There is nothing new about strengthening concrete with steel. One hundred years ago, a patent was filed to incorporate steel shavings into a concrete mix to increase its strength and stability.
However, it was not until the 1960s that the modern development of fibre reinforced concrete (FRC) began. The cracking tensile strength of concrete is one of its main drawbacks but it was realised that this could be significantly increased by adding fibres. Employed initially for applications such as industrial flooring, the 1980s saw FRC begin to be used for underground applications, initially using shotcrete (sprayed concrete or gunite) and then later concrete tunnellining segments.
Reinforced concrete tunnel linings have traditionally been cast insitu. However, the development of tunnel boring machines (TBMs) accelerated the use of precast tunnel segments (Figure 1), and they are now commonly used in tunnels worldwide.
The use of FRC precast tunnel segments provides several advantages. These include reduced cracking during construction, higher impact resistance, high durability in the final stage, cost reductions, improved sustainability and increased productivity.
Bulletin 83 from the Federation Internationale du Beton (fib), based on the Model Code 2010, is the accepted recommendation for the design of FRC for structural precast tunnel segments in underground construction. It provides the structural engineer with advice on how to quantify the reinforcing properties of steel fibres based on the measured post-crack tensile strength of steel fibre reinforced concrete (SFRC).
An introduction to the behaviour of FRC
FRC is a composite material characterised by a cement matrix and discontinuous discrete fibres, which can be steel, polymers, carbon, glass or natural materials. The characteristics of the materials used and their dosage affect the final properties of the FRC.
FRC is also significantly influenced by a range of other factors, such as the geometry, the volume fraction and the mechanical properties of the fibres, the bond between fibres and the concrete matrix, and the mechanical properties of the matrix. However, the behaviour of FRC is more than a simple accumulative effect of the characteristics of the concrete matrix and the fibres. As it is a composite material, its behaviour is also impacted by the interaction between the matrix and the fibres, which means the transfer of load from the concrete matrix to the fibre system.
Conditions for efficient load transfer
For efficient load transfer, the following three conditions must be satisfied:
- There should be a sufficient exchange surface (number, length, diameter of fibres).
- The nature of the fibre-matrix interface should allow for proper load transfer.
- The intrinsic mechanical properties (Young’s modulus, anchorage and tensile strength) of the fibre should allow the forces to be absorbed without breaking or excessively elongating the fibre.
For steel fibre-reinforced concrete (SFRC), a fibre geometry should always be chosen that is relative to the compactness of the matrix, as characterised by its compression resistance, so as to avoid rupture of the fibre when the matrix cracks. Brittle (fibre tensile strength) failure of SFRC can occur at any concrete age, from 1 day to 10 years, and is a consequence of selecting an incorrect fibre type for the concrete, not the age of the concrete.
The ductility and post-crack strength of SFRC are determined by many different aspects, including concrete composition, fibre length and aspect (length/diameter) ratio. A major driver of performance is also a balanced combination of anchorage design, wire strength, wire ductility, and optimum network.
Mix design is also key. By mixing the right amount of aggregates (sand and gravel), one can achieve an optimal density with the lowest volume of pores in between the fine and coarse material, and so less mortar is required to fill these pores and glue everything together. With FRC, the aim should be for sufficient fine material/mortar (the importance of this increases for higher dosages).
The flexural (3-point) bending test
In accordance with fib bulletin 83, the structural design of SFRC elements is based on the post-crack residual tensile strength provided by the steel fibres. Nominal values of the material properties can be determined by performing a flexural bending test. One of the most common refers to EN 14651, which is based on a three-point bending test on a notched beam (Figures 2 and 2a). To obtain statistically reliable results, a minimum of 12 beam tests are recommended.
Figure 3 shows the results of beam bending texts conducted by Rome University. They show how a low variation provides a performance class type 5e according to MC2010. The results of such a bending test are expressed in terms of force (F) vs crack mouth opening displacement (CMOD).
Parameters fR,j representing the residual flexural tensile strengths are evaluated from the F-CMOD relationship according to the equation below (simplified linear elastic behaviour is assumed):
Where: fR,j is the residual flexural tensile strength corresponding to CMOD = CMODj FR,j is the load measured during the test (kN); l is the span length (distance between support) = 500 mm b is the width of the beam = 150 mm hsp is the distance between the tip of the notch and the top of the beam = 125mm
From the above residual flexural tensile strengths, the characteristic values can be evaluated as follows:
fR,jk = fR,jm – k .Vx
Where: k is the student’s factor dependent on the number of the specimens (12 beams is recommended) Vx is the standard deviation of the test results
The standard deviation could be influenced by many parameters such as mix design, casting, and testing, and is also strongly influenced by the fibre number and network effect. A higher fibre network leads to a lower standard deviation, which is key to achieve the required characteristic value for design.
For the classification of the postcrack strength of FRC, a linear elastic behaviour can be assumed by considering the characteristic residual flexural strength values that are significant for serviceability (fR,1k) and ultimate (fR,3k) conditions. Two parameters are especially important, and need to be specified by the designer, namely: fR,1k: the minimum value for SLS fR,3k: the minimum value for ULS.
Materials with fR,1k ranging from 4MPa to 5MPa are commonly used for precast tunnel segments without any bar reinforcement, combined with a fR3k/fR,1k ratio in the ranges 0.9< fR3k/ fR,1k <1.1 or 1.1< fR3k/ fR,1k <1.3 (class c or class d respectively, according to the Model Code 2010 definition.
Hardening post-crack behaviour at section level (through a beam test) immediately allows for crack control and for SLS design.
Dramix 4d steel fibres For FRC
After many years of experience, Bekaert specifically designed its Dramix 4D 80/60BGP for precast tunnel segments. It has a nominal tensile strength of 2,200N/mm2, a Young’s Modulus of 200,000N/mm2, and the strain at ultimate strength is 0.8%. Dramix 4D 80/60BGP is supplied with a fibre length of 60mm and diameter 0.75mm, giving an aspect ratio (length/diameter) of 80.
Dramix steel fibres are bundled with water-soluble glue. The glue helps avoid fibre balling during mixing and ensures a homogeneous distribution of fibres throughout the concrete. Dramix 4D provides optimal crack control for standard, statically-indeterminate concrete structures that are submitted to regular static, fatigue and dynamic loadings with high serviceability. Dramix 4D Premium is a high-performing fibre which creates optimal ductility in highstrength concrete.
Improving anchorage and ductile behaviour
In recent years, demand has increased for higher compressive strengths for precast segments from C40 to C70. This is driven by the need for more structural requirements, to address durability issues, and early age demoulding for increased production capacities. Unfortunately, the increase in concrete strength with age and hence better bond to the fibres leads to fibre failure in the cracks rather than bond failure, resulting in a much more brittle behaviour.
Fibres provide a more ductile behaviour when they are gradually pulled out, and for this, hooked ends are essential. Such a mechanism actually generates the renowned concrete ductility and post-crack strength. Dramix 4D steel fibres use this technology, which translates into improved anchorage and ductile behaviour. The white paper mentioned at the end of this article examines this in more detail.
Maintaining the network effect
A correct network effect is key to optimise cracking control, post-crack behaviour, fibre homogeneity and dispersion in combination with glued fibre, and low dispersion in the result.
Keeping the same network effect is essential to ensure consistent behaviour and cracking control.
For example, a fibre with an aspect (length/diameter ratio) of 80 (60mm length, 0.75mm diameter) offers a network higher than 11km/m3 with a fibre content of 40kg/m3. A minimum network of 10km/m3 is recommended; for this a fibre length/ diameter ratio of 65 (60mm length, 0.9mm diameter) will need a fibre content of about 55kg/m3. This means that using a fibre diameter of 0.9mm versus one of 0.75mm adds about 40% more kg/m3 to achieve the same minimum network. Aside from the extra cost, this additional dosage will also lead to side-effects, both in terms of the mixing and the workability. Table 1 summarises the parameters of two common networks.
Optimising the mix design
Finally, it is worth pointing out that for FRC precast segments to be successful, work needs to be conducted at an early stage of the project on the mix design optimisation, while keeping in mind that a composite material is being developed. In addition, bending tests have to be performed such as the EN 14651 test method described above. These tests allow the classification of the FRC according to fib bulletin 83, Model Code 2010.
Choosing the right fibre to achieve the right performance is essential, but it should be undertaken in a structured way to achieve the full benefits in terms of performance, quality and cost of the project. Dramix 4D 80/60BGP offers a hardening post-crack behaviour (crack-width control, SLS design) and low variation in the result to guarantee a high-performance class according to the MC 2010 classification.
