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POST-CRACKING CHARACTERISATION OF CONCRETE BEAMS REINFORCED WITH
BOND IN CONCRETE 2012BOND IN CONCRETE 2012Bond, Anchorage, DetailingBond, Anchorage, Detailing
Fourth International SymposiumFourth International SymposiumBRESCIABRESCIA-- ITALYITALY
JuneJune 1717thth -- 2020thth, 2012, 2012
CONCRETE BEAMS REINFORCED WITH MIXED LONG/SHORT STEEL FIBERS
Antonio Antonio CaggianoCaggiano, M. Cremona, C. , M. Cremona, C. FaellaFaella, C. Lima and , C. Lima and
E. MartinelliE. Martinelli
a a LMNI, FIUBA, University of Buenos Aires, ArgentinaLMNI, FIUBA, University of Buenos Aires, Argentinabb Officine Officine MaccaferriMaccaferri SpA, Zola SpA, Zola PredosaPredosa (BO), Italy(BO), Italy
c c Department of Civil Engineering, University of Salerno, ItalyDepartment of Civil Engineering, University of Salerno, Italy
� Introduction;
� Experimental campaign;
SUMMARYSUMMARY
� Cracked hinge model;
� Discontinuous FEM for FRC;
� Concluding remarks.
IntroductionIntroduction-- Relevance of the fibers in cement Relevance of the fibers in cement
materials materials --
F. R. C. C.
Fiber
Reinforced
CementitiousCementitious
Composite
Structural material characterised by a significant residualtensile strength in post-cracking regime and an enhancedcapacity to absorb strain energy due to fiber bridgingmechanisms across the crack surfaces.
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
IntroductionIntroduction-- Objectives of the present work Objectives of the present work --
� Experimental investigation on SFRC members
4PB tests on pre-notched beams
Flexural strengths
Ductility measures
Stress-crack opening responses
� Formulation of numerical models
Compressive tests Compressive strength
Cracked hinge model
Meso-mechanical formulation
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Experimental campaigncampaign
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Experimental campaignExperimental campaign-- Materials Materials --
The reference concrete (REF)
Cement
Aggregates
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
sand< 2 mm
N1 type2-10 mm
N2 type10-20 mm
C II A-LL 42,5
Experimental campaignExperimental campaign-- Materials Materials --
Steel fibers: FF3FS7
FF3 FS7
FS7 (long fiber)
FF3 (short fiber)
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Types of fiberLength
[mm]
Diameter
[mm]
Aspect
ratio
N. of
fiber/kg
Failure
strength
[MPa]
Rated failure
elongation
FS7
(long fiber)50 0,75 67 5700 > 1100 < 4%
FF3
(short fiber)33 0,55 60 16100 > 1200 < 2%
Experimental campaignExperimental campaign-- The experimental The experimental programmeprogramme --
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 - - 3 - 3
0,5
L100-05 100 0 3 2 1
L75-05 75 25 3 2 1
LS50-05 50 50 3 2 1
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
0,5 LS50-05 50 50 3 2 1
S75-05 25 75 3 2 1
S100-05 0 100 3 2 1
1,0
L100-1 100 0 3 2 1
L75-1 75 25 3 2 1
LS50-1 50 50 3 2 1
S75-1 25 75 3 2 1
S100-1 0 100 3 2 1
Experimental campaignExperimental campaign-- Experimental results Experimental results --
Compressive test (EN-12390-3 2009)
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Experimental campaignExperimental campaign-- Experimental results Experimental results --
Compressive test (EN-12390-3 2009)
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
It is worth noting that the compressive strength were affected by very low levelsof randomness, as demonstrated by 2.82% and 3.41% coefficient of variation forwhite and SFRCs, respectively.
Experimental campaignExperimental campaign-- Experimental results Experimental results --
Device of application
45 cm
15 cm
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Load cell Transducers
Experimental campaignExperimental campaign-- Experimental results Experimental results --
Four-point bending tests (UNI 11039-1 & 2)
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Experimental campaignExperimental campaign-- Experimental results Experimental results --
Four-point bending tests (UNI 11039-1 & 2)
Ductility indices can be considered as further “measures” of the fiberbridging effect:
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
First crack strengthEquivalent crack strengths
Experimental campaignExperimental campaign-- Experimental results Experimental results --
Detecting of the maximum value of the load Plf
FRCC first crack strength flf [MPa]
Mix
designationSpecimen a Specimen b Specimen c Average
S100-05 3,69 4,02 3,80 3,84
Flexural strengths – first crack strength (according to UNI 11039-1 & 2)
Determination of CTOD0 value
where:
• l is the distance between bottom rollers [mm]
• b is the base of the specimen [mm]h is the height of the specimen [mm]
��� = ��� �
� �ℎ − 0�2
FRCREF FRC
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
S100-05 3,69 4,02 3,80 3,84
S75-05 3,62 2,87 3,73 3,40
LS50-05 2,98 2,85 4,07 3,30
L75-05 3,37 3,37 3,00 3,25
L100-05 4,23 4,45 4,55 4,41
S100-1 3,91 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
L100-1 3,13 3,47 5,22 3,94
• h is the height of the specimen [mm]• a0 is the depth of the notch [mm]
Experimental campaignExperimental campaign-- Experimental results Experimental results --
The values of U and U are
Flexural results (UNI 11039-1 & 2)
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
The values of U1 and U2 areapproximately proportional to thedissipated energies in the average crackopening range considered.
Experimental campaignExperimental campaign-- Experimental results Experimental results --
Flexural results (UNI 11039-1 & 2)
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
In practical designs only if feq(0-0.6) > 0.5×flf or D0 > 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.
Cracked hinge modelmodel
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Cracked hinge model Cracked hinge model -- Main assumptions Main assumptions --
h
h/2
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
( )w
E
y
εσ
σ
=
Precrack state
Cracked state
h/2
Olesen ASCE J Engng Mechs 127(2001):272 –80.
Cracked hinge model Cracked hinge model -- Main assumptions Main assumptions --
Interface constitutive model for FRCC (Caggiano et al 2012)
( )w
E
y
εσ
σ
=
Precrack state
Cracked state
( ) ( ) ( )fn
cr f N ,cr N , f f T ,cr T , f
f 0
u u n u nσ σ σ τ=
= + + ∑
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Fracture energy-based plasticity formulation for plain mortar/concrete interfaces
Fiber bond-slip formulation
Formulation for fiber dowel actionExplicit formulation
Cracked hinge model Cracked hinge model -- FractureFracture--based interface model based interface model ––
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
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
� a cracking surface, within thestress space, defines the stresslevel at which the inelastic slips(inthe joint element) begin;
� a flow rule giving an incremental crack displacement
Cracked hinge model Cracked hinge model -- FractureFracture--based interface model based interface model ––
�a softening rules depending on the work spent during thefracture process
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Cracked hinge model Cracked hinge model -- BondBond--slip model slip model --
Conventional Strength Mortar (CSM)
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
- Equilibrium: - Constitutive law
- Bond-slip law
Model results (continuous lines) vs. experimental data by Shannag et al. 1997 of the pullout behavior of steel fibers from CSM and HSM.
High Strength Mortar (HSM)
Cracked hinge model Cracked hinge model -- Dowel action Dowel action --
Basic equation of the model:
λ [1/length]
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
- when lf > 2 π /λ � seminfinite BEF
[1/length]
- “k” coefficient ranges from 75 to 450 N/mm3 for RC (Dei Poli et al., 1992).
Equivalent shear elastic modulus Dowel force at ultimate limit state, Dulacska,1972.
Cracked hinge model Cracked hinge model -- Results Results --
The mechanical parameters employed in the numerical evaluations are:
• ft = 2.08 MPa, E = 20.0 GPa, s = 75 mm,
Gf = 0.5 N/mm;
• τy,a = 7.0 MPa, kE = 100.0 N/mm3, kS =
0.1 N/mm3
• kdow = 2.8 and c1 = 0.15.
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Discontinuous FEM for FRCCFEM for FRCC
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Discontinuous FEM for FRCC Discontinuous FEM for FRCC -- Definitions Definitions --
Plane stress
state
Displacement-based
control test
FE Analysis FE Analysis -- 3 Points Beam (3 Points Beam (CarpinteriCarpinteri & & BrighentiBrighenti data 2010)data 2010)
Non-linear elastoplastic
FRM joints
Non-linear elastoplastic
coarse aggregates-
mortar joints
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Discontinuous FEM for FRCC Discontinuous FEM for FRCC -- ResultsResults--
FE Analysis FE Analysis -- 3 Points Beam (3 Points Beam (CarpinteriCarpinteri & & BrighentiBrighenti data 2010)data 2010)
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Discontinuous FEM for FRCC Discontinuous FEM for FRCC -- ResultsResults--
FE Analysis FE Analysis -- 3 Points Beam (3 Points Beam (CarpinteriCarpinteri & & BrighentiBrighenti data 2010)data 2010)
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
Concluding remarksremarks
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
� As a matter of fact, the very low influence of fiber combination (long/short) on theobserved FRCC behaviour is the key conclusion of the experimental activity;
Concluding remarksConcluding remarks
� 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 plasticresponse characterised the ρf = 1.0%;
� the two “different” fibers were characterised by the same material, similar geometricdetails (i.e., hooked ends) and rather close values of aspect ratios. The possible
IntroductionExperimental campaign
Cracked hinge model
Discontinuous FEM for FRCC
Concluding remarks
� Two numerical approaches have been presented for simulating the experimentalresponse of FRCC.
� Both models based on the explicit consideration of fiber effects led to accuratesimulations of the observed experimental behaviour.
details (i.e., hooked ends) and rather close values of aspect ratios. The possiblesynergetic effect of combining different fibers should be investigated by considering two(or more) types of really “more different” fibers;
THE ENDTHE ENDThank you for your attentionThank you for your attentionThank you for your attentionThank you for your attention
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