High performance fibre reinforced concrete (HPFRC) is a modern structural material with a high potential and with an increasing number of structural applications. Structural design of HPFRC elements is based on the post-cracking residual strength provided by fibre reinforcement, and for structural use, a minimum mechanical performance of HPFRC must be guaranteed. To optimize the performance of HPFRC in structural members, it is necessary to establish the mechanical properties and the post-cracking and fracture behaviour in a univocal and reliable way. The best test methodology to evaluate the post-cracking and toughness properties of HPFRC is the beam bending test. Two different types of configurations are proposed: the three-point and the four-point bending tests. The overall focus of this paper is to evaluate the mechanical properties and the post-cracking and fracture behaviour of HPFRC, using the two different standard test procedures. To achieve these aims, plain and fibre concrete specimens were tested. All the test specimens were extensively instrumented to establish the strength properties, crack tip and crack mouth opening displacement, and post-cracking behaviour. The results of the two types of bending tests were critically analysed and compared to identify and highlight the differing effects of the bending load configurations on the mechanical parameters of HPFRC material.
High performance fibre reinforced concrete (HPFRC) is a composite material characterized by a cement matrix and discrete fibres. Fibres are active as soon as microcracks are formed in the concrete. The main advantage of adding fibres to concrete is that they generate a post-cracking residual tensile strength in combination with a large tensile strain. As such, the fibre reinforced concrete (FRC) and the HPFRC are characterized by substantial ductility and toughness.
It is well known that the use of an adequate amount and an appropriate shape of steel fibres increases the tensile strength and the ductile behaviour of the concrete matrix. As the fibre volume content increases, the compressive [
To optimize the structural design of HPFRC members, it is essential to know the mechanical and fracture properties of the material. These properties have to be evaluated on standard specimens and with standard recommendations. In the past, various types of specimens, testing procedures, and parameters have been proposed to analyse the post-cracking behaviour in tension and toughness properties; as a result, some aspects were debated and revised by scientific and technical committees. With the purpose of establishing standard procedures, many national and international technical committees published several standards on concrete reinforced with steel fibres. The main standards available in the recent literature are RILEM TC 162-TDF [
By using the beam bending test, that is, the most common experimental test set, the post-cracking tensile behaviour of HPFRC materials has been analysed in this work. Two types of configurations have been recommended by the main standards, such as the three-point bending tests (EN 14651 [ to evaluate the contribution of the fibres with high aspect ratio to the post-cracking behaviour of the high strength concrete; to evaluate the mechanical properties and the post-cracking behaviour of the HPFRC by using the two bending test methodologies; to compare the main results obtained by using the two different standard procedures with particular reference to the mechanical parameters that are used in structural design.
With reference to HPFRC prismatic notched specimens, the experimental and analytical results obtained with three-point bending tests, according to EN 14651 [
The comparison among the main mechanical parameters evaluated by using the two standard recommendations allows to point out the differences in defining the structural design parameters of the HPFRC. Furthermore, ductility indexes of the HPFRC useful in structural design were evaluated.
The experimental analysis was carried out on PC and HPFRC, cube and notched prismatic specimens. The adopted volume fraction of dramix steel (DS) fibres was 1% and 2%. Compressive tests as well as three-point and four-point bending tests were carried out to highlight the role of the steel fibres with high aspect ratio on the compressive and tensile behaviour, respectively.
A generic group of HPFRC specimens has the following label type: DS1% and DS2% for specimens with 1% and 2% of fibre content (percentage by volume), respectively. While for ordinary concrete, the label PC is used.
The concrete components were the following: Portland cement ASTM type I, crushed coarse aggregates, spherical quartz sand, water, condensed silica fume, and superplasticizer. The maximum size of the coarse aggregates was 15 mm. The steel fibres had hooked ends, a tensile strength of 1050 MPa, a length (
Table
Mixture proportions per 1 m3 of PC and HPFRC concrete.
Material | Symbol | Unit | PC | HPFRC | |
---|---|---|---|---|---|
DS1% | DS2% | ||||
Cement | c | (kg) | 500 | 500 | 500 |
| |||||
Quartz | 0/2 mm | (kg) | 406 | 406 | 406 |
3/6 mm | (kg) | 294 | 294 | 294 | |
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Coarse aggregate | 0/5 mm | (kg) | 540 | 462 | 383 |
5/10 mm | (kg) | 222 | 222 | 222 | |
10/15 mm | (kg) | 240 | 240 | 240 | |
| |||||
Fibre |
|
(%) | 0 | 1 | 2 |
— | (kg) | — | 78 | 157 | |
| |||||
Silica fume | sf/c | % | 5 | 5 | 5 |
— | (kg) | 25 | 25 | 25 | |
| |||||
Superplasticizer | sp/c | % | 1.5 | 1.5 | 1.5 |
— | (kg) | 7.5 | 7.5 | 7.5 | |
| |||||
Water | w/c | — | 0.35 | 0.35 | 0.35 |
w | (l) | 175 | 175 | 175 |
The experimental compressive strength varied between 79.2 MPa and 81.0 MPa.
In order to obtain a cohesive and flowable mixture and a uniform fibre distribution, a well-defined mixing procedure was performed. The sample preparation is given elsewhere [
The compressive strength tests were carried out after 28 days from cast on 150 mm cubes, according to UNI EN 12390-3 [
Three-point bending test.
Specimen dimensions
Experimental test setup
Four-point bending test.
Specimen dimensions
Experimental test setup
The cube compressive peak strength of each tested specimen and the mean value of the compressive strength are given in Table
Cube compressive strength.
Specimens | Strength (MPa) | Mean value (MPa) |
---|---|---|
PC_1 | 80.2 | 80.1 |
PC_2 | 81.0 | |
PC_3 | 79.2 | |
| ||
DS1%_1 | 82.7 | 80.5 |
DS1%_2 | 80.7 | |
DS1%_3 | 78.2 | |
| ||
DS2%_1 | 78.4 | 78.2 |
DS2%_2 | 76.0 | |
DS2%_3 | 80.2 |
The behaviour of the ordinary concrete specimens was almost linear-elastic up to the peak load, followed by a slight descending branch up to failure, and then, the complete separation of specimens into two parts occurred. PC specimens subjected to three-point bending tests exhibited the same brittle behaviour as observed in the four-point bending tests.
On the contrary, HPFRC specimens showed a trilinear variation with an extensive cracking process between the first crack load and the peak load that clearly differentiated them from the PC specimens. In the region near the maximum load, there was a stable crack propagation due to the effect of the fibres on the ligament surface. After reaching the peak load, load decay occurred depending on the amount of steel fibres on the fracture surface. As microcracks grew towards larger macrocracks, the use of long hooked end fibres with high aspect ratio became more active in the crack bridging actions. The typical experimental load-CMOD, load-CTOD, and load-deflection (
Typical experimental curves: (a) load-CMOD; (b) load-CTOD; (c) load-deflection.
The comparison of the curves obtained according the two different standard procedures highlights that HPFRC specimens with 1% of fibre content subjected to four-point bending tests showed the same performance of HPFRC specimens with 2% of fibre content subjected to three-point bending tests in terms of peak load and descending branch, while the specimens subjected to three-point bending tests showed more extended deflections compared to the specimens subjected to four-point bending tests. The peak loads of the HPFRC specimens increase with the increase of steel fibre volume content. Specifically, for HPFRC with 1% and 2% of fibre volume content, the maximum load is about two and three times higher, respectively, compared to that of PC for specimens subjected to three-point bending tests (Table
Three-point bending tests: peak loads and corresponding stresses.
Specimens | Peak load | Peak stress |
---|---|---|
kN | MPa | |
PC_1 | 18.7 | 6.0 |
PC_2 | 17.4 | 5.6 |
PC_3 | 17.3 | 5.5 |
Mean value |
|
|
DS1%_1 | 43.8 | 14.0 |
DS1%_2 | 42.4 | 13.6 |
DS1%_3 | 30.8 | 9.9 |
Mean value |
|
|
DS2%_1 | 49.5 | 15.8 |
DS2%_2 | 47.7 | 15.3 |
DS2%_3 | 46.1 | 14.8 |
Mean value |
|
|
Four-point bending tests: peak loads and corresponding stresses.
Peak load (kN) | Peak stress (MPa) | |
---|---|---|
PC_1 | 16.4 | 4.5 |
PC_2 | 13.5 | 3.7 |
PC_3 | 17.3 | 4.7 |
Mean value |
|
|
DS1%_1 | 46.0 | 12.5 |
DS1%_2 | 50.4 | 13.7 |
DS1%_3 | 47.3 | 12.9 |
Mean value |
|
|
DS2%_1 | 84.2 | 22.9 |
DS2%_2 | 80.9 | 22.0 |
DS2%_3 | 67.7 | 18.4 |
Mean value |
|
|
The mean value of the peak load and the strength factors (S.F.) evaluated for all specimens is given in Table
Peak loads and strength factors for three-point and four-point bending tests.
Bending test |
PC | 1% | S.F. | 2% | S.F. |
---|---|---|---|---|---|
kN | kN | — | kN | — | |
Three-point | 17.8 | 39.0 | 2.19 | 47.8 | 2.69 |
Four-point | 15.7 | 47.9 | 3.05 | 77.6 | 4.94 |
Once the peak load is reached, load carrying capacity decays, with a greater amplitude if the number of the fibres on the fracture surface is lesser.
The residual load evaluated at a CTOD value of 3 mm is about 73% and 79% of the peak load for a volume content of steel fibres of 1% and 2%, respectively, in the case of three-point bending tests, and it is about 89% and 90% for 1% and 2% of steel fibre content, respectively, of their peak load, in the case of four-point bending tests (see Figure
With reference to the curves experimentally recorded, the load at the limit of proportionality,
According to this recommendation, the load at the limit of proportionality (
The residual flexural tensile strengths
Typical load-CMOD curve from EN 14651 (2007).
All these expressions were defined assuming a linear stress distribution on the cross section. The results are all reported in Table
Three-point bending tests: tensile strength parameters.
|
|
|
|
|
| |
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kN | MPa | MPa | MPa | MPa | MPa | |
DS1%_1 | 30.2 | 9.7 | 13.8 | 12.6 | 11.6 | 10.7 |
DS1%_2 | 21.5 | 6.9 | 11.8 | 12.4 | 11.4 | 9.8 |
DS1%_3 | 19.1 | 6.1 | 8.0 | 9.7 | 7.1 | 5.4 |
Mean value |
|
|
|
|
|
|
DS2%_1 | 24.7 | 7.9 | 14.1 | 15.7 | 15.4 | 14.7 |
DS2%_2 | 24.2 | 7.7 | 13.7 | 15.1 | 14.3 | 13.1 |
DS2%_3 | 23.5 | 7.5 | 13.5 | 14.7 | 13.0 | 11.0 |
Mean value |
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|
|
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|
In case of testing machine controlling the rate of increase of deflection, the European Committee suggests that the CMOD related parameters are transformed into deflection related parameters. The relation between CMOD and deflection may be approximated by
The strengths at the limit of proportionality reach similar values, and they are not affected by the increase of fibre volume content, while the residual strengths,
According to UNI 11039-2 [
The first crack nominal strength represents the matrix behaviour and can be computed using this expression:
The parameters
These parameters can be computed by using the following expressions:
Typical load P-CTOD curve from UNI 11039-2 (2003).
The ductility indexes can be calculated by the following equations:
These indexes are the slope of the descending branch of the load-CTOD curve that represents the brittleness of the material. All these expressions were defined assuming a linear stress distribution on the cross section. The above parameters are given in Table
Four-point bending tests: tensile strength parameters.
|
|
|
|
|
| |
---|---|---|---|---|---|---|
kN | MPa | MPa | MPa | — | — | |
DS1%_1 | 26.3 | 7.2 | 10.5 | 12.0 | 1.5 | 1.1 |
DS1%_2 | 24.6 | 6.7 | 11.6 | 13.2 | 1.7 | 1.1 |
DS1%_3 | 24.7 | 6.7 | 11.1 | 12.3 | 1.7 | 1.1 |
Mean value |
|
|
|
|
|
|
DS2%_1 | 25.6 | 7.0 | 17.4 | 22.3 | 2.5 | 1.3 |
DS2%_2 | 26.3 | 7.2 | 16.0 | 21.2 | 2.2 | 1.3 |
DS2%_3 | 25.6 | 7.0 | 15.3 | 17.4 | 2.2 | 1.1 |
Mean value |
|
|
|
|
|
|
The loads/strengths at first crack reach similar values with the increase of fibre volume content. The equivalent strengths,
The most common test used for evaluating the mechanical and fracture properties of HPFRC in mode I crack propagation is the bending test. Different configurations of bending test and different specimen geometry are proposed by the current standards. By varying the distribution of the load on the specimen and by varying the geometry of the specimen, the stress redistribution in the midspan section varies as well. The latter plays a critical role in the evaluation of the test results and consequentially in the definition of the parameters that can be used in the design of HPFRC members with conventional steel reinforcements.
In the case of three-point bending tests, in the midspan zone of the specimens, subjected to maximum bending and shear, the fracture process is influenced by a wedge diffusion of the applied load. The uncoupling of bending and shear is generally assumed for the specimens subjected to four-point bending test, in the central region between the applied loads, being the fracture process negligibly influenced by local effects due to load diffusion. However, the presence of the notch in the midspan section modifies the stress pattern, and shear stresses are not irrelevant in the central zone.
The experimental data highlight some important points. Firstly, the notched PC specimens subjected to four-point bending tests show flexural peak stresses which are consistently lower than those obtained in three-point bending tests, whereas for notched HPFRC specimens, the reverse is true (Tables
Specifically, the results on PC specimens lead to peak load values for four-point bending tests lower than three-point bending tests of about 12%. The peak stress values, computed according to a simple elastic analysis considering the different geometry of the two types of tests, are lower of about 25%. This is due to the effect of the point load prevailing in the three-point bending tests. The resulting increase in the internal lever arm, along critical cross section, stands as the reason for the increased nominal stress. These considerations are not confirmed for the HPFRC specimens. For the specimens with 1% of fibre content (DS1%), the difference is very slight. The specimens subjected to three-point bending tests show peak stress values which are lower of about 4% than those obtained from the four-point bending tests. While for specimens with 2% of fibre volume content (DS2%), the difference is of about 27%.
The experimental curves of the same type of HPFRC specimens detected during the bending test, performed according to the EN 14651 [
The results obtained allow to compute the fracture energy directly as the area under the load-deflection curve or indirectly from the load-crack opening displacement curve up to a value that limits the long softening branch and through a suitable model for the kinematics of the bent beam. The area under the load-deflection curve evaluated referring to a limit displacement value of 3.00 mm recorded during three-point bending tests is lower of about 20–40% than that obtained by four-point bending tests. This means that four-point bending tests lead to higher values of fracture energy than those obtained using three-point bending tests results.
From a design point of view, the evaluation of flexural strengths parameters from these bending tests is important. The main differences between the two standards, the European EN 14651 [
A main test parameter is the first crack that is the point on the load-deflection or load-CTOD curve at which the shape of the curve first becomes nonlinear. It approximately corresponds to the onset of cracking in the concrete matrix. Beyond this point, the fibres become more active to reduce the crack opening. According to EN 14651 [
The European standard proposes the concept of residual strength to evaluate the post-cracking response. This method has the advantage of being easier to evaluate, but it is also more susceptible to the irregularities of the load-deflection relationship recorded during the tests. On the other hand, the standard UNI 11039-2 [
The consistency of the experimental curves recorded during the bending tests shows that the fibre concrete mixtures designed and manufactured in this study were all highly cohesive without fibre bundling and fibre segregation. Concrete reinforced with steel fibre with high aspect ratio and high fibre volume content requires a high quality control to produce materials with consistent quality.
In the case of plain concrete, a brittle failure occurred by separating the elements into two parts (Figure
Post-test aspect of the notched specimens without fibres.
Post-test aspect of the notched specimens with 1% of steel fibres volume content.
The following major conclusions can be drawn from this study. The experimental data obtained confirmed that the addition of steel fibres with high aspect ratio into a high strength concrete matrix significantly improves the post-peak behaviour. The HPFRC specimens showed a more extended softening branch and also the slope of the descending branch decreases. Residual loads of 70%–90% of their peak loads at a CTOD value of 3.00 mm were recorded. The loss in load capacity was gradual especially for HPFRC with 2% fibre volume content. The evaluation of the load-displacement curves of both PC and HPFRC materials proves that HPFRC contributes greatly to preserve the structural integrity and structural stability of concrete exposed to real life environments. The comparison between three-point and four-point bending tests highlights that there is not a large difference between them. A significant point is related to the peak stresses. PC notched specimens subjected to four-point bending tests show flexural peak stresses which are slightly lower than those obtained in three-point bending tests, whereas HPFRC specimens subjected to four-point bending tests show slightly higher stress values compared to those obtained in the three-point bending tests. From a design point of view, first crack strength (or LOP) values, evaluated following the two standards, are close with an improvement of 10% in the value obtained according to the European standard procedure. Although the test specimens and the HPFRC concrete composition are exactly the same, the values of the mechanical parameters obtained from the two types of test are quite different, and a notable variation in the “load-deflection,” “load-CMOD,” and “load-CTOD” curves is observed in all the HPFRC specimens, both with 1% and with 2% of fibre volume. The ductility indexes, The fracture energy evaluated in the three-point bending tests is lower of about 20% and 40% than that obtained by four-point bending tests, for HPFRC with 1% and 2% of fibre volume content, respectively.