Fiber Reinforced Concrete in Eurocode 2:basic assumptions for structural design.

M. di PriscoDepartment of Civil and Environmental EngineeringPolitecnico di Milano

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TG2: the balancing act

safeeconomicalas general as possible, as specific as necessarycompliant with EC2 limits

opening up possibilities for wider useno obstruction of established applications

� those not in scope� those in scope

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Kick off meeting in Brussels on October 2012

Secretary: Andreas Schleifer

+ G. Vitt (Bekaert – Germany) + L. Steinar (Standards Norway ) + I. Lofgren (Thomas Concrete Group – Sweden) + S. Wolf (Arcelor & Mittal, Luxembourg) + P. Rossi(IFSTTAR – France) + G. Plizzari (UNI – Italy) + M. Schulz(Eng. GMBH – Germany) + J. C. Lancha (ETS Universidad de Castilla-La Mancha – Spain) + S. Wijte (Hageman BV – Netherland)

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Bruxelles 30/10/2012Stockolm 6-7/5/2013Milano 6-7/2/2013Zurich 6-7/5/2013Bruxelles 29/10/2013Madrid 4-5/2/2014Milano 11/6/2014Milano 17-18/9/2014Delft 5/12/2014Brescia 21/5/2015Milano 9/2015Copenaghen 28/1/2016Milano 13/5/2016Madrid 14/10/201610/2/2015

Brescia 21/5/2015

13 meetings

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European National Standards

Extra European National Standard

Sweden Standard SS812310: 2014Fibre Concrete - Design of Fibre Concrete Structures

Denmark 2014- Design guideline for structural applications of steel fibre reinforced concrete

SpainAnejo 14 EHE08 – Recomandaciones para la utilización de hormigón con fibras

Italy CNR DT204, 2004 – Guide for the design and construction of fibre reinforced concrete structures

Germany DAfStB technical rule 20 2012–Deutscher Ausschuss fur Stahlbeton (German Committee for reinforced concrete)

AFGC France (2002) 2013 – Beton fires a ultra-hautes performances Recommandations

….

USA ACI 544 – Guide to Design with Fiber-Reinforced Concrete in progress

China CECS 38:2004 - Technical Specification for Fiber Reinforced Concrete Structures provides guidelines for various applications

India - ICI – G 501 “Guidelines for Selection, Specification & Acceptance of FIBER & FIBER CONCRETE”

Japan JSCE 2008 –Recommendations for Design and Construction of High Performance FiberReinforced Cement Composites with multiple fine cracks

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Model Code 20105.6 Fibre Reinforced Concrete

5.6.1 Introduction5.6.2 Material properties5.6.2.1 Behaviour in compression5.6.2.2. Behaviour in tension5.6.3 Classification5.6.4 Constitutive laws5.6.5 Stress-strain relationship for SLS5.6.6. Partial safety factors5.6.7 Orientation factor

7.7 FRC structures

7.7.1 Classification7.7.2 Design principles7.7.3 Verification of safety (ULS)7.7.3.1 Bending and/or axial compression in linear members7.7.3.2 Shear in beams7.7.3.2.1 Beams without longitudinal and shear reinforcement7.7.3.2.2 Beams without shear reinforcement7.7.3.2.3 Beams with shear and longitudinal reinforcement7.7.3.2.4 Minimum shear reinforcement7.7.3.3 Torsion in beams7.7.3.3.1 Beams without longitudinal and transverse reinforcement7.7.3.3.2 Beams with longitudinal and transverse reinforcement7.7.3.4 Walls7.7.3.4.1. Walls without conventional reinforcement7.7.3.4.2. Walls with conventional reinforcement7.7.3.5 Slabs7.7.3.5.1 Members without reinforcement7.7.3.5.2 Members with reinforcement7.7.3.5.3. Punching7.7.3.5.4. Shear in Slabs with longitudinal reinforcement7.7.4 Serviceability Limit State (SLS)7.7.4.1 Crack width in members with conventional 7.7.4.2 Minimum reinforcement for crack control

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Today’s Steel Fibre Consumption in Europe(an estimate)

design by• national codes +

guidelines• general approvals• EN standards• design & test• Model Code 2010

~within scope of

current EC2

Industrial Flooring

Tunneling

Housing/Ready-mix

Structural Foundations

Structural, Others

Precast

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Scope of Annex

This annex covers the design and construction of structures in scope of EN 1992-1-1 made of steel fibre reinforced concrete (SFRC)� with or without reinforcement� with or without pre-stressing or post-tensioning.

The design rules are not intended to be used for� lightweight concrete� shotcrete� slabs on ground which are not required for the structural stability

(e.g. industrial floors)� applications with increased resistance to plastic shrinkage,

abrasion or impact

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0.00 0.10 0.20displacement w (mm)

0.0

1.0

2.0

3.0

4.0

5.0

aver

age

tens

ion

σ t (M

Pa)

zoom w = 0.20 mm

TRA0 med

TRA4 med

TRA8 med

0.00 2.50 5.00deflection f (mm)

0.0

4.0

8.0

12.0

load

P (K

N)

zoom w = 5.00 mm

FLE0 med

FLE4 med

FLE8 med

0 5 10

440

60

0

wP [kN]

σN

δ [mm] δ [mm]

P [kN]P

w[mm]

w

δ

30

60

We use residual tensile strength after cracking!

The post-cracking strength significantly affects structural behaviour with the increase of structure redundancy.

V f [%]

0.00.4

0.8

0.8

0.4

0.0

0.8

0.0

V f [%]

V f [%]

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�a residual strength for ductile structures

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1 dm³ steel fibres= 7,85 kg40 kg steel fibres= 5,1 dm³

5,1 dm³ = 0,5 vol. %

10 dm

10 d

m 1 m³

40 kg/m³ steel fibres

169.107 fibersdf = 0,8mm; lf = 60 mm;

601.269 fibersdf = 0,6mm; lf = 30 mm;

19.512.359 fibersdf = 0,16mm; lf = 13 mm;

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Vf = 1% ≅≅≅≅ Vf = 3%

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0 5 10 15 20

displacement wt (mm)

0

10

20

30

40

load(kN)

sandrubber

0.4%

Vf = 0.8%

0.4%

0.8%

plain concrete

Pusplain

23.4 kN

Redundant structure behaviour

by di Prisco & Felicetti, 2004

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Courtesy by Falkner, 2006

M. di Priscoby Falkner, 2006

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(σσσσ - w) in uniaxial tensionis the effective constitutive law

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BehaviorBehaviorBehaviorBehavior in in in in compressioncompressioncompressioncompression

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P

P P

PPcr crP

crack formationcrack

crack formation

localization

Softening material Hardening material

δu

�A unique standard for both the behaviours

Depending on the fibre content the stable crack propagationprogressively grows …

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Tension tests for hardening materialsTension tests for hardening materialsTension tests for hardening materialsTension tests for hardening materials

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2sp

j, 2

3

hb

lFf jR =

hsp = 125 mm

b = 150 mm

S.L.S.

fR,1 fR,3

U.L.S.

Reference test EN 14651

fL,k

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ClassificationClassificationClassificationClassification

slump flow diameter: 690 mmT50 2 secV-funnel time (0 min) 3.5 secV-funnel time (5 min) 4 secL-box (standard) h2/h1 = 1

cement 425: 472 kgfly ash: 45 kgwater 200 l (w/b =0.39) superplast. 1.3%

fine sand 0/4 850kgcoarse sand 4/8 886 kg

hooked-end fibres 65/35 50 kg

4,33

4,47

3,77

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(5) Fibre reinforcement can substitute (also partially) conventional reinforcement at ultimate limit state if the following relationships are fulfilled:

fR1k/fLk > 0.4; fR3k/fR1k > 0.5

CMOD (mm)

σN

fLK

0.5 2.50

fR1k fR3k

�A minimum according to performance based design

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fFtu = fR3/3

WhichWhichWhichWhich modelsmodelsmodelsmodels forforforfor uniaxial uniaxial uniaxial uniaxial tensiontensiontensiontension????

0)2.05.0( 133

≥+−−= RRFtsu

FtsFtu fffCMOD

wff

14.0 RFts ff =

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RigidRigidRigidRigid---- plastic plastic plastic plastic modelmodelmodelmodel

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ε = w /l

χ

σ = E⋅χ ⋅x

y

xC

MM

0.5 fR3 R1- 0.2 ff Ftsi1 cs

f Fts

= 0.45 fR1

Linear postLinear postLinear postLinear post----cracking cracking cracking cracking modelmodelmodelmodel

wil = w1 = 0.5 mm wil = w3 = 2.5 mm

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σ

w0.5 2.5

kafR1kbfR1

if f R3 = 0.5 fR1

kb = 0.45 fR1

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Behaviour in tension:Behaviour in tension:Behaviour in tension:Behaviour in tension:identification from bendingidentification from bendingidentification from bendingidentification from bending

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�the characteristic material length

u

w

Nf

ww

dwwG

=

∫=0

)(σσN σN

w wwuwcr

fracture

aggregate interlock

fracture and fibre delamination

pull-out and aggregate interlock

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�the characteristic materiallengthThe experimental measure according to damage mechanics school(Fokwa and Berthaud 1992)

by di Prisco, Felicetti; Gambarova 1997

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0.0E+0 5.0E-3 1.0E-20.0

3.0

6.0

(MPa)

fc 20 = 72 MPa

ε ∧

σ

0.0

3.0

6.0

g f

0.0E+0 1.0E-3

tan α

ε

σ

ε ∧1

(b)

E0

εp

strain limitof PIED test

f t= 4.0 MPa

0.0 0.2 0.40.0

3.0

6.0

(MPa)

fc 20 = 72 MPa

wcr (mm)

σN

0.0

3.0

6.0

G f

0.00 0.05

tan α '

w

σNf t

N= 4.45 MPa

wcr

1

(a)

][]/[

]/[3

2

, mmNmg

mNmGl

f

f

mch ==

max,,max, 35.0 amcha dld <<

�the characteristic material length

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lcs = min{srm, y}

N.B. In sections without traditional reinforcement under bending or under combined tensile – flexural and compressive – flexural forces with resulting force external to the section, y = h is assumed. The same assumption can be taken for slabs.

�the bridge ... of the characteristic structural length

F.E. approach:

Plane section approach

y= h-x

lcs = localization limiter

steel bar srm

srm

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�the bridge ... of the characteristic structural length

lcs1lcs1

σ

w

σ

ε

lcs2lcs1

w

εεεεlcs

Gf lcs2=srm

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CMOD

xσhn

lcs = hn

σ = 0 σ = 0

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P P

h

a bσN = 6Pa/bh2

lcs = h

φ

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� the limit state definition

wu = min (lcs٠ εFu , 2.5 mm)

valid for all the fibres in the marketFor long steel fibres (crimped or hooked) could be on the safe side!

2% for variable strain distribution along the cross section1% for constant tensile strain distribution along the cross section.

ductility

Fibre geometry

fc = 75 Mpa; Fibre content = 50 kg/m3; Fibre length = 30mm; Aspect ratio = 45; Low carbon

M. di Priscolcs = 125 mm

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Ex: αt3 = 0.5 fR3 - 0.2 fR1

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γsF= 1.5

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beam

T1

be

am T

2

be

am T

3

50mm

150 mm150 mm150 mm 500 mm

beam L3

beam L2

beam L1

150

mm

150

mm

150

mm

50

mm

castingdirection

supposed flow lines0 2 4 6 8 10

COD (mm)

0

2000

4000

6000

8000

10000

load

(N

)

beam L3

beam L1

beam L2

beam T2

beam T1beam T3

by Ferrara et al. 2008

a single a single a single a single materialmaterialmaterialmaterial cannotcannotcannotcannot followfollowfollowfollow twotwotwotwo standardsstandardsstandardsstandards

by Ferrara et al., 2009

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Material properties and experimental tests

Material name Matrix strength Fiber content Aspect Ratio Fiber Length T65 65 MPa 50 kg/m3 45 30 mm T40 40 MPa 35 kg/m3 50 30 mm

t

t = 60, 105 mm

Hooked-end low-carbon steel fibres

150

mm

450 mm

600 mm

150 mm 150 mm 150 mm

45mm

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Material properties and experimental tests

0 1 2 30

2

4

6

8

105B105AUNI

σΝ

w [mm]

(a)

[MPa]

60A60B

T65

0 1 2 30

1

2

3

4

5

105B105AUNI

σΝ

w [mm]

(b)

[MPa]

60A60B

T40

A BNB: each curve represents an average over 4 curves

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5.6.7 Orientation factor

fFtsd,mod=⋅fFtsd/K fFtud,mod=⋅fFtud/K

Isotropic fibre distribution is assumed K = 1.0For favourable effects K < 1.0For unfavourable effects K > 1.0

FRC is not homogeneous and not isotropic!The inhomogeneity and anisotropic effects due to casting procedure can be taken into account by a special coefficient K that is at this time just empirical.

When K < 1.0 is applied in one direction, the K in the other direction direction should be checked!

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k mf f ks= −

0

1

2

3

4

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

CTODm [mm]

Nom

inal

Str

ess

s

N [M

Pa]

Load vs. Central deflection

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6

Central deflection [mm]

Load

[kN

]

Slab P22 50/0,75 Vf=0,38 %

Slab P21 50/0,75 Vf=0,38 %

Slab P20 50/0,75 Vf=0,38 %

di Prisco, M., Failla, C., Plizzari, G.A., Toniolo, G (2004).

P = P (fm)

P = P (fk)

�the key role of the scattering

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�the key role of the scattering

PRd = KRdP(fFd)

25

VV0

KRd = KRd (V/V0 , Pmax/Pcr)

tests

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Models construction by considering heterogeneous materials

Example of CDF discretization with a Heaviside step function

Steps introduced at percentiles α = 0.025, 0.15, 0.5, 0.85, 0.975

� 5 material combinations

Three stochastic variables: fFt, fR1 and fR3

F(fR1)

fR1

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Beam and slab subdivision for the random heterogeneous material assignationModel construction by considering heterogeneous materials

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Results and discussion

Slab numerical response for homogeneous (0.5 and 0.05 percentiles) and

heterogeneous random material (0.5 and 0.05 percentiles)

Log-Normal distribution

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0)2.05.0( 133

≥+−−= RRFtsu

FtsFtu fffCMOD

wff

αt3

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7.7.3 Verification of safety (ULS)7.7.3.1 Bending and/or axial compression in linear members

(1) The bending failure is considered when one of the following conditions is obtained (see Fig.XX.7):• attainment of the maximum compressive strain in the FRC, εcu;• attainment of the maximum tensile strain in the steel (if present), εsu;• attainment of the maximum tensile strain in the FRC, εεεεFu.

M

Fu≤ ε

su≤ ε

cu≤ ε

Asl

cdf

Ftsf /γF

Rd

NSd

cdη · f

Ftuf /γF

λ·xx

y

hardening softening

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RILEM TC CCF on Creep coordinated by Pedro Sernà just started

The creep coefficients already measured for steel fibres are comparable to those of plain concrete, but they affect the elastic values and they have to be compared with large crack openings!by Zhao, di Prisco and Vandewalle , 2014

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THANKS FOR YOUR ATTENTION!