Structural Design of Pavements PART VI Structural ... - TU Delft
Structural Design of Pavements PART VI Structural ... - TU Delft
Structural Design of Pavements PART VI Structural ... - TU Delft
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CT 4860<br />
<strong>Structural</strong> <strong>Design</strong> <strong>of</strong> <strong>Pavements</strong><br />
January 2006<br />
Pr<strong>of</strong>.dr.ir. A.A.A. Molenaar<br />
<strong>PART</strong> <strong>VI</strong><br />
<strong>Structural</strong> Evaluation and<br />
Strengthening <strong>of</strong> Flexible <strong>Pavements</strong><br />
Using Deflection Measurements and<br />
Visual Condition Surveys
<strong>Structural</strong> <strong>Design</strong> <strong>of</strong> <strong>Pavements</strong><br />
<strong>PART</strong> <strong>VI</strong><br />
<strong>Structural</strong> Evaluation and Strengthening<br />
<strong>of</strong> Flexible <strong>Pavements</strong><br />
Using Deflection Measurements<br />
and Visual Condition Surveys<br />
January 2006<br />
Pr<strong>of</strong>.dr.ir. A.A.A. Molenaar
2<br />
Table <strong>of</strong> contents:<br />
Preface 3<br />
1. Introduction 4<br />
2. Usage and condition dependent maintenance 6<br />
3. Deflection measurement tools 7<br />
3.1 Falling weight deflectometer 7<br />
3.2 Benkelman beam 8<br />
3.3 Lacroix deflectograph 9<br />
3.4 Factors influencing the magnitude <strong>of</strong> the measured FWD deflections 10<br />
4. Measurement plan 13<br />
4.1 Estimation <strong>of</strong> the number <strong>of</strong> test points per section 13<br />
4.2 Development <strong>of</strong> a measurement plan 14<br />
5. Statistical treatment <strong>of</strong> raw deflection data and selection <strong>of</strong> a location representative<br />
for the (sub)section 18<br />
6. Back calculation <strong>of</strong> layer moduli 26<br />
6.1 Surface modulus 26<br />
6.2 Back calculation <strong>of</strong> layer moduli 28<br />
6.3 Example 29<br />
7. Analysis <strong>of</strong> Benkelman beam and Lacroix deflectograph deflection bowls 33<br />
8. Estimation <strong>of</strong> the remaining life using an empirical based method 38<br />
9. Mechanistic procedures for remaining life estimations and overlay design 43<br />
9.1 Basic principles 43<br />
9.2 Extension <strong>of</strong> the basic principles 45<br />
10. Extension <strong>of</strong> the simplified procedure to estimate critical stresses and strains 51<br />
10.1 Relations between deflection bowl parameters and stresses and strains<br />
at various locations in the pavement 51<br />
10.2 Temperature correction procedure 54<br />
10.3 Relationships with other strength indicators such as SNC 54<br />
10.4 Relationships between falling weight deflections and deflections<br />
measured with the Benkelman beam 55<br />
11. Remaining life estimation from visual condition surveys 56<br />
12. Procedures to estimate material characteristics 58<br />
12.1 Fatigue characteristics <strong>of</strong> asphalt mixtures 58<br />
12.2 Deformation resistance <strong>of</strong> unbound base materials 59<br />
12.3 Subgrade strain criterion 59<br />
12.4 Maximum tensile strain at bottom <strong>of</strong> the bound base 59<br />
13. Overlay design in relation to reflective cracking 61<br />
13.1 Overlay design method based on effective modulus concept 61<br />
13.2 Method based on stress intensity factors 63<br />
13.3 Ovelay design method based on beam theory 64<br />
13.4 Effects <strong>of</strong> reinforcements, geotextiles, SAMI’s and other interlayer systems 69<br />
13.5 Load transfer across cracks 70<br />
14. Effect <strong>of</strong> pavement roughness on the rate <strong>of</strong> deterioration 72<br />
References 73
3<br />
Preface:<br />
<strong>Pavements</strong> deteriorate due to damaging effects <strong>of</strong> traffic and environmental loads and at a<br />
given moment in time maintenance is needed. Maintenance activities can grossly be divided<br />
into two categories.<br />
The first category is the so called routine maintenance which is mainly applied to keep the<br />
pavement surface in such a condition that it provides good service to the public but also to<br />
limit the effects <strong>of</strong> ageing. Routine maintenance consists e.g. <strong>of</strong> crack filling, local repairs and<br />
the application <strong>of</strong> surface dressings. Normally this type <strong>of</strong> maintenance is not too expensive.<br />
The costs <strong>of</strong> a surface dressing are approximately fl 6/m 2 while filling <strong>of</strong> cracks costs<br />
approximately fl 2.5/m ’ . Routine maintenance is done on a regular basis; the time period<br />
between two successive applications depends <strong>of</strong> course on the rate <strong>of</strong> deterioration which in<br />
turn is affected by the damaging power <strong>of</strong> traffic and climate and by the workmanship <strong>of</strong> the<br />
maintenance crews.<br />
The second category is much more capital intensive. Now we are dealing with strengthening<br />
<strong>of</strong> the pavement for which overlays are needed or partial or complete reconstruction. This<br />
type <strong>of</strong> maintenance is less <strong>of</strong>ten required than routine maintenance.<br />
Because pavement strengthening is such a costly affair, investigations to determine precisely<br />
the extent and severity <strong>of</strong> the damage and the rate <strong>of</strong> progression are strongly recommended.<br />
If a pavement surface e.g. shows severe cracking, removing this layer and replacing it by a<br />
new one seems to be a sensible solution. If however the cracking is due to the very low<br />
stiffness <strong>of</strong> the base and no measure are taken to improve the bending stiffness <strong>of</strong> the base<br />
layer, then the cracking will soon reappear.<br />
This simple example already illustrates that, in order to be able to make a proper selection <strong>of</strong><br />
the maintenance treatments available, one not only should know where something is going<br />
wrong but also why.<br />
Understanding why the pavement fails means that one needs knowledge on the stresses and<br />
strains in the pavement as well as the strength <strong>of</strong> materials. The process <strong>of</strong> gaining this<br />
knowledge is called “evaluation <strong>of</strong> the structural condition <strong>of</strong> pavements”.<br />
As it will be shown in these lecture notes, deflection measurements are an extremely useful<br />
tool in the assessment <strong>of</strong> the structural condition <strong>of</strong> the pavement. During a deflection<br />
measurement, the bending <strong>of</strong> the pavement surface due to a well-defined test load is measured.<br />
This is called the measurement <strong>of</strong> surface deflections. It is clear that the magnitude <strong>of</strong><br />
the deflections and especially the curvature <strong>of</strong> the deflection bowl reveal important information<br />
on the bending stiffness <strong>of</strong> the pavement.<br />
In the notes ample attention is paid to the techniques for measuring deflections, the way how<br />
the measurement results can be processed to obtain information on the stiffness <strong>of</strong> the<br />
individual pavements layers and how they can be used to determine the required thickness <strong>of</strong><br />
the overlays to be applied.<br />
Although all possible care has been given during the preparation <strong>of</strong> these notes to avoid<br />
typing errors etc., it is always possible that some “bugs” are still present. Furthermore the<br />
reader can have suggestions about certain parts <strong>of</strong> the material presented. It would be highly<br />
appreciated if you could send your comments to the author using the following email address.<br />
a.a.a.molenaar@citg.tudelft.nl
4<br />
1. Introduction:<br />
These lecture notes are dealing with deflection measurements, how they should be performed<br />
and how the results can be used to determine the remaining life <strong>of</strong> the pavement and the<br />
maintenance that has to be performed.<br />
The importance <strong>of</strong> deflection measurements can be described by means <strong>of</strong> the following<br />
example. When children have to build a bridge across a creek using a wide variety <strong>of</strong> wooden<br />
beams, their instinct will tell them that they better select those planks that show the lowest deflection<br />
under load. They also know that it is wiser to place the beams like shown in figure 1a<br />
than in figure 1b.<br />
A<br />
B<br />
Figure 1: Children know by instinct that placing a beam according to A is more effective than<br />
placing it according to B.<br />
As civil engineers we know that the selection by the children is a correct one because beam A<br />
has lower stresses and strains at the outer fibres than beam B when both beams are<br />
subjected to the same load. However as civil engineers we also know that the question “is it<br />
safe or not to cross a beam which shows a maximum deflection <strong>of</strong> 2 mm” cannot be<br />
answered without knowledge <strong>of</strong> the span <strong>of</strong> the beam, the load applied and the strength <strong>of</strong> the<br />
material from which it is made. This clearly indicates that measurement <strong>of</strong> only the maximum<br />
deflection gives some information about the strength <strong>of</strong> the beam but that more information is<br />
needed. We would already be in a much better shape if the curvature <strong>of</strong> the deflection bowl<br />
due to the load was known.<br />
The same is true for pavements. In order to get useful information about the flexural stiffness<br />
<strong>of</strong> the pavement one should measure the deflection due to a test load at various distances<br />
from the load centre.<br />
We know that the flexural stiffness is determined by the stiffness <strong>of</strong> the subgrade and the<br />
stiffness modulus and thickness <strong>of</strong> the layers placed on top <strong>of</strong> the subgrade. It will then be<br />
obvious that it must be possible to back calculate the stiffness modulus <strong>of</strong> each <strong>of</strong> the individual<br />
layers if the deflection bowl due to a defined test load is known as well as the thickness<br />
<strong>of</strong> each pavement layer.<br />
If the stiffness modulus <strong>of</strong> each layer is known together with its thickness, then the stresses<br />
and strains in any location in the pavement can be calculated.<br />
Knowledge on the strength <strong>of</strong> materials however is absolutely needed for the determination <strong>of</strong><br />
whether or not the pavement is capable <strong>of</strong> carrying the traffic loads expected in the future and<br />
whether or not it should be strengthened.<br />
All this means that the usefulness <strong>of</strong> a deflection measurement program without paying<br />
proper attention to the strength <strong>of</strong> materials can be doubted.<br />
In order to determine to what extent traffic loads have resulted in a deterioration <strong>of</strong> the pavement<br />
strength, deflections should be measured regularly during the pavement life. Since<br />
deflection measurements are fairly costly, one should make a realistic estimate <strong>of</strong> the number<br />
<strong>of</strong> measurements to obtain a picture <strong>of</strong> the deterioration trend line that develops in time. One<br />
should however be aware <strong>of</strong> the fact that the trend lines one wants to establish are influenced<br />
by variations in temperature (effect on stiffness modulus <strong>of</strong> the asphalt layers) and moisture<br />
(effect on stiffness modulus <strong>of</strong> the subgrade) and that the deflections measured over a certain<br />
stretch <strong>of</strong> road might show a considerable variation because <strong>of</strong> variations in layer thickness<br />
and stiffness modulus. Another question, which then arises, is how many measurement loca-
5<br />
tions should be tested in a certain section in order to obtain a realistic picture <strong>of</strong> the flexural<br />
stiffness <strong>of</strong> the pavement.<br />
In these lecture notes we will deal with all these aspects. The structure <strong>of</strong> the notes is as follows.<br />
Attention will be paid to the development <strong>of</strong> a measurement program. This will be<br />
followed with a discussion on the determination <strong>of</strong> the number <strong>of</strong> measurements required per<br />
section and the statistical treatment <strong>of</strong> the deflection data.<br />
Although the Benkelman beam was developed some 40 years ago, it is still in use in many<br />
countries. This is also the case with the automated version <strong>of</strong> the Benkelman beam called the<br />
Lacroix deflectograph. A chapter has been devoted to these devices and especially<br />
procedures to correct the measured deflections to true deflections are discussed.<br />
After that attention will be paid to some simple techniques allowing the overall stiffness <strong>of</strong> the<br />
pavement structure to be assessed and potential problem layers to be identified. Then the<br />
back calculation <strong>of</strong> stiffness moduli will be treated.<br />
This will be followed by a discussion on the design <strong>of</strong> overlays in which probabilistic principles<br />
are introduced.<br />
After that ample attention will be paid to an analysis method which allows critical strains to be<br />
evaluated without the need to back calculate layer moduli. This method is <strong>of</strong> special interest in<br />
case accurate information on the layer thickness is not available.<br />
Then attention is paid on the importance <strong>of</strong> visual condition surveys. A method will be<br />
presented that allows the remaining life to be estimated from such surveys.<br />
This chapter is followed by a chapter on the estimation <strong>of</strong> material strength characteristics like<br />
the fatigue resistance <strong>of</strong> asphalt mixtures and the resistance to permanent deformation <strong>of</strong><br />
unbound granular materials.<br />
Reflective cracking is an important issue and the commonly used overlay design methods<br />
don’t take into account this important phenomenon. Therefore a chapter dealing with the<br />
design <strong>of</strong> overlays controlling reflective cracking is presented.<br />
Finally the effect <strong>of</strong> pavement roughness on pavement deterioration will be discussed and<br />
simple procedures to estimate pavement roughness will be given.<br />
First <strong>of</strong> all however attention will be paid to the question why pavement maintenance has to<br />
rely on regular monitoring <strong>of</strong> the pavement condition and why the decision on applying<br />
maintenance cannot be taken simply on the basis <strong>of</strong> the number <strong>of</strong> years the pavement is in<br />
service or the number <strong>of</strong> loads that have been applied to the pavement.
6<br />
2. Usage and condition dependent maintenance:<br />
<strong>Pavements</strong> deteriorate due to the combined influences <strong>of</strong> traffic and environmental loads.<br />
This means that at a given moment maintenance activities should be scheduled in order to<br />
restore the level <strong>of</strong> service the pavement should give to the road user. It will be obvious that<br />
careful consideration should be given to the planning and the selection <strong>of</strong> the maintenance<br />
activity. The right strategy should be applied on the right spot at the right time.<br />
Planning <strong>of</strong> maintenance can be sometimes a rather simple task to perform. If we consider<br />
e.g. the maintenance <strong>of</strong> our illumination systems, we observe that in a number <strong>of</strong> cases (e.g.<br />
hospitals) the bulbs are not replaced after failure, but after a certain number <strong>of</strong> burning hours.<br />
This way <strong>of</strong> maintenance is called “usage dependent maintenance”, because the replacement<br />
is done after a certain time period the object to be maintained is used.<br />
There are three important reasons why such a type <strong>of</strong> maintenance is possible and accepted<br />
for illumination.<br />
a. For some reasons we don’t accept to be in the dark (safety, interruption <strong>of</strong> work).<br />
b. We know quite precisely what the mean lifetime is <strong>of</strong> the light bulbs.<br />
c. We know quite precisely what the variation is <strong>of</strong> the lifetime <strong>of</strong> the light bulbs and we<br />
know that this variation is small.<br />
This way <strong>of</strong> performing maintenance is not very suited to be applied on pavements for the<br />
following reasons.<br />
a. In most cases some degree <strong>of</strong> failure is acceptable on pavements. Traffic can e.g. drive<br />
at a fairly high speed level although there is a substantial amount <strong>of</strong> cracking. This implies<br />
that some damage types can be allowed to occur over a significant area and with a<br />
significant severity before an unacceptable level <strong>of</strong> service is reached.<br />
b. Although pavements have been subjected to extensive research, the predictive capability<br />
<strong>of</strong> our performance models is still limited. Even the accuracy <strong>of</strong> our models to predict the<br />
mean pavement life is quite <strong>of</strong>ten disappointing.<br />
c. <strong>Pavements</strong> exhibit a substantial amount <strong>of</strong> variation in performance mainly due to the<br />
variation in layer thickness, material characteristics etc.. This means that two pavements<br />
which are nominally the same and which are loaded under nominally the same conditions<br />
can show a significant difference in initiation and progression <strong>of</strong> damage.<br />
All in all a strategy which implies maintenance to be performed after the pavement has been<br />
in service for a certain number <strong>of</strong> years is not applicable for road networks. A certain amount<br />
<strong>of</strong> damage can mostly be allowed because pavement failure seldom results in catastrophic<br />
events. Furthermore the variation in pavement life is such that usage dependent maintenance<br />
cannot be made cost effective.<br />
This implies that the planning and selection <strong>of</strong> maintenance strategies for pavements heavily<br />
relies on input coming from condition observations and predictions based there on. Such an<br />
approach to maintenance is called “condition dependent maintenance”.<br />
This immediately means that tools should be available to monitor the condition <strong>of</strong> the<br />
pavement. An overview <strong>of</strong> such tools is already given in [1]. The lecture notes we have in<br />
front <strong>of</strong> us are dealing with one <strong>of</strong> the most important evaluation tools being the deflection<br />
measurement device.
7<br />
3. Deflection measurement tools:<br />
The deflection device that currently receives the highest popularity is the falling weight<br />
deflectometer (FWD). Nevertheless other deflection measuring devices like the Benkelman<br />
Beam (BB) and the Lacroix Deflectograph (LD) are still used at different places at the world.<br />
Especially the Benkelman Beam deserves attention since this low cost device (the price is<br />
approximately 1/30 th <strong>of</strong> the price <strong>of</strong> a falling weight deflectometer) is used in many<br />
developing countries. The principles <strong>of</strong> these three devices are given elsewhere [1], here only<br />
the main features will be described.<br />
3.1 Falling weight deflectometer:<br />
The principle <strong>of</strong> the FWD is schematically shown in figure 2.<br />
Figure 2: Principle <strong>of</strong> the falling weight deflectometer.<br />
A weight with a certain mass drops from a certain height on a set <strong>of</strong> springs (normally rubber<br />
buffers) which are connected to a circular loading plate which transmits the load pulse to the<br />
pavement. Load cells are used to monitor the magnitude and duration <strong>of</strong> the load pulse. The<br />
magnitude <strong>of</strong> the load pulse can vary between the 30 and 250 kN depending on the mass <strong>of</strong><br />
the falling weight and the falling height. The duration <strong>of</strong> the load pulse is mainly dependent on<br />
the stiffness <strong>of</strong> the rubber buffers. Usually pulse duration between 0.02 and 0.035 s are<br />
measured.<br />
The surface deflections are measured with so called geophones. These are velocity transducers<br />
which measure the vertical displacement speed <strong>of</strong> the surface. By integration the displacements<br />
are obtained.<br />
Since the electronic circuits are only opened a very short moment before the weight hits the<br />
buffers, the influence <strong>of</strong> passing traffic on the magnitude <strong>of</strong> the deflections is eliminated; only<br />
the displacements due to the impact load are measured.<br />
The advantage <strong>of</strong> the FWD is the short duration <strong>of</strong> the load pulse comparable to the duration<br />
<strong>of</strong> the load pulse caused by a truck driving at approximately 50 km/h. Because <strong>of</strong> the short<br />
pulse duration, the influence <strong>of</strong> viscous effects can be neglected.<br />
One should however be cautious when the modulus <strong>of</strong> a saturated subgrade with a high<br />
ground water level is determined from the deflection measurement results. In that case one<br />
might measure the bulk modulus K <strong>of</strong> the subgrade which, in case <strong>of</strong> a fully saturated<br />
subgrade, can be high. Because road materials are very much sensitive for shear, this high<br />
bulk modulus value gives a wrong idea about the real stiffness <strong>of</strong> the material. This can be<br />
illustrated with the following simple example.
8<br />
When a swimmer makes a nice dive from the diving tower he will hit the water in a gentle<br />
way, without too much <strong>of</strong> splash and without hurting himself. We can say that with such a nice<br />
dive he experiences the shear modulus G <strong>of</strong> water which, as we all know, is very low.<br />
However when he falls flat on his stomach, his dive is causing him much pain and probably a<br />
blue stomach. In this case he experiences the bulk modulus K <strong>of</strong> water which, as we know, is<br />
very high. A fluid with no air bubbles is in fact incompressible.<br />
3.2 Benkelman beam:<br />
The principle <strong>of</strong> the Benkelman beam, invented by A.C. Benkelman is schematically shown in<br />
figure 3.<br />
Figure 3: Principle <strong>of</strong> the Benkelman beam.<br />
The measuring system consists <strong>of</strong> a beam that can rotate around a pivot attached to a<br />
reference frame. The load is supplied by a truck that slowly moves to or from the tip <strong>of</strong> the<br />
beam.<br />
The advantage <strong>of</strong> the BB is the fact that the device is simple and cheap. The disadvantage is<br />
the slow speed <strong>of</strong> the truck that can cause all kinds <strong>of</strong> viscous effects making the<br />
measurements difficult to interpret. Furthermore the effects <strong>of</strong> passing vehicles on the<br />
magnitude <strong>of</strong> the deflection cannot be neglected. Finally it should be mentioned that the<br />
supports <strong>of</strong> the reference frame could stand in the deflection bowl. This means that the frame<br />
is not a true reference and corrections for movement <strong>of</strong> the support system have to be made<br />
in order to obtain the true deflections.<br />
Quite <strong>of</strong>ten only the magnitude <strong>of</strong> the rear axle load <strong>of</strong> the truck used as loading vehicle for<br />
the BB measurements is reported. This is absolutely insufficient; precise knowledge <strong>of</strong> the<br />
tyre pressure, tyre spacing and area <strong>of</strong> the tyre print is necessary in order to allow proper<br />
analyses to be made.<br />
Different measurement procedures exist and one should strictly adhere to the guidelines for<br />
doing the measurements when one <strong>of</strong> such procedures is used.<br />
Furthermore one should realise that the dimensions <strong>of</strong> the BB can differ. There are devices<br />
with shorter and longer measuring beams. One should take good notice <strong>of</strong> this in order to<br />
overcome that a beam is used that doesn’t comply with the requirements set in the procedure<br />
to be used.
9<br />
3.3 Lacroix deflectograph:<br />
Figure 4 shows the Lacroix deflectograph (LD). The principle <strong>of</strong> the measurement is the same<br />
as that <strong>of</strong> the Benkelman beam. The major difference however is that the measuring system<br />
is attached to the loading vehicle and that it is moved automatically to the next measuring<br />
position. This procedure is schematically shown in figure 5.<br />
It is obvious that the LD has large advantages over the BB. First <strong>of</strong> all the measurements are<br />
continuously taken and are far less affected by the varying speed <strong>of</strong> the loading vehicle. With<br />
the BB measurements the speed <strong>of</strong> the truck varies between 0 (at the beginning <strong>of</strong> the<br />
measurements) and approximately 5 km/h when the truck drives at constant speed. The<br />
speed <strong>of</strong> the LD vehicle is more or less constant at 5 km/h.<br />
The LD however suffers from the same disadvantages as the BB. The low speed can cause<br />
that the viscous behaviour <strong>of</strong> the asphalt surfacing cannot be neglected and corrections for<br />
movement <strong>of</strong> the reference frame need to be applied.<br />
Because the entire measurement procedure is automated, much more measurements can be<br />
taken with the LD as with the BB in the same time period. This however has its price; the LD<br />
has about the same price level as the FWD.<br />
Figure 4: Principle <strong>of</strong> the Lacroix deflectograph.
10<br />
Figure 5: Principle <strong>of</strong> the automatic positioning <strong>of</strong> the measuring system <strong>of</strong> the LD.<br />
3.4 Factors influencing the magnitude <strong>of</strong> the measured FWD deflections:<br />
When civil engineers are dealing with measurements they quite <strong>of</strong>ten show a bad habit which<br />
is that they accept the measurement result as “the truth”. They seldom realise that the measurement<br />
result is affected by a large number <strong>of</strong> factors and that the magnitude <strong>of</strong> the<br />
influence <strong>of</strong> these factors should be known in order to avoid misinterpretations. A number <strong>of</strong><br />
such influence factors on deflections measured with a FWD will be discussed here. The<br />
material presented is based on the excellent work done on this topic by van Gurp which is<br />
reported in [10].<br />
When a number <strong>of</strong> FWD devices are used on the same pavement to measure the deflections,<br />
one will notice that all these devices will not measure the same value. This is even true when<br />
the deflections are corrected to a particular load level. Some reasons for that are described<br />
hereafter.<br />
It is a well-known fact that the stiffness <strong>of</strong> rubber is temperature dependent. At higher<br />
temperatures the stiffness will be lower than at lower temperatures. This is nicely shown in<br />
figure 6 where the stiffness <strong>of</strong> a particular rubber buffer used in a particular FWD is given in<br />
relation to the load level and the temperature.<br />
It will be obvious that the temperature in the rubber buffers will vary when a FWD survey is<br />
done starting early morning and ending late afternoon. This is not only because <strong>of</strong> the<br />
variation in air temperature but also because <strong>of</strong> the cumulative energy that is collected in the<br />
buffer, and that is transformed in heat, because <strong>of</strong> the large number <strong>of</strong> measurements that<br />
are taken during the day. This means that the stiffness <strong>of</strong> the rubber buffer will vary during the
11<br />
day. The effect is <strong>of</strong> course more pronounced if measurements done in the winter have to be<br />
compared with those done in the summer.<br />
Figure 6: Static spring constant <strong>of</strong> a particular rubber buffer used in a particular FWD.<br />
If for some reason the spring stiffness decreases, the shape <strong>of</strong> the load pulse changes. Its<br />
peak value will decrease while the duration <strong>of</strong> the pulse will increase. The longer duration <strong>of</strong><br />
the pulse might cause a somewhat s<strong>of</strong>ter response (lower stiffness) <strong>of</strong> the pavement. More<br />
important <strong>of</strong> course is the fact that differences between the devices occur if they have<br />
different buffers and if the deflections have to be corrected to a predefined load level.<br />
Furthermore one has to be careful when using the FWD for studies on the non linearity <strong>of</strong><br />
pavements. Especially pavements where the main body is formed by unbound materials, will<br />
show non linear behaviour. One might try to analyse this by doing deflection measurements at<br />
different load levels but from the text given above it will be clear that at least some <strong>of</strong> the non<br />
linearity that is measured is caused by the device itself!!<br />
Research in [10] has shown that it is wiser to correct the deflections based on the area<br />
enclosed by the load vs time plot rather than based on the peak load.<br />
Other effects, which are unfortunately more <strong>of</strong> the “black box” nature, are the following. As<br />
mentioned, geophones are used to measure the deflections. The nature <strong>of</strong> the geophones<br />
however is that their sensitivity reduce with decreasing frequency. Especially below 10 Hz,<br />
the sensitivity decreases rapidly. However these low frequencies contribute significantly to the<br />
frequency spectrum <strong>of</strong> a single deflection pulse. Especially the frequency spectrum <strong>of</strong><br />
deflection pulses measured on thin pavements laid on s<strong>of</strong>t subgrades will show the great<br />
contribution <strong>of</strong> the low frequencies. If the geophones don’t pick up these low frequencies, a<br />
too low deflection will be recorded and one would expect the pavement to have a higher<br />
flexural stiffness than it really has.<br />
This effect can be compensated by using high gain factors for the low frequencies. The way in<br />
which this is done depends however on the manufacturer and information on this is usually<br />
confidential information.<br />
It has also been shown in [10] that the system processor can deform the deflection readings.<br />
For one FWD system, the influence <strong>of</strong> the system processor appeared to be so large that it<br />
did not pass the calibration procedure and could therefore not be used in FWD surveys.<br />
Another influence factor is the smoothing <strong>of</strong> signals that is applied on the FWD deflections.<br />
This smoothing is done in order to get rid <strong>of</strong> high frequency disturbances. The question then<br />
always is what the cut-<strong>of</strong>f frequency should be. Studies reported in [10] have shown that if f =<br />
60 Hz is chosen as cut-<strong>of</strong>f frequency, the effect <strong>of</strong> the smoothing is minimal. Again it is noted<br />
that one should ask the FWD supplier to give details on this important aspect.
12<br />
From the text given above it is clear that there are several influence factors which cause that<br />
the deflections measured with one device are different from those measured with an other<br />
device. It is clear that calibration is vital in order to avoid unexpected and unacceptable<br />
differences between devices to occur.
13<br />
4. Measurement plan:<br />
The question always is how many measurements should be taken and where should the<br />
measurements be taken on a specific stretch <strong>of</strong> pavement in order to get a reliable picture <strong>of</strong><br />
the flexural stiffness <strong>of</strong> the pavement. Some guidelines for this will be given in this chapter.<br />
4.1 Estimation <strong>of</strong> the number to test points per section:<br />
In this section the method presented in [2] is described which allow the number <strong>of</strong> tests to be<br />
determined that are needed on a particular road section to obtain a proper insight in the<br />
bearing capacity <strong>of</strong> the pavement.<br />
One can calculate a statistical quantity R, called the limit <strong>of</strong> accuracy, which represents the<br />
probable range the true mean differs from the average obtained by “n” tests at a given degree<br />
<strong>of</strong> confidence. The larger n is, the smaller value will be obtained for R which means that the<br />
mean value calculated from the data obtained from the tests will differ less from the true mean<br />
value. The mathematical expression is:<br />
R = K α . ( σ / √ n )<br />
Where: K α<br />
σ<br />
= standardised normal deviate which is a function <strong>of</strong> the desired confidence<br />
level 100 . (1 - α),<br />
= true standard deviation <strong>of</strong> the random variable (parameter) considered.<br />
If the confidence level is chosen and if a proper estimate for σ is obtained, R is inversely<br />
proportional to the square root <strong>of</strong> the number <strong>of</strong> tests.<br />
Figure 7shows the basic shape <strong>of</strong> the relation between n and R.<br />
Figure 7: Typical limit <strong>of</strong> accuracy curve for all pavement variables showing general zones.
14<br />
As shown in figure 7, 3 zones can be discriminated. In zone I a small increase in the number<br />
<strong>of</strong> tests reduces the value <strong>of</strong> R tremendously and the accuracy <strong>of</strong> the predictions will increase<br />
drastically. In other words a small increase in budget to increase the number <strong>of</strong> data points is<br />
really value for money.<br />
In zone III, R hardly reduces with an increasing number <strong>of</strong> tests. This means that in this case<br />
very little extra value is obtained from an increased measurement budget.<br />
The optimal number <strong>of</strong> tests can be found in zone II.<br />
The main problem in calculating R is the assessment <strong>of</strong> the standard deviation σ. Since the<br />
magnitude <strong>of</strong> the deflections can vary quite considerably within one pavement section and<br />
between pavement sections (thick pavements compared with thin pavements), it is not<br />
possible to give a single value for σ. Nevertheless it is possible to give values for the<br />
coefficient <strong>of</strong> variation CV for the measured deflections which are observed in practice.<br />
Typical values are:<br />
CV = standard deviation / mean =<br />
0.15 low variation, typical for pavements which are in<br />
good condition,<br />
0.30 medium variation, typical for pavements which<br />
show a fair amount <strong>of</strong> damage,<br />
0.45 high variation, typical for pavements which<br />
show a large amount <strong>of</strong> damage.<br />
By using these CV values and adopting confidence levels <strong>of</strong> 95% (α = 0.05) and 85% (α =<br />
0.15), figure 8 has been constructed.<br />
The use <strong>of</strong> the procedure is illustrated by means <strong>of</strong> the following example. A deflection survey<br />
has to be performed on a road that is in reasonable condition and the question is how many<br />
measurements need to be taken to obtain a reliable picture <strong>of</strong> the flexural stiffness <strong>of</strong> the<br />
pavement. Because a reliable picture is desired the average deflection is allowed to differ 8%<br />
from the true mean. The required confidence level is 95%. Since the pavement shows some<br />
damage a CV is estimated <strong>of</strong> 20%. By interpolation, the position <strong>of</strong> the line for CV = 20% is<br />
estimated in figure 8a. Using this line and the R-value <strong>of</strong> 8%, the number <strong>of</strong> observations to<br />
be taken is equal to 7.<br />
4.2 Development <strong>of</strong> a measurement program:<br />
Before one decides on where and how many deflection measurements should be taken, a<br />
visual condition survey should preferably be performed. It is e.g. important to know which<br />
types <strong>of</strong> defects are present on the pavement and how the various defect types are<br />
distributed over the pavement surface. Is the damage evenly distributed or is the damage<br />
concentrated in a limited number <strong>of</strong> locations.<br />
A visual condition survey is not only needed to develop an effective measurement plan, but<br />
the condition data are also needed in the evaluation phase when decisions on the<br />
maintenance strategy to be applied need to be taken.<br />
The most important damage types to consider in the structural evaluation <strong>of</strong> pavements are <strong>of</strong><br />
course cracking and deformations because they are related to lack <strong>of</strong> flexural stiffness.<br />
If cracking and deformations occur rather locally it is not recommended to use an equal<br />
spacing between the measurement points but to locate them in such a way that an as good<br />
as possible sample <strong>of</strong> both sound and cracked cq deformed areas is obtained.<br />
For reasons that will be discussed later on, it is recommended to measure both the outer<br />
wheel track as well as the area between the wheel tracks, the latter being representative for<br />
the flexural stiffness <strong>of</strong> the undamaged pavement. These measurements are <strong>of</strong> course only<br />
useful if the area between the wheel tracks is not damaged.<br />
In case <strong>of</strong> severe longitudinal or transverse cracking, it is recommended to perform some<br />
measurements across the crack. This can be done very easily with the FWD using the<br />
geophone positions schematically shown in figure 9.
15<br />
Figure 8a: Graph to estimate the number <strong>of</strong> observations required at<br />
a confidence level <strong>of</strong> 95%.<br />
Figure 8b: Graph to estimate the number <strong>of</strong> observations required at<br />
a confidence level <strong>of</strong> 85%.
16<br />
Figure 9: Placement <strong>of</strong> loading plate <strong>of</strong> FWD and geophones for load transfer measurements.<br />
Deflection measurements across the crack are important in order to be able to determine the<br />
amount <strong>of</strong> load transfer. This parameter has a significant influence on the thickness <strong>of</strong> the<br />
overlay; if there is e.g. no load transfer at all, additional maintenance work like milling and<br />
filling <strong>of</strong> the cracked area might be necessary.<br />
The magnitude <strong>of</strong> the measured deflections is dependent on the temperature, which affects<br />
the stiffness <strong>of</strong> the asphalt layers, and the moisture content, which can have a significant<br />
effect on the stiffness <strong>of</strong> the subgrade and other unbound layers. This means that if measurements<br />
are taken at various periods <strong>of</strong> the year, corrections are needed in order to be able<br />
to compare them. In order to avoid the rather complex corrections due to moisture variation, it<br />
is recommended to take the measurements in the so-called “neutral” period. During such<br />
periods the moisture content in the unbound materials is approximately at its mean level. In<br />
the Netherlands that is the late April – early May period and the October month.<br />
Because BB and LD measurements are taken at relatively low speeds, one should not<br />
perform these measurements at too high temperature levels because otherwise viscous<br />
effects will have a significant influence on the measurements which makes interpretation<br />
there-<strong>of</strong> complicated. Also the temperatures should not be too low because then the<br />
deflections might be so small that accuracy problems occur in the measurement and<br />
monitoring <strong>of</strong> the deflections. For that reason the Transport and Road Research Laboratory<br />
(TRRL) in the UK has suggested the temperature ranges shown in table 1 at which the BB<br />
and LD measurements should preferably be taken.<br />
Maximum temperature 30 o C if bitumen has a penetration lower or equal than 50<br />
25 o C if bitumen has a penetration higher than 50<br />
Minimum temperature 5 – 10 o C depending on the structure<br />
Table 1: Maximum and minimum temperature for deflection measurements<br />
as specified by TRRL.
17<br />
One should realise that the influence <strong>of</strong> temperature always has to be taken into account and<br />
that the deflections measured always should be corrected to a reference temperature. The<br />
temperature correction procedure will be presented in an other chapter.
18<br />
5. Statistical treatment <strong>of</strong> raw deflection data and selection <strong>of</strong><br />
a location representative for the (sub)section:<br />
Statistical treatment <strong>of</strong> the data as measured is always needed in order to be able to recognise<br />
trends and in order to limit the amount <strong>of</strong> work that should be done in the evaluation<br />
process. It is e.g. not necessary and even not useful to back calculate the layer moduli for<br />
each measurement location simply because <strong>of</strong> the fact that it is impossible to obtain accurate<br />
layer thickness information for each and every location. It is therefore much more effective to<br />
concentrate the analysis on locations which can be taken as representative for a particular<br />
section or sub-section.<br />
Simple statistical procedures have shown to be very effective to discriminate homogeneous<br />
sub-sections within a larger section. A homogeneous sub-section is defined as a section<br />
where the deflections and so the flexural stiffness are more or less constant. When such<br />
homogeneous sub-sections have been determined, one has to take a point which can be<br />
taken as being representative for that sub-section. That point can be the location where the<br />
measured deflection bowl comes closest to e.g. the average deflection pr<strong>of</strong>ile or the 85%<br />
deflection pr<strong>of</strong>ile. The 85% pr<strong>of</strong>ile is the pr<strong>of</strong>ile that is exceeded by 15% <strong>of</strong> all the measured<br />
pr<strong>of</strong>iles.<br />
The so-called homogeneous sub-sections can be determined by means <strong>of</strong> the method <strong>of</strong> the<br />
cumulative sums. The cumulative sums are calculated in the following way.<br />
First <strong>of</strong> all the mean <strong>of</strong> a variable over the entire section is calculated (e.g. the mean <strong>of</strong> the<br />
maximum deflection). Then the difference between the actual value <strong>of</strong> the variable and the<br />
mean is calculated. Next these differences are summed. In formula the cumulative sums are<br />
calculated using:<br />
S 1 = x 1 - µ<br />
S 2 = x 2 - µ + S 1<br />
S n = x n - µ + S n-1<br />
Where: S n = cumulative sum at location n,<br />
x n = value <strong>of</strong> the variable considered at location n,<br />
µ = mean <strong>of</strong> variable x over entire section.<br />
The method is illustrated by means <strong>of</strong> an example. Table 2 shows the deflections that were<br />
measured by means <strong>of</strong> a FWD on a particular road in the Netherlands. The load applied was<br />
50 kN, the diameter <strong>of</strong> the loading plate was 300 mm. The table gives values for d 0 , d 300 , etc.;<br />
these are the deflections measured at a distance <strong>of</strong> 0 and 300 mm etc.. An important value is<br />
the surface curvature index SCI, which is the difference between the maximum deflection d0<br />
and the deflection, measured at 600 mm from the loading centre (d 600 ). Also the logarithm <strong>of</strong><br />
the SCI values is reported. Also this is an important characteristic as will be shown later on.<br />
As one will observe from the table, high deflections are measured and the amount <strong>of</strong> variation<br />
in the measured deflections is very high. It should be noted that the pavement considered<br />
was a polder road on a very weak subgrade and showed a significant amount <strong>of</strong> damage.<br />
It should be noted that the example presented is a rather extreme one; normally such large<br />
variations in deflections are not observed.<br />
Figure 10 is a graphical representation <strong>of</strong> the measured deflections, while figure 11 shows the<br />
variation <strong>of</strong> the SCI over the section. Figure 12 shows in a graphical form the variation <strong>of</strong> the<br />
cumsum (cumulative sum) as determined for the SCI. The SCI is selected as parameter<br />
decisive in the determination <strong>of</strong> the homogeneous subsections since the SCI can be<br />
considered to be the most important deflection parameter.<br />
Homogeneous sub-sections can easily be recognised from figure 12 since by definition an<br />
area over which the slope <strong>of</strong> the cumulative sums plot is more or less constant indicates an<br />
area where the differences between the actual measured values and the overall mean value<br />
are approximately the same.
19<br />
Table 2: Deflection testing results obtained on a particular section and summary statistics.
20<br />
Figure 10: Results <strong>of</strong> a deflection survey.
21<br />
Figure 11: Surface curvature index.
22<br />
Figure 12: Cumulative sum <strong>of</strong> the surface curvature index.
23<br />
The following sections are discriminated.<br />
Section<br />
Locations<br />
1 0.05-0.1-0.15<br />
2 0.2-0.25-0.3<br />
3 0.35-0.4-0.45<br />
4 0.5-0.55-0.6<br />
5 0.65 this is a single point clearly visible in the SCI plot<br />
6 0.7-0.75-0.8-0.85-0.9-0.95<br />
7 1 this is a single point clearly visible in the SCI plot<br />
8 1.05-1.1-1.05<br />
9 1.1-1.15-1.2-1.25-1.3-1.35-1.4-1.45<br />
10 1.5 this is a single point clearly visible in the SCI plot<br />
11 1.55-1.6<br />
12 1.65-1.7-1.75-1.8-1.85-1.9-1.95-2<br />
By means <strong>of</strong> the cumsum method we have arrived to a set <strong>of</strong> successive sub-sections, each<br />
<strong>of</strong> them having more or less a certain flexural stiffness. Now it is interesting to determine if we<br />
can combine a few sections. If this is possible we would reduce the work load. The question<br />
now is how to achieve that.<br />
If we compare the slopes <strong>of</strong> the different sections we notice that the slopes <strong>of</strong> sections 2, 4<br />
and 12 are about the same. This means that they can be taken as one section in the further<br />
analysis. This also holds for sections 1 and 6, so also these can be treated as one section.<br />
The same is true for sections 3, 8 and 11.<br />
Then we have a look to the single points that are discriminated and we try to assign them to a<br />
particular subsection. We observe that location 0.65 is clearly an isolated peak value and<br />
should therefore be treated as such. Location 1 however could very well be combined with<br />
section 2. Also location 1.5 is better treated as a single point.<br />
All in all we arrive to the subsections given below.<br />
Section<br />
Locations<br />
1 0.05-0.1-0.15 and 0.7-0.75-0.8-0.85-0.9-0.95<br />
2 0.2-0.25-0.3 and 0.5-0.55-0.6 and 1.65-1.7-1.75-1.8-1.85<br />
-1.9-1.95-2 and 1<br />
3 0.35-0.4-0.45 and 1.05-1.1-1.15 and 1.55-1.6<br />
4 0.65<br />
5 1.1-1.15-1.2-1.25-1.3-1.35-1.4-1.45<br />
6 1.5<br />
The statistics <strong>of</strong> the sub-sections mentioned above are tabulated below.<br />
Section Mean Value SCI Standard Deviation SCI Var. Coeff.<br />
1 420 111 26%<br />
2 175 65 37%<br />
3 494 62 13%<br />
4 962<br />
5 423 77 18%<br />
6 96<br />
As one will notice, rather high values for the coefficient <strong>of</strong> variation are still obtained for<br />
sections 1 and 2. We have to look then in table 2, in order to find out what the possible<br />
reasons for this could be. By doing so we observe that location 0.8 doesn’t really fit in section<br />
1 and should better be moved to section 2. The high variation in section 2 is probably caused<br />
by the inclusion <strong>of</strong> locations 1.7 and 1.75; also location 1.9 could contribute to the high<br />
variation. Therefore it is suggested to move location 1.9 to section 1 and to combine locations<br />
1.7 and 1.75 with location 1.5. We then obtain the sections and summary statistics as shown<br />
in table 3.<br />
As one can observe a better result in terms <strong>of</strong> lower coefficients <strong>of</strong> variation are obtained. The<br />
division in subsections as shown in table 3 will be used for further treatment.
24<br />
Section Locations Mean SCI SD SCI Var. Coeff.<br />
1 0.05-0.1-0.15-0.7-0.75-0.85-0.9<br />
-0.95-1.9 434 87 20%<br />
2 0.2-0.25-0.3-0.5-0.55-0.6-0.8-1<br />
-1.65-1.8-1.85-1.95-2 181 40 22%<br />
3 0.35-0.4-0.45-1.05-1.1-1.15-1.55-1.6 494 62 13%<br />
4 0.65 962<br />
5 1.1-1.15-1.2-1.25-1.3-1.35-1.4-1.45 423 77 18%<br />
6 1.5-1.7-1.75 87 11 13%<br />
Table 3: Homogeneous sub-sections based on SCI<br />
An other approach to the reduction <strong>of</strong> the data is to make a frequency plot <strong>of</strong> the deflections<br />
measured. Figure 13 is an example <strong>of</strong> such a plot based on the measured SCI’s. In making a<br />
frequency plot one has to decide about the number <strong>of</strong> classes to be used. A practical<br />
guideline for this is to take the number <strong>of</strong> classes equal to the square root <strong>of</strong> the number <strong>of</strong><br />
observations.<br />
From figure 13 it is clear that we have 1 observation in the range SCI = 0 – 72 µm, 13<br />
observations in the range SCI = 73 – 220 µm, 6 observations in the range SCI = 221 – 369<br />
µm, 13 observations in the range SCI = 370 – 517 µm, 6 observations in the range SCI = 518<br />
– 665 µm and one extreme value which is the SCI = 962 µm measured at location 0.65. The<br />
locations which belong to the frequency classes and the summary statistics are given in table<br />
4.<br />
Frequency Locations SCI.<br />
Class Mean St. Dev. Var. Coef.<br />
0 – 72 1.75 72<br />
73 – 220 0.2-0.25-0.3-0.5-0.8-1-1.5-1.65-1.7-1.8-1.85<br />
-1.95-2 157 37 24%<br />
221 – 369 0.05-0.55-0.6-1.2-1.3-1.9 306 42 14%<br />
370 – 517 0.1-0.15-0.35-0.45-0.7-0.85-0.95-1.15-1.25<br />
-1.35-1.4-1.45-1.55 430 40 9%<br />
518 – 665 0.4-0.75-0.9-1.05-1.1-1.6 550 33 6%<br />
higher 0.65 962<br />
Table 4: Frequency classes for the SCI, locations and summary statistics.<br />
As one can observe from table 4, this approach results in a grouping <strong>of</strong> the deflection data in<br />
such a way that the coefficient <strong>of</strong> variation in one group is limited to very small.<br />
From the description given above it will be clear that several techniques are available for<br />
reduction <strong>of</strong> the raw deflection data. In principle the cumulative sum technique is a very<br />
powerful tool to discriminate homogeneous sections. However situations might occur that<br />
even the cumsum technique results in sections which exhibit a rather high degree <strong>of</strong> variation.<br />
In that case reduction <strong>of</strong> data through an analysis <strong>of</strong> the frequency distribution can result in<br />
data sets which are rather homogeneous in nature.<br />
The big advantage <strong>of</strong> the cumsum technique is that it results in physical section units ready to<br />
receive maintenance whereas the other approach doesn’t result in such units.<br />
All in all this means that the data reduction process and the statistical analysis <strong>of</strong> the raw data<br />
is not a straightforward process. Each time the data set should be treated carefully in order to<br />
select the most appropriate way to reduce the data.<br />
The selection <strong>of</strong> the location which can be considered to be representative for the entire<br />
(sub)section is done in the following way. First <strong>of</strong> all one has to decide whether one wants to<br />
base the analysis on the mean conditions or whether one wants to do the analysis using a<br />
deflection pr<strong>of</strong>ile that is exceeded by only 15% <strong>of</strong> the measured pr<strong>of</strong>iles. In the first case one<br />
selects a measured pr<strong>of</strong>ile that comes closest to the mean pr<strong>of</strong>ile while in the second case<br />
one selects a measured pr<strong>of</strong>ile that comes closest to the 85% pr<strong>of</strong>ile.
25<br />
In section 1 <strong>of</strong> table 3, location 0.85 has the SCI value (453) that comes closest to the mean<br />
SCI value <strong>of</strong> that section being 434, while location 0.75 has the SCI value (525) that comes<br />
closest to the 85% pr<strong>of</strong>ile <strong>of</strong> that section being 521 (mean plus one standard deviation).<br />
These locations are then selected as being the representative locations for this section. Cores<br />
are taken at those locations to obtain accurate information on the thickness <strong>of</strong> the layers. This<br />
information is needed to allow accurate back calculations <strong>of</strong> the layer moduli to be made.<br />
Figure 13: Frequency distribution <strong>of</strong> the measured SCI values.
26<br />
6. Back calculation <strong>of</strong> layer moduli:<br />
Back calculation <strong>of</strong> layer moduli is quite <strong>of</strong>ten considered as an important step in pavement<br />
evaluation. The reason for this is quite simple; the magnitude <strong>of</strong> the back calculated stiffness<br />
modulus quite <strong>of</strong>ten reveals whether or not the pavement layer is damaged or not. If e.g. a<br />
stiffness modulus <strong>of</strong> 600 MPa is back calculated for a cement treated layer, this layer should<br />
be in a rather deteriorated state because the modulus <strong>of</strong> a sound cement treated layer is<br />
substantially higher.<br />
One <strong>of</strong> the drawbacks <strong>of</strong> back calculating layer moduli is the fact that accurate information on<br />
the thickness <strong>of</strong> the various layers should be available. We know that the deflections are<br />
heavily influenced by the product E.h 3 , which means that a small error in the layer thickness<br />
can have a large effect on the magnitude <strong>of</strong> the back calculated modulus.<br />
Although computer programs are available that back calculate the layer moduli automatically<br />
when the deflections, the load configuration and the thickness <strong>of</strong> the different layers is known,<br />
back calculation <strong>of</strong> layer moduli is certainly not as straightforward as it may look like because<br />
in many cases the solution is not unique. This implies that some pre-treatment <strong>of</strong> the data is<br />
necessary before the actual back calculation process is started.<br />
In the sections hereafter the surface modulus diagram will be discussed first <strong>of</strong> all. This<br />
diagram provides insight in how the overall stiffness <strong>of</strong> the pavement develops from bottom to<br />
top and whether or not weak interlayers are present. After that the actual back calculation<br />
process will be discussed.<br />
It should be noticed that the procedures described are especially valid for the analysis <strong>of</strong><br />
FWD measurements. They can however also be used for the analysis <strong>of</strong> BB and LD<br />
measurements provided that the appropriate corrections are applied. These correction<br />
procedures will be described in a later section.<br />
6.1 Surface modulus:<br />
According to Boussinesq’s theory, the elastic modulus <strong>of</strong> a homogeneous half space can be<br />
calculated from the deflection measured at a given distance following:<br />
E = σ . a 2 . (1 - µ 2 ) / d r . r<br />
E = 2 . σ . a . (1 - µ 2 ) / d 0<br />
Where: E = elastic modulus,<br />
a = radius <strong>of</strong> loading plate,<br />
µ = Poisson’s ratio,<br />
σ = contact pressure under loading plate.<br />
The question now is whether this formula can be <strong>of</strong> use in analysing the stiffness development<br />
in a pavement. Let us consider therefore figure 14.<br />
geophones<br />
a<br />
b<br />
Figure 14: Distribution <strong>of</strong> the vertical stress in a pavement.
27<br />
The way in which the load is distributed depends on the thickness and the stiffness <strong>of</strong> the<br />
layer. In figure 14, the top layer is the stiffest followed by the base and the subgrade. It is<br />
obvious that only that part <strong>of</strong> the pavement that is subjected to stresses, will deform; that is<br />
the area enclosed by the cone. This means that the geophone that is farthest away from the<br />
load centre (geophone a) only measures deformations in the subgrade while the geophone in<br />
the load centre (geophone b) measures the deformations in the subgrade, base and top layer.<br />
This implies that if the Boussinesq formula is applied using the deflection value measured by<br />
geophone a as input, the modulus <strong>of</strong> the subgrade is calculated. In case Boussinesq’s equation<br />
is used using the reading <strong>of</strong> geophone b as input, an overall effective stiffness <strong>of</strong> the<br />
pavement is calculated.<br />
So the stiffness calculated from the geophone readings going from a to b give information<br />
about: the subgrade, the subgrade plus some effect <strong>of</strong> the base, the subgrade plus the base<br />
plus some effect <strong>of</strong> the top layer, the subgrade plus the base plus the top layer; in short:<br />
increasing moduli value will be calculated.<br />
All this means that the deflection readings taken at a certain distance from the load centre<br />
give in fact information on the stiffness <strong>of</strong> the pavement at a certain depth.<br />
Using this information a so-called surface modulus plot is constructed. On the vertical axis<br />
one plots the surface modulus calculated using the Boussinesq formulas and on the<br />
horizontal axis one plots the equivalent depth which is equal to the distance <strong>of</strong> the geophone<br />
considered to the load centre. The principle <strong>of</strong> the plot is schematically shown below.<br />
Surface<br />
Modulus<br />
Equivalent Depth<br />
Figure 15 shows the surface modulus plots as calculated using the deflections measured at<br />
locations 0.65 and 1 (see table 2). The figure indicates that we are dealing with a weak<br />
pavement because the surface modulus values are very low and because the stiffness hardly<br />
increases from bottom to top. Only in location 1 some stiffening due to the base and top layer<br />
is visible.<br />
As shown below, different shapes <strong>of</strong> the surface modulus plot can be obtained.<br />
Surface Modulus<br />
Equivalent Depth
28<br />
The drawn line indicates a pavement where the stiffness gradually increases from bottom to<br />
top while the dashed line indicates a pavement which has layers with a low stiffness on top <strong>of</strong><br />
the subgrade. The reason for this might be stress dependent behaviour, lack <strong>of</strong> compaction,<br />
moisture effects etc.. It might very well be that the material with the lower stiffness is in fact<br />
the same material as the subgrade material. This is e.g. the case with fill material that cannot<br />
be compacted to the density <strong>of</strong> the existing subgrade.<br />
Figure 15: Surface modulus plots for locations 0.65 and 1.<br />
The surface modulus plot assists in deciding how many layers should be taken into account in<br />
the back calculation analysis. As indicated, the number <strong>of</strong> layers to be considered is not only<br />
the number <strong>of</strong> physical layers, top, base, sub-base and subgrade; one also has to take into<br />
account the fact that within one layer, sublayers may occur with a different stiffness.<br />
6.2 Back calculation <strong>of</strong> layer moduli:<br />
Back calculation <strong>of</strong> layer moduli from measured deflection bowls is done in an iterative way.<br />
The input for the calculations consists <strong>of</strong> the measured deflection pr<strong>of</strong>ile, the load geometry<br />
used to generate the deflections and the thickness <strong>of</strong> the layers. Furthermore the cores that<br />
are taken from the pavement to determine the thickness <strong>of</strong> the layers give information on the<br />
materials used and the quality <strong>of</strong> the materials.<br />
From the surface modulus plot an estimate is obtained for the modulus <strong>of</strong> the subgrade and<br />
furthermore the surface modulus plot provides information that helps to decide whether or not<br />
low stiffness sublayers should be introduced in the analysis.<br />
Then moduli values are assigned to the various layers and the deflections are calculated.<br />
Next the calculated deflections are compared with the measured ones. If the differences are<br />
too large, a new set <strong>of</strong> moduli is assumed and the deflections are calculated again. This<br />
process is repeated until there is a good match between the calculated and measured
29<br />
deflections. Normally the analysis is stopped when the difference between the measured and<br />
calculated deflections is 2%.<br />
As has been mentioned before, the iterative back calculation procedure can either be an<br />
“automatic” or a “hand operated” one. In the “automatic” procedures the computer program<br />
automatically performs the iterations while in the “hand operated procedure” it is the<br />
experienced engineer who controls the iteration process. Both procedures have their<br />
advantages. The automatic procedure is fast but might sometimes result in “funny” results. By<br />
“funny” it is meant that the set <strong>of</strong> moduli that is back calculated results in a good fit between<br />
the measured and calculated deflections but the moduli value themselves cannot be true<br />
given the type and condition <strong>of</strong> the materials in the pavement, given the temperature<br />
conditions etc.. Such results can occur because the back calculation procedure doesn’t<br />
necessarily result in a unique answer. In such cases the hand operated procedure is more<br />
powerful because the experienced engineer can adjust the moduli values to such levels which<br />
are reasonable for the type and condition <strong>of</strong> the pavement materials present and still result in<br />
a good fit between measured and calculated deflections.<br />
Problems with back calculating layer moduli can occur when the top layer is thin (< 60 mm) or<br />
when the base layer has a higher stiffness than the top layer.<br />
A golden rule in the back calculation analyses is that one never must vary the moduli values<br />
<strong>of</strong> all layers in the same time. This should be done in a step by step procedure. First <strong>of</strong> all one<br />
should try to find a modulus value for the subgrade by finding a good fit between the<br />
deflections measured and calculated at the largest distance to the load centre (see also figure<br />
14). Then one tries to fit the deflections at intermediate distance from the load centre; this will<br />
result in the moduli for the sub-base and base. Finally one should fit the deflections at the<br />
shortest distance to the load centre and the maximum deflection; this results in the modulus<br />
for the top layer.<br />
Furthermore one should realise that a good fit <strong>of</strong> the measured SCI is <strong>of</strong> great importance<br />
since this value gives a lot <strong>of</strong> information on the strain levels in the pavement. Sometimes the<br />
measured deflection pr<strong>of</strong>iles are not easy to match. In such cases one should notice that a<br />
good match <strong>of</strong> the SCI is to be preferred over a good match <strong>of</strong> the deflections measured at a<br />
greater distance from the load centre.<br />
6.3 Example:<br />
The example that will be given here is taken from the OECD FORCE test pavements that<br />
were built at the LCPC test facilities in Nantes, France. These pavements were tested by<br />
means <strong>of</strong> the accelerated load testing device <strong>of</strong> the LCPC. The aim <strong>of</strong> the project was to<br />
study pavement response and performance <strong>of</strong> three types <strong>of</strong> pavements under accelerated<br />
loading. The results <strong>of</strong> the FWD data evaluation <strong>of</strong> two test pavements are discussed here [3,<br />
4].<br />
Figure 16 shows the two pavement sections analysed.<br />
I<br />
II<br />
60 mm asphalt<br />
120 mm asphalt<br />
300 mm base<br />
300 mm base<br />
subgrade<br />
Figure 16: Structures I and II <strong>of</strong> OECD’s FORCE project.
30<br />
The clayey subgrade was covered with a 300 mm thick base on which 60 mm resp. 120 mm<br />
asphalt was placed.<br />
Figure 17 shows the maximum deflection level as measured on the top <strong>of</strong> the base as well as<br />
the maximum deflections that were measured after placing the asphalt layers. Figure 18<br />
shows the thickness <strong>of</strong> the top and base layer as determined by means <strong>of</strong> the Penetradar.<br />
Figure 17: Deflections measured on top <strong>of</strong> the base and top <strong>of</strong> the asphalt layer.<br />
Figure 18: Thickness <strong>of</strong> the layers <strong>of</strong> sections I and II.<br />
Figure 19 shows the surface modulus plots representative for both sections determined from<br />
the deflections measured on top <strong>of</strong> the completed sections.
31<br />
Figure 19: Surface modulus plots representative for the OECD FORCE sections.<br />
Three things appear from this figure. First <strong>of</strong> all the additional 60 mm asphalt which is present<br />
on section II contributes significantly to the stiffness <strong>of</strong> the pavement. Secondly, the modulus<br />
<strong>of</strong> the base and subgrade seems to be highly sensitive to the stress level. In both sections<br />
materials were used which are nominally the same. In section II however, the stresses in the<br />
base and subgrade are much smaller because <strong>of</strong> the thicker asphalt layer on top. The effect<br />
<strong>of</strong> the lower stress level in base and subgrade results in higher values for the surface<br />
modulus.<br />
Furthermore one should realise that the plot was made based on measurements which were<br />
taken at a temperature <strong>of</strong> approximately 6 0 C which means that the stiffness <strong>of</strong> the asphalt<br />
layer was fairly high and the stress levels in the base and subgrade are rather low .<br />
Thirdly the figure shows that on top <strong>of</strong> the subgrade, layers are present with a much lower<br />
stiffness. It appeared that a fill had to be placed in order to have the pavement surface at the<br />
right level. The fill was made with the subgrade material but problems during compaction had<br />
occurred. This lack <strong>of</strong> density <strong>of</strong> the fill has <strong>of</strong> course a direct effect on the density and so the<br />
stiffness <strong>of</strong> the base layer placed on top. The low surface modulus values could, in this case,<br />
easily be explained from the construction history.<br />
Based on this knowledge it was decided to divide the base layer in two sublayers, each being<br />
50% <strong>of</strong> the total base thickness, and to divide the subgrade in two sublayers. This was done<br />
by assuming a thickness <strong>of</strong> 500 mm <strong>of</strong> low stiffness subgrade material on top <strong>of</strong> the stiff deep<br />
subgrade. The selection <strong>of</strong> this thickness is based on experience, sometimes a thickness <strong>of</strong><br />
1000 mm is chosen.<br />
All in all it means that for the back calculation analysis, the pavement was divided in 5 layers<br />
(top layer, two base layers, two subgrade layers).<br />
The results <strong>of</strong> the analysis are shown in table 5.
32<br />
Section I<br />
Temp Force Layer E-mod Position Meas. Calc. Diff.<br />
Thickn. Defl. Defl.<br />
[ 0 C] [kN] [mm] [Mpa] [mm] [µm] [µm] [%]<br />
6.4 57.0 56 15980 0 1049 1050 0.1<br />
146 106 300 655 655 0<br />
146 150 600 318 318 0<br />
500 37 900 158 163 3.2<br />
171 1200 92 92 0<br />
1500 63 60 -4.8<br />
1800 46 46 0<br />
Section II<br />
Temp Force Layer E-mod Position Meas. Calc. Diff.<br />
Thickn. Defl. Defl.<br />
[ 0 C] [kN] [mm] [Mpa] [mm] [µm] [µm] [%]<br />
6.8 58.0 145 10514 0 415 417 0.5<br />
130 117 300 329 326 -0.9<br />
130 239 600 217 216 -0.5<br />
500 48 900 133 135 1.5<br />
276 1200 83 83 0<br />
1500 50 51 2.0<br />
1800 34 33 -2.9<br />
Table 5: Results <strong>of</strong> the back calculation analysis for the OECD FORCE sections.<br />
It should be noted that the FORCE examples are complicated ones; normally one has to deal<br />
with less complicated deflection pr<strong>of</strong>iles.<br />
6.4 Computer program:<br />
As had been mentioned before, several computer programs are available that allow the<br />
values for the layer moduli to be backcalculated in an automatic way. One <strong>of</strong> those programs<br />
is the program MODCOMP 5 developed by pr<strong>of</strong>. Irwin <strong>of</strong> the Cornell university in the USA.<br />
The program can be found on the cd which is part <strong>of</strong> these lecture notes. At the end <strong>of</strong> these<br />
lecture notes an appendix, appendix I, is given which contains a description <strong>of</strong> how the<br />
program has to be used.<br />
7. Analysis <strong>of</strong> Benkelman beam and Lacroix deflectograph<br />
deflection bowls:
33<br />
BB and LD measurements are usually related to empirical evaluation and overlay design<br />
methods. However an elegant procedure has been developed [5] which allows these<br />
deflection readings also to be used for back calculation purposes. The procedure is correcting<br />
the measured deflections that might be influenced by the movement <strong>of</strong> the support system to<br />
true deflections. One drawback <strong>of</strong> the method is that it doesn’t take into account viscous<br />
effects that might occur due to the slow speed <strong>of</strong> the loading vehicle.<br />
The basis <strong>of</strong> the method is the Hogg model which consists <strong>of</strong> a plate (E 1 , h, µ 1 ) resting on an<br />
elastic foundation (E 2 , µ 2 ). The assumption that the top layer behaves like a plate implies that<br />
no vertical displacements are developed in this layer. The characteristics <strong>of</strong> the pavement<br />
structure are characterised by:<br />
D = E 1 . h 3 1 / {12 . (1 - µ 2 1 )} stiffness <strong>of</strong> the top layer(s)<br />
R = 2 . E 2 . (1 - µ 2 ) / {(1 + µ 2 ) . (3 - 4µ 2 )} reaction <strong>of</strong> the subgrade<br />
L 0 = ( D / R ) 0.33 critical length<br />
The shape <strong>of</strong> the deflection pr<strong>of</strong>iles is described following<br />
d 0 / d r – 1 = γ + α . (r / L 0 ) β<br />
Where: d 0<br />
d r<br />
= maximum deflection,<br />
= deflection at distance r from the load centre.<br />
This equation is graphically represented in figure 20. Using the specific dimensions <strong>of</strong> both<br />
the deflectograph and the BB (figure 21) as well as the above mentioned pavement<br />
characteristics, true deflection pr<strong>of</strong>iles as well deflection pr<strong>of</strong>iles that would be measured were<br />
calculated; typical results are shown in figure 22.<br />
Figure 20: Graphical representation <strong>of</strong> an equation used to describe<br />
the shape <strong>of</strong> deflection pr<strong>of</strong>iles.<br />
In the development <strong>of</strong> the model the following values were assumed for the wheel and axle<br />
loads as well as contact pressures.<br />
Axle P fa /P ra P 1 I 1 W 1 σ 1 P 2 I 2 W 2 σ 2 -σ 1 P axle
34<br />
[N] [mm] [mm] [MPa] [N] [mm] [mm] [MPa] [N]<br />
rear 0.6 1750 250 177 0.05 21750 192 136 1.062 94000<br />
front 0.6 336o 320 220 0.061 25040 270 186 0.635 56800<br />
Figure 21: Dimensions <strong>of</strong> the LD and BB as well as <strong>of</strong> the loading vehicle.
35<br />
Figure 22: Recorded and true LD (lac) and BB (ben) deflections.
36<br />
Based on these calculations, evaluation diagrams were developed which allow true<br />
deflections to be calculated from the measured LD and BB deflections. These diagrams are<br />
shown in figure 23. In this figure some abbreviations are used which are not explained in the<br />
figure; the meaning there<strong>of</strong> is described hereafter.<br />
D CGRA = maximum deflection according to the Canadian Good Roads Association method,<br />
D AI = maximum deflection according to the Asphalt Institute method,<br />
D TRRL = maximum deflection according to the Transport and Road Research Laboratory<br />
method.<br />
The method will be illustrated with some examples. Let us assume that a maximum deflection<br />
was measured with the LD <strong>of</strong> 393 µm. From the measured deflection pr<strong>of</strong>ile it was determined<br />
that the distance at which the deflection was 50% <strong>of</strong> the maximum deflection (L x , x = 50%)<br />
was 368 mm. From the evaluation charts one can derive that L 0 = 178 mm and the ratio<br />
D 00 /D lac = 1.226. This means that the true maximum deflection is 482 µm.<br />
The ratio D 00 . R / P ra equals 0.47 and with a rear axle load P ra = 91.6 kN this results in an R<br />
value <strong>of</strong> 89.5 Mpa and a subgrade modulus <strong>of</strong> 149 Mpa (assuming µ 2 = 0.35). Since L 0 and R<br />
are known, D can be calculated.<br />
Furthermore we can determine the maximum BB deflection that would be obtained following<br />
the TRRL procedure. One observes that D TRRL /D lac = 0.98 which means that the value that<br />
has to be used in the TRRL evaluation procedure equals 385 µm.<br />
It is stressed that figure 23 is only applicable for the load and LD and BB geometries shown in<br />
figure 21.<br />
One should keep in mind that the moduli obtained in this way are quasi-static moduli. It is a<br />
well-known fact however that for most materials there is a difference between the static and<br />
the dynamic modulus. From an extensive correlation study it was observed that the subgrade<br />
modulus as determined by means <strong>of</strong> the BB or LD and the FWD relate to each other<br />
following:<br />
1.4576 (t – 0.255)<br />
E FWD / E lac = 10<br />
Where: t<br />
= loading time <strong>of</strong> the LD or BB [s].
37<br />
Figure 23: Evaluation chart to determine true LD and BB deflections from measured<br />
deflections.
38<br />
8. Estimation <strong>of</strong> the remaining pavement life using an empirical<br />
based approach:<br />
A number <strong>of</strong> empirical pavement evaluation and overlay design methods have been<br />
developed in time. Well known are the methods developed by the Asphalt Institute and the<br />
Transport and Road Research Laboratory. Although extensively used all over the world, this<br />
author believes strongly that one has to be very cautious in using these methods for situations<br />
they have not been developed for. The hart <strong>of</strong> the TRRL method e.g. are the performance<br />
charts developed for several pavement types. An example <strong>of</strong> such a chart is given in figure 24<br />
[6]. For the sake <strong>of</strong> completeness the load and load configuration used for the BB<br />
measurements according to the TRRL procedure are shown in figure 25.<br />
The point is that pavement performance is dependent on the traffic, the materials and<br />
structures used, and the climate, all <strong>of</strong> them are typical British in case <strong>of</strong> the TRRL method.<br />
This means that the chances are very small that the method can be used without modifications<br />
in countries like e.g. Pakistan or Yemen where traffic, climate, and materials are<br />
significantly different from UK conditions.<br />
Another severe problem with the TRRL method is that an important input parameter, being<br />
the number <strong>of</strong> equivalent 80 kN single axles that have passed the pavement, is not known in<br />
many cases.<br />
Nevertheless the author also believes that the TRRL method can be used in other conditions<br />
as well provided this is done by making the evaluation charts dimensionless. The procedure<br />
to do so is outlined hereafter.<br />
Let us define the following variables:<br />
DeltaDef n<br />
DeltaDef c<br />
n<br />
N c<br />
= increase in deflection since time <strong>of</strong> construction,<br />
= difference between the initial deflection and the critical deflection, this latter<br />
value depends on the probability <strong>of</strong> achieving life that is used to define pavement<br />
failure,<br />
= applied number <strong>of</strong> load repetitions,<br />
= number <strong>of</strong> load repetitions at which critical deflection level is reached.<br />
Work presented in [7] has shown that performance curves like the one presented in figure 24<br />
can be written in a dimensionless shape following:<br />
DeltaDef n / DeltaDef c<br />
= (n / N c ) b<br />
The shape parameter b seemed to be dependent on the initial deflection level following:<br />
for granular bases: b<br />
0.4639<br />
= 0.06 Def 0<br />
for bituminous bases: b<br />
0.7186<br />
= 0.0185 Def 0<br />
An important question in all this is how DeltaDef c and the initial deflection Def 0 are related.<br />
From the analysis in [7] it appeared that for pavements with granular bases and accepting<br />
50% <strong>of</strong> achieving life as the failure condition, the ratio DeltaDef 0 / Def 0 can be expressed as<br />
follows:<br />
DeltaDef c / Def 0 = 0.4767 – 0.000299 Def 0<br />
Where: Def 0<br />
= maximum deflection measured with the BB according to the TRRL<br />
procedure [µm] <strong>of</strong> the pavement when not subjected tot traffic loads.<br />
For bituminous bases this relation can be written as:<br />
DeltaDef c / Def 0 = 0.34833 – 0.000198 Def 0<br />
If we don’t know the number <strong>of</strong> load repetitions applied to the pavement, how do we derive<br />
DeltaDefn? It will be shown hereafter that we can obtain that value in a relatively simple way.
39<br />
Figure 24: Example <strong>of</strong> a TRRL performance chart.
40<br />
Figure 25: Load configuration used for the BB measurements according to TRRL.
41<br />
Normally BB measurements are only taken in the wheel tracks. These values are in fact the<br />
Def n values since that pavement area has been subjected to n load repetitions. If we also take<br />
deflection measurements between the wheel tracks, then we get a good estimate <strong>of</strong> the<br />
flexural stiffness <strong>of</strong> that part <strong>of</strong> the pavement that is not subjected to traffic loads. These<br />
deflections can be taken as representative for Def 0 .<br />
Assume that the deflection measured between the wheel tracks is 350 µm and that the<br />
deflection in the wheel tracks is 390 µm. The pavement has an unbound base. Then we arrive<br />
to:<br />
DeltaDef n = 390 – 350 = 40<br />
and<br />
DeltaDef c / Def 0 = 0.4767 – 0.000299 x 350 = 0.372<br />
so<br />
DeltaDef c = 0.372 x 350 = 130<br />
We also calculate:<br />
b = 0.91<br />
so<br />
DeltaDef n / DeltaDef c = (n / N) b<br />
40 / 130 = (n / N) 0.91<br />
n / N = 0.27<br />
Normally road authorities are not interested in a damage ratio or a remaining pavement life<br />
expressed in a number <strong>of</strong> allowable load repetitions but much more in a remaining life in<br />
years. This can be estimated in the following way.<br />
Assume the traffic composition has not changed in time and for reasons <strong>of</strong> simplicity we also<br />
assume that no growth in the number. <strong>of</strong> vehicles per day has taken place. This means that<br />
the area indicated in figure 26 is representative for the cumulative amount <strong>of</strong> traffic n that has<br />
passed the road during time period t.<br />
Traffic intensity<br />
n<br />
N<br />
t<br />
T<br />
Time<br />
Figure 26: Procedure to estimate the remaining life in years from the n/N ratio.<br />
In the same way the allowable number <strong>of</strong> load repetitions N is arrived after T years. From this<br />
simple example it is clear that in this case:<br />
t / T = n / N
42<br />
If we assume e.g. that the deflection survey <strong>of</strong> the above mentioned example was taken 5<br />
years after the pavement has been put in service, we calculate that:<br />
t / T = n / N = 0.27, t = 5 so T = 18 years and the remaining life is 13 years.<br />
The procedure described above cannot be used if variations occur in the cross section <strong>of</strong> the<br />
pavement due to variations in the thickness <strong>of</strong> the layers and because different types <strong>of</strong><br />
material are used over the width <strong>of</strong> the pavement. Those conditions can occur if e.g. ruts are<br />
filled, the pavement is widened or <strong>of</strong> mill and fill operations have been carried out.<br />
Of course unknown changes in the traffic growth, composition <strong>of</strong> the traffic and the axle loads<br />
have also a negative effect on the results obtained by the procedure described above.
43<br />
9. Mechanistic procedures for remaining life estimations and<br />
overlay design:<br />
Mechanistic overlay design methods are based on the analysis <strong>of</strong> stresses and strains in the<br />
existing pavement. The calculated values are then compared with the allowable values and<br />
based on this comparison, conclusions are drawn with respect to the most appropriate<br />
maintenance strategy.<br />
One <strong>of</strong> the most important differences between a mechanistic and an empirical approach is<br />
the fact that in the latter, the interactions between stresses, strains, strength, fatigue,<br />
resistance to deformation etc are not visible; they are hidden in the procedure. This makes<br />
the empirical methods unreliable as soon as different materials and structures are used than<br />
those for which the procedure was developed. On the other hand empirical methods are<br />
based on observed performance which is an advantage over mechanistic models especially if<br />
these models are used in a too simplistic way.<br />
The big advantage <strong>of</strong> the mechanistic models <strong>of</strong> course is that they are based on sound<br />
analyses <strong>of</strong> stresses, and strength <strong>of</strong> the materials used.<br />
9.1 Basic principles:<br />
In classical mechanistic overlay design methods, only the strain levels in the existing<br />
pavement are considered as well as the required reduction in those strain levels in order to<br />
obtain the required extension <strong>of</strong> the pavement life. The overlay is designed in such a way that<br />
the necessary reduction <strong>of</strong> the strain level in the existing pavement is realised. The effect <strong>of</strong><br />
damage in the existing pavement on the performance <strong>of</strong> the overlay is normally not<br />
considered. This makes the classical mechanistic methods rather straightforward.<br />
The following steps can be recognised. First <strong>of</strong> all the moduli <strong>of</strong> the various layers are<br />
calculated in the way described earlier. Secondly the asphalt layer modulus is corrected to a<br />
reference temperature; for Dutch conditions this is 18 0 C. This correction can be applied using<br />
the asphalt mix stiffness vs temperature chart as developed by Shell [8]; this chart is given in<br />
figure 27. Then the stresses and strains due to an equivalent single axle load are calculated.<br />
The tensile strain calculated at the bottom <strong>of</strong> the asphalt layer is introduced in a fatigue<br />
relation and the allowable number <strong>of</strong> load repetitions is calculated. The same is done for the<br />
subgrade strain. The amount <strong>of</strong> damage, being the ratio n/N, is then calculated where n is the<br />
applied number <strong>of</strong> load repetitions and N is the allowable number. The remaining life ratio is<br />
calculated as 1 – n/N.<br />
If the pavement life should be extended, the number <strong>of</strong> load repetitions that are expected<br />
needs to be calculated. This results in a figure n + ∆n. Then the pavement thickness should<br />
be increased in order to decrease the tensile strain at the bottom <strong>of</strong> the asphalt layer and to<br />
increase the allowable number <strong>of</strong> load repetitions from N to N + ∆N. The appropriate overlay<br />
thickness is obtained if:<br />
1 – n/N = ∆n / (N + ∆N)<br />
The procedure is illustrated with an example.<br />
Assume that the tensile strain that is calculated at the bottom <strong>of</strong> the asphalt layer due to a<br />
standard axle load equals:<br />
ε = 2 . 10 -4 [m / m]<br />
Fatigue tests carried out on the material resulted in the following fatigue relation.<br />
Log N = -13 – 5 . log ε<br />
The allowable number <strong>of</strong> load repetitions is then N = 312500.<br />
If we assume that the pavement has already carried 200000 standard loads, then the damage<br />
ratio equals n / N = 0.64.
44<br />
Figure 27: Relationship between the stiffness <strong>of</strong> asphalt mixtures and temperature for a<br />
loading time <strong>of</strong> 0.02 s.
45<br />
The remaining life ratio equals:<br />
1 – n/N = 0.36<br />
Assume that another 500000 standard axles should be carried by the pavement. This means<br />
that:<br />
∆n = 500000<br />
The tensile strain at the bottom <strong>of</strong> the asphalt layer should be decreased to a level where N +<br />
∆N load repetitions can be taken. This value is calculated from:<br />
N + ∆N = ∆n / (1 – n/N) = 500000 / 0.36 = 1.39 . 10 6<br />
By using the fatigue relation we calculate that this new number <strong>of</strong> allowable load repetitions<br />
can be obtained if the strain is reduced to ε = 1.48 . 10 -4 [m / m]. This means that the overlay<br />
needs such a thickness that the strain at the bottom <strong>of</strong> the existing asphalt layer is reduced to<br />
this value.<br />
The approach described here gives rise to some comments. It is quite clear that a very large<br />
overlay thickness is needed when the ratio n/N approaches 1. The reason is that the fatigue<br />
relation is based on beam fatigue tests. This implies that failure means that the specimen is in<br />
two parts if the allowable number <strong>of</strong> load repetitions is reached (at least in load controlled<br />
fatigue tests) which implies that the beam lost its functionality. In reality however the cracked<br />
asphalt slab is still supported by the base and other layers; the cracked slab is still functional.<br />
All this indicates that the procedure results in unrealistic designs in case <strong>of</strong> high values <strong>of</strong> the<br />
damage ratio.<br />
Furthermore the example indicates that in general fairly small strain reductions are needed<br />
which results in rather thin overlays.<br />
Because the overlay design is only based on the reduction <strong>of</strong> the strain level in the existing<br />
pavement, only the thickness and the stiffness <strong>of</strong> the overlay are <strong>of</strong> importance. From practice<br />
one knows that this cannot be true. The existing pavement normally exhibits a certain amount<br />
<strong>of</strong> cracking when an overlay is applied and these cracks tend to propagate through the<br />
overlay. This means that reduction <strong>of</strong> the strain level in the existing pavement cannot be the<br />
only design criterion for overlays; also the resistance to crack reflection <strong>of</strong> the overlay should<br />
be considered. This aspect will be discussed later in these lecture notes.<br />
Finally the procedure described above doesn’t take into account the large amount <strong>of</strong> variation<br />
in deflections and material characteristics that can occur in pavements.<br />
9.2 Extension <strong>of</strong> the basic principles:<br />
In this section an extension <strong>of</strong> the basic principles presented in the previous section will be<br />
given. The extension is dealing with the fact that in case the n/N ratio reaches 1, realistic<br />
values for the overlay thickness should still be obtained. Furthermore the extension takes into<br />
account the variation in deflection level and material characteristics that occur in practice.<br />
If there was no variation in deflection level along the section under consideration, and if there<br />
was no variation in the thickness <strong>of</strong> the pavement layers, then there would be no variation in<br />
the elastic modulus <strong>of</strong> the layers and there would be no variation in strain level. If there also<br />
would be no variation in the fatigue characteristics, then the pavement would fail precisely at<br />
the number <strong>of</strong> load repetitions predicted and the pavement would fail from one moment to the<br />
other. This particular behaviour is illustrated in figure 28a. Such a performance however is<br />
never observed, pavements don’t collapse in the way indicated by this figure. In reality a more<br />
gradual deterioration is observed as is indicated by figure 28b.<br />
If we use the mean strain level <strong>of</strong> figure 28b as design criterion and we use this strain value<br />
together with the mean fatigue characteristic (the solid fatigue line in figure 28b) then we<br />
determine the mean number <strong>of</strong> load repetitions. At that number <strong>of</strong> load repetitions there is a<br />
50% chance that the pavement is failed. It can easily be shown that this means that 50% <strong>of</strong><br />
the trafficked pavement surface shows cracking. Because <strong>of</strong> the variation in the fatigue
46<br />
resistance, some parts <strong>of</strong> the pavement will live longer and some shorter. Furthermore the<br />
strain level in some parts <strong>of</strong> the pavement are lower than at other parts because <strong>of</strong> e.g. the<br />
variation in thickness. The variation in strain level combined with the variation in fatigue<br />
resistance results in a variation <strong>of</strong> pavement life over the section considered. This is shown in<br />
figure 28b. Figure 28b also clearly shows that pavements don’t fail in a catastrophic way but<br />
show a gradual deterioration. The overlay design procedure should take this into account.<br />
Log n<br />
Thickness <strong>of</strong> the pavement layers<br />
and the layer moduli are constant,<br />
so strain is constant.<br />
N<br />
Fatigue<br />
characteristics<br />
show no<br />
variation<br />
Condition<br />
Logε<br />
N<br />
Log n<br />
Figure 28a: Condition deterioration when there is no variation in pavement properties.<br />
Log n<br />
Fatigue characteristics<br />
show variation<br />
Thickness and modulus <strong>of</strong><br />
the layers show variation so<br />
strain is variable.<br />
N<br />
Condition<br />
Log ε<br />
50% failed and<br />
50% sound Mean strain<br />
level<br />
N<br />
Log n<br />
Figure 28b: Condition deterioration when there is variation in pavement properties.
47<br />
In order to take the variation <strong>of</strong> input parameters into account, probabilistic analyses should<br />
be made. Several procedures are available to determine which combinations <strong>of</strong> layer<br />
thickness, layer modulus and fatigue relation should be used in the calculations in order to enable<br />
to estimate the variation in strain level and pavement life. A far more effective approach<br />
is to make use <strong>of</strong> simple relations that exist between e.g. the surface curvature <strong>of</strong> the deflection<br />
pr<strong>of</strong>ile on one hand and the tensile strain at the bottom <strong>of</strong> the asphalt layer, the tensile<br />
strain at the bottom <strong>of</strong> the bound base or the vertical compressive strain at the top <strong>of</strong> the<br />
subgrade, on the other hand. This will be shown in the following part.<br />
Let us consider the bending <strong>of</strong> a slab as shown in figure 29.<br />
Figure 29: Bending moments in a slab.<br />
The magnitude <strong>of</strong> the bending moments can be calculated a follows:<br />
M 1x = E h 3 ( 1/R x + µ 1/R y ) / 12 ( 1 - µ 2 ) and M 1y = E h 3 ( 1/R y + µ 1/R x ) / 12 ( 1 - µ 2 )<br />
Where: M 1x = bending moment in the x direction,<br />
M 1y = bending moment in the y direction,<br />
R x = radius <strong>of</strong> curvature in the x direction,<br />
R y = radius <strong>of</strong> curvature in the y direction,<br />
E = elastic modulus <strong>of</strong> the slab,<br />
h = thickness <strong>of</strong> the slab,<br />
µ = Poisson’s ratio.<br />
The stresses can be calculated as σ x = 6 M 1x / h 2 and σ y = 6 M 1y / h 2 . If we are dealing with a<br />
circular load in the centre <strong>of</strong> a large slab, R x = R y and σ x = σ y .<br />
Because: ε x = ( σ x - µ σ y ) / E = ( 1 - µ ) σ x / E we can now develop a relation between the<br />
curvature and the tensile strain by substitution <strong>of</strong> σ x by M 1x and by substitution <strong>of</strong> M 1x by the<br />
equation that relates the bending moment to the radius <strong>of</strong> curvature. We obtain then:<br />
ε x = 6 ( 1 - µ ) M / E h 2 = h / 2 R x ≅ 1 / R x<br />
This indicates that the strain at the bottom <strong>of</strong> the asphalt layer is related to the radius <strong>of</strong><br />
curvature <strong>of</strong> the deflection bowl due to the applied load.<br />
Extensive research [9,10], has shown that there exists a direct relation between the tensile<br />
strain at the bottom <strong>of</strong> the asphalt layer and the surface curvature index following:<br />
log ε<br />
= C 0 + C 1 log SCI<br />
For pavements with an asphalt thickness ≥ 150 mm the relation becomes:
48<br />
Log ε = 0.481 + 0.881 log SCI 300<br />
Where: SCI 300 = difference in maximum deflection and the deflection measured at a distance<br />
<strong>of</strong> 300 mm,<br />
ε = tensile strain at the bottom <strong>of</strong> the asphalt layer [µm / m].<br />
This relation is shown in figure 30.<br />
Figure 30: Relation between SCI 300 and the tensile strain at the bottom <strong>of</strong> the asphalt layer.<br />
Since log N = A 0 + A 1 log ε, we can write:<br />
log N = A 0 + A 1 C 0 + A 1 C 1 log SCI<br />
It can be shown that the variance <strong>of</strong> log N (the squared standard deviation <strong>of</strong> log N) can be<br />
calculated from:<br />
S 2 logN<br />
= A 1 2 . C 1 2 . S 2 logSCI + S 2 l<strong>of</strong><br />
Where: S logSCI = standard deviation <strong>of</strong> the logarithm <strong>of</strong> the measured SCI’s (see also table 2)<br />
S l<strong>of</strong> = standard deviation <strong>of</strong> log N at a given log ε; it describes the variation in<br />
fatigue life.<br />
We can now write:<br />
log N P = log N – u . S logN<br />
Where: log N = logarithm <strong>of</strong> the mean number <strong>of</strong> load repetitions to failure,<br />
log N P = logarithm <strong>of</strong> the number <strong>of</strong> load repetitions to failure at level <strong>of</strong> confidence P<br />
u = factor from the tables for the normal distribution related to confidence<br />
level P
49<br />
From the equations given above it becomes clear that the quality <strong>of</strong> the predictions increases<br />
when S logN decreases. This means that S logSCI and S l<strong>of</strong> should be as low as possible. A low<br />
S logSCI stresses the need to pay ample attention to the discrimination <strong>of</strong> homogeneous subsections.<br />
The only factor that cannot be easily assessed is the variation in fatigue characteristics.<br />
Although this value can be estimated (see e.g. lecture notes CT4850 part III<br />
Asphaltic Materials) if mixture composition data are available, extensive fatigue testing has<br />
shown that S l<strong>of</strong> = 0.25 is a reasonable first estimate.<br />
Overlay calculations based on the confidence level or probability <strong>of</strong> survival level P are made<br />
in the following way. As is shown above, the number <strong>of</strong> load repetitions until a certain<br />
probability <strong>of</strong> survival level P 1 is reached can be calculated using:<br />
log N P1 = A 0 + A 1 C 0 + A 1 C 1 log SCI 1 – u 1 S logN<br />
If the pavement life has to be extended to N + ∆N load repetitions and after that number <strong>of</strong><br />
load repetitions, the probability <strong>of</strong> survival should be P 2 , the needed SCI level to achieve this<br />
can be calculated using:<br />
Log (N + ∆N) P2 = A 0 + A 1 C 0 + A 1 C 1 log SCI 2 – u 2 S log(N+∆N)<br />
After subtracting <strong>of</strong> both equations one obtains:<br />
Log {N P1 / (N + ∆N) P2 } = A 1 C 1 log {SCI 1 / SCI 2 } – u 1 S logN + u 2 S log(N+∆N)<br />
By writing<br />
N P1 / (N + ∆N) P2 = 1 / X<br />
I 1 = 10**(u 1 S logN )<br />
I 2<br />
= 10**(u 2 S log(N+∆N)<br />
We arrive to<br />
Log {1 / X} = A 1 C 1 log {SCI 1 / SCI 2 } – log I 1 + log I 2<br />
This can be written as:<br />
SCI 2<br />
= SCI 1 (X I 2 / I 1 ) 1/A1C1<br />
In these equations SCI 1 can be considered as the SCI before the overlay is placed and SCI 2<br />
as the SCI after overlaying. In the same way S logN is valid before overlaying and S log(N+∆N) is<br />
valid after the overlay is placed.<br />
We still need equations to predict the SCI 2 in relation to the overlay thickness and stiffness as<br />
well as the SCI 1 . Furthermore an equation is needed to predict S logSCI2 because from this<br />
value S log(N+∆N) can be calculated. These equations are given below:<br />
Log SCI 2 = b 0 + b 1 E o + b 2 h o + b 3 log SCI 1 + b 4 E o log SCI 1 + b 5 h o log SCI 1<br />
+ b 6 h o log E o log SCI 1<br />
S 2 logSCI2<br />
= {b 1 + b 4 log SCI 1 + b 6 h o log SCI 1 / E o } 2 S 2 Eo<br />
+ {b 2 + b 5 log SCI 1 + b 6 log E o log SCI 1 } 2 S 2 ho<br />
+ {b 3 + b 4 E o + b 5 h o + b 6 h o log E o } 2 S 2 logSCI1<br />
Where: SCI 1<br />
SCI 2<br />
h o<br />
E o<br />
= surface curvature index (d 0 – d 300 ) before overlaying [µm]<br />
= surface curvature index (d 0 – d 300 ) after overlaying [µm]<br />
= overlay thickness [mm]<br />
= elastic modulus <strong>of</strong> the overlay [Mpa]<br />
b o = -0.0506<br />
b 1 = 1.178 10 -5<br />
b 2 = 0.0094
50<br />
b 3 = 1.0153<br />
b 4 = -7.73 x 10 -6<br />
b 5 = -3.778 x 10 -4<br />
b 6 = -1.4971 x 10 -3<br />
With respect to the procedures discussed above, it is once again stressed that they are based<br />
on limiting the strains in the existing pavement. Also it should be noted that it is assumed that<br />
the overlay is fully bonded to the existing pavement. This however is not always the case<br />
especially in cases where, because <strong>of</strong> reasons to be discussed later, an interface layer is<br />
placed between the overlay and the existing pavement allowing the overlay to behave more<br />
or less independently from the existing pavement. Furthermore the effect <strong>of</strong> cracks in the<br />
existing pavement on the performance <strong>of</strong> the overlay is not taken into account. This effect<br />
however cannot be ignored in cases where the existing pavement shows moderate to severe<br />
cracking. Also this will be discussed in a later chapter.<br />
One important point remains to be discussed which is the estimation <strong>of</strong> the probability <strong>of</strong><br />
survival <strong>of</strong> the existing pavement P.<br />
Without going into all the details (for these the reader is referred to [9]), it can be shown that P<br />
can be estimated from the ratio <strong>of</strong> the surface curvature index measured in and between the<br />
wheel tracks following:<br />
P<br />
= (SCI b / SCI in ) q<br />
Where: SCI b = SCI measured between the wheel tracks (d 0 – d 500 )<br />
SCI in = SCI measured in the wheel tracks (d o – d 500 )<br />
q = dependent on the type <strong>of</strong> structure taking a value between 0.6 and 0.4 for<br />
pavements with an unbound base and between 0.7 and 0.5 for pavements<br />
with a bound base; the higher values are for a 150 mm thick base, the<br />
lower values are for a 300 mm thick base.<br />
If for reasons mentioned earlier, the SCI ratio cannot be used, P can also be estimated from<br />
the percentage <strong>of</strong> the wheel track area that shows cracking following:<br />
P = 1 – percentage cracked area / 100<br />
It should be noted that a substantial part <strong>of</strong> the cracking that is visible at the pavement is<br />
surface cracking. This type <strong>of</strong> cracking is initiated at the pavement surface and normally<br />
progresses downwards to approximately 40 mm. It is clear that this type <strong>of</strong> cracking cannot be<br />
associated to the fatigue type cracking for which the above mentioned procedures are developed.<br />
All in all this means that P values estimated in this way might be too high, the real<br />
structural condition might be better than it appears from the P value estimated in this way.<br />
If P is known as well as S logN , the damage ratio n / N can easily be determined using the<br />
equations given above or by means <strong>of</strong> figure 31.
51<br />
Figure 31: Relation between P, S logN and n / N.
52<br />
10. Extension <strong>of</strong> the simplified procedure to estimate critical<br />
stresses and strains:<br />
In many cases the thickness <strong>of</strong> the pavement layers is unknown or highly variable. In that<br />
case a pavement evaluation that relies on the back calculation <strong>of</strong> layer moduli is less effective<br />
and estimation <strong>of</strong> critical stresses and strains using simple methods as described in the<br />
previous chapter are extremely useful. In a joint research effort by the Government Service<br />
for Land and Water Use (LWU) <strong>of</strong> the Dutch Ministry <strong>of</strong> Agriculture, Nature Management and<br />
Fisheries, KOAC consultants and the <strong>Delft</strong> University <strong>of</strong> Technology, a pavement evaluation<br />
and overlay design method was developed which completely relies on such simple relations<br />
[11]. The hart <strong>of</strong> the method being the relations to estimate the stresses and strains will be<br />
reproduced here.<br />
The basis <strong>of</strong> the method is the large number <strong>of</strong> calculations on stresses and strains in on four<br />
layer pavement systems due to a FWD load. The calculated values are schematically shown<br />
in figure 32.<br />
FWD load 50<br />
kN, φ = 300 mm<br />
Asphalt<br />
Unbound or<br />
Bound<br />
Base<br />
Subbase<br />
Subgrade<br />
1. Tensile strain at<br />
pavement surface.<br />
2. Tensile strain at<br />
bottom asphalt.<br />
3. Compressive<br />
stresses in top<br />
unbound base.<br />
4.Tensile strain at<br />
bottom bound base<br />
5. Vertical compressive<br />
strain at<br />
top subbase.<br />
6. Vertical compressive<br />
strain at<br />
top subgrade.<br />
Figure 32: Analysed structures and locations where stresses and strains were calculated.<br />
The analyses have been made for pavements with E asphalt > E base > E subbase > E subgrade and for<br />
pavements where E subbase < E subgrade .<br />
One will notice that the equations are much more complex than the ones described until now.<br />
The reason for this is that thin asphalt surfacings had to be considered and for those<br />
pavements the simple relations between e.g. the SCI and the tensile strain at the bottom <strong>of</strong><br />
the asphalt layer are not valid anymore.<br />
Also one will notice that in a number <strong>of</strong> cases information on the thickness <strong>of</strong> some layers is<br />
required. From the type <strong>of</strong> equation one will notice however that the influence <strong>of</strong> the thickness<br />
information on the magnitude <strong>of</strong> the estimated strains and stresses is limited.<br />
10.1 Relations between deflection bowl parameters and stresses and strains at various<br />
locations in the pavement:<br />
From the extensive analyses, the following results were obtained:<br />
Tensile strain at the bottom <strong>of</strong> the asphalt layer:<br />
log ε r1,0 = -1.06755 + 0.56178 log h 1 + 0.03233 log d 1800 + 0.47462 log SCI 300<br />
+ 1.15612 log BDI – 0.68266 log BCI
53<br />
Where: ε r1,0 = maximum horizontal strain at the bottom <strong>of</strong> the asphalt layer [µm/m]<br />
h 1 = thickness <strong>of</strong> the asphalt layer [mm]<br />
d r = deflection at distance r <strong>of</strong> the load centre [µm]<br />
SCI 300 = d 0 – d 300 [µm]<br />
BDI = base damage index = d 300 – d 600 [µm]<br />
BCI = base curvature index = d 600 – d 900 [µm]<br />
Tensile strain at pavement surface:<br />
Many cracks that are visible at the pavement surface are initiated at the top <strong>of</strong> the pavement.<br />
These cracks are the result <strong>of</strong> the complex stress distribution under tyres; especially the<br />
horizontal shear stresses are <strong>of</strong> importance. These are not caused by braking but by the fact<br />
that free horizontal expansion <strong>of</strong> the tyre when loaded can not occur due to friction forces. In<br />
order to take these stresses into account the stress conditions under a tyre were modelled in<br />
the way shown in figure 33.<br />
Position [mm] Radius Stress [kPa]<br />
Load X y [mm] X y Z<br />
1 +60 +90 52.57 -200 0 +400<br />
2 +70 0 42.57 -200 0 0<br />
3 +60 -90 52.57 -200 0 +400<br />
4 -60 +90 52.57 -200 0 +400<br />
5 -70 0 42.57 -200 0 0<br />
6 -60 -90 52.57 -200 0 +400<br />
7 +90 0 22.57 -180 0 0<br />
8 -90 0 22.57 -180 0 0<br />
9 0 0 112.57 0 +150 +750<br />
10 0 0 50.00 0 -60 +750<br />
Figure 33: Schematisation <strong>of</strong> the contact stresses under a tyre.<br />
The following relation was found:<br />
ε r1,b = 194.895 – 20.7769 SCI 300<br />
0.5<br />
Where: ε rt,b<br />
= tensile strain at pavement surface [µm/m]
54<br />
Compressive vertical strain at the top <strong>of</strong> the unbound base:<br />
The vertical compressive strain at the top <strong>of</strong> the subgrade is a well known design criterion.<br />
Such a criterion doesn’t exist for e.g. unbound base materials. Nevertheless it can be<br />
expected that if the compressive strains at the top <strong>of</strong> the unbound base become too large,<br />
excessive deformations might develop there as well.<br />
In order to develop an estimation procedure for the compressive strain at the top <strong>of</strong> the<br />
unbound base, Alemgena [25] analysed the same structures as were analysed by van Gurp.<br />
It appeared that the development <strong>of</strong> such a relation was rather complicated and was only<br />
possible for particular types <strong>of</strong> pavement.<br />
Alemgena found the following predictive equation:<br />
Log ε vb = 1.5615 + 0.3743 log SCI 300 + 1.0067 log BDI + 0.8378 log d 0<br />
- 1.9949 log d 1800 + 0.6288 log d 300<br />
This equation is only valid for the following conditions:<br />
a. the pavement shouldn’t be an inverted pavement so E 1 > E 2 > E 3 > E 4 ,<br />
b. the stiffness <strong>of</strong> the upper layer shouldn’t exceed four times the underlying<br />
layer (e.g. E 2 ≤ 4 E 3 ),<br />
c. applicable only for weak bases (i.e. E 2 < 1000 Mpa).<br />
Tensile strain at the bottom <strong>of</strong> the bound base:<br />
The following relation was developed:<br />
log ε r2,o = 0.0931 + 0.4011 log d 0 + 0.3243 log d 1800 + 0.4504 log d 300 – 0.9958 log d 900<br />
+ 0.8367 log BDI<br />
Where: ε r2,o<br />
= tensile strain at the bottom <strong>of</strong> the bound base [µm/m]<br />
Compressive vertical strain at the top <strong>of</strong> the subbase and subgrade:<br />
Two cases have to be considered which are the case where the stiffness <strong>of</strong> the subbase is<br />
higher than that <strong>of</strong> the subgrade and the case where the stiffness <strong>of</strong> the subbase is smaller<br />
than that <strong>of</strong> the subgrade. In the first case the surface modulus plot will shown an increase in<br />
stiffness going from bottom to top while in the second case the surface modulus plot indicates<br />
the presence <strong>of</strong> low stiffness layers on top <strong>of</strong> the subgrade.<br />
The following results were obtained:<br />
a. Subbase is stiffer than the subgrade:<br />
log ε v3 = 2.48589 + 0.34582 log SCI 300 + 0.16638 log d 1800 – 0.68746 log (h 1 + h 2 )<br />
+ 0.47432 log BDI<br />
b. Subbase is less stiff than subgrade:<br />
log ε v3,s = 1.52887 + 0.39502 log SCI 300 – 0.84168 log d 1800 – 0.60888 log (h 1 + h 2 )<br />
+ 0.43195 log BDI – 0.78407 log BCI + 1.73707 log d 600<br />
c. Subgrade:<br />
log ε v4 = 2.48589 + 0.34582 log SCI 300 + 0.16638 log d 1800 – 0.68746 log (h 1 + h 2 + h 3 )<br />
+ 0.47432 log BDI<br />
Where: ε v3<br />
ε v4<br />
ε v3,s<br />
= vertical compressive strain at the top <strong>of</strong> the subbase [µm/m]<br />
= vertical compressive strain at the top <strong>of</strong> the subgrade [µm/m]<br />
= vertical compressive strain at the top <strong>of</strong> the subbase when this layer<br />
has a lower stiffness than the subgrade [µm/m]
55<br />
10.2 Temperature correction method:<br />
As mentioned before, temperature has a large influence on the magnitude <strong>of</strong> the measured<br />
deflections. In order to be able to use the simplified relations between SCI and strain in the<br />
asphalt layer which were discussed in the previous paragraph, a temperature correction<br />
procedure adaptable to these relations should be available. Furthermore the correction<br />
procedure should take into account the effect <strong>of</strong> cracks present in the pavement. A fully<br />
cracked pavement e.g. acts like a block pavement and in such conditions a temperature<br />
correction is not needed on the measured deflections. On the other hand it is obvious that the<br />
effect <strong>of</strong> temperature is the largest on a sound asphalt layer.<br />
A procedure taking into account both effects is described in [10] and is discussed hereafter.<br />
The surface curvature index measured at a specific temperature can be corrected to a<br />
reference temperature using:<br />
TNF = 1 + {(a 1 + a 2 / h 1 ) . (T A – 20) + (a 3 + a 4 / h 1 ) . (T A – 20) 2 } . (1 – SR t )<br />
Where: TNF = temperature normalisation factor,<br />
T A = asphalt temperature [ 0 C],<br />
h 1 = thickness <strong>of</strong> the asphalt layer [mm],<br />
SR t = percentage area cracked / 100.<br />
TNF takes values smaller than 1 if the measurements are taken below the reference<br />
temperature <strong>of</strong> 20 0 C (which is the reference temperature in the Netherlands). Consequently<br />
TNF is larger than 1 if the measurements were taken above 20 0 C.<br />
The constants a 1 to a 4 take the following values:<br />
Variable a 1 [ 0 C -1 ] a 2 [mm / 0 C] a 3 [0.001 0 C -2 ] a 4 [mm / 0 C 2 ]<br />
D 0 0.01661 -0.67095 0.28612 -0.01408<br />
SCI 225 0.05955 -2.73223 1.48011 -0.08171<br />
SCI 300 0.05398 -2.61130 1.28439 -0.07493<br />
SCI 450 0.04720 -2.39175 1.05022 -0.06371<br />
SCI 600 0.04190 -2.15168 0.87228 -0.05301<br />
The correction is applied in the following way. The SCI 300, T measured at temperature T is<br />
corrected to a SCI 300, 20C at 20 0 C following:<br />
SCI 300, 20C<br />
= SCT 300, T / TNF<br />
A simple but highly effective technique to estimate the temperature in the asphalt layer is<br />
given below. The procedure has been developed in [12] and is slightly modified in [10].<br />
T 3 = 8.77 + 0.649 T 0 + (2.20 + 0.044 T 0 ) . sin {2 π (h r – 14) / 24}<br />
+ log (h 1 / 100) . [-0.503 T 0 + 0.786 T 5 + 4.79 sin {2 π (h r – 18) / 24}]<br />
Where: T 3 = temperature at third point in the asphalt layer [ 0 C]<br />
T 0 = pavement surface temperature [ 0 C]<br />
T 5 = prior mean five days air temperature [ 0 C]<br />
h 1 = asphalt thickness [mm]<br />
= time <strong>of</strong> the day in 24 hour system [hr]<br />
h r<br />
10.3 Relationships with other pavement strength indicators such as SNC:<br />
Also in [11], valuable relationships are presented which relate the deflection bowl to the<br />
modified structural number SNC as used in the Highway <strong>Design</strong> Model. The relationship that<br />
was developed is shown here-after.<br />
log SNC<br />
= 1.82472 + 0.03344 log h 1 + 0.11832 log BCI – 0.16207 log BDI<br />
+ 0.12659 log d 0 – 0.57878 log d 900 + 0.19996 log d 1800 - 0.19829 log SCI 300
56<br />
This relationship opens possibilities for characterising pavement strength by means <strong>of</strong> a well<br />
known physical quantity.<br />
10.4 Relationships between the falling weight deflections and deflections measured<br />
with the Benkelman beam:<br />
Furthermore an extensive study was made in [11] <strong>of</strong> the relationships that could exist<br />
between the deflections as measured by means <strong>of</strong> a BB and those by means <strong>of</strong> a FWD. The<br />
relations that were developed are reported hereafter.<br />
It should be noted that the BB measurements were done with a rear axle load <strong>of</strong> the loading<br />
vehicle <strong>of</strong> 63.5 kN (this is the same axle load as used in the TRRL procedure). As mentioned<br />
before the FWD measurements were taken at a load level <strong>of</strong> 50 kN.<br />
It should also be noted that the relations shown are those between the BB values which are<br />
not corrected for the movement <strong>of</strong> the support system and the FWD values. Table 6 gives the<br />
results.<br />
FWD deflection [µm]<br />
Variable Unit log d 0 log d 300 log d 600 log d 900 log d 1200 log d 1500 log d 1800<br />
Constant µm + 1.61 + 1.44 +1.40 + 1.31 + 1.23 + 1.19 + 1.14<br />
log BB 0 µm + 0.49 + 0.29 0 0 0 0 0<br />
log BB 500 µm + 1.23 + 1.11 + 0.83 + 0.38 + 0.23 + 0.13 + 0.33<br />
log BB 1000 µm - 1.53 - 1.06 - 0.43 0 0 0 - 0.48<br />
log BB 2000 µm + 0.47 + 0.32 + 0.31 + 0.34 + 0.55 + 0.67 + 0.96<br />
log BB 3500 µm 0 0 - 0.08 - 0.10 - 0.14 - 0.15 - 0.16<br />
log h 1 mm - 0.33 - 0.27 - 0.25 - 0.25 - 0. 26 - 0.27 - 0.27<br />
Table 6: Regression coefficients <strong>of</strong> the conversion formulas BB values to FWD values.<br />
The variables BB x are related to the deflections which are measured when the rear axle <strong>of</strong> the<br />
loading truck is at a distance <strong>of</strong> x mm from the tip <strong>of</strong> the beam. An example how the equations<br />
should read is given below.<br />
log d 900 = + 1.31 + 0.38 log BB 500 + 0.34 log BB 2000 - 0.1 log BB 3500 – 0.26 log h 1<br />
It should be mentioned that these relations have been developed using a BB with the<br />
following dimensions.<br />
pivot<br />
610 mm<br />
2695 mm<br />
915
57<br />
11. Remaining life estimation from visual condition surveys:<br />
As has been indicated in the previous chapters, visual condition surveys give important information<br />
on the condition <strong>of</strong> the pavement. With respect to the structural condition <strong>of</strong> the<br />
pavement, two damage types are <strong>of</strong> importance which are cracking and permanent<br />
deformation especially when the deformation is due to deformation <strong>of</strong> the base subbase or<br />
subgrade.<br />
In the past, several condition prediction models using visual condition surveys as input have<br />
been developed (e.g. [9]). Mostly these models suffer from accuracy because in practice the<br />
damage is seldom allowed to grow to such an extent and severity that models describing the<br />
progression <strong>of</strong> the damage completely could not be developed. Fortunately such information<br />
can be obtained from sections tested by accelerated loading facilities. In this chapter the<br />
models will be discussed which have been developed from observations made on test<br />
sections at the outside facilities <strong>of</strong> the Road and Railways Research Laboratory <strong>of</strong> the <strong>Delft</strong><br />
University, which were tested by means <strong>of</strong> the <strong>Delft</strong> University accelerated pavement testing<br />
facility called LINTRACK [13, 14].<br />
Before going into the discussion <strong>of</strong> the models developed, attention is called for the fact that<br />
in the analysis <strong>of</strong> visual condition survey data one always has to consider the way in which<br />
the information is obtained.<br />
The models for the prediction <strong>of</strong> the development <strong>of</strong> the amount <strong>of</strong> cracking that are going to<br />
be presented are based on the visual condition survey system used by the Road and<br />
Hydraulics Engineering Division <strong>of</strong> the Dutch Ministry <strong>of</strong> Transport. The unit section length is<br />
100m. The length over which longitudinal cracking is visible in the left and right hand wheel<br />
track is determined and divided by 200; the ratio obtained is called LC. In the same way the<br />
amount <strong>of</strong> alligator cracking is determined and again this number is divided by 200 in order to<br />
obtain the ratio AC. The amount <strong>of</strong> cracking is then calculated from the sum LC + AC.<br />
It has been shown that the progression <strong>of</strong> cracking can very well be described by means <strong>of</strong> a<br />
Weibull function following [15, 16]:<br />
F w (n) = 1 – exp [-( n/µ) β ]<br />
Where: F w (t) = probability that failure has occurred before n load repetitions,<br />
n = number <strong>of</strong> load repetitions,<br />
µ = number <strong>of</strong> load repetitions at which 63% <strong>of</strong> the area considered is cracked,<br />
β = curvature parameter.<br />
Analysis <strong>of</strong> the World Bank cracking models incorporated in the HDM III design system [7]<br />
showed that β was dependent on the stiffness <strong>of</strong> the pavement. The LINTRACK experiments<br />
indicated that β was dependent on the asphalt thickness following:<br />
log β<br />
= -0.08 + log h<br />
Where: h<br />
= asphalt thickness [mm].<br />
In the LINTRACK test sections also permanent deformation was observed. It was shown that<br />
this deformation was due to deformation <strong>of</strong> the subgrade. The permanent deformation was<br />
measured at several locations under a 1.2 m long straight edge and the mean value was<br />
determined. The maximum allowable rut depth was set at 18 mm and the number <strong>of</strong> load<br />
repetitions needed to arrive to this depth was determined. The rut formation could then be<br />
described using the following non dimensional model:<br />
S n / S N = ( n / N ) 0.41<br />
Where: S n<br />
S N<br />
n<br />
N<br />
= rut depth after n load repetitions [mm],<br />
= rut depth at which pavement is considered to be failed = 18 mm,<br />
= number <strong>of</strong> load repetitions applied,<br />
= number <strong>of</strong> load repetitions needed for a rut depth <strong>of</strong> 18 mm.
58<br />
The remaining pavement life can easily be predicted by means <strong>of</strong> these normalised<br />
equations. One measures the amount <strong>of</strong> damage that is present and one sets the maximum<br />
amount <strong>of</strong> damage which is just acceptable before maintenance is needed. From the ratio<br />
present amount <strong>of</strong> damage over allowable amount <strong>of</strong> damage the pavement life ratio can be<br />
determined. By using the procedure outlined in chapter 8, the damage ratio can be translated<br />
in a number <strong>of</strong> years before maintenance is required.
59<br />
12. Procedures to estimate material characteristics:<br />
In the previous chapters ample attention has been paid to the assessment <strong>of</strong> the stresses and<br />
strains at critical locations in the pavement. It has also been stressed that a proper evaluation<br />
<strong>of</strong> the remaining life and determination <strong>of</strong> the required overlay thickness cannot be made<br />
without knowledge on the strength <strong>of</strong> materials. Especially knowledge on the fatigue<br />
characteristics <strong>of</strong> the asphalt and the resistance to permanent deformation <strong>of</strong> the unbound<br />
base, subbase and subgrade is <strong>of</strong> importance.<br />
In this chapter transfer functions that allow the pavement life to be assessed will be<br />
presented.<br />
12.1 Fatigue characteristics <strong>of</strong> asphalt mixtures:<br />
The fatigue resistance <strong>of</strong> asphalt mixtures is usually described following:<br />
Log N = log k 1 – n log ε<br />
Where: N<br />
k 1 , n<br />
ε<br />
= number <strong>of</strong> load repetitions to failure,<br />
= material parameters,<br />
= applied strain level.<br />
It has been shown that the exponent n strongly depends on the slope <strong>of</strong> the master curve <strong>of</strong><br />
the stiffness modulus. Figure 34 is an example <strong>of</strong> such an relationship.<br />
Figure 34: Example <strong>of</strong> the relationship between the loading time and the stiffness <strong>of</strong> an<br />
asphalt mixture.<br />
Relationships like those shown in figure 34 can be determined experimentally by means <strong>of</strong><br />
e.g. repeated load indirect tensile tests. If such tests cannot be performed, the stiffness<br />
modulus <strong>of</strong> the asphalt mixture can also be estimated using the Shell nomographs for the
60<br />
estimation <strong>of</strong> the bitumen and mixture stiffness. Input that is needed to feed those<br />
nomographs is the T R&B and PI <strong>of</strong> the bitumen as well as the volumetric composition.<br />
If we call the slope <strong>of</strong> the relationship between log t and log S mix , m, then this value can be<br />
calculated using the following relationship.<br />
m = d (log S mix ) / d (log t)<br />
The exponent <strong>of</strong> the fatigue relationship, n, can then be calculated using [17]:<br />
n = 2 / {m . (0.541 + 0.346 / m – 0.0325 V a )<br />
Where: V a = void content <strong>of</strong> the asphalt mixture [%]<br />
The intercept value log k 1 is calculated in the following way [17].<br />
log k 1<br />
= 6.589 – 3.762 n + 3209 / S mix + 2.332 log V b + 0.149 V b / V a + 0.928 PI<br />
-0 .0721 T R&B<br />
Where: n = slope <strong>of</strong> the fatigue relation,<br />
S mix = stiffness <strong>of</strong> the asphalt mixture [MPa],<br />
V b = volume percentage <strong>of</strong> bitumen [%],<br />
V a = void percentage [%],<br />
PI = penetration index <strong>of</strong> the bitumen,<br />
= s<strong>of</strong>tening point <strong>of</strong> the bitumen [ 0 C].<br />
T R&B<br />
The relationship for log k 1 was established using the fatigue test results performed on over<br />
100 mixtures. Results involved were those reported by the SHRP A-003 team, by Shell<br />
researchers, researchers <strong>of</strong> the <strong>Delft</strong> University and by researchers <strong>of</strong> the Road and<br />
Hydraulics Engineering Division <strong>of</strong> the Dutch Ministry <strong>of</strong> Transport.<br />
The relationship for n was established using the results obtained for over 30 mixtures. All<br />
tests considered were displacement controlled tests.<br />
12.2 Deformation resistance <strong>of</strong> unbound base materials:<br />
The vertical permanent deformation in unbound base materials is usually described using:<br />
ε p<br />
= 10 a . N b<br />
Where: ε p = permanent strain [µm/m],<br />
a, b = material constants,<br />
N =number <strong>of</strong> load repetitions.<br />
The parameters a and b are dependent on the type <strong>of</strong> material, the gradation, the degree <strong>of</strong><br />
compaction and the moisture content. It is common practice to determine these parameters<br />
by means <strong>of</strong> repeated load triaxial tests.<br />
At the <strong>Delft</strong> University, an extensive testing program has been performed by van Niekerk [26]<br />
on base materials composed <strong>of</strong> crushed concrete and crushed masonry. Recycling <strong>of</strong> old<br />
concrete and masonry is a very important issue in the Dutch road industry. Van Niekerk’s<br />
results were used by Alemgena to develop base compressive strain criteria. This was<br />
possible since both permanent deformation as well as resilient modulus tests were performed.<br />
From the permanent deformation tests it was determined at which number <strong>of</strong> load repetitions<br />
a permanent deformation <strong>of</strong> 4% occurred. This number <strong>of</strong> load repetitions is <strong>of</strong> course<br />
dependent on the material type and the stress conditions. For each stress condition applied<br />
also the resilient modulus could be determined and so the elastic strain. Using all this<br />
information relations between the elastic strain and the number <strong>of</strong> load repetitions at which a<br />
permanent deformation <strong>of</strong> 4% occurred was determined. Typical examples <strong>of</strong> such criteria are<br />
shown in figure 35 while figure 36 gives the gradations. The code UL-65-100 e.g. means that<br />
the gradation is the UL gradation, that the mixture is composed with 65% crushed concrete
61<br />
and 35% crushed masonry (mass percentages) and that the samples were compacted to<br />
100% <strong>of</strong> standard proctor.<br />
Allowable vertical compressive strain at top <strong>of</strong> base<br />
log eps [mum/m]<br />
3,4<br />
3,3<br />
3,2<br />
3,1<br />
3<br />
2,9<br />
2,8<br />
2,7<br />
2,6<br />
2,5<br />
2 3 4 5 6 7 8<br />
log N<br />
CO-65-100<br />
AL-65-100<br />
UL-65-100<br />
LL-65-100<br />
Figure 35: Base strain criteria.<br />
100<br />
cummulative percentage passing<br />
[%]<br />
80<br />
60<br />
40<br />
20<br />
0<br />
UL<br />
UN<br />
LL<br />
CO<br />
AL<br />
FL<br />
0.063 0.125 0.25 0.5 1 2 4 8 16 31.5<br />
sieve diameter [mm]<br />
Figure 36: Gradations tested by van Niekerk.<br />
Figure 35 clearly shows that base strain criteria can be developed but that there doesn’t exist<br />
a single base strain criterion. The criterion is clearly dependent on the gradation but also on
62<br />
the composition and the degree <strong>of</strong> compaction (these later two influence factors are not<br />
shown here).<br />
12.3 Subgrade strain criterion:<br />
Research with the LINTRACK [13] has shown the following criterion to be applicable for a<br />
typical Dutch fore shore sand. The relationship is based on allowing a maximum rut depth <strong>of</strong><br />
18 mm.<br />
log N<br />
= - 7.461 – 4.33 log ε v<br />
Where: ε v<br />
= subgrade strain [µm/m]<br />
12.4 Maximum tensile strain at bottom <strong>of</strong> the bound base:<br />
The terminology “bound base” is used for any base materials to which some kind <strong>of</strong> binding<br />
agent is added or for base materials which shown some kind <strong>of</strong> self cementing action. Such<br />
materials will always show cracks due to shrinkage. With appropriate measures, the influence<br />
<strong>of</strong> that type <strong>of</strong> cracking can be kept under control. Nevertheless also deterioration due to<br />
traffic loads will occur. Given the shrinkage cracks that are already present in the base, it is<br />
not realistic to assume that the base is a homogeneous material and it is not realistic to<br />
analyse the possibility <strong>of</strong> fatigue cracking as is usually done for asphalt layers. It is however<br />
wise to limit the tensile strains due to traffic in order to avoid extensive traffic related damage.<br />
For that reason it is proposed to keep the tensile strain due to traffic loads below 50% <strong>of</strong> the<br />
tensile strain at failure, so below a level <strong>of</strong> approximately 60 µm/m.
63<br />
13. Overlay design in relation to reflective cracking:<br />
The main purpose <strong>of</strong> the overlay design procedure that was presented in one <strong>of</strong> the previous<br />
chapters was to limit the tensile strain at the bottom <strong>of</strong> the existing asphalt layer and the<br />
compressive vertical strain at the top <strong>of</strong> the subgrade. As was indicated such a method<br />
doesn’t take into account the effect <strong>of</strong> cracks in the existing pavement on the performance <strong>of</strong><br />
the overlay. This is a serious issue since these cracks tend to propagate through the overlay<br />
and can reduce the effective life <strong>of</strong> the overlay significantly. The conclusion therefore must be<br />
that crack reflection must be considered when designing an overlay.<br />
Linear elastic theory applied on homogeneous, isotropic layers can be used in overlay design<br />
procedures which are based on limitation <strong>of</strong> the stresses and strains in the existing pavement.<br />
Cracked pavement however cannot be analysed in this way. In fact principles <strong>of</strong> fracture<br />
mechanics have to be applied to analyse the effects <strong>of</strong> cracks. This immediately implies that<br />
finite element programs need to be used for the analysis <strong>of</strong> crack propagation. Although such<br />
programs can easily be used on today’s personal computers, they are still considered to be<br />
not practical for every day’s use. Therefore there has always been a strong need for so called<br />
“engineering tools” which allow the complex phenomenon <strong>of</strong> reflective cracking to be analysed<br />
with rather simple tools.<br />
Although the author fully understands this need <strong>of</strong> practice, he also likes to stress that each<br />
model is a schematisation <strong>of</strong> reality and that too simple models will be a too simple schematisation<br />
<strong>of</strong> reality which can result in less optimal or even wrong results.<br />
In spite <strong>of</strong> these drawbacks, some simplistic models are presented here-after because they<br />
are based on sound analyses <strong>of</strong> pavement structures using fracture mechanics principles.<br />
13.1 Overlay design method based on effective modulus concept:<br />
The first method to be presented is based on the effective modulus concept. This concept is<br />
schematically shown in figure 37.<br />
A B layer has reduced, effective modulus<br />
Figure 37: Concept <strong>of</strong> effective modulus method.<br />
Figure 37a shows the condition one is dealing with in reality when designing an overlay. The<br />
overlay is placed on the cracked pavement and this crack wants to propagate through the<br />
overlay because <strong>of</strong> stress concentrations at the tip <strong>of</strong> the crack due to the bending and<br />
shearing action <strong>of</strong> the load. The stress concentrations due to the bending action are indicated<br />
by K 1 (the horizontal arrow), those due to the shearing action are indicated by K 2 (the vertical<br />
arrows). It should be noted that in fracture mechanics K is called the “stress intensity factor”.<br />
The growth <strong>of</strong> the crack due to K is described using:<br />
dc / dN = A . K eff<br />
n<br />
Where: dc / dN = increase in crack length c per load repetiton,<br />
K eff = effective stress intensity factor combining the bending and shearing<br />
effects and taking into account the fact that the K 1 and K 2 are not constant<br />
when the crack progresses through the overlay,<br />
A, n = material parameters.
64<br />
The life <strong>of</strong> the overlay N can simply be calculated using:<br />
N = h o / { dc / dN }<br />
Where: h o = overlay thickness [mm].<br />
In the effective modulus method (figure 37b), the tensile strain at the bottom <strong>of</strong> the asphalt<br />
layer is calculated, indicated by the horizontal arrow, and the fatigue life <strong>of</strong> the overlay is<br />
calculated using the appropriate fatigue relation. The magnitude <strong>of</strong> the tensile strain at the<br />
bottom <strong>of</strong> the overlay, and so the life <strong>of</strong> the overlay, is <strong>of</strong> course dependent on the modulus <strong>of</strong><br />
the existing asphalt layer. This modulus value should be reduced to such a level that the<br />
fatigue life <strong>of</strong> the overlay, calculated according to the principle <strong>of</strong> figure 37b, equals the life <strong>of</strong><br />
the overlay based on the crack propagation principles shown in figure 37a. The reduced<br />
modulus so obtained is called the effective modulus <strong>of</strong> the existing asphalt layer.<br />
Using these principles, figure 38 was developed [19]. In principle this figure is only valid for<br />
the following conditions.<br />
E 1 = modulus existing asphalt layer = 3000 MPa,<br />
h 1 = thickness <strong>of</strong> existing asphalt layer = 100 and 300 mm,<br />
h 2 = thickness <strong>of</strong> the base = 300 mm,<br />
E 2 = modulus <strong>of</strong> the base = 200 MPa,<br />
E 3 = subgrade modulus = 100 MPa,<br />
= modulus <strong>of</strong> the overlay = 5000 MPa.<br />
E o<br />
The graph shows that if the effect <strong>of</strong> a 60 mm overlay is to be analysed when placed on a<br />
severely cracked pavement where load transfer takes place across the crack, that an effective<br />
modulus for the existing asphalt has to be used <strong>of</strong> approximately 900 MPa.<br />
Figure 38: Effective modulus <strong>of</strong> the existing asphalt layer in relation to the thickness <strong>of</strong> the<br />
existing asphalt layer and overlay, and the amount <strong>of</strong> load transfer across a crack.
65<br />
13.2 Method based on stress intensity factors:<br />
This method is in fact an extension <strong>of</strong> the crack growth calculations that were made to<br />
develop the effective modulus method presented in the previous section. For this method [20]<br />
a number <strong>of</strong> pavement structures was considered and the propagation through the overlay <strong>of</strong><br />
cracks which were fully developed through the existing asphalt layer as well as 50 mm deep<br />
surface cracks was analysed. Figure 39 shows the analysed pavements as well as the three<br />
load conditions considered.<br />
Figure 39: Analysed pavement structures.<br />
Table 7 gives the regression equations and values for the regression parameters for the<br />
calculation <strong>of</strong> K 1eq and K eff for all three loading conditions. First <strong>of</strong> all the K 1eq should be<br />
estimated. This value represents the combined effect <strong>of</strong> K 1 and K 2 . Than K eff is determined;<br />
this value takes into account the variation <strong>of</strong> the K 1eq over the height <strong>of</strong> the overlay.<br />
Table 7a: Relationship between K 1eq and several pavement parameters.
66<br />
Table 7b: Relationship between K eff / K 1eq and several pavement parameters.<br />
When using these equations for the determination <strong>of</strong> the thickness <strong>of</strong> the overlay, values for A<br />
and n should be available.<br />
It has extensively been shown [ e.g. 9] that the value <strong>of</strong> the exponent n <strong>of</strong> the crack growth<br />
relation is equal to the value <strong>of</strong> the exponent n <strong>of</strong> the fatigue relation. For the estimation <strong>of</strong> n,<br />
the reader is therefore referred to section 12.1.<br />
Furthermore A and n appear to be strongly correlated following [17]:<br />
log A<br />
0.273 log Smix<br />
= - 2.890 – 0.308 n – 0.739 n<br />
Where: n<br />
S mix<br />
= slope <strong>of</strong> crack growth relation which is equal to the slope <strong>of</strong> the fatigue<br />
relationship, see section 12.1,<br />
= stiffness <strong>of</strong> the asphalt mixture [MPa].<br />
13.3 Overlay design method based on beam theory:<br />
The disadvantage <strong>of</strong> the method presented in section 13.2 is that it is only applicable for the<br />
conditions for which it has been developed. This means that there is a big chance that the<br />
real conditions are different from the conditions for which the method is developed which<br />
implies that the method only has a limited field <strong>of</strong> application.<br />
A more general applicable simple design system has therefore been developed in [21]. This<br />
method is based on the propagation <strong>of</strong> cracks in fully supported beams as described in [22].<br />
In the text hereafter the equations given in [22] will be given first <strong>of</strong> all. This is followed by an<br />
explanation how this method can be generalised to pavement systems.<br />
Let us consider the two loading conditions as shown in figure 40.<br />
The stress intensity factors at the tip <strong>of</strong> the crack due to bending and shearing can be<br />
calculated in the following way.<br />
K bending = k b . q . e -β/2 . sin (β . l / 2) / β 2 d 1.5<br />
K shearing = k s . q [1 + e -βl . [sin (β . l) – cos (β . l) / 4 β √ d<br />
β<br />
Where: k b<br />
k s<br />
q<br />
l<br />
= (E s / E) 0.33 / 0.55 d<br />
= dimensionless stress intensity factor due to bending,<br />
= dimensionless stress intensity factor due to shearing,<br />
= contact pressure [MPa],<br />
= width <strong>of</strong> loading strip [mm],
67<br />
c<br />
d<br />
E<br />
E s<br />
= length <strong>of</strong> the crack [mm],<br />
= thickness <strong>of</strong> the beam [mm],<br />
= modulus <strong>of</strong> the beam [MPa],<br />
= modulus <strong>of</strong> the supporting layer [MPa].<br />
l<br />
q<br />
E<br />
c<br />
d<br />
E s<br />
Bending<br />
Shearing<br />
Figure 40: Crack propagation in a fully supported beam as a result <strong>of</strong> bending and shearing.<br />
Figure 41 shows how the dimensionless stress intensity factors change in relation to the ratio<br />
c / d. As one observes the stress intensity factor due to shearing increases with increasing<br />
crack length. This is logical because with increasing crack length, the area that has to transfer<br />
the load decreases so the stresses in that area increase.<br />
Figure 41 however also shows that the stress intensity factor due to bending increases first<br />
with increasing crack length but then decreases to a value <strong>of</strong> zero. This is because <strong>of</strong> the fact<br />
that the crack reaches the neutral axis <strong>of</strong> the pavement at a given moment and penetrates the<br />
zone where horizontal compressive stresses are acting. Then the cracks stops to grow since<br />
the driving force has disappeared.
68<br />
Figure 41: Relationship between c / d and the dimensionless stress intensity factors.
69<br />
The question now <strong>of</strong> course is how this beam approach can be used for the design <strong>of</strong><br />
overlays on cracked pavements. The first step how to schematise a cracked pavement with<br />
overlay is shown in figure 42.<br />
overlay<br />
existing<br />
asphalt<br />
bound<br />
b<br />
d<br />
base<br />
subgrade<br />
Figure 42a: Pavement structures to be schematised.<br />
c = h existing asphalt + h bound base c = h existing asphalt<br />
d = h overlay + h existing asphalt + h bound base d = h overlay + h existing asphalt<br />
E s = E subgrade E s = combined modulus <strong>of</strong><br />
E = combined modulus <strong>of</strong> overlay, existing subgrade and base<br />
asphalt and bound base E = combined modulus <strong>of</strong><br />
overlay and existing<br />
asphalt<br />
Figure 42b: Schematised structures.<br />
The question now is how to arrive to the combined modulus values. This is done in the<br />
following way. First <strong>of</strong> all the layer moduli <strong>of</strong> the existing pavement are back calculated. In<br />
case the modulus <strong>of</strong> the subgrade and the unbound base have to be combined, the following<br />
equation has been suggested by Odemark.<br />
1 / E s = (1 / E 2 ) . {1 - √ [(a 2 + h e1 2 ) / (a 2 + (h e1 + g e2 ) 2 )]}<br />
+ (1 / E 3 ) . √ [(a 2 + h e1 2 ) / (a 2 + (h e1 + h e2 ) 2 )]<br />
Where: E s = combined modulus <strong>of</strong> subgrade and base,<br />
E 2 = modulus <strong>of</strong> the unbound base,<br />
E 3 = modulus <strong>of</strong> the subgrade,<br />
a = radius <strong>of</strong> loading area,<br />
h e1 = 0.9 h 1 (E 1 / E s ) 0.33 ,<br />
h 1 = thickness <strong>of</strong> the existing asphalt layer,<br />
E 1 = modulus <strong>of</strong> the existing asphalt layer,<br />
g e2 = 0.9 h 2 ,<br />
h 2 = thickness <strong>of</strong> the unbound base,<br />
h e2 = 0.9 h 2 (E 2 / E 3 ) 0.33 .
70<br />
From the nature <strong>of</strong> the equation it is clear that it has to be solved by iteration since E s can<br />
only be calculated if an initial value for E s is assumed.<br />
The combined modulus <strong>of</strong> the existing asphalt layer and the overlay can be calculated using<br />
Nijboer’s equation.<br />
E = E a . {[b 4 + 4 b 3 n + 6 b 2 n + 4 b n + n 2 ] / [n . (b + n) . (b + 1) 3 ]}<br />
Where: E<br />
E a<br />
b<br />
n<br />
= combined modulus <strong>of</strong> existing asphalt layer and overlay,<br />
= modulus <strong>of</strong> the existing asphalt layer,<br />
= thichkness <strong>of</strong> existing asphalt layer / thickness overlay,<br />
= modulus <strong>of</strong> overlay / modulus <strong>of</strong> existing asphalt layer<br />
In case one has to determine the combined modulus <strong>of</strong> the base, existing asphalt and<br />
overlay, then the combined modulus <strong>of</strong> the base and existing asphalt layer has to be<br />
determined first <strong>of</strong> all. Then the combined modulus <strong>of</strong> this value and the overlay has to be<br />
determined using the same equations. This means that in that case E a = combined modulus<br />
<strong>of</strong> the existing asphalt layer and the base, n = modulus <strong>of</strong> overlay / combined modulus <strong>of</strong><br />
existing asphalt and base, b = total thickness <strong>of</strong> existing asphalt layer and base / thickness <strong>of</strong><br />
the overlay.<br />
The procedure is illustrated by means <strong>of</strong> an example.<br />
Example:<br />
Assume a given pavement consisting <strong>of</strong> a 100 mm thick asphalt layer on a 300 mm thick base<br />
which in turn is placed on a subgrade. From the back calculation analysis it appeared that the<br />
modulus <strong>of</strong> the existing asphalt layer was 9000 MPa. The base had a modulus <strong>of</strong> 130 MPa<br />
and the subgrade a modulus <strong>of</strong> 50 MPa.<br />
First <strong>of</strong> all the E s value had to be calculated using the above mentioned equation. As a<br />
starting value for E s a value <strong>of</strong> 130 MPa was assumed. This resulted in a calculated E s value<br />
<strong>of</strong> 74 MPa. This value was used as starter for a second iteration, then a value for E s <strong>of</strong> 71<br />
MPa was obtained. A third iteration resulted in the same E s value so E s = 71 MPa.<br />
Then the stiffness <strong>of</strong> the overlay was determined from the mixture composition, the bitumen<br />
characteristics and the temperature and loading conditions. This procedure will not be<br />
illustrated here. The interested reader is referred to the lecture notes on Asphalt Materials<br />
CT4850. The modulus <strong>of</strong> the overlay was determined to be 8000 MPa.<br />
Using Nijboer’s equation a combined modulus for the existing asphalt layer and the overlay<br />
was calculated using:<br />
n = E overlay / E existing asphalt = 8000 / 9000 = 0.89<br />
b = h existing asphalt / h overlay = 100 / 50 = 2<br />
The combined modulus <strong>of</strong> existing asphalt and the overlay was calculated to be E = 8496<br />
MPa.<br />
The question now is what the stress intensity factors are at the tip <strong>of</strong> the crack that wants to<br />
penetrate the overlay. The pavement is severely cracked so only a limited amount <strong>of</strong> load<br />
transfer through aggregate interlock will occur.<br />
From the pavement geometry we know:<br />
c =length <strong>of</strong> the crack = thickness <strong>of</strong> the existing asphalt layer = 100 mm,<br />
d = thickness <strong>of</strong> existing asphalt layer + thickness <strong>of</strong> the overlay = 150 mm,<br />
so<br />
c / d = 0.66.<br />
From figure 41 it appears that one only has to take into account the shearing action.
71<br />
The pavement is loaded by truck wheels having a contact pressure q = 0.7 MPa. The radius<br />
<strong>of</strong> the loaded area = 150 mm, this means that l = 300 mm.<br />
We calculate:<br />
β = (E s / E) 0.33 / 0.55 d = (71 / 8496) 0.33 / 0.55 . 150 = 0.0025<br />
K shearing = k s . q . [1 + e -βl (sin βl – cos βl)] / 4 β √d<br />
= k s 0.7 [1 + e -0.0025 x 300 (sin 0.0025 x 400 – cos 0.0025 x 400)] / 4 x 0.0025 x √150<br />
= k s 0.7 [ 1 + 0.472 (0.841 – 0.540)] / 0.122 = k s 6.553<br />
Please note that in the calculation <strong>of</strong> the sin and cos, βl is in radians.<br />
If the K values are known, the number <strong>of</strong> load repetitions that is needed to allow the crack to<br />
reflect through the overlay can be calculated using the procedures given earlier.<br />
The question now <strong>of</strong> course is to what extent beam theory is representative for real pavement<br />
problems. This is <strong>of</strong> course not the case and some shift factors resulting in similar stress<br />
conditions in the beam as in the real pavement are therefore necessary. The easiest way is to<br />
do is to compare the stresses at the bottom <strong>of</strong> the beam with the stresses that would occur at<br />
the bottom <strong>of</strong> the top layer in the two layer system. Most probably the stresses at the bottom<br />
<strong>of</strong> the beam are higher than the stresses at the bottom <strong>of</strong> the layer. The correction factor that<br />
is needed to fit the stresses at the bottom <strong>of</strong> the beam to the stresses at the bottom <strong>of</strong> the<br />
layer can also be used as correction factor for the stress intensity factors.<br />
13.4 Effects <strong>of</strong> reinforcements, geotextiles, SAMI’s and other interlayer systems:<br />
In order to retard reflective cracking, various systems have been developed in time which can<br />
be used to do so. Examples <strong>of</strong> such systems are:<br />
1. Application <strong>of</strong> polymer modifications in the overlay mixture to enhance the crack<br />
resistance <strong>of</strong> the overlay material.<br />
2. Reinforcement <strong>of</strong> the overlay material in order to improve the crack growth resistance <strong>of</strong><br />
the material.<br />
3. Application <strong>of</strong> a low stiffness material between the existing pavement and the overlay in<br />
order to let the overlay behave independently from the existing pavement.<br />
Re 1: Polymer modifications have shown to be very effective in improving the crack resistance<br />
<strong>of</strong> asphalt mixtures. Especially SBS modifications have proven to be very useful. It is<br />
beyond the scope <strong>of</strong> these lecture notes to discuss in detail the selection <strong>of</strong> the most<br />
appropriate polymer modification. Nevertheless some practical guidelines will be given.<br />
It had been shown (e.g. in the lecture notes on asphalt materials) that a material has a high<br />
crack resistance when its tensile strength is high and when its fracture energy is high.<br />
Materials with such characteristics can easily be discriminated by tests like the indirect tensile<br />
test. This is schematically shown in figure 43.<br />
By measuring the load and the displacements, one can derive a plot showing the growth <strong>of</strong><br />
the tensile stress in relation to the growth <strong>of</strong> the tensile strain. A picture like figure 40 is then<br />
obtained. The peak value represents the tensile strength σ t , while the area enclosed by the<br />
plot represents the energy that is needed to fracture the specimen. This parameter is<br />
indicated by Γ.<br />
A modification should preferably have a positive effect on both the tensile strength and the<br />
fracture energy. In practice however it has been observed that modifiers that increase the<br />
tensile strength, decrease the fracture energy and vice versa. Only a limited number <strong>of</strong><br />
modifiers produce an improvement <strong>of</strong> both. By comparing plots like figure 43, the most<br />
effective modifier can easily be determined.
72<br />
σ<br />
σ t<br />
Γ<br />
ε<br />
Figure 43: Strength and fracture energy obtained in a (indirect) tensile test.<br />
Re 2: Asphalt mixtures can be reinforced in the same way as cement concrete can be<br />
reinforced. Vital aspects with respect to reinforcement are the modulus <strong>of</strong> the reinforcing<br />
material, its total cross sectional area, and the bond between the reinforcement and the<br />
surrounding asphalt.<br />
Materials like meshes made <strong>of</strong> polypropylene, glass fibres and steel are <strong>of</strong>ten propagated as<br />
reinforcing materials. The question however is whether they really can act as a reinforcing<br />
material. There are two reasons to doubt this. First <strong>of</strong> all the mesh might be a woven material<br />
which means that not the stiffness <strong>of</strong> the material from which the mesh is made is <strong>of</strong><br />
importance, but the stiffness <strong>of</strong> the mesh which might be fairly low. Secondly many meshes<br />
have a low physical thickness and are glued to the pavement by means <strong>of</strong> a tack coat. The<br />
question in such cases is whether the tack coat is stiff enough to provide a good bond<br />
between the reinforcing material and the surrounding asphalt. All this doesn’t necessarily say<br />
that such products are useless; what it really says that these products certainly can have an<br />
effect but that the effect is not likely to be a reinforcing effect. In some cases the effect <strong>of</strong> such<br />
materials is somewhere between reinforcing and separating.<br />
Although the effect <strong>of</strong> reinforcements including the effect <strong>of</strong> the bond stiffness should be<br />
analysed by means <strong>of</strong> finite element programs, the procedures presented above can be used<br />
as well. In such cases it is common practice to describe the effect <strong>of</strong> the reinforcement by<br />
using a lower value for the crack growth parameter A for the reinforced overlay than for the<br />
unreinforced overlay. No general applicable values for the way in which reinforcing materials<br />
reduce the A values when compared with reference unreinforced mixtures. These values<br />
should be derived by means <strong>of</strong> properly designed experiments. Excellent guidelines for such<br />
tests can be found in [23] and [24].<br />
Re 3: Cracks will not propagate into the overlay if the overlay behaves independently from the<br />
existing pavement. This can be accomplished by placing a chewing gum type layer between<br />
the existing pavement and the overlay. Such a chewing gum layer might be a 1.2 mm layer <strong>of</strong><br />
polymer modified bitumen sprayed on the existing pavement, but it might also be a non<br />
woven geotextile soaked with bitumen. In this case the geotextile acts as a container for the<br />
bitumen.<br />
The effect <strong>of</strong> such interlayers can easily be assessed by assuming that such layers have a<br />
thickness <strong>of</strong> 1 mm and having a stiffness <strong>of</strong> about 50 MPa.<br />
In general one will observe that the overlay thickness that should be used on top <strong>of</strong> such a<br />
chewing gum interlayer system is limited in thickness. This is because thick overlays attract<br />
tensile strains and will therefore not perform as good as one would expect.<br />
13.5 Load transfer across cracks:<br />
Especially in cases where the pavement has a cement treated base, ample attention should<br />
be given to the load transfer that takes place across a crack. This is because at low
73<br />
temperatures, the cement treated base will shrink. This shrinkage not only introduces extra<br />
stresses in the overlay but also has a significant effect on the load transfer that takes place<br />
across the crack. This load transfer will be zero when the crack is so wide that the crack faces<br />
don’t touch each other.<br />
A typical example <strong>of</strong> how the load transfer can vary during the year is given in figure 44. This<br />
figure shows the deflection bowls measured with a FWD (load was 85 kN) around a specific<br />
crack in the winter and in the summer. The pavement consisted <strong>of</strong> 200 mm asphalt on top <strong>of</strong><br />
a 300 mm thick sand cement base. The pavement showed transverse cracking due to<br />
shrinkage.<br />
It should be noted that in position a, six <strong>of</strong> the seven geophones are on one side <strong>of</strong> the crack<br />
where the loading plate is placed. In position f, only one geophone is on the side <strong>of</strong> the crack<br />
where the loading plate is.<br />
From the figure it is clear that in summer the load transfer is rather good. In general the<br />
deflection bowl is a fluid line. However in the winter the deflection bowls show that almost no<br />
load is transferred across the crack indicating that in that period <strong>of</strong> the year the shearing<br />
conditions <strong>of</strong> an overlay placed on top <strong>of</strong> such a crack will be severe.<br />
In such conditions only thick overlays or overlays with a heavy reinforcement have a chance<br />
to survive.<br />
Figure 44a: Surface deflections at a transverse crack in the summer.<br />
Figure 44b: Surface deflections at a transverse crack in the winter.
74<br />
14. Effects <strong>of</strong> pavement roughness on the rate <strong>of</strong> deterioration:<br />
It is a well known fact that driving over a rough pavement results in dynamic axle loads which<br />
can be fairly high. This is <strong>of</strong> special importance for rather thin pavements because repeated<br />
high dynamic wheel loads on one particular spot can result in premature failure at that<br />
location. Some knowledge on the effect <strong>of</strong> pavement roughness on pavement deterioration is<br />
therefore needed.<br />
The magnitude <strong>of</strong> the dynamic axle load depends on the pavement roughness, the speed <strong>of</strong><br />
the vehicle and characteristics <strong>of</strong> the vehicle like size, weight and properties <strong>of</strong> the spring<br />
suspension system. All this means that no unique relationship can be given between the<br />
pavement roughness and the dynamic axle loads.<br />
This means that the relationships given hereafter must be taken as indicative and not as hard<br />
predictions.<br />
It is not the intention to give here all the backgrounds <strong>of</strong> vehicle pavement interactions. Only<br />
some useful formula’s will be given. For further details the reader is e.g. referred to [15].<br />
In [21] two relationships are derived for the standard deviation <strong>of</strong> the dynamic axle loads <strong>of</strong> a<br />
particular truck with particular characteristics, which had a static axle load <strong>of</strong> 10 tons. The<br />
relationships are as follows:<br />
log σ<br />
log σ<br />
= - 0.5184 + 0.4075 log SV<br />
= 0.892 – 2.151 log PSI<br />
Where: σ = standard deviation <strong>of</strong> the dynamic loads due to a static axle load <strong>of</strong> 10 tons<br />
<strong>of</strong> a truck driving at 63 km / h [tons],<br />
SV = slope variance <strong>of</strong> the road pr<strong>of</strong>ile multiplied by 10 6 [rad 2 ],<br />
PSI = present service ability index = 3.27 – 1.37 (log SV – 0.78).<br />
In many countries <strong>of</strong> the world however the international roughness index IRI is used to<br />
characterise the pavement roughness.<br />
According to [15] the relation between PSI and IRI is as follows.<br />
PSI<br />
IRI<br />
-0.18 IRI<br />
= 5.0 e<br />
= 5.5 ln (5.0 / PSI)<br />
Where: IRI<br />
= in [m/km].<br />
The problem in these analysis is how to obtain the PSI or IRI; normally quite sophisticated<br />
equipment is used to measure pavement roughness and to derive PSI or IRI value from these<br />
measurements. Fortunately it is shown in [15] that the IRI can be obtained using straightedge<br />
measurements. The relationships given in [15] are:<br />
2m straightedge: PD mean = 1.23 IRI<br />
3m straightedge: PD mean = 1.58 IRI<br />
Where: PD mean = mean deviation <strong>of</strong> the pr<strong>of</strong>ile from the straightedge [mm].<br />
It is believed that these relationships help in identifying locations where high dynamic axle<br />
loads occur so where rapid deterioration might occur as well.<br />
In order to allow a more precise analysis <strong>of</strong> the effects <strong>of</strong> a rough road on the dynamic axle<br />
loads, the computer program ROUGHNESS, has been developed by Huurman <strong>of</strong> the <strong>Delft</strong><br />
University. The program can be found on the cd which is part <strong>of</strong> these lecture notes. The<br />
user’s manual for this program is given in appendix II.
75<br />
References:<br />
1. Molenaar, A.A.A.<br />
Pavement management systems, Part I, II and III.<br />
Lecture notes e54; Faculty <strong>of</strong> Civil Engineering; <strong>Delft</strong> University <strong>of</strong> Technology;<br />
<strong>Delft</strong> – 1993.<br />
2. AASHTO<br />
AASHTO guide <strong>of</strong> design <strong>of</strong> pavement structures 1986.<br />
Washington D.C. - 1986<br />
3. Holster, A.M.; Molenaar, A.A.A.; Van den Bosch, H.G.; Van Gurp, C.A.P.M.<br />
Comparison between observed and predicted pavement response.<br />
Report 7-91-209-14; Road and Railway Research Laboratory; <strong>Delft</strong> University <strong>of</strong><br />
Technology; <strong>Delft</strong> – 1991<br />
4. Stas, W.F.; Molenaar, A.A.A.; Van Gurp, C.A.P.M.<br />
Evaluation <strong>of</strong> the structural condition <strong>of</strong> test pavements FORCE project.<br />
Report 7-91-209-16; Road and Railway Research Laboratory; <strong>Delft</strong>University <strong>of</strong><br />
Technology; <strong>Delft</strong> - 1991<br />
5. Hoyinck, W.; Van den Ban, R.; Gerritsen, W.<br />
Lacroix overlay design by three layer analyses.<br />
Proc. 5 th Int. Conf. <strong>Structural</strong> <strong>Design</strong> <strong>of</strong> Asphalt <strong>Pavements</strong>.<br />
Vol 1, pp 410 – 420; <strong>Delft</strong> – 1982<br />
6. Kennedy, C.K.; Lister, N.W.<br />
Prediction <strong>of</strong> pavement performance and the design <strong>of</strong> overlays.<br />
TRRL Laboratory Report 833.<br />
Crowthorne – 1978<br />
7. Groenendijk, J.; Molenaar, A.A.A.<br />
Pavement design methods, a literature survey into linear elastic theory and condition<br />
prediction models.<br />
Report 7-93-209-31; Road and Railway Research Laboratory; <strong>Delft</strong> University <strong>of</strong><br />
Technology; <strong>Delft</strong> – 1993<br />
8. Shell International Petroleum Company Ltd.<br />
Shell pavement design manual; asphalt pavements and overlays for road traffic.<br />
London – 1978.<br />
9. Molenaar, A.A.A.<br />
<strong>Structural</strong> performance and design <strong>of</strong> flexible pavements and asphalt concrete overlays.<br />
PhD dissertation; <strong>Delft</strong> University <strong>of</strong> Technology; <strong>Delft</strong> – 1983.<br />
10. Van Gurp, C.A.P.M.<br />
Characterization <strong>of</strong> seasonal influences on asphalt pavements with the use <strong>of</strong> falling<br />
weight deflectometers.<br />
PhD dissertation; <strong>Delft</strong> University <strong>of</strong> Technology; <strong>Delft</strong> – 1995.<br />
11. Van Gurp, C.A.P.M.; Wennink, P.M.<br />
<strong>Design</strong>, structural evaluation and overlay design <strong>of</strong> rural roads (in Dutch).<br />
KOAC-WMD consultants; Apeldoorn - 1997.<br />
12. Stubstad, R.N.; Lukanene, E.O.; Baltzer, S.; Ertman-Larsen, H.J.<br />
Prediction <strong>of</strong> AC mat temperatures for routine load/deflection measurements.<br />
Proc. 4 th Int. Conf. On Bearing Capacity <strong>of</strong> Roads and Airfields.<br />
Vol. 1, pp 661 – 682; Minneapolis – 1994.<br />
13. Groenendijk, J.<br />
Accelerated testing and surface cracking <strong>of</strong> asphaltic concrete pavements.<br />
PhD Dissertation; <strong>Delft</strong> University <strong>of</strong> Technology; <strong>Delft</strong> – 1998.<br />
14. Molenaar, A.A.A.; Groenendijk, J.; Van Dommelen, A.<br />
Development <strong>of</strong> performance models from APT.<br />
Proc. 1 st Int. Conference on Accelerated Pavement Testing; Reno – 1999.<br />
15. Paterson, W.D.O.<br />
Road deterioration and maintenance effects.<br />
John Hopkins University press; Baltimore – 1987.
76<br />
16. Bekker, P.C.F.<br />
Pavement performance modelling.<br />
Proc. Closing conf. TEMPUS JEP-1180 “Educational developments in pavement<br />
management systems”, pp 263 – 288: <strong>Delft</strong> University <strong>of</strong> Technology; <strong>Delft</strong> – 1993.<br />
17. Medani, T.O.<br />
Characterisation <strong>of</strong> crack growth and fatigue behaviour <strong>of</strong> asphalt mixtures using simple<br />
tests.<br />
MSc Thesis; International Institute for Infrastructural, Hydraulic and Environmental<br />
Engineering; <strong>Delft</strong> – 1999.<br />
18. Kloosterman, H.J.; Molenaar, A.A.A.<br />
Model for the prediction <strong>of</strong> permanent deformation <strong>of</strong> unbound granular materials.<br />
Report WB-13 (7-79-115-5); Road and Railroad Research Laboratory; <strong>Delft</strong> University <strong>of</strong><br />
Technology; <strong>Delft</strong> – 1979.<br />
19. Van Gurp, C.A.P.M.; Molenaar, A.A.A.<br />
Simplified method to predict reflective cracking in asphalt overlays.<br />
Proc. 1 st RILEM Conf. On Reflective Cracking in <strong>Pavements</strong>, pp 190 – 198; Liege – 1989.<br />
20. Jacobs, M.M.J.; De Bondt, A.H.; Molenaar, A.A.A.; Hopman, P.C.<br />
Cracking in asphalt concrete pavements.<br />
Proc. 7 th Int. Conf. on Asphalt <strong>Pavements</strong>; Vol 1, pp 89 – 105; Nottingham – 1992.<br />
21. Molenaar, A.A.A.; Nods, M.<br />
<strong>Design</strong> method for plain and geogrid reinforced overlays on cracked pavements.<br />
Proc. 3 rd Int. RILEM Conference on Reflective Cracking in <strong>Pavements</strong>, pp 311 - 320.<br />
Maastricht – 1996.<br />
22. Lytton, R.L.<br />
Use <strong>of</strong> geotextiles for reinforcement and strain relief in asphalt concrete.<br />
Geotextiles and Geomembranes, Vol. 8, No. 3, 1989.<br />
23. De Bondt, A.H.<br />
Anti-reflective cracking design <strong>of</strong> (reinforced) asphaltic overlays.<br />
PhD Dissertation; <strong>Delft</strong> University <strong>of</strong> Technology; <strong>Delft</strong> – 1999.<br />
24. Francken, L.; Vanelstraete, A.<br />
Prevention <strong>of</strong> reflective cracking in pavements.<br />
RILEM Report 18; E & F.N. Spon; London – 1997.<br />
25. Alemgena Alene Araya<br />
Estimation <strong>of</strong> maximum strains in road bases and pavement performance prediction.<br />
MSc thesis TRE 127.<br />
International Institute for Infrastructural Hydraulic and Environmental Engineering.<br />
<strong>Delft</strong> – 2002.<br />
26. Van Niekerk, A.A.<br />
Mechanical behavior and performance <strong>of</strong> granular bases and sub-bases in pavements.<br />
PhD Dissertation; <strong>Delft</strong> University <strong>of</strong> Technology; <strong>Delft</strong> - 2002