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

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 elements, the mechanical properties of PFRC should fulfil certain requirements established in several standards and recommendations. Conventionally, as the most widespread struc‐ tural fibres have been steel fibres almost all regulations have considered some of the require‐ ments and borne in mind the properties of SFRC. However, if the fracture behaviours of SFRC and PFRC are compared, it can be noted that there are certain differences that should be underlined. If the fracture behaviours of a certain SFRC and PFRC are sketched as they are in **Figure 17**, such differences are perceived. As regards the peak load, there are no remarkable differences because this value both in SFRC and in PFRC is directly related with the proper‐ ties of the bulk concrete due to the low volume fractions of fibres used. Nevertheless, once the unloading process that takes place after reaching the peak load starts, the first differences appear. Where SFRC is concerned, the decrement of the load‐bearing capacity of the mate‐ rial is more reduced than in the case of the PFRC. This phenomenon appears even in the case of using high dosages of polyolefin fibres, which might be related, with the comparatively lower modulus of elasticity of these fibres if compared with steel fibres. Another difference that can be perceived is that the maximum post‐peak load in the case of a PFRC takes place at higher deformation states than in the case of SFRC. Moreover, when *L*REM is reached, the final unloading branch of SFRC will have been progressing for a while. Taking into account the aforementioned characteristics, it can be stated that for limited deformation states, such as those that correspond to SLS, SFRC might be more suitable than PFRC. On the contrary, if ULS is considered, then the most suitable option would be PFRC.

In any case and in order to supply structural requirements to design engineers, some national codes have offered several tests and guidelines. In 1992, the German Code [40, 45] proposed a *σ*‐*ε* relationship for the structural design of tunnel linings that use steel fibres in concrete. In the last 15 years, many European countries, as well as Japan and the United States, have published codes and guidelines that allow the practical design of structures by considering fracture mechanics concepts aimed at taking into account the post‐cracking residual strength under tension stress. Responding to their own internal demands, Germany [46], Italy [41] and Spain [12] have produced and even revised their codes and design guidelines. A com‐ plete review of the European codes can be seen in [11, 48, 49]. A summary of the types of tests and requirements can be seen in **Table 2**. At the time of writing, CEB‐FIB Model Code 2010, MC2010 [50] is considered as a reference for newer revisions of Eurocode 2 and the guidelines of various European nation‐states. Model Code 2010 establishes a material clas‐ sification based on the results obtained by the earlier mentioned three‐point bending tests as per EN 14651 [38] or [39, 51]. Model Code considers that the contribution of the fibres can be considered in the structural design if the following conditions are met. The value of the load at a crack mouth‐opening displacement (CMOD) of 0.5 mm should be greater than 40% of the peak load, and when a CMOD reaches 2.5 mm the value of the load should be at least 20% of

CMOD, as can be better understood by consulting **Figure 18**. The first requirement is set for avoiding brittle failures of the structure and the second one seeks to set a minimum contribu‐

Although in some cases the requirements set by the standards are based on load values, in some others it is necessary to transform the load obtained from the fracture tests performed into residual strength values. This task can be accomplished in accordance with EHE‐08 [12] and the Model Code [50] by Eq. (1) that transforms load values into strength, with *L* being the

j

ct,*<sup>j</sup>* <sup>=</sup> \_\_3 2 *f <sup>j</sup> <sup>L</sup>* \_\_\_\_ *b h*sp

When comparing **Figure 18** with **Figures 14** and **17**, the shapes of the curves are remarkably different. The fracture curves obtained in the PFRC of material after reaching the minimum post‐peak load value (*L*MIN) are capable of sustaining higher loads and reaching a maximum post‐peak value (*L*REM). As previously mentioned, structural requirements are related to

R1 and *f*

significance when these regulations are used to assess the performance of PFRC. However,

SCC10) met the aforementioned requirements. By contrast, when a VCC or an SCC with 6 or

did not fulfil the requirements, such mixes were able to avoid brittleness. The latter is shown by the increment of the load that takes place in all mixes, after reaching *L*MIN. Regarding a

(VCC6, SCC6, VCC4.5 and SCC4.5) was studied, although it is clear that these mixes

of fibres (VCC4.5 and SCC3), although brittleness is avoided due to the

R1 and *f*

Polyolefin Fibres for the Reinforcement of Concrete http://dx.doi.org/10.5772/intechopen.69318 163

the force registered by the load cell, *b* the width

R3 at crack openings of 0.5 and 2.5 mm.

R1might be of relative

of fibres (VCC10 and

R3 at 0.5 and 2.5 mm of

(1)

the peak load. Those values in terms of strength are known as *f*

tion of the fibres to the ultimate failure of the concrete element.

of the sample and *h*sp the length of the ligament, is as follows:

Consequently, the brittleness limitation stated by the strength value at *f*

the analysis of **Table 3** reveals that an SCC and a VCC with 10 kg/m<sup>3</sup>

distance between the supporting cylinders, *f*

*f*

the most representative residual strengths *f*

4.5 kg/m3

PFRC with 3 kg/m3

**Figure 17.** Schematic shape of the typical load‐deflection curve obtained in a fracture test of PFRC compared with SFRC.

In any case and in order to supply structural requirements to design engineers, some national codes have offered several tests and guidelines. In 1992, the German Code [40, 45] proposed a *σ*‐*ε* relationship for the structural design of tunnel linings that use steel fibres in concrete. In the last 15 years, many European countries, as well as Japan and the United States, have published codes and guidelines that allow the practical design of structures by considering fracture mechanics concepts aimed at taking into account the post‐cracking residual strength under tension stress. Responding to their own internal demands, Germany [46], Italy [41] and Spain [12] have produced and even revised their codes and design guidelines. A com‐ plete review of the European codes can be seen in [11, 48, 49]. A summary of the types of tests and requirements can be seen in **Table 2**. At the time of writing, CEB‐FIB Model Code 2010, MC2010 [50] is considered as a reference for newer revisions of Eurocode 2 and the guidelines of various European nation‐states. Model Code 2010 establishes a material clas‐ sification based on the results obtained by the earlier mentioned three‐point bending tests as per EN 14651 [38] or [39, 51]. Model Code considers that the contribution of the fibres can be considered in the structural design if the following conditions are met. The value of the load at a crack mouth‐opening displacement (CMOD) of 0.5 mm should be greater than 40% of the peak load, and when a CMOD reaches 2.5 mm the value of the load should be at least 20% of the peak load. Those values in terms of strength are known as *f* R1 and *f* R3 at 0.5 and 2.5 mm of CMOD, as can be better understood by consulting **Figure 18**. The first requirement is set for avoiding brittle failures of the structure and the second one seeks to set a minimum contribu‐ tion of the fibres to the ultimate failure of the concrete element.

elements, the mechanical properties of PFRC should fulfil certain requirements established in several standards and recommendations. Conventionally, as the most widespread struc‐ tural fibres have been steel fibres almost all regulations have considered some of the require‐ ments and borne in mind the properties of SFRC. However, if the fracture behaviours of SFRC and PFRC are compared, it can be noted that there are certain differences that should be underlined. If the fracture behaviours of a certain SFRC and PFRC are sketched as they are in **Figure 17**, such differences are perceived. As regards the peak load, there are no remarkable differences because this value both in SFRC and in PFRC is directly related with the proper‐ ties of the bulk concrete due to the low volume fractions of fibres used. Nevertheless, once the unloading process that takes place after reaching the peak load starts, the first differences appear. Where SFRC is concerned, the decrement of the load‐bearing capacity of the mate‐ rial is more reduced than in the case of the PFRC. This phenomenon appears even in the case of using high dosages of polyolefin fibres, which might be related, with the comparatively lower modulus of elasticity of these fibres if compared with steel fibres. Another difference that can be perceived is that the maximum post‐peak load in the case of a PFRC takes place at higher deformation states than in the case of SFRC. Moreover, when *L*REM is reached, the final unloading branch of SFRC will have been progressing for a while. Taking into account the aforementioned characteristics, it can be stated that for limited deformation states, such as those that correspond to SLS, SFRC might be more suitable than PFRC. On the contrary, if

**Figure 17.** Schematic shape of the typical load‐deflection curve obtained in a fracture test of PFRC compared with SFRC.

ULS is considered, then the most suitable option would be PFRC.

162 Alkenes

Although in some cases the requirements set by the standards are based on load values, in some others it is necessary to transform the load obtained from the fracture tests performed into residual strength values. This task can be accomplished in accordance with EHE‐08 [12] and the Model Code [50] by Eq. (1) that transforms load values into strength, with *L* being the distance between the supporting cylinders, *f* j the force registered by the load cell, *b* the width of the sample and *h*sp the length of the ligament, is as follows:

$$f\_{ct,j} = \frac{3}{2} \frac{f\_l L}{b} \tag{1}$$

When comparing **Figure 18** with **Figures 14** and **17**, the shapes of the curves are remarkably different. The fracture curves obtained in the PFRC of material after reaching the minimum post‐peak load value (*L*MIN) are capable of sustaining higher loads and reaching a maximum post‐peak value (*L*REM). As previously mentioned, structural requirements are related to the most representative residual strengths *f* R1 and *f* R3 at crack openings of 0.5 and 2.5 mm. Consequently, the brittleness limitation stated by the strength value at *f* R1might be of relative significance when these regulations are used to assess the performance of PFRC. However, the analysis of **Table 3** reveals that an SCC and a VCC with 10 kg/m<sup>3</sup> of fibres (VCC10 and SCC10) met the aforementioned requirements. By contrast, when a VCC or an SCC with 6 or 4.5 kg/m3 (VCC6, SCC6, VCC4.5 and SCC4.5) was studied, although it is clear that these mixes did not fulfil the requirements, such mixes were able to avoid brittleness. The latter is shown by the increment of the load that takes place in all mixes, after reaching *L*MIN. Regarding a PFRC with 3 kg/m3 of fibres (VCC4.5 and SCC3), although brittleness is avoided due to the

**Test** Four point bending

CNR‐DT204

**Standard**

**Parameters** *f*Fts, *f*Ftu, *f*eq1, *f*eq2

**Constitutive models for structural design**

Lineal‐Elástic

*f*Fts = 0,45· *f*eq1

*f*Ftu*=k[f*Fts *‐ Wu* \_\_\_\_ *Wi*2

(*f*Fts−*0,5f*eq2*+0,2f*eq1*)*

*k*=1(flexural) ò *k*=0.7(tensile)

*ε*2=*ε*u (20% softening; 10‰ hardening)

Rigid‐PLASTIC

*f*

eq2

\_\_\_

3

*ε*1=*ε*lim =10% hardening; 20% softening

DBV

*f*ctk,fl, *f*eq,ctk,I, *f*eq,ctk,II

Trilineal

*σ*<sup>1</sup> = *ff*ctd = *αfc* · *f*ctk,*fl* /*γ*ct*<sup>f</sup>*

*σ*

= *f*

· *α<sup>f</sup>*

· *α*

/*γ*ct*<sup>f</sup>*

2

*σ*

= *f*

· *α<sup>f</sup>*

· *α*

/*γ*ct*<sup>f</sup>* ≤ *f*eq,ctd,*I*

3

*ε*1 = *σ*

/*E*

; *ε*2 = *ε*1 + 0.1‰; *ε*3 = *εu* = 25%

1

Bilineal

*σ*

= *f*

· *α<sup>f</sup>*

· *α*

/*γ*ct*<sup>f</sup>*

1

*σ*

= *f*

· *α<sup>f</sup>*

· *α*

/*γ*ct*<sup>f</sup>* ≤ *f*eq,ctd,I

2

*εu* = *ε*2 = 10%

> Rectangular

*σ*<sup>1</sup> = *f*eq,ctd,II = *f*eq,ctk,II · *αfc* · *α*sys /*γ*ct*<sup>f</sup>* ≤ *f*eq,ctd,I

*ε*1 = *εu* = 10%

Polyolefin Fibres for the Reinforcement of Concrete http://dx.doi.org/10.5772/intechopen.69318 165

**Table 2.**

Comparison of some of the recommendations and standards.

eq,ctd,II

*c*

sys

eq,ctk,I

*c*

sys

HRF

eq,ctd,*II*

*c*

sys

eq,ctd,*I*

*c*

sys

*f*Ftu =

**Test** Three point bending

EHE

**Standard**

**Parameters**

*f*R1*, f*R3*, f*L

**Constitutive models for structural design**

Rectangular

*f*ctR,d= 0.33 fR3,d

164 Alkenes

*ε*lim=20% (flexural)

εlim=10‰ (tensile)

Trilineal

*f*ct*,d* *f*ct*R1,d* *f*ct*R3,d*

*= k* (*0.5 f*R,3,d*−0.2 f*R,1,d),

*con k=1(flexural) ò k=07(tensile)*

*ε*1 *= 0,1 + 1000\*f*ct,d*/E*c,0

*ε*2 *= 2,5/l*cs

*ε*lim *=* 20% *(flexural) ò* 10% *(tensile)*

FIB model code

*f*R1*, f*R3*, f*Ftu, *f*Fts

Rigid‐Plástic

Lineal

fFts=0.45 fR1

fFtu= fFts−

*wu*

\_\_\_\_\_\_\_

*CMOD*3(fFts−0.5fR3+0.2fR1)

*ε*ELS = CMOD1/*l*cs; *ε*SLU=Wu/*l*cs = min(*ε*Fu, 2.5/*l*cs,

2.5/y); *ε*Fu=10‰ end; 20‰ ablan

*f*R1*, f*R4*f*R1 (CMOD=0.5) ≥ 1.5 MPa

*f*R4 (CMOD=3.5 mm) ≥ 1 MPa

UNE 14889

*f*Ftu =

*fR*<sup>3</sup>

\_\_

3

ε1=εlim =10%hardening; 20% softening

*= 0.45 f*R,1,d

*= 0.6 f*ct,fl*,d*

**Author details**

**References**

compstruct.2015.12.068

conbuildmat.2014.01.024

conbuildmat.2015.03.007

and Materials. 2014;**8**(4):279‐287

and Building Materials. 2010;**24**(6):1078‐1085

Marcos G. Alberti, Alejandro Enfedaque and Jaime C. Gálvez\*

Civil Engineering Department, Construction, E.T.S de Ingenieros de Caminos, Canales y

Polyolefin Fibres for the Reinforcement of Concrete http://dx.doi.org/10.5772/intechopen.69318 167

[1] Ugbolue SC. Polyolefin Fibres: Industrial and Medical Applications. CRC Press; 2009

[3] Alberti MG, Enfedaque A, Gálvez JC, Agrawal V. Reliability of polyolefin fibre rein‐ forced concrete beyond laboratory sizes and construction procedures. Composite Structures. 15 April 2016;**140**:506‐524. ISSN 0263‐8223. DOI: http://dx.doi.org/10.1016/j.

[4] Alberti MG, Enfedaque A, Gálvez JC. On the mechanical properties and fracture behav‐ ior of polyolefin fiber‐reinforced self‐compacting concrete. Construction and Building Materials. 31 March 2014;**55**:274‐288. ISSN 0950‐0618. DOI: http://dx.doi.org/10.1016/j.

[5] Alberti MG, Enfedaque A, Gálvez JC. Comparison between polyolefin fibre reinforced vibrated conventional concrete and self‐compacting concrete. Construction and Building Materials. 15 June 2015;**85**:182‐194. ISSN 0950‐0618. DOI: http://dx.doi.org/10.1016/j.

[6] Alberti MG, Enfedaque A, Gálvez JC. Fracture mechanics of polyolefin fibre reinforced concrete: Study of the influence of the concrete properties, casting procedures, the fibre length and specimen size. Engineering Fracture Mechanics. March 2016;**154**:225‐244.

[7] Sorensen C, Berge E, Nikolaisen EB. Investigation of fiber distribution in concrete batches discharged from ready‐mix truck. International Journal of Concrete Structures

[8] Alberti MG, Enfedaque A, Gálvez JC, Ferreras A. Pull‐out behaviour and interface criti‐ cal parameters of polyolefin fibres embedded in mortar and self‐compacting concrete

[9] Torrijos MC, Barragán BE, Zerbino RL. Placing conditions, mesostructural characteristics and post‐cracking response of fibre reinforced self‐compacting concretes. Construction

matrixes. Construction and Building Materials. 2016;**112**:607‐622. ISSN 0950‐0618

ISSN 0013‐7944. DOI: http://dx.doi.org/10.1016/j.engfracmech.2015.12.032

[2] McIntyre JE. Synthetic Fibres: Nylon, Polyester, Acrylic, Polyolefin. Elsevier; 2004

\*Address all correspondence to: jaime.galvez@upm.es

Puertos, Technical University of Madrid, Madrid, Spain

**Figure 18.** Load‐CMOD curve of a FRC as stated in [12] with structural requirements.


**Table 3.** Residual strength of concrete.

increment of load that the material can bear at *f* R3, there is only a 10% improvement of the strength between *f* R1 and *f* R3. A wider view and detailed results with additional tools to con‐ sider fibre positioning as a function of the influencing parameters can be seen in Ref. [28].
