Fatigue and Fracture Behavior of Airfield Concrete Slabs

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

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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 foundation
Slab on elastic foundation
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Research Objectives

• 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.

2-D Model
Fatigue load
Monotonic load
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Experimental Design

• Beam Tests

• 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.

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Experimental Design

• Slab Tests

• 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.

• Concrete Mix

• Standard Paving Concrete ¾ limestone coarse
  crushed aggregate, 100 mm slump and Modulus of
  Rupture 650 psi at 28 days

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Experimental Results

• Results on Beams

• Monotonic Load

• Full Load-CMOD curve.
• Peak Load.
• Critical Stress Intensity Factor (KIC) .
• Critical CTOD (CTODc).
• Compliance for each load Cycle (Ci).

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Beam FEM Setup
Small Beam
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UIUC Testing
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Monotonic Results and Crack Length
From FEM
From Testing
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Experimental Results

• Results on Beams

• Fatigue Load in FSB

• Load vs. CMOD curves
• Compliance vs. number of cycles
• Peak Load.
• Stress Intensity Factor (KI) .
• Compliance for each load Cycle (Ci).

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Experimental Results

• Results on Slabs

• Monotonic Load

• Full Load-CMOD curve.
• Peak Load.
• Compliance for each load Cycle (Ci).

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Experimental Results

• Results on Slabs

• Fatigue Load

• Load vs. CMOD curves
• Compliance vs. number of cycles
• Peak Load.
• Stress Intensity Factor (KI) .
• Compliance for each load Cycle (Ci).

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2-D Fatigue Model

• 2-D Fatigue Model

(Kolluru, Popovics and Shah, 2000)

• Monotonic Test of TPB

• Fatigue Test of TPB

Relation between load and effective crack length
aeff is obtained !!
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2-D Fatigue Model

• 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 C1, n1, C2, n2 are constants Da
incremental crack growth between DN DN
incremental number of cycles DKI stress
intensity factor amplitude of a load cycle
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Finite Element Analysis

• FEM Mesh
• Computation of the Stress Intensity Factor
  Ci(a)

An indirect method was used to calculate KI,
called Modified Crack Closure Integral Method.
(Rybicki and Kanninen, 1977)
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Finite Element Analysis

• Relation between Crack length, Compliance and CMOD

• Normal equations for TPB Beams are not
  applicable. FEM Modelation is required.
• CMOD vs. Crack Length
• Compliance vs. Crack Length

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.
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Finite Element Analysis

• Relation between Stress Intensity Factor and
  Crack Length
• Relation between CMOD and Crack Length

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Application of FEM Model

• Step 1 Experimental Relation between CMOD and
  the Displacement

• Experimental relation between CMOD measurements
  and displacement.

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Application of FEM Model

• 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

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Application of FEM Model

• Step 3 Estimation of the Crack Length

• The crack length is estimated using this modified
  equation from the FEM model and the CMOD

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Application of FEM Model

• Step 4 Estimation of the Normalized Compliance
  (FEM)

• The normalized compliance obtained from the FEM
  Model for different crack length is multiplied by
  the experimental initial compliance

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Application of FEM Model

• Step 5 Experimental Compliance vs. Crack Length
  curves

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Fatigue Model Calibration

• Step 1 The Compliance is measured for each
  fatigue load cycle of slab T2

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Fatigue Model Calibration

• Step 2 The Crack length is obtained for each
  cycle using the FEM Model for slab T2.

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Fatigue Model Calibration

• Step 3 The Critical Crack acrit is Critical
  Number of Cycles Ncrit is obtained for slab T2.

• This point of critical crack length is a point of
  inflexion in the curve

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Fatigue Model Calibration

• Step 4 The two sections of the model are
  calibrated

Different fatigue equations apply for crack
length bigger or smaller than acrit

• Log C1 17.6

• Log C2 -15.0

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Fatigue Model Application

• Estimation of N1

• N1 is he required number of cycles to achieve
  acrit
• This fatigue equation allows to predict crack
  propagation for any number of cycles NltN1
• If we have an unnotched slab, a0 0

• Log C1 17.6

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Fatigue Model Application

• Estimation of N2

• N2 is he required number of cycles to achieve
  afailure
• This fatigue equation allows to predict crack
  propagation for any number of cycles N1ltNltN2

• Log C2 -15.0

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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

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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

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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

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Fracture Mechanics Size Effect

• Size Effect Method (SEM)
• Two-Parameter Fracture Model (TPFM)
• Equivalent elastic crack model
• Two size-independent fracture parameters KI and
  CTODc

Strength Theory

• Energy concept
• Equivalent elastic crack model
• Two size-independent fracture
• parameters Gf and cf

Quasi-brittle
LEFM

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.
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What is the Cohesive Zone Model?

• Modeling approach that defines cohesive stresses
  around the tip of a crack

• Cohesive stresses are related to the crack
  opening width (w)
• Crack will propagate, when s ft

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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 properties

• Cohesive law

Cohesive Elements

• Cohesive Finite Element

• Cohesive Elements are located in Slab FEM model

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Why is CZM better for fracture?

• The potential to predict slab behavior under
  monotonic and fatigue load

• Cohesive laws

• 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 Elements

• Cohesive Finite Element

• Monotonic and Fatigue Slab behavior

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Proposed Ideas

• Laboratory Testing and Modeling of Separated
  (Unbonded) Concrete Overlays
• Advanced Concrete Fracture Characterization and
  Modeling for Rigid Pavement Systems

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Laboratory Testing and Modeling of Separated
Concrete Overlays
hol
Concrete Overlay

he
Existing Concrete Pavement
Bond Breaker
- Asphalt Concrete Bond Breaker 2
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Laboratory Testing and Modeling of Separated
Concrete Overlays
Cohesive elements
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Advanced Concrete Fracture Characterization and
Modeling for Rigid Pavement Systems

• Concrete properties

• Cohesive law

Cohesive Elements

• Cohesive Elements are located in Slab FEM model

• Cohesive Finite Element

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Remaining Steps

• Testing
• Analysis

Completion of fatigue tests on small-scale
specimens (notched) to verify the 2-D model for
the case of beams on foundation

• 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