1. Fang-Ju Chou and William G. Buttlar FAA COE Annual Review Meeting October 7, 2004 Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign Analysis of Flexible Overlay Systems: Application of Fracture Mechanics to Assess Reflective Cracking Potential in Airfield Pavements

2. 2 - Progress Since Last Review Meeting  Development/Verification of Fracture Mechanics tools for ABAQUS  Application of Tools to Study Reflective Cracking Mechanisms in AC Overlays Placed on PCC Pavements - Current/Future Work Outline

3. 3 Problem statement - Review Functions of Asphalt Overlays (OL):  To restore smoothness, structure, and minimize moisture infiltration on existing airfield pavements. Problem:  The new asphalt overlay often fails before achieving its design life. Cause: Reflective cracking (RC).

4. 4 Problem statement ~ Cont. Current FAA Flexible OL Design Methodology: Rollings (1988’s) Assumptions used: 1.The environmental loading (i.e. temperature) is excluded. 2.A 25% load transfer is assumed to present between slabs. 3.Structural deterioration is assumed to start from underlying slabs.  Reflective cracking (RC) will initiate when structural strength of slabs is consumed completely.  RC will grow upward at a rate of 1-inch per year. However, joint RC often appears shortly after the construction especially in very cold climatic zones.

5. 5 Ongoing/Upcoming Research Expand 3D Parametric Study to Investigate: –Additional Pavement Configurations and Loading Conditions –Effect of Joint LTE on Critical Responses and Crack Propagation Development of Two Possible Methods to Consider Reflective Cracking Potential –Simpler than Crack Propagation Simulation –Less Sensitive to Singularity at Crack/Joint

6. 6 Fracture Analysis: J-integral Estimate Stress Intensity Factors (KI and KII) at Tip of an Inserted Crack (Length will be Varied) Compute Path Integral Around Various Contours

7. 7 Ph.D. Thesis of Fang-Ju Chou: Objectives: 1.Introduce a robust & reliable method (J-integral & interaction-integral) to obtain accurate critical OL responses. 2.Understand the effect of temp. loading by introducing temp. gradients in models. 3.Identify critical loading conditions for rehab. airfield pavements subjected to thermo-mechanical loadings. 4.To investigate how the following parameters affect the potential for joint RC in rehab. airfield pavements.  Bonding condition between slabs & CTB  Load transfer between the underlying concrete slabs  Subgrade support  Structural condition (modulus value) of the underlying slabs

8. 8 Limitation of traditional FE modeling at joint Limitation:  The accuracy of the predicted critical OL responses immediately above the PCC joint was highly dependent on the degree of mesh refinement around the joint. FEA  applied † on modeling of asphalt overlaid JCP. † Kim and Buttlar (2002); Bozkurt and Buttlar (2002); Sherman (2003) To seek reliable critical stress predictions, LEFM will be applied in an attempt to arrive at non-arbitrary critical overlay responses around a joint or crack. Concrete Slab Subgrade CTB AC Overlay No. of Elements?

9. 9 The J-Integral: Path Independence A closed contour =  1 +  2 +  3 +  4 On the crack faces (  3 and  4 )  n 1 = 0 ; Assuming traction free:  ij n j = 0  No contributions to J-integral from segments  3 &  4  J 3 = J 4 = 0; J 2 = -J 1 reverse the normal of segment  1 ; new normal m j (points away from tip) Rename m j = n j J2J2 = J1J1 J-integral is independent of the contour taken around the crack tip 11 22 33 44 njnj y x njnj mjmj Crack faces Elastic homogeneous material

10. 10 Relation between J and G IntroductionLiterature Review Principals of LEFM & Appl. 2D Pav. ModelModel Appl.Summary 1.Rice (1968) showed that the J-integral is equivalent to the energy release rate (G) in elastic materials. (section 3.2.3) J G Ks For a linear elastic, isotropic material (at  =  ) For an elastic material J = G For a linear elastic, isotropic material (at  =  ) Take Ks as critical stress predictions Use J to quantify the propensity of joint RC

11. 11 Extraction of Stress Intensity Factors 1.Numerically it is usually not straightforward to extract † K of each mode from a value of the J-integral for the mixed-mode problem. 2.The finite element program ABAQUS uses the interaction integral method (Shih and Asaro, 1988) to extract the individual stress intensity factor. 3.The interaction integral method of homogeneous, isotropic, and linear elastic materials is introduced in section 3.3.1. (at  =  ) † ABAQUS users manual, 2003, Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, Rhode Island.

12. 12 2D Model Description--Geometry & Material Purpose: analyze a typical pavement section of an airport that serves Boeing 777 aircraft The selected model geometry and pavement cross sections are based on the structure and geometric info. † of un-doweled sections of runway 34R/16L at DIA in Colorado. Concrete Slabs E CTB = 2,000 ksi; CTB = 0.20 k = 200 pci Subgrade CTB 18 in 8 in AC Overlay 5 in E AC = 200 ksi; AC = 0.35 0.5 in 0.2 in E PCC = 4,000 ksi PCC = 0.15 Cross section Note: 1-inch = 25.4 mm; 1-psi = 6.89 kPa; 1 pci = 271.5  10 3 N/m 3 Traffic Direction Transverse Joint = 0.5in Longitudinal Joint = 0.5in 240 in 225 in Top view C L † Hammons, M. I., 1998b, Validation of three- dimensional finite element modeling technique for jointed concrete airport pavements, Transportation Research Record 1629.

13. 13 36 ft (10.97 m) Boeing 777-200 2D Model Description--Loading 57 in 21.82 in 13.64 in 55in One Boeing-777 200 aircraft: 2 dual-tridem main gears Gear width = 36 ft main gear (6 wheels; 215 psi) Gross weight = 634,500 lbs (287,800 kg) Each gear carries 47.5% loading = 301,387.5 lb

14. 14 Boeing777-200: larger gear width (36 ft = 432 in) The 2 nd gear is about 2 slabs away from 1 st gear Assumption: the distance between gears is large enough such that interactions may be neglected for the study of the OL responses 57 in 55in 225 in Gear 1 6.82 in 225 in 240 in 432 in 57 in 16.32 in Note: Dimensions not drawn to scale Gear 2 55in 1Slab 2 Slab 3 4 2D Model Description--Loading

15. 15 2D Model Description--Gear Loading Position not practical to investigate every possible gear position four selected positions: have the greatest potential to induce the highest pavement responses under one gear Position A AC Overlay Concrete Slab CTB Subgrade 2-D pavement cross- section (Cut A-A) AC Overlay Concrete Slab CTB Subgrade Modeled range 2-D pavement cross- section (Cut B-B) Position B Position A: edge loading condition; Position B: joint loading condition Corner loading cond. (dash lines) cannot be considered in 2-D models, since the effect of the 3rd dimension cannot be distinguished. Cut A-A Cut B-B Pos. A Pos. B Corner Top view Modeled range

16. 16 2D Model Description--Gear Loading Position The other two positions: Position C: selected to study the case where the gear is centered over the joint to maximize bending stresses in the OL Position D: also has the potential to induce higher bending stresses in an OL Position C AC Overlay Concrete Slab CTB Subgrade 2-D pavement cross- section (Cut C-C) AC Overlay Concrete Slab CTB Subgrade Modeled range 2-D pavement cross- section (Cut D-D) Position D Cut D-D Pos. C Pos. D Top view Cut C-C  Rehab. pavements subjected to Pos. A~D modeled as 2D pl-  condition.  Joint discontinuity cannot be correctly modeled using 2D axisymmetric model Modeled range

17. 17 2D Model Description--Load Adjustment Factor (LAF) One B777-200 wheel P = 50231.25lb 2D axisymmetric model: circular loading q = 215 psi CTB Concrete Slabs Overlay 240 in σ X1 = -119.1 psi C L r = 8.624 in CTB Concrete Slabs Overlay q =215 psi 240 in 17.248 in σ X2 =-170.8 psi 2D pl-  model: strip loading 1.Correct excessive wheel load: need to adjust the applied load for pl-  models 2.LAF: obtained by reducing the q of the 2-D pl-  model until the horiz. stress prediction at the bottom of the asphalt OL matches the 2-D axisymmetric prediction. 3.For this 2-D rehab. pavement model of 5-inch OL under pl-  cond., the adjustment factor = 0.697. 4.Reduced contact tire pressure p = 69.7%  q will be imposed on 2-D pl-  pavement models. 5.Limitations: location, no. of wheel Most simple, effective way

18. 18 Results of Selected Loading Positions Before inserting a sharp joint RC into OL, four un-cracked rehab. models subjected to gear loading positions A~D are analyzed. Position A (Cut A-A) Long. Joint Overlay Concrete Slabs CTB 225 in Position C (Cut C-C) Long. Joint Overlay Concrete Slabs CTB 225 in Position B (Cut B-B) Overlay Concrete Slabs CTB 240 in Trans. Joint Position D (Cut D-D) Overlay Concrete Slabs CTB 240 in Trans. Joint

19. 19 Tension Comp. PosA: tensile fields are induced at the bottom of OL above PCC joint Results of Selected Loading Positions (Position A)

20. 20 Results of Selected Loading Positions (Position C) Tension Comp. PosC: tensile fields are also induced at the bottom of OL above PCC joint

21. 21 Results of Selected Loading Positions (Position B) Tension Comp. PosB: compressive fields are present at the bottom of OL above PCC joint

22. 22 Tension Comp. PosD: compressive fields are also present at the bottom of OL above PCC joint Results of Selected Loading Positions (Position D)

23. 23 Inserting Joint RC Contour No.8 Coarse crack-tip mesh Contour No.2 0.025” ℓ Crack Faces 8 Contour No.5 Contour No.9 0.025” Fine crack-tip mesh Crack Faces 24 ℓ 4 C2 C1 B2 B1 y, v x, u  r ℓ Crack-tip element (Singular Element)  Size of crack-tip element influences the accuracy of the numerical solution.  two mesh types are used in the crack-tip region to ensure that a fine enough mesh has been applied around the crack-tip

24. 24 Fracture Model Verification 1.Shih et al. (1976) proposed a disp. correction technique (DCT) to calculate (K I )s using the disp. responses of a singular element 2.Ingraffea and Manu (1980) generalized this approach for mixed- mode stress fields at the crack-tip. 3.Showed that the ℓ/a ratio had a pronounce effect on the evaluation of Ks. (note: a = crack length) 4.Using DCT, we can calculate the separate (K I )s & (K II )s in a mixed- mode problem based on the displacements of crack flank nodes of singular elements u = the sliding disp. at the crack flank nodes = the opening disp. at the crack flank nodes ℓ 4 C2 C1 B2 B1 y, v x, u  r ℓ Crack-tip element (Singular Element) Crack faces

25. 25 Verification of Reference Sol. (using DCT) v.s. Analytical Sol. 1.To confirm the accuracy of predicting Ks using DCT, a flat plate with an angled crack is modeled under pl-  cond. with unit thickness. 2.The closed form solutions for Mode I and Mode II stress intensity factors at either crack-tip are: K I (0) = Mode I stress intensity factor (  =0) a = half of the crack width c = half of the plate width 2a = 3.873093344E-02  =1000 psi 10" 2a  2c = 10" u v u v E = 200 ksi = 0.35  = tan -1 (0.5) Note: drawing not to scale Deformation scale factor = 15.0 Deformation scale factor = 27.5 Right crack tip Left crack tip 22

26. 26 Verification of Reference Sol. (using DCT) v.s. Analytical Sol. 1.Supplying the disp. responses of the crack flank nodes computed via ABAQUS, the reference Ks using DCT are obtained for both crack tips. 2.Reference Ks compare well with the analytical solutions for both crack tips with the error percentages of 1.58% and 2.8 % for the right and left crack tip.

27. 27 Results of Selected Loading Positions 1.Magnitudes of stress predictions immediately above the PCC joint are influenced by the degree of mesh refinement around the joint; not recommended to be taken as critical pavement responses directly 2.In addition to loading positions 1 and 2 (same as positions A and C), 9 gear loading positions are also analyzed for rehabilitated pavements with an initial sharp joint RC of 0.5” or 2.5”. x = 189.51” Fine & coarse mesh employed Pos1 (PosC) 5 in 18 in 8 in 0.5 in 0.2 in 4.5 in 13.5 in Subgrade 225 in Crack Length = 0.5” or 2.5” AC Overlay Concrete Slab CTB † Pavement geometry not drawn to scale x = 0” x = 34.57” x = 113.46” Pos2 (PosA) Pos7 Pos11 225 in

28. 28 Position 7 Determination of Critical Loading Situation (Traffic Loading Only) Eleven traffic loading positions (gear loading positions 1 to 11) Two lengths of joint RC (0.5-in and 2.5-in) Two mesh types (fine & coarse at the crack-tip region) 44 Sets of Numerical Results

29. 29 Determination of Critical Loading Situation (Aircraft Loading Only) Stabilized J-value is obtained when the integral is evaluated a few contours away from the crack tip J-value of the first contour is least accurate and should never be used in the estimation. The accuracy of the numerical J-value eventually degrades due to the relatively poor mesh resolution in regions far away from the crack-tip. Stable J-value of coarse mesh begins last available contour or contour far away from the crack-tip Stable J-value of fine mesh begins

30. 30 (Aircraft Loading Only)  Tensile mode I SIFs are predicted starting from loading position 6, where the center of B777 main gear is at least 93.45” away from the PCC joint.  Both mesh types give about the same predictions of mode I SIFs Reduced contact tire pressure = 69.7%  215 psi Mode I SIFs vs. 2 a/h AC ratios -- 11 positions -- Fine & coarse meshes

31. 31 1.Castell et al. (2000) applied LEFM for flexible pavement systems and modeled the fatigue crack growth using FRANC2D and FRANC2D/L. 2.A distributed wheel load of 10,000 lb with a 100 psi contact tire pressure was applied above the crack. A compressive K I was found to exist at the crack tip.  Differences: conventional FP: softer material below surface; Rehab. pavement: much stiffer slabs below surface.  Horiz. Stress distribution would not follow the similar trends. Comparison of Results Study of Castell et al. agrees with the present work:  The compressive stresses can be predicted at the crack-tip for 2-D pavement models when distributed wheel loads are applied above a crack.

32. 32 Application 1 (Traffic vs. Combined Loadings) Three loading scenarios Aircraft loading position 7 only Aircraft loading position 7 & Temperature loading (  T PCC =-23  F) Aircraft loading position 7 & Temperature loading (  T PCC =-15.3  F) 225 in Longitudinal Joint Overlay=5”;  AC =1.38889  10 -5 1/  F Concrete slabs=18”  PCC =5.5  10 -6 1/  F CTB=8”;  CTB =7.5  10 -6 1/  F 70  F 47.5  F 40  F  T PCC =-1.25  F/in  T PCC =-0.85  F/in Subgrade 113.46-in 70  F 54.7  F 47.2  F  T AC =-1.5  F/in Position 7

33. 33 IntroductionLiterature Review Principals of LEFM & Appl. 2D Pav. ModelModel Appl.Summary  the predicted mode I SIF is raised dramatically from 168.3 psi-in 0.5 to 1669 psi-in 0.5 or 2260 psi-in 0.5 depending on  T PCC  The predicted mode II SIF is also raised from 14.2 psi-in 0.5 to 104 psi-in 0.5 or 146.4 psi-in 0.5 depending on  T PCC. Num. mode I and mode II SIFs a/h AC = 0.1 and 0.5

34. 34 1.Under the combined loadings, the predicted J-value is much bigger than the one induced by aircraft loading only. 2.The critical loading condition of this 2-D rehabilitated pavement (i.e. 5-inch asphalt overlay on the rigid pavement) is the aircraft loading position 7 plus negative temperature gradients. The bigger the negative temperature differential through the underlying concrete slabs, the higher the predicted mode I SIF. Application 1 (Traffic vs. Combined Loadings)

35. 35 Recent Findings Based on the findings of this study, the following conclusions can be drawn: 1.By applying LEFM on modeling of rehab. airfield pavement, reliable critical OL responses (i.e., the J-value, and stress intensity factors at a crack-tip) can be obtained. 2.For the OL system considered in this study, which involved a 5-inch thick asphalt OL placed on a typical jointed concrete airfield pavement system serving the Boeing 777 aircraft, gear loads applied in the vicinity of the PCC joint were found to induce horiz. compressive stress at the RC tip for all load positions considered. The crack lengths studied ranged from 0.5-inch to 2.5- inch. 3.Whereas, for un-cracked asphalt OLs, highly localized horiz. tension was found to exist in the asphalt OL just above the PCC joint. 4.Temperature cycling appears to be a major contributor to joint reflective cracking.

36. 36 Research Products 1.UIUC Ph.D Thesis – Fang-Ju Chou: October 1, 2004. 2.FAA COE Report – Fall, 2004. 3.Conference, Journal Papers – In preparation. 4.Models, models, models!

37. 37 Current and Future Work 1.To better simulate the behavior of asphalt OLs, an advanced material model that accounts for the viscoelastic behavior of the asphalt concrete can be implemented in the FEA. However, a thorough understanding of a nonlinear fracture mechanics will be required to properly interpret the modeling results. 2.The use of actual temperature profiles versus the critical OL responses are recommended. This analysis should be conducted in conjunction with the implementation of a viscoelastic constitutive model for the asphalt OL. 3.By inserting appropriate interface elements such as cohesive elements immediately above the PCC joint, a more realistic simulation of crack initiation and propagation can be obtained. 4.Modeling limitations must be addressed. The move to 3D, crack propagation modeling in composite pavements subjected to thermo-mechanical loading pushes the limits of current FEA capabilities. Modeling simplifications and advances in numerical modeling efficiencies are needed. 5.Field Verification

38. Thank you!