Analysis of the Performance of Flexible Pavement under the Effect of Wheel and Thermal Loads

One of the major sources of distress in roads is the cracks that appear in flexible asphalt pavements. Combined wheel and thermal load induced cracking in the form of bottom-up and top-down fatigue cracking. In this paper, combined effect of wheel loads and temperature is consid ered in finite element anal ysis of fl exible pavement l ayers. The heat flow e quations are derived and the program (ANSYS V 5.4) is utilized to carry out the analysis. The subgrade layer is modeled as an elasto-plastic material following Drucker – Prager model for yielding of the isotropic material, while both the asphalt and base layers are considered elastic. Three different thicknesses for the asphalt layer are tried; namely, 0.05 m, 0.10 m and 0.15 m, respectively. A temperature rise of 40 o C was considered in addition to wheel pressures. It was found that an increase of wheel pressure from (500) to (700) kN/m 2 leads to increase in vertical displacement of about (4 – 8)%. This increase becomes (10 – 22%) when the wheel pressure becomes 1000 kN/m 2 . The temperature rise leads to decrease in the effect of wheel pressure because temperatur e leads to expansion (upward movement) reverse to wheel load effect. The effect of wheel load is transmitted directly to the underlying subgra de within the wheel zone. The def ormed zone under the wheel becomes larger when t he load increases. The maximum displacement increases by about (24%) when the l oad is duplicated.


Introduction
Temperature has a significant effect on the stiffness as well as the fatigue and permanent deformation resistance of asphalt mixtures.It is therefore quite obvious that accurate knowledge of the temperature distribution in the pavement should be available in order to allow realistic analyses of the stresses and strains in asphalt pavements to be made.Furthermore moisture has a significant effect on the stiffness and strength characteristics of unbound materials and soils.Temperature Distribution in Pavement The temperature distribution in the pavement layers can vary significantly during the day and during the seasons of the year.Figure 1 shows the temperature distribution during a hot spring and a hot summer day.One should realize that the surface temperatures can easily be 5 0 C higher than the temperatures measured at 10 mm below the pavement surface.Figure 2 shows the temperature gradient that exists over the asphalt layer thickness in case of the hot summer day shown in Figure 1.Because the stiffness of asphalt layers changes with temperature, allowance must be made in the design of these pavements for the different temperatures at which they will operate (Pavement Design Manual, 2005).
From these figures, it is clear that assuming a constant temperature over the thickness of the asphalt layer is far from reality unless one is dealing with thin asphalt layers.Furthermore, the total asphalt thickness is commonly made of different types of asphalt mixtures, especially in case the total thickness is larger than 100 mm, which implies that even when the temperature is constant over the entire thickness, different stiffness values will be found for the different layers of which the total asphalt thickness is made of.Van Gurp (1995) presented a method to deal with temperature variations over the total asphalt thickness.He divided the total thickness into three sub-layers (Figure 3) and defined an equivalent asphalt thickness, h 1,eq in the way as described in Figure 4.This equivalent thickness has a modulus value equal to the modulus of the third sub-layer.Where: h1, eq = equivalent total asphalt thickness with stiffness E 1,3 : This equation is valid under the assumption that h 1,1 = ¼ h 1 and h 1,3 = ¼ h 1 and that the temperature is uniformly distributed over each of the sub-layers.The mean temperature of each sublayer is used to calculate the modulus of that sublayer.

Reflective cracking
Reflective cracking cannot be analyzed by means of linear elastic multi layer theory.The finite element method needs to be used in order to be able to model the effects of discontinuities like cracks.Furthermore, principles of fracture mechanics need to be used in order to be able to analyze the rate at which the crack will propagate through the asphalt layer.In principle, there are two mechanisms that are responsible for the crack propagation being temperature effects and traffic loads.Both effects are schematically represented in Figures 5, 6 and 7.
Before one is going in detailed finite element analyses, it might be wise to analyze the crack reflection due to traffic loads first of all with a simplified procedure.Such a simplified procedure is presented hereafter.
A general applicable simple design system has been developed by Lytton (1989); this method is based on the propagation of cracks in fully supported beams.
Alkaiss and Al-Maliky ( 2009) studied the behavior of flexible pavement under wheel and thermal loading conditions using the finite element method.They investigated the stress distribution within the asphalt concrete pavement that influences the direction of crack propagation.The results showed that a maximum stress intensity factor value is obtained at surface and then decrease with depth about (0.75 of asphalt layer thickness) due to reduction in temperature in asphalt layer, which indicates that crack will initiate at surface and extend throughout asphalt layer.The horizontal stress for both top and bottom layers increases with the variation of thermal coefficient expansion factor.High values of stresses at top surface of asphalt layer due to high contact stress were induced under wheel and thermal load conditions.

Heat Flow Fundamentals
The first law of thermodynamics states that thermal energy is conserved.Specializing this to a differential control volume: T S = temperature at the surface of the model.Note that positive specified heat flow is into the boundary (i.e., in the direction opposite of { η}), which accounts for the negative signs in equations ( 6) and ( 7).Combining equation ( 2) with equations ( 6) and ( 7 8) and ( 9) with some manipulation yield: ….(10) where: vol = volume of the element, and δT = an allowable virtual temperature (= δT (x, y, z, t)).Expanding the Stefan-Boltzmann Law to a two-surface radiation equation, the heat transfer rate between two surfaces i and j is: where: The rest nodal points including those on surface are unconstrained as shown in Figure 8. 2. The subgrade layer is modeled as elasto-plastic material following Drucker-Prager model for yielding of the isotropic material, while both the asphalt and base layers are considered elastic.A plane 42, 2-D structural solid has been adopted in this research.The element can be used as a plane element (plane strain or plane stress) or as an axis symmetric element.The element is defined by four nodes having two degrees of freedom at each node, translations and the nodal x and y directions.The element has plasticity, and large strain capability.Therefore a stiffness elastic modulus (E) and Poisson's ratio (ν), cohesion (c), angle on internal friction ( φ) are used to represent their behavior.The coefficient of thermal linear expansion is used to model thermal behavior.Temperature dependent stiffness modulus is used for the asphalt layer.The coefficient of thermal expansion for the asphalt material is 4x10 -4 / o C, (Huang, 1993).A temperature rise of 40 o C was considered.

Computing
strains, stresses displacements and stress intensity.

Contact pressures
The well known dual tire configuration is used all over the world for the driven and towed axles.Normally these tires have an inflation pressure of around 700 kPa.The steering axle of a truck always has a single tire, having the same dimensions as one of the dual tires.In Western Europe however, most of the towed axles are equipped nowadays with a so called wide base or super single tire.Normally the tire has an inflation pressure of 800 -850 kPa.The super single tire is still under development but will be used under the driven axle of trucks thereby replacing the dual wheel configuration.In between the super single and the dual wheel is a small size dual wheel.This tire is not very much used yet.The idea behind it was that a smaller size tire would allow lowering the loading platform resulting in a larger loading capacity.In order to avoid excessive wear to the tire, the tire pressure should be selected in relation to the tire load.
The following relationships can be used for this.The pressure used in the tires for dual wheels (1 axle has two dual wheels on either side of the axle; total number of wheels = 4) can be estimated from (Molenaar, 2007): where: p = tire pressure (MPa), and L = axle load (kN).The pressure in the super single tires (1 axle has one wheel on either side of the axle; total number of wheels = 2) can be estimated using: p = 0.42 + 0.0038 L …. ( 13) In this paper, the pressure caused by axles was calculated using equations PDF created with pdfFactory Pro trial version www.pdffactory.com(12) and ( 13).They were 500, 700 and 1000 kN/m 2 .

Results and Discussion
Figures 9, 10 and 11 show the surface settlement under the effect of loads without considering temperature effects.It can be noticed that a considerable increase in settlement takes place under the wheels when the wheel pressure increases from 500 to 700 and 1000 kN/m 2 .As the thickness of the asphalt layer increses from 0.05 m to 0.10 m, an increase in displacement of the order of about (61-73%) is noticed.This increase becomes about (122-147%) when the thickness is incresed to 0.15 m.In Figure 10, the case of temperature effect (no load) is presented.It can be noticed that the temperature causes uniform deformation in the layers which was about (21.6 mm).The same effect was found when the thickness of asphalt layer was changed to (0.10) or (0.15) m.
In these figures, the magnitude of wheel pressure is important.An increase of wheel pressure from (500) to (700) kN/m 2 leads to increase in vertical displacement of about (4 -8)%.This increase becomes (10 -22%) when the wheel pressure becomes 1000 kN/m 2 .
It can be noticed that under the locations of wheels, the deformation takes the form of ruttings.
Figure 12 illustrates the distribution of vertical displacement in the road layers under the effect of temperature rise of 40 o C only.It can be seen that the maximum uniform displacement is about (0.0216 m).This leads to the conclusion that the temperature rise leads to decrease in the effect of wheel pressure because temperature leads to expansion (upward movement) reverse to wheel load effect.
Figures 13 to 15 show the deformed layers of road under the effect of wheel pressure and temperature rise when the asphalt layer thickness is 0.05 m.It is apparent that the effect of wheel load is transmitted directly to the underlying subgrade within the wheel zone.The deformed zone under the wheel becomes larger when the load increases.The maximum displacement increases by about (24%) when the load is duplicated.
This was also concluded from Figures 16 to 18 Figures 22 to 24 present the distribution of deviator stress (principal stress difference σ 1 -σ 3 ) in the subgrade layer.It can be noticed that the increase of wheel pressure leads to increase in deviator stresses within the wheel zone and hence, the probability of failure in these zones becomes larger.The increase of asphalt layer thickness decreases the loads transmitted to the subgrade layer.It is evident in these figures that when the wheel pressure reaches (1000 kN/m 2 ), the maximum deviator stress exceeds the strength of the subgrade layer and hence failure is expected.

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(=T(x, y, z, t)), and t = time PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal, Vol.28, No.18, 2010 Analysis of Flexible the Performance Pavement under the Effect of Wheel and Thermal Loads 5785 = velocity vector for mass transport of heat.{q} = heat flux vector (output as TFX, TFY, and TFZ) = heat generation rate per unit volume.Next, Fourier's law is used to relate the heat flux vector to the thermal gradients: = Conductivity matrix ….(2) Combining equations (1) and (2), ….. (3) Expanding equation (3) to its more familiar form: ….(4)It will be assumed that all effects are in the global Cartesian system.Three types of boundary conditions are considered.It is presumed that these cover the entire element.1. Specified temperatures acting over surface S 1 : …. (5 ) where T* is the specified temperature 2. Specified heat flows acting over surface S 2 : … (6) where: {η} = unit outward normal vector q* = specified heat flow.3. Specified convection surfaces acting over surface S 3 (Newton's law of cooling): …..(7) where: h f = film coefficient, evaluated at (T B + T S )/2 unless otherwise specified for the element, T B = bulk temperature of the adjacent fluid, and PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal, Vol.28, No.18, 2010 Analysis of Flexible the Performance Pavement under the Effect of Wheel and Thermal Loads 5786 volume of the element, and combining with equations ( heat transfer rate from surface, σ = Stefan-Boltzmann, ε i = effective emissivity, F ij = view factor from surface I to surface j, A i = area of surface i, and = absolute temperature at surface i and surface j, respectively.Description of the Problem The finite element program ANSYS (V 5.4) has been used in this study to simulate the flexible pavement under mechanical loads (traffic load applied) and thermal load conditions (temperature field).A schematic representation of flexible pavement is shown in Figure8which consists of three layers: asphalt layer, base and subgrade layer.The properties for each material are given in Table1.Three different thicknesses for the asphalt layer were tried; namely, 0.05 m, 0.10 m and 0.15 m, respectively.The finite element work was carried out through the following stages:1.Generation of the finite element mesh and defining the load, boundary conditions and material properties as shown in Figure8.The mesh consists of fine elements near the loaded area and at the asphalt layer interface.The left and right vertical boundaries are constrained to move only in vertical direction whereas those on bottom boundary are all fixed.PDF created with pdfFactory Pro trial version www.pdffactory.com for asphalt layer thickness of 0.1 m and Figures 19 to 21 for asphalt layer thickness of 0.15 m.

Figure 10 :Figure 11 :
Figure 10: Surface settlement of the asphalt layer under different wheel pressures when the thickness is 0.10 m.

Figure 12 :Figure 13 :
Figure 12: Distribution of vertical displacement in the road layers under the effect of temperature rise of 40 o C when the thickness is 0.05 m.

Figure 14 :Figure 15 :
Figure 14: Distribution of vertical displacement in the road layers under the effect of wheel pressure = 700 kN/m 2 and temperature rise of 40 o C when the thickness is 0.05 m.

Figure 16 :Figure 17 :
Figure 16: Distribution of vertical displacement in the road layers under the effect of wheel pressure = 500 kN/m 2 and temperature rise of 40 o C when the thickness is 0.10 m.

Figure 18 :Figure 19 :
Figure 18: Distribution of vertical displacement in the road layers under the effect of wheel pressure = 1000 kN/m 2 and temperature rise of 40 o C when the thickness is 0.10 m.

Figure 20 :Figure 21 :
Figure 20: Distribution of vertical displacement in the road layers under the effect of wheel pressure = 700 kN/m 2 and temperature rise of 40 o C when the thickness is 0.15 m.

Figure 22 :
Figure 22: Distribution of the maximum deviatoric stress in the subgrade layer under the effect of different wheel pressures and temperature rise of 40 o C when the thickness is 0.05 m