Fiber-reinforced concrete

Fiber-reinforced concrete

11

Giovanni Plizzari1 and Sidney Mindess2 1 Universita` degli Studi di Brescia, Brescia, Italy, 2University of British Columbia, Vancouver, BC, Canada

11.1

Introduction

Plain concrete is a brittle material with low tensile strain and strength capacities. The use of short, discontinuous fibers to strengthen and toughen such materials, which are much weaker in tension than in compression, goes back to ancient times. Probably, the oldest written account of such a composite material (clay bricks reinforced with straw) occurs in Exodus 5:6
7: And Pharaoh commanded the same day the task-masters of the people, and their officers, saying: ‘Ye shall no more give the people straw to make bricks, as heretofore: let them go and gather straw for themselves.

Even today, adobe bricks (pressed mud reinforced with straw, then baked in the sun) are still made in some parts of the world. In modern times the use of fibers to reinforce cementitious materials goes back to about 1900, when the invention of the Hatschek process enabled the production of asbestos cement. Over the past 50 years there has been a steady increase in the use of fibers in cement and concrete. Today, several hundred million cubic meters of fiber-reinforced concrete (FRC) are produced annually. Fibers are not generally added to concrete to increase its strength; the main role of the fibers is to bridge across the matrix cracks that develop as concrete is loaded, and thus to provide some postcracking ductility (or toughness). Fibers should not be considered a replacement for conventional reinforcing bars, even though in some applications, this may be the case. They are, in fact, complementary methods of reinforcing concrete, and there are many applications in which they should be used together. It should be noted that, for perhaps, the first 40 years after the pioneering studies of FRC by Romualdi and Batson (1963a, 1963b), most of the FRC research (as summarized by Bentur & Mindess, 2007) was focused on the effects of various fiber types and geometries on the behavior of FRC as a material. There was

Developments in the Formulation and Reinforcement of Concrete. DOI: https://doi.org/10.1016/B978-0-08-102616-8.00011-3 Copyright © 2019 Elsevier Ltd. All rights reserved.

258

Developments in the Formulation and Reinforcement of Concrete

relatively little research on the structural behavior of FRC, and almost all of the early applications of FRC were in nonstructural applications, such as slabs on grade, tunnel linings, or fiber shotcrete. There was insufficient effort into developing methods of characterizing the behavior of FRC in a manner that could be quantified unambiguously, and thus used in design. Unfortunately, this delayed the use of FRC as a truly structural material; indeed, it was only fairly recently that consideration of FRC entered into concrete building codes. Thus it was that this chapter in the first edition of this book (Mindess, 2008), dealt only very briefly with structural applications. Happily, this has now turned around, with an everincreasing use of FRC in structural applications. The focus here is much more on the use of FRC in structures, with only a briefer account of the material properties of FRC.

11.2

Material properties

11.2.1 How do fibers work? The mechanical behavior of FRC depends largely on the interactions between the fibers and the brittle concrete matrix: physical and chemical adhesion, friction and mechanical anchorage induced by complex fiber geometry or by deformations or other treatments on the fiber surface. Many different fiber geometries have been developed over the years (Fig. 11.1) to improve the mechanical anchorage, which is by far the most important of the bonding mechanisms. Surface treatments of synthetic fibers have similarly been employed to improve the fiber
matrix bond. As FRC is stressed (external loads, shrinkage, and thermal stresses), there is initially elastic stress transfer between the fibers and the matrix. Because the fibers and the matrix have very different elastic moduli, shear stresses develop at

Figure 11.1 Some types of available steel fibers.

Fiber-reinforced concrete

259

the fiber/matrix interface. When the shear strength at the interface is exceeded, debonding begins to occur, and frictional shear stresses become the dominant stress transfer mechanism. At some point during this gradual transition from elastic to frictional stress transfer, some cracking of the matrix occurs, and some frictional slip takes place in the debonded area. However, we are primarily interested in how the fibers inhibit crack extension once the matrix has cracked, that is, how they behave in the postcracking zone. This is governed primarily by the nature of the pullout of the fibers from the matrix. It must be emphasized that failure by fiber pullout is much the preferred mode of failure; much more energy is consumed in pulling the fibers out of the matrix than in breaking them. It is possible to determine a critical length, lc, at which the fibers break rather than pulling out. This must be taken into account when choosing or designing fibers for a particular application. In a properly designed FRC, following the appearance of the first crack, a process of multiple cracking begins, during which the brittle matrix cracks into successively smaller segments (held together by the fibers bridging these cracks). This process leads to the toughening of the composite. The crack width and crack spacing during this process can be controlled by proper selection of both the fibers and the matrix.

11.2.2 Types of fibers A number of different types of fibers have been developed for the use specifically with concrete. However, it must be emphasized that within each fiber type, there are a number of different producers and fiber geometries, leading to different properties. The principal types of fibers may be classified as follows: Steel fibers may be produced by cutting wires, shearing sheets, or from a hot-melt extract, and still are the most commonly used fibers. As shown in Fig. 11.1, they are almost always deformed in some way to enhance the fiber
matrix bond. They have been found to be extremely durable in concrete, even though they may rust visibly when exposed at the concrete surface. In some cases, where surface rusting is unacceptable, or in very aggressive environments (e.g., refractory applications), stainless steel fibers may be used. Glass fibers are produced by drawing molten glass in the form of fine filaments through a special bushing. Typically, 204 filaments are drawn simultaneously, and after solidification, these are formed into a single strand. Ordinary soda
lime glass (E-glass) fibers and borosilicate glass (A-glass) fibers are not stable in the highly alkaline concrete environment. Thus for use in concrete, alkali-resistant glass fibers, typically containing about 16%
20% zirconia, must be used. Asbestos fibers have been used since about 1900 in the manufacture of asbestos cement pipes, roofing materials, and other building components. They have a particular affinity for the cement matrix and are very effective as reinforcement. Unfortunately, there are significant health risks associated with the production and use of the asbestos fibers themselves, and their use has been banned in many

260

Developments in the Formulation and Reinforcement of Concrete

jurisdictions. They have largely been replaced with other types of fibers, primarily cellulose fibers. Synthetic fibers have become very common in recent years. Unlike the abovementioned fibers, they generally have a significantly lower elastic modulus than does the concrete matrix. Short microfibers (length , 15 mm, diameter , 0.4 mm) at relatively low fiber volumes are effective mostly for the control of plastic shrinkage cracking. Longer macrosynthetic fibers (length . 15 mm, diameter . 0.4 mm) may provide significant toughening and some strengthening may also be achieved when included with a proper volume fraction. The most common synthetic fibers are polypropylene or polypropylene
polyethylene blends. Carbon fibers and aramid (Kevlar) fibers are high elastic modulus fibers that are very effective in FRC, but which are still too expensive to be widely used. High-strength acrylic fibers and polyvinyl alcohol fibers have been introduced as replacements for asbestos fibers, though their use is generally limited to specialized applications. Natural organic fibers are also sometimes used in FRC, primarily for the production of low-cost housing elements in developing countries. These low modulus fibers, such as sisal, jute, coir, elephant grass, and sugarcane bagasse, tend to deteriorate in damp or alkaline environments and must be specially treated for the use in FRC. However, cellulose fibers, derived from wood pulp, which are stiffer and stronger than the other natural fibers, are now being used extensively as a replacement for asbestos fibers, though they too need special processing before they can be used in FRC.

11.2.3 Mix proportioning, fabrication, and placement For the fiber volumes, generally used for ordinary FRC (,1%), the procedures for mix proportioning of FRC are generally the same as those used for plain concrete, though rather more “trial and error” is usually involved when fibers are incorporated. Generally, the addition of fibers reduces the concrete workability; this may be compensated by increasing the ratio of fine-to-coarse aggregate, or by the addition of more pozzolanic material, or by the addition of superplasticizers. It should also be noted that fiber concretes are more difficult to compact than plain concrete. FRC can also be produced in much the same way as plain concrete, using the same equipment and procedures. However, particular care must be taken to ensure that the fibers are uniformly dispersed, by avoiding “balling” or clumping of the fibers. This requires some attention to the way in which the fibers are introduced into the concrete and adequate mixing. In the field, FRC appears to be stiff as compared to plain concrete, but a properly designed mix will flow readily under vibration. FRC can be pumped and can be placed as fiber-reinforced shotcrete (see Chapter 12).

Fiber-reinforced concrete

261

11.2.4 What do fibers actually do? 11.2.4.1 Toughness Postcracking strength in hardening or softening materials varies with the increase of deformation [or crack mouth opening displacement (CMOD)] in the specimen. It must be emphasized again that, at the volume fractions normally used (,1.0%), fibers are not added to improve the strength; their principal role is to bridge across the cracks that develop in concrete as it is stressed. If the fibers are well bonded to the matrix, and if they are sufficiently stiff and strong, they will permit the FRC to sustain significant loads over relatively large deformations in the postcracking (or strain softening) stage. That is, the fibers will provide some postcracking “ductility” or toughness to the composite. The higher the fiber volume, and the more efficient the fibers, the more the toughness will increase. There is, unfortunately, still no general agreement on an unambiguous method to quantify this behavior, particularly in such a way as to introduce it into standard building codes. According to Mindess, Young, and Darwin (2003), any toughness or residual strength parameter used for specification of FRC should, ideally, satisfy the following criteria: G

G

G

G

G

G

It should have a physical meaning that is readily understandable. It should be able to quantify some important aspect of FRC behavior (e.g., strength, toughness, and crack resistance) and should reflect some characteristics of the load versus deflection curve. It should be largely independent of specimen size and geometry. Although the uniaxial tensile test seems to be the most appropriate method for measuring the postcracking behavior of FRC, it requires very stiff closed-loop testing machines that are not usually available in many laboratories; furthermore, fiber orientation may significantly influence the experimental results. For these reasons, standard tests for determining the postcracking performance of FRC are based on bending tests on small beams or slabs. Since bending behavior is markedly different from uniaxial tension behavior, it may happen that softening materials in tension present a hardening behavior in bending. In the United States, three test methods have been standardized by ASTM: ASTM C1609 (2012): Standard Test Method for Flexural Performance of FiberReinforced Concrete (using beam with third-point loading) ASTM C1399 (2015): Standard Test Method for Obtaining Average Residual-Strength of Fiber-Reinforced Concrete ASTM C1550 (2012): Standard Test Method for Flexural Toughness of Fiber-Reinforced Concrete (using centrally loaded round panel)

European standard EN 14651 (2005) requires a bending test on a notched beam under three-point loading (Fig. 11.2); typical experimental results in terms of load versus CMOD are shown in Fig. 11.3. Four different values of the residual strength (fR1, fR2, fR3, and fR4), corresponding to different values of the CMOD (0.5, 1.5, 2.5, and 3.5 mm, respectively), of the notched specimen are defined as reference

262

Developments in the Formulation and Reinforcement of Concrete

Figure 11.2 Test setup required by EN 14651 (2005) (dimensions in mm).

Load F F1 F2 F3 F4 CMOD (mm)

CMOD1 = 0.5

CMOD2 = 1.5

CMOD3 = 2.5

CMOD4 = 3.5

Figure 11.3 Typical load
CMOD curve for FRC (fib Model Code for Concrete Structures, 2010). CMOD, Crack mouth opening displacement; FRC, fiber-reinforced concrete.

parameters. Conforti, Minelli, Plizzari, and Tiberti (2018) underlined that for softening materials under flexure, design parameters of fR1 and fR3 can be also estimated from ASTM C1609. In particular, fR,1 is the nominal stress evaluated at a value of deflection of about 0.27 mm for ASTM 1609, while fR3 can be estimated adopting a deflection of 1.31 mm. Since four different values may be too many for the FRC design formulation, for structural design fib Model Code 2010 (2012) (hereafter MC2010) assumes fR1 and fR3 for characterizing the FRC residual strength for SLS (serviceability limit state) and ULS (ultimate limit state) analysis, respectively. In particular, performance classes defined by MC2010 are based on two parameters, namely, fR1 and the ratio fR3/fR1. The strength classes for fR1k (characteristic value of fR1) are defined by the following values: 1:0; 1:5; 2:0; 2:5; 3:0; 4:0; 5:0; 6:0; 7:0; 8:0 MPa

(11.1)

Fiber-reinforced concrete

263

The fR3k/fR1k ratio can be represented with letters a, b, c, d, e, corresponding to the values: fR3k fR1k fR3k 0:7 # fR1k fR3k 0:9 # fR1k fR3k 1:1 # fR1k fR3k 1:3 # fR1k

‘‘a’’

if 0:5 #

, 0:7

‘‘b’’

if

, 0:9

‘‘c’’

if

‘‘d’’

if

‘‘e’’

if

, 1:1

(11.2)

, 1:3

This classification properly represents the most common cases of softening FRCs, but it can also be adopted for hardening FRCs. By using the proposed classification a material having, for example, fR1k 5 4.5 MPa and fR3k 5 4.2 MPa is classified as “4c.” On the other hand, when the designer assumes the use of a material 4c, the FRC provided has to have fR1k not lower than 4.0 MPa and fR3k not lower than 3.6 MPa. Postcracking classification for FRC is based on nominal properties that characterize its postcracking tensile strength. Since brittleness must be avoided in structural behavior, according to MC2010, FRC can be used as a substitution (even partially) of conventional reinforcement (at ULS), if the following relationships are fulfilled: fR1k $ 0:4 fLk

(11.3)

fR3k $ 0:5 fR1k

(11.4)

where fLk is the characteristic value of the nominal strength, corresponding to the peak load (or the highest load value in the interval 0
0.05 mm), determined from the beam test required by EN 14651 (2005) (Fig. 11.3).

11.2.4.2 Impact resistance As stated earlier, under static loading, fibers do not contribute to the strength of concrete, though small increases of the maximum load in tensile and flexural tests may be found. Under impact loading, however, fibers may well increase both the strength and the toughness (or fracture energy) of the composite, as compared to the behavior of the plain matrix under similar loading conditions. The reasons for

264

Developments in the Formulation and Reinforcement of Concrete

the improved behavior of FRC under impact loading are still not completely understood. In part, this may be due to the fact that FRC becomes increasingly strain rate sensitive at higher fiber contents and fiber aspect ratios. This is generally attributed to the strain rate sensitivity of the fiber
matrix bond strength (Naaman & Gopalaratnam, 1983). Similarly, adding fibers to the concrete matrix will significantly improve the bond between the concrete and conventional steel reinforcement under impact loading. Again, the composite exhibits a higher bond strength, becomes more ductile, and absorbs more energy (Yan & Mindess, 1994, 2001). The effects of fibers are even more dramatic when the concrete is subjected to impact while under lateral confinement. When compression specimens are laterally confined (Sukontasukkul, Mindess, Banthia, & Mikami, 2001), under impact loading, their mode of failure changes from the normal shear cone type to a columnar or vertical splitting type, accompanied by increases in strength and strain at peak load. Higher confining stresses and/or higher fiber contents lead to higher energy absorption by the specimen. Unfortunately, it is not possible to predict the behavior of FRC under high loading rates from static tests. The problem is further complicated by the fact that, depending on the particular FRC system and the strain rate, the failure mechanisms may be quite different. FRC systems may also be subjected to very different strain rates, ranging from about 1026 s21 to about 106 s21, depending on the source of the dynamic event. Thus because of the enormous range of possible strain rates, and the complexity of the FRC system itself, the high strain rate and impact properties of FRC are still poorly understood. Nonetheless, based on a great deal of empirical evidence, it is certain that fibers can be very effective in improving the impact resistance of concrete; we are simply unable at this time to quantify these improvements in an unambiguous manner.

11.2.4.3 Shrinkage Up to fiber volumes of about 1%, fibers have little effect on the magnitude of the drying shrinkage of concrete, though they tend to reduce the resulting crack widths considerably. However, microfibers can be very effective in reducing plastic shrinkage cracking; indeed, this is one of the principal applications of synthetic fibers.

11.2.5 Hybrid fiber systems The combination of two or more different types of fibers (different fiber types and/ or geometries and/or materials) can help to optimize overall system behavior. The intention is that the performance of these hybrid systems would exceed that induced by each fiber type alone, that is, there would be synergy. Banthia and Gupta (2004) classified these synergies into three groups, depending on the mechanisms involved: G

Hybrids based on the fiber constitutive response, in which one fiber is stronger and stiffer and provides strength, while the other is more ductile and provides toughness at high strains.

Fiber-reinforced concrete

265

Figure 11.4 Postcracking behavior of an FRC with a combination of shorter and longer fibers. FRC, Fiber-reinforced concrete. G

G

Hybrids based on fiber dimensions, where one fiber is very small and provides microcrack control at early stages of loading and the other fiber is larger, to provide a bridging mechanism across macrocracks (Fig. 11.4). Hybrids based on fiber function, where one type of fiber provides strength or toughness in the hardened composite, while the second type provides fresh mix properties suitable for processing.

These concepts have been applied for both thin sheet FRC (particularly for asbestos fiber replacement) and for high-performance
high-ductility systems, with fiber volumes from 2% to 10%. It is evident that, by using a hybrid system of fibers, a “tailor-made” postcracking resistance can be obtained.

11.2.6 High-performance fiber-reinforced concrete The discussion mentioned above has dealt primarily with “ordinary” FRC. However, there are now a number of more sophisticated FRC systems, which can greatly extend the performance limits of FRC.

11.2.6.1 Engineered cementitious composites One way to minimize crack widths in concrete is through the use of “engineered cementitious composites” (ECCs), as developed by Li (2003, 2005). ECC is a fiber-reinforced cementitious composite containing typically about 2% fibers by volume, and generally no coarse aggregate. Using a micromechanics-based approach to the mix design, involving careful matching of the matrix strength and the fiber pullout strength, it is possible to achieve “ductility” values of up to 3% in direct tension. This material can be placed in many ways—by ordinary casting

266

Developments in the Formulation and Reinforcement of Concrete

Figure 11.5 Typical tensile stress
strain curve and crack width development of ECC (Li, 2005). ECC, Engineered cementitious composite.

techniques, as self-consolidating concrete, and by shotcreting. However, because it contains no coarse aggregate and has a relatively high cement content, it is suitable primarily for thin applications, for example, as an overlay. Because of its ductility and its ability to keep crack widths small (Fig. 11.5), this material can lead to more durable and sustainable structures, even though the initial costs can be substantial.

11.2.6.2 Ultrahigh-performance fiber-reinforced concrete A family of materials with very high fiber contents, strengths, and durability have been developed over the past 20 years or so. The common features of these materials are very low water:binder ratios, high fiber contents, severe limitations on the maximum aggregate size (often less than 1 or 2 mm), careful control of the particle size distribution of all of the solid materials in the mix, the use of silica fume and superplasticizers, and tight quality control in their production, placement, and curing. The particle size distribution is of critical importance since it is essential to optimize the particle packing of all of the solid materials taken together. Commonly, these materials are proprietary. These materials are very expensive, though they are now sometimes used in certain specialized applications. Some examples are as follows: DUCTAL: Ductal (produced by LafargeHolcim) consists of fine aggregate (,2 mm), crushed quartz, silica fume, and of course cement, water and superplasticizer, and up to 2% by volume of fibers. Using steel fibers, compressive strengths of about 150
180 MPa may be achieved, with flexural strengths of about 32 MPa. Using polypropylene fibers, these strengths are reduced by about 25%. BSI-CERACEM (produced by Eiffage and Sika) was used to construct the toll gate roofs for the Millau viaduct in the south of France (Thibaux, Hajar, Simon, & Chanut, 2004). With about 2.5% of steel fibers, it achieved a compressive strength of 165 MPa and a tensile strength of 8.8 MPa. It was also self-consolidating.

Fiber-reinforced concrete

267

Table 11.1 Composition of two ultrahigh-performance fiber-reinforced concretes. Material

DUCTAL (kg/m3)

CEMTECmultiscale (kg/m3)

Portland cement Silica fume Crushed quartz Sand Water Fibers Superplasticizer

710 230 210 1020 140 40
160a 10

1050.1 268.1
514.3 180.3 858b 44

a

Either steel or polypropylene fibers (13 mm 3 0.20 mm). A mixture of three different geometries of steel fibers.

b

CEMTECmultiscale (patented by LCPC, France) has much higher cement and fiber contents than the two previous materials, though the underlying principles remain the same. This material can achieve flexural strengths of 60 MPa and has a very low permeability (Parent & Rossi, 2004). Typical mix proportions for DUCTAL and CEMTEC are given in Table 11.1. It should be noted that while all of these materials are promoted largely on the basis of their strength (since this is still the principal obsession of structural engineers), it is their high impermeability and durability, which are probably of greater importance in the long run. In spite of their high initial costs, this evergrowing family of materials will become increasingly important as sustainability considerations are embraced by the industry.

11.3

Structural use of fiber-reinforced concrete

11.3.1 Introduction As mentioned above, FRC is a composite material characterized by a postcracking residual strength that enhances the tensile behavior of concrete structures in terms of crack control and bearing capacity. Therefore FRC might be particularly useful for structural elements both at SLS and ULS, depending on its mechanical properties. The latter may allow for a reduction of conventional reinforcement and, in structures with a high degree of redundancy, a complete replacement of rebars. When this happens, the structural element also has the advantage of an enhanced crack control and of a significant reduction in the time of construction and costs, since rebars involve relatively high labor input to bend and fix in place. The labor time reduction becomes a key issue for the industrialization process in the precast industry, where the rebar substitution becomes particularly convenient in thin or irregularly shaped sections, and where it may be very difficult to place conventional reinforcement. FRC might be particularly useful as secondary reinforcement required for stress redistribution in many structural elements. The enhanced crack control

268

Developments in the Formulation and Reinforcement of Concrete

makes FRC particularly suitable also when reinforcement is not replaced, for longer durability and service life of the structure; here, the additional cost of fiber reinforcement may be justified by savings in the maintenance costs. FRC with short synthetic or cellulose microfibers may also enhance fire resistance to avoid concrete spalling. When FRC allows the replacement of a significant percentage of conventional reinforcement, the global structural ductility has to be verified, since the ultimate deformation of FRC is significantly lower than that of rebar. This clearly shows that FRC is particularly suitable in structures with a high degree of redundancy where a significant stress redistribution may occur. The design of FRC structures is generally quite difficult as the nonlinear tensile properties of the composite material have to be properly included in the calculations.

11.3.2 Performance-based design The structural design process requires performance-based specifications because designers need to rely on material performance during the design process; the latter has then to be guaranteed by the contractor during the construction process. The common performance parameters are strength, workability, and exposure classes for durability requirements. As far as the compressive and tensile strength as well as the elastic modulus are concerned, FRC mechanical properties can be assumed to be the same as those of a plain concrete (without fibers) having the same composition of FRC (up to a volume fraction of 1% of fibers). The enhanced mechanical performance characterizing FRC is then represented by its postcracking tensile strength, also referred to toughness herein. It is well known that fibers reduce the workability of fresh concrete but workability classes for plain concrete can also be adopted for FRC. As mentioned above, FRC allows a reduction of crack width, but the durability enhancement of FRC elements (with respect to reinforced concrete) still requires further research before introducing different rules for FRC elements (for instance, smaller concrete covers). One of the main international building codes including FRC as a structural material is the fib MC2010 (2012) whose design rules are based on FRC performance. In the following, fib MC2010 (2012) is used as the reference document for the design rules. According to MC2010, a stress
crack opening law in uniaxial tension is defined for the postcracking behavior of FRC. In particular, two simplified stress
crack opening constitutive laws may be deduced from the bending test (EN 14651, 2005) results: a plastic rigid behavior or a linear postcracking behavior (hardening or softening) as schematically shown in Fig. 11.6, where fFts represents the serviceability residual strength, defined as the postcracking strength for serviceability crack openings, and fFtu represents the ultimate residual strength.

Fiber-reinforced concrete

269

Figure 11.6 Simplified postcracking constitutive laws: stress
crack opening (continuous and dashed lines refer to softening and hardening postcracking behavior, respectively, MC2010).

When using the “rigid-plastic model,” a single reference value, fFtu, is adopted, the latter is defined as fR3 fFtu 5 (11.5) 3 When using the “linear model” two reference values, namely, fFts and fFtu, are adopted. They can be determined as fFts 5 0:45fR1 fFtu 5 fFts 2

wu ðfFts 2 0:5fR3 1 0:2fR1 Þ $ 0 CMOD3

(11.6) (11.7)

where wu is the maximum crack opening accepted in structural design, whose value depends on the ductility required.

11.3.3 Optimized reinforcement Conventional rebars certainly represent the best reinforcement for localized stresses, while fibers represent the best reinforcement for diffused stresses (Di Prisco, Plizzari, & Vandewalle, 2014). Since in structural elements both distributed and localized stresses are generally present, structural optimization generally requires the use of a combination of rebars and fibers. This means that one can use fiber reinforcement only, but the amount of fibers must be significantly increased in the whole structure in order to resist high stresses acting only in small areas. This usually results in a higher amount of total reinforcement as compared to alternative solutions based on a combination of fibers and rebars, herein defined as hybridreinforced concrete (HRC) (Chiaia, Fantilli, & Vallini, 2009; Facconi, Minelli, & Plizzari, 2016; Mobasher, Yao, & Soranakom, 2015; Tiberti, Minelli, & Plizzari, 2014; Vandewalle, 2000). Furthermore, it has to be remarked that the use of high fiber contents for resisting high stresses may cause a loss of workability and compactness of FRC leading to a possible reduction of the material tensile properties.

270

Developments in the Formulation and Reinforcement of Concrete

11.3.4 Fiber-reinforced concrete for service conditions The main requirements for structural elements at SLS concern: G

G

G

stress control, cracking, and deformability.

FRC does not significantly influence the existing design rules for reinforced concrete elements. Crack control is one of the main benefits provided by FRC to structural elements; once the crack appears, its development and width are influenced by the FRC toughness. For cracks due to external loads, in MC2010 (2012), the design crack width (wd) is introduced by considering a prismatic RC element subjected to axial tension (tensile ties). The approach proposed for evaluating the crack width of conventional nonfibrous RC members was originally based on the simplified analytical description of a tensile tie presented in the previous CEB-FIP Model Code 1990 (1993). This model was later slightly modified by Walraven (1999). Some of the basic principles of the model are briefly repeated in MC2010 (2012) and are summarized in Fig. 11.7. A constant bar-to-concrete bond (τ bm) is assumed; accordingly, the distribution of concrete (and steel stresses) in the D-regions astride the crack is linear. sc = fctm

(A)

sc = fctm

(B)

t bm

t bm

sc = 0

lt

sc = fFtsm

x

x

ltFRC ltFRC

lt

sc = fctm

sc = fctm

concrete stress

sc = 0

t bm

sc = fFtsm t bm

bond stress

Figure 11.7 Schematization of the basic equilibrium for evaluating the introduction length for a nonfibrous RC member (A) and schematization for fibrous RC elements reinforced by conventional rebars and fibers (B) (Tiberti, 2014).

Fiber-reinforced concrete

271

In Fig. 11.7 the “introduction length” lt, corresponding to the length necessary to reintroduce stresses (by means of bond) in the uncracked portions of concrete between cracks, is shown. Based on this approach, lt can be calculated by means of a simple equilibrium of the uncracked concrete prism between a cracked section and a section where the concrete stress reaches the mean tensile strength, fctm (basically a new crack is forming). This condition is schematically represented in Fig. 11.7A for a conventional (nonfibrous) RC member and in Fig. 11.7B for an FRC tie. 1 fctm [ lt 5 U U for a nonfibrous tensile tie ðreinforced only by rebarsÞ 4 τ bm ρs;eff (11.8) 1 ðfctm 2 fFtsm Þ [ U for a fibrous tensile tie ðfibres 1 rebarsÞ lt 5 U 4 τ bm ρs;eff

(11.9)

In the latter equation, it is assumed that, at the crack location, the concrete stresses in the FRC are not 0 (Fig. 11.7B), as in plain concrete (Fig. 11.7A). In fact, at the crack location, because of fiber postcracking resistance, a residual tensile strength, equal to fFtsm, is considered. In other words the length (measured from the crack) necessary to reintroduce the stresses into the uncracked concrete portions, by means of bond, is shorter in FRC. The value of the parameter fFtsm is considerably higher than zero depending on the “postcracking performance level” guaranteed by the FRC under service conditions. Therefore the first effect due to the addition of fibers is the reduction of the introduction length, which depends on fFtsm and the bond stress (τ bm). The latter is often assumed equal to that of plain concrete (without considering the FRC contribution). However, Plizzari (1999) has demonstrated that fiber addition increases the bond strength, especially in the presence of splitting cracks; on the contrary, if a full pullout failure occurs, the fiber contribution to bond tends to be reasonably negligible (Harajli & Mabsout, 2002). It is worth mentioning that a reduction of the introduction length corresponds to a proportional reduction of the crack spacing (sr) that varies from lt to slightly less than 2 3 lt (maximum crack spacing sr,maxD2 3 lt). Consequently, the reduction of the crack spacing corresponds to a reduction of the expected crack width, since wmax 5 2lt ðεsm 2 εcm Þ

(11.10)

where εsm and εcm are the mean steel and concrete strains. However, it should be considered that the crack spacing is strongly influenced by transverse reinforcement, when present. According to some building codes (MC2010, 2012), when considering a beam under flexure, the crack spacing is also influenced by the concrete cover, which is as follows: 1 fctm [ lt 5 kUc 1 U U for a nonfibrous tensile tie ðreinforced only by rebarsÞ 4 τ bm ρs;eff (11.11)

272

Developments in the Formulation and Reinforcement of Concrete

Figure 11.8 Simplified load-strain for a centrally reinforced member subjected to tension with the corresponding simplified behavior of an FRC tensile tie superimposed. FRC, Fiberreinforced concrete.

1 ðfctm 2 fFtsm Þ [ lt 5 kUc 1 U U for a fibrous tensile tie ðfibres 1 rebarsÞ 4 τ bm ρs;eff (11.12) The coefficient k is an empirical parameter to take the influence of the concrete cover into account, as a first approximation k 5 1.0 can be assumed. The introduction of the concrete cover is mainly related to the fact that a formulation based only on φ/ρs,eff is primarily consistent for elements with one concentric rebar (Beeby, 2004). As far as the deflection control is concerned, for the reasons mentioned above, FRC reduces the crack distance and makes the concrete contribution (around a reinforcing bar) stiffer (Fig. 11.8); therefore the increase of tension stiffening reduces the structural deformation.

11.3.5 Fiber-reinforced concrete at ultimate limit state for linear elements 11.3.5.1 Bending and axial compression Flexural behavior of FRC beams strongly depends on the reinforcing ratio of the longitudinal rebars; the latter cannot really be substituted by FRC because the fibers are not particularly efficient for resisting localized tensile stresses due to bending. As a consequence, the increase in bearing capacity of FRC beams is limited and mainly depends on the ratio between the FRC toughness and the percentage of longitudinal rebars (i.e., the higher this ratio, as in lightly reinforced slabs, the higher

Fiber-reinforced concrete

273

is the fiber contribution). FRC does not change significantly the flexural capacity of beams with the usual percentages of rebars (ρsl . 0.7%
0.8%), unless FRC with very high toughness is adopted. For modeling the contribution of fiber reinforcement to the cross-sectional resistance, the linear or constant tensile stress diagram proposed by MC2010 (2012) can be used (Fig. 11.9). The bending failure stage is assumed to be reached when one of the following conditions applies: G

G

G

attainment of the ultimate compressive strain in the FRC, εcu; attainment of the ultimate tensile strain in the steel (if present), εsu;or attainment of the ultimate tensile strain in the FRC, εFu.

If rebars are present, the contribution of FRC can be accounted for until the attainment of the ultimate tensile strain of the FRC, εFu; beyond this tensile deformation, the contribution of fibers cannot be considered. If rebars are not present, bending failure is assumed to be reached when the ultimate tensile strain in the FRC, εFu, is reached. According to MC2010 (2012), the ultimate deformation of FRC can be assumed equal to 2%. FRC generally increases the deflection capacity of structural members due to its higher energy absorption (Cunha, Barros, & Sena-Cruz, 2008). However, depending on the hardening ratio of the rebars (ft/fy), with lower values of ρsl, and higher postcracking resistance of FRC, a loss of ductility may occur in FRC beams due to the increase of the bar-to-concrete bond that induces strain localization (Meda, Minelli, & Plizzari, 2012; Schumacher, 2006). FRC influence on the beam ductility is mainly due to: G

G

the higher ultimate deformation of FRC in compression (Campione & La Mendola, 2004; Fantilli, Mihashi, & Vallini, 2007) and the negative effect of the strain localization (reduction of yield length) of the longitudinal rebar at the cracked section (Schumacher, 2006); the latter is related to the higher steelto-concrete bond provided by FRC (Plizzari, 1999).

(A)

(B)

≤ εcu

(C) fcd λ⋅x

x

NSd

fFtd Asl

η⋅fcd

y MRd

≤ εsu ≤ εFu

Hardening

Softening

fFtud

Figure 11.9 ULS for bending moment and axial force: the use of the simplified stress/strain relationship (λ and η coefficients in accordance with specific building codes; MC2010, 2012). ULS, Ultimate limit state.

274

Developments in the Formulation and Reinforcement of Concrete

The increase or the reduction of ductility strongly depends on the ratio between the FRC toughness (in particular fR3) and the reinforcement ratio of longitudinal rebar (ρsl). More research is still needed to better quantify this aspect. With a quite simple procedure, it is possible to calculate a complete axial force versus moment-resistant domain. When referring to a typical beam cross section having two longitudinal reinforcing ratios (ρsl 5 0.75% or 1.50%, fck 5 35 MPa, fck, cube 5 45 MPa, fyk 5 450 MPa, and fR3k 5 2.5 or 5 MPa), the resistant domains for the different FRC properties are plotted in Fig. 11.10 by neglecting the ductility increase of FRC in compression; note the limited contribution of fibers that disappears in the area of failure due to the concrete being in compression.

Domain MRd -N - ULS

(A)

400

ρ=0.75% - fR3k =0.0 MPa ρ=0.75% - fR3k =2.5 MPa

300

ρ=0.75% - fR3k =5.0 MPa

200

MRd (kN/m)

100 0

–4000

–3000

–2000

–1000

0

1000

0

1000

–100 –200 –300 –400

N (kN)

(B)

Domain MRd -N - ULS 400

ρ=1.50% - fR3k =0.0 MPa ρ=1.50% - fR3k =2.5 MPa

300

ρ=1.50% - fR3k =5.0 MPa

200

MRd (kN/m)

100 0 –4000

–3000

–2000

–1000 –100 –200 –300 –400

N (kN)

Figure 11.10 Complete M
N resistant domain: longitudinal reinforcement ratio ρsl 5 0.75% (A) and 1.5% (B).

Fiber-reinforced concrete

275

11.3.5.2 Shear in beams FRC is particularly suitable for enhancing the shear behavior of structural elements (Fig. 11.11) due to the diffused cracking phenomena present at ULS. FRC may totally or partially replace stirrups, thus relieving reinforcement congestion at critical sections such as beam
column junctions in seismic applications. Research studies have mainly focused on the total substitution of stirrups with fibers in all regions requiring the minimum amount of transverse reinforcement (that is necessary for increasing the bearing capacity, the ductility and for giving warning of impending collapse), which is quite promising for structural applications, above all for heavy and light prefabrication. The shear resistance of beams with longitudinal reinforcement without stirrups, according to MC2010 (2012), is given by the following equation (Minelli and Plizzari, 2013): (

) 
 1=3 0:18 fFtuk UkU 100U ρ1U 117:5U 1 0:15UσCP UbWUd VRd;F 5 Ufck γc fctk

(11.13)

where γ c is the partial safety factor for concrete, k is a factor taking into account the size effect (k 5 1 1 (200/d)1/2, with d in mm being the effective depth, # 2); ρsl is the longitudinal reinforcement ratio (#2%); fFtuk is the characteristic value of the ultimate residual tensile strength for FRC at the crack width wu 5 1.5 mm; fck is the characteristic value of the compressive strength; σcp is the average axial stress on 3.0 Fibre contribution on shear strength [37] [37]

[32]

Vu,FRC /Vu,RS (–)

2.5

[37]

[33]

[37]

[32] [33] [33]

2.0

[32] [29] [39] [29] [39] [28]

[28] [33] [36] [28] [30]

[29] [37] [29]

1.5

[32]

Quadratic polynomial curve R 2 =0.35

[32]

[39]

[36] [33] [31][28]

[32] [39]

[36]

[29]

1.0 0

1

2

3

4

5 6 7 8 fR,3 (MPa)

9 10 11 12

Figure 11.11 Increase in shear strength due to fibers: Vu,FRC 5 shear strength of an FRC element; Vu,RS 5 shear strength of a reference sample in RC without transverse reinforcement (Cuenca et al., 2018). FRC, Fiber-reinforced concrete.

276

Developments in the Formulation and Reinforcement of Concrete

the cross section, due to the loads or to prestressing; bw is the minimum crosssectional width; and d is the effective depth. It can be seen that, since fibers act as distributed reinforcement, FRC modifies the longitudinal reinforcement ratio with a factor depending on the FRC toughness. Although based on an empirical approach, this equation applies for diagonal shear failure (beam behavior). This equation is easily applicable, and it is consistent with Eurocode 2 EN 1992-1-1 (2005) proposal for the shear design of RC beams that is extensively used. Furthermore, this equation assumes FRC as a concrete having a remarkable toughness that can be taken into account for shear resistance; when toughness is negligible or absent (fFtuk  0), as in plain concrete, shear resistance returns to the classical one proposed by Eurocode 2 EN 1992-1-1 (2005). When stirrups are present, building codes generally suggest adding the FRC contribution to shear resistance to the classical contribution provided by web reinforcement. However, the combination of stirrups and fibers should be better supported by analytical models based on suitable compatibility conditions at a crack between the classical reinforcement and fibers (Fig. 11.12). Research is still in progress on how to best combine rebars and fibers for enhancing their mutual contribution to shear. In summary, fibers improve the shear resisting mechanisms since they provide a residual tensile strength on crack and an enhanced aggregate interlock. From a practical point of view the real benefit from using fiber reinforcement for shear behavior is often related to the possibility of substituting fibers for (A)

ε1

d

f1

θ

Asz fsz

x z

s V (B)

ε1 vcl

fFtu

d

Asz fszcr

s V

Figure 11.12 Equilibrium of a beam loaded in shear: (A) calculated average stresses and (B) local stresses at crack (Minelli & Plizzari, 2010). fszcr is the tensile stress in the stirrup at the crack face and vcl is the shear stress along the crack.

Fiber-reinforced concrete

277

stirrups, at least in some regions of the structure. The practical benefits from a higher stirrup spacing are limited, unless the latter is close to the maximum aggregate size and technological difficulties in pouring concrete may occur.

11.3.5.3 Torsion in beams According to MC2010 (2012), in beams without longitudinal and transverse reinforcement, when FRC with hardening tensile behavior is used and members without longitudinal rebars and transverse reinforcement are considered, the principal tensile stress shall not be higher than the design tensile strength: σ1 #

f Ftuk γF

(11.14)

where fFtuk (MPa) is the characteristic value of the ultimate residual tensile strength for FRC, by considering wu 5 1.5 mm. In beams with longitudinal and transverse reinforcement the presence of fibers increases the torsion capacity; however, since design models are not currently available, models should be verified by experiments on real size elements.

11.3.6 Fiber-reinforced concrete slabs Slabs are typical applications of cast-in-place FRC, as they are used to build industrial pavements (Sorelli, Meda, & Plizzari, 1997), and floors for multistory buildings (ACI 544.6R-15, 2015) or foundations (Falkner, Huang, & Teutsch, 1995). Stress redistribution resulting from the high internal redundancy of these structures may allow for the exploitation of the postcracking strength and toughness of FRC, leading to a possible reduction of conventional reinforcement.

11.3.6.1 Slabs on grade One of the earliest and, therefore, most widespread applications of FRC are represented by slabs on grade, which are typical for industrial floors or foundation slabs where the subgrade is often assumed as elastic (Silfwerbrand, 2004). Even though FRC was not yet present in building codes, industrial floors were accepted because they were not considered main structural elements. Due to the very high degree of redundancy of these structures, FRC may completely replace the conventional reinforcement (rebars or welded mesh) with the exception of areas under concentrated loads, especially when they are present close to edges or corners, where conventional reinforcement may be necessary (Belletti, Cerioni, Meda, & Plizzari, 2008).

11.3.6.2 Elevated slabs Another structural applications of FRC is represented by elevated slabs due to the high degree of redundancy (lower than in slabs on grade but still significant) of

278

Developments in the Formulation and Reinforcement of Concrete

these structures. The real applications worldwide available (Barros, Salehian, Pires, & Gonc¸alves, 2012; Destre´e, 2004; Parmentier, Van Itterbeeck, & Skowron, 2014) often used high amounts of steel fibers as main flexural reinforcement, whereas conventional rebars were mainly used as structural integrity reinforcement along columns (or piles alignments) in order to avoid progressive collapse of the structure (Mitchell & Cook, 1984; Sasani & Sagiroglu, 2008). Accordingly, ACI 544.6R-15 (2015) suggests the construction of FRC elevated slabs by using steel fibers as the only primary reinforcement in combination with a minimum amount of rebars used as “antiprogressive collapse reinforcement.” However, when considering the remarkably concentrated tensile stresses present in the bottom side of a slab along the alignments of the columns or at the top side on the columns (Fig. 11.13), an optimized reinforcement can be obtained by using a few rebars where tensile stress concentrations are present. This choice generally reduces the necessary FRC toughness that brings about a reduction of the entire structural cost. Referring to FRC slabs, the design procedures suggested by the codes are usually based on the yield line theory. The latter is certainly a powerful analytical tool, but it cannot be easily implemented for proportioning and verifying slabs made with optimized reinforcement. The use of advanced analysis procedures, such as those based on nonlinear finite element (NLFE) models, is generally more suitable to get a proper prediction of the structural behavior but is not widespread among structural designers since NLFE codes are not readily available. Based on the design requirements reported by fib MC2010 (2012), a simplified procedure for designing HRC elevated slabs was proposed by Facconi et al. (2019). In addition to the bottom reinforcement generally used in FRC elevated mEd,x Lint,5=L/2+Lp/2 Lint,8

Lint,7=L/2 Lint,9

mRd,FRC

y distance from slab border 3L/2+Lp/2

L+Lp/2

mRd,FRC

Lint,1

Lint,2

Lint,3=L/2

Lint,4

Moments line A Moments line B

Distance y

Lp/2

Lint,6=L/2

Moments line C Moments line D

x y

A

B

C

D

Figure 11.13 Typical distribution of the maximum and minimum design bending moments mEd,x acting along the most critical section lines (lines A, B, C, and D) (Facconi, Plizzari, & Minelli, 2019).

Fiber-reinforced concrete

279

slabs (i.e., rebars along column alignments), top reinforcement is also placed over the columns in order to get the best performance in terms of the global capacity of the structure (Fig. 11.14). The resulting combination of fibers and rebars aims at minimizing total reinforcement (fibers 1 rebars) leading to an overall reduction of construction time and costs. The design method is based on an initial linear elastic finite element analysis to determine the bending moments used for proportioning the hybrid reinforcement. The verification of the structural safety factors is performed by NLFE analyses including the postcracking tensile behavior of FRC. The approach proposed for the reinforcement of slabs allows designing the required amount of conventional reinforcement once the residual strength of the

Figure 11.14 Additional reinforcement detailing: (A) typical slab section; (B) top reinforcement layout; (C) bottom reinforcement layout; and (D) rules for determining top reinforcement length.

280

Developments in the Formulation and Reinforcement of Concrete

FRC is selected. It is worth remarking that the choice of the FRC postcracking strength is not of minor importance as it affects the total amount of rebars. Case studies, carried out by Facconi et al. (2019) on traditional slabs (span 5 6.0 m, thickness 5 span/30, total load 5 10
12 kN/m2), demonstrate a saving of about 30% of the total reinforcement when using an FRC having fR3k ranging between 3 and 5 MPa (Fig. 11.15). The authors demonstrated that the use of top reinforcement on the columns in combination with bottom rebars appears to be fundamental to optimize the total reinforcement (Facconi et al., 2019). In fact, if top reinforcement is not adopted, a remarkable amount of fibers must be used for increasing the FRC toughness in order to resist negative moments acting on the columns supporting the slab.

11.3.6.3 Punching in slabs Punching is an important issue for thin slabs supported on columns, since it governs their strength and deformation capacity. Failure in punching is brittle for slabs without transverse reinforcement and can lead to the progressive collapse of the structure. Due to the significance of this failure mode, punching shear has been the object of large experimental and theoretical efforts since the 1950s. Following these efforts, a number of design approaches have been developed. MC2010 (2012) adopts the critical shear crack theory (CSCT) (Muttoni & Ferna´ndez Ruiz, 2010), which is based on a physical model to provide a rational tool for design. According

Indicative fiber content (kg/m3) 15 20 25 30 35 40

0

50

70

60

Total steel content (fibers+rebars) (kg/m3)

110 G2,k +Q k=8Qk=4kN/m2 kN/m2 Overload With rebar detailing

100

G2,k +Q k=6 kN/m2 Serie8

90 No rebar detailing

80

Minimum : Fiber content = 40 kg/m3 Total steel content=62 kg/m3

70

Fiber dosage

Fiber aspect ratio

Fiber tensile strength

fR3k

(kg/m3)

(–)

(GPa)

(MPa)

0

0.0

15

2.1

20

2.7

25 30

60 Minimum : Fiber content = 35 kg/m3 Total steel content=51 kg/m3

50 40 0

1

2

3

4

5

6

7

8

9

3.4 80

2

4.1

40

5.5

50

6.9

60

8.2

70

9.6

10

f R3k (MPa)

Figure 11.15 Total steel content versus fR3k response, resulting from a parametric study on a 200 mm thick slab containing hybrid reinforcement designed according to the design method proposed by Facconi et al. (2019).

Fiber-reinforced concrete

281

(A)

(B)

(C)

(D)

(E)

Figure 11.16 Fiber-reinforced members: (A) behavior of FRC after cracking; (B) critical shear crack in slabs; (C) assumed distribution of crack widths along the failure surface; (D) profile of fiber’s stresses along the failure surface; and (E) matrix (concrete) and fiber contributions to punching shear strength (Muttoni & Ferna´ndez Ruiz, 2010). FRC, Fiberreinforced concrete.

to the CSCT model, FRC behavior after cracking depends both on the matrix and on the activation and strength of the fibers (Fig. 11.16). A detailed investigation on the application of the CSCT to punching design of FRC has been presented in Maya Duque, Ferna´ndez Ruiz, Muttoni, and Foster (2012).

11.3.7 Fiber-reinforced concrete tunnel segments FRC has been widely used in conventional tunnels as temporary lining before the final cast-in-situ lining is applied. Currently, there is a growing interest in using FRC as the final lining in conventional tunnels. However, most of the FRC structural applications in tunnels are for segmental lining (when precast tunnel segments are adopted; Fig. 11.17).

282

Developments in the Formulation and Reinforcement of Concrete

Figure 11.17 Typical precast tunnel lining.

In the last two decades, FRC was progressively adopted (with or without conventional rebars) in several precast tunnel lining projects (ACI 544.7R-16, 2016; fib Bulletin 83, 2017; Hansel & Guirguis, 2011; ITA Report n.16, 2016; De la Fuente, Pujadas, Blanco, & Aguado, 2012). The main reasons for using FRC in segmental lining are summarized as follows: G

G

G

FRC allows for better crack control, especially when used in combination with traditional reinforcing bars. Hence, smaller crack openings are expected at SLS resulting in a considerable improvement of the durability of the structure. FRC has a higher resistance to impact loading; hence, no significant detachment of cracked concrete blocks in tunnels is expected. FRC allows an improvement of the industrial process due to the reduction or elimination of rebars, which means time reduction in handling and placing of curved rebars. Furthermore, storage areas for reinforcement cages can be reduced or avoided.

Most of the early applications were initially based on steel FRC even though there is now a growing interest in the technical community on macrosynthetic fibers for the use in underground structures (Conforti, Tiberti, Plizzari, Caratelli, & Meda, 2017; Di Prisco, Tomba, Bonalumi, & Meda, 2015). One of the most severe loading conditions occurs during tunnel boring machine (TBM) operations, when the thrust jack forces are applied (Liao, De la Fuente, Cavalaro, & Aguado, 2015; Tiberti, Conforti, & Plizzari, 2015). Actually, although this phenomenon occurs as a temporary loading condition, it tends to govern the amount of reinforcement of the segment that contributes also to the final state when the lining is loaded by the ground pressure for the entire service life. Furthermore, during TBM operations, a complex stress distribution occurs in tunnel segments, and cracks may occur, thus compromising the use of the segment in the lining. Depending on the lining geometry (in particular the slenderness) and on the tunnel overburden, the precast segment may be constructed with FRC only (Fig. 11.18A) or with a combination of FRC and rebars (Fig. 11.18B). Special attention has to be devoted to possible irregularities (e.g., eccentric placement of TBM thrust shoes or an irregular support of the segment on the previous ring), since they greatly influence both the local and global behaviors of segments. In the most severe conditions (i.e., occurrence of uneven supports combined with outward eccentricity), in general a combination of a low amount of conventional rebars and

Fiber-reinforced concrete

283

Figure 11.18 Possible reinforcement configurations in tunnel segments.

Figure 11.19 Typical water tank (A) with optimized reinforcement (B).

FRC is able to guarantee both the local and global behaviors of segments similar to that observed in the traditional RC segments. The use of FRC (with or without rebars) generally allows a reduction of the reinforcement based on conventional rebars only (Fig. 11.18C).

11.3.8 Fiber-reinforced concrete for precast elements FRC is already a reality for the precast industry due to the enhanced industrialization process allowed by the reduction or removal of conventional rebars. Significant applications of FRC in the precast industry are represented by beams, thin-web roof elements, fac¸ade panels, water tanks (Fig. 11.19), and pipes.

11.3.9 Fiber-reinforced concrete for structural rehabilitation FRC having high performance (high-performance FRC or ultrahigh-performance FRC) has been widely used for repair and strengthening of bridge decks, bridge piers (as external jacketing), beams, and columns. When used for jacketing, high-performance FRC increases the structural resistance and significantly enhances the durability by providing a new service life to the structure.

284

Developments in the Formulation and Reinforcement of Concrete

References ACI 544. 6R-15. (2015). Report on design and construction of steel fiber-reinforced concrete elevated slabs. ACI Committee 544 R16. (2016). Report on design and construction of fiber reinforced precast concrete tunnel segments. In ACI 544.7R-16 (p. 36). American Concrete Institute. ASTM C1399. (2015). Standard test method for obtaining average residual-strength of fibrereinforced concrete. West Conshohocken, PA: ASTM International. ASTM C1550. (2012). Standard test method for flexural toughness of fiber reinforced concrete (using centrally loaded round panel). West Conshohocken, PA: ASTM International. ASTM C1609. (2012). Standard test method for flexural performance of fiber-reinforced concrete (using beam with third-point loading). West Conshohocken, PA: ASTM International. Banthia, N., & Gupta, R. (2004). Hybrid fibre reinforced concrete (HyFRC): Fibre synergy in high strength matrices. Materials and Structures (RILEM), 37, 707
716. Barros, J. A. O., Salehian, H., Pires, N. M. M. A., & Gonc¸alves, D. M. F. (2012). Design and testing elevated steel fiber reinforced self-compacting concrete slabs. In BEFIB2012— Fiber reinforced concrete (p. 12). Beeby, A. W. (2004). The influence of the parameter φ/ρeff on crack widths. Structural Concrete, 5(2), 71
83. Belletti, B., Cerioni, R., Meda, A., & Plizzari, G. A. (2008). Design aspects on steel fiber reinforced concrete pavements. ASCE Journal of Materials in Civil Engineering, 20(9), 599
607. Bentur, A., & Mindess, S. (2007). Fibre reinforced cementitious composites (2nd ed.). London and New York: Taylor & Francis, 601 pp. Campione, G., & La Mendola, L. (2004). Behaviour in compression of lightweight fibre reinforced concrete confined with transverse steel reinforcement. Elsevier Cement and Concrete Composites, 26(6), 645
656. CEB-FIP Model Code 1990. (1993). Model Code 1990: Final version, Bulletins 213 and 214. Fe´de´ration Internationale du Be´ton (fib). Chiaia, B., Fantilli, A., & Vallini, P. (2009). Combining fiber-reinforced concrete with traditional reinforcement in tunnel linings. Engineering Structures, 31(7), 1600
1606. Conforti, A., Minelli, F., Plizzari, G. A., & Tiberti, G. (2018). Comparing test methods for the mechanical characterization of fiber reinforced concrete. Structural Concrete, 19, 656
669. Available from https://doi.org/10.1002/suco.201700057. Conforti, A., Tiberti, G., Plizzari, G. A., Caratelli, A., & Meda, A. (2017). Precast tunnel segments reinforced by macro-synthetic fibers. Tunnelling and Underground Space Technology, 63, 1
11. Cuenca, E., Conforti, A., Minelli, F., Plizzari, G. A., Navarro-Gregori, J., & Serna, P. (2018). A material-performance-based database for FRC and RC elements under shear loading. Materials and Structures, 51, 11. Available from https://doi.org/10.1617/s11527-0171130-7. Cunha, V. M. C. F., Barros, J. A. O., & Sena-Cruz, J. M. (2008). Modelling the influence of age of steel fibre reinforced self-compacting concrete on its compressive behavior. RILEM Materials and Structures Journal, 41(3), 465
478. Destre´e, X. (2004). Structural application of steel fibers as only reinforcing in free suspended elevated slabs: Conditions—Design examples. In Sixth RILEM symposium on fiberreinforced concrete (Vol. 2, pp. 1073
1082).

Fiber-reinforced concrete

285

EN 14651. (2005). Test method for metallic fibre concrete—Measuring the flexural tensile strength (limit of proportionally (LOP), residual) (p. 18). European Committee for Standardization. Eurocode 2 EN 1992-1-1. (2005). Design of concrete structures—Part 1-1: General rules and rules for buildings. European Commission. Facconi, L., Minelli, F., & Plizzari, G. (2016). Steel fiber reinforced self-compacting concrete thin slabs—Experimental study and verification against Model Code 2010 provisions. Engineering Structures, 122, 226
237. Facconi, L., Plizzari, G., & Minelli, F. (2019). Elevated slabs made of hybrid reinforced concrete: Proposal of a new design approach in flexure. Structural Concrete, 20, 52
67. Available from http://doi.org/10.1002/suco.201700278. Falkner, H., Huang, Z., & Teutsch, M. (1995). Comparative study of plain and steel fiber reinforced concrete ground slabs. Concrete International, 17(1), 45
51. Fantilli, A. P., Mihashi, H., & Vallini, P. (2007). Post-peak behaviour of cement-based materials in compression. ACI Materials Journal, 104(5), 501
510. fib Bulletin 83. (2017). Precast tunnel segments in fibre-reinforced concrete, W.P. 1.4.1 tunnels in fiber reinforced concrete. ISSN 1562-3610, ISBN 978-2-88394-123-6. fib Model Code for Concrete Structures. (2010). Lausanne, Switzerland: International Federation for Structural Concrete (fib). Lausanne, Switzerland. De la Fuente, A., Pujadas, P., Blanco, A., & Aguado, A. (2012). Experiences in Barcelona with the use of fibres in segmental linings. Tunnelling and Underground Space Technology, 27(1), 60
71. Hansel, D., & Guirguis, P. (2011). Steel-fibre-reinforced segmental linings: State-of-the-art and completed projects. Tunnel, 30(1), 14
24. Harajli, M. H., & Mabsout, M. E. (2002). Evaluation of bond strength of steel reinforcing bars in plain and fibre-reinforced concrete. ACI Structural Journal, 99(4), 509
517. ITA Report n. 16. (2016). Twenty years of FRC tunnel segments practice: Lessons learnt and proposed design principles (p. 71). ISBN 978-2-970-1013-5-2. Li, V. C. (2003). On engineered cementitious composites (EEC)—A review of the material and its applications. Journal of Advanced Concrete Technology, 1, 215
230. Li, V. C. (2005). Engineered cementitious composites. In N. Banthia, T. Uomoto, A. Bentur, & S. P. Shah (Eds.), Construction materials, proceedings of ConMat ’05 and Mindess symposium. Vancouver, BC: University of British Columbia, CD-ROM. Liao, L., De la Fuente, A., Cavalaro, S., & Aguado, A. (2015). Design of FRC tunnel segments considering the ductility requirements of the Model Code 2010. Tunnelling and Underground Space Technology, 47, 200
210. Maya Duque, L. F., Ferna´ndez Ruiz, M., Muttoni, A., & Foster, S. J. (2012). Punching shear strength of steel fibre reinforced concrete slabs. Engineering Structures, 40, 93
94. Meda, A., Minelli, F., & Plizzari, G. A. (2012). Flexural behaviour of RC beams in fibre reinforced concrete. Composites Part B: Engineering, 43(8), 2930
2937, ISSN 1359-8368. Mindess, S. (2008). Fibrous concrete reinforcement. In S. Mindess (Ed.), Developments in the formulation and reinforcement of concrete (pp. 154
166). Cambridge, England: Woodhead Publishing Limited. Mindess, S., Young, J. F., & Darwin, D. (2003). Concrete (2nd ed.). Upper Saddle River, NJ: Prentice-Hall. Minelli, F., & Plizzari, G. A. (2010). Shear strength of FRC members with little or no shear reinforcement: A new analytical model. In fib Bulletin 57: Shear and punching shear in

286

Developments in the Formulation and Reinforcement of Concrete

RC and FRC elements (Vol. unico, pp. 211
225). Workshop 15
16 October 2010, Salo`, Italy. ISSN 1562-3610, ISBN 978-2-88394-097-0. Minelli, F., & Plizzari, G. A. (2013). On the effectiveness of steel fibres as shear reinforcement. ACI Structural Journal, 110(3), 379
389, ISSN 0889-3241. Mitchell, D., & Cook, W. D. (1984). Preventing progressive collapse of slab structures. Journal of Structural Engineering, 110(7), 1513
1532. Available from https://doi.org/ 10.1061/(ASCE)0733-9445(1984)110:7(1513). Mobasher, B., Yao, Y., & Soranakom, C. (2015). Analytical solutions for flexural design of hybrid steel fiber reinforced concrete beams. Engineering Structures, 100, 164
177, ISSN 0141-0296. Muttoni, A., & Ferna´ndez Ruiz, M. (2010). The critical shear crack theory as a mechanical model for punching shear design and its application to code provisions. In Bulletin 57 (pp. 31
60). Lausanne, Switzerland: Fe´de´ration Internationale du Be´ton (fib). Naaman, A. E., & Gopalaratnam, V. S. (1983). Impact properties of steel fibre reinforced concrete in bending. International Journal of Cement Composites and Lightweight Concrete, 5(4), 225
237. Parent, E., & Rossi, P. (2004). A new multi-scale cement composite for civil engineering and building construction fields. Advance in cement composites through science and engineering. Bagneux, France: RILE MPublications, CD-ROM Paper No. 14, Hybrid Fiber Session. Parmentier, B., Van Itterbeeck, P., & Skowron, A., (2014). The behavior of SFRC flat slabs: The Limelette full-scale experiments for supporting design model codes. In J. P. Charron, B. Massicotte, B. Mobasher, & G. Plizzari (Eds.), FRC 2014 joint ACI-fib Intl. workshop—Fibre-reinforced concrete: From design to structural applications. Montreal, Canada. Plizzari, G. A. (1999). Bond and splitting crack development in normal and high strength fibre reinforced concrete. In N. P. Jones, & R. G. Ghanem (Eds.), Proceedings of ASCE engineering mechanics division conference (pp. 13
16). The Johns Hopkins University. Di Prisco, M., Plizzari, G., & Vandewalle, L. (2014). Structural design according to fib MC 2010: Comparison between RC and FRC elements. In Proceedings of FRC 2014 joint ACI-fib international workshop, fibre reinforced concrete: From design to structural applications (pp. 69
87). Di Prisco, M., Tomba, S., Bonalumi, P., & Meda, A. (2015). On the use of macro synthetic fibres in precast tunnel segments. In Proceedings of World Tunnel Congress 2015 SEE tunnel: Promoting tunneling in SEE region. Dubrovnik, Croatia: Lacroma Valamar Congress Center. Romualdi, J. P., & Batson, G. B. (1963a). Mechanics of crack arrest in concrete. Journal of Engineering Mechanics, ASCE, 89, 147
168. Romualdi, J. P., & Batson, G. B. (1963b). Behaviour of reinforced concrete beams with closely spaced reinforcement. Journal of the American Concrete Institute, 60, 775
789. Sasani, M., & Sagiroglu, S. (2008). Progressive collapse of reinforced concrete structures: A multihazard perspective. ACI Structural Journal, 105(1), 96
103. Schumacher, P. (2006). Rotation capacity of self-compacting steel fibre reinforced concrete (Ph.D. thesis). Delft University. Silfwerbrand, J. (2004). Design of steel fiber-reinforced concrete slabs on grade for restrained loading. In M. Di Prisco, G. A. Plizzari, & F. Roberto (Eds.), Sixth RILEM symposium on fiber-reinforced concretes (FRC) (pp. 975
984). Sorelli, L., Meda, A., & Plizzari, G. (1997). Steel fiber concrete slabs on ground: A structural matter. ACI Structural Journal, 103(4), 551
558.

Fiber-reinforced concrete

287

Sukontasukkul, P., Mindess, S., Banthia, N., & Mikami, T. (2001). Impact resistance of laterally confined fiber reinforced concrete plates. Materials and Structures (RILEM), 34, 612
618. Thibaux, T., Hajar, Z., Simon, A., & Chanut, S. (2004), Construction of an ultra-highperformance fibre-reinforced concrete thin-shelled structure over the Millau viaduct toll gates. In M. di Prisco, R. Felicetti, & G. A. Plizzari (Eds.), Fibre-reinforced concrete, BEFIB 2004 (Vol. 2, pp. 1183
1192). RILEM Proceedings PRO39, Bagneux, France: RILEM Publications. Tiberti, G. (2014). Concrete tunnel segments with combined traditional and fibre reinforcement: Optimization of the structural behaviour and design aspects (Ph.D. thesis). Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia. Roma, Italy: Aracne editrice s.r.l., p. 396. ISBN 978-88-5487005-5. Tiberti, G., Conforti, A., & Plizzari, G. A. (2015). Precast segments under TBM hydraulic jacks: Experimental investigation on the local splitting behavior. Tunnelling and Underground Space Technology, 50, 438
450. Tiberti, G., Minelli, F., & Plizzari, G. (2014). Reinforcement optimization of fiber reinforced concrete linings for conventional tunnels. Composites Part B: Engineering, 58, 199
207, ISSN 1359-8368. Vandewalle, L. (2000). Cracking behaviour of concrete beams reinforced with a combination of ordinary reinforcement and steel fibers. Materials and Structures, 33(3), 164
170. Walraven, J. C. (1999). Tension stiffening, textbook on behaviour, design and performance update knowledge of the CEB/FIP Model Code 1990 (Vol. 1, pp. 189
196). ISSN 1562-3610, ISBN 2-88394-041-X. Yan, C., & Mindess, S. (1994). Bond between epoxy coated reinforcing bars and concrete under impact loading. Canadian Journal of Civil Engineering, 21(1), 89
100. Yan, C., & Mindess, S. (2001). Bond between concrete and steel reinforcing bars under impact loading. In A. H. Brandt, & I. H. Marshall (Eds.), Brittle matrix composites 3 (pp. 318
327). Elsevier Applied Science.