Fatigue and Fracture Behavior of Airfield Concrete Slabs

1. FAA Center Annual Review – Champaign, IL, October 7, 2004 Fatigue and Fracture Behavior of Airfield Concrete Slabs Prof. S.P. Shah (Northwestern University) Prof. J.R. Roesler (UIUC) Dr. Bin Mu David Ey (NWU) Amanda Bordelon (UIUC)

2. Research Work Plan • Finite Element Simulation of Cracked Slab • Concrete slab compliance • Develop preliminary R-curve for concrete slab • Small-scale fracture parameters • Fatigue crack growth model • Model Validation

3. Large-Scale Concrete Slab Tests

4. Typical S-N Curves for Concrete Fatigue

5. Summary of Approach • The load – crack length (compliance) response obtained from static loading acts as an envelope curve for fatigue loading. • The condition KI = KIC can be used to predict fatigue failure. • Fatigue crack growth rate has two stages: deceleration stage and acceleration stage.

6. Static Envelope Static loading acts as an envelope curve for fatigue loading (Subramaniam, K. V., Popovics, J.S., & Shah, S. P. (2002), Journal of Engineering Mechanics, ASCE 128(6): 668-676.)

7. The crack growth in deceleration stage is governed by R-curve. • The crack growth in acceleration stage is governed by KI.

8. Static and Fatigue Envelope

9. Crack growth during fatigue test (a) crack length vs. cycles (b) rate of crack growth

10. a Phase –1: Fatigue test Step 1 FEM Simulation of Cracked Slab C=C(a)and KI=KI(a) FEM

11. 2000 mm 1000 mm 100 mm Symmetric line a Elastic support 200 mm Experimental setup and FEM mesh UIUC setup FEM mesh with a=400 mm

12. FEM Contours Deformation (a=400 mm) Node force (a=400mm)

13. KI Determination Y, v Fc Element-1 Element-2 a c X, u e O’ f d b Element-4 Element-3 Calculation of KI: A modified crack closure integral Rybicki, E. F., and Kanninen, M. F., Eng. Fracture Mech., 9, 931-938, 1977. Young, M. J., Sun C. T., Int J Fracture 60, 227-247, 1993. If < 20% crack length, then accuracies are within 6% of the reference solutions. Finite element mesh near a crack tip

14. Deflection vs. Crack Length Vertical displacement at the mid point of edge

15. FEM Compliance Results Compliance and crack length

16. KI vs Crack Length (a) Stress intensity factor and crack length

17. CMOD vs Crack Length

18. Processing Lab Fatigue Data • Single pulse loading • Tridem pulse loading

19. Pmax Loading Unloading Pmin Single Pulse Fatigue Loading (1 Cycle)

20. Pmax Pint Loading L3 Unloading U1 Loading L2 Unloading U2 Loading L1 Unloading L3 Pmin Tridem Pulse Fatigue Loading (1 Cycle)

21. Deflection vs. Number of Cycles (Single Pulse Slab 4)

22. Deflection vs. Number of Cycles (Tridem Pulse Slab 7)

23. Compliance Plots • Loading vs. Unloading Compliance • Single vs. Tridem Pulses • Need to measure CMOD in future!!!

24. Loading Compliance Unloading Compliance Single Pulse Loading vs. Unloading Compliance Load vs Rebound Deflection for S4 Cycle 85529

25. Single Pulse Compliance (Slab 9) Pmax = 96.9 kN Pmin = 67.7 kN Nfail = 352

26. Unloading U1, Loading L2, Unloading L2 and Loading L3 Compliances Loading L1 Compliance Unloading U3 Compliance Tridem Pulse Loading vs. Unloading Compliance Load vs Rebound Deflection for T4 Cycle 3968

27. Tridem Pulse Compliance (Slab 2) Pmax = 91.5 kN Pmin = 7.0 kN Nfail = 61,184

28. Tridem Pulse Compliance (Slab 4) Pmax = 90.7 kN Pmin = 7.5 kN Nfail = 4,384

29. Normalized Compliance Slab-4

30. Single Pulse Slab4 Compliance, crack length and da/dN for Slab-4

31. Tridem Slab (T2) T-2

32. Crack Growth for Slab T2 Compliance, crack length and da/dN for T-2

33. Tridem Slab (T4) T-4

34. Crack Growth for Slab T2 Compliance, crack length and da/dN for T-4

35. Fatigue Crack Growth Model Models for Slab-4, T2 & T4 Accel. Decel.

36. Challenges • Need to calibrate material constants C1,n1, C2, n2 with slab monotonic data and small-scale results • Explore other crack configurations modes (partial depth and quarter-elliptical cracks) • Size Effect….

37. Concrete Property Testing • Test Setup • Two Parameter Fracture Model (KI and CTODc) • Size Effect Law (KIf and cf)

38. Concrete Material Property Setup • Three Beam Sizes • Small • Medium • Large

39. Large Beam LVDT notch Clip gauge CMOD 50 mm 50 mm S = 1 m D = 250 mm Initial crack length = 83 mm 10 mm CMOD W = 80 mm Top View LVDT

40. Testing Apparatus Before Loading After Loading

41. Load vs. CMOD (Small Beam) Cast Date: 06-14-04 Test Date: 06-22-04

42. Load vs. CMOD (Large Beam) Cast Date: 06-14-04 Test Date: 06-22-04

43. Two Parameter Fracture Model Results Jenq and Shah

44. Size Effect Law Results Bazant et al

45. b Slab Tests • Partial Depth Crack • Edge Notch Crack • Quarter-Elliptical Crack a c d

46. r Applied total load (P) P b a b a0 Foundation p = k0 * w * y S L a0 b t L L Foundation Analysis of Slabs on Elastic Foundation using FM- Overview • Slab on Elastic Foundation • Beam on Elastic Foundation • Beam

47. Crack Growth Validation from Monotonic Slab Tests C i Load C u K IC CMOD Static Mode I SIF Compliance vs. crack length

48. Future Direction • Complete Monotonic Slab Testing** • develop failure envelope • Validate for fatigue edge notch slabs** • Validate for fully-supported beams** • testing and FEM • Develop Partial-Depth Notch and Size Effect • Incorporate small-scale fracture parameters into fatigue crack growth model

49. Compliance vs. Crack Length for Fully Supported Beam • λ4 (1 - e-λw cos (λ w)) = 3(k2 b w C) / (d2 q) • λ2 / (e-λw sin (λ w)) = 3(q √(π a0) F(α0)) / (KIC b d2) • λ = characteristic (dimension is length-1) • w = ½ the length of load distribution • k = modulus of subgrade reaction • b = width of the beam • C = Compliance • d = depth of the beam • q = distributed load • a0 = crack length • F(α0) = -3.035α04 + 2.540α03 + 1.137α02 – 0.690α0 + 1.334 • α0 = a0 / b • KIC = Critical Stress Intensity Factor for Mode I q w a0