BOND IN CONCRETE 2012 - laboratorios.fi.uba.arlaboratorios.fi.uba.ar/lmni/paper caggiano/Proceedings/2012_BIC... · BOND IN CONCRETE 2012 Bond, Anchorage, ... (EN-12390-3 2009) Introduction

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


Cracked hinge model


Concluding remarks

Experimental campaigncampaign


Cracked hinge model


Concluding remarks

Experimental campaignExperimental campaign-- Materials Materials --

The reference concrete (REF)

Cement

Aggregates


Cracked hinge model


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)


Cracked hinge model


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


Cracked hinge model


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)


Cracked hinge model


Concluding remarks


Compressive test (EN-12390-3 2009)


Cracked hinge model


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.


Device of application

45 cm

15 cm


Cracked hinge model


Concluding remarks

Load cell Transducers


Four-point bending tests (UNI 11039-1 & 2)


Cracked hinge model


Concluding remarks


Four-point bending tests (UNI 11039-1 & 2)

Ductility indices can be considered as further “measures” of the fiberbridging effect:


Cracked hinge model


Concluding remarks

First crack strengthEquivalent crack strengths


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


Cracked hinge model


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]


The values of U and U are

Flexural results (UNI 11039-1 & 2)


Cracked hinge model


Concluding remarks

The values of U1 and U2 areapproximately proportional to thedissipated energies in the average crackopening range considered.


Flexural results (UNI 11039-1 & 2)


Cracked hinge model


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


Cracked hinge model


Concluding remarks

Cracked hinge model Cracked hinge model -- Main assumptions Main assumptions --

h

h/2


Cracked hinge model


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=

= + + ∑


Cracked hinge model


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


Cracked hinge model


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


Cracked hinge model


Concluding remarks

Cracked hinge model Cracked hinge model -- BondBond--slip model slip model --

Conventional Strength Mortar (CSM)


Cracked hinge model


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]


Cracked hinge model


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.


Cracked hinge model


Concluding remarks

Discontinuous FEM for FRCCFEM for FRCC


Cracked hinge model


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


Cracked hinge model


Concluding remarks

Discontinuous FEM for FRCC Discontinuous FEM for FRCC -- ResultsResults--



Cracked hinge model


Concluding remarks

Discontinuous FEM for FRCC Discontinuous FEM for FRCC -- ResultsResults--



Cracked hinge model


Concluding remarks

Concluding remarksremarks


Cracked hinge model


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


Cracked hinge model


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

Documents

BOND IN CONCRETE 2012 - laboratorios.fi.uba.arlaboratorios.fi.uba.ar/lmni/paper caggiano/Proceedings/2012_BIC... · BOND IN CONCRETE 2012 Bond, Anchorage, ... (EN-12390-3 2009) Introduction