Steel-Fibre-Reinforced Concrete Pavements

Naeimeh Jafarifar, Kypros Pilakoutas, Kyriacos NeocleousDepartment of Civil and Structural Engineering, The University of Sheffield

Concrete Communication Conference1-2 September 2008, University of Liverpool

1

Outline

• Introduction

• Review of Existing Theories and Methods

• Finite Element Analysis (Models, Fatigue?)

• Comparisons

• Conclusions

Flexible Pavements Rigid Pavements

Tensile strength of rigid pavements usually

dominates the design

Types of Pavement

Plain Concrete

Crack Control Joint Expansion Joint

Due to Brittle Cracking, Elastic Analysis Can be Used

Joints Must be Allowed as Prearranged Cracks

Short Joint Spacing

Rigid Body Movement

Lower Stresses in Concrete

Costly to Install Joints

More Deterioration

Long Joint Spacing

Bending

Higher Stresses in Concrete

Need for Reinforcement (Conventional or SF)

Joint Spacing

Reinforced Concrete or SFRC

Due to Ductile Cracking, a Significant Part of Loading Capacity is Developed after Cracking

Elastic Analysis Not AppropriateNon-Linear Analysis more appropriate

Road Pavements still designed using Classical Elastic Methods

For industrial floors TR34 allows cracking on the bottom side of the slab and uses Non-Elastic Methods

Enhanced Toughness

Important in Statically Indeterminate Structures

Redistribution of Forces after Cracking

Major Advantages :Strain Capacity Energy Absorption

Increased Collapse Load Crack Propagation Resistance

Crack Bridging

Factors Affecting Redistribution of Loads:

•Material Toughness•Structural Geometry•Boundary Conditions

SFRC in Ground-Supported-Slabs

Fatigue Strength: is a Fraction of the Static Strength for a Given Number of Cycles

(ACI 544.4R 1999) (for 1-2 Million Cycles)SFRC 65% to 95 % of the First-Crack StrengthPlain Concrete about 50-55 % of Static Strength

Other AdvantagesResistance to material deterioration(Fatigue, impact, shrinkage, thermal stresses)Protection from Aggressive Environmental Attack

SFRC in Ground-Supported-Slabs

• Westergaard’s Theory (1920):

(based on linear elasticity)

Homogeneous, Isotropic, Elastic Slab Perfect Sub-grade

imposed vertical reactive pressure at each point in proportion to the deflection of the slab at that point

(Winkler Foundation)

Review of Classical Methods

• Burmister’s Theory (1943):

(Layered Solid Theory based on linear elasticity)

Infinite Extent, Finite Thickness, Slab Elastic, Isotropic, solid Sub-grade

• Losberg’s Theory & Meyerhof’s Theory (1960-1962):

(Based on yield-line concept)

Rigid-Plastic Slab Elastic Sub-grade

Review of Theories and Methods

Summary of Design Theories :

Two models used for the subgrade:• Elastic-Isotropic Solid • Winkler Sub-grade

Three different models used for the slab:• Thin Elastic Slab• Thin Elastic-Plastic Slab• Elastic-Isotropic Solid Slab

Existing Design Theories Use Different Combinations of the above Models

Winkler model:A plate supported by a “dense liquid” foundation

Deflection in Direct Proportion to the Force without Shear Transmission

Elastic Solid model:Load Applied to the Surface of the Foundation Produces a

Continuous Basin

Subgrade Models

Issues with Classical Methods

Solving deferential equationsFeasible only for simplified models (continuous and homogeneous slab and sub-grade)

Real rigid pavementsContains discontinuities (joints and cracks)Geometry and Sub-grade support non-uniform

Closed form analytical equationsVery limited, but can be used as bench marks for numerical models, e.g. an infinitely extended plate:Timoshenko’s equations (1952) Westergaard’s equations (1926)

FE Method

AdvantagesCan solve more complex problemCan be used for rigid pavements in general

ABAQUS softwareFlexibility in Defining the Strain-Softening Behaviour of Cracked Concrete Capability for Modelling the Winkler Foundation

Elements Used for the Slab : 3-D & Shell 8-NodedModel Used for the Foundation : Winkler Foundation

FE Analysis

Concrete Pavement Carrying a Single Concentrated LoadLinear Elastic Behaviour for Concrete Non-Linear Behaviour for Concrete (Smeared Crack Model, for Post-Cracking Behaviour of SFRC)

SlabModels :Infinite Slab: to Compare the Results with Closed form Equations (6×6m)

Finite Width Slab: To be Tested as Part of “Ecolanes”, Subjected to Accelerated Load Testing at TUI, Romania (3×6m)

Load: Double Wheel Load 57.5 kN

Position Moving along the centre line

Number of load cycles 1.5 million

Slab: Track width 3.00 m

Slab thickness 200 mm

Elastic modulus 32GPa

Support: Equivalent Reaction Modulus 0.4 N/mm³

Truck tyre: Size 12.00R20

Section Width 308 mm

Pressure 850 kPa

0.0

10.0

20.0

30.0

40.0

50.0

0.000 0.001 0.002 0.003 0.004

Compressive Stress (M

Pa)

Compressive Strain (εc)

E = 32 GPaν=0.2fc= 42 MPa

0.0

1.0

2.0

3.0

4.0

5.0

0.00 0.01 0.02 0.03 0.04 0.05

Tensile

 Stress (Mpa

)

Tensile Strain (εt)

Slab Details

Tension

Compression

48%

15%

2%0%

50%

19%

6%4%

0%

10%

20%

30%

40%

50%

1 2 3 4

Perc

entag

e of

Diff

eren

ce w

ithCl

osed

-For

m E

quati

ons

Mesh NO.

Difference of FE & Timoshenko’s Eq. Difference of FE & Westergaard’s Eq.

Method Mesh No. Element Size (mm)

Maximum tensile stress at the bottom face (MPa)

FE Analysis

1 300 0.7112 150 1.1593 50 1.3394 25 1.363

Closed-FormSolution

Timoshenko 1.36Westergaard 1.423

Mesh Sensitivity for Elastic Analysis of an Infinite Slab

57.5KN

200m

m3000mm

300mm 300mm

Concrete SlabCement Stabilized sub-baseBallast Foundation

Sub-Grade

A Double Wheel Load with Two Contact Areas, Each

110×300mm Applied Centrally

Analysis of Finite Width Slab

Under the Service Load Stresses are Much Less than Cracking

To Monitor the Post-Cracking Behaviour Load Was Increased Gradually Until Complete Collapse

Bottom

Analysis of Finite Width Slab

To Account for the Fatigue Effects in FE Analysis, the Material Capacity Was Reduced

to 65% of the Static Strength, and the Structure Was Analysed as for Static Loading

0.0

10.0

20.0

30.0

40.0

50.0

0.000 0.001 0.002 0.003 0.004

Compressive

 Stress (MPa)

Compressive Strain (εc)

Full 

Reduced due to Fatigue

E = 32 GPaν=0.2fc= 42 MPa

0.0

1.0

2.0

3.0

4.0

5.0

0.00 0.02 0.04

Tensile

 Stress (M

pa)

Tensile Strain (εt)

ft = 4.2 MPaRe,3 = 0.79

Fatigue?

Results

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.5 1 1.5 2 2.5 3 3.5

Load

(kN)

Displacement at the centre (mm)

Without Fatigue

With Fatigue

First Crack at the Bottom in Transversal Direction

First Crack at the Bottom in Longitudinal Direction

Circular Cracking at the Top Face

Transversal Crack Reaches the Edge

Service Load

Cracking stage

FE Model Concrete Society 

Central load (kN) Load bearing ratio

(Fatigue/No fatigue)

Central load (kN)

No

fatigue

With

fatigue

No fatigue

First transversal

crack at the bottom175 115 66 % -

First longitudinal

crack at the bottom320 215 67 % -

Circumferential

crack at the top face1250 850 68 % 790

Cracking all over the

transversal

direction

1500 1200 80 % -

Results & Comparison TR34

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Conclusions• FE Analysis can be used to Predict the Behaviour Provided the

Appropriate Elements and Boundary Conditions and Material Modelsare Selected.

• Non-linear Slab Capacity Exceeds the Elastic Capacity and Service Load by Many Times.

• Fatigue was taken into Account by Reducing the Material Properties. Better models are needed.

• A Comparison With the Concrete Society Method for Ground Slabs Shows that More Work Needs to be Done to Bring the Two Approaches Together.

23

Thank You

This research has been financially supported by the 6th FP of the European Community within the framework of specific research and technological development programme “Integrating and strengthening the European Research Area”, under contract number 031530.