Zoorob, S. E.
(2006b). “A study of the fatigue properties of grouted macadams.”
Paper submitted to the International Journal of Pavements, IJP.
25
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26
27
Table 1 – Design characteristics of pavement foundations
FoundationClass
Stiffness (MPa)
Poisson’s Ratio
1 50 0.352 100 0.353 200 0.354 400 0.35
28
Table 2 – Mechanical properties of considered materials
MaterialStiffness(MPa)
Poisson’s
RatioGroutedMacadam 8000 0.25
DBM 50 4700 0.35
29
Figure 1 – Example designs for foundation classes 1 to 4 on 5%
CBR subgrade (Nunn, 2004)
30
50
100
150
200
250
300
350
0.01 0.1 1 10 100 1000 10000
Number of load applications (million ESALs)
Thick
ness (mm)
DBM 50 (Found1) DBM 50 (Found2) DBM 50 (Found3) DBM 50 (Found4)GM (Found1) GM (Found2) GM (Found3) GM (Found4)
Foundation 1 432 - DBM 50
Foundation 1 432 - GM
Figure 2 – Design of a pavement incorporating either a grouted
macadam or a DBM 50 layer applied directly on top of the
foundation
70 m m
25 m m 25 m m
250 m
m
Figure 3 – Dimensions of trapezoidal specimen used in two-point
bending tests (not to scale)
31
No. of loading cycles
Stiffness
Figure 4 – Typical trend of four-point bending strain-controlled
fatigue tests on grouted macadams
No. of loading cycles
Stiffness
Figure 5 – Typical trend of strain-controlled fatigue tests
(Rowe, 1993; Kim et al., 2003; Lundstrom et al., 2004)
32
Grouted M acadams Fatigue Tests
y = 2648.6x-0.2631
R2 = 0.8925
y = 2535.3x-0.2477
R2 = 0.9838
10
100
1000
100 1000 10000 100000 1000000 10000000No. of cycles
Tensile Strain (microstra
in)GM - 4PB
GM - 2PB
Potência (GM -2PB)Potência (GM -4PB)
Figure 6 – Two-point and four-point bending fatigue test results
obtained for the standard grouted macadam mixture
Two-point bending strain-controlled fatigue tests
y = 1913x-0.2145
R2 = 0.8767
y = 2648.6x-0.2631
R2 = 0.8925
10
100
1000
100 1000 10000 100000 1000000 10000000No. of cycles
Tensile strain (m
icrostra
in)
DBM 50
Grouted M acadam
Potência (DBM 50)
Potência (GroutedM acadam)
Figure 7 – Two-point bending fatigue test results obtained for
the standard grouted macadam and a DBM 50 mixture
33
Grouted macadam two-point bending strain-controlled fatigue tests
0102030405060708090100
0 50000 100000 150000 200000 250000 300000No. of cycles
% In
itial Stiffness 110 με
150 με160 με
200 με
170 με
300 με
400 με
Figure 8 – Two-point bending fatigue test results obtained for
the standard grouted macadam mixture
Two-point bending fatigue tests - strain-control - DBM 50
0102030405060708090100
0 5000 10000 15000 20000 25000 30000 35000 40000No. of cycles
% In
itial Stiffness
250 με
350 με
300 με
400 με
500 με
Figure 9 – Two-point bending fatigue test results obtained for
the DBM 50 mixture
34
Grouted macadam normalised two-point bending fatigue tests - strain-control
0102030405060708090100
0 1 2 3 4 5 6 7 8 9 10Relative tim e to 50% stiffness reduction
% Initial Stiffness
110 με
150 με160 με
170 με
200 με 300με
400 με
Figure 10 – Normalized two-point bending fatigue test results
obtained for the standard grouted macadam mixture
Normalised two-point bending fatigue tests - strain controlDBM 50
0102030405060708090100
0 0.5 1 1.5 2 2.5Relative tim e to 50% stiffness reduction
% In
itial Stiffness 250 με
35 0με
300 με
400 με
500 με
Figure 11 – Normalized two-point bending fatigue test results
obtained for the DBM 50 mixture
35
Normalised two-point bending fatigue tests - strain controlGrouted macadam
y = -10.531Ln(x) + 48.337R2 = 0.9787
0102030405060708090100
0 2 4 6 8 10Relative tim e to 50% stiffness reduction
% In
itial Stiffness
Average of original data
Logarithmic fitting
Registo. (Average oforiginal data)
Figure 12 – Normalized standard grouted macadam fatigue test
results (2PB)Normalised two-point bending fatigue tests - strain control
DBM 50
y = -38.529x4 + 243.75x3 - 527.82x2 + 418.42x - 47.102R2 = 0.9967
y = 95.245x4 - 268.81x3 + 247.94x2 - 124.37x + 98.428R2 = 0.9954
0102030405060708090100
0 0.5 1 1.5 2 2.5 3Relative tim e to 50% stiffness reduction
% In
itial Stiffness
before 1
after 1
Polinómio(after 1)Polinómio(before 1)
Figure 13 – Normalized DBM 50 fatigue test results (2PB)
0102030405060708090100
0 1 2 3 4 5 6 7 8 9 10Relative tim e to 50% stiffness reduction
% Initial Stiffness Grouted macadam
DBM 50
36
Figure 14 – Comparison between grouted macadam and DBM 50
normalized data
Grouted macadam stiffness intervals considered forfatigue life calculations
0102030405060708090100
0.0 0.5 1.0 1.5 2.0Relative tim e to 50% stiffness reduction
% In
itial Stiffness
Stiffness intervalsAverage of interval
Figure 15 – Stiffness intervals used for the calculation of
grouted macadam’s cumulative fatigue life
Stiffness level i
(average of interval i)
Strain level i
(from BISAR)
Fatigue life
(traditional fatigue line)
Relative tim e
(interval i)
Fatigue life consum ed during interval i
Cum ulative fatigue life
n
i 1 Fatigue life consum ed during interval i
×
Figure 16 – Cumulative fatigue life calculations
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Fatigue life comparison
1 10 100 1000 10000 100000
1 (50 M Pa)
2 (100 M Pa)
3 (200 M Pa)
4 (400 M Pa)
Foundation Class
No. of cycles up to 50% stiffness reduction
GM - CumulativeGM - TraditionalDBM - CumulativeDBM - Traditional
Figure 17 – Traditional and cumulative fatigue life of grouted
macadam and DBM
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% Initial Stiffness
Tensile Stra
in (m
icrostra
in) .
DBM 50 - Foundation1 GM - Foundation1DBM 50 - Foundation2 GM - Foundation2DBM 50 - Foundation3 GM - Foundation3DBM 50 - Foundation4 GM - Foundation4
Figure 18 – Tensile strain obtained on the underside of the
surface course of each pavement structure
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0102030405060708090100
1 10 100 1000 10000 100000 1000000
Cumulative No. of cycles% Initial Stiffness
DBM 50 - Found1 DBM 50 - Found2 DBM 50 - Found3 DBM 50 - Found4GM - Found1 GM - Found2 GM - Found3 GM - Found4
Figure 19 – Cumulative fatigue life of grouted macadam and DBM 50
including degradation of the mixtures
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1 10 100 1000 10000 100000 1000000
Cumulative No. of cycles
Tensile Stra
in (m
icrostra
in) .
DBM 50 - Foundation1GM - Foundation1DBM 50 - Foundation2GM - Foundation2DBM 50 - Foundation3GM - Foundation3DBM 50 - Foundation4GM - Foundation4
Figure 20 – Tensile strain developed under the surface course
with the cumulative number of cycles for each studied pavement
structure
39