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)

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

Large-Scale Concrete Slab Tests

Typical S-N Curves for Concrete Fatigue

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.

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): 668-676.)

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

Static and Fatigue Envelope

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

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

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

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

KI Determination 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. 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

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

FEM Compliance Results Compliance and crack length

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

CMOD vs Crack Length

Processing Lab Fatigue Data Single pulse loading Tridem pulse loading

Single Pulse Fatigue Loading (1 Cycle) Unloading Pmax Pmin

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

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

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

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

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

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

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

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

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

Normalized Compliance Slab-4

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

Tridem Slab (T2) T-2

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

Tridem Slab (T4) T-4

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

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

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….

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

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

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

Testing Apparatus Before Loading After Loading

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

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

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

Size Effect Law Results Bazant et al

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

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

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

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

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