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2.2.1 Basic properties and characteristics of SFRC

Steel fibres can be classified according to the production process, shape and material (i.e. steel with low and high carbon contents, stainless steel). The behaviour of steel fibres is characterised by the cross-section shape, aspect ratio, tensile strength, orientation and fibre volume fraction (National Research Council, 2007; Concrete Society, 2007). Figure 2.1 shows some of the shapes available for steel fibres. Plain-

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straight and hooked-end steel fibres are commonly used in experimental investigations (e.g. Henagar, 1977; Gefken and Ramey, 1989; Kotsovos et al., 2007; Ozcan et al., 2009 etc). Modulus of elasticity of steel fibres can be assumed to be 200 GPa for steel with low or high carbon contents and 170 GPa for stainless steel (National Research Council, 2007). Smaller fibre volume fractions (i.e. ) normally produce post- cracking softening behaviour, whereas, higher fibre volume fractions (i.e. ) may contributed to hardening behaviour, due to multiple cracking occurrences as stated by National Research Council (2007).

Figure 2.1: Types of steel fibres (adapted from Concrete Society, 2007)

Previous studies (e.g. Sharma, 1986; Trottier and Banthia, 1994; Robins et al., 2002; Khaloo and Afshari, 2005 etc) show that the performance of SFRC is influenced by many factors including the fibre shape, aspect ratio and volume fraction. Deformed steel fibres (i.e. hooked-end, crimped and twin-cone) with appropriate fibre content and aspect ratio require more energy absorption as they undergo the pull-out process, which in turn enhances the toughness characteristic of the FRC (e.g. Narayanan and Darwish, 1987; Lim et al., 1987; Trottier and Banthia, 1994; Robins et al., 2002). Trottier and Banthia (1994) observed that steel fibres with deformed shapes at the end (i.e. hooked- end and twin-cone) produce higher strength and ductility than fibres with a deformed shape along the length (i.e. crimped). Furthermore, most of the experimental work (e.g. Filiatrault et al., 1994, 1995; Bayasi and Gebman, 2002; Campione et al., 2006; and Campione and Mangiavillano, 2008) was carried out using hooked-end steel fibres.

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The amount of fibres added in a structure has been a subject of interest due to practical issues such workability of the mixtures and fibre spalling. An appropriate fibre volume fraction is required in order to provide sufficient enhancement in the strength and ductility of SFRC structures. Therefore, based on the studies carried out it is recommended that the fibre volume fractions of steel fibres are limited to 2% (Sharma, 1986; Narayanan and Darwish, 1987; Khaloo and Afshari, 2005), unless enough plasticizer is considered to address the aforementioned concerns (i.e. workability and fibre spalling). Many researchers (i.e. Sharma, 1986; Mansur and Ong, 1991; Oh et al., 1998; Kwak et al., 2002; Campione et al., 2006) studied the effect of fibre content on confinement and enhancement of shear capacity, especially in the absence of conventional shear reinforcement (see Section 2.3.2).

2.2.2 Behaviour of SFRC

Many investigations (i.e. Lok and Pei, 1998; Lok and Xiao, 1999; Barros and Figueiras, 1999; 2001; RILEM TC 162-TDF, 2000; 2003; and Tlemat et al., 2006) proposed that addition of steel fibres may improve the post-cracking behaviour of concrete from a sharp drop, associated with plain concrete, to either tension softening or hardening characteristics depending on the fibre dosage, geometry and bond stress. These suggested constitutive models for SFRC are discussed in Section 2.3.

The effect of the steel fibres on the moment-curvature curve is shown in Figure 2.2 (Lok and Xiao, 1999). It is apparent that the effect of fibres will only take place after the onset of cracking (i.e. after the stress reaches concrete tensile strength ft). The post-

cracking residual tensile stress (ftu) improves the flexural behaviour of the SFRC

structure and is governed by the fibre geometry and fibre volume fraction. On the stress-strain diagram, the zone between the origin and the cracking strain ( )

represents the region before cracking. The post-cracking zone between the strains and is the region where both fibres and concrete between the cracks are resisting the load. Finally, the zone between the strains and is the region where the fibres are

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Figure 2.2: Relationship between (a) Moment-curvature response and (b) Tensile stress-

strain behaviour (adapted from Lok and Xiao, 1999)

The flexural moment-curvature response obtained can be classified as softening (case 1), idealised elasto-plastic (Case 2), or hardening (Case 3) depending on the fibres pull- out and bridging behaviour. Furthermore, increases in the fibre volume fraction (with the fibre geometry being kept the same) change the pattern of the moment curves from Case 1 to Case 3. The first crack is observed at point A. The ultimate load carrying capacity for the SFRC specimen can be seen from B1, B2 and B3. As the tensile strains

in the SFRC stress-strain behaviour are constrained, the crack propagation is controlled and reduced through pull-out resistance of fibres bridging the cracks.

2.2.3 Crack propagation

The failure of plain concrete is governed by the formation of a single crack. Before the initiation of the first crack, the material exhibits linear elastic behaviour. Once the crack initiates, the energy absorption capacity is increased until it is exceeded (Kotsovos and Pavlović, 1995). As the loading continues to increase, the crack expansion is resisted by the aggregate interlock effect in the concrete. Consequently, with any additional energy induced by the applied load, the crack expands more which, subsequently, reduces the

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energy capacity of the system further and creates an instable state. Once the energy is released during the fracture processes, the stress and strain concentration at the crack tips orthogonally to the path of the crack extension decreases (Kotsovos and Pavlović, 1995). These fracture processes create voids within the concrete as shown in Figure 2.3. Additionally, as these high tensile stress and strain concentrations reduce, the material is compressed in the direction normal to the crack-extension path, while void formation continues to extend increasing propagation of the crack.

Figure 2.3: Schematic representation of changes in crack geometry and stress fields associated with crack extension (adapted from Kotsovos & Pavlović, 1995)

When a crack is initiated in SFRC elements, the propagation of cracks is controlled by the presence of the fibres in the concrete. Fibres provide crack arresting or bridging effect to resist further cracks opening, during crack propagation. Two potential failure modes (depending on the effectiveness of the fibres in providing crack bridging) are shown in Figure 2.4. According to RILEM TC 162-TDF (2002), failure by a single crack (Figure 2.4(a)) occurs when the first cracking strength is the ultimate strength of concrete and further deformation is governed by the opening of a single crack and fibres pulling out and/or breaking along the edges of the crack. In this case, the fibres are pulled-out or break during crack initiation, or if the maximum load sustained by the fibres exceeded after the formation of the first crack. On the contrary, if the fibres were able to carry more load after the first crack, more cracks will be formed in the nearby

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region, which is known as multiple cracking (Figure 2.4(b)). The behaviours are also referred to as tension softening and strain hardening.

Figure 2.4: The principle of single and multiple cracking. The specimens are loaded in uniaxial tension and the schematic load versus deformation (P-) relationship is shown

together with the cracking pattern (a) single cracking (or tension softening) (b multiple cracking (or strain hardening) (adapted from RILEM TC 162-TDF, 2002)