CT 4860 Structural Design of Pavements January 2006 Prof.dr.ir. A.A.A. Molenaar

PART VI

Structural Evaluation and Strengthening of Flexible Pavements Using Deflection Measurements and Visual Condition Surveys

Structural Design of Pavements

PART VI

Structural Evaluation and Strengthening of Flexible Pavements

Using Deflection Measurements and Visual Condition Surveys

January 2006 Prof.dr.ir. A.A.A. Molenaar

2

Table of contents: Preface 3 1. Introduction 4 2. Usage and condition dependent maintenance 6 3. Deflection measurement tools 7 3.1 Falling weight deflectometer 7 3.2 Benkelman beam 8 3.3 Lacroix deflectograph 9 3.4 Factors influencing the magnitude of the measured FWD deflections 10 4. Measurement plan 13 4.1 Estimation of the number of test points per section 13 4.2 Development of a measurement plan 14 5. Statistical treatment of raw deflection data and selection of a location representative for the (sub)section 18 6. Back calculation of layer moduli 26 6.1 Surface modulus 26 6.2 Back calculation of layer moduli 28 6.3 Example 29 7. Analysis of Benkelman beam and Lacroix deflectograph deflection bowls 33 8. Estimation of the remaining life using an empirical based method 38 9. Mechanistic procedures for remaining life estimations and overlay design 43 9.1 Basic principles 43 9.2 Extension of the basic principles 45 10. Extension of the simplified procedure to estimate critical stresses and strains 51 10.1 Relations between deflection bowl parameters and stresses and strains at various locations in the pavement 51 10.2 Temperature correction procedure 54 10.3 Relationships with other strength indicators such as SNC 54 10.4 Relationships between falling weight deflections and deflections measured with the Benkelman beam 55 11. Remaining life estimation from visual condition surveys 56 12. Procedures to estimate material characteristics 58 12.1 Fatigue characteristics of asphalt mixtures 58 12.2 Deformation resistance of unbound base materials 59 12.3 Subgrade strain criterion 59 12.4 Maximum tensile strain at bottom of the bound base 59 13. Overlay design in relation to reflective cracking 61 13.1 Overlay design method based on effective modulus concept 61 13.2 Method based on stress intensity factors 63 13.3 Ovelay design method based on beam theory 64 13.4 Effects of reinforcements, geotextiles, SAMIs and other interlayer systems 69 13.5 Load transfer across cracks 70 14. Effect of pavement roughness on the rate of deterioration 72 References 73

3

Preface: Pavements deteriorate due to damaging effects of traffic and environmental loads and at a given moment in time maintenance is needed. Maintenance activities can grossly be divided into two categories. The first category is the so called routine maintenance which is mainly applied to keep the pavement surface in such a condition that it provides good service to the public but also to limit the effects of ageing. Routine maintenance consists e.g. of crack filling, local repairs and the application of surface dressings. Normally this type of maintenance is not too expensive. The costs of a surface dressing are approximately fl 6/m2 while filling of cracks costs approximately fl 2.5/m. Routine maintenance is done on a regular basis; the time period between two successive applications depends of course on the rate of deterioration which in turn is affected by the damaging power of traffic and climate and by the workmanship of the maintenance crews. The second category is much more capital intensive. Now we are dealing with strengthening of the pavement for which overlays are needed or partial or complete reconstruction. This type of maintenance is less often required than routine maintenance. Because pavement strengthening is such a costly affair, investigations to determine precisely the extent and severity of the damage and the rate of progression are strongly recommended. If a pavement surface e.g. shows severe cracking, removing this layer and replacing it by a new one seems to be a sensible solution. If however the cracking is due to the very low stiffness of the base and no measure are taken to improve the bending stiffness of the base layer, then the cracking will soon reappear. This simple example already illustrates that, in order to be able to make a proper selection of the maintenance treatments available, one not only should know where something is going wrong but also why. Understanding why the pavement fails means that one needs knowledge on the stresses and strains in the pavement as well as the strength of materials. The process of gaining this knowledge is called evaluation of the structural condition of pavements. As it will be shown in these lecture notes, deflection measurements are an extremely useful tool in the assessment of the structural condition of the pavement. During a deflection measurement, the bending of the pavement surface due to a well-defined test load is mea-sured. This is called the measurement of surface deflections. It is clear that the magnitude of the deflections and especially the curvature of the deflection bowl reveal important information on the bending stiffness of the pavement. In the notes ample attention is paid to the techniques for measuring deflections, the way how the measurement results can be processed to obtain information on the stiffness of the individual pavements layers and how they can be used to determine the required thickness of the overlays to be applied. Although all possible care has been given during the preparation of these notes to avoid typing errors etc., it is always possible that some bugs are still present. Furthermore the reader can have suggestions about certain parts of the material presented. It would be highly appreciated if you could send your comments to the author using the following email address. a.a.a.molenaar@citg.tudelft.nl

4

1. Introduction: These lecture notes are dealing with deflection measurements, how they should be performed and how the results can be used to determine the remaining life of the pavement and the maintenance that has to be performed. The importance of deflection measurements can be described by means of the following example. When children have to build a bridge across a creek using a wide variety of wooden beams, their instinct will tell them that they better select those planks that show the lowest de-flection under load. They also know that it is wiser to place the beams like shown in figure 1a than in figure 1b. A B Figure 1: Children know by instinct that placing a beam according to A is more effective than

placing it according to B.

As civil engineers we know that the selection by the children is a correct one because beam A has lower stresses and strains at the outer fibres than beam B when both beams are subjected to the same load. However as civil engineers we also know that the question is it safe or not to cross a beam which shows a maximum deflection of 2 mm cannot be answered without knowledge of the span of the beam, the load applied and the strength of the material from which it is made. This clearly indicates that measurement of only the maximum deflection gives some information about the strength of the beam but that more information is needed. We would already be in a much better shape if the curvature of the deflection bowl due to the load was known. The same is true for pavements. In order to get useful information about the flexural stiffness of the pavement one should measure the deflection due to a test load at various distances from the load centre. We know that the flexural stiffness is determined by the stiffness of the subgrade and the stiffness modulus and thickness of the layers placed on top of the subgrade. It will then be obvious that it must be possible to back calculate the stiffness modulus of each of the indi-vidual layers if the deflection bowl due to a defined test load is known as well as the thickness of each pavement layer. If the stiffness modulus of each layer is known together with its thickness, then the stresses and strains in any location in the pavement can be calculated. Knowledge on the strength of materials however is absolutely needed for the determination of whether or not the pavement is capable of carrying the traffic loads expected in the future and whether or not it should be strengthened. All this means that the usefulness of a deflection measurement program without paying proper attention to the strength of materials can be doubted. In order to determine to what extent traffic loads have resulted in a deterioration of the pave-ment strength, deflections should be measured regularly during the pavement life. Since deflection measurements are fairly costly, one should make a realistic estimate of the number of measurements to obtain a picture of the deterioration trend line that develops in time. One should however be aware of the fact that the trend lines one wants to establish are influenced by variations in temperature (effect on stiffness modulus of the asphalt layers) and moisture (effect on stiffness modulus of the subgrade) and that the deflections measured over a certain stretch of road might show a considerable variation because of variations in layer thickness and stiffness modulus. Another question, which then arises, is how many measurement loca-

5

tions should be tested in a certain section in order to obtain a realistic picture of the flexural stiffness of the pavement. In these lecture notes we will deal with all these aspects. The structure of the notes is as fol-lows. Attention will be paid to the development of a measurement program. This will be followed with a discussion on the determination of the number of measurements required per section and the statistical treatment of the deflection data. Although the Benkelman beam was developed some 40 years ago, it is still in use in many countries. This is also the case with the automated version of the Benkelman beam called the Lacroix deflectograph. A chapter has been devoted to these devices and especially procedures to correct the measured deflections to true deflections are discussed. After that attention will be paid to some simple techniques allowing the overall stiffness of the pavement structure to be assessed and potential problem layers to be identified. Then the back calculation of stiffness moduli will be treated. This will be followed by a discussion on the design of overlays in which probabilistic principles are introduced. After that ample attention will be paid to an analysis method which allows critical strains to be evaluated without the need to back calculate layer moduli. This method is of special interest in case accurate information on the layer thickness is not available. Then attention is paid on the importance of visual condition surveys. A method will be presented that allows the remaining life to be estimated from such surveys. This chapter is followed by a chapter on the estimation of material strength characteristics like the fatigue resistance of asphalt mixtures and the resistance to permanent deformation of unbound granular materials. Reflective cracking is an important issue and the commonly used overlay design methods dont take into account this important phenomenon. Therefore a chapter dealing with the design of overlays controlling reflective cracking is presented. Finally the effect of pavement roughness on pavement deterioration will be discussed and simple procedures to estimate pavement roughness will be given. First of all however attention will be paid to the question why pavement maintenance has to rely on regular monitoring of the pavement condition and why the decision on applying maintenance cannot be taken simply on the basis of the number of years the pavement is in service or the number of loads that have been applied to the pavement.

6

2. Usage and condition dependent maintenance: Pavements deteriorate due to the combined influences of traffic and environmental loads. This means that at a given moment maintenance activities should be scheduled in order to restore the level of service the pavement should give to the road user. It will be obvious that careful consideration should be given to the planning and the selection of the maintenance activity. The right strategy should be applied on the right spot at the right time. Planning of maintenance can be sometimes a rather simple task to perform. If we consider e.g. the maintenance of our illumination systems, we observe that in a number of cases (e.g. hospitals) the bulbs are not replaced after failure, but after a certain number of burning hours. This way of maintenance is called usage dependent maintenance, because the replacement is done after a certain time period the object to be maintained is used. There are three important reasons why such a type of maintenance is possible and accepted for illumination. a. For some reasons we dont accept to be in the dark (safety, interruption of work). b. We know quite precisely what the mean lifetime is of the light bulbs. c. We know quite precisely what the variation is of the lifetime of the light bulbs and we

know that this variation is small. This way of performing maintenance is not very suited to be applied on pavements for the following reasons. a. In most cases some degree of failure is acceptable on pavements. Traffic can e.g. drive

at a fairly high speed level although there is a substantial amount of cracking. This implies that some damage types can be allowed to occur over a significant area and with a significant severity before an unacceptable level of service is reached.

b. Although pavements have been subjected to extensive research, the predictive capability of our performance models is still limited. Even the accuracy of our models to predict the mean pavement life is quite often disappointing.

c. Pavements exhibit a substantial amount of variation in performance mainly due to the variation in layer thickness, material characteristics etc.. This means that two pavements which are nominally the same and which are loaded under nominally the same conditions can show a significant difference in initiation and progression of damage.

All in all a strategy which implies maintenance to be performed after the pavement has been in service for a certain number of years is not applicable for road networks. A certain amount of damage can mostly be allowed because pavement failure seldom results in catastrophic events. Furthermore the variation in pavement life is such that usage dependent maintenance cannot be made cost effective. This implies that the planning and selection of maintenance strategies for pavements heavily relies on input coming from condition observations and predictions based there on. Such an approach to maintenance is called condition dependent maintenance. This immediately means that tools should be available to monitor the condition of the pavement. An overview of such tools is already given in [1]. The lecture notes we have in front of us are dealing with one of the most important evaluation tools being the deflection measurement device.

7

3. Deflection measurement tools: The deflection device that currently receives the highest popularity is the falling weight deflectometer (FWD). Nevertheless other deflection measuring devices like the Benkelman Beam (BB) and the Lacroix Deflectograph (LD) are still used at different places at the world. Especially the Benkelman Beam deserves attention since this low cost device (the price is approximately 1/30 th of the price of a falling weight deflectometer) is used in many developing countries. The principles of these three devices are given elsewhere [1], here only the main features will be described. 3.1 Falling weight deflectometer: The principle of the FWD is schematically shown in figure 2.

Figure 2: Principle of the falling weight deflectometer.

A weight with a certain mass drops from a certain height on a set of springs (normally rubber buffers) which are connected to a circular loading plate which transmits the load pulse to the pavement. Load cells are used to monitor the magnitude and duration of the load pulse. The magnitude of the load pulse can vary between the 30 and 250 kN depending on the mass of the falling weight and the falling height. The duration of the load pulse is mainly dependent on the stiffness of the rubber buffers. Usually pulse duration between 0.02 and 0.035 s are measured. The surface deflections are measured with so called geophones. These are velocity trans-ducers which measure the vertical displacement speed of the surface. By integration the dis-placements are obtained. Since the electronic circuits are only opened a very short moment before the weight hits the buffers, the influence of passing traffic on the magnitude of the deflections is eliminated; only the displacements due to the impact load are measured. The advantage of the FWD is the short duration of the load pulse comparable to the duration of the load pulse caused by a truck driving at approximately 50 km/h. Because of the short pulse duration, the influence of viscous effects can be neglected. One should however be cautious when the modulus of a saturated subgrade with a high ground water level is determined from the deflection measurement results. In that case one might measure the bulk modulus K of the subgrade which, in case of a fully saturated subgrade, can be high. Because road materials are very much sensitive for shear, this high bulk modulus value gives a wrong idea about the real stiffness of the material. This can be illustrated with the following simple example.

8

When a swimmer makes a nice dive from the diving tower he will hit the water in a gentle way, without too much of splash and without hurting himself. We can say that with such a nice dive he experiences the shear modulus G of water which, as we all know, is very low. However when he falls flat on his stomach, his dive is causing him much pain and probably a blue stomach. In this case he experiences the bulk modulus K of water which, as we know, is very high. A fluid with no air bubbles is in fact incompressible. 3.2 Benkelman beam: The principle of the Benkelman beam, invented by A.C. Benkelman is schematically shown in figure 3.

Figure 3: Principle of the Benkelman beam.

The measuring system consists of a beam that can rotate around a pivot attached to a reference frame. The load is supplied by a truck that slowly moves to or from the tip of the beam. The advantage of the BB is the fact that the device is simple and cheap. The disadvantage is the slow speed of the truck that can cause all kinds of viscous effects making the measurements difficult to interpret. Furthermore the effects of passing vehicles on the magnitude of the deflection cannot be neglected. Finally it should be mentioned that the supports of the reference frame could stand in the deflection bowl. This means that the frame is not a true reference and corrections for movement of the support system have to be made in order to obtain the true deflections. Quite often only the magnitude of the rear axle load of the truck used as loading vehicle for the BB measurements is reported. This is absolutely insufficient; precise knowledge of the tyre pressure, tyre spacing and area of the tyre print is necessary in order to allow proper analyses to be made. Different measurement procedures exist and one should strictly adhere to the guidelines for doing the measurements when one of such procedures is used. Furthermore one should realise that the dimensions of the BB can differ. There are devices with shorter and longer measuring beams. One should take good notice of this in order to overcome that a beam is used that doesnt comply with the requirements set in the procedure to be used.

9

3.3 Lacroix deflectograph: Figure 4 shows the Lacroix deflectograph (LD). The principle of the measurement is the same as that of the Benkelman beam. The major difference however is that the measuring system is attached to the loading vehicle and that it is moved automatically to the next measuring position. This procedure is schematically shown in figure 5. It is obvious that the LD has large advantages over the BB. First of all the measurements are continuously taken and are far less affected by the varying speed of the loading vehicle. With the BB measurements the speed of the truck varies between 0 (at the beginning of the measurements) and approximately 5 km/h when the truck drives at constant speed. The speed of the LD vehicle is more or less constant at 5 km/h. The LD however suffers from the same disadvantages as the BB. The low speed can cause that the viscous behaviour of the asphalt surfacing cannot be neglected and corrections for movement of the reference frame need to be applied. Because the entire measurement procedure is automated, much more measurements can be taken with the LD as with the BB in the same time period. This however has its price; the LD has about the same price level as the FWD.

Figure 4: Principle of the Lacroix deflectograph.

10

Figure 5: Principle of the automatic positioning of the measuring system of the LD.

3.4 Factors influencing the magnitude of the measured FWD deflections: When civil engineers are dealing with measurements they quite often show a bad habit which is that they accept the measurement result as the truth. They seldom realise that the mea-surement result is affected by a large number of factors and that the magnitude of the influence of these factors should be known in order to avoid misinterpretations. A number of such influence factors on deflections measured with a FWD will be discussed here. The material presented is based on the excellent work done on this topic by van Gurp which is reported in [10]. When a number of FWD devices are used on the same pavement to measure the deflections, one will notice that all these devices will not measure the same value. This is even true when the deflections are corrected to a particular load level. Some reasons for that are described hereafter. It is a well-known fact that the stiffness of rubber is temperature dependent. At higher temperatures the stiffness will be lower than at lower temperatures. This is nicely shown in figure 6 where the stiffness of a particular rubber buffer used in a particular FWD is given in relation to the load level and the temperature. It will be obvious that the temperature in the rubber buffers will vary when a FWD survey is done starting early morning and ending late afternoon. This is not only because of the variation in air temperature but also because of the cumulative energy that is collected in the buffer, and that is transformed in heat, because of the large number of measurements that are taken during the day. This means that the stiffness of the rubber buffer will vary during the

11

day. The effect is of course more pronounced if measurements done in the winter have to be compared with those done in the summer.

Figure 6: Static spring constant of a particular rubber buffer used in a particular FWD.

If for some reason the spring stiffness decreases, the shape of the load pulse changes. Its peak value will decrease while the duration of the pulse will increase. The longer duration of the pulse might cause a somewhat softer response (lower stiffness) of the pavement. More important of course is the fact that differences between the devices occur if they have different buffers and if the deflections have to be corrected to a predefined load level. Furthermore one has to be careful when using the FWD for studies on the non linearity of pavements. Especially pavements where the main body is formed by unbound materials, will show non linear behaviour. One might try to analyse this by doing deflection measurements at different load levels but from the text given above it will be clear that at least some of the non linearity that is measured is caused by the device itself!! Research in [10] has shown that it is wiser to correct the deflections based on the area enclosed by the load vs time plot rather than based on the peak load. Other effects, which are unfortunately more of the black box nature, are the following. As mentioned, geophones are used to measure the deflections. The nature of the geophones however is that their sensitivity reduce with decreasing frequency. Especially below 10 Hz, the sensitivity decreases rapidly. However these low frequencies contribute significantly to the frequency spectrum of a single deflection pulse. Especially the frequency spectrum of deflection pulses measured on thin pavements laid on soft subgrades will show the great contribution of the low frequencies. If the geophones dont pick up these low frequencies, a too low deflection will be recorded and one would expect the pavement to have a higher flexural stiffness than it really has. This effect can be compensated by using high gain factors for the low frequencies. The way in which this is done depends however on the manufacturer and information on this is usually confidential information. It has also been shown in [10] that the system processor can deform the deflection readings. For one FWD system, the influence of the system processor appeared to be so large that it did not pass the calibration procedure and could therefore not be used in FWD surveys. Another influence factor is the smoothing of signals that is applied on the FWD deflections. This smoothing is done in order to get rid of high frequency disturbances. The question then always is what the cut-off frequency should be. Studies reported in [10] have shown that if f = 60 Hz is chosen as cut-off frequency, the effect of the smoothing is minimal. Again it is noted that one should ask the FWD supplier to give details on this important aspect.

12

From the text given above it is clear that there are several influence factors which cause that the deflections measured with one device are different from those measured with an other device. It is clear that calibration is vital in order to avoid unexpected and unacceptable differences between devices to occur.

13

4. Measurement plan: The question always is how many measurements should be taken and where should the measurements be taken on a specific stretch of pavement in order to get a reliable picture of the flexural stiffness of the pavement. Some guidelines for this will be given in this chapter. 4.1 Estimation of the number to test points per section: In this section the method presented in [2] is described which allow the number of tests to be determined that are needed on a particular road section to obtain a proper insight in the bearing capacity of the pavement. One can calculate a statistical quantity R, called the limit of accuracy, which represents the probable range the true mean differs from the average obtained by n tests at a given degree of confidence. The larger n is, the smaller value will be obtained for R which means that the mean value calculated from the data obtained from the tests will differ less from the true mean value. The mathematical expression is: R = K . ( / n ) Where: K = standardised normal deviate which is a function of the desired confidence level 100 . (1 - ),

= true standard deviation of the random variable (parameter) considered. If the confidence level is chosen and if a proper estimate for is obtained, R is inversely proportional to the square root of the number of tests. Figure 7shows the basic shape of the relation between n and R.

Figure 7: Typical limit of accuracy curve for all pavement variables showing general zones.

14

As shown in figure 7, 3 zones can be discriminated. In zone I a small increase in the number of tests reduces the value of R tremendously and the accuracy of the predictions will increase drastically. In other words a small increase in budget to increase the number of data points is really value for money. In zone III, R hardly reduces with an increasing number of tests. This means that in this case very little extra value is obtained from an increased measurement budget. The optimal number of tests can be found in zone II. The main problem in calculating R is the assessment of the standard deviation . Since the magnitude of the deflections can vary quite considerably within one pavement section and between pavement sections (thick pavements compared with thin pavements), it is not possible to give a single value for . Nevertheless it is possible to give values for the coefficient of variation CV for the measured deflections which are observed in practice. Typical values are: CV = standard deviation / mean = 0.15 low variation, typical for pavements which are in good condition, 0.30 medium variation, typical for pavements which show a fair amount of damage, 0.45 high variation, typical for pavements which show a large amount of damage. By using these CV values and adopting confidence levels of 95% ( = 0.05) and 85% ( = 0.15), figure 8 has been constructed. The use of the procedure is illustrated by means of the following example. A deflection survey has to be performed on a road that is in reasonable condition and the question is how many measurements need to be taken to obtain a reliable picture of the flexural stiffness of the pavement. Because a reliable picture is desired the average deflection is allowed to differ 8% from the true mean. The required confidence level is 95%. Since the pavement shows some damage a CV is estimated of 20%. By interpolation, the position of the line for CV = 20% is estimated in figure 8a. Using this line and the R-value of 8%, the number of observations to be taken is equal to 7. 4.2 Development of a measurement program: Before one decides on where and how many deflection measurements should be taken, a visual condition survey should preferably be performed. It is e.g. important to know which types of defects are present on the pavement and how the various defect types are distributed over the pavement surface. Is the damage evenly distributed or is the damage concentrated in a limited number of locations. A visual condition survey is not only needed to develop an effective measurement plan, but the condition data are also needed in the evaluation phase when decisions on the maintenance strategy to be applied need to be taken. The most important damage types to consider in the structural evaluation of pavements are of course cracking and deformations because they are related to lack of flexural stiffness. If cracking and deformations occur rather locally it is not recommended to use an equal spacing between the measurement points but to locate them in such a way that an as good as possible sample of both sound and cracked cq deformed areas is obtained. For reasons that will be discussed later on, it is recommended to measure both the outer wheel track as well as the area between the wheel tracks, the latter being representative for the flexural stiffness of the undamaged pavement. These measurements are of course only useful if the area between the wheel tracks is not damaged. In case of severe longitudinal or transverse cracking, it is recommended to perform some measurements across the crack. This can be done very easily with the FWD using the geophone positions schematically shown in figure 9.

15

Figure 8a: Graph to estimate the number of observations required at a confidence level of 95%.

Figure 8b: Graph to estimate the number of observations required at a confidence level of 85%.

16

Figure 9: Placement of loading plate of FWD and geophones for load transfer measurements.

Deflection measurements across the crack are important in order to be able to determine the amount of load transfer. This parameter has a significant influence on the thickness of the overlay; if there is e.g. no load transfer at all, additional maintenance work like milling and filling of the cracked area might be necessary. The magnitude of the measured deflections is dependent on the temperature, which affects the stiffness of the asphalt layers, and the moisture content, which can have a significant effect on the stiffness of the subgrade and other unbound layers. This means that if mea-surements are taken at various periods of the year, corrections are needed in order to be able to compare them. In order to avoid the rather complex corrections due to moisture variation, it is recommended to take the measurements in the so-called neutral period. During such periods the moisture content in the unbound materials is approximately at its mean level. In the Netherlands that is the late April early May period and the October month. Because BB and LD measurements are taken at relatively low speeds, one should not perform these measurements at too high temperature levels because otherwise viscous effects will have a significant influence on the measurements which makes interpretation there-of complicated. Also the temperatures should not be too low because then the deflections might be so small that accuracy problems occur in the measurement and monitoring of the deflections. For that reason the Transport and Road Research Laboratory (TRRL) in the UK has suggested the temperature ranges shown in table 1 at which the BB and LD measurements should preferably be taken. Maximum temperature 30 oC if bitumen has a penetration lower or equal than 50 25 oC if bitumen has a penetration higher than 50 Minimum temperature 5 10 oC depending on the structure

Table 1: Maximum and minimum temperature for deflection measurements as specified by TRRL.

17

One should realise that the influence of temperature always has to be taken into account and that the deflections measured always should be corrected to a reference temperature. The temperature correction procedure will be presented in an other chapter.

18

5. Statistical treatment of raw deflection data and selection of a location representative for the (sub)section:

Statistical treatment of the data as measured is always needed in order to be able to recog-nise trends and in order to limit the amount of work that should be done in the evaluation process. It is e.g. not necessary and even not useful to back calculate the layer moduli for each measurement location simply because of the fact that it is impossible to obtain accurate layer thickness information for each and every location. It is therefore much more effective to concentrate the analysis on locations which can be taken as representative for a particular section or sub-section. Simple statistical procedures have shown to be very effective to discriminate homogeneous sub-sections within a larger section. A homogeneous sub-section is defined as a section where the deflections and so the flexural stiffness are more or less constant. When such homogeneous sub-sections have been determined, one has to take a point which can be taken as being representative for that sub-section. That point can be the location where the measured deflection bowl comes closest to e.g. the average deflection profile or the 85% deflection profile. The 85% profile is the profile that is exceeded by 15% of all the measured profiles. The so-called homogeneous sub-sections can be determined by means of the method of the cumulative sums. The cumulative sums are calculated in the following way. First of all the mean of a variable over the entire section is calculated (e.g. the mean of the maximum deflection). Then the difference between the actual value of the variable and the mean is calculated. Next these differences are summed. In formula the cumulative sums are calculated using: S1 = x1 - S2 = x2 - + S1 Sn = xn - + Sn-1 Where: Sn = cumulative sum at location n, xn = value of the variable considered at location n, = mean of variable x over entire section. The method is illustrated by means of an example. Table 2 shows the deflections that were measured by means of a FWD on a particular road in the Netherlands. The load applied was 50 kN, the diameter of the loading plate was 300 mm. The table gives values for d0, d300, etc.; these are the deflections measured at a distance of 0 and 300 mm etc.. An important value is the surface curvature index SCI, which is the difference between the maximum deflection d0 and the deflection, measured at 600 mm from the loading centre (d600). Also the logarithm of the SCI values is reported. Also this is an important characteristic as will be shown later on. As one will observe from the table, high deflections are measured and the amount of variation in the measured deflections is very high. It should be noted that the pavement considered was a polder road on a very weak subgrade and showed a significant amount of damage. It should be noted that the example presented is a rather extreme one; normally such large variations in deflections are not observed. Figure 10 is a graphical representation of the measured deflections, while figure 11 shows the variation of the SCI over the section. Figure 12 shows in a graphical form the variation of the cumsum (cumulative sum) as determined for the SCI. The SCI is selected as parameter decisive in the determination of the homogeneous subsections since the SCI can be considered to be the most important deflection parameter. Homogeneous sub-sections can easily be recognised from figure 12 since by definition an area over which the slope of the cumulative sums plot is more or less constant indicates an area where the differences between the actual measured values and the overall mean value are approximately the same.

19

Table 2: Deflection testing results obtained on a particular section and summary statistics.

20

Figure 10: Results of a deflection survey.

21

Figure 11: Surface curvature index.

22

Figure 12: Cumulative sum of the surface curvature index.

23

The following sections are discriminated.

Section Locations 1 0.05-0.1-0.15 2 0.2-0.25-0.3 3 0.35-0.4-0.45 4 0.5-0.55-0.6 5 0.65 this is a single point clearly visible in the SCI plot 6 0.7-0.75-0.8-0.85-0.9-0.95 7 1 this is a single point clearly visible in the SCI plot 8 1.05-1.1-1.05 9 1.1-1.15-1.2-1.25-1.3-1.35-1.4-1.45 10 1.5 this is a single point clearly visible in the SCI plot 11 1.55-1.6 12 1.65-1.7-1.75-1.8-1.85-1.9-1.95-2 By means of the cumsum method we have arrived to a set of successive sub-sections, each of them having more or less a certain flexural stiffness. Now it is interesting to determine if we can combine a few sections. If this is possible we would reduce the work load. The question now is how to achieve that. If we compare the slopes of the different sections we notice that the slopes of sections 2, 4 and 12 are about the same. This means that they can be taken as one section in the further analysis. This also holds for sections 1 and 6, so also these can be treated as one section. The same is true for sections 3, 8 and 11. Then we have a look to the single points that are discriminated and we try to assign them to a particular subsection. We observe that location 0.65 is clearly an isolated peak value and should therefore be treated as such. Location 1 however could very well be combined with section 2. Also location 1.5 is better treated as a single point. All in all we arrive to the subsections given below. Section Locations 1 0.05-0.1-0.15 and 0.7-0.75-0.8-0.85-0.9-0.95 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

-1.9-1.95-2 and 1 3 0.35-0.4-0.45 and 1.05-1.1-1.15 and 1.55-1.6 4 0.65 5 1.1-1.15-1.2-1.25-1.3-1.35-1.4-1.45 6 1.5 The statistics of the sub-sections mentioned above are tabulated below. Section Mean Value SCI Standard Deviation SCI Var. Coeff. 1 420 111 26% 2 175 65 37% 3 494 62 13% 4 962 5 423 77 18% 6 96 As one will notice, rather high values for the coefficient of variation are still obtained for sections 1 and 2. We have to look then in table 2, in order to find out what the possible reasons for this could be. By doing so we observe that location 0.8 doesnt really fit in section 1 and should better be moved to section 2. The high variation in section 2 is probably caused by the inclusion of locations 1.7 and 1.75; also location 1.9 could contribute to the high variation. Therefore it is suggested to move location 1.9 to section 1 and to combine locations 1.7 and 1.75 with location 1.5. We then obtain the sections and summary statistics as shown in table 3. As one can observe a better result in terms of lower coefficients of variation are obtained. The division in subsections as shown in table 3 will be used for further treatment.

24

Section Locations Mean SCI SD SCI Var. Coeff. 1 0.05-0.1-0.15-0.7-0.75-0.85-0.9

-0.95-1.9 434 87 20% 2 0.2-0.25-0.3-0.5-0.55-0.6-0.8-1

-1.65-1.8-1.85-1.95-2 181 40 22% 3 0.35-0.4-0.45-1.05-1.1-1.15-1.55-1.6 494 62 13% 4 0.65 962 5 1.1-1.15-1.2-1.25-1.3-1.35-1.4-1.45 423 77 18% 6 1.5-1.7-1.75 87 11 13%

Table 3: Homogeneous sub-sections based on SCI An other approach to the reduction of the data is to make a frequency plot of the deflections measured. Figure 13 is an example of such a plot based on the measured SCIs. In making a frequency plot one has to decide about the number of classes to be used. A practical guideline for this is to take the number of classes equal to the square root of the number of observations. From figure 13 it is clear that we have 1 observation in the range SCI = 0 72 m, 13 observations in the range SCI = 73 220 m, 6 observations in the range SCI = 221 369 m, 13 observations in the range SCI = 370 517 m, 6 observations in the range SCI = 518 665 m and one extreme value which is the SCI = 962 m measured at location 0.65. The locations which belong to the frequency classes and the summary statistics are given in table 4. Frequency Locations SCI. Class Mean St. Dev. Var. Coef. 0 72 1.75 72 73 220 0.2-0.25-0.3-0.5-0.8-1-1.5-1.65-1.7-1.8-1.85 -1.95-2 157 37 24% 221 369 0.05-0.55-0.6-1.2-1.3-1.9 306 42 14% 370 517 0.1-0.15-0.35-0.45-0.7-0.85-0.95-1.15-1.25 -1.35-1.4-1.45-1.55 430 40 9% 518 665 0.4-0.75-0.9-1.05-1.1-1.6 550 33 6% higher 0.65 962

Table 4: Frequency classes for the SCI, locations and summary statistics. As one can observe from table 4, this approach results in a grouping of the deflection data in such a way that the coefficient of variation in one group is limited to very small. From the description given above it will be clear that several techniques are available for reduction of the raw deflection data. In principle the cumulative sum technique is a very powerful tool to discriminate homogeneous sections. However situations might occur that even the cumsum technique results in sections which exhibit a rather high degree of variation. In that case reduction of data through an analysis of the frequency distribution can result in data sets which are rather homogeneous in nature. The big advantage of the cumsum technique is that it results in physical section units ready to receive maintenance whereas the other approach doesnt result in such units. All in all this means that the data reduction process and the statistical analysis of the raw data is not a straightforward process. Each time the data set should be treated carefully in order to select the most appropriate way to reduce the data. The selection of the location which can be considered to be representative for the entire (sub)section is done in the following way. First of all one has to decide whether one wants to base the analysis on the mean conditions or whether one wants to do the analysis using a deflection profile that is exceeded by only 15% of the measured profiles. In the first case one selects a measured profile that comes closest to the mean profile while in the second case one selects a measured profile that comes closest to the 85% profile.

25

In section 1 of table 3, location 0.85 has the SCI value (453) that comes closest to the mean SCI value of that section being 434, while location 0.75 has the SCI value (525) that comes closest to the 85% profile of that section being 521 (mean plus one standard deviation). These locations are then selected as being the representative locations for this section. Cores are taken at those locations to obtain accurate information on the thickness of the layers. This information is needed to allow accurate back calculations of the layer moduli to be made.

Figure 13: Frequency distribution of the measured SCI values.

26

6. Back calculation of layer moduli: Back calculation of layer moduli is quite often considered as an important step in pavement evaluation. The reason for this is quite simple; the magnitude of the back calculated stiffness modulus quite often reveals whether or not the pavement layer is damaged or not. If e.g. a stiffness modulus of 600 MPa is back calculated for a cement treated layer, this layer should be in a rather deteriorated state because the modulus of a sound cement treated layer is substantially higher. One of the drawbacks of back calculating layer moduli is the fact that accurate information on the thickness of the various layers should be available. We know that the deflections are heavily influenced by the product E.h3, which means that a small error in the layer thickness can have a large effect on the magnitude of the back calculated modulus. Although computer programs are available that back calculate the layer moduli automatically when the deflections, the load configuration and the thickness of the different layers is known, back calculation of layer moduli is certainly not as straightforward as it may look like because in many cases the solution is not unique. This implies that some pre-treatment of the data is necessary before the actual back calculation process is started. In the sections hereafter the surface modulus diagram will be discussed first of all. This diagram provides insight in how the overall stiffness of the pavement develops from bottom to top and whether or not weak interlayers are present. After that the actual back calculation process will be discussed. It should be noticed that the procedures described are especially valid for the analysis of FWD measurements. They can however also be used for the analysis of BB and LD measurements provided that the appropriate corrections are applied. These correction procedures will be described in a later section. 6.1 Surface modulus: According to Boussinesqs theory, the elastic modulus of a homogeneous half space can be calculated from the deflection measured at a given distance following: E = . a2 . (1 - 2) / dr . r E = 2 . . a . (1 - 2) / d0 Where: E = elastic modulus, a = radius of loading plate, = Poissons ratio,

= contact pressure under loading plate. The question now is whether this formula can be of use in analysing the stiffness develop-ment in a pavement. Let us consider therefore figure 14.

Figure 14: Distribution of the vertical stress in a pavement.

geophones

a b

27

The way in which the load is distributed depends on the thickness and the stiffness of the layer. In figure 14, the top layer is the stiffest followed by the base and the subgrade. It is obvious that only that part of the pavement that is subjected to stresses, will deform; that is the area enclosed by the cone. This means that the geophone that is farthest away from the load centre (geophone a) only measures deformations in the subgrade while the geophone in the load centre (geophone b) measures the deformations in the subgrade, base and top layer. This implies that if the Boussinesq formula is applied using the deflection value measured by geophone a as input, the modulus of the subgrade is calculated. In case Boussinesqs equa-tion is used using the reading of geophone b as input, an overall effective stiffness of the pavement is calculated. So the stiffness calculated from the geophone readings going from a to b give information about: the subgrade, the subgrade plus some effect of the base, the subgrade plus the base plus some effect of the top layer, the subgrade plus the base plus the top layer; in short: increasing moduli value will be calculated. All this means that the deflection readings taken at a certain distance from the load centre give in fact information on the stiffness of the pavement at a certain depth. Using this information a so-called surface modulus plot is constructed. On the vertical axis one plots the surface modulus calculated using the Boussinesq formulas and on the horizontal axis one plots the equivalent depth which is equal to the distance of the geophone considered to the load centre. The principle of the plot is schematically shown below. Figure 15 shows the surface modulus plots as calculated using the deflections measured at locations 0.65 and 1 (see table 2). The figure indicates that we are dealing with a weak pavement because the surface modulus values are very low and because the stiffness hardly increases from bottom to top. Only in location 1 some stiffening due to the base and top layer is visible. As shown below, different shapes of the surface modulus plot can be obtained.

Surface Modulus

Equivalent Depth

Equivalent Depth

Surface Modulus

28

The drawn line indicates a pavement where the stiffness gradually increases from bottom to top while the dashed line indicates a pavement which has layers with a low stiffness on top of the subgrade. The reason for this might be stress dependent behaviour, lack of compaction, moisture effects etc.. It might very well be that the material with the lower stiffness is in fact the same material as the subgrade material. This is e.g. the case with fill material that cannot be compacted to the density of the existing subgrade.

Figure 15: Surface modulus plots for locations 0.65 and 1. The surface modulus plot assists in deciding how many layers should be taken into account in the back calculation analysis. As indicated, the number of layers to be considered is not only the number of physical layers, top, base, sub-base and subgrade; one also has to take into account the fact that within one layer, sublayers may occur with a different stiffness. 6.2 Back calculation of layer moduli: Back calculation of layer moduli from measured deflection bowls is done in an iterative way. The input for the calculations consists of the measured deflection profile, the load geometry used to generate the deflections and the thickness of the layers. Furthermore the cores that are taken from the pavement to determine the thickness of the layers give information on the materials used and the quality of the materials. From the surface modulus plot an estimate is obtained for the modulus of the subgrade and furthermore the surface modulus plot provides information that helps to decide whether or not low stiffness sublayers should be introduced in the analysis. Then moduli values are assigned to the various layers and the deflections are calculated. Next the calculated deflections are compared with the measured ones. If the differences are too large, a new set of moduli is assumed and the deflections are calculated again. This process is repeated until there is a good match between the calculated and measured

29

deflections. Normally the analysis is stopped when the difference between the measured and calculated deflections is 2%. As has been mentioned before, the iterative back calculation procedure can either be an automatic or a hand operated one. In the automatic procedures the computer program automatically performs the iterations while in the hand operated procedure it is the experienced engineer who controls the iteration process. Both procedures have their advantages. The automatic procedure is fast but might sometimes result in funny results. By funny it is meant that the set of moduli that is back calculated results in a good fit between the measured and calculated deflections but the moduli value themselves cannot be true given the type and condition of the materials in the pavement, given the temperature conditions etc.. Such results can occur because the back calculation procedure doesnt necessarily result in a unique answer. In such cases the hand operated procedure is more powerful because the experienced engineer can adjust the moduli values to such levels which are reasonable for the type and condition of the pavement materials present and still result in a good fit between measured and calculated deflections. Problems with back calculating layer moduli can occur when the top layer is thin (< 60 mm) or when the base layer has a higher stiffness than the top layer. A golden rule in the back calculation analyses is that one never must vary the moduli values of all layers in the same time. This should be done in a step by step procedure. First of all one should try to find a modulus value for the subgrade by finding a good fit between the deflections measured and calculated at the largest distance to the load centre (see also figure 14). Then one tries to fit the deflections at intermediate distance from the load centre; this will result in the moduli for the sub-base and base. Finally one should fit the deflections at the shortest distance to the load centre and the maximum deflection; this results in the modulus for the top layer. Furthermore one should realise that a good fit of the measured SCI is of great importance since this value gives a lot of information on the strain levels in the pavement. Sometimes the measured deflection profiles are not easy to match. In such cases one should notice that a good match of the SCI is to be preferred over a good match of the deflections measured at a greater distance from the load centre. 6.3 Example: The example that will be given here is taken from the OECD FORCE test pavements that were built at the LCPC test facilities in Nantes, France. These pavements were tested by means of the accelerated load testing device of the LCPC. The aim of the project was to study pavement response and performance of three types of pavements under accelerated loading. The results of the FWD data evaluation of two test pavements are discussed here [3, 4]. Figure 16 shows the two pavement sections analysed. I II

subgrade

Figure 16: Structures I and II of OECDs FORCE project.

60 mm asphalt 300 mm base

120 mm asphalt 300 mm base

30

The clayey subgrade was covered with a 300 mm thick base on which 60 mm resp. 120 mm asphalt was placed. Figure 17 shows the maximum deflection level as measured on the top of the base as well as the maximum deflections that were measured after placing the asphalt layers. Figure 18 shows the thickness of the top and base layer as determined by means of the Penetradar.

Figure 17: Deflections measured on top of the base and top of the asphalt layer.

Figure 18: Thickness of the layers of sections I and II.

Figure 19 shows the surface modulus plots representative for both sections determined from the deflections measured on top of the completed sections.

31

Figure 19: Surface modulus plots representative for the OECD FORCE sections. Three things appear from this figure. First of all the additional 60 mm asphalt which is present on section II contributes significantly to the stiffness of the pavement. Secondly, the modulus of the base and subgrade seems to be highly sensitive to the stress level. In both sections materials were used which are nominally the same. In section II however, the stresses in the base and subgrade are much smaller because of the thicker asphalt layer on top. The effect of the lower stress level in base and subgrade results in higher values for the surface modulus. Furthermore one should realise that the plot was made based on measurements which were taken at a temperature of approximately 6 0C which means that the stiffness of the asphalt layer was fairly high and the stress levels in the base and subgrade are rather low . Thirdly the figure shows that on top of the subgrade, layers are present with a much lower stiffness. It appeared that a fill had to be placed in order to have the pavement surface at the right level. The fill was made with the subgrade material but problems during compaction had occurred. This lack of density of the fill has of course a direct effect on the density and so the stiffness of the base layer placed on top. The low surface modulus values could, in this case, easily be explained from the construction history. Based on this knowledge it was decided to divide the base layer in two sublayers, each being 50% of the total base thickness, and to divide the subgrade in two sublayers. This was done by assuming a thickness of 500 mm of low stiffness subgrade material on top of the stiff deep subgrade. The selection of this thickness is based on experience, sometimes a thickness of 1000 mm is chosen. All in all it means that for the back calculation analysis, the pavement was divided in 5 layers (top layer, two base layers, two subgrade layers). The results of the analysis are shown in table 5.

32

Section I

Temp Force Layer E-mod Position Meas. Calc. Diff. Thickn. Defl. Defl.

[ 0C] [kN] [mm] [Mpa] [mm] [m] [m] [%] 6.4 57.0 56 15980 0 1049 1050 0.1 146 106 300 655 655 0 146 150 600 318 318 0 500 37 900 158 163 3.2 171 1200 92 92 0 1500 63 60 -4.8 1800 46 46 0

Section II

Temp Force Layer E-mod Position Meas. Calc. Diff. Thickn. Defl. Defl. [ 0C] [kN] [mm] [Mpa] [mm] [m] [m] [%] 6.8 58.0 145 10514 0 415 417 0.5 130 117 300 329 326 -0.9 130 239 600 217 216 -0.5 500 48 900 133 135 1.5 276 1200 83 83 0 1500 50 51 2.0 1800 34 33 -2.9

Table 5: Results of the back calculation analysis for the OECD FORCE sections.

It should be noted that the FORCE examples are complicated ones; normally one has to deal with less complicated deflection profiles. 6.4 Computer program: As had been mentioned before, several computer programs are available that allow the values for the layer moduli to be backcalculated in an automatic way. One of those programs is the program MODCOMP 5 developed by prof. Irwin of the Cornell university in the USA. The program can be found on the cd which is part of these lecture notes. At the end of these lecture notes an appendix, appendix I, is given which contains a description of how the program has to be used. 7. Analysis of Benkelman beam and Lacroix deflectograph

deflection bowls:

33

BB and LD measurements are usually related to empirical evaluation and overlay design methods. However an elegant procedure has been developed [5] which allows these deflection readings also to be used for back calculation purposes. The procedure is correcting the measured deflections that might be influenced by the movement of the support system to true deflections. One drawback of the method is that it doesnt take into account viscous effects that might occur due to the slow speed of the loading vehicle. The basis of the method is the Hogg model which consists of a plate (E1, h, 1) resting on an elastic foundation (E2, 2). The assumption that the top layer behaves like a plate implies that no vertical displacements are developed in this layer. The characteristics of the pavement structure are characterised by: D = E1 . h13 / {12 . (1 - 12)} stiffness of the top layer(s) R = 2 . E2 . (1 - 2) / {(1 + 2) . (3 - 42)} reaction of the subgrade L0 = ( D / R )0.33 critical length The shape of the deflection profiles is described following d0 / dr 1 = + . (r / L0)

Where: d0 = maximum deflection, dr = deflection at distance r from the load centre. This equation is graphically represented in figure 20. Using the specific dimensions of both the deflectograph and the BB (figure 21) as well as the above mentioned pavement characteristics, true deflection profiles as well deflection profiles that would be measured were calculated; typical results are shown in figure 22.

Figure 20: Graphical representation of an equation used to describe

the shape of deflection profiles. In the development of the model the following values were assumed for the wheel and axle loads as well as contact pressures. Axle Pfa/Pra P1 I1 W1 1 P2 I2 W2 2-1 Paxle

34

[N] [mm] [mm] [MPa] [N] [mm] [mm] [MPa] [N] rear 0.6 1750 250 177 0.05 21750 192 136 1.062 94000 front 0.6 336o 320 220 0.061 25040 270 186 0.635 56800

Figure 21: Dimensions of the LD and BB as well as of the loading vehicle.

35

Figure 22: Recorded and true LD (lac) and BB (ben) deflections.

36

Based on these calculations, evaluation diagrams were developed which allow true deflections to be calculated from the measured LD and BB deflections. These diagrams are shown in figure 23. In this figure some abbreviations are used which are not explained in the figure; the meaning thereof is described hereafter. DCGRA = maximum deflection according to the Canadian Good Roads Association method, DAI = maximum deflection according to the Asphalt Institute method, DTRRL = maximum deflection according to the Transport and Road Research Laboratory method. The method will be illustrated with some examples. Let us assume that a maximum deflection was measured with the LD of 393 m. From the measured deflection profile it was determined that the distance at which the deflection was 50% of the maximum deflection (Lx, x = 50%) was 368 mm. From the evaluation charts one can derive that L0 = 178 mm and the ratio D00/Dlac = 1.226. This means that the true maximum deflection is 482 m. The ratio D00 . R / Pra equals 0.47 and with a rear axle load Pra = 91.6 kN this results in an R value of 89.5 Mpa and a subgrade modulus of 149 Mpa (assuming 2 = 0.35). Since L0 and R are known, D can be calculated. Furthermore we can determine the maximum BB deflection that would be obtained following the TRRL procedure. One observes that DTRRL/Dlac = 0.98 which means that the value that has to be used in the TRRL evaluation procedure equals 385 m. It is stressed that figure 23 is only applicable for the load and LD and BB geometries shown in figure 21. One should keep in mind that the moduli obtained in this way are quasi-static moduli. It is a well-known fact however that for most materials there is a difference between the static and the dynamic modulus. From an extensive correlation study it was observed that the subgrade modulus as determined by means of the BB or LD and the FWD relate to each other following: EFWD / Elac = 101.4576 (t 0.255) Where: t = loading time of the LD or BB [s].

37

Figure 23: Evaluation chart to determine true LD and BB deflections from measured deflections.

38

8. Estimation of the remaining pavement life using an empi-rical based approach:

A number of empirical pavement evaluation and overlay design methods have been developed in time. Well known are the methods developed by the Asphalt Institute and the Transport and Road Research Laboratory. Although extensively used all over the world, this author believes strongly that one has to be very cautious in using these methods for situations they have not been developed for. The hart of the TRRL method e.g. are the performance charts developed for several pavement types. An example of such a chart is given in figure 24 [6]. For the sake of completeness the load and load configuration used for the BB measurements according to the TRRL procedure are shown in figure 25. The point is that pavement performance is dependent on the traffic, the materials and structures used, and the climate, all of them are typical British in case of the TRRL method. This means that the chances are very small that the method can be used without modifi-cations in countries like e.g. Pakistan or Yemen where traffic, climate, and materials are significantly different from UK conditions. Another severe problem with the TRRL method is that an important input parameter, being the number of equivalent 80 kN single axles that have passed the pavement, is not known in many cases. Nevertheless the author also believes that the TRRL method can be used in other conditions as well provided this is done by making the evaluation charts dimensionless. The procedure to do so is outlined hereafter. Let us define the following variables: DeltaDefn = increase in deflection since time of construction, DeltaDefc = difference between the initial deflection and the critical deflection, this latter value depends on the probability of achieving life that is used to define pa- vement failure, n = applied number of load repetitions, Nc = number of load repetitions at which critical deflection level is reached. Work presented in [7] has shown that performance curves like the one presented in figure 24 can be written in a dimensionless shape following: DeltaDefn / DeltaDefc = (n / Nc)b The shape parameter b seemed to be dependent on the initial deflection level following: for granular bases: b = 0.06 Def00.4639 for bituminous bases: b = 0.0185 Def00.7186 An important question in all this is how DeltaDefc and the initial deflection Def0 are related. From the analysis in [7] it appeared that for pavements with granular bases and accepting 50% of achieving life as the failure condition, the ratio DeltaDef0 / Def0 can be expressed as follows: DeltaDefc / Def0 = 0.4767 0.000299 Def0 Where: Def0 = maximum deflection measured with the BB according to the TRRL procedure [m] of the pavement when not subjected tot traffic loads. For bituminous bases this relation can be written as: DeltaDefc / Def0 = 0.34833 0.000198 Def0 If we dont know the number of load repetitions applied to the pavement, how do we derive DeltaDefn? It will be shown hereafter that we can obtain that value in a relatively simple way.

39

Figure 24: Example of a TRRL performance chart.

40

Figure 25: Load configuration used for the BB measurements according to TRRL.

41

Normally BB measurements are only taken in the wheel tracks. These values are in fact the Defn values since that pavement area has been subjected to n load repetitions. If we also take deflection measurements between the wheel tracks, then we get a good estimate of the flexural stiffness of that part of the pavement that is not subjected to traffic loads. These deflections can be taken as representative for Def0. Assume that the deflection measured between the wheel tracks is 350 m and that the deflection in the wheel tracks is 390 m. The pavement has an unbound base. Then we arrive to: DeltaDefn = 390 350 = 40 and DeltaDefc / Def0 = 0.4767 0.000299 x 350 = 0.372 so DeltaDefc = 0.372 x 350 = 130 We also calculate: b = 0.91 so DeltaDefn / DeltaDefc = (n / N)b 40 / 130 = (n / N)0.91 n / N = 0.27 Normally road authorities are not interested in a damage ratio or a remaining pavement life expressed in a number of allowable load repetitions but much more in a remaining life in years. This can be estimated in the following way. Assume the traffic composition has not changed in time and for reasons of simplicity we also assume that no growth in the number. of vehicles per day has taken place. This means that the area indicated in figure 26 is representative for the cumulative amount of traffic n that has passed the road during time period t.

Figure 26: Procedure to estimate the remaining life in years from the n/N ratio.

In the same way the allowable number of load repetitions N is arrived after T years. From this simple example it is clear that in this case: t / T = n / N

Traffic intensity

Time

n

t

N

T

42

If we assume e.g. that the deflection survey of the above mentioned example was taken 5 years after the pavement has been put in service, we calculate that: t / T = n / N = 0.27, t = 5 so T = 18 years and the remaining life is 13 years. The procedure described above cannot be used if variations occur in the cross section of the pavement due to variations in the thickness of the layers and because different types of material are used over the width of the pavement. Those conditions can occur if e.g. ruts are filled, the pavement is widened or of mill and fill operations have been carried out. Of course unknown changes in the traffic growth, composition of the traffic and the axle loads have also a negative effect on the results obtained by the procedure described above.

43

9. Mechanistic procedures for remaining life estimations and overlay design:

Mechanistic overlay design methods are based on the analysis of stresses and strains in the existing pavement. The calculated values are then compared with the allowable values and based on this comparison, conclusions are drawn with respect to the most appropriate maintenance strategy. One of the most important differences between a mechanistic and an empirical approach is the fact that in the latter, the interactions between stresses, strains, strength, fatigue, resistance to deformation etc are not visible; they are hidden in the procedure. This makes the empirical methods unreliable as soon as different materials and structures are used than those for which the procedure was developed. On the other hand empirical methods are based on observed performance which is an advantage over mechanistic models especially if these models are used in a too simplistic way. The big advantage of the mechanistic models of course is that they are based on sound analyses of stresses, and strength of the materials used. 9.1 Basic principles: In classical mechanistic overlay design methods, only the strain levels in the existing pavement are considered as well as the required reduction in those strain levels in order to obtain the required extension of the pavement life. The overlay is designed in such a way that the necessary reduction of the strain level in the existing pavement is realised. The effect of damage in the existing pavement on the performance of the overlay is normally not considered. This makes the classical mechanistic methods rather straightforward. The following steps can be recognised. First of all the moduli of the various layers are calculated in the way described earlier. Secondly the asphalt layer modulus is corrected to a reference temperature; for Dutch conditions this is 18 0C. This correction can be applied using the asphalt mix stiffness vs temperature chart as developed by Shell [8]; this chart is given in figure 27. Then the stresses and strains due to an equivalent single axle load are calculated. The tensile strain calculated at the bottom of the asphalt layer is introduced in a fatigue relation and the allowable number of load repetitions is calculated. The same is done for the subgrade strain. The amount of damage, being the ratio n/N, is then calculated where n is the applied number of load repetitions and N is the allowable number. The remaining life ratio is calculated as 1 n/N. If the pavement life should be extended, the number of load repetitions that are expected needs to be calculated. This results in a figure n + n. Then the pavement thickness should be increased in order to decrease the tensile strain at the bottom of the asphalt layer and to increase the allowable number of load repetitions from N to N + N. The appropriate overlay thickness is obtained if: 1 n/N = n / (N + N) The procedure is illustrated with an example. Assume that the tensile strain that is calculated at the bottom of the asphalt layer due to a standard axle load equals: = 2 . 10-4 [m / m] Fatigue tests carried out on the material resulted in the following fatigue relation. Log N = -13 5 . log The allowable number of load repetitions is then N = 312500. If we assume that the pavement has already carried 200000 standard loads, then the damage ratio equals n / N = 0.64.

44

Figure 27: Relationship between the stiffness of asphalt mixtures and temperature for a loading time of 0.02 s.

45

The remaining life ratio equals: 1 n/N = 0.36 Assume that another 500000 standard axles should be carried by the pavement. This means that: n = 500000 The tensile strain at the bottom of the asphalt layer should be decreased to a level where N + N load repetitions can be taken. This value is calculated from: N + N = n / (1 n/N) = 500000 / 0.36 = 1.39 . 106 By using the fatigue relation we calculate that this new number of allowable load repetitions can be obtained if the strain is reduced to = 1.48 . 10-4 [m / m]. This means that the overlay needs such a thickness that the strain at the bottom of the existing asphalt layer is reduced to this value. The approach described here gives rise to some comments. It is quite clear that a very large overlay thickness is needed when the ratio n/N approaches 1. The reason is that the fatigue relation is based on beam fatigue tests. This implies that failure means that the specimen is in two parts if the allowable number of load repetitions is reached (at least in load controlled fatigue tests) which implies that the beam lost its functionality. In reality however the cracked asphalt slab is still supported by the base and other layers; the cracked slab is still functional. All this indicates that the procedure results in unrealistic designs in case of high values of the damage ratio. Furthermore the example indicates that in general fairly small strain reductions are needed which results in rather thin overlays. Because the overlay design is only based on the reduction of the strain level in the existing pavement, only the thickness and the stiffness of the overlay are of importance. From practice one knows that this cannot be true. The existing pavement normally exhibits a certain amount of cracking when an overlay is applied and these cracks tend to propagate through the overlay. This means that reduction of the strain level in the existing pavement cannot be the only design criterion for overlays; also the resistance to crack reflection of the overlay should be considered. This aspect will be discussed later in these lecture notes. Finally the procedure described above doesnt take into account the large amount of variation in deflections and material characteristics that can occur in pavements. 9.2 Extension of the basic principles: In this section an extension of the basic principles presented in the previous section will be given. The extension is dealing with the fact that in case the n/N ratio reaches 1, realistic values for the overlay thickness should still be obtained. Furthermore the extension takes into account the variation in deflection level and material characteristics that occur in practice. If there was no variation in deflection level along the section under consideration, and if there was no variation in the thickness of the pavement layers, then there would be no variation in the elastic modulus of the layers and there would be no variation in strain level. If there also would be no variation in the fatigue characteristics, then the pavement would fail precisely at the number of load repetitions predicted and the pavement would fail from one moment to the other. This particular behaviour is illustrated in figure 28a. Such a performance however is never observed, pavements dont collapse in the way indicated by this figure. In reality a more gradual deterioration is observed as is indicated by figure 28b. If we use the mean strain level of figure 28b as design criterion and we use this strain value together with the mean fatigue characteristic (the solid fatigue line in figure 28b) then we determine the mean number of load repetitions. At that number of load repetitions there is a 50% chance that the pavement is failed. It can easily be shown that this means that 50% of the trafficked pavement surface shows cracking. Because of the variation in the fatigue

46

resistance, some parts of the pavement will live longer and some shorter. Furthermore the strain level in some parts of the pavement are lower than at other parts because of e.g. the variation in thickness. The variation in strain level combined with the variation in fatigue resistance results in a variation of pavement life over the section considered. This is shown in figure 28b. Figure 28b also clearly shows that pavements dont fail in a catastrophic way but show a gradual deterioration. The overlay design procedure should take this into account. Thickness of the pavement layers and the layer moduli are constant, so strain is constant.

Figure 28a: Condition deterioration when there is no variation in pavement properties.

Figure 28b: Condition deterioration when there is variation in pavement properties.

Log

Log n

Condition

Log n

N

N

Log n

Fatigue characteristics show no variation

Fatigue characteristics show variation

Log

Thickness and modulus of the layers show variation so strain is variable.

Condition

Log n

50% failed and 50% sound Mean strain

level

N

N

47

In order to take the variation of input parameters into account, probabilistic analyses should be made. Several procedures are available to determine which combinations of layer thickness, layer modulus and fatigue relation should be used in the calculations in order to en- able to estimate the variation in strain level and pavement life. A far more effective approach is to make use of simple relations that exist between e.g. the surface curvature of the deflec-tion profile on one hand and the tensile strain at the bottom of the asphalt layer, the tensile strain at the bottom of the bound base or the vertical compressive strain at the top of the subgrade, on the other hand. This will be shown in the following part. Let us consider the bending of a slab as shown in figure 29.

Figure 29: Bending moments in a slab.

The magnitude of the bending moments can be calculated a follows: M1x = E h3 ( 1/Rx + 1/Ry ) / 12 ( 1 - 2 ) and M1y = E h3 ( 1/Ry + 1/Rx ) / 12 ( 1 - 2 ) Where: M1x = bending moment in the x direction, M1y = bending moment in the y direction, Rx = radius of curvature in the x direction, Ry = radius of curvature in the y direction, E = elastic modulus of the slab, h = thickness of the slab,

= Poissons ratio. The stresses can be calculated as x = 6 M1x / h2 and y = 6 M1y / h2. If we are dealing with a circular load in the centre of a large slab, Rx = Ry and x = y. Because: x = ( x - y ) / E = ( 1 - ) x / E we can now develop a relation between the curvature and the tensile strain by substitution of x by M1x and by substitution of M1x by the equation that relates the bending moment to the radius of curvature. We obtain then: x = 6 ( 1 - ) M / E h2 = h / 2 Rx 1 / Rx This indicates that the strain at the bottom of the asphalt layer is related to the radius of curvature of the deflection bowl due to the applied load. Extensive research [9,10], has shown that there exists a direct relation between the tensile strain at the bottom of the asphalt layer and the surface curvature index following: log = C0 + C1 log SCI For pavements with an asphalt thickness 150 mm the relation becomes:

48

Log = 0.481 + 0.881 log SCI300 Where: SCI300 = difference in maximum deflection and the deflection measured at a distance of 300 mm, = tensile strain at the bottom of the asphalt layer [m / m]. This relation is shown in figure 30.

Figure 30: Relation between SCI300 and the tensile strain at the bottom of the asphalt layer. Since log N = A0 + A1 log , we can write: log N = A0 + A1C0 + A1C1 log SCI It can be shown that the variance of log N (the squared standard deviation of log N) can be calculated from: S2logN = A12. C12 . S2logSCI + S2lof Where: SlogSCI = standard deviation of the logarithm of the measured SCIs (see also table 2) Slof = standard deviation of log N at a given log ; it describes the variation in fatigue life. We can now write: log NP = log N u . SlogN Where: log N = logarithm of the mean number of load repetitions to failure, log NP = logarithm of the number of load repetitions to failure at level of confidence P u = factor from the tables for the normal distribution related to confidence level P

49

From the equations given above it becomes clear that the quality of the predictions increases when SlogN decreases. This means that SlogSCI and Slof should be as low as possible. A low SlogSCI stresses the need to pay ample attention to the discrimination of homogeneous sub-sections. The only factor that cannot be easily assessed is the variation in fatigue charac-teristics. Although this value can be estimated (see e.g. lecture notes CT4850 part III Asphaltic Materials) if mixture composition data are available, extensive fatigue testing has shown that Slof = 0.25 is a reasonable first estimate. Overlay calculations based on the confidence level or probability of survival level P are made in the following way. As is shown above, the number of load repetitions until a certain probability of survival level P1 is reached can be calculated using: log NP1 = A0 + A1 C0 + A1 C1 log SCI1 u1 SlogN

If the pavement life has to be extended to N + N load repetitions and after that number of load repetitions, the probability of survival should be P2, the needed SCI level to achieve this can be calculated using: Log (N + N)P2 = A0 + A1 C0 + A1 C1 log SCI2 u2 Slog(N+N) After subtracting of both equations one obtains: Log {NP1 / (N + N)P2} = A1 C1 log {SCI1 / SCI2} u1 SlogN + u2 Slog(N+N) By writing NP1 / (N + N)P2 = 1 / X I1 = 10**(u1 SlogN) I2 = 10**(u2 Slog(N+N) We arrive to Log {1 / X} = A1 C1 log {SCI1 / SCI2} log I1 + log I2 This can be written as: SCI2 = SCI1 (X I2 / I1)1/A1C1 In these equations SCI1 can be considered as the SCI before the overlay is placed and SCI2 as the SCI after overlaying. In the same way SlogN is valid before overlaying and Slog(N+N) is valid after the overlay is placed. We still need equations to predict the SCI2 in relation to the overlay thickness and stiffness as well as the SCI1. Furthermore an equation is needed to predict SlogSCI2 because from this value Slog(N+N) can be calculated. These equations are given below: Log SCI2 = b0 + b1 Eo + b2 ho + b3 log SCI1 + b4 Eo log SCI1 + b5 ho log SCI1 + b6 ho log Eo log SCI1 S2logSCI2 = {b1 + b4 log SCI1 + b6 ho log SCI1 / Eo}2 S2Eo + {b2 + b5 log SCI1 + b6 log Eo log SCI1}2 S2ho + {b3 + b4 Eo + b5 ho + b6 ho log Eo}2 S2logSCI1 Where: SCI1 = surface curvature index (d0 d300) before overlaying [m] SCI2 = surface curvature index (d0 d300) after overlaying [m] ho = overlay thickness [mm] Eo = elastic modulus of the overlay [Mpa] bo = -0.0506 b1 = 1.178 10-5 b2 = 0.0094

50

b3 = 1.0153 b4 = -7.73 x 10-6 b5 = -3.778 x 10-4 b6 = -1.4971 x 10-3

With respect to the procedures discussed above, it is once again stressed that they are based on limiting the strains in the existing pavement. Also it should be noted that it is assumed that the overlay is fully bonded to the existing pavement. This however is not always the case especially in cases where, because of reasons to be discussed later, an interface layer is placed between the overlay and the existing pavement allowing the overlay to behave more or less independently from the existing pavement. Furthermore the effect of cracks in the existing pavement on the performance of the overlay is not taken into account. This effect however cannot be ignored in cases where the existing pavement shows moderate to severe cracking. Also this will be discussed in a later chapter. One important point remains to be discussed which is the estimation of the probability of survival of the existing pavement P. Without going into all the details (for these the reader is referred to [9]), it can be shown that P can be estimated from the ratio of the surface curvature index measured in and between the wheel tracks following: P = (SCIb / SCIin)q Where: SCIb = SCI measured between the wheel tracks (d0 d500) SCIin = SCI measured in the wheel tracks (do d500) q = dependent on the type of structure taking a value between 0.6 and 0.4 for pavements with an unbound base and between 0.7 and 0.5 for pavements with a bound base; the higher values are for a 150 mm thick base, the lower values are for a 300 mm thick base. If for reasons mentioned earlier, the SCI ratio cannot be used, P can also be estimated from the percentage of the wheel track area that shows cracking following: P = 1 percentage cracked area / 100 It should be noted that a substantial part of the cracking that is visible at the pavement is surface cracking. This type of cracking is initiated at the pavement surface and normally progresses downwards to approximately 40 mm. It is clear that this type of cracking cannot be associated to the fatigue type cracking for which the above mentioned procedures are de-veloped. All in all this means that P values estimated in this way might be too high, the real structural condition might be better than it appears from the P value estimated in this way. If P is known as well as SlogN, the damage ratio n / N can easily be determined using the equations given above or by means of figure 31.

51

Figure 31: Relation between P, SlogN and n / N.

52

10. Extension of the simplified procedure to estimate critical stresses and strains: In many cases the thickness of the pavement layers is unknown or highly variable. In that case a pavement evaluation that relies on the back calculation of layer moduli is less effective and estimation of critical stresses and strains using simple methods as described in the previous chapter are extremely useful. In a joint research effort by the Government Service for Land and Water Use (LWU) of the Dutch Ministry of Agriculture, Nature Management and Fisheries, KOAC consultants and the Delft University of Technology, a pavement evaluation and overlay design method was developed which completely relies on such simple relations [11]. The hart of the method being the relations to estimate the stresses and strains will be reproduced here. The basis of the method is the large number of calculations on stresses and strains in on four layer pavement systems due to a FWD load. The calculated values are schematically shown in figure 32.

Figure 32: Analysed structures and locations where stresses and strains were calculated. The analyses have been made for pavements with Easphalt > Ebase > Esubbase > Esubgrade and for pavements where Esubbase < Esubgrade. One will notice that the equations are much more complex than the ones described until now. The reason for this is that thin asphalt surfacings had to be consid