EFFECT OF TEMPERATURE ON PAVEMENT FRACTURE PERFORMANCE

EFFECT OF TEMPERATURE ON PAVEMENTFRACTURE PERFORMANCE

PROJECT DESCRIPTION 1

submitted toDr. Denis Jelagin

AH2905 - Advanced Pavement Engineering Analysis and DesignOctober 14, 2014

byOctavian Babiuc

Ali Taher

Table of Contents

1 Introduction 1

2 Methods 2

2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2.1 Subgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2.2 Sub-base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.3 Road base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.4 Bituminouse layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Solid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Heat Transfer in Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.5 Study scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Results 14

3.1 Bottom - up cracking (Fatigue cracking) . . . . . . . . . . . . . . . . . . . . 14

3.2 Top-down cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Vertical strain at the top of the subgrade (Rutting) . . . . . . . . . . . . . . 18

4 Conclusions 20

A first section 21

B second section 21

List of Figures

1 Multilayer Pavement system . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 COMSOL geometry creator . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Multilayer Pavement system . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

4 Material definings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

5 COMSOL subgrade material proprieties . . . . . . . . . . . . . . . . . . . . 3

6 COMSOL sub-base material proprieties . . . . . . . . . . . . . . . . . . . . 4

7 COMSOL road base material proprieties . . . . . . . . . . . . . . . . . . . . 4

8 Step function 2 description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

9 COMSOL bituminouse material proprieties . . . . . . . . . . . . . . . . . . 5

10 MATLAB code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

11 MATLAB curve fitting for Prony series (initial value=1000 seconds) . . . . 7

12 Results obtained from the curve fitting . . . . . . . . . . . . . . . . . . . . . 7

13 Boundary of the fixed constraint . . . . . . . . . . . . . . . . . . . . . . . . 8

14 Roller support position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

15 Constant load along the surface of the AC layer . . . . . . . . . . . . . . . . 8

16 Defining the boundary load in COMSOL . . . . . . . . . . . . . . . . . . . . 9

17 Defining the location of the boundary load in COMSOL . . . . . . . . . . . 9

18 Defining of Long-term elastic proprieties and coefficients for the GeneralisedMaxwell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

19 Initial starting temperature for all three scenarios . . . . . . . . . . . . . . . 10

20 Scenario 1 temperature for 24 hours . . . . . . . . . . . . . . . . . . . . . . 11

21 Scenario 2 temperature for 24 hours in Heat transfer . . . . . . . . . . . . . 11

22 Interpolation function for Scenario 2 . . . . . . . . . . . . . . . . . . . . . . 11

23 Plot for int1 for Scenario 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

24 Interpolation function for Scenario 3 . . . . . . . . . . . . . . . . . . . . . . 12

25 Plot for int1 for Scenario 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

26 Study settings for Time-dependency . . . . . . . . . . . . . . . . . . . . . . 13

27 Plot Scenario 1 - "Bottom-up" cracking . . . . . . . . . . . . . . . . . . . . 14



30 Plot Scenario 1 - "Top-down" cracking . . . . . . . . . . . . . . . . . . . . . 16


Effect of temperature on pavement fracture performance


33 Plot Scenario 1 - Rutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18



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1 Introduction

The goal of this project is to evaluate the effect of temperature on pavement fracture per-formance. As it is already known, asphalt materials are extremely sensitive to temperatureboth due to their visco-elastic nature as well as due to the thermally induced stresses. Thestudy will be performed on a multilayer pavement system (Figure 1) under different coolingscenarios.

Figure 1: Multilayer Pavement system

Although the cooling scenarios are being performed for the duration of just 24 hours, intime, the potential for low temperature cracking will increase. This is a major distressin many regions with cold climates and it is believed that the excessive brittleness dueto increase in stiffness and decrease in the ability to relax stress, leads to a buildup ofthermally induced stresses and ultimately cracking of mixtures in pavements. [1]The cooling scenarios for the project are:

The constant temperature of 2C during the whole day.

The temperature drops with a constant rate from 2C to 12C in 24 hours. The initial temperature of the pavement system is 2C. In two hours the temperature

drops to 5C and during the next 10 hours it reaches to 10C. The temperaturekeeps on being constant for the next 5 hours and after that it drops to 15C untilthe end of the day.

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2 Methods

In order to achieve the goal, a Finite Element program had to be used in order to simulatethe different scenarios, in our case, "COMSOL Multiphysics 4.3b", to create the model andobtain the required outcomes.

2.1 Geometry

In order to draw the geometry of the pavement system we need to define each layer(Subgrade, Sub-base, Road Base and Bituminouse) as a rectangle, complying with theparticular size of each of them. The points are being created in order to define the area ofinterest when obtaining results.

Figure 2: COMSOL geometry creator

Some assumptions have been made for the width and the height of the subgrade. The finalgeometry can be observed in Figure 3.

Width of the entire geometry Assumed subgrade height2 [m] 1 [m]

Figure 3: Multilayer Pavement system

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2.2 Materials

Based on the provided pavement system, all 4 layers have different material proprieties thatdefine them.

(a) Pavement system (b) COMSOL Material Defining

Figure 4: Material definings

2.2.1 Subgrade

The proprieties for the Subgrade are defined in Figure 5.

Figure 5: COMSOL subgrade material proprieties

Assumptions:

Subgrade density: 1800 kg/m3 - Taken from previously solved COMSOL models

Poissons ratio : 0.35 - Given from the project description

Youngs Modulus : 1000 109 Pa - Assumed 100x bigger than the given one Thermal conductivity: 1.48 W/(m K) - Taken from http: // pubs. usgs. gov/ of/1988/ 0441/ report. pdf , pg22, as for "Sandstone with air in the pores"

Heat capacity at constant pressure: 920 J/(kg K) - Taken from http: // www.engineeringtoolbox. com/ specific-heat-solids-d_ 154. html , as for sandstone

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2.2.2 Sub-base

The proprieties for the Sub base are defined in Figure 6.

Figure 6: COMSOL sub-base material proprieties

Assumptions:

Note: Excepting Youngs modulus, all other parameters are assumed the same.

Youngs modulus: 450 106 Pa - Given from the project description

2.2.3 Road base

The proprieties for the Roadbase are defined in Figure 7.

Figure 7: COMSOL road base material proprieties

Assumptions:

Note: Excepting Youngs modulus, all other parameters are assumed the same.

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Youngs modulusBased on the project description, the mechanical proprieties for Road Base Unboundmaterials are assumed to vary due to temperature difference in Winter( < 0C) andThaw( 0C), thus a variation between 300 MPa to 1000 MPa had to be definedin COMSOL by using a Step Function(Figure 8) command from Global definition.Location is the threshold that differentiates Winter from Thaw values for Youngsmodulus.

Figure 8: Step function 2 description

2.2.4 Bituminouse layer

Figure 9: COMSOL bituminouse material proprieties

Assumptions:

Density: 2400 kg/m3 - Taken from previous COMSOL tutorials

Thermal conductivity: 0.75 W/(mK) - Taken from http: // www. engineeringtoolbox.com/ thermal-conductivity-d_ 429. html

Heat capacity at constant pressure: 920 J/(kg K) - Taken from http: // www.engineeringtoolbox. com/ specific-heat-solids-d_ 154. html

Coefficient of thermal expansion: 3105 1/K -Taken from http://books.google.se/books?id=bA1tIkRJL8kC&pg=PA197&lpg=PA197&dq=coefficient+of+thermal+expansion+for+asphalt&source=bl&ots=pcNeGixZXP&sig=CsFpvsb-0GWZVaskQ2i8dn0MChY&hl=en&sa=X&ei=aG8pVNa0FaSGywOJqICIDQ&sqi=2&ved=0CCAQ6AEwAA#v=onepage&q=coefficient%20of%20thermal%20expansion%20for%20asphalt&f=false

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For the bituminous layer it has been used the Bulk modulus, K and shear modulus, Gbecause these long term elastic proprieties take care of Time-dependency and also due tothe fact that asphalt is a visco-elastic material.In order to calculate Youngs modulus which describes the materials response to linear stressand Shear modulus which describes the materials response to shear stress, the compliancecurve for asphalt materials has been defined as a power law with the coefficients providedfrom the project description as:

D(t) = D1 tm +D0D1 = 7.12e 4 MPa1D0 = 5.95e 5 MPa1

m = 0.634

Based on the given coefficients and by the Methods of interconversion between linearviscoelastic material functions.Part II - an approximate analytical method which has beenprovided by the supervisor, we could convert by using Lams parameters from page 1685,Table 1 to get the required material proprieties.A MATLAB code has been created in orderto simply our calculations:

Figure 10: MATLAB code

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From the MATLAB function we extract E0 = 2.0851e10 Pa as the first term from theobtained matrix which is the required Youngs modulus and then, by using the Laplacetransformation, we have performed the Curve fitting from the following general model:

G(t) = G0+G1 exp(x/tau1)+G2 exp(x/tau2)+G3 exp(x/tau3)+G4 exp(x/tau4)

Figure 11: MATLAB curve fitting for Prony series (initial value=1000 seconds)

Figure 12: Results obtained from the curve fitting

From the results of the Curve fitting we obtain the Shear modulus G0 = 8.396 MPa.

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2.3 Solid Mechanics

In Solid Mechanics, boundary conditions are defined such as:

Fixed constraint

Figure 13: Boundary of the fixed constraint

Roller support

Figure 14: Roller support position

Boundary load

Figure 15: Constant load along the surface of the AC layer

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The pressure has been defined from the project as 800 kPa, but its position has not beenspecified.

Figure 16: Defining the boundary load in COMSOL

As we have a load of 50 kPa, we can calculate the position at which it must act as follows:

Pressure = Load/Area

800 103 = 50103piradius2

radius = 0.14 m = 14 cm

Reference: Lecture Stress analysis of flexible pavements, Road and Railway Engineer-ing Course

In COMSOL, this is introduced as a Step function (step1) as:

Figure 17: Defining the location of the boundary load in COMSOL

The Step function (step1) has been introduced in Figure 16.

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Linear Viscoelastic materialAlso in Solid Mechanics, the proprieties of the material which define it as time-dependent is represented, by selecting "Bulk and shear modulus" from the "Long-termElastic proprieties" and by introducing the coefficients for shear modulus G, andrelaxation time tau. These coefficients have been taken from the MATLAB Curvefitting as seen in Figure 12 and were used for the Generalised Maxwell model.

Figure 18: Defining of Long-term elastic proprieties and coefficients for the GeneralisedMaxwell model

2.4 Heat Transfer in Solids

As the purpose of this project is to investigate different temperature scenarios, Heat transfermust be introduced. The Initial values were constant throughout all three scenarios, to avalue of 2C or 275.15 K.

Figure 19: Initial starting temperature for all three scenarios

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In Temperature, the three scenarios will be defined, based on their specific criteria.

Scenario 1

Figure 20: Scenario 1 temperature for 24 hours

Scenario 2For Scenario 2, the temperature in Heat transfer is defined as an Interpolation (int1),as seen in Figure 21.

Figure 21: Scenario 2 temperature for 24 hours in Heat transfer

The Interpolation (int1), is defined as follows:

Figure 22: Interpolation function for Scenario 2

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The plot for the Interpolation function can be seen in Figure 23 as Time on the x-axis andTemperature on the y-axis.

Figure 23: Plot for int1 for Scenario 2

Scenario 3For Scenario 3, the temperature in Heat transfer is also defined as an Interpolation(int1), and is defined as in Figure 24.

Figure 24: Interpolation function for Scenario 3

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The plot for the Interpolation function can be seen in Figure 25 as Time on the x-axis andTemperature on the y-axis.

Figure 25: Plot for int1 for Scenario 3

2.5 Study scenarios

The Study has been peformed as a Time-dependent one, over a period of 24 hours, butalso due to the viscoelasticity of the asphalt material.

Scenario 1 and 2 had a Step of 15 minutes (900 seconds),Figure 26a, whereas Scenario3 had a Step of 5 minutes (300 seconds),Figure 26b, due to the multiple changes thatoccurred during the 24 hours interval.

(a) Study settings Scenario 1 and 2 (b) Study settings Scenario 3

Figure 26: Study settings for Time-dependency

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3 Results

The purpose of this project was to examine the effect of all three cooling scenarios ondifferent fracture modes. The fracture modes are defined as failure criteria in general, butin our case, we will examine:

Bottom - up cracking (Fatigue cracking)

Top - down cracking (Thermal cracking)

Vertical strain at the top of the subgrade (Rutting)

3.1 Bottom - up cracking (Fatigue cracking)

Pavement cracking initiates at the bottom of the HMA layer, where the tensile bendingstresses are the greatest, then progresses up to the surface.

Results obtained from COMSOL for all three scenarios:

Scenario 1

Figure 27: Plot Scenario 1 - "Bottom-up" cracking

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Scenario 2


Scenario 3


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In order to inspect "Bottom-up" cracking, we need to plot from the obtained Results inCOMSOL, a Point Graph with Time on the x-axis and the Stress tensor,r - component onthe y-axis. This will be investigated at the bottom of the HMA layer in the defined point.For all three scenarios, tensile stresses can be observed at the beginning (until 0 on the "rcomponent"), followed after the 0 marker by compressive stresses.One other aspect is the limitation that has been imposed by the project to only simulate24 hours, thus no significant stresses could occur, numerically it can be observed from allthree scenarios outcomes. (Goes down to 0.4 106 N/m2 Figure 27,28,29)Scenario2 indicates, due to the constant drop rate from 2C to 12C, from approximately42000 seconds that the Base layer will freeze, and so, stresses will transfer to the lowerlayers, and it continues to decrease in all layers throughout the entire period. (Figure 28)Scenario3 is almost the same as scenario two, the difference being that freezing startsat approximately 17000 seconds. This is due to the fact that the drop rate is higher,in a shorter period, in Scenario3 than Scenario2 at the beginning.The decrease of thetemperature in all layers is still valid as in the previous one. (Figure 29)

3.2 Top-down cracking

Usually occurs due to a low stiffness on a upper layer caused by high surface temperature,but it may be also caused by a thick HMA pavement.Throughout all scenarios simulate forour project, temperatures are decreasing thus stiffness will increase.


Scenario 1

Figure 30: Plot Scenario 1 - "Top-down" cracking

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Scenario 2


Scenario 3


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Top-down cracking is investigated in a similar matter as for "Bottom-up" cracking, theonly difference is that the point which has to be selected in COMSOL, is at the top of theAC layer. Due to the fact that there is a constant load applied on the pavement system,Scenario 1 and 2 have no top-down cracking initiation. Numerically, the Stress tensorindicates this pattern.Scenario 3 on the other hand, indicates, both numerically and graphically, that there willbe a crack initiation in-between 18000 seconds and 30000 seconds. This may result as aconsequence of the frozen Base thus there would be tensile stresses occurring at the top ofthe AC layer. The reason behind this is unforeseen as it may be also caused, due to thefact that also the AC layer could be an explanation of its failure because stiffness increasesas temperature decrease. Further analysis must be performed by using maybe differentmixtures or by applying different load patterns.

3.3 Vertical strain at the top of the subgrade (Rutting)

Permanent deformation or rutting is a manifestation of both densification and permanentshear deformation. Rutting criterion is based on limiting the vertical compressive subgradestrain, if the maximum vertical compressive strain at the surface of the subgrade is lessthan a critical value, then rutting will not occur for a specific number of traffic loadings.The magnitude of rutting has been correlated with the amount of traffic and the verticalcompressive strain level at the surface of the subgrade. [2]


Scenario 1

Figure 33: Plot Scenario 1 - Rutting

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Scenario 2


Scenario 3


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In order to obtain the Vertical compressive strain at the top of the subgrade, a plot shouldbe made in Results -> Point graph, having Time on the x-axis and the Strain tensor onthe y-axis. The location for the investigation is just below the subgrade threshold.One important aspect we can notice from all three scenarios is a sudden change in directionimmediately after loading, which may suggest that there might be a problem with the Pronyseries Curve fitting. This might be as a result of using an initial value of 1000 seconds inthe fitting options.Secondly, Scenarios 2 and 3 have almost the same output plot. In Scenario 2 (Figure34), around 42000 seconds, there is an unpredictable outcome which is hard to explain,but might be explained considering that the material changes its stiffness due to the lowtemperature, followed by an increase of strain until the end, as a result of the decrease ofthe subgrade stiffness.Scenario 3 is different for the reason that its Interpolation function(int1) (Figure 24) has a more sudden drop in temperature at the beginning than the onein Scenario 2 (Figure 22), which explains why the same situation which has happened inScenario 2 around 42000 seconds, happens in Scenario 3 around 5000 seconds. Afterwards,there is a decrease of strain until the end of the period, due to an increase of the subgradestiffness.

4 Conclusions

The project goal, the effect of temperature on pavement fracture performance, is a topic ofgreat interest for the reason that it tries to observe the response of a pavement structureto different temperature cooling scenarios and it provides the knowledge to create a morereliable asphalt mixture.COMSOL resulted in the end to test our abilities to learn a new software, of great interestto todays developing pavement industry.The results experienced by our model might not be sufficient for some situations, asencountered in the Rutting chapter in Scenarios 2 and 3 (Figure 34,35), and furtheranalysis of these kind of specific situations must be engaged, to achieve more detailed plotsthat can analyze them. One step in carrying out this, might be to increase the time-spanto a greater extent.

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References

[1] University of Wisconsin-Madison, "Task 5- Modeling of Asphalt Mix-tures Contraction and Expansion Due to Thermal Cycling"// https://www.google.se/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0CDUQFjAD&url=http%3A%2F%2Fwww.dot.state.mn.us%2Fmnroad%2Fprojects%2FLow_Temp_Cracking%2Fpdfs%2FTask%2520Reports%2FT5%2520-%2520Thermal%2520Modeling%2520(revised%252029mar12).docx&ei=J3stVLHHM-HMyAOvpILgDA&usg=AFQjCNEE4LV4EQYBZSKnvSOsa-4CSxlfng&sig2=7JHFFWeLPgFb7dyrwGReoQ&bvm=bv.76477589,d.bGQ&cad=rja

[2] Emmanuel O. Ekwulo and Dennis B. Eme, "Fatigue and rutting strain analysis of flex-ible pavements designed using CBR methods"// https://www.google.se/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CCMQFjAB&url=http%3A%2F%2Fwww.ajol.info%2Findex.php%2Fajest%2Farticle%2Fdownload%2F56271%2F44715&ei=l0E9VI-1CuroywOFxYK4Cg&usg=AFQjCNGzaQNVdCzHqlUCkB-3Q_EplcjRlg&sig2=8g33Dd_U_d6aIvd9gszIWg&bvm=bv.77412846,d.bGQ&cad=rja

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Project Description 1.pdf (p.1-25)IntroductionMethodsGeometryMaterialsSubgradeSub-baseRoad baseBituminouse layer

Solid MechanicsHeat Transfer in SolidsStudy scenarios

ResultsBottom - up cracking (Fatigue cracking)Top-down crackingVertical strain at the top of the subgrade (Rutting)

Conclusionsfirst sectionsecond section

Binder1.pdf (p.26-34)Bottom upwards (r component) Scenario 1Bottom-upwards (r component) Scenario 2Bottom-upwards (r component) Scenario 3Top down cracking (r component) Scenario 1Top down cracking (r component) Scenario 2Top down cracking (r component) Scenario 3Vertical strain top subgrade (Rutting) (z component)Scenario1Vertical strain top subgrade (Rutting) (z component)Scenario2Vertical strain top subgrade (Rutting) (z component)Scenario3

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EFFECT OF TEMPERATURE ON PAVEMENT FRACTURE PERFORMANCE