# CHAPTER 7 ASPHALT PAVEMENTS

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1 CHAPTER 7 ASPHALT PAVEMENTS 207

4 Figure 7.2: Stresses in a half-space due to a circular load (1). Figure 7.3 gives in a graphical way the vertical, radial, tangential and shear stresses as a function of the depth z, the distance to the load center z and Poisson s ratio ν. The use of the graphs is illustrated by means of a practical example that deals with the evaluation of an earth road in a tropical African country. The trucks on the road transport cacao, trees, cement etc. and in general they are overloaded: axle loads of 150 kn frequently occur. The number of trucks is however low, say a few trucks per day. The unpaved road has a top layer of laterite (a red-colored tropical weathered material) and for reason of simplicity it is assumed that this may be considered as a half-space. The question now is whether damage will occur on this road, while it is known that the cohesion and the angle of internal friction of the applied laterite have the following values. Cohesion c [kpa] Angle of internal friction ϕ [ 0 ] Dry season Wet season

5 Figure 7.3: Stresses in a half-space due to a circular load (1). Assume that wide base tyres are mounted on all the truck axles; this means that at either side of any axle there is one tyre with a load of 75 kn. It is further assumed that the tyre pressure in all cases is 850 kpa. As stated earlier, as a first approximation the contact pressure between the tyre and the road surface can be taken equal to the tyre pressure. This implies that p = 850 kpa. The radius a of the circular contact area then follows from: a = ( 75 / [ 850 x π ] ) = m The Poisson s ratio is taken as

8 Figure 7.5: Graphs for determination of the radial stress in the load center at the bottom of the top-layer of a two-layer system (1). 214

9 Figure 7.6: Graph for determination of the vertical stress in the load center at the top of the bottom layer of a two-layer system (1). Figure 7.7: Graph for determination of the vertical displacement (deflection) in the load center at the surface of a two-layer system (1). 215

12 7.4 Stresses, strains and displacements in multi-layer systems: Graphs are also available to determine the occurring stresses, strains and displacements in three-layer systems. The use of these graphs is however rather complicated and therefore no attention is given to them. Another reason to do so is that the analyses can also be done fast and easy with one of the available linear-elastic multi-layer computer programs. In this paragraph therefore the computer program WESLEA is discussed that is added to these lecture notes on a CD-ROM. Appendix I gives a short description how the input for this program has to be prepared and how the output is obtained. The use of the WESLEA program is further explained here by discussing a small example problem. The example problem concerns the calculation, for the three-layer system depicted in figure 7.9, of the stresses and strains at the bottom of the asphalt layer and at the top of the subgrade, in both cases in the load centre. The required input parameters are all given in figure 7.9. Full bond between the various layers is assumed. The location at the bottom of the asphalt layer is referred to as position 1 and the location at the top of the subgrade as position 2. After having prepared the input as explained in Appendix I and having done the calculation, the results given in table 7.1 are obtained. Remark! The sign convention used in WESLEA is different from the one used until now. WESLEA uses the so-called soil mechanics convention; in this convention a tensile stress or tensile strain gets the sign, while a compressive stress or compressive strain gets the + sign. 50 kn wheel load tyre pressure 700 kpa 200 mm asphalt, E = 5000 MPa, ν = 0.35 ε r, σ r 300 mm unbound base, E = 400 MPa, ν = 0.35 ε z, σ z subgrade (sand), E = 150 MPa, ν = 0.35 Figure 7.9: Input for the calculation example with WESLEA. 218

13 Position 1 X Y Z Normal stress [kpa] Normal strain [µm/m] Displacement [µm] Position 2 X Y Z Normal stress [kpa] Normal strain [µm/m] Displacement [µm] Table 7.1: The stresses and strains calculated with WESLEA in the two positions indicated in figure 7.9. In figure 7.9 the stress and the strain at the bottom of the asphalt layer are indicated as σ r and ε r respectively, while WESLEA gives the stresses in Cartesian coordinates. However, for an axial symmetric load (such as the one in this example) in the vertical line through the load center is valid: σ r = σ t = σ x = σ y. So it is very easy to calculate the occurring stresses and strains in any point of a certain asphalt pavement structure by means of the WESLEA program. The obtained output allows a pavement life analysis that is discussed in the following paragraph. 7.5 Pavement life calculation: Introduction: In this paragraph the principles of the structural design of an asphalt pavement and the determination of its life are discussed. Prior to that however attention is paid to the various types of damage that may occur on asphalt pavements and that in principle should be taken into account in the structural design. It will appear from the overview of damage types that in this course only a limited number of damage types is addressed and that only a limited number of design criteria is taken into account Damage types on asphalt roads and design criteria to be used: When determining the required thickness of an asphalt pavement structure two design criteria should be taken into account, i.e. cracking and permanent deformation. It already has been explained that horizontal tensile stresses and horizontal tensile strains occur at the bottom of an asphalt layer, laid directly on the subgrade or on an unbound base, due to bending of the structure under the traffic load. After many load repetitions these flexural tensile stresses/strains may lead to fatigue cracking. This fatigue cracking starts at the bottom of the asphalt layer, gradually propagates upward and finally 219

14 appears at the road surface as so-called alligator cracking in the wheel tracks. Figure 7.10 shows an example of this particular type of cracking. An asphalt pavement structure must be designed in such a way that this type of serious damage does not occur too early. Figure 7.10: Example of alligator cracking on an asphalt pavement. Besides of alligator cracking in the wheel tracks also frequently longitudinal cracks are observed. These longitudinal cracks mostly penetrate to a depth of not more than about 50 mm. The cause and propagation of this type of cracking is not yet fully understood. It is however clear that they occur due to the complex distribution of stresses in the contact area between the tyre and the road surface. In the contact area not only vertical stresses occur but also horizontal shear stresses. In regular asphalt pavement design calculations these shear stresses are however not taken into account (in the proceeding examples also a uniform vertical contact pressure over a circular contact area was assumed) and by consequence the development of this surface cracking cannot be analyzed. The propagation of these surface cracks is most probably the result of traffic and climatic influences. To a great extent surface cracking can be prevented by a correct asphalt mix composition. This course 220

15 is not the right place to extensively discuss the occurrence and propagation of surface cracking; reference is made to the course CT4860 Structural design of pavements. One should however realize that surface cracking is a major reason for maintenance of asphalt wearing courses. Asphalt layers are not only applied on an unbound base but also frequently on a cement-bound base. For instance, on Amsterdam Airport Schiphol the pavement structure on a runway consists of 200 mm polymer-modified asphalt layers on 600 mm lean concrete base. Although a linear elastic multilayer calculation reveals that no tensile stresses or tensile strains occur at the bottom of the asphalt layer, there are however cracks present in the asphalt. The causes of these cracks are the following. Each cement-bound material will try to shrink due to the hardening process and due to a decrease of temperature. The shrinkage is however to a great extent obstructed because of the friction with the underlying layer and this results in tensile stresses in the cement-bound material. If these tensile stresses become too great (shrinkage) cracks occur. This type of cracking is thus strongly dependent on the climatic conditions and on the properties of the cement-bound material. The shrinkage cracks remain not exclusively within the cement-bound base but they want to propagate into the bonded asphalt layers. This mechanism is schematically shown in figure 7.11a. The material properties of the cement-bound base exhibit quite some variation and as a result also the distance between the (transverse) cracks varies. The greater the strength of the cement-bound base material, the greater both the crack distance and the crack width and the movements around the crack due to temperature variations. So the greater the crack distance the greater the movements at the crack and the more heavily loaded the bonded asphalt. asphalt originally closed crack opens because of shrinkage cement-bound base a: Shrinkage in the cement-bound b: The traffic wheel loadings base results in tensile stresses result in great shear stresses in the bonded asphalt layer in the asphalt layer Figure 7.11: Propagation of cracks from the cement-bound base into the bonded asphalt layer. The effects of the temperature movements can be reduced by regulation of the crack distance in the cement-bound base. On Amsterdam Airport Schiphol this has been done by creating notches, to a depth of 1/3 of the base 221

16 thickness, at regular distances (about 7 m). Through these notches the base weakens to such an extent that the shrinkage cracks will occur there. The limited crack distance results in smaller movements around the crack and as a result the asphalt layer is less heavily loaded. The principle of a notch is similar to that of a contraction joint in plain concrete pavements (see chapter 5). But even a narrow crack always is a weak point in the pavement structure. At such a crack bending moments cannot be transmitted, load transfer is only possible through cross-forces. As indicated in figure 7.11b, during the passage of a wheel load not only substantial shear stresses occur in the asphalt layer above the crack but also an extra large bending moment, and as a result the crack wants to propagate from the base into the asphalt layer. The asphalt layer also has to be designed to resist this type of cracking. This subject is however outside the scope of this course; reference is made to the course CT4860 Structural design of pavements. Permanent deformation of the various pavement layers due to the repeated traffic loadings is another important type of damage that should be taken into account in the structural pavement design. Such permanent deformations manifest themselves as rutting in the wheel tracks. Figure 7.12 is an example of this type of damage. Figure 7.12: Example of rutting on an asphalt pavement. The rutting observed at the road surface results from visco-plastic deformations of the asphalt layers and from plastic deformations of the 222

19 - asphalt at high temperatures and long loading times, saturated clay: 0.5, - cement-bound base materials: 0.2, - concrete: In the calculations much care must be taken that the correct units are used because nonsense in = nonsense out. Also realistic layer thicknesses should be used! The minimum thickness of a layer is about 2.5 to 3 times the maximum grain size. Probably a number of calculations, with different layer thicknesses, are required to obtain the desired pavement life. Adapting the layer thicknesses has to be done in a systematic way and care must be taken that the stresses and strains are calculated at the correct positions within the (modified) pavement structure. It is recalled that WESLEA uses the soil mechanics sign convention, so the sign means tension and the + sign means compression. Pavement life The fatigue life of the asphalt can be determined on the basis of the calculated strain at the bottom of the asphalt layer. The fatigue life resulting from the (laboratory) fatigue relationship has to be multiplied with the factors for healing (see chapter 4, paragraph ) and for lateral wander (as stated earlier, a value of 2.5 is a reasonable assumption for the lateral wander factor). The pavement life based on the subgrade criterion is found by inputting the calculated vertical compressive strain in the subgrade criterion given in chapter 4, paragraph 4.3. This found pavement life of course should not be multiplied with the healing factor and the lateral wander factor (you should be able to explain why this should not be done). 7.6 References: 1. Meier, H.; Eisenmann, J.; Koroneos, E. Effects of traffic loadings on pavement structures (in German) Forschungsarbeiten aus dem Strassenwesen. Kirschbaum Verlag; Bonn/Bad Godesberg

20 APPENDIX I MANUAL FOR THE PROGRAM WESLEA 226

21 Introduction: The WESLEA program has been developed for the American Waterways Experiment Station (WES) of the US Army Corps of Engineers. It is a linear elastic multi-layer program that enables the analysis of a pavement structure consisting of maximum 5 layers (the subgrade counts as one layer). The number of circular loads is maximum 20. This is a very useful option because it enables to analyze the effects of complex load systems such as the landing gears of a Boeing 747 aircraft. There are two options with respect to the bond between the layers: a. the subsequent layers are fully bonded to each other (this is the most commonly used option), b. the subsequent layers are not bonded to each other, so they can slip along each other without any friction (this option is only used for very special cases). The starting point in the following description of the input and output of the program is the example given in figure 7.9. The input: On the main screen you first click units and then SI. You have to realize that the WESLEA program has originally been developed for the American system of units. Your input in SI-units therefore is converted into American units and then of course some round-off errors occur. Also in the output you will notice this. Next you click input and then structure. You input that the number of layers is 3. The next step is the input of the properties of the various pavement layers. As material for layer 1 you chose asphalt and for the elastic modulus you fill in 5000 MPa. As material for the layers 2 and 3 you chose other. The reason for doing so is that the choice for GB (= granular base) yields a confrontation with a maximum value for the elastic modulus that is hidden in the program. This limitation is by-passed through the choice of the material other. Next you input the values for the elastic modulus of the unbound base and the subgrade in MPa. Also the values of the Poisson s ratio have to be input but you will observe that the value 0.35 is set as default value. Next the thickness (in cm!) of the asphalt layer and the base has to be input. Then you have to input whether the asphalt layer is fully bonded to the base and whether the base is fully bonded to the subgrade. As stated earlier this is a very reasonable assumption for most of the cases. You now click the button ok. You click again on input and then on loads. There is the possibility to analyze various load configurations, which are: a. a single axle with dual tyre wheels, b. a tandem axle with dual tyre wheels, c. a triple axle with dual tyre wheels, d. a single axle with wide base tyre wheels ( steer ), 227

23 The calculated damage factor is the ratio between the applied (the occurring) and the allowable number of load repetitions. Finally you can have a look to the fatigue relationship for the asphalt ( fatigue ) and the criterion for the allowable permanent deformation in the subgrade ( rutting ) by means of the button view transferfunctions. It is stressed again that these functions are not universal applicable. The relations that normally used in The Netherlands already have been given in chapter 4. Final remark: The WESLEA program generates numerical solutions. The accuracy of the obtained calculation results depends among other things on the magnitude of the integration steps. In this calculation process errors may be introduced. Simple checks are possible to investigate whether these errors have occurred and whether the program has functioned well. This is however beyond the scope of this course; reference is made to the course CT4860 Structural design of pavements. In that course also other programs will be discussed. 229

24 229-a

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