Mechanical Parameters and Post-Cracking Behaviour of HPFRC according to Three-Point and Four-Point Bending Test

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 fourpoint 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 themechanical parameters of HPFRC material.


Introduction
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 [1][2][3] and the tensile post-peak behaviour improve as well as a greater fracture energy can be observed [4][5][6].
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 postcracking 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 [7][8][9]; UNI 11039-1 [10]; UNI 11039-2 [11]; ASTM C 1550 [12]; ASTM C 1609 [13]; ASTM C 1399 [14]; EN 14651 [15].The most common experimental test set up for post-cracking and toughness measurement is the beam bending test carried out on beams with a notch at the tensile side [16].Recently, the European Committee has proposed a three-point bending test procedure, while the Italian Committee has suggested a four-point bending test configuration.Furthermore, the recent guidelines CNR-DT 204 [17] and Fib 55 [18] have proposed, for analysis and design of FRC (or HPFRC) structural members, stress-opening and stress-strain relationship in uniaxial tension identified by means of four-point and three-point bending tests, respectively.Nevertheless, recent literature [19,20] underlines how the scientific community is still debating to single out the best bending test between the two configurations and/or to define a relationship between them.
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 [15]) and the four-point bending tests (UNI 11039-2 [11]).With reference to these standards, experimental bending tests were carried out on HPFRC notched beams with the following goals: (i) to evaluate the contribution of the fibres with high aspect ratio to the post-cracking behaviour of the high strength concrete; (ii) to evaluate the mechanical properties and the postcracking behaviour of the HPFRC by using the two bending test methodologies; (iii) 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.

Research Significance
With reference to HPFRC prismatic notched specimens, the experimental and analytical results obtained with three-point bending tests, according to EN 14651 [15], and those obtained with four-point bending tests, according to UNI 11039-2 [11], are critically examined.The purpose of this work is to analyse and compare the obtained results with reference to peak load, post-peak behaviour, and residual strengths, also highlighting the fibre contribution in mode I fracture behaviour with respect to the plain concrete (PC) matrix.
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.

Test Program
3.1.Specimens.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 fourpoint 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  1 shows the PC and HPFRC (DS1% and DS2%) composition for 1 m 3 of concrete batch used in the experimental program.Plain concrete was designed for a 28-day cubic strength of 80 MPa.
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 [6].All the test specimens were removed from the moulds within 24 hours and cured for 27 more days under water saturated sand.

Instrumentation and Test
Procedure.The compressive strength tests were carried out after 28 days from cast on 150 mm cubes, according to UNI EN 12390-3 [21].A Zwick/Roell servo hydraulic closed-loop test machine with a capacity of 3000 kN was used.The bending tests were performed after 28 days from cast on 150 × 150 × 600 mm prismatic specimens.At the midspan of the specimens, a single notch was sawn with a diamond blade to localize the crack, with a depth of 25 mm, according to EN 14651 [15], Advances in Civil Engineering  or a depth of 45 mm, according to UNI 11039-2 [11].The specimens dimensions and the test setup required by the two standards are shown in Figures 1 and 2. In these figures, the total applied load is labelled with the letter , in the case of three-point bending test according to EN 14651 [15], and with the letter  in the case of four-point bending test according to UNI 11039-2 [11].The tests were carried out by imposing a displacement rate of 0.05 mm/min.A 100 kN type C1 HBM load cell was mounted on an INSTRON 1195 electromechanical testing machine.Two or four WA20 HBM linear variable displacement transducers (LVDTs) inductive displacement transducers were used to measure the vertical displacement under the load point on the two specimen faces.The transducers were fixed on a rigid yoke accurately mounted on the specimen in order to minimize the effect of rotation during the test.Furthermore, two WI10 HBM LVDTs were placed at the tip notch on the two faces of the specimens to measure the crack tip opening displacement (CTOD).The crack mouth opening displacement (CMOD) was measured by a TML resistive full bridge transducer astride the notch.The data acquisition and signal control were carried out by using an HBM Spider 8 control unit.The experimental setup used to carry out the three-point bending tests is shown in

Behaviour in Compression.
The cube compressive peak strength of each tested specimen and the mean value of the compressive strength are given in Table 2.It can be noticed that the cube compressive peak strength is not substantially   influenced by the addition of steel fibres.This result was made possible because all specimens (PC and HPFRC) were made from mixes with the same fineness modulus; the effect of the addition of fibres to the compressive peak strength was negligible.

Peak Load and Deflections in the Bending
Tests.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 () curves of the HPFRC specimens are shown in Figure 3.The CTOD given here is the average value between the front and the rear measurements.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 threepoint 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 3), while it is about three and five times higher for specimens subjected to four-point bending tests (Table 4).
The mean value of the peak load and the strength factors (S.F.) evaluated for all specimens is given in Table 5 for both three-point and four-point bending tests.
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 threepoint 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 3).The higher residual forces at a greater deflection value is due to the presence of the hooked end fibres with a long embedded length.In fact, both these aspects provide higher pull out force at larger crack widths.(2007).With reference to the curves experimentally recorded, the load at the limit of proportionality,   , the corresponding strength,   ct, , and the residual flexural strengths,  , , were evaluated according to EN 14651 [15].

EN 14651
According to this recommendation, the load at the limit of proportionality (  ) is equal to the highest value of the load recorded up to CMOD value of 0.05 mm, and the strength corresponding to the limit of proportionality (LOP) can be computed using the following expression: where  (150 mm), ℎ sp (125 mm), and  (500 mm) are the width, the distance between the tip of the notch and the top of the specimen, and the span of the specimen, respectively.The residual flexural tensile strengths  ,1 ,  ,2 ,  ,3 , and  ,4 at the CMOD value of 0.5 mm, 1.5 mm, 2.5 mm, and 3.5 mm (Figure 4) were also computed.In general, the residual flexural strength  , is given by the following expression: Advances in Civil Engineering All these expressions were defined a linear stress distribution the cross section.The results are all reported Table 6.
In case of testing machine controlling the 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  = 0.85 ⋅ CMOD + 0.04 (mm) . ( ,1 can be used in the verification of the serviceability limit states, while  ,4 is applied in the ultimate limit state analysis.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,  ,1 ,  ,2 ,  ,3 , and  ,4 increase of about 23%, 31%, 42% and 50%, respectively, for specimens with 2% of fibre volume content compared to the specimens with 1% of fibre volume content.This highlights that the volume content of steel fibres contributes mainly on the post-peak behaviour (Table 6).4.4.UNI 11039-2 (2003).According to UNI 11039-2 [11], the following parameters have to be evaluated to describe the post-cracking behaviour of HPFRC materials: the first crack load ( If ), the first crack nominal strength ( If ), the equivalent strengths ( eq(0−0.6),  eq(0.6−3) ), and the ductility indexes ( 0 ,  1 ).The first crack nominal strength represents the matrix behaviour and can be computed using this expression:

CMOD (mm)
where  (150 mm), ℎ (150 mm), and  (450 mm) are the width, the height, and the span of the specimen, respectively, and  0 (45 mm) is the height of the notch, and  If corresponds to the value of the load recorded for a crack tip opening displacement equal to CTOD 0 ; the latter is the CTOD corresponding to the peak load of a reference PC specimen (mean value).The parameters  eq(0−0.6)and  eq(0.6−3) are the average nominal stresses in the CTOD range between 0 and 0.6 mm and in the range between 0.6 mm and 3 mm, respectively.These two parameters are the post-cracking equivalent strength useful for the serviceability limit state and for the ultimate limit state, respectively.
These parameters can be computed by using the following expressions: where  1 and  2 can be evaluated as (Figure 5): The ductility indexes can be calculated by the following equations: eq(0−0.6) .
(  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 7. The loads/strengths at first crack reach similar values with the increase of fibre volume content.The equivalent strengths,  eq(0−0.6)and  eq(0.6−3), and the ductility indexes,  0 and  1 , increase of about 46% and 62% and of about 44% and 9%, respectively, for specimens with 2% and 1% of fibre volume content (Table 7).

Three-Point versus Four-Point Bending Tests
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 fourpoint 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 3, 4, and 5).
Specifically, the results on PC specimens lead to peak load values for four-point bending tests lower than threepoint 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 threepoint 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 [15] and to the UNI 11039-2 [11], have similar shapes.The curves recorded during the four-point bending tests are more stable compared to those of threepoint bending tests.The curves of the HPFRC specimens with 1% and 2% of fibre volume fraction, recorded during the three-point bending tests, show in general peak and postpeak stress values that are lower than those reached during the four-point bending tests.In fact, the residual stresses evaluated at a CTOD value of 3.00 mm with reference to the typical curves recorded during the three-point bending tests are lower of about 20-30%, respectively, than those recorded during the four-point bending tests, for HPFRC specimens with 1% and 2% of fibre volume content (Figure 3).
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 fourpoint 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 [15] and the UNI 11039-2 [11], concern the determination of the first crack point, the way of using the post-cracking response to evaluate the equivalent/residual strengths within ranges of practical interest.
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 [15], the first crack point corresponds to the maximum load recorded in the range between 0.00 and 0.05 mm of CMOD.In this study, the first crack point matches the 0.05 mm.It is important to underline that it is a similar approach to the one proposed by the RILEM TC 162-TDF [8].According to the RILEM indication, the first crack point corresponds to the maximum load recorded in the range between 0.00 and 0.05 mm of the deflection.The range proposed in both cases is arbitrary, and scientific considerations are not available.According to UNI 11039-2 [11], the first crack point of the HPFRC specimens can be joined to the crack of the concrete matrix.So, it can be assumed that the first crack arises when the extreme tensile concrete fibre at the tip of the mouth reaches the maximum tensile strain.It is possible to evaluate directly, on three PC notched specimens, the value of CTOD 0 as the mean value of the CTOD measured during the four-point bending tests that corresponds to the maximum load.In the case studied, the value of CTOD 0 assumed is 0.023 mm.It is also possible to evaluate CTOD 0 indirectly, assuming the value of 25 m.Despite these two different procedures, the first crack strengths evaluated according to the standard UNI 11039-2 [11] ( If ) and to the European standard EN 14651 [15] (  ct, ) lead to similar values.The European standard showed a higher value of about 10% compared to the UNI standard.
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 [11] proposes the concept of equivalent strength to evaluate parameters that are used to define

Figure 1 (
b), while the one used in the case of four-point bending tests is shown in Figure 2(b).

Table 1 :
Mixture proportions per 1 m 3 of PC and HPFRC concrete.

Table 3 :
Three-point bending tests: peak loads and corresponding stresses.

Table 4 :
Four-point bending tests: peak loads and corresponding stresses.

Table 5 :
Peak loads and strength factors for three-point and fourpoint bending tests.