Structural Design of Pavements PART VI Structural Evaluation and

CT 4860
Structural Design of Pavements
January 2009
Prof.dr.ir. A.A.A. Molenaar
PART VI
Structural Evaluation and
Strengthening of Flexible Pavements
Using Deflection Measurements and
Visual Condition Surveys
2
Table of contents:
Preface
1. Introduction
2. Usage and condition dependent maintenance
3. Deflection measurement tools
3.1 Falling weight deflectometer
3.2 Benkelman beam
3.3 Lacroix deflectograph
3.4 Factors influencing the magnitude of the measured FWD deflections
4. Measurement plan
4.1 Estimation of the number of test points per section
4.2 Development of a measurement plan
5. Statistical treatment of raw deflection data and selection of a location representative
for the (sub)section
6. Back calculation of layer moduli
6.1 Surface modulus
6.2 Back calculation of layer moduli
6.3 Example
7. Analysis of Benkelman beam and Lacroix deflectograph deflection bowls
8. Estimation of the remaining life using an empirical based method
9. Mechanistic procedures for remaining life estimations and overlay design
9.1 Basic principles
9.2 Extension of the basic principles
10. Extension of the simplified procedure to estimate critical stresses and strains
10.1 Relations between deflection bowl parameters and stresses and strains
at various locations in the pavement
10.2 Temperature correction procedure
10.3 Relationships with other strength indicators such as SNC
10.4 Relationships between falling weight deflections and deflections
measured with the Benkelman beam
11. Remaining life estimation from visual condition surveys
12. Procedures to estimate material characteristics
12.1 Fatigue characteristics of asphalt mixtures
12.2 Deformation resistance of unbound base materials
12.3 Subgrade strain criterion
12.4 Maximum tensile strain at bottom of the bound base
13. Overlay design in relation to reflective cracking
13.1 Overlay design method based on effective modulus concept
13.2 Method based on stress intensity factors
13.3 Ovelay design method based on beam theory
13.4 Effects of reinforcements, geotextiles, SAMI’s and other interlayer systems
13.5 Load transfer across cracks
14. Effect of pavement roughness on the rate of deterioration
References
3
4
6
7
7
8
9
10
13
13
14
18
26
26
28
29
33
38
43
43
45
51
51
54
54
55
56
58
58
59
59
59
61
61
63
64
69
70
72
73
3
Preface:
Pavements deteriorate due to damaging effects of traffic and environmental loads and at a
given moment in time maintenance is needed. Maintenance activities can grossly be divided
into two categories.
The first category is the so called routine maintenance which is mainly applied to keep the
pavement surface in such a condition that it provides good service to the public but also to
limit the effects of ageing. Routine maintenance consists e.g. of crack filling, local repairs and
the application of surface dressings. Normally this type of maintenance is not too expensive.
The costs of a surface dressing are approximately fl 6/m2 while filling of cracks costs
approximately fl 2.5/m’. Routine maintenance is done on a regular basis; the time period
between two successive applications depends of course on the rate of deterioration which in
turn is affected by the damaging power of traffic and climate and by the workmanship of the
maintenance crews.
The second category is much more capital intensive. Now we are dealing with strengthening
of the pavement for which overlays are needed or partial or complete reconstruction. This
type of maintenance is less often required than routine maintenance.
Because pavement strengthening is such a costly affair, investigations to determine precisely
the extent and severity of the damage and the rate of progression are strongly recommended.
If a pavement surface e.g. shows severe cracking, removing this layer and replacing it by a
new one seems to be a sensible solution. If however the cracking is due to the very low
stiffness of the base and no measure are taken to improve the bending stiffness of the base
layer, then the cracking will soon reappear.
This simple example already illustrates that, in order to be able to make a proper selection of
the maintenance treatments available, one not only should know where something is going
wrong but also why.
Understanding why the pavement fails means that one needs knowledge on the stresses and
strains in the pavement as well as the strength of materials. The process of gaining this
knowledge is called “evaluation of the structural condition of pavements”.
As it will be shown in these lecture notes, deflection measurements are an extremely useful
tool in the assessment of the structural condition of the pavement. During a deflection
measurement, the bending of the pavement surface due to a well-defined test load is measured. This is called the measurement of surface deflections. It is clear that the magnitude of
the deflections and especially the curvature of the deflection bowl reveal important information
on the bending stiffness of the pavement.
In the notes ample attention is paid to the techniques for measuring deflections, the way how
the measurement results can be processed to obtain information on the stiffness of the
individual pavements layers and how they can be used to determine the required thickness of
the overlays to be applied.
Although all possible care has been given during the preparation of these notes to avoid
typing errors etc., it is always possible that some “bugs” are still present. Furthermore the
reader can have suggestions about certain parts of the material presented. It would be highly
appreciated if you could send your comments to the author using the following email address.
a.a.a.molenaar@citg.tudelft.nl
4
1. Introduction:
These lecture notes are dealing with deflection measurements, how they should be performed
and how the results can be used to determine the remaining life of the pavement and the
maintenance that has to be performed.
The importance of deflection measurements can be described by means of the following
example. When children have to build a bridge across a creek using a wide variety of wooden
beams, their instinct will tell them that they better select those planks that show the lowest deflection under load. They also know that it is wiser to place the beams like shown in figure 1a
than in figure 1b.
A
B
Figure 1: Children know by instinct that placing a beam according to A is more effective than
placing it according to B.
As civil engineers we know that the selection by the children is a correct one because beam A
has lower stresses and strains at the outer fibres than beam B when both beams are
subjected to the same load. However as civil engineers we also know that the question “is it
safe or not to cross a beam which shows a maximum deflection of 2 mm” cannot be
answered without knowledge of the span of the beam, the load applied and the strength of the
material from which it is made. This clearly indicates that measurement of only the maximum
deflection gives some information about the strength of the beam but that more information is
needed. We would already be in a much better shape if the curvature of the deflection bowl
due to the load was known.
The same is true for pavements. In order to get useful information about the flexural stiffness
of the pavement one should measure the deflection due to a test load at various distances
from the load centre.
We know that the flexural stiffness is determined by the stiffness of the subgrade and the
stiffness modulus and thickness of the layers placed on top of the subgrade. It will then be
obvious that it must be possible to back calculate the stiffness modulus of each of the individual layers if the deflection bowl due to a defined test load is known as well as the thickness
of each pavement layer.
If the stiffness modulus of each layer is known together with its thickness, then the stresses
and strains in any location in the pavement can be calculated.
Knowledge on the strength of materials however is absolutely needed for the determination of
whether or not the pavement is capable of carrying the traffic loads expected in the future and
whether or not it should be strengthened.
All this means that the usefulness of a deflection measurement program without paying
proper attention to the strength of materials can be doubted.
In order to determine to what extent traffic loads have resulted in a deterioration of the pavement strength, deflections should be measured regularly during the pavement life. Since
deflection measurements are fairly costly, one should make a realistic estimate of the number
of measurements to obtain a picture of the deterioration trend line that develops in time. One
should however be aware of the fact that the trend lines one wants to establish are influenced
by variations in temperature (effect on stiffness modulus of the asphalt layers) and moisture
(effect on stiffness modulus of the subgrade) and that the deflections measured over a certain
stretch of road might show a considerable variation because of variations in layer thickness
and stiffness modulus. Another question, which then arises, is how many measurement loca-
5
tions should be tested in a certain section in order to obtain a realistic picture of the flexural
stiffness of the pavement.
In these lecture notes we will deal with all these aspects. The structure of the notes is as follows. Attention will be paid to the development of a measurement program. This will be
followed with a discussion on the determination of the number of measurements required per
section and the statistical treatment of the deflection data.
Although the Benkelman beam was developed some 40 years ago, it is still in use in many
countries. This is also the case with the automated version of the Benkelman beam called the
Lacroix deflectograph. A chapter has been devoted to these devices and especially
procedures to correct the measured deflections to true deflections are discussed.
After that attention will be paid to some simple techniques allowing the overall stiffness of the
pavement structure to be assessed and potential problem layers to be identified. Then the
back calculation of stiffness moduli will be treated.
This will be followed by a discussion on the design of overlays in which probabilistic principles
are introduced.
After that ample attention will be paid to an analysis method which allows critical strains to be
evaluated without the need to back calculate layer moduli. This method is of special interest in
case accurate information on the layer thickness is not available.
Then attention is paid on the importance of visual condition surveys. A method will be
presented that allows the remaining life to be estimated from such surveys.
This chapter is followed by a chapter on the estimation of material strength characteristics like
the fatigue resistance of asphalt mixtures and the resistance to permanent deformation of
unbound granular materials.
Reflective cracking is an important issue and the commonly used overlay design methods
don’t take into account this important phenomenon. Therefore a chapter dealing with the
design of overlays controlling reflective cracking is presented.
Finally the effect of pavement roughness on pavement deterioration will be discussed and
simple procedures to estimate pavement roughness will be given.
First of all however attention will be paid to the question why pavement maintenance has to
rely on regular monitoring of the pavement condition and why the decision on applying
maintenance cannot be taken simply on the basis of the number of years the pavement is in
service or the number of loads that have been applied to the pavement.
6
2. Usage and condition dependent maintenance:
Pavements deteriorate due to the combined influences of traffic and environmental loads.
This means that at a given moment maintenance activities should be scheduled in order to
restore the level of service the pavement should give to the road user. It will be obvious that
careful consideration should be given to the planning and the selection of the maintenance
activity. The right strategy should be applied on the right spot at the right time.
Planning of maintenance can be sometimes a rather simple task to perform. If we consider
e.g. the maintenance of our illumination systems, we observe that in a number of cases (e.g.
hospitals) the bulbs are not replaced after failure, but after a certain number of burning hours.
This way of maintenance is called “usage dependent maintenance”, because the replacement
is done after a certain time period the object to be maintained is used.
There are three important reasons why such a type of maintenance is possible and accepted
for illumination.
a. For some reasons we don’t accept to be in the dark (safety, interruption of work).
b. We know quite precisely what the mean lifetime is of the light bulbs.
c. We know quite precisely what the variation is of the lifetime of the light bulbs and we
know that this variation is small.
This way of performing maintenance is not very suited to be applied on pavements for the
following reasons.
a. In most cases some degree of failure is acceptable on pavements. Traffic can e.g. drive
at a fairly high speed level although there is a substantial amount of cracking. This implies
that some damage types can be allowed to occur over a significant area and with a
significant severity before an unacceptable level of service is reached.
b. Although pavements have been subjected to extensive research, the predictive capability
of our performance models is still limited. Even the accuracy of our models to predict the
mean pavement life is quite often disappointing.
c. Pavements exhibit a substantial amount of variation in performance mainly due to the
variation in layer thickness, material characteristics etc.. This means that two pavements
which are nominally the same and which are loaded under nominally the same conditions
can show a significant difference in initiation and progression of damage.
All in all a strategy which implies maintenance to be performed after the pavement has been
in service for a certain number of years is not applicable for road networks. A certain amount
of damage can mostly be allowed because pavement failure seldom results in catastrophic
events. Furthermore the variation in pavement life is such that usage dependent maintenance
cannot be made cost effective.
This implies that the planning and selection of maintenance strategies for pavements heavily
relies on input coming from condition observations and predictions based there on. Such an
approach to maintenance is called “condition dependent maintenance”.
This immediately means that tools should be available to monitor the condition of the
pavement. An overview of such tools is already given in [1]. The lecture notes we have in
front of us are dealing with one of the most important evaluation tools being the deflection
measurement device.
7
3. Deflection measurement tools:
The deflection device that currently receives the highest popularity is the falling weight
deflectometer (FWD). Nevertheless other deflection measuring devices like the Benkelman
Beam (BB) and the Lacroix Deflectograph (LD) are still used at different places at the world.
Especially the Benkelman Beam deserves attention since this low cost device (the price is
approximately 1/30 th of the price of a falling weight deflectometer) is used in many
developing countries. The principles of these three devices are given elsewhere [1], here only
the main features will be described.
3.1 Falling weight deflectometer:
The principle of the FWD is schematically shown in figure 2.
Figure 2: Principle of the falling weight deflectometer.
A weight with a certain mass drops from a certain height on a set of springs (normally rubber
buffers) which are connected to a circular loading plate which transmits the load pulse to the
pavement. Load cells are used to monitor the magnitude and duration of the load pulse. The
magnitude of the load pulse can vary between the 30 and 250 kN depending on the mass of
the falling weight and the falling height. The duration of the load pulse is mainly dependent on
the stiffness of the rubber buffers. Usually pulse duration between 0.02 and 0.035 s are
measured.
The surface deflections are measured with so called geophones. These are velocity transducers which measure the vertical displacement speed of the surface. By integration the displacements are obtained.
Since the electronic circuits are only opened a very short moment before the weight hits the
buffers, the influence of passing traffic on the magnitude of the deflections is eliminated; only
the displacements due to the impact load are measured.
The advantage of the FWD is the short duration of the load pulse comparable to the duration
of the load pulse caused by a truck driving at approximately 50 km/h. Because of the short
pulse duration, the influence of viscous effects can be neglected.
One should however be cautious when the modulus of a saturated subgrade with a high
ground water level is determined from the deflection measurement results. In that case one
might measure the bulk modulus K of the subgrade which, in case of a fully saturated
subgrade, can be high. Because road materials are very much sensitive for shear, this high
bulk modulus value gives a wrong idea about the real stiffness of the material. This can be
illustrated with the following simple example.
8
When a swimmer makes a nice dive from the diving tower he will hit the water in a gentle
way, without too much of splash and without hurting himself. We can say that with such a nice
dive he experiences the shear modulus G of water which, as we all know, is very low.
However when he falls flat on his stomach, his dive is causing him much pain and probably a
blue stomach. In this case he experiences the bulk modulus K of water which, as we know, is
very high. A fluid with no air bubbles is in fact incompressible.
3.2 Benkelman beam:
The principle of the Benkelman beam, invented by A.C. Benkelman is schematically shown in
figure 3.
Figure 3: Principle of the Benkelman beam.
The measuring system consists of a beam that can rotate around a pivot attached to a
reference frame. The load is supplied by a truck that slowly moves to or from the tip of the
beam.
The advantage of the BB is the fact that the device is simple and cheap. The disadvantage is
the slow speed of the truck that can cause all kinds of viscous effects making the
measurements difficult to interpret. Furthermore the effects of passing vehicles on the
magnitude of the deflection cannot be neglected. Finally it should be mentioned that the
supports of the reference frame could stand in the deflection bowl. This means that the frame
is not a true reference and corrections for movement of the support system have to be made
in order to obtain the true deflections.
Quite often only the magnitude of the rear axle load of the truck used as loading vehicle for
the BB measurements is reported. This is absolutely insufficient; precise knowledge of the
tyre pressure, tyre spacing and area of the tyre print is necessary in order to allow proper
analyses to be made.
Different measurement procedures exist and one should strictly adhere to the guidelines for
doing the measurements when one of such procedures is used.
Furthermore one should realise that the dimensions of the BB can differ. There are devices
with shorter and longer measuring beams. One should take good notice of this in order to
overcome that a beam is used that doesn’t comply with the requirements set in the procedure
to be used.
9
3.3 Lacroix deflectograph:
Figure 4 shows the Lacroix deflectograph (LD). The principle of the measurement is the same
as that of the Benkelman beam. The major difference however is that the measuring system
is attached to the loading vehicle and that it is moved automatically to the next measuring
position. This procedure is schematically shown in figure 5.
It is obvious that the LD has large advantages over the BB. First of all the measurements are
continuously taken and are far less affected by the varying speed of the loading vehicle. With
the BB measurements the speed of the truck varies between 0 (at the beginning of the
measurements) and approximately 5 km/h when the truck drives at constant speed. The
speed of the LD vehicle is more or less constant at 5 km/h.
The LD however suffers from the same disadvantages as the BB. The low speed can cause
that the viscous behaviour of the asphalt surfacing cannot be neglected and corrections for
movement of the reference frame need to be applied.
Because the entire measurement procedure is automated, much more measurements can be
taken with the LD as with the BB in the same time period. This however has its price; the LD
has about the same price level as the FWD.
Figure 4: Principle of the Lacroix deflectograph.
10
Figure 5: Principle of the automatic positioning of the measuring system of the LD.
3.4 Factors influencing the magnitude of the measured FWD deflections:
When civil engineers are dealing with measurements they quite often show a bad habit which
is that they accept the measurement result as “the truth”. They seldom realise that the measurement result is affected by a large number of factors and that the magnitude of the
influence of these factors should be known in order to avoid misinterpretations. A number of
such influence factors on deflections measured with a FWD will be discussed here. The
material presented is based on the excellent work done on this topic by van Gurp which is
reported in [10].
When a number of FWD devices are used on the same pavement to measure the deflections,
one will notice that all these devices will not measure the same value. This is even true when
the deflections are corrected to a particular load level. Some reasons for that are described
hereafter.
It is a well-known fact that the stiffness of rubber is temperature dependent. At higher
temperatures the stiffness will be lower than at lower temperatures. This is nicely shown in
figure 6 where the stiffness of a particular rubber buffer used in a particular FWD is given in
relation to the load level and the temperature.
It will be obvious that the temperature in the rubber buffers will vary when a FWD survey is
done starting early morning and ending late afternoon. This is not only because of the
variation in air temperature but also because of the cumulative energy that is collected in the
buffer, and that is transformed in heat, because of the large number of measurements that
are taken during the day. This means that the stiffness of the rubber buffer will vary during the
11
day. The effect is of course more pronounced if measurements done in the winter have to be
compared with those done in the summer.
Figure 6: Static spring constant of a particular rubber buffer used in a particular FWD.
If for some reason the spring stiffness decreases, the shape of the load pulse changes. Its
peak value will decrease while the duration of the pulse will increase. The longer duration of
the pulse might cause a somewhat softer response (lower stiffness) of the pavement. More
important of course is the fact that differences between the devices occur if they have
different buffers and if the deflections have to be corrected to a predefined load level.
Furthermore one has to be careful when using the FWD for studies on the non linearity of
pavements. Especially pavements where the main body is formed by unbound materials, will
show non linear behaviour. One might try to analyse this by doing deflection measurements at
different load levels but from the text given above it will be clear that at least some of the non
linearity that is measured is caused by the device itself!!
Research in [10] has shown that it is wiser to correct the deflections based on the area
enclosed by the load vs time plot rather than based on the peak load.
Other effects, which are unfortunately more of the “black box” nature, are the following. As
mentioned, geophones are used to measure the deflections. The nature of the geophones
however is that their sensitivity reduce with decreasing frequency. Especially below 10 Hz,
the sensitivity decreases rapidly. However these low frequencies contribute significantly to the
frequency spectrum of a single deflection pulse. Especially the frequency spectrum of
deflection pulses measured on thin pavements laid on soft subgrades will show the great
contribution of the low frequencies. If the geophones don’t pick up these low frequencies, a
too low deflection will be recorded and one would expect the pavement to have a higher
flexural stiffness than it really has.
This effect can be compensated by using high gain factors for the low frequencies. The way in
which this is done depends however on the manufacturer and information on this is usually
confidential information.
It has also been shown in [10] that the system processor can deform the deflection readings.
For one FWD system, the influence of the system processor appeared to be so large that it
did not pass the calibration procedure and could therefore not be used in FWD surveys.
Another influence factor is the smoothing of signals that is applied on the FWD deflections.
This smoothing is done in order to get rid of high frequency disturbances. The question then
always is what the cut-off frequency should be. Studies reported in [10] have shown that if f =
60 Hz is chosen as cut-off frequency, the effect of the smoothing is minimal. Again it is noted
that one should ask the FWD supplier to give details on this important aspect.
12
From the text given above it is clear that there are several influence factors which cause that
the deflections measured with one device are different from those measured with an other
device. It is clear that calibration is vital in order to avoid unexpected and unacceptable
differences between devices to occur.
13
4. Measurement plan:
The question always is how many measurements should be taken and where should the
measurements be taken on a specific stretch of pavement in order to get a reliable picture of
the flexural stiffness of the pavement. Some guidelines for this will be given in this chapter.
4.1 Estimation of the number to test points per section:
In this section the method presented in [2] is described which allow the number of tests to be
determined that are needed on a particular road section to obtain a proper insight in the
bearing capacity of the pavement.
One can calculate a statistical quantity R, called the limit of accuracy, which represents the
probable range the true mean differs from the average obtained by “n” tests at a given degree
of confidence. The larger n is, the smaller value will be obtained for R which means that the
mean value calculated from the data obtained from the tests will differ less from the true mean
value. The mathematical expression is:
R = Kα . ( σ / √ n )
Where: Kα
σ
= standardised normal deviate which is a function of the desired confidence
level 100 . (1 - α),
= true standard deviation of the random variable (parameter) considered.
If the confidence level is chosen and if a proper estimate for σ is obtained, R is inversely
proportional to the square root of the number of tests.
Figure 7shows the basic shape of the relation between n and R.
Figure 7: Typical limit of accuracy curve for all pavement variables showing general zones.
14
As shown in figure 7, 3 zones can be discriminated. In zone I a small increase in the number
of tests reduces the value of R tremendously and the accuracy of the predictions will increase
drastically. In other words a small increase in budget to increase the number of data points is
really value for money.
In zone III, R hardly reduces with an increasing number of tests. This means that in this case
very little extra value is obtained from an increased measurement budget.
The optimal number of tests can be found in zone II.
The main problem in calculating R is the assessment of the standard deviation σ. Since the
magnitude of the deflections can vary quite considerably within one pavement section and
between pavement sections (thick pavements compared with thin pavements), it is not
possible to give a single value for σ. Nevertheless it is possible to give values for the
coefficient of variation CV for the measured deflections which are observed in practice.
Typical values are:
CV = standard deviation / mean =
0.15 low variation, typical for pavements which are in
good condition,
0.30 medium variation, typical for pavements which
show a fair amount of damage,
0.45 high variation, typical for pavements which
show a large amount of damage.
By using these CV values and adopting confidence levels of 95% (α = 0.05) and 85% (α =
0.15), figure 8 has been constructed.
The use of the procedure is illustrated by means of the following example. A deflection survey
has to be performed on a road that is in reasonable condition and the question is how many
measurements need to be taken to obtain a reliable picture of the flexural stiffness of the
pavement. Because a reliable picture is desired the average deflection is allowed to differ 8%
from the true mean. The required confidence level is 95%. Since the pavement shows some
damage a CV is estimated of 20%. By interpolation, the position of the line for CV = 20% is
estimated in figure 8a. Using this line and the R-value of 8%, the number of observations to
be taken is equal to 7.
4.2 Development of a measurement program:
Before one decides on where and how many deflection measurements should be taken, a
visual condition survey should preferably be performed. It is e.g. important to know which
types of defects are present on the pavement and how the various defect types are
distributed over the pavement surface. Is the damage evenly distributed or is the damage
concentrated in a limited number of locations.
A visual condition survey is not only needed to develop an effective measurement plan, but
the condition data are also needed in the evaluation phase when decisions on the
maintenance strategy to be applied need to be taken.
The most important damage types to consider in the structural evaluation of pavements are of
course cracking and deformations because they are related to lack of flexural stiffness.
If cracking and deformations occur rather locally it is not recommended to use an equal
spacing between the measurement points but to locate them in such a way that an as good
as possible sample of both sound and cracked cq deformed areas is obtained.
For reasons that will be discussed later on, it is recommended to measure both the outer
wheel track as well as the area between the wheel tracks, the latter being representative for
the flexural stiffness of the undamaged pavement. These measurements are of course only
useful if the area between the wheel tracks is not damaged.
In case of severe longitudinal or transverse cracking, it is recommended to perform some
measurements across the crack. This can be done very easily with the FWD using the
geophone positions schematically shown in figure 9.
15
Figure 8a: Graph to estimate the number of observations required at
a confidence level of 95%.
Figure 8b: Graph to estimate the number of observations required at
a confidence level of 85%.
16
Figure 9: Placement of loading plate of FWD and geophones for load transfer measurements.
Deflection measurements across the crack are important in order to be able to determine the
amount of load transfer. This parameter has a significant influence on the thickness of the
overlay; if there is e.g. no load transfer at all, additional maintenance work like milling and
filling of the cracked area might be necessary.
The magnitude of the measured deflections is dependent on the temperature, which affects
the stiffness of the asphalt layers, and the moisture content, which can have a significant
effect on the stiffness of the subgrade and other unbound layers. This means that if measurements are taken at various periods of the year, corrections are needed in order to be able
to compare them. In order to avoid the rather complex corrections due to moisture variation, it
is recommended to take the measurements in the so-called “neutral” period. During such
periods the moisture content in the unbound materials is approximately at its mean level. In
the Netherlands that is the late April – early May period and the October month.
Because BB and LD measurements are taken at relatively low speeds, one should not
perform these measurements at too high temperature levels because otherwise viscous
effects will have a significant influence on the measurements which makes interpretation
there-of complicated. Also the temperatures should not be too low because then the
deflections might be so small that accuracy problems occur in the measurement and
monitoring of the deflections. For that reason the Transport and Road Research Laboratory
(TRRL) in the UK has suggested the temperature ranges shown in table 1 at which the BB
and LD measurements should preferably be taken.
Maximum temperature 30 oC if bitumen has a penetration lower or equal than 50
25 oC if bitumen has a penetration higher than 50
Minimum temperature 5 – 10 oC depending on the structure
Table 1: Maximum and minimum temperature for deflection measurements
as specified by TRRL.
17
One should realise that the influence of temperature always has to be taken into account and
that the deflections measured always should be corrected to a reference temperature. The
temperature correction procedure will be presented in an other chapter.
18
5. Statistical treatment of raw deflection data and selection of
a location representative for the (sub)section:
Statistical treatment of the data as measured is always needed in order to be able to recognise trends and in order to limit the amount of work that should be done in the evaluation
process. It is e.g. not necessary and even not useful to back calculate the layer moduli for
each measurement location simply because of the fact that it is impossible to obtain accurate
layer thickness information for each and every location. It is therefore much more effective to
concentrate the analysis on locations which can be taken as representative for a particular
section or sub-section.
Simple statistical procedures have shown to be very effective to discriminate homogeneous
sub-sections within a larger section. A homogeneous sub-section is defined as a section
where the deflections and so the flexural stiffness are more or less constant. When such
homogeneous sub-sections have been determined, one has to take a point which can be
taken as being representative for that sub-section. That point can be the location where the
measured deflection bowl comes closest to e.g. the average deflection profile or the 85%
deflection profile. The 85% profile is the profile that is exceeded by 15% of all the measured
profiles.
The so-called homogeneous sub-sections can be determined by means of the method of the
cumulative sums. The cumulative sums are calculated in the following way.
First of all the mean of a variable over the entire section is calculated (e.g. the mean of the
maximum deflection). Then the difference between the actual value of the variable and the
mean is calculated. Next these differences are summed. In formula the cumulative sums are
calculated using:
S1 = x1 - µ
S2 = x2 - µ + S1
Sn = xn - µ + Sn-1
Where: Sn
xn
µ
= cumulative sum at location n,
= value of the variable considered at location n,
= mean of variable x over entire section.
The method is illustrated by means of an example. Table 2 shows the deflections that were
measured by means of a FWD on a particular road in the Netherlands. The load applied was
50 kN, the diameter of the loading plate was 300 mm. The table gives values for d0, d300, etc.;
these are the deflections measured at a distance of 0 and 300 mm etc.. An important value is
the surface curvature index SCI, which is the difference between the maximum deflection d0
and the deflection, measured at 600 mm from the loading centre (d600). Also the logarithm of
the SCI values is reported. Also this is an important characteristic as will be shown later on.
As one will observe from the table, high deflections are measured and the amount of variation
in the measured deflections is very high. It should be noted that the pavement considered
was a polder road on a very weak subgrade and showed a significant amount of damage.
It should be noted that the example presented is a rather extreme one; normally such large
variations in deflections are not observed.
Figure 10 is a graphical representation of the measured deflections, while figure 11 shows the
variation of the SCI over the section. Figure 12 shows in a graphical form the variation of the
cumsum (cumulative sum) as determined for the SCI. The SCI is selected as parameter
decisive in the determination of the homogeneous subsections since the SCI can be
considered to be the most important deflection parameter.
Homogeneous sub-sections can easily be recognised from figure 12 since by definition an
area over which the slope of the cumulative sums plot is more or less constant indicates an
area where the differences between the actual measured values and the overall mean value
are approximately the same.
19
Table 2: Deflection testing results obtained on a particular section and summary statistics.
20
Figure 10: Results of a deflection survey.
21
Figure 11: Surface curvature index.
22
Figure 12: Cumulative sum of the surface curvature index.
23
The following sections are discriminated.
Section
1
2
3
4
5
6
7
8
9
10
11
12
Locations
0.05-0.1-0.15
0.2-0.25-0.3
0.35-0.4-0.45
0.5-0.55-0.6
0.65 this is a single point clearly visible in the SCI plot
0.7-0.75-0.8-0.85-0.9-0.95
1 this is a single point clearly visible in the SCI plot
1.05-1.1-1.05
1.1-1.15-1.2-1.25-1.3-1.35-1.4-1.45
1.5 this is a single point clearly visible in the SCI plot
1.55-1.6
1.65-1.7-1.75-1.8-1.85-1.9-1.95-2
By means of the cumsum method we have arrived to a set of successive sub-sections, each
of them having more or less a certain flexural stiffness. Now it is interesting to determine if we
can combine a few sections. If this is possible we would reduce the work load. The question
now is how to achieve that.
If we compare the slopes of the different sections we notice that the slopes of sections 2, 4
and 12 are about the same. This means that they can be taken as one section in the further
analysis. This also holds for sections 1 and 6, so also these can be treated as one section.
The same is true for sections 3, 8 and 11.
Then we have a look to the single points that are discriminated and we try to assign them to a
particular subsection. We observe that location 0.65 is clearly an isolated peak value and
should therefore be treated as such. Location 1 however could very well be combined with
section 2. Also location 1.5 is better treated as a single point.
All in all we arrive to the subsections given below.
Section
1
2
3
4
5
6
Locations
0.05-0.1-0.15 and 0.7-0.75-0.8-0.85-0.9-0.95
0.2-0.25-0.3 and 0.5-0.55-0.6 and 1.65-1.7-1.75-1.8-1.85
-1.9-1.95-2 and 1
0.35-0.4-0.45 and 1.05-1.1-1.15 and 1.55-1.6
0.65
1.1-1.15-1.2-1.25-1.3-1.35-1.4-1.45
1.5
The statistics of the sub-sections mentioned above are tabulated below.
Section
1
2
3
4
5
6
Mean Value SCI
420
175
494
962
423
96
Standard Deviation SCI
111
65
62
77
Var. Coeff.
26%
37%
13%
18%
As one will notice, rather high values for the coefficient of variation are still obtained for
sections 1 and 2. We have to look then in table 2, in order to find out what the possible
reasons for this could be. By doing so we observe that location 0.8 doesn’t really fit in section
1 and should better be moved to section 2. The high variation in section 2 is probably caused
by the inclusion of locations 1.7 and 1.75; also location 1.9 could contribute to the high
variation. Therefore it is suggested to move location 1.9 to section 1 and to combine locations
1.7 and 1.75 with location 1.5. We then obtain the sections and summary statistics as shown
in table 3.
As one can observe a better result in terms of lower coefficients of variation are obtained. The
division in subsections as shown in table 3 will be used for further treatment.
24
Section Locations
1
0.05-0.1-0.15-0.7-0.75-0.85-0.9
-0.95-1.9
2
0.2-0.25-0.3-0.5-0.55-0.6-0.8-1
-1.65-1.8-1.85-1.95-2
3
0.35-0.4-0.45-1.05-1.1-1.15-1.55-1.6
4
0.65
5
1.1-1.15-1.2-1.25-1.3-1.35-1.4-1.45
6
1.5-1.7-1.75
Mean SCI
SD SCI
Var. Coeff.
434
87
20%
181
494
962
423
87
40
62
22%
13%
77
11
18%
13%
Table 3: Homogeneous sub-sections based on SCI
An other approach to the reduction of the data is to make a frequency plot of the deflections
measured. Figure 13 is an example of such a plot based on the measured SCI’s. In making a
frequency plot one has to decide about the number of classes to be used. A practical
guideline for this is to take the number of classes equal to the square root of the number of
observations.
From figure 13 it is clear that we have 1 observation in the range SCI = 0 – 72 µm, 13
observations in the range SCI = 73 – 220 µm, 6 observations in the range SCI = 221 – 369
µm, 13 observations in the range SCI = 370 – 517 µm, 6 observations in the range SCI = 518
– 665 µm and one extreme value which is the SCI = 962 µm measured at location 0.65. The
locations which belong to the frequency classes and the summary statistics are given in table
4.
Frequency
Class
0 – 72
73 – 220
221 – 369
370 – 517
518 – 665
higher
Locations
1.75
0.2-0.25-0.3-0.5-0.8-1-1.5-1.65-1.7-1.8-1.85
-1.95-2
0.05-0.55-0.6-1.2-1.3-1.9
0.1-0.15-0.35-0.45-0.7-0.85-0.95-1.15-1.25
-1.35-1.4-1.45-1.55
0.4-0.75-0.9-1.05-1.1-1.6
0.65
Mean
72
SCI.
St. Dev. Var. Coef.
157
306
37
42
24%
14%
430
550
962
40
33
9%
6%
Table 4: Frequency classes for the SCI, locations and summary statistics.
As one can observe from table 4, this approach results in a grouping of the deflection data in
such a way that the coefficient of variation in one group is limited to very small.
From the description given above it will be clear that several techniques are available for
reduction of the raw deflection data. In principle the cumulative sum technique is a very
powerful tool to discriminate homogeneous sections. However situations might occur that
even the cumsum technique results in sections which exhibit a rather high degree of variation.
In that case reduction of data through an analysis of the frequency distribution can result in
data sets which are rather homogeneous in nature.
The big advantage of the cumsum technique is that it results in physical section units ready to
receive maintenance whereas the other approach doesn’t result in such units.
All in all this means that the data reduction process and the statistical analysis of the raw data
is not a straightforward process. Each time the data set should be treated carefully in order to
select the most appropriate way to reduce the data.
The selection of the location which can be considered to be representative for the entire
(sub)section is done in the following way. First of all one has to decide whether one wants to
base the analysis on the mean conditions or whether one wants to do the analysis using a
deflection profile that is exceeded by only 15% of the measured profiles. In the first case one
selects a measured profile that comes closest to the mean profile while in the second case
one selects a measured profile that comes closest to the 85% profile.
25
In section 1 of table 3, location 0.85 has the SCI value (453) that comes closest to the mean
SCI value of that section being 434, while location 0.75 has the SCI value (525) that comes
closest to the 85% profile of that section being 521 (mean plus one standard deviation).
These locations are then selected as being the representative locations for this section. Cores
are taken at those locations to obtain accurate information on the thickness of the layers. This
information is needed to allow accurate back calculations of the layer moduli to be made.
Figure 13: Frequency distribution of the measured SCI values.
26
6. Back calculation of layer moduli:
Back calculation of layer moduli is quite often considered as an important step in pavement
evaluation. The reason for this is quite simple; the magnitude of the back calculated stiffness
modulus quite often reveals whether or not the pavement layer is damaged or not. If e.g. a
stiffness modulus of 600 MPa is back calculated for a cement treated layer, this layer should
be in a rather deteriorated state because the modulus of a sound cement treated layer is
substantially higher.
One of the drawbacks of back calculating layer moduli is the fact that accurate information on
the thickness of the various layers should be available. We know that the deflections are
heavily influenced by the product E.h3, which means that a small error in the layer thickness
can have a large effect on the magnitude of the back calculated modulus.
Although computer programs are available that back calculate the layer moduli automatically
when the deflections, the load configuration and the thickness of the different layers is known,
back calculation of layer moduli is certainly not as straightforward as it may look like because
in many cases the solution is not unique. This implies that some pre-treatment of the data is
necessary before the actual back calculation process is started.
In the sections hereafter the surface modulus diagram will be discussed first of all. This
diagram provides insight in how the overall stiffness of the pavement develops from bottom to
top and whether or not weak interlayers are present. After that the actual back calculation
process will be discussed.
It should be noticed that the procedures described are especially valid for the analysis of
FWD measurements. They can however also be used for the analysis of BB and LD
measurements provided that the appropriate corrections are applied. These correction
procedures will be described in a later section.
6.1 Surface modulus:
According to Boussinesq’s theory, the elastic modulus of a homogeneous half space can be
calculated from the deflection measured at a given distance following:
E = σ . a . (1 - µ ) / dr . r
2
E = 2 . σ . a . (1 - µ ) / d0
2
Where: E
a
µ
σ
2
= elastic modulus,
= radius of loading plate,
= Poisson’s ratio,
= contact pressure under loading plate.
The question now is whether this formula can be of use in analysing the stiffness development in a pavement. Let us consider therefore figure 14.
geophones
a
b
Figure 14: Distribution of the vertical stress in a pavement.
27
The way in which the load is distributed depends on the thickness and the stiffness of the
layer. In figure 14, the top layer is the stiffest followed by the base and the subgrade. It is
obvious that only that part of the pavement that is subjected to stresses, will deform; that is
the area enclosed by the cone. This means that the geophone that is farthest away from the
load centre (geophone a) only measures deformations in the subgrade while the geophone in
the load centre (geophone b) measures the deformations in the subgrade, base and top layer.
This implies that if the Boussinesq formula is applied using the deflection value measured by
geophone a as input, the modulus of the subgrade is calculated. In case Boussinesq’s equation is used using the reading of geophone b as input, an overall effective stiffness of the
pavement is calculated.
So the stiffness calculated from the geophone readings going from a to b give information
about: the subgrade, the subgrade plus some effect of the base, the subgrade plus the base
plus some effect of the top layer, the subgrade plus the base plus the top layer; in short:
increasing moduli value will be calculated.
All this means that the deflection readings taken at a certain distance from the load centre
give in fact information on the stiffness of the pavement at a certain depth.
Using this information a so-called surface modulus plot is constructed. On the vertical axis
one plots the surface modulus calculated using the Boussinesq formulas and on the
horizontal axis one plots the equivalent depth which is equal to the distance of the geophone
considered to the load centre. The principle of the plot is schematically shown below.
Surface
Modulus
Equivalent Depth
Figure 15 shows the surface modulus plots as calculated using the deflections measured at
locations 0.65 and 1 (see table 2). The figure indicates that we are dealing with a weak
pavement because the surface modulus values are very low and because the stiffness hardly
increases from bottom to top. Only in location 1 some stiffening due to the base and top layer
is visible.
As shown below, different shapes of the surface modulus plot can be obtained.
Surface Modulus
Equivalent Depth
28
The drawn line indicates a pavement where the stiffness gradually increases from bottom to
top while the dashed line indicates a pavement which has layers with a low stiffness on top of
the subgrade. The reason for this might be stress dependent behaviour, lack of compaction,
moisture effects etc.. It might very well be that the material with the lower stiffness is in fact
the same material as the subgrade material. This is e.g. the case with fill material that cannot
be compacted to the density of the existing subgrade.
Figure 15: Surface modulus plots for locations 0.65 and 1.
The surface modulus plot assists in deciding how many layers should be taken into account in
the back calculation analysis. As indicated, the number of layers to be considered is not only
the number of physical layers, top, base, sub-base and subgrade; one also has to take into
account the fact that within one layer, sublayers may occur with a different stiffness.
6.2 Back calculation of layer moduli:
Back calculation of layer moduli from measured deflection bowls is done in an iterative way.
The input for the calculations consists of the measured deflection profile, the load geometry
used to generate the deflections and the thickness of the layers. Furthermore the cores that
are taken from the pavement to determine the thickness of the layers give information on the
materials used and the quality of the materials.
From the surface modulus plot an estimate is obtained for the modulus of the subgrade and
furthermore the surface modulus plot provides information that helps to decide whether or not
low stiffness sublayers should be introduced in the analysis.
Then moduli values are assigned to the various layers and the deflections are calculated.
Next the calculated deflections are compared with the measured ones. If the differences are
too large, a new set of moduli is assumed and the deflections are calculated again. This
process is repeated until there is a good match between the calculated and measured
29
deflections. Normally the analysis is stopped when the difference between the measured and
calculated deflections is 2%.
As has been mentioned before, the iterative back calculation procedure can either be an
“automatic” or a “hand operated” one. In the “automatic” procedures the computer program
automatically performs the iterations while in the “hand operated procedure” it is the
experienced engineer who controls the iteration process. Both procedures have their
advantages. The automatic procedure is fast but might sometimes result in “funny” results. By
“funny” it is meant that the set of moduli that is back calculated results in a good fit between
the measured and calculated deflections but the moduli value themselves cannot be true
given the type and condition of the materials in the pavement, given the temperature
conditions etc.. Such results can occur because the back calculation procedure doesn’t
necessarily result in a unique answer. In such cases the hand operated procedure is more
powerful because the experienced engineer can adjust the moduli values to such levels which
are reasonable for the type and condition of the pavement materials present and still result in
a good fit between measured and calculated deflections.
Problems with back calculating layer moduli can occur when the top layer is thin (< 60 mm) or
when the base layer has a higher stiffness than the top layer.
A golden rule in the back calculation analyses is that one never must vary the moduli values
of all layers in the same time. This should be done in a step by step procedure. First of all one
should try to find a modulus value for the subgrade by finding a good fit between the
deflections measured and calculated at the largest distance to the load centre (see also figure
14). Then one tries to fit the deflections at intermediate distance from the load centre; this will
result in the moduli for the sub-base and base. Finally one should fit the deflections at the
shortest distance to the load centre and the maximum deflection; this results in the modulus
for the top layer.
Furthermore one should realise that a good fit of the measured SCI is of great importance
since this value gives a lot of information on the strain levels in the pavement. Sometimes the
measured deflection profiles are not easy to match. In such cases one should notice that a
good match of the SCI is to be preferred over a good match of the deflections measured at a
greater distance from the load centre.
6.3 Example:
The example that will be given here is taken from the OECD FORCE test pavements that
were built at the LCPC test facilities in Nantes, France. These pavements were tested by
means of the accelerated load testing device of the LCPC. The aim of the project was to
study pavement response and performance of three types of pavements under accelerated
loading. The results of the FWD data evaluation of two test pavements are discussed here [3,
4].
Figure 16 shows the two pavement sections analysed.
I
II
60 mm asphalt
120 mm asphalt
300 mm base
300 mm base
subgrade
Figure 16: Structures I and II of OECD’s FORCE project.
30
The clayey subgrade was covered with a 300 mm thick base on which 60 mm resp. 120 mm
asphalt was placed.
Figure 17 shows the maximum deflection level as measured on the top of the base as well as
the maximum deflections that were measured after placing the asphalt layers. Figure 18
shows the thickness of the top and base layer as determined by means of the Penetradar.
Figure 17: Deflections measured on top of the base and top of the asphalt layer.
Figure 18: Thickness of the layers of sections I and II.
Figure 19 shows the surface modulus plots representative for both sections determined from
the deflections measured on top of the completed sections.
31
Figure 19: Surface modulus plots representative for the OECD FORCE sections.
Three things appear from this figure. First of all the additional 60 mm asphalt which is present
on section II contributes significantly to the stiffness of the pavement. Secondly, the modulus
of the base and subgrade seems to be highly sensitive to the stress level. In both sections
materials were used which are nominally the same. In section II however, the stresses in the
base and subgrade are much smaller because of the thicker asphalt layer on top. The effect
of the lower stress level in base and subgrade results in higher values for the surface
modulus.
Furthermore one should realise that the plot was made based on measurements which were
taken at a temperature of approximately 6 0C which means that the stiffness of the asphalt
layer was fairly high and the stress levels in the base and subgrade are rather low .
Thirdly the figure shows that on top of the subgrade, layers are present with a much lower
stiffness. It appeared that a fill had to be placed in order to have the pavement surface at the
right level. The fill was made with the subgrade material but problems during compaction had
occurred. This lack of density of the fill has of course a direct effect on the density and so the
stiffness of the base layer placed on top. The low surface modulus values could, in this case,
easily be explained from the construction history.
Based on this knowledge it was decided to divide the base layer in two sublayers, each being
50% of the total base thickness, and to divide the subgrade in two sublayers. This was done
by assuming a thickness of 500 mm of low stiffness subgrade material on top of the stiff deep
subgrade. The selection of this thickness is based on experience, sometimes a thickness of
1000 mm is chosen.
All in all it means that for the back calculation analysis, the pavement was divided in 5 layers
(top layer, two base layers, two subgrade layers).
The results of the analysis are shown in table 5.
32
Section I
Temp
Force
[ 0C]
[kN]
6.4
57.0
Layer E-mod
Thickn.
[mm] [Mpa]
56
146
146
500
15980
106
150
37
171
Position
[mm]
Meas.
Defl.
[µm]
Calc.
Defl.
[µm]
Diff.
[%]
0
300
600
900
1200
1500
1800
1049
655
318
158
92
63
46
1050
655
318
163
92
60
46
0.1
0
0
3.2
0
-4.8
0
Calc.
Defl.
[µm]
Diff.
[mm]
Meas.
Defl.
[µm]
[%]
0
300
600
900
1200
1500
1800
415
329
217
133
83
50
34
417
326
216
135
83
51
33
0.5
-0.9
-0.5
1.5
0
2.0
-2.9
Section II
Temp
Force
[ 0C]
[kN]
6.8
58.0
Layer E-mod
Thickn.
[mm] [Mpa]
145
130
130
500
10514
117
239
48
276
Position
Table 5: Results of the back calculation analysis for the OECD FORCE sections.
It should be noted that the FORCE examples are complicated ones; normally one has to deal
with less complicated deflection profiles.
6.4 Computer program:
As had been mentioned before, several computer programs are available that allow the
values for the layer moduli to be backcalculated in an automatic way. One of those programs
is the program MODCOMP 5 developed by prof. Irwin of the Cornell university in the USA.
The program can be found on the cd which is part of these lecture notes. At the end of these
lecture notes an appendix, appendix I, is given which contains a description of how the
program has to be used.
7. Analysis of Benkelman beam and Lacroix deflectograph
deflection bowls:
33
BB and LD measurements are usually related to empirical evaluation and overlay design
methods. However an elegant procedure has been developed [5] which allows these
deflection readings also to be used for back calculation purposes. The procedure is correcting
the measured deflections that might be influenced by the movement of the support system to
true deflections. One drawback of the method is that it doesn’t take into account viscous
effects that might occur due to the slow speed of the loading vehicle.
The basis of the method is the Hogg model which consists of a plate (E1, h, µ1) resting on an
elastic foundation (E2, µ2). The assumption that the top layer behaves like a plate implies that
no vertical displacements are developed in this layer. The characteristics of the pavement
structure are characterised by:
D
R
L0
= E1 . h1 / {12 . (1 - µ1 )}
= 2 . E2 . (1 - µ2) / {(1 + µ2) . (3 - 4µ2)}
= ( D / R )0.33
3
2
stiffness of the top layer(s)
reaction of the subgrade
critical length
The shape of the deflection profiles is described following
d0 / dr – 1 = γ + α . (r / L0)β
Where: d0
dr
= maximum deflection,
= deflection at distance r from the load centre.
This equation is graphically represented in figure 20. Using the specific dimensions of both
the deflectograph and the BB (figure 21) as well as the above mentioned pavement
characteristics, true deflection profiles as well deflection profiles that would be measured were
calculated; typical results are shown in figure 22.
Figure 20: Graphical representation of an equation used to describe
the shape of deflection profiles.
In the development of the model the following values were assumed for the wheel and axle
loads as well as contact pressures.
Axle
Pfa/Pra P1
I1
W1
σ1
P2
I2
W2
σ2-σ1
Paxle
34
rear
front
0.6
0.6
[N]
[mm]
[mm]
[MPa] [N]
1750
336o
250
320
177
220
0.05
0.061
[mm]
21750 192
25040 270
[mm]
[MPa] [N]
136
186
1.062
0.635
94000
56800
Figure 21: Dimensions of the LD and BB as well as of the loading vehicle.
35
Figure 22: Recorded and true LD (lac) and BB (ben) deflections.
36
Based on these calculations, evaluation diagrams were developed which allow true
deflections to be calculated from the measured LD and BB deflections. These diagrams are
shown in figure 23. In this figure some abbreviations are used which are not explained in the
figure; the meaning thereof is described hereafter.
DCGRA = maximum deflection according to the Canadian Good Roads Association method,
DAI
= maximum deflection according to the Asphalt Institute method,
DTRRL = maximum deflection according to the Transport and Road Research Laboratory
method.
The method will be illustrated with some examples. Let us assume that a maximum deflection
was measured with the LD of 393 µm. From the measured deflection profile it was determined
that the distance at which the deflection was 50% of the maximum deflection (Lx, x = 50%)
was 368 mm. From the evaluation charts one can derive that L0 = 178 mm and the ratio
D00/Dlac = 1.226. This means that the true maximum deflection is 482 µm.
The ratio D00 . R / Pra equals 0.47 and with a rear axle load Pra = 91.6 kN this results in an R
value of 89.5 Mpa and a subgrade modulus of 149 Mpa (assuming µ2 = 0.35). Since L0 and R
are known, D can be calculated.
Furthermore we can determine the maximum BB deflection that would be obtained following
the TRRL procedure. One observes that DTRRL/Dlac = 0.98 which means that the value that
has to be used in the TRRL evaluation procedure equals 385 µm.
It is stressed that figure 23 is only applicable for the load and LD and BB geometries shown in
figure 21.
One should keep in mind that the moduli obtained in this way are quasi-static moduli. It is a
well-known fact however that for most materials there is a difference between the static and
the dynamic modulus. From an extensive correlation study it was observed that the subgrade
modulus as determined by means of the BB or LD and the FWD relate to each other
following:
EFWD / Elac
= 101.4576 (t – 0.255)
Where: t
= loading time of the LD or BB [s].
37
Figure 23: Evaluation chart to determine true LD and BB deflections from measured
deflections.
38
8. Estimation of the remaining pavement life using an empirical based approach:
A number of empirical pavement evaluation and overlay design methods have been
developed in time. Well known are the methods developed by the Asphalt Institute and the
Transport and Road Research Laboratory. Although extensively used all over the world, this
author believes strongly that one has to be very cautious in using these methods for situations
they have not been developed for. The hart of the TRRL method e.g. are the performance
charts developed for several pavement types. An example of such a chart is given in figure 24
[6]. For the sake of completeness the load and load configuration used for the BB
measurements according to the TRRL procedure are shown in figure 25.
The point is that pavement performance is dependent on the traffic, the materials and
structures used, and the climate, all of them are typical British in case of the TRRL method.
This means that the chances are very small that the method can be used without modifications in countries like e.g. Pakistan or Yemen where traffic, climate, and materials are
significantly different from UK conditions.
Another severe problem with the TRRL method is that an important input parameter, being
the number of equivalent 80 kN single axles that have passed the pavement, is not known in
many cases.
Nevertheless the author also believes that the TRRL method can be used in other conditions
as well provided this is done by making the evaluation charts dimensionless. The procedure
to do so is outlined hereafter.
Let us define the following variables:
DeltaDefn
DeltaDefc
n
Nc
= increase in deflection since time of construction,
= difference between the initial deflection and the critical deflection, this latter
value depends on the probability of achieving life that is used to define pavement failure,
= applied number of load repetitions,
= number of load repetitions at which critical deflection level is reached.
Work presented in [7] has shown that performance curves like the one presented in figure 24
can be written in a dimensionless shape following:
DeltaDefn / DeltaDefc
= (n / Nc)b
The shape parameter b seemed to be dependent on the initial deflection level following:
for granular bases:
for bituminous bases:
b
b
0.4639
= 0.06 Def0
= 0.0185 Def00.7186
An important question in all this is how DeltaDefc and the initial deflection Def0 are related.
From the analysis in [7] it appeared that for pavements with granular bases and accepting
50% of achieving life as the failure condition, the ratio DeltaDef0 / Def0 can be expressed as
follows:
DeltaDefc / Def0 = 0.4767 – 0.000299 Def0
Where: Def0
= maximum deflection measured with the BB according to the TRRL
procedure [µm] of the pavement when not subjected tot traffic loads.
For bituminous bases this relation can be written as:
DeltaDefc / Def0 = 0.34833 – 0.000198 Def0
If we don’t know the number of load repetitions applied to the pavement, how do we derive
DeltaDefn? It will be shown hereafter that we can obtain that value in a relatively simple way.
39
Figure 24: Example of a TRRL performance chart.
40
Figure 25: Load configuration used for the BB measurements according to TRRL.
41
Normally BB measurements are only taken in the wheel tracks. These values are in fact the
Defn values since that pavement area has been subjected to n load repetitions. If we also take
deflection measurements between the wheel tracks, then we get a good estimate of the
flexural stiffness of that part of the pavement that is not subjected to traffic loads. These
deflections can be taken as representative for Def0.
Assume that the deflection measured between the wheel tracks is 350 µm and that the
deflection in the wheel tracks is 390 µm. The pavement has an unbound base. Then we arrive
to:
DeltaDefn
= 390 – 350 = 40
and
DeltaDefc / Def0 = 0.4767 – 0.000299 x 350 = 0.372
so
DeltaDefc
= 0.372 x 350 = 130
We also calculate:
b
= 0.91
so
DeltaDefn / DeltaDefc = (n / N)b
40 / 130
n/N
= (n / N)0.91
= 0.27
Normally road authorities are not interested in a damage ratio or a remaining pavement life
expressed in a number of allowable load repetitions but much more in a remaining life in
years. This can be estimated in the following way.
Assume the traffic composition has not changed in time and for reasons of simplicity we also
assume that no growth in the number. of vehicles per day has taken place. This means that
the area indicated in figure 26 is representative for the cumulative amount of traffic n that has
passed the road during time period t.
Traffic intensity
n
N
Time
t
T
Figure 26: Procedure to estimate the remaining life in years from the n/N ratio.
In the same way the allowable number of load repetitions N is arrived after T years. From this
simple example it is clear that in this case:
t/T=n/N
42
If we assume e.g. that the deflection survey of the above mentioned example was taken 5
years after the pavement has been put in service, we calculate that:
t / T = n / N = 0.27, t = 5 so T = 18 years and the remaining life is 13 years.
The procedure described above cannot be used if variations occur in the cross section of the
pavement due to variations in the thickness of the layers and because different types of
material are used over the width of the pavement. Those conditions can occur if e.g. ruts are
filled, the pavement is widened or of mill and fill operations have been carried out.
Of course unknown changes in the traffic growth, composition of the traffic and the axle loads
have also a negative effect on the results obtained by the procedure described above.
43
9. Mechanistic procedures for remaining life estimations and
overlay design:
Mechanistic overlay design methods are based on the analysis of stresses and strains in the
existing pavement. The calculated values are then compared with the allowable values and
based on this comparison, conclusions are drawn with respect to the most appropriate
maintenance strategy.
One of the most important differences between a mechanistic and an empirical approach is
the fact that in the latter, the interactions between stresses, strains, strength, fatigue,
resistance to deformation etc are not visible; they are hidden in the procedure. This makes
the empirical methods unreliable as soon as different materials and structures are used than
those for which the procedure was developed. On the other hand empirical methods are
based on observed performance which is an advantage over mechanistic models especially if
these models are used in a too simplistic way.
The big advantage of the mechanistic models of course is that they are based on sound
analyses of stresses, and strength of the materials used.
9.1 Basic principles:
In classical mechanistic overlay design methods, only the strain levels in the existing
pavement are considered as well as the required reduction in those strain levels in order to
obtain the required extension of the pavement life. The overlay is designed in such a way that
the necessary reduction of the strain level in the existing pavement is realised. The effect of
damage in the existing pavement on the performance of the overlay is normally not
considered. This makes the classical mechanistic methods rather straightforward.
The following steps can be recognised. First of all the moduli of the various layers are
calculated in the way described earlier. Secondly the asphalt layer modulus is corrected to a
reference temperature; for Dutch conditions this is 18 0C. This correction can be applied using
the asphalt mix stiffness vs temperature chart as developed by Shell [8]; this chart is given in
figure 27. Then the stresses and strains due to an equivalent single axle load are calculated.
The tensile strain calculated at the bottom of the asphalt layer is introduced in a fatigue
relation and the allowable number of load repetitions is calculated. The same is done for the
subgrade strain. The amount of damage, being the ratio n/N, is then calculated where n is the
applied number of load repetitions and N is the allowable number. The remaining life ratio is
calculated as 1 – n/N.
If the pavement life should be extended, the number of load repetitions that are expected
needs to be calculated. This results in a figure n + ∆n. Then the pavement thickness should
be increased in order to decrease the tensile strain at the bottom of the asphalt layer and to
increase the allowable number of load repetitions from N to N + ∆N. The appropriate overlay
thickness is obtained if:
1 – n/N = ∆n / (N + ∆N)
The procedure is illustrated with an example.
Assume that the tensile strain that is calculated at the bottom of the asphalt layer due to a
standard axle load equals:
ε
= 2 . 10-4 [m / m]
Fatigue tests carried out on the material resulted in the following fatigue relation.
Log N = -13 – 5 . log ε
The allowable number of load repetitions is then N = 312500.
If we assume that the pavement has already carried 200000 standard loads, then the damage
ratio equals n / N = 0.64.
44
Figure 27: Relationship between the stiffness of asphalt mixtures and temperature for a
loading time of 0.02 s.
45
The remaining life ratio equals:
1 – n/N = 0.36
Assume that another 500000 standard axles should be carried by the pavement. This means
that:
∆n
= 500000
The tensile strain at the bottom of the asphalt layer should be decreased to a level where N +
∆N load repetitions can be taken. This value is calculated from:
N + ∆N = ∆n / (1 – n/N) = 500000 / 0.36 = 1.39 . 10
6
By using the fatigue relation we calculate that this new number of allowable load repetitions
can be obtained if the strain is reduced to ε = 1.48 . 10-4 [m / m]. This means that the overlay
needs such a thickness that the strain at the bottom of the existing asphalt layer is reduced to
this value.
The approach described here gives rise to some comments. It is quite clear that a very large
overlay thickness is needed when the ratio n/N approaches 1. The reason is that the fatigue
relation is based on beam fatigue tests. This implies that failure means that the specimen is in
two parts if the allowable number of load repetitions is reached (at least in load controlled
fatigue tests) which implies that the beam lost its functionality. In reality however the cracked
asphalt slab is still supported by the base and other layers; the cracked slab is still functional.
All this indicates that the procedure results in unrealistic designs in case of high values of the
damage ratio.
Furthermore the example indicates that in general fairly small strain reductions are needed
which results in rather thin overlays.
Because the overlay design is only based on the reduction of the strain level in the existing
pavement, only the thickness and the stiffness of the overlay are of importance. From practice
one knows that this cannot be true. The existing pavement normally exhibits a certain amount
of cracking when an overlay is applied and these cracks tend to propagate through the
overlay. This means that reduction of the strain level in the existing pavement cannot be the
only design criterion for overlays; also the resistance to crack reflection of the overlay should
be considered. This aspect will be discussed later in these lecture notes.
Finally the procedure described above doesn’t take into account the large amount of variation
in deflections and material characteristics that can occur in pavements.
9.2 Extension of the basic principles:
In this section an extension of the basic principles presented in the previous section will be
given. The extension is dealing with the fact that in case the n/N ratio reaches 1, realistic
values for the overlay thickness should still be obtained. Furthermore the extension takes into
account the variation in deflection level and material characteristics that occur in practice.
If there was no variation in deflection level along the section under consideration, and if there
was no variation in the thickness of the pavement layers, then there would be no variation in
the elastic modulus of the layers and there would be no variation in strain level. If there also
would be no variation in the fatigue characteristics, then the pavement would fail precisely at
the number of load repetitions predicted and the pavement would fail from one moment to the
other. This particular behaviour is illustrated in figure 28a. Such a performance however is
never observed, pavements don’t collapse in the way indicated by this figure. In reality a more
gradual deterioration is observed as is indicated by figure 28b.
If we use the mean strain level of figure 28b as design criterion and we use this strain value
together with the mean fatigue characteristic (the solid fatigue line in figure 28b) then we
determine the mean number of load repetitions. At that number of load repetitions there is a
50% chance that the pavement is failed. It can easily be shown that this means that 50% of
the trafficked pavement surface shows cracking. Because of the variation in the fatigue
46
resistance, some parts of the pavement will live longer and some shorter. Furthermore the
strain level in some parts of the pavement are lower than at other parts because of e.g. the
variation in thickness. The variation in strain level combined with the variation in fatigue
resistance results in a variation of pavement life over the section considered. This is shown in
figure 28b. Figure 28b also clearly shows that pavements don’t fail in a catastrophic way but
show a gradual deterioration. The overlay design procedure should take this into account.
Log n
Fatigue
characteristics
show no
variation
Thickness of the pavement layers
and the layer moduli are constant,
so strain is constant.
N
Condition
Logε
Log n
N
Figure 28a: Condition deterioration when there is no variation in pavement properties.
Log n
Fatigue characteristics
show variation
Thickness and modulus of
the layers show variation so
strain is variable.
N
Condition
Log ε
50% failed and
50% sound
N
Mean strain
level
Log n
Figure 28b: Condition deterioration when there is variation in pavement properties.
47
In order to take the variation of input parameters into account, probabilistic analyses should
be made. Several procedures are available to determine which combinations of layer
thickness, layer modulus and fatigue relation should be used in the calculations in order to enable to estimate the variation in strain level and pavement life. A far more effective approach
is to make use of simple relations that exist between e.g. the surface curvature of the deflection profile on one hand and the tensile strain at the bottom of the asphalt layer, the tensile
strain at the bottom of the bound base or the vertical compressive strain at the top of the
subgrade, on the other hand. This will be shown in the following part.
Let us consider the bending of a slab as shown in figure 29.
Figure 29: Bending moments in a slab.
The magnitude of the bending moments can be calculated a follows:
M1x = E h3 ( 1/Rx + µ 1/Ry ) / 12 ( 1 - µ2 ) and M1y = E h3 ( 1/Ry + µ 1/Rx ) / 12 ( 1 - µ2 )
Where: M1x
M1y
Rx
Ry
E
h
µ
= bending moment in the x direction,
= bending moment in the y direction,
= radius of curvature in the x direction,
= radius of curvature in the y direction,
= elastic modulus of the slab,
= thickness of the slab,
= Poisson’s ratio.
The stresses can be calculated as σx = 6 M1x / h2 and σy = 6 M1y / h2. If we are dealing with a
circular load in the centre of a large slab, Rx = Ry and σx = σy.
Because: εx = ( σx - µ σy ) / E = ( 1 - µ ) σx / E we can now develop a relation between the
curvature and the tensile strain by substitution of σx by M1x and by substitution of M1x by the
equation that relates the bending moment to the radius of curvature. We obtain then:
εx = 6 ( 1 - µ ) M / E h = h / 2 Rx ≅ 1 / Rx
2
This indicates that the strain at the bottom of the asphalt layer is related to the radius of
curvature of the deflection bowl due to the applied load.
Extensive research [9,10], has shown that there exists a direct relation between the tensile
strain at the bottom of the asphalt layer and the surface curvature index following:
log ε
= C0 + C1 log SCI
For pavements with an asphalt thickness ≥ 150 mm the relation becomes:
48
Log ε
= 0.481 + 0.881 log SCI300
Where: SCI300 = difference in maximum deflection and the deflection measured at a distance
of 300 mm,
ε
= tensile strain at the bottom of the asphalt layer [µm / m].
This relation is shown in figure 30.
Figure 30: Relation between SCI300 and the tensile strain at the bottom of the asphalt layer.
Since log N = A0 + A1 log ε, we can write:
log N = A0 + A1C0 + A1C1 log SCI
It can be shown that the variance of log N (the squared standard deviation of log N) can be
calculated from:
S2logN
= A12. C12 . S2logSCI + S2lof
Where: SlogSCI = standard deviation of the logarithm of the measured SCI’s (see also table 2)
= standard deviation of log N at a given log ε; it describes the variation in
Slof
fatigue life.
We can now write:
log NP = log N – u . SlogN
Where: log N = logarithm of the mean number of load repetitions to failure,
log NP = logarithm of the number of load repetitions to failure at level of confidence P
u
= factor from the tables for the normal distribution related to confidence
level P
49
From the equations given above it becomes clear that the quality of the predictions increases
when SlogN decreases. This means that SlogSCI and Slof should be as low as possible. A low
SlogSCI stresses the need to pay ample attention to the discrimination of homogeneous subsections. The only factor that cannot be easily assessed is the variation in fatigue characteristics. Although this value can be estimated (see e.g. lecture notes CT4850 part III
Asphaltic Materials) if mixture composition data are available, extensive fatigue testing has
shown that Slof = 0.25 is a reasonable first estimate.
Overlay calculations based on the confidence level or probability of survival level P are made
in the following way. As is shown above, the number of load repetitions until a certain
probability of survival level P1 is reached can be calculated using:
log NP1 = A0 + A1 C0 + A1 C1 log SCI1 – u1 SlogN
If the pavement life has to be extended to N + ∆N load repetitions and after that number of
load repetitions, the probability of survival should be P2, the needed SCI level to achieve this
can be calculated using:
Log (N + ∆N)P2 = A0 + A1 C0 + A1 C1 log SCI2 – u2 Slog(N+∆N)
After subtracting of both equations one obtains:
Log {NP1 / (N + ∆N)P2} = A1 C1 log {SCI1 / SCI2} – u1 SlogN + u2 Slog(N+∆N)
By writing
NP1 / (N + ∆N)P2 = 1 / X
I1
= 10**(u1 SlogN)
I2
= 10**(u2 Slog(N+∆N)
We arrive to
Log {1 / X}
= A1 C1 log {SCI1 / SCI2} – log I1 + log I2
This can be written as:
SCI2
1/A1C1
= SCI1 (X I2 / I1)
In these equations SCI1 can be considered as the SCI before the overlay is placed and SCI2
as the SCI after overlaying. In the same way SlogN is valid before overlaying and Slog(N+∆N) is
valid after the overlay is placed.
We still need equations to predict the SCI2 in relation to the overlay thickness and stiffness as
well as the SCI1. Furthermore an equation is needed to predict SlogSCI2 because from this
value Slog(N+∆N) can be calculated. These equations are given below:
Log SCI2
= b0 + b1 Eo + b2 ho + b3 log SCI1 + b4 Eo log SCI1 + b5 ho log SCI1
+ b6 ho log Eo log SCI1
S2logSCI2
= {b1 + b4 log SCI1 + b6 ho log SCI1 / Eo}2 S2Eo
+ {b2 + b5 log SCI1 + b6 log Eo log SCI1}2 S2ho
+ {b3 + b4 Eo + b5 ho + b6 ho log Eo}2 S2logSCI1
Where: SCI1
SCI2
ho
Eo
bo
b1
b2
= surface curvature index (d0 – d300) before overlaying [µm]
= surface curvature index (d0 – d300) after overlaying [µm]
= overlay thickness [mm]
= elastic modulus of the overlay [Mpa]
= -0.0506
-5
= 1.178 10
= 0.0094
50
b3
b4
b5
b6
= 1.0153
-6
= -7.73 x 10
= -3.778 x 10-4
= -1.4971 x 10-3
With respect to the procedures discussed above, it is once again stressed that they are based
on limiting the strains in the existing pavement. Also it should be noted that it is assumed that
the overlay is fully bonded to the existing pavement. This however is not always the case
especially in cases where, because of reasons to be discussed later, an interface layer is
placed between the overlay and the existing pavement allowing the overlay to behave more
or less independently from the existing pavement. Furthermore the effect of cracks in the
existing pavement on the performance of the overlay is not taken into account. This effect
however cannot be ignored in cases where the existing pavement shows moderate to severe
cracking. Also this will be discussed in a later chapter.
One important point remains to be discussed which is the estimation of the probability of
survival of the existing pavement P.
Without going into all the details (for these the reader is referred to [9]), it can be shown that P
can be estimated from the ratio of the surface curvature index measured in and between the
wheel tracks following:
P
= (SCIb / SCIin)q
Where: SCIb
SCIin
q
= SCI measured between the wheel tracks (d0 – d500)
= SCI measured in the wheel tracks (do – d500)
= dependent on the type of structure taking a value between 0.6 and 0.4 for
pavements with an unbound base and between 0.7 and 0.5 for pavements
with a bound base; the higher values are for a 150 mm thick base, the
lower values are for a 300 mm thick base.
If for reasons mentioned earlier, the SCI ratio cannot be used, P can also be estimated from
the percentage of the wheel track area that shows cracking following:
P
= 1 – percentage cracked area / 100
It should be noted that a substantial part of the cracking that is visible at the pavement is
surface cracking. This type of cracking is initiated at the pavement surface and normally
progresses downwards to approximately 40 mm. It is clear that this type of cracking cannot be
associated to the fatigue type cracking for which the above mentioned procedures are developed. All in all this means that P values estimated in this way might be too high, the real
structural condition might be better than it appears from the P value estimated in this way.
If P is known as well as SlogN, the damage ratio n / N can easily be determined using the
equations given above or by means of figure 31.
51
Figure 31: Relation between P, SlogN and n / N.
52
10. Extension of the simplified procedure to estimate critical
stresses and strains:
In many cases the thickness of the pavement layers is unknown or highly variable. In that
case a pavement evaluation that relies on the back calculation of layer moduli is less effective
and estimation of critical stresses and strains using simple methods as described in the
previous chapter are extremely useful. In a joint research effort by the Government Service
for Land and Water Use (LWU) of the Dutch Ministry of Agriculture, Nature Management and
Fisheries, KOAC consultants and the Delft University of Technology, a pavement evaluation
and overlay design method was developed which completely relies on such simple relations
[11]. The hart of the method being the relations to estimate the stresses and strains will be
reproduced here.
The basis of the method is the large number of calculations on stresses and strains in on four
layer pavement systems due to a FWD load. The calculated values are schematically shown
in figure 32.
FWD load 50
kN, φ = 300 mm
Asphalt
Unbound or
Bound
Base
Subbase
Subgrade
1. Tensile strain at
pavement surface.
2. Tensile strain at
bottom asphalt.
3. Compressive
stresses in top
unbound base.
4.Tensile strain at
bottom bound base
5. Vertical compressive strain at
top subbase.
6. Vertical compressive strain at
top subgrade.
Figure 32: Analysed structures and locations where stresses and strains were calculated.
The analyses have been made for pavements with Easphalt > Ebase > Esubbase > Esubgrade and for
pavements where Esubbase < Esubgrade.
One will notice that the equations are much more complex than the ones described until now.
The reason for this is that thin asphalt surfacings had to be considered and for those
pavements the simple relations between e.g. the SCI and the tensile strain at the bottom of
the asphalt layer are not valid anymore.
Also one will notice that in a number of cases information on the thickness of some layers is
required. From the type of equation one will notice however that the influence of the thickness
information on the magnitude of the estimated strains and stresses is limited.
10.1 Relations between deflection bowl parameters and stresses and strains at various
locations in the pavement:
From the extensive analyses, the following results were obtained:
Tensile strain at the bottom of the asphalt layer:
log εr1,0
= -1.06755 + 0.56178 log h1 + 0.03233 log d1800 + 0.47462 log SCI300
+ 1.15612 log BDI – 0.68266 log BCI
53
Where: εr1,0
h1
dr
SCI300
BDI
BCI
= maximum horizontal strain at the bottom of the asphalt layer [µm/m]
= thickness of the asphalt layer [mm]
= deflection at distance r of the load centre [µm]
= d0 – d300 [µm]
= base damage index = d300 – d600 [µm]
= base curvature index = d600 – d900 [µm]
Tensile strain at pavement surface:
Many cracks that are visible at the pavement surface are initiated at the top of the pavement.
These cracks are the result of the complex stress distribution under tyres; especially the
horizontal shear stresses are of importance. These are not caused by braking but by the fact
that free horizontal expansion of the tyre when loaded can not occur due to friction forces. In
order to take these stresses into account the stress conditions under a tyre were modelled in
the way shown in figure 33.
Load
Position [mm]
X
y
Radius
[mm]
Stress [kPa]
X
y
Z
1
2
3
4
5
6
7
8
9
10
+60
+70
+60
-60
-70
-60
+90
-90
0
0
52.57
42.57
52.57
52.57
42.57
52.57
22.57
22.57
112.57
50.00
-200
-200
-200
-200
-200
-200
-180
-180
0
0
+400
0
+400
+400
0
+400
0
0
+750
+750
+90
0
-90
+90
0
-90
0
0
0
0
0
0
0
0
0
0
0
0
+150
-60
Figure 33: Schematisation of the contact stresses under a tyre.
The following relation was found:
εr1,b
= 194.895 – 20.7769 SCI3000.5
Where: εrt,b
= tensile strain at pavement surface [µm/m]
54
Compressive vertical strain at the top of the unbound base:
The vertical compressive strain at the top of the subgrade is a well known design criterion.
Such a criterion doesn’t exist for e.g. unbound base materials. Nevertheless it can be
expected that if the compressive strains at the top of the unbound base become too large,
excessive deformations might develop there as well.
In order to develop an estimation procedure for the compressive strain at the top of the
unbound base, Alemgena [25] analysed the same structures as were analysed by van Gurp.
It appeared that the development of such a relation was rather complicated and was only
possible for particular types of pavement.
Alemgena found the following predictive equation:
Log εvb = 1.5615 + 0.3743 log SCI300 + 1.0067 log BDI + 0.8378 log d0
- 1.9949 log d1800 + 0.6288 log d300
This equation is only valid for the following conditions:
a. the pavement shouldn’t be an inverted pavement so E1 > E2 > E3 > E4,
b. the stiffness of the upper layer shouldn’t exceed four times the underlying
layer (e.g. E2 ≤ 4 E3),
c. applicable only for weak bases (i.e. E2 < 1000 Mpa).
Tensile strain at the bottom of the bound base:
The following relation was developed:
log εr2,o = 0.0931 + 0.4011 log d0 + 0.3243 log d1800 + 0.4504 log d300 – 0.9958 log d900
+ 0.8367 log BDI
Where: εr2,o
= tensile strain at the bottom of the bound base [µm/m]
Compressive vertical strain at the top of the subbase and subgrade:
Two cases have to be considered which are the case where the stiffness of the subbase is
higher than that of the subgrade and the case where the stiffness of the subbase is smaller
than that of the subgrade. In the first case the surface modulus plot will shown an increase in
stiffness going from bottom to top while in the second case the surface modulus plot indicates
the presence of low stiffness layers on top of the subgrade.
The following results were obtained:
a. Subbase is stiffer than the subgrade:
log εv3 = 2.48589 + 0.34582 log SCI300 + 0.16638 log d1800 – 0.68746 log (h1 + h2)
+ 0.47432 log BDI
b. Subbase is less stiff than subgrade:
log εv3,s = 1.52887 + 0.39502 log SCI300 – 0.84168 log d1800 – 0.60888 log (h1 + h2)
+ 0.43195 log BDI – 0.78407 log BCI + 1.73707 log d600
c.
Subgrade:
log εv4 = 2.48589 + 0.34582 log SCI300 + 0.16638 log d1800 – 0.68746 log (h1 + h2 + h3)
+ 0.47432 log BDI
Where: εv3
εv4
εv3,s
= vertical compressive strain at the top of the subbase [µm/m]
= vertical compressive strain at the top of the subgrade [µm/m]
= vertical compressive strain at the top of the subbase when this layer
has a lower stiffness than the subgrade [µm/m]
55
10.2 Temperature correction method:
As mentioned before, temperature has a large influence on the magnitude of the measured
deflections. In order to be able to use the simplified relations between SCI and strain in the
asphalt layer which were discussed in the previous paragraph, a temperature correction
procedure adaptable to these relations should be available. Furthermore the correction
procedure should take into account the effect of cracks present in the pavement. A fully
cracked pavement e.g. acts like a block pavement and in such conditions a temperature
correction is not needed on the measured deflections. On the other hand it is obvious that the
effect of temperature is the largest on a sound asphalt layer.
A procedure taking into account both effects is described in [10] and is discussed hereafter.
The surface curvature index measured at a specific temperature can be corrected to a
reference temperature using:
TNF
= 1 + {(a1 + a2 / h1) . (TA – 20) + (a3 + a4 / h1) . (TA – 20)2} . (1 – SRt)
Where: TNF
TA
h1
SRt
= temperature normalisation factor,
= asphalt temperature [0C],
= thickness of the asphalt layer [mm],
= percentage area cracked / 100.
TNF takes values smaller than 1 if the measurements are taken below the reference
temperature of 20 0C (which is the reference temperature in the Netherlands). Consequently
TNF is larger than 1 if the measurements were taken above 20 0C.
The constants a1 to a4 take the following values:
Variable
a1 [ 0C-1]
a2 [mm / 0C]
a3 [0.001 0C-2]
a4 [mm / 0C2]
D0
SCI225
SCI300
SCI450
SCI600
0.01661
0.05955
0.05398
0.04720
0.04190
-0.67095
-2.73223
-2.61130
-2.39175
-2.15168
0.28612
1.48011
1.28439
1.05022
0.87228
-0.01408
-0.08171
-0.07493
-0.06371
-0.05301
The correction is applied in the following way. The SCI300,
corrected to a SCI300, 20C at 20 0C following:
SCI300, 20C
T
measured at temperature T is
= SCT300, T / TNF
A simple but highly effective technique to estimate the temperature in the asphalt layer is
given below. The procedure has been developed in [12] and is slightly modified in [10].
T3
= 8.77 + 0.649 T0 + (2.20 + 0.044 T0) . sin {2 π (hr – 14) / 24}
+ log (h1 / 100) . [-0.503 T0 + 0.786 T5 + 4.79 sin {2 π (hr – 18) / 24}]
Where: T3
T0
T5
h1
hr
= temperature at third point in the asphalt layer [ 0C]
= pavement surface temperature [ 0C]
= prior mean five days air temperature [ 0C]
= asphalt thickness [mm]
= time of the day in 24 hour system [hr]
10.3 Relationships with other pavement strength indicators such as SNC:
Also in [11], valuable relationships are presented which relate the deflection bowl to the
modified structural number SNC as used in the Highway Design Model. The relationship that
was developed is shown here-after.
log SNC
= 1.82472 + 0.03344 log h1 + 0.11832 log BCI – 0.16207 log BDI
+ 0.12659 log d0 – 0.57878 log d900 + 0.19996 log d1800 - 0.19829 log SCI300
56
This relationship opens possibilities for characterising pavement strength by means of a well
known physical quantity.
10.4 Relationships between the falling weight deflections and deflections measured
with the Benkelman beam:
Furthermore an extensive study was made in [11] of the relationships that could exist
between the deflections as measured by means of a BB and those by means of a FWD. The
relations that were developed are reported hereafter.
It should be noted that the BB measurements were done with a rear axle load of the loading
vehicle of 63.5 kN (this is the same axle load as used in the TRRL procedure). As mentioned
before the FWD measurements were taken at a load level of 50 kN.
It should also be noted that the relations shown are those between the BB values which are
not corrected for the movement of the support system and the FWD values. Table 6 gives the
results.
Variable
Constant
log BB0
log BB500
log BB1000
log BB2000
log BB3500
log h1
Unit log d0
µm
µm
µm
µm
µm
µm
mm
log d300
+ 1.61 + 1.44
+ 0.49 + 0.29
+ 1.23 + 1.11
- 1.53
- 1.06
+ 0.47 + 0.32
0
0
- 0.33 - 0.27
FWD deflection [µm]
log d600 log d900 log d1200 log d1500 log d1800
+1.40
0
+ 0.83
- 0.43
+ 0.31
- 0.08
- 0.25
+ 1.31
0
+ 0.38
0
+ 0.34
- 0.10
- 0.25
+ 1.23
0
+ 0.23
0
+ 0.55
- 0.14
- 0. 26
+ 1.19
0
+ 0.13
0
+ 0.67
- 0.15
- 0.27
+ 1.14
0
+ 0.33
- 0.48
+ 0.96
- 0.16
- 0.27
Table 6: Regression coefficients of the conversion formulas BB values to FWD values.
The variables BBx are related to the deflections which are measured when the rear axle of the
loading truck is at a distance of x mm from the tip of the beam. An example how the equations
should read is given below.
log d900 = + 1.31 + 0.38 log BB500 + 0.34 log BB2000 - 0.1 log BB3500 – 0.26 log h1
It should be mentioned that these relations have been developed using a BB with the
following dimensions.
610 mm
pivot
2695 mm
915
57
11. Remaining life estimation from visual condition surveys:
As has been indicated in the previous chapters, visual condition surveys give important information on the condition of the pavement. With respect to the structural condition of the
pavement, two damage types are of importance which are cracking and permanent
deformation especially when the deformation is due to deformation of the base subbase or
subgrade.
In the past, several condition prediction models using visual condition surveys as input have
been developed (e.g. [9]). Mostly these models suffer from accuracy because in practice the
damage is seldom allowed to grow to such an extent and severity that models describing the
progression of the damage completely could not be developed. Fortunately such information
can be obtained from sections tested by accelerated loading facilities. In this chapter the
models will be discussed which have been developed from observations made on test
sections at the outside facilities of the Road and Railways Research Laboratory of the Delft
University, which were tested by means of the Delft University accelerated pavement testing
facility called LINTRACK [13, 14].
Before going into the discussion of the models developed, attention is called for the fact that
in the analysis of visual condition survey data one always has to consider the way in which
the information is obtained.
The models for the prediction of the development of the amount of cracking that are going to
be presented are based on the visual condition survey system used by the Road and
Hydraulics Engineering Division of the Dutch Ministry of Transport. The unit section length is
100m. The length over which longitudinal cracking is visible in the left and right hand wheel
track is determined and divided by 200; the ratio obtained is called LC. In the same way the
amount of alligator cracking is determined and again this number is divided by 200 in order to
obtain the ratio AC. The amount of cracking is then calculated from the sum LC + AC.
It has been shown that the progression of cracking can very well be described by means of a
Weibull function following [15, 16]:
Fw(n)
= 1 – exp [-( n/µ)β ]
Where: Fw(t)
n
µ
β
= probability that failure has occurred before n load repetitions,
= number of load repetitions,
= number of load repetitions at which 63% of the area considered is cracked,
= curvature parameter.
Analysis of the World Bank cracking models incorporated in the HDM III design system [7]
showed that β was dependent on the stiffness of the pavement. The LINTRACK experiments
indicated that β was dependent on the asphalt thickness following:
log β
= -0.08 + log h
Where: h
= asphalt thickness [mm].
In the LINTRACK test sections also permanent deformation was observed. It was shown that
this deformation was due to deformation of the subgrade. The permanent deformation was
measured at several locations under a 1.2 m long straight edge and the mean value was
determined. The maximum allowable rut depth was set at 18 mm and the number of load
repetitions needed to arrive to this depth was determined. The rut formation could then be
described using the following non dimensional model:
Sn / SN = ( n / N )0.41
Where: Sn
SN
n
N
= rut depth after n load repetitions [mm],
= rut depth at which pavement is considered to be failed = 18 mm,
= number of load repetitions applied,
= number of load repetitions needed for a rut depth of 18 mm.
58
The remaining pavement life can easily be predicted by means of these normalised
equations. One measures the amount of damage that is present and one sets the maximum
amount of damage which is just acceptable before maintenance is needed. From the ratio
present amount of damage over allowable amount of damage the pavement life ratio can be
determined. By using the procedure outlined in chapter 8, the damage ratio can be translated
in a number of years before maintenance is required.
59
12. Procedures to estimate material characteristics:
In the previous chapters ample attention has been paid to the assessment of the stresses and
strains at critical locations in the pavement. It has also been stressed that a proper evaluation
of the remaining life and determination of the required overlay thickness cannot be made
without knowledge on the strength of materials. Especially knowledge on the fatigue
characteristics of the asphalt and the resistance to permanent deformation of the unbound
base, subbase and subgrade is of importance.
In this chapter transfer functions that allow the pavement life to be assessed will be
presented.
12.1 Fatigue characteristics of asphalt mixtures:
The fatigue resistance of asphalt mixtures is usually described following:
Log N = log k1 – n log ε
Where: N
k1, n
ε
= number of load repetitions to failure,
= material parameters,
= applied strain level.
It has been shown that the exponent n strongly depends on the slope of the master curve of
the stiffness modulus. Figure 34 is an example of such an relationship.
Figure 34: Example of the relationship between the loading time and the stiffness of an
asphalt mixture.
Relationships like those shown in figure 34 can be determined experimentally by means of
e.g. repeated load indirect tensile tests. If such tests cannot be performed, the stiffness
modulus of the asphalt mixture can also be estimated using the Shell nomographs for the
60
estimation of the bitumen and mixture stiffness. Input that is needed to feed those
nomographs is the TR&B and PI of the bitumen as well as the volumetric composition.
If we call the slope of the relationship between log t and log Smix, m, then this value can be
calculated using the following relationship.
m
= d (log Smix) / d (log t)
The exponent of the fatigue relationship, n, can then be calculated using [17]:
n
= 2 / {m . (0.541 + 0.346 / m – 0.0325 Va )
Where: Va
= void content of the asphalt mixture [%]
The intercept value log k1 is calculated in the following way [17].
log k1
= 6.589 – 3.762 n + 3209 / Smix + 2.332 log Vb + 0.149 Vb / Va + 0.928 PI
-0 .0721 TR&B
Where: n
Smix
Vb
Va
PI
TR&B
= slope of the fatigue relation,
= stiffness of the asphalt mixture [MPa],
= volume percentage of bitumen [%],
= void percentage [%],
= penetration index of the bitumen,
= softening point of the bitumen [0C].
The relationship for log k1 was established using the fatigue test results performed on over
100 mixtures. Results involved were those reported by the SHRP A-003 team, by Shell
researchers, researchers of the Delft University and by researchers of the Road and
Hydraulics Engineering Division of the Dutch Ministry of Transport.
The relationship for n was established using the results obtained for over 30 mixtures. All
tests considered were displacement controlled tests.
12.2 Deformation resistance of unbound base materials:
The vertical permanent deformation in unbound base materials is usually described using:
εp
= 10a . Nb
Where: εp
a, b
N
= permanent strain [µm/m],
= material constants,
=number of load repetitions.
The parameters a and b are dependent on the type of material, the gradation, the degree of
compaction and the moisture content. It is common practice to determine these parameters
by means of repeated load triaxial tests.
At the Delft University, an extensive testing program has been performed by van Niekerk [26]
on base materials composed of crushed concrete and crushed masonry. Recycling of old
concrete and masonry is a very important issue in the Dutch road industry. Van Niekerk’s
results were used by Alemgena to develop base compressive strain criteria. This was
possible since both permanent deformation as well as resilient modulus tests were performed.
From the permanent deformation tests it was determined at which number of load repetitions
a permanent deformation of 4% occurred. This number of load repetitions is of course
dependent on the material type and the stress conditions. For each stress condition applied
also the resilient modulus could be determined and so the elastic strain. Using all this
information relations between the elastic strain and the number of load repetitions at which a
permanent deformation of 4% occurred was determined. Typical examples of such criteria are
shown in figure 35 while figure 36 gives the gradations. The code UL-65-100 e.g. means that
the gradation is the UL gradation, that the mixture is composed with 65% crushed concrete
61
and 35% crushed masonry (mass percentages) and that the samples were compacted to
100% of standard proctor.
Allowable vertical compressive strain at top of base
3,4
log eps [mum/m]
3,3
3,2
3,1
CO-65-100
3
AL- 65-100
UL- 65-100
2,9
LL-65-100
2,8
2,7
2,6
2,5
2
3
4
5
6
7
8
log N
Figure 35: Base strain criteria.
cummulative percentage passing
[%]
100
80
UL
UN
LL
CO
AL
FL
60
40
20
0
0.063 0.125 0.25
0.5
1
2
4
sieve diameter [mm]
8
16
31.5
Figure 36: Gradations tested by van Niekerk.
Figure 35 clearly shows that base strain criteria can be developed but that there doesn’t exist
a single base strain criterion. The criterion is clearly dependent on the gradation but also on
62
the composition and the degree of compaction (these later two influence factors are not
shown here).
12.3 Subgrade strain criterion:
Research with the LINTRACK [13] has shown the following criterion to be applicable for a
typical Dutch fore shore sand. The relationship is based on allowing a maximum rut depth of
18 mm.
log N
= - 7.461 – 4.33 log εv
Where: εv
= subgrade strain [µm/m]
12.4 Maximum tensile strain at bottom of the bound base:
The terminology “bound base” is used for any base materials to which some kind of binding
agent is added or for base materials which shown some kind of self cementing action. Such
materials will always show cracks due to shrinkage. With appropriate measures, the influence
of that type of cracking can be kept under control. Nevertheless also deterioration due to
traffic loads will occur. Given the shrinkage cracks that are already present in the base, it is
not realistic to assume that the base is a homogeneous material and it is not realistic to
analyse the possibility of fatigue cracking as is usually done for asphalt layers. It is however
wise to limit the tensile strains due to traffic in order to avoid extensive traffic related damage.
For that reason it is proposed to keep the tensile strain due to traffic loads below 50% of the
tensile strain at failure, so below a level of approximately 60 µm/m.
63
13. Overlay design in relation to reflective cracking:
The main purpose of the overlay design procedure that was presented in one of the previous
chapters was to limit the tensile strain at the bottom of the existing asphalt layer and the
compressive vertical strain at the top of the subgrade. As was indicated such a method
doesn’t take into account the effect of cracks in the existing pavement on the performance of
the overlay. This is a serious issue since these cracks tend to propagate through the overlay
and can reduce the effective life of the overlay significantly. The conclusion therefore must be
that crack reflection must be considered when designing an overlay.
Linear elastic theory applied on homogeneous, isotropic layers can be used in overlay design
procedures which are based on limitation of the stresses and strains in the existing pavement.
Cracked pavement however cannot be analysed in this way. In fact principles of fracture
mechanics have to be applied to analyse the effects of cracks. This immediately implies that
finite element programs need to be used for the analysis of crack propagation. Although such
programs can easily be used on today’s personal computers, they are still considered to be
not practical for every day’s use. Therefore there has always been a strong need for so called
“engineering tools” which allow the complex phenomenon of reflective cracking to be analysed with rather simple tools.
Although the author fully understands this need of practice, he also likes to stress that each
model is a schematisation of reality and that too simple models will be a too simple schematisation of reality which can result in less optimal or even wrong results.
In spite of these drawbacks, some simplistic models are presented here-after because they
are based on sound analyses of pavement structures using fracture mechanics principles.
13.1 Overlay design method based on effective modulus concept:
The first method to be presented is based on the effective modulus concept. This concept is
schematically shown in figure 37.
A
B
layer has reduced, effective modulus
Figure 37: Concept of effective modulus method.
Figure 37a shows the condition one is dealing with in reality when designing an overlay. The
overlay is placed on the cracked pavement and this crack wants to propagate through the
overlay because of stress concentrations at the tip of the crack due to the bending and
shearing action of the load. The stress concentrations due to the bending action are indicated
by K1 (the horizontal arrow), those due to the shearing action are indicated by K2 (the vertical
arrows). It should be noted that in fracture mechanics K is called the “stress intensity factor”.
The growth of the crack due to K is described using:
dc / dN = A . Keffn
Where: dc / dN = increase in crack length c per load repetiton,
Keff
= effective stress intensity factor combining the bending and shearing
effects and taking into account the fact that the K1 and K2 are not constant
when the crack progresses through the overlay,
A, n
= material parameters.
64
The life of the overlay N can simply be calculated using:
N
= ho / { dc / dN }
Where: ho
= overlay thickness [mm].
In the effective modulus method (figure 37b), the tensile strain at the bottom of the asphalt
layer is calculated, indicated by the horizontal arrow, and the fatigue life of the overlay is
calculated using the appropriate fatigue relation. The magnitude of the tensile strain at the
bottom of the overlay, and so the life of the overlay, is of course dependent on the modulus of
the existing asphalt layer. This modulus value should be reduced to such a level that the
fatigue life of the overlay, calculated according to the principle of figure 37b, equals the life of
the overlay based on the crack propagation principles shown in figure 37a. The reduced
modulus so obtained is called the effective modulus of the existing asphalt layer.
Using these principles, figure 38 was developed [19]. In principle this figure is only valid for
the following conditions.
E1
= modulus existing asphalt layer = 3000 MPa,
h1
= thickness of existing asphalt layer = 100 and 300 mm,
= thickness of the base = 300 mm,
h2
= modulus of the base = 200 MPa,
E2
E3
= subgrade modulus = 100 MPa,
Eo
= modulus of the overlay = 5000 MPa.
The graph shows that if the effect of a 60 mm overlay is to be analysed when placed on a
severely cracked pavement where load transfer takes place across the crack, that an effective
modulus for the existing asphalt has to be used of approximately 900 MPa.
Figure 38: Effective modulus of the existing asphalt layer in relation to the thickness of the
existing asphalt layer and overlay, and the amount of load transfer across a crack.
65
13.2 Method based on stress intensity factors:
This method is in fact an extension of the crack growth calculations that were made to
develop the effective modulus method presented in the previous section. For this method [20]
a number of pavement structures was considered and the propagation through the overlay of
cracks which were fully developed through the existing asphalt layer as well as 50 mm deep
surface cracks was analysed. Figure 39 shows the analysed pavements as well as the three
load conditions considered.
Figure 39: Analysed pavement structures.
Table 7 gives the regression equations and values for the regression parameters for the
calculation of K1eq and Keff for all three loading conditions. First of all the K1eq should be
estimated. This value represents the combined effect of K1 and K2. Than Keff is determined;
this value takes into account the variation of the K1eq over the height of the overlay.
Table 7a: Relationship between K1eq and several pavement parameters.
66
Table 7b: Relationship between Keff / K1eq and several pavement parameters.
When using these equations for the determination of the thickness of the overlay, values for A
and n should be available.
It has extensively been shown [ e.g. 9] that the value of the exponent n of the crack growth
relation is equal to the value of the exponent n of the fatigue relation. For the estimation of n,
the reader is therefore referred to section 12.1.
Furthermore A and n appear to be strongly correlated following [17]:
log A
= - 2.890 – 0.308 n – 0.739 n0.273 log Smix
Where: n
Smix
= slope of crack growth relation which is equal to the slope of the fatigue
relationship, see section 12.1,
= stiffness of the asphalt mixture [MPa].
13.3 Overlay design method based on beam theory:
The disadvantage of the method presented in section 13.2 is that it is only applicable for the
conditions for which it has been developed. This means that there is a big chance that the
real conditions are different from the conditions for which the method is developed which
implies that the method only has a limited field of application.
A more general applicable simple design system has therefore been developed in [21]. This
method is based on the propagation of cracks in fully supported beams as described in [22].
In the text hereafter the equations given in [22] will be given first of all. This is followed by an
explanation how this method can be generalised to pavement systems.
Let us consider the two loading conditions as shown in figure 40.
The stress intensity factors at the tip of the crack due to bending and shearing can be
calculated in the following way.
Kbending = kb . q . e-β/2 . sin (β . l / 2) / β2 d1.5
Kshearing = ks . q [1 + e-βl . [sin (β . l) – cos (β . l) / 4 β √ d
β
Where: kb
ks
q
l
= (Es / E)0.33 / 0.55 d
= dimensionless stress intensity factor due to bending,
= dimensionless stress intensity factor due to shearing,
= contact pressure [MPa],
= width of loading strip [mm],
67
c
d
E
Es
= length of the crack [mm],
= thickness of the beam [mm],
= modulus of the beam [MPa],
= modulus of the supporting layer [MPa].
l
q
E
d
c
Es
Bending
Shearing
Figure 40: Crack propagation in a fully supported beam as a result of bending and shearing.
Figure 41 shows how the dimensionless stress intensity factors change in relation to the ratio
c / d. As one observes the stress intensity factor due to shearing increases with increasing
crack length. This is logical because with increasing crack length, the area that has to transfer
the load decreases so the stresses in that area increase.
Figure 41 however also shows that the stress intensity factor due to bending increases first
with increasing crack length but then decreases to a value of zero. This is because of the fact
that the crack reaches the neutral axis of the pavement at a given moment and penetrates the
zone where horizontal compressive stresses are acting. Then the cracks stops to grow since
the driving force has disappeared.
68
Figure 41: Relationship between c / d and the dimensionless stress intensity factors.
69
The question now of course is how this beam approach can be used for the design of
overlays on cracked pavements. The first step how to schematise a cracked pavement with
overlay is shown in figure 42.
overlay
existing
asphalt
bound
b
base
d
subgrade
Figure 42a: Pavement structures to be schematised.
c
d
Es
E
= hexisting asphalt + hbound base
= hoverlay + hexisting asphalt + hbound base
= Esubgrade
= combined modulus of overlay, existing
asphalt and bound base
c
d
Es
E
= hexisting asphalt
= hoverlay + hexisting asphalt
= combined modulus of
subgrade and base
= combined modulus of
overlay and existing
asphalt
Figure 42b: Schematised structures.
The question now is how to arrive to the combined modulus values. This is done in the
following way. First of all the layer moduli of the existing pavement are back calculated. In
case the modulus of the subgrade and the unbound base have to be combined, the following
equation has been suggested by Odemark.
1 / Es
= (1 / E2) . {1 - √ [(a2 + he12) / (a2 + (he1 + ge2)2)]}
+ (1 / E3) . √ [(a2 + he12) / (a2 + (he1 + he2)2)]
Where: Es
E2
E3
a
he1
h1
E1
ge2
h2
he2
= combined modulus of subgrade and base,
= modulus of the unbound base,
= modulus of the subgrade,
= radius of loading area,
= 0.9 h1 (E1 / Es)0.33,
= thickness of the existing asphalt layer,
= modulus of the existing asphalt layer,
= 0.9 h2,
= thickness of the unbound base,
= 0.9 h2 (E2 / E3)0.33.
70
From the nature of the equation it is clear that it has to be solved by iteration since Es can
only be calculated if an initial value for Es is assumed.
The combined modulus of the existing asphalt layer and the overlay can be calculated using
Nijboer’s equation.
E
= Ea . {[b4 + 4 b3 n + 6 b2 n + 4 b n + n2] / [n . (b + n) . (b + 1)3]}
Where: E
Ea
b
n
= combined modulus of existing asphalt layer and overlay,
= modulus of the existing asphalt layer,
= thichkness of existing asphalt layer / thickness overlay,
= modulus of overlay / modulus of existing asphalt layer
In case one has to determine the combined modulus of the base, existing asphalt and
overlay, then the combined modulus of the base and existing asphalt layer has to be
determined first of all. Then the combined modulus of this value and the overlay has to be
determined using the same equations. This means that in that case Ea = combined modulus
of the existing asphalt layer and the base, n = modulus of overlay / combined modulus of
existing asphalt and base, b = total thickness of existing asphalt layer and base / thickness of
the overlay.
The procedure is illustrated by means of an example.
Example:
Assume a given pavement consisting of a 100 mm thick asphalt layer on a 300 mm thick base
which in turn is placed on a subgrade. From the back calculation analysis it appeared that the
modulus of the existing asphalt layer was 9000 MPa. The base had a modulus of 130 MPa
and the subgrade a modulus of 50 MPa.
First of all the Es value had to be calculated using the above mentioned equation. As a
starting value for Es a value of 130 MPa was assumed. This resulted in a calculated Es value
of 74 MPa. This value was used as starter for a second iteration, then a value for Es of 71
MPa was obtained. A third iteration resulted in the same Es value so Es = 71 MPa.
Then the stiffness of the overlay was determined from the mixture composition, the bitumen
characteristics and the temperature and loading conditions. This procedure will not be
illustrated here. The interested reader is referred to the lecture notes on Asphalt Materials
CT4850. The modulus of the overlay was determined to be 8000 MPa.
Using Nijboer’s equation a combined modulus for the existing asphalt layer and the overlay
was calculated using:
n
b
= Eoverlay / Eexisting asphalt = 8000 / 9000 = 0.89
= hexisting asphalt / hoverlay = 100 / 50 = 2
The combined modulus of existing asphalt and the overlay was calculated to be E = 8496
MPa.
The question now is what the stress intensity factors are at the tip of the crack that wants to
penetrate the overlay. The pavement is severely cracked so only a limited amount of load
transfer through aggregate interlock will occur.
From the pavement geometry we know:
c =length of the crack = thickness of the existing asphalt layer = 100 mm,
d = thickness of existing asphalt layer + thickness of the overlay = 150 mm,
so
c / d = 0.66.
From figure 41 it appears that one only has to take into account the shearing action.
71
The pavement is loaded by truck wheels having a contact pressure q = 0.7 MPa. The radius
of the loaded area = 150 mm, this means that l = 300 mm.
We calculate:
β
= (Es / E)0.33 / 0.55 d = (71 / 8496)0.33 / 0.55 . 150 = 0.0025
Kshearing = ks . q . [1 + e-βl (sin βl – cos βl)] / 4 β √d
= ks 0.7 [1 + e-0.0025 x 300 (sin 0.0025 x 400 – cos 0.0025 x 400)] / 4 x 0.0025 x √150
= ks 0.7 [ 1 + 0.472 (0.841 – 0.540)] / 0.122 = ks 6.553
Please note that in the calculation of the sin and cos, βl is in radians.
If the K values are known, the number of load repetitions that is needed to allow the crack to
reflect through the overlay can be calculated using the procedures given earlier.
The question now of course is to what extent beam theory is representative for real pavement
problems. This is of course not the case and some shift factors resulting in similar stress
conditions in the beam as in the real pavement are therefore necessary. The easiest way is to
do is to compare the stresses at the bottom of the beam with the stresses that would occur at
the bottom of the top layer in the two layer system. Most probably the stresses at the bottom
of the beam are higher than the stresses at the bottom of the layer. The correction factor that
is needed to fit the stresses at the bottom of the beam to the stresses at the bottom of the
layer can also be used as correction factor for the stress intensity factors.
13.4 Effects of reinforcements, geotextiles, SAMI’s and other interlayer systems:
In order to retard reflective cracking, various systems have been developed in time which can
be used to do so. Examples of such systems are:
1. Application of polymer modifications in the overlay mixture to enhance the crack
resistance of the overlay material.
2. Reinforcement of the overlay material in order to improve the crack growth resistance of
the material.
3. Application of a low stiffness material between the existing pavement and the overlay in
order to let the overlay behave independently from the existing pavement.
Re 1: Polymer modifications have shown to be very effective in improving the crack resistance of asphalt mixtures. Especially SBS modifications have proven to be very useful. It is
beyond the scope of these lecture notes to discuss in detail the selection of the most
appropriate polymer modification. Nevertheless some practical guidelines will be given.
It had been shown (e.g. in the lecture notes on asphalt materials) that a material has a high
crack resistance when its tensile strength is high and when its fracture energy is high.
Materials with such characteristics can easily be discriminated by tests like the indirect tensile
test. This is schematically shown in figure 43.
By measuring the load and the displacements, one can derive a plot showing the growth of
the tensile stress in relation to the growth of the tensile strain. A picture like figure 40 is then
obtained. The peak value represents the tensile strength σt, while the area enclosed by the
plot represents the energy that is needed to fracture the specimen. This parameter is
indicated by Γ.
A modification should preferably have a positive effect on both the tensile strength and the
fracture energy. In practice however it has been observed that modifiers that increase the
tensile strength, decrease the fracture energy and vice versa. Only a limited number of
modifiers produce an improvement of both. By comparing plots like figure 43, the most
effective modifier can easily be determined.
72
σ
σt
Γ
ε
Figure 43: Strength and fracture energy obtained in a (indirect) tensile test.
Re 2: Asphalt mixtures can be reinforced in the same way as cement concrete can be
reinforced. Vital aspects with respect to reinforcement are the modulus of the reinforcing
material, its total cross sectional area, and the bond between the reinforcement and the
surrounding asphalt.
Materials like meshes made of polypropylene, glass fibres and steel are often propagated as
reinforcing materials. The question however is whether they really can act as a reinforcing
material. There are two reasons to doubt this. First of all the mesh might be a woven material
which means that not the stiffness of the material from which the mesh is made is of
importance, but the stiffness of the mesh which might be fairly low. Secondly many meshes
have a low physical thickness and are glued to the pavement by means of a tack coat. The
question in such cases is whether the tack coat is stiff enough to provide a good bond
between the reinforcing material and the surrounding asphalt. All this doesn’t necessarily say
that such products are useless; what it really says that these products certainly can have an
effect but that the effect is not likely to be a reinforcing effect. In some cases the effect of such
materials is somewhere between reinforcing and separating.
Although the effect of reinforcements including the effect of the bond stiffness should be
analysed by means of finite element programs, the procedures presented above can be used
as well. In such cases it is common practice to describe the effect of the reinforcement by
using a lower value for the crack growth parameter A for the reinforced overlay than for the
unreinforced overlay. No general applicable values for the way in which reinforcing materials
reduce the A values when compared with reference unreinforced mixtures. These values
should be derived by means of properly designed experiments. Excellent guidelines for such
tests can be found in [23] and [24].
Re 3: Cracks will not propagate into the overlay if the overlay behaves independently from the
existing pavement. This can be accomplished by placing a chewing gum type layer between
the existing pavement and the overlay. Such a chewing gum layer might be a 1.2 mm layer of
polymer modified bitumen sprayed on the existing pavement, but it might also be a non
woven geotextile soaked with bitumen. In this case the geotextile acts as a container for the
bitumen.
The effect of such interlayers can easily be assessed by assuming that such layers have a
thickness of 1 mm and having a stiffness of about 50 MPa.
In general one will observe that the overlay thickness that should be used on top of such a
chewing gum interlayer system is limited in thickness. This is because thick overlays attract
tensile strains and will therefore not perform as good as one would expect.
13.5 Load transfer across cracks:
Especially in cases where the pavement has a cement treated base, ample attention should
be given to the load transfer that takes place across a crack. This is because at low
73
temperatures, the cement treated base will shrink. This shrinkage not only introduces extra
stresses in the overlay but also has a significant effect on the load transfer that takes place
across the crack. This load transfer will be zero when the crack is so wide that the crack faces
don’t touch each other.
A typical example of how the load transfer can vary during the year is given in figure 44. This
figure shows the deflection bowls measured with a FWD (load was 85 kN) around a specific
crack in the winter and in the summer. The pavement consisted of 200 mm asphalt on top of
a 300 mm thick sand cement base. The pavement showed transverse cracking due to
shrinkage.
It should be noted that in position a, six of the seven geophones are on one side of the crack
where the loading plate is placed. In position f, only one geophone is on the side of the crack
where the loading plate is.
From the figure it is clear that in summer the load transfer is rather good. In general the
deflection bowl is a fluid line. However in the winter the deflection bowls show that almost no
load is transferred across the crack indicating that in that period of the year the shearing
conditions of an overlay placed on top of such a crack will be severe.
In such conditions only thick overlays or overlays with a heavy reinforcement have a chance
to survive.
Figure 44a: Surface deflections at a transverse crack in the summer.
Figure 44b: Surface deflections at a transverse crack in the winter.
74
14. Effects of pavement roughness on the rate of deterioration:
It is a well known fact that driving over a rough pavement results in dynamic axle loads which
can be fairly high. This is of special importance for rather thin pavements because repeated
high dynamic wheel loads on one particular spot can result in premature failure at that
location. Some knowledge on the effect of pavement roughness on pavement deterioration is
therefore needed.
The magnitude of the dynamic axle load depends on the pavement roughness, the speed of
the vehicle and characteristics of the vehicle like size, weight and properties of the spring
suspension system. All this means that no unique relationship can be given between the
pavement roughness and the dynamic axle loads.
This means that the relationships given hereafter must be taken as indicative and not as hard
predictions.
It is not the intention to give here all the backgrounds of vehicle pavement interactions. Only
some useful formula’s will be given. For further details the reader is e.g. referred to [15].
In [21] two relationships are derived for the standard deviation of the dynamic axle loads of a
particular truck with particular characteristics, which had a static axle load of 10 tons. The
relationships are as follows:
log σ
= - 0.5184 + 0.4075 log SV
log σ
= 0.892 – 2.151 log PSI
Where: σ
SV
PSI
= standard deviation of the dynamic loads due to a static axle load of 10 tons
of a truck driving at 63 km / h [tons],
= slope variance of the road profile multiplied by 106 [rad2],
= present service ability index = 3.27 – 1.37 (log SV – 0.78).
In many countries of the world however the international roughness index IRI is used to
characterise the pavement roughness.
According to [15] the relation between PSI and IRI is as follows.
PSI
= 5.0 e-0.18 IRI
IRI
= 5.5 ln (5.0 / PSI)
Where: IRI
= in [m/km].
The problem in these analysis is how to obtain the PSI or IRI; normally quite sophisticated
equipment is used to measure pavement roughness and to derive PSI or IRI value from these
measurements. Fortunately it is shown in [15] that the IRI can be obtained using straightedge
measurements. The relationships given in [15] are:
2m straightedge: PDmean = 1.23 IRI
3m straightedge: PDmean = 1.58 IRI
Where: PDmean = mean deviation of the profile from the straightedge [mm].
It is believed that these relationships help in identifying locations where high dynamic axle
loads occur so where rapid deterioration might occur as well.
In order to allow a more precise analysis of the effects of a rough road on the dynamic axle
loads, the computer program ROUGHNESS, has been developed by Huurman of the Delft
University. The program can be found on the cd which is part of these lecture notes. The
user’s manual for this program is given in appendix II.
75
References:
1. Molenaar, A.A.A.
Pavement management systems, Part I, II and III.
Lecture notes e54; Faculty of Civil Engineering; Delft University of Technology;
Delft – 1993.
2. AASHTO
AASHTO guide of design of pavement structures 1986.
Washington D.C. - 1986
3. Holster, A.M.; Molenaar, A.A.A.; Van den Bosch, H.G.; Van Gurp, C.A.P.M.
Comparison between observed and predicted pavement response.
Report 7-91-209-14; Road and Railway Research Laboratory; Delft University of
Technology; Delft – 1991
4. Stas, W.F.; Molenaar, A.A.A.; Van Gurp, C.A.P.M.
Evaluation of the structural condition of test pavements FORCE project.
Report 7-91-209-16; Road and Railway Research Laboratory; DelftUniversity of
Technology; Delft - 1991
5. Hoyinck, W.; Van den Ban, R.; Gerritsen, W.
Lacroix overlay design by three layer analyses.
Proc. 5th Int. Conf. Structural Design of Asphalt Pavements.
Vol 1, pp 410 – 420; Delft – 1982
6. Kennedy, C.K.; Lister, N.W.
Prediction of pavement performance and the design of overlays.
TRRL Laboratory Report 833.
Crowthorne – 1978
7. Groenendijk, J.; Molenaar, A.A.A.
Pavement design methods, a literature survey into linear elastic theory and condition
prediction models.
Report 7-93-209-31; Road and Railway Research Laboratory; Delft University of
Technology; Delft – 1993
8. Shell International Petroleum Company Ltd.
Shell pavement design manual; asphalt pavements and overlays for road traffic.
London – 1978.
9. Molenaar, A.A.A.
Structural performance and design of flexible pavements and asphalt concrete overlays.
PhD dissertation; Delft University of Technology; Delft – 1983.
10. Van Gurp, C.A.P.M.
Characterization of seasonal influences on asphalt pavements with the use of falling
weight deflectometers.
PhD dissertation; Delft University of Technology; Delft – 1995.
11. Van Gurp, C.A.P.M.; Wennink, P.M.
Design, structural evaluation and overlay design of rural roads (in Dutch).
KOAC-WMD consultants; Apeldoorn - 1997.
12. Stubstad, R.N.; Lukanene, E.O.; Baltzer, S.; Ertman-Larsen, H.J.
Prediction of AC mat temperatures for routine load/deflection measurements.
Proc. 4th Int. Conf. On Bearing Capacity of Roads and Airfields.
Vol. 1, pp 661 – 682; Minneapolis – 1994.
13. Groenendijk, J.
Accelerated testing and surface cracking of asphaltic concrete pavements.
PhD Dissertation; Delft University of Technology; Delft – 1998.
14. Molenaar, A.A.A.; Groenendijk, J.; Van Dommelen, A.
Development of performance models from APT.
Proc. 1st Int. Conference on Accelerated Pavement Testing; Reno – 1999.
15. Paterson, W.D.O.
Road deterioration and maintenance effects.
John Hopkins University press; Baltimore – 1987.
76
16. Bekker, P.C.F.
Pavement performance modelling.
Proc. Closing conf. TEMPUS JEP-1180 “Educational developments in pavement
management systems”, pp 263 – 288: Delft University of Technology; Delft – 1993.
17. Medani, T.O.
Characterisation of crack growth and fatigue behaviour of asphalt mixtures using simple
tests.
MSc Thesis; International Institute for Infrastructural, Hydraulic and Environmental
Engineering; Delft – 1999.
18. Kloosterman, H.J.; Molenaar, A.A.A.
Model for the prediction of permanent deformation of unbound granular materials.
Report WB-13 (7-79-115-5); Road and Railroad Research Laboratory; Delft University of
Technology; Delft – 1979.
19. Van Gurp, C.A.P.M.; Molenaar, A.A.A.
Simplified method to predict reflective cracking in asphalt overlays.
Proc. 1st RILEM Conf. On Reflective Cracking in Pavements, pp 190 – 198; Liege – 1989.
20. Jacobs, M.M.J.; De Bondt, A.H.; Molenaar, A.A.A.; Hopman, P.C.
Cracking in asphalt concrete pavements.
Proc. 7th Int. Conf. on Asphalt Pavements; Vol 1, pp 89 – 105; Nottingham – 1992.
21. Molenaar, A.A.A.; Nods, M.
Design method for plain and geogrid reinforced overlays on cracked pavements.
Proc. 3rd Int. RILEM Conference on Reflective Cracking in Pavements, pp 311 - 320.
Maastricht – 1996.
22. Lytton, R.L.
Use of geotextiles for reinforcement and strain relief in asphalt concrete.
Geotextiles and Geomembranes, Vol. 8, No. 3, 1989.
23. De Bondt, A.H.
Anti-reflective cracking design of (reinforced) asphaltic overlays.
PhD Dissertation; Delft University of Technology; Delft – 1999.
24. Francken, L.; Vanelstraete, A.
Prevention of reflective cracking in pavements.
RILEM Report 18; E & F.N. Spon; London – 1997.
25. Alemgena Alene Araya
Estimation of maximum strains in road bases and pavement performance prediction.
MSc thesis TRE 127.
International Institute for Infrastructural Hydraulic and Environmental Engineering.
Delft – 2002.
26. Van Niekerk, A.A.
Mechanical behavior and performance of granular bases and sub-bases in pavements.
PhD Dissertation; Delft University of Technology; Delft - 2002