POST-CRACKING CHARACTERISATION OF CONCRETE BEAMS REINFORCED WITH MIXED LONG/SHORT STEEL FIBERS

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Jacopo Giglio
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BOND IN CONCRETE 2012 Bond, Anchorage, Detailing Fourth International Symposium BRESCIA- ITALY June 17 th - 20 th, 2012 POST-CRACKING CHARACTERISATION OF CONCRETE BEAMS REINFORCED WITH MIXED

1 BOND IN CONCRETE 2012 Bond, Anchorage, Detailing Fourth International Symposium BRESCIA- ITALY June 17 th - 20 th, 2012 POST-CRACKING CHARACTERISATION OF CONCRETE BEAMS REINFORCED WITH MIXED LONG/SHORT STEEL FIBERS Antonio Caggiano, M. Cremona, C. Faella, C. Lima and E. Martinelli a LMNI, FIUBA, University of Buenos Aires, Argentina b Officine Maccaferri SpA, Zola Predosa (BO), Italy c Department of Civil Engineering, University of Salerno, Italy

2 SUMMARY ; ; ; FEM for FRC;.

3 - Relevance of the fibers in cement materials - F. R. C. C. Fiber Reinforced Cementitious Composite Structural material characterised by a significant residual tensile strength in post-cracking regime and an enhanced capacity to absorb strain energy due to fiber bridging mechanisms across the crack surfaces.

4 - Objectives of the present work - investigation on SFRC members 4PB tests on prenotched beams Compressive tests Flexural strengths Ductility measures Stress-crack opening responses Compressive strength Formulation of numerical s Meso-mechanical formulation

6 - Materials The reference concrete (REF) Cement Aggregates C II ALL 42,5 N1 type 2-10 mm sand < 2 mm N2 type mm

7 - Materials FF3 FS7 Steel fibers: FF3 FS7 FS7 (long fiber) FF3 (short fiber) Types of fiber Length [mm] Diameter [mm] Aspect ratio N. of fiber/kg Failure strength [MPa] Rated failure elongation FS7 (long fiber) 50 0, > 1100 < 4% FF3 (short fiber) 33 0, > 1200 < 2%

8 - The experimental programme - Fiber volume fraction [%] Mix designation Long fiber volume fraction [%] Short fiber volume fraction [%] N. of beams N. of SFRC cubes N. of PC cubes - REF L L ,5 LS ,0 S S L L LS S S

9 - results - Compressive test (EN )

10 - results - Compressive test (EN ) It is worth noting that the compressive strength were affected by very low levels of randomness, as demonstrated by 2.82% and 3.41% coefficient of variation for white and SFRCs, respectively.

11 - results - Device of application 15 cm 45 cm Load cell Transducers

12 - results - Four-point bending tests (UNI & 2)

13 - results - Four-point bending tests (UNI & 2) Ductility indices can be considered as further measures of the fiber bridging effect: Equivalent crack strengths First crack strength

- results - Flexural strengths first crack strength (according to UNI 11039-1 & 2) REF Detecting Determination of the maximum of CTOD value 0 of value the load P lf = h 0 2 FRC where: FRC Mix

14 - results - Flexural strengths first crack strength (according to UNI & 2) REF Detecting Determination of the maximum of CTOD value 0 of value the load P lf = h 0 2 FRC where: FRC Mix designation FRCC first crack strength f lf [MPa] Specimen a Specimen b Specimen c Average S ,69 4,02 3,80 3,84 S ,62 2,87 3,73 3,40 LS ,98 2,85 4,07 3,30 L ,37 3,37 3,00 3,25 L ,23 4,45 4,55 4,41 S ,91 4,45 5,34 4,57 S75-1 4,85 5,34 4,54 4,91 LS50-1 4,90 4,23 3,89 4,34 L75-1 3,81 3,17 3,82 3,60 L ,13 3,47 5,22 3,94 l is the distance between bottom rollers [mm] b is the base of the specimen [mm] h is the height of the specimen [mm] a 0 is the depth of the notch [mm]

- results - Flexural results (UNI 11039-1 &

15 - results - Flexural results (UNI & 2) The values of U 1 and U 2 are approximately proportional to the dissipated energies in the average crack opening range considered.

- results - Flexural results (UNI 11039-1 & 2) In practical designs

16 - results - Flexural results (UNI & 2) In practical designs only if f eq(0-0.6) > 0.5 fl f or D 0 > 0.5 then the post-cracking resistance can be considered. If these characteristics of SFRCs do not comply with the above limits so they must be neglected in design calculations.

18 - Main assumptions - h h/2 Eε Precrack state σ = σ w ( y ) Cracked state Olesen ASCE J Engng Mechs 127(2001):

19 - Main assumptions - Eε Precrack state σ = σ w ( y ) Cracked state Interface constitutive for FRCC (Caggiano et al 2012) n f σ = σ u + σ u n + τ u n ( ) ( ) ( ) cr f N,cr N, f f T,cr T, f f = 0 Fracture energy-based plasticity formulation for plain mortar/concrete interfaces Fiber bond-slip formulation Explicit formulation Formulation for fiber dowel action

20 - Fracture-based interface Base on the classical Plasticity Theory, the relative displacement rate is decomposed into an elastic and a plastic (cracking) part: a cracking surface, within the stress space, defines the stress level at which the inelastic slips(in the joint element) begin; a flow rule giving an incremental crack displacement

21 - Fracture-based interface a softening rules depending on the work spent during the fracture process

22 - Bond-slip - Conventional Strength Mortar (CSM) - Equilibrium: - Constitutive law High Strength Mortar (HSM) - Bond-slip law Model results (continuous lines) vs. experimental data by Shannag et al of the pullout behavior of steel fibers from CSM and HSM.

23 - Dowel action - Basic equation of the : λ [1/length] - when l f > 2 π /λ seminfinite BEF - k coefficient ranges from 75 to 450 N/mm 3 for RC (Dei Poli et al., 1992). Equivalent shear elastic modulus Dowel force at ultimate limit state, Dulacska,1972.

24 - Results - The mechanical parameters employed in the numerical evaluations are: f t = 2.08 MPa, E = 20.0 GPa, s = 75 mm, G f = 0.5 N/mm; τ y,a = 7.0 MPa, k E = N/mm 3, k S = 0.1 N/mm 3 k dow = 2.8 and c 1 = 0.15.

26 - Definitions - FE Analysis - 3 Points Beam (Carpinteri & Brighenti data 2010) Displacement-based control test Plane stress state Non-linear elastoplastic FRM joints Non-linear elastoplastic coarse aggregatesmortar joints

27 - Results- FE Analysis - 3 Points Beam (Carpinteri & Brighenti data 2010)

28 - Results- FE Analysis - 3 Points Beam (Carpinteri & Brighenti data 2010)

30 the post-cracking behaviors of FRCC are mainly influenced by the amount of fibers: softening response was observed for all specimens with ρf = 0.5%, while a rather plastic response characterised the ρf = 1.0%; As a matter of fact, the very low influence of fiber combination (long/short) on the observed FRCC behaviour is the key conclusion of the experimental activity; the two different fibers were characterised by the same material, similar geometric details (i.e., hooked ends) and rather close values of aspect ratios. The possible synergetic effect of combining different fibers should be investigated by considering two (or more) types of really more different fibers; Two numerical approaches have been presented for simulating the experimental response of FRCC. Both s based on the explicit consideration of fiber effects led to accurate simulations of the observed experimental behaviour.

31 THE END Thank you for your attention

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