1. Principal Investigators: Jeffery Roesler, Ph.D., P.E. Surendra Shah, Ph.D. Fatigue and Fracture Behavior of Airfield Concrete Slabs Graduate Research Assistants: Cristian Gaedicke, UIUC David Ey, NWU Urbana-Champaign, November 9 th, 2005

2. Outline Objectives Experimental Design Experimental Results 2-D Fatigue Model Finite Element Analysis Application of FEM Model Fatigue Model Calibration Fatigue Model Application Summary The Future  Cohesive Zone Model

3. Research Objectives Predicting crack propagation and failure under monotonic and fatigue loading Can fracture behavior from small specimens predict crack propagation on slabs. Three point bending beam (TPB) Beam on elastic foundationSlab on elastic foundation Load CMOD

4. Integrate full-scale experimental slab data and a 2-D analytical fracture model (Kolluru, Popovics and Shah) Check if the monotonic slab failure envelope controls the fatigue cracking life of slabs as in small scale test configuration. Research Objectives Fatigue load Monotonic load 2-D Model

5. Experimental Design Simple supported beams: 2 beams, 1100 x 80 x 250 mm. 2 beams, 700 x 80 x 150 mm. 2 beams, 350 x 80 x 63 mm. The beams have a notch in the middle whose length is 1/3 of the beam depth. Beams on clay subgrade: 2 beams, 1200 x 80 x 250 mm. 2 beams, 800 x 80 x 150 mm. 2 beams, 400 x 80 x 63 mm. The beams have a notch in the middle whose length is 1/3 of the beam depth. Beam Tests

6. Experimental Design Large-scale concrete slabs on clay subgrade: 2 slabs, 2010 x 2010 x 64 mm. 4 slabs, 2130 x 2130 x 150 mm. The load was applied on the edge through an 200 x 200 mm. steel plate. The subgrade was a layer of low-plasticity clay with a thickness of 200 mm. Standard Paving Concrete: ¾” limestone coarse crushed aggregate, 100 mm slump and Modulus of Rupture 650 psi at 28 days Slab Tests Concrete Mix

7. Experimental Results Results on Beams Full Load-CMOD curve. Peak Load. Critical Stress Intensity Factor (K IC ). Critical CTOD (CTOD c ). Compliance for each load Cycle (C i ). Monotonic Load Compliance vs. load cycle

8. Beam FEM Setup Small Beam

9. UIUC Testing

10. Monotonic Results and Crack Length From FEM From Testing

11. Experimental Results Results on Beams Load vs. CMOD curves Compliance vs. number of cycles Peak Load. Stress Intensity Factor (K I ). Compliance for each load Cycle (C i ). Fatigue Load in FSB

12. Experimental Results Results on Slabs Full Load-CMOD curve. Peak Load. Compliance for each load Cycle (C i ). Monotonic Load ≈ 5 mm

13. Experimental Results Results on Slabs Fatigue Load Load vs. CMOD curves Compliance vs. number of cycles Peak Load. Stress Intensity Factor (K I ). Compliance for each load Cycle (C i ).

14. 2-D Fatigue Model (Kolluru, Popovics and Shah, 2000) P max CMOD P *Ci*Ci * C (loop) P min *Secant compliance C u (1) PcPc CMOD P CiCi ½ P c C u (2) C u (3) PcPc a eff P O’ a0a0 O PcPc a eff P a0a0 P max a \failure P min Relation between load and effective crack length a eff is obtained !! Monotonic Test of TPBFatigue Test of TPB PcPc a eff P O’ a0a0 O P max A B C D a \failure s a t w

15. 2-D Fatigue Model O’-O: no crack growth, linear part of the load-CMOD curve. O-B: Crack Deceleration Stage, Stable crack growth, nonlinear part of the load-CMOD curve until peak load. B-D: Crack Acceleration Stage Post peak load-CMOD. Where: C 1, n 1, C 2, n 2 are constants  a = incremental crack growth between  N  N = incremental number of cycles  K I =stress intensity factor amplitude of a load cycle a PcPc a P O’ a0a0 O P max A B C D a \failure a \crit Log  a/  N) a0a0 O B C D a \failure a \crit -3 -5 -7 # cycles a a0a0 a \crit a \failure NfNf 0.4N f B C

16. Finite Element Analysis FEM Mesh Computation of the Stress Intensity Factor & C i (a) An indirect method was used to calculate K I, called “Modified Crack Closure Integral Method. (Rybicki and Kanninen, 1977)

17. Normal equations for TPB Beams are not applicable. FEM Modelation is required. CMOD vs. Crack Length Compliance vs. Crack Length Finite Element Analysis Relation between Crack length, Compliance and CMOD The CMOD increases its value with the increase of the Crack Length. The normalized compliance at the midslab edge predicted using the FEM model shows a quadratic behavior.

18. Finite Element Analysis Relation between Stress Intensity Factor and Crack Length Relation between CMOD and Crack Length

19. Application of FEM Model Step 1: Experimental Relation between CMOD and the Displacement Experimental relation between CMOD measurements and displacement.

20. Step 2: Determination of the Load vs. CMOD curves The relation between CMOD and displace- ments allows to estimate the CMOD for the unnotched specimen Application of FEM Model

21. Step 3: Estimation of the Crack Length The crack length is estimated using this modified equation from the FEM model and the CMOD Application of FEM Model

22. Step 4: Estimation of the Normalized Compliance (FEM) Application of FEM Model The normalized compliance obtained from the FEM Model for different crack length is multiplied by the experimental initial compliance

23. Step 5: Experimental Compliance vs. Crack Length curves Application of FEM Model

24. Fatigue Model Calibration Step 1: The Compliance is measured for each fatigue load cycle of slab T2

25. Fatigue Model Calibration Step 2: The Crack length is obtained for each cycle using the FEM Model for slab T2.

26. Fatigue Model Calibration Step 3: The Critical Crack a crit is Critical Number of Cycles N crit is obtained for slab T2. a crit = 41 mm N crit = 25000 This point of critical crack length is a point of inflexion in the curve

27. Fatigue Model Calibration a crit = 41 mm Step 4: The two sections of the model are calibrated Different fatigue equations apply for crack length bigger or smaller than a crit Log C 2 = -15.0 Log C 1 = 17.6

28. Fatigue Model Application Estimation of N 1 N 1 is he required number of cycles to achieve a crit This fatigue equation allows to predict crack propagation for any number of cycles N<N 1 If we have an unnotched slab, a 0 = 0 Log C 1 = 17.6

29. Fatigue Model Application Estimation of N 2 N 2 is he required number of cycles to achieve a failure This fatigue equation allows to predict crack propagation for any number of cycles N 1 <N<N 2 Log C 2 = -15.0

30. Summary Currently, empirical fatigue curves don't consider crack propagation. Fracture mechanics approach has clear advantages to predict crack propagation. Monotonic tests are failure envelope for fatigue. Mechanics of model work but model coefficients need to be improved. A Cohesive Zone Model has greater potential to give a more conceptual and accurate solution to cracking in concrete pavements

31. Tasks Remaining Fatigue crack growth prediction of beams on elastic foundation (NWU) Complete model calibration on remaining slabs Several load (stress) ratios Tridem vs. single pulse crack growth rates Write final report

32. Current Model Limitations Crack propagation assumed to be full-depth crack across slab pre-defined crack shape Need geometric correction factors for all expected slab sizes, configurations, support conditions Need further validation/calibration with other materials and load levels

33. Size Effect Method (SEM) Two-Parameter Fracture Model (TPFM) –Equivalent elastic crack model –Two size-independent fracture parameters : K I and CTOD c Bazant ZP, Kazemi MT. 1990, Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete, International Journal of Fracture, 44, 111-131. Jenq, Y. and Shah, S.P. 1985, Two parameter fracture model for concrete, Journal of Engineering Mechanics, 111, 1227-1241. Quasi-brittle Strength Theory LEFM ► Energy concept ► Equivalent elastic crack model ►Two size-independent fracture parameters: G f and c f Fracture Mechanics Size Effect

34. What is the Cohesive Zone Model? Modeling approach that defines cohesive stresses around the tip of a crack Traction-free macrocrackBridging zoneMicrocrack zone Cohesive stresses are related to the crack opening width (w) Crack will propagate, when  = f t

35. How can it be applied to rigid pavements? The cohesive stresses are defined by a cohesive law that can be calculated for a given concrete Concrete propertiesCohesive law Cohesive Finite Element Cohesive Elements are located in Slab FEM model Cohesive Elements

36. Why is CZM better for fracture? The potential to predict slab behavior under monotonic and fatigue load The cohesive relation is a MATERIAL PROPERTY Predict fatigue using a cohesive relation that is sensitive to applied cycles, overloads, stress ratio, load history. Allows to simulate real loads Cohesive laws Cohesive Finite Element Monotonic and Fatigue Slab behavior Cohesive Elements

38. Proposed Ideas Laboratory Testing and Modeling of Separated (Unbonded) Concrete Overlays Advanced Concrete Fracture Characterization and Modeling for Rigid Pavement Systems

39. Laboratory Testing and Modeling of Separated Concrete Overlays Concrete Overlay h ol Existing Concrete Pavement hehe Bond Breaker - Asphalt Concrete Bond Breaker ~ 2”

40. Laboratory Testing and Modeling of Separated Concrete Overlays New PCC Old PCC AC Interlayer Rigid Support New PCC Old PCC AC Interlayer Support Cohesive elements

41. Advanced Concrete Fracture Characterization and Modeling for Rigid Pavement Systems Concrete propertiesCohesive law Cohesive Finite Element Cohesive Elements are located in Slab FEM model Cohesive Elements

46. Remaining Steps Testing Analysis Calculation of the relationship between the crack length and loading cycles. Calibration of the model using this data. The static load - crack length relationship will be checked to see if it is an envelope for the fatigue test. Comparison of Fracture Parameters on different type of specimens and boundary conditions Load a a critical … Static envelope Fatigue test Completion of fatigue tests on small-scale specimens (notched) to verify the 2-D model for the case of beams on foundation