1. Field Validation and Parametric Study of a Thermal Crack Spacing Model David H. Timm - Auburn University Vaughan R. Voller - University of Minnesota Presented at the Annual Meeting of the Association of Asphalt Paving Technologists Lexington, Kentucky March 10 – 12, 2003

2. Cracking Characteristics Thermal cracking common in cold climates Features –Transverse cracks –Regular spacing

3. Crack Spacing Focus of this Study is the question What features control the spaces between Cracks?

4. Model Stress Profile in Thermally Cooled Asphalt Layer on Granular Base E,, , H,  E,, , c,  Modeled in Two ways

5. Finite Difference Code--FLAC x 50x250 mm Grid Element Sizes 63x315 mm 313x1563 mm Asphalt Concrete (Elastic Model) z Granular Base (Mohr Coulomb Model)

6. 1-D Semi-Analytical Model Elastic Layer with Elastic-Plastic Restraint  c a  tan  q=ku x Timm, Guzina and Voller Int J Solids and Structures, 2002 xtxt

7. Form of Stress Profile Curling Stress Rate of Strees Increase Distance from free end

8. Comparison of Models

9. Crack Spacing from Stress Curve StSt xcxc 11 x Cracking may occur Cracking will not occur Sliding On Rigid Base

10. 11 StSt x Crack Spacing from Stress Curve xcxc xcxc Average Spacing = 1.5·X c

11. Validate thermal crack spacing model with field data Perform sensitivity analysis on length scale –Help guide future laboratory work –Develop more complete understanding –Identify how material selection will affect spacing Objectives

12. Field Validation –4 similar sections at Mn/ROAD Parametric Study –10 input variables Layer 1 –Stiffness, Poisson, Density, Thickness, Thermal Coef. Layer 2 –Stiffness, Poisson, Density, Cohesion, Friction Angle Scope E,, , H,  E,, , c, 

13. 1.Select MnROAD sections 2.Analyze thermal crack spacing by section 3.Analyze in situ thermal conditions 4.Gather material property data for model 5.Simulate pavement, determine spacing 6.Compare predictions to measured 7.Assess validity Field Validation Methodology

14. Similar thickness designs Identical binders Common subgrade Different base layers MnROAD Sections 150 155 160 231 838 102 711 838 0 200 400 600 800 1000 1200 Cell 1Cell 2Cell 3Cell 4 Depth Below Pavement Surface, mm HMAC Class 4 G.B. Class 6 G.B. Class 5 G.B. Class 3 G.B. LEGEND

15. Average Crack Spacing Avg Spacing Cell 1: 12 m Cell 2: 8 m Cell 3: 13 m Cell 4: 9 m

16. Top of pavement Bottom of pavement Feb 1 Feb 2 Feb 3 Temperature Cycling

17. Backcalculation Laboratory testing as part of Mn/ROAD project Derived values –Thermal coefficient = fn (Volumetrics) Model ‘tuned’ with friction and cohesion Material Property Data E,, , H,  E,, , c, 

18. Resulting Friction and Cohesion CellFriction Angle, o Cohesion, kPa 13010 25015 33510 42510 Mohr-Coulomb Properties of Material Directly Beneath HMA

19. Model Comparison 0 2 4 6 8 10 12 14 16 0246810121416 Measured Average Spacing, m Predicted Spacing, m Line of Equality Cell 1 Cell 2 Cell 3 Cell 4

20. Crack spacings pass reasonableness check Recently, model has been used to predict other crack spacing phenomenon Model Assessment TiN Coating

21. Curling Stress Rate of Stress Increase Max stress Factors that Influence Stress Profile

22. Uniform temperature change 2-layer structure 10 input parameters varied from low, medium, and high Maximum tensile stress curves plotted and evaluated –Maximum Stress –Rate of Stress Increase –Curling Stress Parametric Investigation Methodology

23. Input Parameters LayerInputUnitsLowMedium (Baseline) High 1E1E1 Pa5*10 9 1.4*10 10 3*10 10  unitless0.150.200.25  kg/m 3 2,2002,3002,400 H1H1 cm7.61530  /C/C1.33*10 -5 2.15*10 -5 2.97*10 -5 2E2E2 Pa5.5*10 7 5.5*10 8 5.5*10 9  unitless0.350.40.45  kg/m 3 1,8002,0002,200 c2c2 kPa0, 0.1, 1, 10, 70, 140 22  204060

24. HMAC Stiffness (E 1 )

25. HMAC Poisson Ratio ( 1 )

26. HMAC Thickness (H 1 )

27. HMAC Thermal Coeff. (  1 )

28. Base Stiffness (E 2 )

29. Base Cohesion (c 2 ) As c gets Large Only elastic resistance

30. Base Friction Angle (  2 ) Note: c = 10 kPa

31. Curling Stress Rate of Stress Increase Max stress Factors that Influence Stress Profile

32. Relative Influence on Each Criteria Input Parameter Maximum Stress Rate of Stress Increase Curling Stress E1E1 31--  2 11 H1H1 3 11 31 E2E2 3  22 c2c2 33 22 2

33. Model compared favorably to field data Model is sensitive to base material properties Model is simple, yet provides length scale to thermal cracking problem Key input parameters are… –Stiffnesses of HMAC and Base –Thermal coefficient –Frictional properties of Base material Conclusions

34. Further validation with field sections –Model has compared favorable to other types of cracking Incorporate a fracture mechanics model to simulate crack propagation Examine viscoelastic constitutive models Recommendations

35. Plan mitigation strategies –Saw and seal –Material selection Assess probability and expectation of cracking Potential Uses of Model

36. Dr. Bojan Guzina Minnesota Department of Transportation –Minnesota Road Research Project Acknowledgements

37. Thank You! Questions?