1. Fatigue and Fracture Behavior of Airfield Concrete Slabs
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 loading acts as an envelope curve for fatigue loading
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): )

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

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

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

13. KI Determination Calculation of KI: A modified crack closure integral
Rybicki, E. F., and Kanninen, M. F., Eng. Fracture Mech., 9, , 1977.
Young, M. J., Sun C. T., Int J Fracture 60, , 1993. a c b d e f
Element-1
Element-2
Element-4
Element-3
Y, v
X, u O’ Fc
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. Stress intensity factor and crack length
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. Single Pulse Fatigue Loading (1 Cycle)
Unloading
Pmax
Pmin

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

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. 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. Tridem Pulse Loading vs. Unloading Compliance
Loading L1 Compliance
Unloading U3 Compliance
Unloading U1, Loading L2, Unloading L2 and Loading L3 Compliances
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. Compliance, crack length and da/dN for Slab-4
Single Pulse Slab4
Compliance, crack length and da/dN for Slab-4

31. Tridem Slab (T2)
T-2

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

33. Tridem Slab (T4)
T-4

34. Compliance, crack length and da/dN for T-4
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
Size
Depth
Width
Length
Span
Notch Length
Notch Width
(mm)
(in) 1
62.5
2.461 80
3.15
350
13.78
250
9.843
20.8
0.82 3
0.118 2
150
5.906
700
27.56
600
23.62 50
1.969
1100
43.31
1000
39.37
83.3
3.281

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: Test Date:

42. Load vs. CMOD (Large Beam)
Cast Date: Test Date:

43. Two Parameter Fracture Model Results
Test #
Dimensions (mm)
ftc
w/c da
(mm) E
ao/b
ac/b
KsIc
CTODc (mm)
GsIc (N/m)b S b t
(MPa)
(GPa)
(MPa m1/2) 1
250
62.5 80
35.7
0.45 19
27.3
0.333
0.417
1.177
0.0072
50.73 2
600
150
39.6
0.538
1.735
0.0402
76.08 3
1000
39.4
0.460
1.788
0.0321
81.06 4
37.9
28.0
0.524
1.314
0.0254
61.67 5
46.1
0.515
1.699
0.0292
62.63 6
34.0
0.461
1.693
0.0352
84.18
Jenq and Shah

44. Size Effect Law Results
Bazant et al

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

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

47. Crack Growth Validation from Monotonic Slab Tests
Load C i 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) = α α α02 – 0.690α
α0 = a0 / b
KIC = Critical Stress Intensity Factor for Mode I q w a0