Fiber Reinforced Concrete, Chalmers research “ - an … concrete σ fct ∆l w FRC Concrete w l...

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  • Seminar Fibre reinforced concrete and durability:

    Fiber Reinforced Concrete, Chalmers research

    - an expos

  • From micro to macro - or small-scale to large-scale

  • Carlos Gil Berrocal. Corrosion of steel bars in fibre reinforced concrete: corrosion mechanisms and structural performance. PhD thesis, 2017.

    Jonas Ekstrm. Concrete Structures Subjected to Blast Loading: Fracture due to dynamic response. Licentiate Thesis, 2015. (PhD defence November 10th)

    Natalie Williams Portal. Usability of Textile Reinforced Concrete: Structural Performance, Durability and Sustainability. PhD thesis, 2015.

    David Fall. Steel Fibres in Reinforced Concrete Structures of Complex Shapes: Structural Behaviour and Design Perspectives. PhD thesis, 2014.

    Ulrika Nystrm. Modelling of Concrete Structures Subjected to Blast and Fragment Loading. PhD thesis, 2013.

    Anette Jansson. Effects of Steel Fibres on Cracking in Reinforced Concrete. PhD thesis, 2011.

    Peter Harryson. Industrial Bridge EngineeringStructural developments for more efficient bridge construction. PhD thesis, 2008.

    Ingemar Lfgren. Fibre-reinforced Concrete for Industrial Constructiona fracture mechanics approach to material testing and structural analysis. PhD thesis, 2005.

    Chalmers research (PhD & licentiate):

  • Fibre-reinforced concrete

    fct

    l

    w FRC

    Concrete

    w l

    l

    wc 0.3 mm wc = lf / 2 w 0.05 mm

    Fibre

    contribution Residual tensile

    stress

    Schematic description of the tensile behaviour

    When fibre-reinforcement is added an additional material property have to be

    taken into account, i.e. the -w relationship, or the fibre bridging or the residual tensile strength.

  • Material testing approch

    The approach is based on three steps:

    1) Material testing (fracture mechanics based)

    2) Invers analysis -w relationship

    3) Adjustment of -w relationship considering the number of fibres in the specimen

  • Material testing

    UTT Three-Point Bending

    Test

    RILEM TC 162-TDF

    WST

    Indirect methods

    Direct method

    load cell

    steel loading

    device with

    roller bearings wedging

    device

    linear support

    Clip

    gauge

    cube

    specimen

    piston with

    constant cross-

    head displacement

    starter notch

    (cut-in)

    groove (cast)

    Fsp

  • Mateial testing & structural analysis

    Material testing

    Sectional analysis

    Inverse analysis

    Structural analysis

  • Analytical model non-linear hinge

    Moment

    Curvature

    R

    d

    x

    N

    w

    M

    s

    M

    N

    c (

    ,y)

    y

    y 0

    s

    d1

    c (w

    ,y)

    a

    h /

    2

    h /

    2

    a

    c (y)

    s

    * / 2

    Non-linear hinge model

    Stress-strain

    relationship

    Concrete

    -110

    -90

    -70

    -50

    -30

    -10

    -5 -4 -3 -2 -1 0

    Strain, c, [10-3

    ]

    Str

    ess,

    c,

    [M

    Pa]

    0

    s

    s

    Stress-strain

    relationship

    Reinforcement

    Ec

    fct

    ()

    1

    wc w1

    b2

    a1

    a2 w

    ( )

    ctf

    w

    Stress-crack opening relationship

    Concrete

  • Comparison: experiments / analysis

    -50

    -40

    -30

    -20

    -10

    0

    0 10 20 30 40

    Nedbjning [mm]

    Las

    t [k

    N]

    FE 'bond-slip'

    FE 'embedded

    reinforcement'

    Analytisk

    Experiment

    S1:2 7-150/700

    (Mix 1)

    -70

    -60

    -50

    -40

    -30

    -20

    -10

    0

    0 10 20 30 40 50

    Nedbjning [mm]

    Las

    t [k

    N]

    FE 'bond-slip'

    FE 'embedded

    reinforcement'

    Analytisk

    Experiment

    S4:2 7-150/700

    (Mix 4)

    R2 = 0.982

    -80

    -60

    -40

    -20

    0

    -80-60-40-200

    FE analyses

    Q E

    xp

    . [k

    N]

    Q Model [kN]

    Correlation: 0,99

    R2 = 0.882

    -80

    -60

    -40

    -20

    0

    -80-60-40-200

    Analytical

    Bi-linear

    Q E

    xp

    . [k

    N]

    Q Model [kN]

    Correlation: 0,94

    Midspan deflection [mm]

    Midspan deflection [mm]

    Load

    [kN

    ]Load

    [kN

    ]

  • Comparison conventional vs. FRC

    0

    15

    30

    45

    60

    75

    90

    0.0 0.2 0.4 0.6 0.8 1.0

    Crack opening [mm]

    Mom

    ent

    [kN

    m]

    Conventional

    10-s150

    FRC 40 kg/m3

    7-s150

    FRC 60 kg/m3

    7-s150

    Comparison:

    crack opening

    crack opening

    MM

    -70

    -60

    -50

    -40

    -30

    -20

    -10

    0

    0 10 20 30 40 50

    Nedbjning [mm]

    Las

    t [k

    N]

    Plain: 10-s150

    FRC: 39 kg/m3 &

    7-s150

    FRC: 59 kg/m3 &

    7-s150

    Plain: 12-s175

    Load-deflection rel.

    Load

    [kN

    ]

    Midspan deflection [mm]

  • Effect of fibres on the cracking process

    N N

    u Crack

    u u

    N N

    Stadium II

    (neglecting tension

    stiffening)

    Tension

    stiffening Ncr Ncr

    u

    N

    Ncr

    Small reinforcement

    ratio

    Force Imposed deformation

    Large reinforcement

    ratio

    Imposed deformation

    When cracking is caused by an external applied force the crack width depends on the

    applied force.

    If cracking is caused by an imposed deformation the force in the member depends on

    the actual stiffness and the crack width on the number of cracks formed.

    However, most codes do not distinguish between these two cases.

  • Force induced cracking Ncr Ncr

    Forces acting on the concrete:

    cc tcfbmaxr,bm AfAs =+ )5.0(

    Stress introduced to concrete

    through bond, c (x)

    Fibre bridging stress, fb (w)

    Total concrete stress, ct (x,w)

    lt,max

    ct fct

    Possible location of new crack

    New crack

    Crack Crack

    fb bm

    ct fct

    Ac

    As

    lt,max

    sr,max

    lt,max

    0.5 sr,max

    Can be used to derive the crack

    spacing expression

    (+ effect of concrete cover & spacing)

  • Force induced cracking

    =

    ct

    fb

    ff

    k

    1

    effs

    r kkkcks,

    4213max,

    +=

    According to EC 2 the crack spacing can be

    calculated using the following expression:

    +=

    effs

    fmr kkkkcks,

    4213,7.1

    1

    This can be modified to take into account the

    effect of fibres (the residual tensile strength)

    by introducing a new coefficient (k5):

    ( )mcmsmrm sw ,,, =and the crack width can be calculated as:

    ( )( ) ( )( ) ( )

    s

    effsef

    effs

    ctftts

    mcmsE

    fkkk ,

    ,

    ,,

    111

    ++

    =e.g. DAfStb (UA SFB N 0171):

  • Experiments

    1800

    2000

    600

    Q Q

    C L

    LVDT

    b=150

    h=

    22

    5

    d=

    20

    0

    A-A ELEVATION

    A

    A

    Reinf.

    600 600

    Roller Roller

    Test series without and with fibre reinforcement (type Dramix

    RC-65/35

    from Bekaert) and amount of conventional reinforcement.

    Fibre dosage Reinforcement Beams

    Series [vol-%] and [kg/m3] Number and diameter [mm] [No.]

    1 Vf = 0 % (0 kg/m3) 3 8 3

    2 Vf = 0.5 % (39.3 kg/m3) 3 8 3

    3 Vf = 0.25 % (19.6 kg/ m3) 3 6 3

    4 Vf = 0.5 % (39.3 kg/ m3) 3 6 3

    5 Vf = 0.75 % (58.9 kg/ m3) 3 6 3

  • Results

    78

    59

    71

    66

    55

    77

    60

    81

    66

    54

    40

    50

    60

    70

    80

    90

    100

    Av

    era

    ge c

    rack

    sp

    acin

    g [

    mm

    ]

    Experiment Model

    38

    V f = 0%

    38

    V f = 0.5%

    36

    V f = 0.25%

    36

    V f = 0.5%

    36

    V f = 0.75%

    Vf = 0.5% and 8

    Gustafsson, M. and Karlsson, S. (2006): Fiberarmerade betongkonstruktioner Analys av sprickavstnd och sprickbredd.

    MSCe thesis 2006:105, Dep. of Civil & Environmental Eng., Chalmers Technical University, Gteborg, Sverige, 2006.

  • Results

    Vf = 0.5% and 8

    0

    5

    10

    15

    20

    0.00 0.05 0.10 0.15 0.20 0.25

    Crack width [mm]

    Mo

    men

    t [k

    Nm

    ]

    0

    5

    10

    15

    20

    0.00 0.05 0.10 0.15 0.20 0.25

    Crack width [mm]

    Mo

    men

    t [k

    Nm

    ]

    Vf = 0.5% and 8

    Vf = 0.75% and 6

    Non-linear hinge model

    DAfStb

  • Focus on:

    Combined reinforcement, i.e. steel bars + (steel) fibres

    Crack control Service state

    Effects of Steel Fibres on Cracking in Reinforced Concrete

    Investigation of:

    Cracking process, i.e. crack width and crack spacing.

    Bond-slip relationship

    Material properties

  • Experiments: tension rods

    For investigation of the cracking process Digital Image Correlation

    Tensile member

    Relative elongation , / L

    Axia

    l fo

    rce,

    N

    Reinforcement bar

    N cr

    N y1

    N y2

    N s

    N c

    Fibre reinforced

    concrete

    Concrete

    Yield load for reinforcemen t bar

    N

    L

    N

  • 0

    0.1

    0.2

    0.3

    0.4

    0 0.2 0.4 0.6 0.8 1

    No

    rmali

    zed

    bo

    nd

    str

    ess

    /f

    c

    Active slip [mm]

    1.0b

    0.25

    0.5

    1.0a

    0.0

    Bond-slip relationship

    For confined conditions, the fibres (steel fibres, Dramix RC-65/35-BN) showed no

    effect on the bond-slip relationship.

    For unconfined conditions (i.e. splitting cracks) the fibres provide confinement and

    inhibit splitting cracks.

  • Bond-slip relationship confinement effect

    0

    10

    20

    30

    0 2 4 6 8

    Bo

    nd

    str

    ess

    [MP

    a]

    Slip [mm]

    Series 0.25ExpConfinedSplit-stirrups

    0

    10

    20

    30

    0 2 4 6 8Slip [mm]

    Series 0.5ExpConfinedSplit-stirrups

    0

    10

    20

    30

    0 2 4 6 8

    Bo

    nd

    str

    ess

    [MP

    a]

    Slip [mm]

    Series 1.0aExpConfinedSplit-stirrups

    0

    10

    20

    30

    0 2 4 6 8

    Bo

    nd

    str

    ess

    [MP

    a]

    Slip [mm]

    Series 1.0bExpConfinedSplit-stirrups

    Series

    -stirrup[mm]

    Sv[mm]

    Ktr[%]

    0.25 6 300 1.2

    0.5 10 200 4.9

    1.0a 12 80 18

    1.0b 12 80 18

    Corresponding transversal reinforcement:

  • 0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    20 40 60 80 100

    Cra

    ck w

    idth

    [mm

    ]

    Load [kN]

    0.0

    0.25

    0.5

    1.0a

    1.0b

    0 kg

    14 kg

    35 kg

    78 kg

    66 kg

    Cracking & tension stiffening

    0

    20

    40

    60

    80

    100

    0 0,5 1 1,5 2 2,5

    Ten

    sile

    load

    [k

    N]

    Deformation [mm]

    66 kg78 kg35 kg14 kg0 kg

    Reinf.

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    0 0.001 0.002 0.003

    Bon

    d f

    acto

    r

    [ -

    ]

    Member strain [ - ]

    a. - cb. -FRC

    b.

    a.

    c(x)

    s(x)

    sm

    cm

    is used to calculate the average steel strain

    between cracks

    Result show higher and that at high fibre dosage almost constant

    and no degradation

    Tension rod

  • Restraint induced cracking combined reinf.

    l

    Crack, modelled as

    non-linear springs

    w(s)

    ( )

    4

    122.0

    42.0

    826.0

    2

    +

    +

    =

    s

    s

    ef

    s

    c

    sscm

    ss

    E

    A

    A

    E

    EEf

    w

    Bond-slip relationship => crack width as a

    function of the steel stress:

    N(s)

    N(s)

    N(s)

    N(s)

    N(s)

    N(s)

    N(s)

    N(s)

    Forces acting on un-cracked parts

    (with only bar reinforcement)

    N(fft.res) N(fft.res) Forces acting on un-cracked parts for

    combined reinforcement (fibre and bar reinforcement), with fft.res as FRCs

    residual tensile strength

    Friction between slab and

    sub-base is neglected

    Engstrm, B. (2006): Restraint cracking of reinforced

    concrete structures, Chalmers University of Technology.

  • The response during the cracking process can described with the following

    deformation criteria:

    ( ) lRwnAE

    lfNcssef

    Ic

    resfts=++

    )(1

    ),( .

    where N(s, fft.res) is the force acting on un-cracked parts, n is the number of cracks and R is the degree of restraint. N(s, fft.res) can be calculated as:

    ( )sefresftssresfts AAfAfN += .. ),(

    If N(s, fft.res) is larger than the force required to initiate a new crack, N1, more cracks will be formed. However, if it is smaller only one crack will be

    formed. The force required to initiate a new crack, N1, can be calculated as:

    += s

    c

    sefctm A

    E

    EAfN 11

    Engstrm, B. (2006): Restraint cracking of reinforced

    concrete structures, Chalmers University of Technology.

  • Exemple

    A reinforced slab on grade, 20 meter long, with full restraint (R=1).

    Reinforced with 8, 10 or 12 (0.2% < < 0.8%)

    Material properties, concrete C30/37 (vct 0.55): Tensile strength: fctm = 2.9 MPa (fctk, 0.05 = 2.0 MPa)

    Residual tensile strength: 0 MPa < fft.res < 2.5 MPa

    Creep coefficient: ef = 2.5 Concrete shrinkage: cs = 600 10

    -6

    250

    1 m c = 30

    20 m

  • Exampel crack widths with combined reinforcement

    0.0

    0.5

    1.0

    1.5

    2.0

    2.5

    0.0 0.1 0.2 0.3 0.4 0.5 0.6

    Crack width [mm]

    Resi

    du

    al

    ten

    sile

    str

    en

    gth

    [M

    Pa]

    0.3%

    0.4%0.5%0.6%

    C 30/37 10

    = 0.8%0.0

    0.5

    1.0

    1.5

    2.0

    2.5

    0.0 0.1 0.2 0.3 0.4 0.5 0.6

    Crack width [mm]

    Resi

    du

    al

    ten

    sile

    str

    en

    gth

    [M

    Pa]

    0.3%

    0.4%

    0.5%0.6% = 0.8%

    C 30/37 12

    The normal / recommended reinforcement ratio is typically 0.4-0.6%.

    A conservative estimate on the residual strength with steel fibres:

    20 kg/m3 => 0.8 MPa residual strength

    30 kg/m3 => 1.1 MPa residual strength

    40 kg/m3 => 1.3 MPa residual strength

  • Concrete structures square and boring ?

  • TailorCrete - Rationel design and production of

    structures with complex geometries

  • TailorCrete - Rationel design and production of

    structures with complex geometries

  • Tailorcrete

    Interesting results regarding:- Load redistribution

    - Membrane action

  • Blast and Fragment Impacts effect of fibres

    From PhD thesis, by Jonas Ekstrm, to be presented November 10th

  • Blast and Fragment Impacts effect of fibres

    From PhD thesis, by Jonas Ekstrm, to be presented November 10th

  • Durability Effect of fibres on corrosion

    Crack morphologyno fibres

    Crack morphologywith fibres