1. Residual capacity from aggregate interlock
Case: cracked concrete slab bridge
11-07-2012
Eva Lantsoght, Cor van der Veen, Joost Walraven
Delft
University of
Technology
Challenge the future
2. Introduction (1)
• 50-year-old concrete slab bridge with
traffic restrictions
• Extensive cracking in southern
concrete approach bridge
• Result of settlement
• Flexural reinforcement yielded at
crack
• Cores: C33/45
• Reinforcement QR 240:
fyd =209 MPa; εsu = 19% – 38%
Residual capacity from aggregate interlock of cracked concrete slab bridge 2
3. flexural through crack
Introduction (2)
d = 413mm (side) to 493mm (mid)
φbottom 14mm – 200mm
φtop 25mm – 100mm
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4. through crack
Aggregate interlock
• Aggregates stronger than cement paste
• Particles interlock with opposite face + resist shear displacement
• Contribution to shear capacity: 33% - 90%
• Slab bridge, 1% rebar: aggregate interlock is main shear carrying
mechanism
• Fundamental model by Walraven
• Shear + axial stress: σ & τ, ∆ & w
• Unreinforced sections: crack-opening
• Reinforced sections: capacity
Residual capacity from aggregate interlock of cracked concrete slab bridge 4
5. Calculations (1)
Shear & Aggregate interlock
• Shear capacity (inclined cracking load)
• VVBC = 273 kN/m (side) and 325 kN/m (mid)
• Aggregate interlock – no tension on cross-section
• Based on shear stress capacity τ of reinforced crack
• Plain reinforcement => 0.5ρl
• Vagg = 1575 kN/m (side) and 1679 kN/m (mid)
• Large resistance provided by aggregate interlock action
• Rusted bearings => deformation due to ∆T is restrained
• Conservative assumption: full concrete cross-section in tension
Fclamp As ,bottom As ,top f y f ctk d i b
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6. Calculations (2)
Maximum crack width (1)
• Relation between w and aggregate interlock capacity
• Expressions for unreinforced section
• Based on graph (Walraven, 1981): Δ = 1.25w
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7. Calculations (3)
Maximum crack width (2)
• Find: crack width Vu_unr < VVBC or Fax < Fclamp
wmax ≈ 1 mm
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8. Calculations (4)
Axial force equilibrium
• wmax ~ rebar, tension in concrete cross-section (vary % Ftc)
• Requirement: Vagg ≥ 2VVBC
• Find associated ∆
• Find Nagg(wmax,∆) (clamping effect)
• Remaining capacity of top reinforcement to resist tension:
Ntension = As,topfy – Nagg
• Compare to Ftc => Equilibrium?
• Result: maximum 71% of restraint
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9. Proposed actions + Conclusions
• Replace rusted steel bearings by elastomeric bearings
• Open bridge for all traffic
• Quantify amount of restraint through measurements at support
• Measurement points for cracks every 3m (lane width)
• Special cases: use aggregate interlock to check cracked cross-
sections in shear
• Quantifies residual bearing capacity
• Shear and axial compression
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