**5. Fracture behaviour and residual load‐bearing capacity of polyolefin fibre‐reinforced concrete**

As previously mentioned, the main reason for adding fibres to a concrete formulation lies in the improvement of the flexural and tensile behaviour of plain concrete. The description of the fracture behaviour of plain concrete has significant differences due to the fibre‐rein‐ forcement nature, first and foremost, as regards the post‐peak behaviour of the material. The response of concrete‐reinforced with polyolefin fibres is conventionally characterized by testing specimens in the mesoscale under direct or flexural tensile stresses.

The uniaxial tension test, as described in several recommendations [30], can be used to deter‐ mine the tensile strength and the softening parameters and define the stress‐crack‐opening curve in FRC. The test uses a notched cylindrical specimen with both ends fixed with respect to rotation. It is conducted under controlled tensile displacements. The test setup, as shown in **Figure 10**, is rather complex and demands highly trained and experienced personnel. Therefore, as it is somewhat expensive and time‐consuming, it is not considered an appropriate method for practical material testing (only being suitable for research purposes in specialized laboratories).

The most economical and practical tests available to determine the post‐crack behaviour and assess the influence of conditions such as fibre types and dosage are bending tests. The three‐ point bending (TPB) test uses beams with a cross section of 150 × 150 mm and a span of 500 mm loaded in the middle of the upper face. A transverse notch of standard dimensions is made in the middle of the lower specimen face, in the same cross section where the load is applied. This setup, as shown in **Figure 11**, ensures that the crack is formed in this predefined position, making crack control simpler than in un‐notched beams [30, 39].

**Figure 10.** Uni‐axial tension testing for concrete [30].

such environments depends on the action of the chemical compounds that ingress in the con‐ crete bulk through the connected network of pores. In that sense, it should be underlined that the presence of fibres might offer preferential ways for such ingress. As can be seen in **Figure 9**, the permeability of the material under pressure of water is uninfluenced by the presence of fibres as there is no dependency of the penetration depth and the fibre content. Therefore, as happens with plain concretes, permeability is related to parameters such as the paste aggregate ratio and the size distribution of the aggregates used. If the type of aggregates and their pro‐ portion in the concrete mix are adequate, PFRC may be a material that bears the most hazardous of environments considered in some recommendations [12] such as those in direct contact with

marine water, erosive materials, freeze‐thaw conditions or even chemical industries.

specimens in the mesoscale under direct or flexural tensile stresses.

**Figure 9.** Permeability under pressure of water of VCC and SCC PFRC.

**fibre‐reinforced concrete**

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**5. Fracture behaviour and residual load‐bearing capacity of polyolefin** 

As previously mentioned, the main reason for adding fibres to a concrete formulation lies in the improvement of the flexural and tensile behaviour of plain concrete. The description of the fracture behaviour of plain concrete has significant differences due to the fibre‐rein‐ forcement nature, first and foremost, as regards the post‐peak behaviour of the material. The response of concrete‐reinforced with polyolefin fibres is conventionally characterized by testing

The uniaxial tension test, as described in several recommendations [30], can be used to deter‐ mine the tensile strength and the softening parameters and define the stress‐crack‐opening curve in FRC. The test uses a notched cylindrical specimen with both ends fixed with respect to rotation. It is conducted under controlled tensile displacements. The test setup, as shown in

**Figure 11.** Test set‐up in [38]. Measures in mm.

Four‐point bending tests have also been adopted by some country national recommenda‐ tions. The cross section of 150 × 150 mm has two equal loads applied in both sides of the middle third of the span [41, 45]. A typical setup is shown in **Figure 12**. The advantage of the four‐point un‐notched test is that the first crack will appear at the weakest section, there‐ fore providing for the effect of a variation of material strength. The disadvantage is that the measuring of the crack opening is harder because the crack position cannot be predicted. Therefore, obtaining a complete characterization of the material is not always possible.

Evidently, there are certain characteristics of the curves shown in **Figure 13** that depend not only on the amount of fibres used but also on the geometrical and mechanical properties of the fibres, the orientation and distribution of the fibres within the concrete element, the fresh properties of the concrete, the pouring process and, among others, the consolidation method. It is worth noting that predictive models and tools to consider such differences can be consulted in detail in references [28] and [47]. In any case, the main factor is the amount of fibres added. **Figure 14** shows how the amount of fibres changes the post‐peak mechanical

Polyolefin Fibres for the Reinforcement of Concrete http://dx.doi.org/10.5772/intechopen.69318 159

The curves depicted in **Figure 14** have several common characteristics that should be men‐ tioned. The behaviour of each curve is defined by the presence of three turning points. The first turning point took place when the loading process reached the maximum value and only a few inelastic processes were apparent (the behaviour of concrete is mostly lin‐ ear if compared with subsequent stages). The turning point where the load reaches the maximum is commonly known as the load at the limit of proportionality (*L*LOP), with it being the overall maximum load in plain concrete. A softening behaviour may also be

behaviour of PFRC.

**Figure 14.** Fracture behaviour of PFRC with several amounts of fibres.

Regardless of the testing method employed, the curves obtained show the enhancement of the mechanical properties provided by the fibres. Furthermore, the behaviour or the compos‐ ite material could be examined by taking into account the main effects regarding the plain concrete behaviour added to the contribution of the fibre reinforcement. Such a contribution depends on the crack opening and appears in the form of fibre bridging, fibre debonding and even fibre tensile failure. A theoretical scheme can be seen in **Figure 13**.

**Figure 12.** Four‐point bending test [38, 46].

**Figure 13.** Conceptual bases of the discrete entities contribution to FRC constitutive relation [28].

Evidently, there are certain characteristics of the curves shown in **Figure 13** that depend not only on the amount of fibres used but also on the geometrical and mechanical properties of the fibres, the orientation and distribution of the fibres within the concrete element, the fresh properties of the concrete, the pouring process and, among others, the consolidation method. It is worth noting that predictive models and tools to consider such differences can be consulted in detail in references [28] and [47]. In any case, the main factor is the amount of fibres added. **Figure 14** shows how the amount of fibres changes the post‐peak mechanical behaviour of PFRC.

Four‐point bending tests have also been adopted by some country national recommenda‐ tions. The cross section of 150 × 150 mm has two equal loads applied in both sides of the middle third of the span [41, 45]. A typical setup is shown in **Figure 12**. The advantage of the four‐point un‐notched test is that the first crack will appear at the weakest section, there‐ fore providing for the effect of a variation of material strength. The disadvantage is that the measuring of the crack opening is harder because the crack position cannot be predicted. Therefore, obtaining a complete characterization of the material is not always possible.

Regardless of the testing method employed, the curves obtained show the enhancement of the mechanical properties provided by the fibres. Furthermore, the behaviour or the compos‐ ite material could be examined by taking into account the main effects regarding the plain concrete behaviour added to the contribution of the fibre reinforcement. Such a contribution depends on the crack opening and appears in the form of fibre bridging, fibre debonding and

even fibre tensile failure. A theoretical scheme can be seen in **Figure 13**.

**Figure 12.** Four‐point bending test [38, 46].

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**Figure 13.** Conceptual bases of the discrete entities contribution to FRC constitutive relation [28].

The curves depicted in **Figure 14** have several common characteristics that should be men‐ tioned. The behaviour of each curve is defined by the presence of three turning points. The first turning point took place when the loading process reached the maximum value and only a few inelastic processes were apparent (the behaviour of concrete is mostly lin‐ ear if compared with subsequent stages). The turning point where the load reaches the maximum is commonly known as the load at the limit of proportionality (*L*LOP), with it being the overall maximum load in plain concrete. A softening behaviour may also be

**Figure 14.** Fracture behaviour of PFRC with several amounts of fibres.

identified that governs the branch after *L*LOP, as reported in many FRC types and espe‐ cially for PFRC [3]. The softening behaviour is a distinctive characteristic in plain concrete fracture and, in such a case a steep unloading process leads to the specimen failure and collapse. Nonetheless, the polyolefin fibres are able to absorb the energy released by the concrete in the fracture processes by the so‐called fibre bridging and change the loading tendency. At such a point, the curve reaches the minimum post‐cracking load (*L*MIN) while another uploading process starts again. The end of the load‐increasing ramp is the third remarkable point of the curve. The descending slope drawn after *L*REM continues until the end of the test. It should be noted that even at great deformation states, PFRC does not fail or collapse and that it shows remarkable improvements in ductility and toughness with respect to plain concrete.

Based on the previous description, it is easier to perceive the influence that the changes have on the behaviour that can appear when varying the amounts of polyolefin fibres added. The amount of fibres has a negligible influence on the peak load recorded in the fracture tests, and therefore *L*LOP does not change with fibre dosage. The value of *L*LOP is mainly determined by the tensile strength of the plain concrete. After reaching the peak load, the unloading part of the curve appears and such a part ends at *L*MIN that is related with the amount of fibres added. The higher volumetric fraction of fibres the greater is the value of *L*MIN obtained. It should be highlighted that, in contrast with the behaviour of an SFRC, even with volumetric fractions around 1% the value of *L*MIN greatly differs from *L*LOP. The slope of the curve between *L*MIN and *L*REM is greater as the amount of fibres added increases. In this case, it is important to note that the deflection value where *L*MIN takes place does not depend remarkably on the dosage of fibres. Nevertheless, the maximum post‐peak value *L*REM is greatly modified by the amount of fibres added.

The number of fibres present in the fracture surface generated during the tests greatly influ‐ ences the values of *L*MIN and *L*REM alike. However, not all the fibres that appear in the fracture surface influence the value of *L*MIN. Due to the limited deformation state that the sample is bearing when *L*MIN occurs, which is commonly used for service limit state (SLS) design, the contribution of fibres placed in the tensioned part of the section is more important than the rest of fibres. This corresponds to the lower third of the fracture surface generated. For high deformations, almost the whole cross section is in tension and, due to the quasi‐brittle nature of the material, would already be almost fully cracked. Therefore, the total number of fibres would bear the final load obtained in the tests. These advanced deformations would corre‐ spond to ultimate limit state design (ULS). The situations that take place in the case of SLS and ULS are shown in **Figure 15**.

fibres present in the fracture surfaces. Therefore, there are certain variations in the mechanical properties of the material that rely on other parameters unrelated with the amount of fibres added, such as the material rheology, pouring method and, among others, size of the element

**Figure 16.** Relation between the number of fibres present in the fracture surfaces and the residual loads *L*MIN and *L*REM for vibrated conventional PFRC (VCC) and self‐compacting PFRC (SCC). Tests performed following EN‐14651 in reference

Polyolefin Fibres for the Reinforcement of Concrete http://dx.doi.org/10.5772/intechopen.69318 161

In previous sections, the improvement of properties provided by the fibres in PFRC has been shown. In order to take advantage of these benefits in the structural design of concrete

**6. PFRC properties and their relation with the standards and** 

manufactured.

[5].

**recommendations**

**Figure 15.** Deformation states of SLS or ULS.

In order to relate the presence and distribution of fibres to the mechanical behaviour of the material, the values of *L*MIN and *L*REM versus the amount of fibres in the lower third of the fracture surface and the total amount of fibres in the fracture surface are plotted in **Figure 16**. This figure shows that there is a linear relation between the presence of fibres both in the lower third and the complete fracture surface with the values of *L*MIN and *L*REM in both con‐ ventional and self‐compacting PFRC. It is also worth noting that the presence of fibres in the fracture surfaces does not correspond directly to the amount of fibres added. In such a sense, it should be noted that in not all cases higher dosages of fibres result in a greater number of

identified that governs the branch after *L*LOP, as reported in many FRC types and espe‐ cially for PFRC [3]. The softening behaviour is a distinctive characteristic in plain concrete fracture and, in such a case a steep unloading process leads to the specimen failure and collapse. Nonetheless, the polyolefin fibres are able to absorb the energy released by the concrete in the fracture processes by the so‐called fibre bridging and change the loading tendency. At such a point, the curve reaches the minimum post‐cracking load (*L*MIN) while another uploading process starts again. The end of the load‐increasing ramp is the third remarkable point of the curve. The descending slope drawn after *L*REM continues until the end of the test. It should be noted that even at great deformation states, PFRC does not fail or collapse and that it shows remarkable improvements in ductility and toughness with

Based on the previous description, it is easier to perceive the influence that the changes have on the behaviour that can appear when varying the amounts of polyolefin fibres added. The amount of fibres has a negligible influence on the peak load recorded in the fracture tests, and therefore *L*LOP does not change with fibre dosage. The value of *L*LOP is mainly determined by the tensile strength of the plain concrete. After reaching the peak load, the unloading part of the curve appears and such a part ends at *L*MIN that is related with the amount of fibres added. The higher volumetric fraction of fibres the greater is the value of *L*MIN obtained. It should be highlighted that, in contrast with the behaviour of an SFRC, even with volumetric fractions around 1% the value of *L*MIN greatly differs from *L*LOP. The slope of the curve between *L*MIN and *L*REM is greater as the amount of fibres added increases. In this case, it is important to note that the deflection value where *L*MIN takes place does not depend remarkably on the dosage of fibres. Nevertheless, the maximum post‐peak value *L*REM is greatly modified by the

The number of fibres present in the fracture surface generated during the tests greatly influ‐ ences the values of *L*MIN and *L*REM alike. However, not all the fibres that appear in the fracture surface influence the value of *L*MIN. Due to the limited deformation state that the sample is bearing when *L*MIN occurs, which is commonly used for service limit state (SLS) design, the contribution of fibres placed in the tensioned part of the section is more important than the rest of fibres. This corresponds to the lower third of the fracture surface generated. For high deformations, almost the whole cross section is in tension and, due to the quasi‐brittle nature of the material, would already be almost fully cracked. Therefore, the total number of fibres would bear the final load obtained in the tests. These advanced deformations would corre‐ spond to ultimate limit state design (ULS). The situations that take place in the case of SLS and

In order to relate the presence and distribution of fibres to the mechanical behaviour of the material, the values of *L*MIN and *L*REM versus the amount of fibres in the lower third of the fracture surface and the total amount of fibres in the fracture surface are plotted in **Figure 16**. This figure shows that there is a linear relation between the presence of fibres both in the lower third and the complete fracture surface with the values of *L*MIN and *L*REM in both con‐ ventional and self‐compacting PFRC. It is also worth noting that the presence of fibres in the fracture surfaces does not correspond directly to the amount of fibres added. In such a sense, it should be noted that in not all cases higher dosages of fibres result in a greater number of

respect to plain concrete.

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amount of fibres added.

ULS are shown in **Figure 15**.

**Figure 16.** Relation between the number of fibres present in the fracture surfaces and the residual loads *L*MIN and *L*REM for vibrated conventional PFRC (VCC) and self‐compacting PFRC (SCC). Tests performed following EN‐14651 in reference [5].

fibres present in the fracture surfaces. Therefore, there are certain variations in the mechanical properties of the material that rely on other parameters unrelated with the amount of fibres added, such as the material rheology, pouring method and, among others, size of the element manufactured.
