Concrete Communication Conference 1-2 September 2008, University of Liverpool Steel-Fibre-Reinforced Concrete Pavements Naeimeh Jafarifar, Kypros Pilakoutas, Kyriacos Neocleous Department of Civil and Structural Engineering, The University of Sheffield
Outline Introduction Review of Existing Theories and Methods Finite Element Analysis (Models, Fatigue?) Comparisons Conclusions 1
Types of Pavement Flexible Pavements Rigid Pavements Tensile strength of rigid pavements usually dominates the design
Plain Concrete Due to Brittle Cracking, Elastic Analysis Can be Used Joints Must be Allowed as Prearranged Cracks Crack Control Joint Expansion Joint
Joint Spacing 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)
Reinforced Concrete or SFRC Due to Ductile Cracking, a Significant Part of Loading Capacity is Developed after Cracking Elastic Analysis Not Appropriate Non-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
SFRC in Ground-Supported-Slabs Major Advantages : Strain Capacity Energy Absorption Enhanced Toughness Important in Statically Indeterminate Structures Redistribution of Forces after Cracking Factors Affecting Redistribution of Loads: Material Toughness Structural Geometry Boundary Conditions Increased Collapse Load Crack Propagation Resistance Crack Bridging
SFRC in Ground-Supported-Slabs Other Advantages Resistance to material deterioration (Fatigue, impact, shrinkage, thermal stresses) Protection from Aggressive Environmental Attack 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 Strength Plain Concrete about 50-55 % of Static Strength
Review of Classical Methods 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 Theories and 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
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: Subgrade Models 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
Issues with Classical Methods Solving deferential equations Feasible only for simplified models (continuous and homogeneous slab and sub-grade) Real rigid pavements Contains discontinuities (joints and cracks) Geometry and Sub-grade support non-uniform Closed form analytical equations Very 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)
Advantages FE Method Can solve more complex problem Can be used for rigid pavements in general ABAQUS software Flexibility in Defining the Strain-Softening Behaviour of Cracked Concrete Capability for Modelling the Winkler Foundation Elements Used for the Slab : 3-D & Shell 8-Noded Model Used for the Foundation : Winkler Foundation
FE Analysis Concrete Pavement Carrying a Single Concentrated Load Linear 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)
Slab Details Load: Double Wheel Load 57.5 kn Position Number of load cycles Moving along the centre line 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 Compressive Stress (MPa) 50.0 40.0 30.0 20.0 10.0 0.0 Compression E = 32 GPa ν=0.2 fc= 42 MPa 0.000 0.001 0.002 0.003 0.004 Compressive Strain (εc) Tensile Stress (Mpa) 5.0 4.0 3.0 2.0 1.0 0.0 Tension 0.00 0.01 0.02 0.03 0.04 0.05 Tensile Strain (εt)
Method FE Analysis Closed-Form Solution Mesh Sensitivity for Elastic Analysis of an Infinite Slab Mesh No. Element Size Maximum tensile stress at (mm) the bottom face (MPa) 1 300 0.711 2 150 1.159 3 50 1.339 4 25 1.363 Timoshenko 1.36 Westergaard 1.423 Percentage of Difference with Closed -Form Equations 50% 40% 30% 20% 10% 0% 50% 48% 19% 15% Difference of FE & Timoshenko s Eq. Difference of FE & Westergaard s Eq. 1 2 3 4 Mesh NO. 6% 2% 4% 0%
Analysis of Finite Width Slab 3000mm 300mm 300mm 57.5KN A Double Wheel Load with Two Contact Areas, Each 110 300mm Applied Centrally 200mm Concrete Slab Cement Stabilized sub-base Ballast Foundation Sub-Grade Under the Service Load Stresses are Much Less than Cracking To Monitor the Post-Cracking Behaviour Load Was Increased Gradually Until Complete Collapse
Analysis of Finite Width Slab Bottom
Fatigue? 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 Compressive Stress (MPa) 50.0 40.0 30.0 20.0 10.0 0.0 E = 32 GPa ν=0.2 fc= 42 MPa Full Reduced due to Fatigue 0.000 0.001 0.002 0.003 0.004 Compressive Strain (εc) Tensile Stress (Mpa) 5.0 4.0 3.0 2.0 1.0 0.0 ft = 4.2 MPa Re,3 = 0.79 0.00 0.02 0.04 Tensile Strain (εt)
Results Load(kN) 1800 1600 1400 1200 1000 800 600 400 200 0 Service Load Without Fatigue With Fatigue First Crack at the Bottom in Transversal Direction Circular Cracking at the Top Face First Crack at the Bottom in Longitudinal Direction 0 0.5 1 1.5 2 2.5 3 3.5 Displacement at the centre (mm) Transversal Crack Reaches the Edge
Results & Comparison TR34 Cracking stage FE Model Central load (kn) Load bearing ratio No With (Fatigue/No fatigue) fatigue fatigue Concrete Society Central load (kn) No fatigue First transversal crack at the bottom 175 115 66 % - First longitudinal crack at the bottom 320 215 67 % - Circumferential crack at the top face 1250 850 68 % 790 Cracking all over the transversal direction 1500 1200 80 % -
Conclusions FE Analysis can be used to Predict the Behaviour Provided the Appropriate Elements and Boundary Conditions and Material Models are 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. 22
This research has been financially supported by the 6 th 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. Thank You 23