Compressive behaviour of steel fibre reinforced concrete
- —- A study by Rui D Neves, and Joao C. O. Fernandes : Lisbon, Portugal
An experimental study to investigate the influence of matrix strength, fibre content and diameter on the compressive behaviour of steel fibre reinforced concrete is presented. Two types of matrix and fibres were tested. Concrete compressive strengths of 35 and 60 MPa, 0.38 and 0.55 mm fibre diameter, and 30 mm fibre length, were considered. The volume of fibre in the concrete was varied up to 1.5%. Test results indicated that the addition of fibres to concrete enhances its toughness and strain at peak stress, but can slightly reduce the Young’s modulus.
Simple expressions are proposed to estimate the Young’s modulus and the strain at peak stress, from the compressive strength results, knowing fibre volume, length and diameter. An analytical model to predict the stress–strain relationship for steel fibre concrete in compression is also proposed. The model results are compared with experimental stress–strain curves.
by means of confinement with transverse reinforcement. For structures where ductility is very important, such as seismic-resistant reinforced concrete structures, the design and detailing of confinement reinforcement is often difficult, requiring more labour and quality control and affecting construction costs. The recognised ability of fibres to improve ductility of concrete1 –5may be used to overcome that difficulty. Other potential uses of steel fibre reinforced concrete are the compressive layers of block-and-beam and pre-cast permanent formwork floors, or discontinuity regions, where loading paths are complex, such as corbels, deep beams and post-tensioning anchorage zones.
In this context, it is important for designers to know the compressive behaviour of steel fibre reinforced concrete. The aim of the present work was to develop analytical expressions to estimate the main parameters that characterise the behaviour of steel fibre reinforced concrete in compression.
To evaluate the influence of steel fibres on the compressive behaviour of concrete, two different mixes and two different fibres were used. Concrete mix proportions are indicated in Table 1. The aggregates were siliceous natural sand and crushed limestone (gradings shown on Figure 1). The steel fibres were hook-ended of length lf = 30 mm, diameter df = 0.55 mm and df = 0.38 mm (Table 2), and they were added to the two mixes in volume contents up to Vf = 1.5%.
The concrete was mixed using a laboratory pan-mixer, with mixing times ranging from 3 to 6 min, and compacted on a vibrating table. The compacting time varied between 40 and 60 s, depending on the concrete workability.
Demoulding occurred 24 h after mixing and then the specimens were kept in a wet chamber until required for testing at 42 days.
As matrix and fibre type and content varied, different composites were tested. Their identification is shown in Table 3, which shows the mix designation (A, B), followed by the fibre content (in kg/m3) and then the fibre type (Z, R). Each composite was represented by a set of six cylinders, 150 mm in diameter and 300 mm in height.
Tests were performed in a closed-loop, servo-controlled compression testing machine with a load capacity of 5000 kN and an
The development of concrete technology has made it possible to reach, for ordinary production processes, compressive strengths as high as 100 MPa. However, such an increase in compressive strength is in general associated with brittler behaviour of the concrete. In structural applications brittleness can be prevented
approximate stiffness of 2300 kN/mm.6 Before testing, the two ends of each specimen were made parallel by grinding. The tests were performed under displacement control with a plate displacement rate of 0.01 mm/s, which corresponds to the lowest limit of the interval identified in Ref. 7. To measure the deformations of the specimens and the force, a clamp type extensometer (HBM DD1) and a load cell HBM P3MB were used. The methods used to determine Q–e curves from load–displacement data and to calculate the average curve
representing each composite are described in Neves.8
Test results and analysis
The main parameters that characterise the compressive behaviour of concrete are the slope of the ascending branch (Young’s modulus), the compressive strength, the strain at peak stress and the area under the Q–e curve (toughness). These parameters were determined from the respective average curve
for each composite and are presented in Table 4.
The test results (Figure 2) illustrate the well-known relation between compressive strength and Young’s modulus, and also show that the presence of fibres causes a slight decrease in Young’s modulus. Similar behaviour has been reported by other authors9,10 and can be explained because fibres parallel to the load direction can act like voids and also due to the eventual additional voids caused by fibre addition.
The reinforcement provided by fibres can work at both a micro and macro level. At a micro level fibres arrest the development of micro-cracks, leading to higher compressive strengths, whereas at a macro level fibres control crack opening, increasing the energy absorption capacity of the composite. Although the primary purpose of fibre reinforcement is to improve energy absorption capacity after macrocracking of the matrix has occurred, this reinforcement often works also at a micro level. The ability of the fibre to control microcracking growth depends mainly on the number of fibres, deformability and bond to the matrix.11 A higher number of fibres in the matrix leads to a higher probability of a micro-crack being intercepted by a fibre. If the fibre is
stiff enough and it is well bonded to the matrix, it can prevent the microcrack developing.
On the other hand, fibre addition causes some perturbation of the matrix, which can result in higher voidage.12 Voids can be seen as defects where microcracking starts. In addition to fibre quantity, perturbation also depends on the ability of the matrix to accommodate fibres, which is an important property of the mortar fraction of the concrete.
Therefore the influence of fibres on the compressive strength may be seen as the balance between microcrack bridging and additional voids caused by fibre addition. In the present study different influences were observed (Figure 3): the R fibres increased the strength of the composites by up to 9% whereas the Z fibres reduced it by up to 20%.
As the compressive strength of the steel fibre reinforced concrete depends not only on the fibre type and volume, but mainly on the mix characteristics and as compression testing is quite simple, it is recommended to evaluate the compressive strength by testing, rather than by analytical expressions.
Strain at peak stress
The strains at peak stress obtained in this work
(Figure 4) indicate an increase of e0 with compressive strength, as already observed by other
Knowing Young’s modulus, compressive strength and strain at peak stress, one can express q as a function of p, using equation (7), thus reducing to 1 the number of parameters to be determined. Assuming different values for p, and calculating the sum of square errors (SSE) between points of the experimental curve and the points of the analytical one, led to a value of p that minimises the error between both curves. Figures 7 to 10 show the suitability of the proposed expression to model the compressive behaviour of plain and steel fibre reinforced concrete with strengths and fibre volumes up to 60 MPa and 1.5%, respectively.
The sets of p values that minimise the error between experimental and theoretical curves of each composite are presented in Figure 11.
The ability of the proposed set of expressions to predict the stress–strain curve of steel fibre reinforced concrete, even for concrete with compressive strength up to 80 MPa or fibre volumes up to 2.0% is illustrated in Figure 13. The results presented by Otter and Naaman,24 and Hsu and Hsu,25 are compared with the theoretical behaviour given by the proposed model.
It should be pointed out that the results presented in Refs 24 and 25 were also obtained for concrete reinforced with hook-end steel fibres. However, when comparing the proposed model application with the results from other researchers using different experimental conditions, namely straight fibres or smaller specimens, such as cylinders with 100 mm diameter and 200 mm height, the agreement was not so good. So, in situations in which the fibres are of different shape, different specimens or even different coarse aggregate is used, the proposed model needs further calibration.