High Strength Concrete (HSC) use in modern construction is becoming increasingly popular as opposed to Normal Strength Concrete (NSC). HSC has inherent favourable properties such as higher mechanical properties, a more linear behaviour under load and reduced micro-cracking when subjected to higher loads. These enhanced material properties allow for the design and construction of smaller member sections compared to NSC when expected to undergo the same load levels. HSC offers a more cost-effective solution (Diniz & Frangopol, 1997; Wu, 2010).

One of the drawbacks of the application of HSC is its inferior ductility performance when compared to NSC. From a structural safety point of view, the design for ductility is as important as strength properties (Ho et al., 2004). Ductile performance gains even more importance when considering the seismic design of structural members. It is a key determinant of structures’ ability to deform inelastically without encountering fracture or brittle structural failure.

Many studies have been conducted to design and improve the ductility performance of HSC structures (Chunxiang & Patnaik, 1999; Mydin, 2013; Tablan, 2007). Many failures have been observed during construction because of intrinsic thermal and/or mechanical stresses imposed on maturing concrete (Sofi et al. 2014, 2019). In summary, it is established that if the correct design approach is adopted, the ductility of HSC can be restored to the levels of NSC (Pam et al., 2001). Addition of steel fibres has been shown to improve ductility properties. For instance, Tablan (2007) has explored the inclusion of various types of fibres within the HSC mix to improves its ductile performance. These include naturally occurring coconut fibres and steel fibres (Tablan, 2007).

Steel Fibre (SF) reinforcement is the most widely used material in structural concrete. The popularity of SF is due to its low water absorption characteristics, increase in impact and abrasion resistance properties, its lower maintenance and increased durability compared to other types of fibres. Other factors include economy and savings will be greater for heavier crack control systems. Studies found that the inclusion of SF at approximately 0.75%–1.00% content in volume within a concrete mixture helped improve its ductility tensile and flexural strength properties (Mydin, 2013). Similarly, Chunxiang and Patnaik investigated the effects of SF on HSC beams with longitudinal reinforcement.

Results showed that fibre reinforcement led to an increased flexural rigidity before yielding and improved ductility performance due to an increased displacement at failure (Chunxiang & Patnaik, 1999). Further research into SF and its impact on strength, such as compressive and flexural capacity, have been undertaken. In addition to improving ductility performance, the presence of SFs improve the tensile and flexural capacities of HSC (Song & Hwang, 2004).

A study by Hsu and Hsu analysing multiple cylindrical specimens, both with and without confinement, presented a stress–strain relationship of Steel Fiber Reinforced Concrete (SFRC). Results suggested that there was a clear increase in post-peak loading stresses at any given strain level, hence improving the ductility and toughness (Hsu & Hsu, 1994).

There is currently no predictive models describing the effect of the addition of SF accurately due to the irregular distribution and orientation of fibres across the member section.

Current methods described in AS 5100.5–2017 used to determine the strength capacity of proposed steel fibre reinforced concrete (SFRC) structural elements relies solely on the individual testing of each composite mixture (Standards Australia, 2017). The test is required before the use of SFRC, thus limiting its potential application and inclusion in early design phases of construction projects.

### 1.1 Fibre Bond Stress-Slip Relationship

Influences on both the average interfacial bond stress and the pullout load per fibre were investigated as early as 1984 (Mangat et al., 1984). The effect of several parameters, such as spacing and aspect ratio, fibre embedment length, and diameter on the interfacial bond strength between the steel fibres and mortar matrix was experimentally investigated. A flexural load was generally applied to simulate the state of stress commonly experienced by the structural elements. The investigation established that the average pullout bond strength per fibre increases with increasing fibre embedment length and decreases with increasing fibre diameter. Further, the authors have found that fibres spacing has no significant influence on bond strength. The average bond stress decreases when the cement matrix is modified with steel fibre reinforcement, the reduction being greater at higher fibre contents. The effects of matrix strength, hooked-end fibre embedment length and orientation were later investigated (Robins et al., 2002). It was found from the studies that the pullout response of a hooked-end fibre is mainly influenced by three parameters: fibre embedment length, fibre orientation and matrix strength. The pullout response was characterised by one of two pullout modes: either the hooked-end is straightened as it is pulled out from the matrix or the fibre fractures at the hook portion. The matrix strength increases the magnitude and toughness of the pullout response. As the fibre orientation deviates from the direction of the pullout load, its response becomes increasingly less influenced by matrix strength and increasingly on the mechanical properties of the fibre itself as it attempts to straighten in line with the direction of load.

### 1.2 Numerical Models To Predict The Performance Of SFRC

To lower the hurdle of considering SF in the early design phase, various theoretical models have been proposed to find the effects of SF on the concrete properties. A model derived to estimate the upper and lower bounds of the tensile strength of SFRC (Grimaldi & Luciano, 2000), was shown to accurately model the tensile strength of SFRC. However, drawback from this model is the complexity of analysis and theoretical application which make it difficult for useful day-to-day application (Olivito & Zuccarello, 2010). Alternatively, a regression analysis conducted on varying SFRC mixtures demonstrated that there is a simple yet direct relationship between volumetric fibre content and flexural and tensile strengths (Song & Hwang, 2004).

A correlation between SF content and tensile strength is seen to be evident, therefore, providing justification for expanding research into analysing the effect of SF on ultimate flexural strength capacities. Studies investigating SF discussed above rely heavily on a theoretical approach, with limited laboratory testing or other methods. The conclusion drawn from models seems to be valid. However, the complexity of mathematical modelling and forecasting provide limitations of these models in day-to-day application.

A theoretical model based on fibre surface abrasion was developed for synthetic fibres to predict the load–displacement relationship (Wang et al., 1988). The effects of Poisson’s ratio, elastic-frictional bond strengths, and bond strength variation with slippage distance on the pullout relation were investigated. Bond strength was found to increase with the slippage distance during the process of pullout. Hajsadeghi et al., (2018) used contact elements to simulate the fibre-matrix interaction in which the Coulomb friction model was used to account for the physicochemical bond and the fibre-matrix interface friction. The model considered geometric and material nonlineariti3es accurately simulating the steel fibre pullout mechanism and showing good agreement with the experimental results. They suggested that their proposed model could be used to conduct parametric studies with the aim of designing and optimisation of new types of steel fibres. They noted that cracks could initiate at any point along the fibre which typically slips on the shorter embedded side. This will affect the pullout performance of steel fibres, especially those which are fully deformed such as crimped and twisted. They suggested that a pullout study should be performed on fibres with various embedded lengths and angles of inclinations.

### 1.3 SF Measurement And Effective Area

There is a degree of uncertainty when it comes to the distribution of fibres, as they are orientated and located randomly throughout a concrete sample. This makes their contribution within a sample and their proportion as tensile reinforcement very difficult to measure. Soroushian and Lee (1990) attempted to analyse SF distribution within cross-sections of concrete beams. It was concluded that the distribution of SFs is influenced directly by both the boundaries conditions, the beam cross-sectional area and the vibration placement of SFRC (Soroushian & Lee, 1990). The vibrational placement was shown to settle down and reorient fibres horizontally. To calculate flexural capacities of SFRC, a relationship between volumetric fibre content and the effective area of cross section of the SFRC was proposed. To evaluate the effective area, a method of dividing the cross-section of the SFRC beam into three regions (top, middle and bottom) was proposed. Each region has then been given an orientation factor, which could be modelled into an effective area of that region. All three effective areas were then implemented in a theoretical relationship, resulting in an overall effective area for the cross-section. Results found that the effective area of SF within a cross-section is only 54% effective compared to the effective area with SF with the most desirable alignment. This is due to the random orientation of fibres throughout the section (Soroushian & Lee, 1990).

Another method used to determine SF cross-sectional area is the destructive methods of cutting and polishing concrete specimens. From the cross-section obtained, the area of fibre in a cross-section can be determined through software imaging analysis. Destructive measurement of SF area is found to be the most accurate method to determine SF cross-sectional area (Akkaya et al., 2000).

### 1.4 Research Significance

Through the combination of a proposed theoretical model based on classical flexural stress distribution model and laboratory data obtained around SF, the study aims to draw some simple yet meaningful relationships between SF and its subsequent interaction with concrete. The interaction between SF and key structural properties of concrete such as ductility and flexural behaviour will be investigated. As a result, the outcomes of the study will contribute to expand the database on SFRC and lead to further research in the field.