Annex ADesign of Steel Fibre Reinforced Concrete

A-1 General

This annex shall apply where steel fibres are used to improve the performance and capacity of reinforced and prestressed concrete structures.

The design of steel fibre reinforced concrete (SFRC) at both the ultimate and serviceability limit states shall be based on the stress $(\sigma) \neq \text{strain} (\varepsilon)$ relationships for SFRC as specified in A-3.3 (see Note 1).

Steel fibres shall not be relied upon in plastic hinge regions for strength requirements (see Note 2).

Steel fibres shall not be relied upon at constructions joints for either serviceability or strength requirements. Design procedure in this clause is for steel-fibre-reinforced concrete with a softening classification only (see Fig. 25). Hardening SFRC and the use of synthetic fibres is beyond the scope of this annex.

1 When using brittle fibres that rely on a fibre pullout failure mechanism to obtain member ductility, care is required for cases where a significant number of fibres fracture or where fibres result in local crushing of the concrete due to the local forces imposed on the matrix by the fibres. Fibre fracture may occur where the bond between the fibre and the matrix is high, and this is more likely in a high strength concrete combined with fibres of high bond capacity and of lower strength steels. 2 The anchorage capacity of steel fibres may be lost in areas where crack widths exceed about $3.5\mathrm{mm}$. Cracking of this

magnitude can be expected in regions where plastic rotations are expected.

For the purpose of this annex the following definitions shall apply.

A-2.1 Crack Mouth Opening Displacement (CMOD) — The width of a crack shall be measured at its mouth in a flexural tensile test. To measure the CMOD, a displacement transducer/clip gauge shall be mounted along the longitudinal axis at the mid width of the test specimen (beam with nominal size of 150 mm × 150 mm and length L so that 550 mm < L < 700 mm).

A-2.2 Crack Opening Displacement (COD) — The width of a single localized crack, taken as an average on four sides, for a direct tensile test on a strain softening SFRC dog-bone shaped specimen in accordance with A-3.3.7.

A-2.3 Steel Fibre Reinforced Concrete (SFRC) — A mixture of concrete and steel fibres.

A-2.4 Hardening Behaviour — A material that displays an enhanced strength with increasing crack widths beyond that measured at the point of initial cracking of the cementitious matrix.

A-2.5 Softening Behaviour A material that exhibits a loss of strength upon cracking.

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

A-2.6 Target Dosage — The specified quantity of fibres in kilograms per cubic metre of concrete (kg/m³).

A-3 Properties of Sfrc

A-3.1 General

SFRC shall be classified in terms of both its characteristic compressive (cylinder) strength ($f_{\mathrm{c}}'$) (see A-3.2) and its characteristic residual tensile strength ($f_{1.5}'$) (see A-3.3.3).

The characteristic compressive strength of SFRC at 28 days ( $f_{c}^{\prime}$ ) shall be determined in accordance with good practice [6-5A(14)].

In the absence of more accurate data, the mean value of the in situ compressive strength ( $f_{cmi}$ ) shall be taken as 90 percent of the mean value of the cylinder strength ( $f_{cm}$ ).

NOTE — The compressive strength of steel fibre reinforced concrete (SFRC) should be determined by means of standard tests on concrete cylinders. The addition of steel fibres to concrete in conventional dosages (less than $100 \, kg/m^{3}$ ) does not change the compressive properties of the concrete.

A-3.3 Tensile Properties

SFRC shall be classified as either softening or hardening as shown in Fig. 25. Hardening SFRC is outside the scope of this annex.

1 A hardening material is defined as one with a tensile strength equal to or greater than 1.1 times the strength of the matrix without fibres and taken at a crack opening displacement (COD) of equal to or greater than $0.3\mathrm{mm}$.

2 A hardening material is one where multiple cracks can occur prior to crack localization. For material hardening to occur, the fibre dosage is typically such that the strength of the SFRC is at least 10 percent greater than the strength of the same concrete mix without fibres. The value of COD of 0.3 is sufficiently high such that matrix contribution to the strength of the composite is minimal and the tension at this point is substantially taken by the fibres alone. Hardening SFRC is outside of the scope of this annex.

The matrix tensile strength of the softening SFRC ($f_{\mathrm{ct}}$) shall be obtained using flexural tensile testing, in accordance with good practice [6-5A(14)].

When only the characteristic compressive (cylinder) strength $(f_{\mathrm{c}}^{\prime})$ has been determined, the mean and characteristic flexural tensile strength of SFRC shall be calculated in accordance with 5.2.2.

NOTE — For strain softening SFRC, the peak strength of the composite may be approximated as the strength of the concrete mix without fibres.

25A STRAIN SOFTENING SFRC

25B STRAIN HARDENING SFRC

FIG. 25 CLASSIFICATION OF SFRC

The standard characteristic residual tensile strength grades $(f_{1,5}^{\prime})$ are $0.4\mathrm{MPa}$, $0.6\mathrm{MPa}$, $0.8\mathrm{MPa}$, $1.2\mathrm{MPa}$, $1.6\mathrm{MPa}$ and $2.0\mathrm{MPa}$.

The characteristic residual tensile strengths of concrete at 28 days $(f_{1.5}^{\prime})$ shall be determined statistically from tests carried out in accordance A-3.3.4 or A-3.3.5.

NOTE — The characteristic residual tensile strength depends on the fibre-matrix bond strength, which is usually a function of the compressive strength of the parent concrete, as well as the fibre content. It may be unrealistic to specify a high value of $f_{1.5}^{\prime}$ when using a relatively low value of $f_{c}^{\prime}$ .

The characteristic residual tensile strength $(f_{1.5}^{\prime})$ shall be obtained using direct tensile tests as specified in A-3.3.7.

Alternatively, where matched direct and indirect testing has been undertaken in accordance with A-3.3.6 for similar SFRC mixtures, the characteristic residual tensile may be determined as:

Where $f_{\mathrm{R},4}'$ is determined in accordance with A-3.3.8 and calculated statistically, and the factor $k_{\mathrm{R},4}$ determined from A-3.3.6.

For the purposes of this clause, similar SFRC mixtures are defined as having the same,

a) fibre type and content,

b) water to cementitious material ratio,

c) maximum aggregate particle size, and

d) compressive strength $(f_{\mathrm{c}}^{\prime})$

1 In calculating the characteristic strength, the population may be treated normally distributed and the strength determined in accordance with accepted standard. A confidence level of 75 percent shall be used such that 95 percent of the population exceeds the characteristic value.

2 The sample standard deviation shall not exceed 25 percent.

A-3.3.5 Determination of Strength by Indirect Testing

The characteristic residual tensile strength $(f_{1.5}^{\prime})$ may be obtained using indirect tests as specified in A-3.3.8 and calculated as:

The relationship between residual tensile strength and the residual flexural strength shall be obtained by matched using the same SFRC mixture. Residual tensile strength specimens shall be prepared and tested in accordance with A-3.3.7. Residual flexural tensile tests shall be in accordance with the procedure as mentioned below:

The average width of the specimen and distance between the tip of the notch and the top of the specimen in the mid-span section shall be determined from two measurement to nearest 0.1 mm width and distance in the notch port of the specimen using calipers.

When the CMOD is measured, the displacement transducer shall be mounted along the longitudinal axis at mid width of test specimen such that the distance 'y' between the bottom of specimen and line of measurement is 5 mm or less as mentioned in Fig. 26.

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

a) The concrete mix shall be batched to ensure a uniform distribution of fibres, the SFRC shall be placed in the moulds in a manner that does not interfere with the distribution of the fibres and, the SFRC shall be compacted using lightly applied external vibration; and

b) A minimum of 12 specimens shall be tested. The reference factor $k _ { \mathrm { R } , 4 }$ shall be determined as:

where

f1.5 = mean residual tensile strengths corresponding to a COD of 1.5 mm,

determined in accordance with A-3.3.7.

$f _ { \mathrm { R } , 4 \mathrm { m } }$ = mean residual flexural tensile strengths corresponding to a CMOD of 3.5 mm, determined in accordance with A-3.3.8.

NOTE — The residual tensile strength (as obtained from a direct tensile test) is a fundamental material property of SFRC. This clause allows the concrete producer and steel fibre manufacturer to correlate the direct tensile strength of their particular SFRC mix design with the flexural tensile strength.