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8/13/2019 Norfibre Paper

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DESIGN OF STEEL FIBRE REINFORCED CONCRETE SLABS ONGROUND AND SHOTCRETE LININGS

Frank Papworth, Royce Ratclif fe, Peter Norton.

SUMMARY

This paper describes design procedures for slabs on grade and shotcrete ground supportconstructed with steel fibre reinforced concrete. The area beneath the load/deflectiongraph is a measure of the energy required to achieve a certain deflection and leads to the concept of"toughness" for a fibre reinforced concrete. This toughness can be then used to determine an equivalentflexural strength "fe" for use in determining the load carrying capacity of the steel fibre reinforced concrete(SFRC). However, as fe is specific to the fibre type and dosage the performance of various fibres areoutlined, showing how for the same performance the dosage may vary by 3-4 times for different fibre types.

1.0 INTRODUCTION

The principle effect of steel fibres in concrete is toenhance the concrete's post crack strength.Increases in concrete characteristic strength

values such as compressive strength and flexuraltensile strength are typically quite small at

economic fibre dosage rates (1% by volume) and

not of significance for design purposes. A muchmore economic way to achieve high characteristicstrength values is by improving the concrete mixdesign e.g. by employing silica fume and/or lowerwater/cement ratios. To benefit from the use offibres, it is necessary to adopt a design procedureto take account of the strength after cracking i.e.away from the area of elastic behaviour on the

load/deflection graph (Figure 1) and into the plasticor hinge forming area of the graph which permits aredistribution of stresses.

The area beneath this load/deflection graph is ameasure of the energy required to achieve acertain deflection and leads to the concept of"toughness" for a fibre reinforced concrete. Thistoughness can be then used to determine anequivalent flexural strength "fe" for use indetermining the load carrying capacity of the steelfibre reinforced concrete (SFRC). However, fe isvery specific and varies dependent on the fibretype, dosage and deflection limit. Using fe criteria,steel fibre reinforced concrete flexural elements

become an extremely attractive proposition withreductions of concrete thickness of up to 25% witha fibre dosage rate of 20kg/m

3 not being

uncommon. With higher performance fibresdosages of 15kg/m

3are possible. In Europe, 50%

of concrete tunnel linings are made from steel fibresilica fume concrete. Plain concrete slabsconstructed using steel fibres are increasing innumber and unjointed bay size.

The growth in demand for steel fibre has led to alarge range of fibres being developed. It isimportant, however, to remember not all fibres are

created equal with the fibre dosages required toachieve a given performance varying considerably.Fibre geometry, strength, deformations and theirability to be evenly distributed through the concreteall have a bearing on the load carrying capacity ofSFRC.

2.0 FIBRE CHARACTERISTICS

There are four properties of fibres that areimportant:

i) fibre geometryii) fibre deformations to improve bond

iii) physical properties of the steeliv) fibre packaging to simplify mixing

2.1 Fibre Geometry

Fibres geometry is described by the "Aspect Ratio

L = l/d

where:- l = fibre lengthd = fibre diameter

High aspect ratio fibres bond into the concrete (i.e.they don't pull out at a fraction of their ultimate

Figure 1 - Load Deflection Curve


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strength) and are generally highly efficient instructural terms. Unfortunately, they tend to ball whenmixed into concrete, unless special precautions aretaken.

Fibres can be glued together in strips of about 30-50fibres with water-soluble glue (these collated fibres

look like staples). High aspect ratio fibres whencollated in this way can be added to the mix as 'extraaggregate' and no balling occurs.

2.2 Fibre Deformation

In order for the SFRC to continue to carry load anddeform plastically after cracking has occurred, it isessential the fibres is sufficiently anchored in theconcrete matrix to enable the full tensile strength ofthe fibre to be harnessed.

Physical testing of steel fibres for pullout values hasshown that "hooked end fibres pull through as the

ultimate fibre capacity is reached. This means the fullcapacity of the fibre is achieved over highdeformations giving high-energy absorption and thecharacteristic ductility required to preventing brittlefailure.

Research in 1997/99 in Japan has shown that tomaintain the optimum anchorage capacity/fibretensile capacity ratio additional deformation to thehooked end are necessary as the concrete strengthsdecreases. These "double anchorages" need to begentle deformations in the fibre without changing thefibre cross-section to ensure non-brittle failure.

In very high strength concrete the hooked endbecomes too effective and more brittle failure canoccur. The reduction in ductility is not generallysignificant below 80MPa but above that strengthhigher tensile wire (>1800MPa) may be used.

2.3 Physical Properties o f the Steel

To maintain the ductility of SFRC and ensure thereliability of the plastic deformation, it is imperativethe well-anchored fibres do not break. Breakingfibres equates to a brittle failure mode. To preventbreakage, steel fibres should be manufactured withsufficient tensile strength to ensure the ultimate

failure mode is pullout rather than breakage. Fibresmanufactured from hard drawn steel wire makeavailable tensile strengths in excess of 1200MPa.

3.0 CHARACTERISTICS OF SFRC3.1 Bond Strength

Bond strength is a key factor in all physical propertiesof SFRC. If the steel fibre slips uncontrollably (as instraight fibres), then post crack strength can bedramatically impaired.

Antoine (1991) investigated the performance of

smooth, deformed and hooked fibres in low, mediumand high strength concrete. Their research identified:

The slip at maximum load for hooked ordeformed fibres is one or two orders ofmagnitude less than that of a smooth fibre.Consequently the pullout force up to peak loadcan be upto one hundred times that of smoothfibres.

The improved mechanical bond will notinfluence first crack strength where the fibredosage is less than the critical fibre volume.

3.2 Toughness

The main reason for incorporating steel fibres inconcrete is to impart ductility to an otherwise brittlematerial. They enable concrete to continue to carryload after cracking has occurred, the so-called post

crack behaviour, or toughness (Figure 2).

Several countries have introduced tests to quantifythis toughness which in all cases is based on the

area beneath the load deflection graph up to acertain deflection value.

The two countries which have enjoyed the widestacceptance for their tests are the USA and Japanwho have introduced standards for this work.

USA Standard C1018 and Japanese Standard JCI-

SF4 are both based on the third point loading of abeam as shown in Figure 3.

A very important aspect of this test is that the rate offlexure of the beam is controlled whilst the force ismeasured.

In subsequent procedures, the two codes differ intheir approach.

Figure 2 - Stress Lines In Concrete Under Tension


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where fu= Pu/b.h2

l, b and h are defined in figure 3

In a similar way it is possible to give a measure of thetoughness by defining an equivalent flexural strength(fe) which is in effect an average load value over adefined area of the load deflection graph.

fe,= T/bh2

fe, =equivalent flexural strength up to adeflection T = area under the load deflection curve upto a deflection

The equivalent flexural strength is a value that can beused directly for design. The value fe,3, whichcorresponds to a final deflection of 3mm (l/150) isoften chosen as it reflects the strength at anacceptable deflection.

In relation to the ASTM standard the concept ofequivalent flexural ratio (Re) can also be introduced,

where Re, = Re at a deflection and is determinedfrom:-

Re,= 100 fe,/ fct,fl

where fct,fl= characteristic flexural tensile strength ofthe reference concrete without steel fibres

In practice, f ct,fl varies only slightly from fo, the firstcrack strength of SFRC.

The Re,3ratio is considered suitable for the design ofloading situations where relatively great deformationsmay occur (e.g. settlement) as this value isdetermined at a total deflection of 3mm, muchgreater than the deflection used to determine R10,30in

the ASTM Standard (i.e. for I30, deflection = 15.5

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