Guidance for the design of steel-fibre-reinforced concrete

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Acknowledgements The work of preparing this Report was funded by the following organisations: Arcelor, Bekaert, Propex Concrete Systems, The Highways Agency

The Concrete Society is grateful to the following for providing photographs for inclusion in the Report: Arcelor (Figures 3, 4, 7, 8,10, 11 and 36) Bekaert (Figures 6, 9,12,16,17, 20, 22, 24 and 38) Halcrow (Figure 23) Kingspan (Figures 13 and 14) Propex Concrete Systems (Figures 5,15,21 and 37)

Published by The Concrete Society

CCIP-017 Published March 2007 ISBN 1-904482-32-5 0 The Concrete Society

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Guidance for the Design of

~ Contents V

~

1 Members of the Project Steering Group List of figures vi List of tables vi i

... Notation Vl l l

1. Introduction 1 1.1 Background 1 1.2 Aims and scope of document 1 1.3 Terminology 2

2. Fibres and their behaviour 4 2.1 Types of fibre 4 2.2 How steel fibres work 5

2.21 Enhancement of concrete properties 5 2.2.2 Comparison with concrete reinforced with conventional steel

bars or fabric 6

2.4 7 3. Overview of typical applications 8

3.1 Ground-supported slabs 8 3.1.1 Industrial floors 8 3.1.2 Roads and external paving 8

2.3 Combination with micro synthetic fibres 7 5 ust a i na bi li tyhecycli ng

3.1.3 Overlays 9 31.4 Railways 10

3.2 Suspended slabs 10

3.2.1 General 10

3.2.2 Pile-supported slabs 10

3.2.3 Elevated suspended slabs 11

3.3 In-situ concrete 12 ~

3.4 Composite slabs on steel decking 13 3.5 Precast units 14

3.51 Tunnel lining segments 14 15

3.5.3 Precast beams and panels 15 3.6 Sprayed concrete (shotcrete) 16

3.6.1 General 16 3.6.2 Tunnel linings 17 3.6.3 Slope and rock stabilisation 18

3.5.2 Storage tanks, pipes, etc.

3.6.4 Repairs 19 3.7 Structures subjected to blast and ballistic loading 19

4. Test methods to establish material properties of SFRC 20 4.1 General 20

4.1.1 Axial tensile strength of SFRC 20 41.2 Flexural strength of SFRC 21

4.2 Beam tests to determine residual flexural strength 21 4.2.1 Introduction 21 4.2.2 BS EN 14651: 2005 22 4.2.3 RlLEM TC-162 TDF 23 4.2.4 JCI-SF4 test 23 4.2.5 EFNARC beam test 24 4.2.6 BS EN 14488 beam test 24 4.2.7 DIN beam test 24 4.2.8 ASTM beam tests 24

4.3 Slab tests to determine toughness 2s 4.31 EFNARC 2s 4.3.2 BS EN 14488 plate test 25 4.3.3 ASTM tests 25 4.3.4 Statically indeterminate slab tests not covered by Standards 26 4.3.5 Discussion 26

5. Overview of design processes 28 5.1 General 28 5.2 Design on the basis of material properties 28 5.3 Design assisted by testing 28 5.4 Design on the basis of performance 29

ii

6. General design approaches 30 61 Background 30

611 General 30 61.2 Elastic design 33 61.3 Yield line design 33

6.2 Design recommendations for flexure 34 6.21 Design in terms of Re,3: Sections without conventional steel

reinforcement 34 6.2.2 Sections with conventional steel reinforcement 36

37 6.2.4 Flexural size effects 39

6.3 Shear strength 39 6.31 Beam shear 39 6.3.2 Punching shear 41

6.4 Serviceability limit state 42 6.41 Deflections 42 6.4.2 Cracking 42 6.4.3 Causes of cracking 42 6.4.4 Crack control 43 6.4.5 Minimum reinforcement 43

6.5 Durability 44

7. Design for specific applications 45 7.l Fire design 45 7.2 Ground-supported slabs 45

7.21 Industrial floors 45 7.2.2 External paving 46

7.3 Pile-supported slabs 46 7.3.1 Background 46

48 7.3.4 Serviceability limit state check 50 7.3.5 Construction details 51

7.4 Composite floors on steel decking 51

53

6.2.3 Design in terms of BS EN 14651 - Moment:crack width response

7.3.2 Elastic design methods 47 7.3.3 Yield line design of piled rafts

7.5 Sprayed concrete for rock support 53

7.5.2 Semi-empirical approach 54 7.5.3 Use of toughness characterisation 55 7.5.4 Deterministic design 57

7.5 1 I n t rod u c t i o n

7.5.5 Use of ASTM C 1550 round panel tests 60

... 111

7.6 Precast products 62 7.6.1 General design approach 62 7.6.2 Tunnel lining segments 62 7.6.3 Pipes and ancillary products 64

8. Construction aspects 65 81 Cast in-situ or precast concrete 65

811 Specification 65 81.2 Adding fibres to the concrete 65 81.3 Pumping 66 81.4 Placing 67 8.1.5 Compacting and finishing 67 81.6 Health and safety 69 81.7 Testing for fibre quantity and distribution 69

8.2 Sprayed concrete 70 8.21 General guidance 70 8.2.2 Testing for fibre quantity and distribution 70 8.2.3 Health and safety 71

9. In-service performance 72 91 Durability 72 9.2 Inspection and repair 72 9.3 Surface appearance 73 9.4 Demolition and recycling 73

References 74

Appendices 79 A. Design of ground-supported slabs 79

A 1 Bending 79 A.2 Punching shear 81 A.3 Other design considerations 82 A.4 Comparison of test results with the design approach in TR 34 82

B1 Design for flexure 84 8.2 Flexural size effects 85

B.21 Size effects in plain concrete beams 85 B.2.2 Size effects in fibre-reinforced concrete 88 8.2.3 Size effects in RILEM B--E method 90

I

I B. Design 84

iv

Members of the Project Steering Group

Full members Neil Loudon Derrick Beckett John Clarke Xavier Destree

' David Dibb-Fuller

* Lead author for general chapters

** Lead author for sections dealing with

sprayed concrete *** Lead author for

design chapters

Corresponding members

Simon Evans John Greenhalgh Anne Hoekstra Tilo Hoelzel Nary Narayanan Paul Noble Chris Peaston Tony Rice David S t Quinton lan Simms Nick Swannell Tim Viney Robert Vollum

Kevin Baker Brian Bell Tom Clasby Phil Rhodes Phi1 Ridge Copal Sangarapillai Marios Soutsos

Highways Agency (Chairman) Consultant The Concrete Society* (Secretary) Arcelor Bissen Cifford Consulting Propex Concrete Systems Be kaert Bekaert Burks Green Clark Smith Partnership Abbey Pynford Arup Arcelor Sheffield Ltd Kingspan Steel Construction Institute Halcrow** Bekaert Imperial College***

Jordan Pritchard Corman Network Rail Cement, Concrete and Aggregates Australia Waterman Group WA Fairhurst & Partners NHBC Technical Liverpool University

V

List of figures

Figure 1 Derivation of equivalent flexural stress. Figure 2 Types of steel fibre. Figure 3 Casting industrial floor. Figure 4 Industrial floor in service. Figure 5 Storage area in Southampton Docks. Figure 6 Aircraft hard-standing. Figure 7 Testing elevated suspended slab. Figure 8 Construction of steel-free elevated suspended slab in Walmley, Birmingham. Figure 9 Construction of basement using Insulating Concrete Formwork. Figure 10 In-situ concrete wall. Figure 11 Motorway barrier in Austria. Figure 12 Lining water supply channel. Figure 13 Casting concrete on steel decking. Figure 14 Retail development incorporating composite slabs. Figure 15 Precast tunnel lining units for the ChannelTunnel Rail Link. Figure 16 Trial assembly of tunnel lining ring. Figure 17 Completed tunnel lining. Figure 18 Long-term test on precast beam with fibre reinforcement. Figure 19 Precast roof beams for distribution centre in Erfurt, Germany. Figure 20 Precast wall panels. Figure 21 Sprayed concrete using hand-held ‘gun’. Figure 22 Spraying concrete using robotic arm. Figure 23 Stockholm Metro with permanent shotcrete linings. Figure 24 Stabilised rock face. Figure 25 Typical graph of load against CMOD for SFRC. Figure 26 Typical load: deflection response for SFRC in a beam test. Figure 27 Idealised moment:curvature diagram for strain hardening material. Figure 28 Simplified stress block for SFRC. Figure 29 Simplified stress block for SFRC with supplementary reinforcement. Figure 30 Simplified stress block for deriving M-w response for SFRC. Figure 31 Typical M-w response for SFRC section. Figure 32 EFNARC residual strength and deformation classes. Figure 33 Rock block or zone of loose rock loading sprayed concrete. Figure 34 Potential modes of sprayed concrete failure. Figure 35 Stress block for steel-fibre-reinforced sprayed concrete tunnel linings derived

from DBV guidelines. Figure 36 Blast machine adding fibres on site. Figure 37 Adding fibres on site via conveyor. Figure 38 Pumping steel fibre concrete for slabs of 10 storey building.

Figure B1 Structural model for Oleson o-w method. Figure B2 Fictitious crack model. Figure 83 Idealised o-w relationship for plain concrete. Figure 84 Load displacement response of plain concrete beam and associated stress

blocks. Figure B5 Influence of doubling beam length and depth on flexural strength. Figure B6 Relative contributions of fibre and concrete t o o-w response of SFRC. Figure 87 Influence of beam depth and crack width on flexural resistance for Oleson o-w

relationship with b, = 0.75. Figure 88 Influence of beam depth and crack width on flexural resistance for Oleson o-w

relationship with b, = 0.5. Figure B9 RlLEM o-E design method. Figure B10 Stress blocks used in derivation of RlLEM o-E method.

List of tables

Table 1

Table 2 Table 3 Table 4 Table 5 Table 6

Table 7

Table 8

Table 9 Table AI

Table B1

Properties of steel-fibre-reinforced concrete in relation to unreinforced concrete. Examples of fibre-only pile-supported slabs. Current state of the art. EFNARC residual strength class definition points. Toughness Performance Levels for different tunnel conditions. Correlation of Toughness Performance Level (TPL), Q System rock support classes and fibre reinforced spayed concrete performance. Correlation between EFNARC beam tests and ASTM C 1550 round panel tests by energy equivalence. Correlation between equivalent flexural strength and energy absorption for low deflection situations. Precast concrete segment loading history. Comparison between measured and predicted strengths of ground-supported slabs. Material properties assumed in Figures 87 and 88.

vii

Notation

[Note that only terms that are used a t a number of locations throughout the Report are defined here.]

fibre cross-sectional area area of tensile reinforcement total area under the load deflection relationship to a deflection of 3.0mm secant modulus of elasticity of concrete span peak moment in bending test or peak moment capacity flexural resistance plastic moment of resistance (Section 4.2.2) peak negative moment (used for sections a t which cracking leads to immediate failure in TR34) peak positive moment (used for sections in which plastic redistribution of moment occurs after cracking in TR34) residual moment at the support when the section reaches M, axial force due to load or prestress test load, or peak post-cracking load or average load to a deflection of span/l50 equivalent flexural ratio, maximum deflection 1.5mm equivalent flexural ratio, maximum deflection 3mm toughness from JCl SF4 test critical fibre fraction volume fraction of fibres

dimensions defined in Figure 5 section width width of web effective depth design compressive strength of concrete (cylinder) characteristic compressive strength of concrete (cylinder) lower characteristic concrete flexural strength mean concrete flexural strength equivalent flexural strength at a deflection of 3mm lower characteristic tensile strength of concrete mean concrete tensile strength equivalent flexural strength flexural strength from BS EN 14651

f,, and f,, characteristic residual strengths at CMOD of 0.5 and 3.5mm respectively f h shrinkage stress

<d

h design residual tensile strength of concrete section depth or slab thickness depth of beam above notch in BS EN 14651 test hSP

viii

uniformly distributed load uniformly 'distributed load a t ultimate stirrup spacing or spacing between fibres perimeter of loaded area length of the shear perimeter a t 2h from the face of the loaded area crack width depth to the neutral axis

material partial safety factor deflection strain strain a t the extreme tensile fibre shrinkage strain hinge rotation Poisson's ratio (taken as 0.2) Aibd stress bond strength creep coefficient

1. I ntroductio n

1 .I Background Concrete is strong in compression but weak in tension. In structural applications this is overcome by providing steel reinforcing bars to carry the tensile forces once the concrete has cracked or by prestressing the concrete so that it remains largely in compression under load. In reinforced concrete, the tensile failure strain of the concrete is significantly lower than the yield strain of the steel reinforcement and the concrete cracks before any significant load is transferred to the steel. In addition to providing sufficient area of steel to carry the tensile stresses a t the ultimate load that is to be applied to the member, the reinforcement is detailed so as to limit the width of the cracks under serviceability conditions to specified levels. In some applications, a nominal or minimum amount of steel is provided to prevent uncontrolled crack development or to prevent failure in the event of accidental overload. In such cases crack widths cannot be predicted accurately.

Steel fibres mixed into the concrete can provide an alternative to the provision of conventional steel bars or welded fabric in some applications. The concept has been in existence for many years (the first patent was applied for in 1874) and it has been used in a limited range of applications: among the first major uses was the patching of bomb craters in runways during World War II. However, it was during the 1970s that commercial use of this material began to gather momentum, particularly in Europe, Japan and the USA.

Today, industrial floors and pavements are major applications for steel-fibre-reinforced concrete. In the United Kingdom, several million square metres of steel-fibre-reinforced slabs have been installed over the past ten years, both for ground-supported and pile- supported floors. Other major applications for fibre-reinforced concrete include external paved areas, sprayed concrete, composite slabs on steel decking and precast elements.

Fibres are often used to replace the nominal conventional steel fabric in ground-bearing slabs. Increasingly, steel fibres are being used in suspended ground floor slabs on piles to replace much, and in many cases all, of the reinforcement. Savings in the cost of supplying and fixing the conventional welded fabric reinforcement that is replaced can offset the extra cost of adding fibres to the concrete. There may also be health and safety benefits resulting from the reduced handling of reinforcement. In addition, problems caused by misplacement of conventional steel in the depth of the slab are avoided.

Although steel fibres are widely used in the UK and elsewhere, clear information is still lacking about the nature, use and properties of fibre-reinforced concrete. This document is intended to provide an introduction to this type of reinforcement, with guidelines on design and application.

1.2 Aims and Scope Of

document Although steel-fibre-reinforced concrete (SFRC) has been used in the UK and elsewhere for a number of years, there are no agreed design approaches for many of the current applications. This differs from conventional reinforced concrete using steel bars or welded fabric, which has been covered by national and international design codes for many years.

1

I

One example is the design of pile-supported floors, which are widely used for industrial buildings, warehouses and similar applications, for which various fibre manufacturers and specialist contractors have produced guidelines. RILEM (the International Union of Labora- tories and Experts in Construction Materials, Systems and Structures) published a design method for steel fibres combined with reinforcement in 2003('). This used the draft Euro- code 2, ENV 1992-1-V2), as a framework but modified it to reflect the behaviour of fibre- reinforced concrete observed in beam tests. In the Netherlands, CUR (the Centre for Civil Engineering Research and Codes) is preparing recommendations for SFRC industrial floors on piles(3); this guidance will be restricted to applications beneath which there will be neither occupancy nor crawl spaces. This restriction is presumably aimed at limiting the risk to life from a failure. It should be noted that in some cases failures of such floors could still lead to a risk to life due to collapse of supported structures or fittings. The choice of design method should take into account this risk.

This Technical Report summarises the wide range of current applications for SFRC, including ground-supported and pile-supported slabs, sprayed concrete, composite slabs on steel decking and precast units. The Report also considers practical aspects such as production and quality control. Where possible it presents a detailed review of the design methodolo- gies currently in use, with the aim of promoting an understanding of the technical issues involved. Normally, it is not possible to give definitive design guidelines but the information provided will allow the designers to exercise judgement in this area of evolving technology.

In general, the concrete in these applications has a fibre content of around 40kg/m3. Ele- vated suspended slabs with dosage in the region of 100kg/m3 have been built but elements with such dosages are outside the scope of this Report, as are ultra-high performance concreted4) which are highly specialised materials that may have a dosage of 150kg/m3 or more.

1.3 Terminology Some of the terms used in this Report may not be familiar to designers more used to conventional reinforced concrete and, hence, some explanations are given below. Some of the literature dealing with fibre-reinforced concrete uses some of the terms interchangeably and occasionally incorrectly. It is important therefore to adopt consistent terminology and definitions. Specific values for the various properties will depend on the strength of the concrete and on the type and dosage of fibres used.

Aspect ratio is the ratio of the length to diameter of a fibre, in which the diameter may be the equivalent diameter, as defined below.

Ball up or balling describes the formation of large clumps of entangled fibres that may occur during the mixing process.

Ductility is the general ability of a material to sustain load beyond a yield point that defines the limit of elastic behaviour (onset of cracking), i.e. as opposed to a brittle material that demonstrates abrupt loss of strength beyond the elastic range.

2

Equivalent diameter of a fibre is the diameter of a circle with an area equal to the average cross-sectional area of the fibre.

Equivalent flexural strength or equivalent flexural stress is the average flexural stress measured in the Japanese beam test described in Section 4.2.4, up to a specified deflection, in excess of the deflection required to cause cracking. Figure 1 illustrates the derivation of equivalent flexural stress.

Equivalent flexural strength ratio is the value of the equivalent flexural strength expressed as a proportion of the flexural strength.

Fibre count is the fibre concentration measured by the number of fibres in a unit volume of concrete.

Flexural strength or peak flexural strength is the maximum flexural tensile stress achieved in a beam test.

Residual flexural strength is the flexural tensile retained by fibre-reinforced concrete after cracking, generally at a specified deflection of the specimen in a test.

Re,3 is the equivalent flexural strength ratio determined up to a deflection of 3mm. (The Re,, value should usually be more than 0.3, otherwise the concrete has to be considered as effectively unreinforced and remains a brittle material.)

Toughness is the ability of fibre-reinforced concrete to sustain loads after cracking of the concrete, i.e. its energy absorption capacity. It should be noted that, in connection with fibre concrete, reference to toughness is to flexural toughness or toughness in bending.

Figure 1 Derivation of equivalent flexural stress.

Load at first crack

Average load under plot to

3mm

3 mm Deflection

2.1 Types of fibre

Figure 2 Types of steel fibre.

2. Fibres and their behaviour

Steel fibres are produced by various processes and are supplied in many different shapes and sizes as shown in Figure 2. They may be either straight or deformed. However, most are round in cross-section with diameters between 0.4 and 1.3mm and lengths ranging between about 25 and 60mm. Steel fibres have a tensile strength typically 2-3 times greater than traditional fabric reinforcement and a significantly greater surface area (for a given mass of steel) to develop bond with the concrete matrix.

Smooth surface (round, flat or of any shape) t a

Indented. etched, roughened surface

E Round with end paddles

7

c Round with end buttons Q - Round with hooked ends

Crimped (round, flat or any section) 1 7

Polveonal twisted fnewl

Some of the physical characteristics of fibres directly affect key aspects of concrete performance while others are less important. The factors considered to have the strongest influence on the performance of a steel fibre in concrete are: rn Bond and anchorage mechanisms (e.g. straight or deformed shape, end cones or

' looked ends) ibre length and diameter, and hence the aspect ratio )osage ( kg/m3)

dosage ensile strength lastic modulus.

- . ibre count (number of fibres per kg of fibre), which is a function of fibre size and

The BS EN 14889-1(5) classifies steel fibres into five Groups, according to the method of manufacture, as follows: Group I Cold-drawn wire Group 11 Cut sheet Group Ill Melt extract Group IV Group V Milled from blocks.

Shaved cold drawn wire

4

Similarly the American Society for Testing and Materials (ASTM) A 820-96a categorises steel fibres by their method of manufacture, but in addition sets minimum requirements for tensile strength, dimensional tolerance, purity, etc. The four basic categories are: Type 1 Drawn wire Type 2 Sl i t sheet Type 3 Melt extract Type 4 Other.

Further methods of characterisation and typical properties include: Cross-section round, flat, crescent, etc. Deformations straight, wavy, end hook, etc. Length 19-60mm Aspect ratio (length/diameter) 30-100 Tensile strength 345-2800MPa Young’s modulus 205CPa Ductility able to bend through 180Owithout rupture.

The behaviour of a concrete element that incorporates fibres is more critical than the properties of the fibres themselves. For this reason, BS EN 14889-1(5) requires the effect of fibres on the strength of concrete t o be determined in accordance with BS EN 14845(7), using the standard notched beam test in BS EN 14651(8).The supplier is required t o declare the amount of fibres in kg/m3 t o achieve a residual (post-cracking) flexural strength of 1.SMPa at a 0Smm opening of the crack and a residual strength of 1MPa at a 3.5mm opening. Details of the test are given in Section 4.2.2.

Various types of polymeric fibres are also available. These may be divided broadly into two types, as follows:

Micro fibres, which mainly influence the fresh properties of the concrete and can also improve the fire resistance. These may be used in combination with steel fibres, see Section 2.3.

capacity. These are covered in another Concrete Society Technical Macro fibres, which, like steel fibres, can provide the concrete with post-cracking

2.2 How steel fibres work 2.21 Enhancement O f

concrete properties Concrete is a brittle material with a low tensile strength. Adding steel fibres to concrete enhances its toughness, ductility and energy absorption capacity under impact. However, at normal dosages, fibres do not affect the flexural strength of the concrete. Fibres in concrete act in various ways, as outlined by Hannant(loJ1l). Firstly, they can reduce the formation and development of cracks due to early-age plastic settlement and drying shrinkage. Secondly, they may provide a degree of post-cracking load-carrying capacity.

5

Table 1 Properties of steel-fibre-reinforced concrete

in relation t o unreinforced concrete.

Notes: * Abrasion resistance is

essentially a function of the concrete matrix

However, if the abrasion is of a gouging nature, e g tracked vehicles or objects dragged across

the floor, steel-fibre- reinforced concrete has

substantial ability to control the micro-

fracture cracking caused by this type of 'impact

abrasion'. * * Because the electrical

conductivity of the concrete IS unaffected,

wire guidance systems in floors can be operated

without difficulty.

2.2.2 Comparison with concrete reinforced with

conventional steel bars or fabric

The mechanisms are as follows: 0 Steel fibres, being randomly distributed in the concrete, intercept micro-cracks as they

0 After cracking, the fibres spanning the crack will provide a degree of residual load- form, inhibiting the tendency for them t o form into larger cracks.

carrying capacity. This capacity can be considerable, depending on the dosage and the type of fibre used, and can be used in plastic design approaches.

The mechanical properties of fibre-reinforced concrete are governed by the fibre type and volume fraction. The level of improvement achieved, compared to plain concrete, depends on the dosage rate and type of fibre used. Some of the properties affected are listed in Table 1.

Abrasion resistance*

Compressive strength

Electrical resistance**

Fatigue resistance

Flexural strength

Freeze-thaw resistance

Impact resistance

Modulus of elasticity

Restrained shrinkage

Shear strength

Spalling resistance

Thermal shock resistance

Toughness

Improvement may be achieved as a result of reduced bleeding.

Little change.

No significant change at fibre dosages generally used.

Improvements even at low dosages.

Little change in first crack strength at dosage rates commonly used.

Can reduce the deterioration caused by freeze-thaw cycling.

Major improvements.

No significant change at fibre dosages generally used.

Even at low dosages, better distribution of stresses can reduce crack widths.

Improvements even at low dosages can be achieved in combination with reinforcing bars.

Being dispersed throughout the matrix, steel fibre reinforcement gives superior protection to exposed areas such as the joint arris.

As with impact resistance, there are improvements even at low dosage rates, a typical application being foundry floors.

Major improvements, even at low dosages.

The purpose of steel fibre reinforcement and conventional reinforcement are distinctly different. Steel fibres are added to concrete mainly t o influence the way in which concrete cracks as it fails. Micro-cracks form when concrete is loaded. Subsequently, the micro- cracks coalesce t o form macro-cracks. Fibres can bridge cracks during loading and, hence, influence mechanical performance. Steel fibres do provide the concrete with a significant post-cracking strength (perhaps half the capacity of the uncracked cross-section) that can be taken into account in design. This is discussed in more detail in Section 61.

In most structural applications, sufficient conventional reinforcement is provided to ensure that the load-bearing capacity of the cracked section exceeds the capacity of the plain concrete. Generally, the steel fibre dosage required t o achieve this level of post-cracking capacity will need t o be in excess of 80kg/m3, which is twice that used in current applications and outside the scope of this Report.

6

2.3 Combination with

micro synthetic fibres

The fibre size plays a significant part in determining the stage a t which fibres are effective during cracking. Research suggests that fine micro fibres (with diameters less than 0.05mm) can increase the elastic limit and strength of concrete by bridging micro-cracks, whilst macro fibres (typically with diameters greater than 0.5mm) can improve post-peak toughness by bridging larger cracks. This observation has led to the practice of fibre hybridisation where material performance is optimised by combining fibres of varying size and moduli to control the cracking process a t different stages in loading.

Polypropylene micro fibres, a t a dosage of about 0.9kg/m3, can be used to improve the properties of the fresh concrete. The fibres make the concrete more cohesive and are found to reduce the risk of blockages during pumping. During compaction, the fibres reduce the amount of bleeding and reduce the risk of segregation. This can lead to a reduction in the risk of plastic settlement cracking and early plastic shrinkage cracking.

In the hardened state, polypropylene micro fibres provide no significant post-cracking strength. However, they have been shown to improve the impact and abrasion resistance. In addition, they are used on some contracts in place of air entrainment to improve the freeze-thaw resistance of exposed concrete. Finally, in applications where the concrete may be exposed to fire, micro fibres are used to reduce the risk of explosive spalling. Part

1-2 of Eurocode 2(lZ) suggests the addition of 2kg/m3 of polypropylene micro fibres as one of the methods used to reduce explosive spalling for high strength concrete.

2.4 Sustainability/recycling As indicated earlier, one of the main reasons for using SFRC is to improve and simplify the construction process, with resulting health and safety implications. In many applications the use of steel fibres in place of bar or fabric has the potential to reduce the member thickness, which will result in the use of less material. When required, demolition should be straightforward (although currently there is l i tt le experience) and it should be possible to fully recycle the materials.

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3.1 Ground-supported slabs 31 1 Industrial floors

3. Overview of typical applications

Steel fibres are widely used for ground-supported industrial floor slabs as the easy and fast installation of the slab reduces the total time of construction. The first applications in the UK were in the early 1980s. Over the years floor areas have increased and construction techniques have developed. In 1991, Tilden Smith(13) described the first 'jointless' slab to be constructed in the UK, with a total area of 4800m'. This would also appear to be one of the first slabs constructed using laser-controlled equipment. Harvey(14) gives details of the construction of a 38,000m2 fibre-reinforced ground-supported floor slab. The thickness was 2OOmm and the fibre dosage varied between 25kg/m3 and 30kg/m3, depending on the ground conditions and the loading requirement. Eddy(15) describes the use of steel fibres for the internal (and external) slab of a distribution centre in Doncaster with a total area of the two slabs in excess of 125,000m2. The slab thickness was 175mm and the fibre dosage 35kg/m3. Figures 3 and 4 depict the casting and service use of industrial floors.

Right Figure 3 Casting industrial floor.

farright Figure 4 Industrial floor in rorvice.

m u

31.2 Roads and external paving

There are numerous examples of steel-fibre-reinforced concrete being used for external paving. As noted above, Eddy(ls) describes the construction of the external slab of a distribution centre in Doncaster. There are various examples of the use of steel-fibre-reinforced concrete in Southampton Docks (see Figure 5), both for areas used for the handling and storage of containers and for access roads.

Steel fibres have been used in airfield construction (see Figure 6). They are used for the forecourts of filling stations in the Netherlands, where there are guidelines for the design and construction of suitable slabs.

8

d

I . J' r 1 P

Aboveleft Figure 5

Above right Figure 6 Aircraft hard-standing.

An unpublished TRL (Transport Research Laboratory) Report(16) has reviewed the use of steel- fibre-reinforced concrete for highways and similar applications. The authors report that steel-fibre-reinforced pavements have been constructed throughout New South Wales in situations such as roundabouts and intersections where high centrifugal loading induces

Stwage Southampton

extreme stresses. Elsewhere in Australia, steel-fibre-reinforced concrete has been used for major arterial roads since the 1970s. In Spain, steel-fibre-reinforced concrete has been used where the loading was very high or where there was a particular need to reduce the slab thickness. A number of applications are reported from the USA. In France, and elsewhere, steel-fibre-reinforced roller-compacted concrete (with a fibre dosage of around 30kg/m3) has been used for road construction, with a thin top layer of asphalt.

AASHTO (American Association of State Highway and Transportation Officials) Report S-TF36-1(17) gives information and guidelines on fibre-reinforced concrete, covering propor- tioning, mixing, placing and finishing for applications in pavements, bridges and overlays.

31.3 Overlays Trials were carried out on part of the M10 motorway in Hertfordshire in the late 1970s. Sections of the concrete road had weathered badly after a short period in service and were overlaid with steel-fibre-reinforced concrete(ls). The approach would appear to have been effective, with any cracks that formed being well controlled. Cores were taken through some of the cracks; corrosion of the fibres was observed at cracks of 'medium' width (0.5-1.2mm) but no corrosion at 'fine' cracks (below 0.5mm). Monitoring was only carried out for two years and the report does not draw any firm conclusions on the effectiveness of the overlay

The use of fibre-reinforced overlays (or 'white topping') would appear to be a popular method for rehabilitating both concrete and asphalt roads in the USA because of the speed of installation and the reduced thickness of material required. Chandler and Hassan(16) note that overlay trials were carried out in Iowa in the mid-I970s, with a 100-125mm thick layer of concrete. Vandewalle('9) reported on similar overlays applied to both concrete and asphalt pavements in the mid-I980s, which performed very well under heavy and dense traffic.

31.4 Railways Steel-fibre-reinforced concrete was used for the replacement of 260m of the track bed slab in the Thameslink tunnels in London(zo). Fibres were selected in preference to traditional bar reinforcement so that the thickness of the slab could be reduced, allowing a larger loading gauge for the railway. Extensive trials were carried out, to ensure that the 50MPa concrete containing 50kg/m3 of 60mrn-long fibres could be successfully pumped into position.

3.2 Suspended slabs 3.2.1 General In a suspended slab al l the load is carried by discrete supporting elements rather than by

the ground beneath the slab. The support may be an array of piles or columns. Although the structural behaviour of the slab is the same in both cases, the two types of slab are discussed separately in the following Sections as the consequences of failure are very different.

3.2.2 Pile-supported slabs Pile-supported ground floor slabs are currently being designed using steel fibres to replace some or al l of the traditional reinforcement. The result is a homogeneous concrete slab, which can be installed quickly. It should be noted that a slip joint is commonly introduced a t the interface between the top of the piles and the slab to minimise the risk of cracking caused by restrained movements including shrinkage, see also Section 7.3.5.

Pile-supported slabs without any conventional reinforcement for structural purposes have been constructed in the UK since the mid-1990s. In 2001 DestreeP') reported that over 5,000,000m2 of this type of flooring had been constructed worldwide. It has been estimated that about 2,000,000m2 of pile-supported floors reinforced only with fibres have now been constructed in the UK; one supplier provides details of over 20 contracts, varying in size from 5000 to 100,000m2. Some examples are given in Table 2.The type of fibre used and the applied loading will dictate the spacing of the piles, the slab thickness and fibre dosage. It should be noted that the slab described by Eddy(22) was required to carry very heavy racking loads, leading to the requirement for the 400mm thick floor. Some conventional reinforcement was included in the slab described by Little(23) but this was only to provide ties between the feet of the portal frames of the building.

Table 2 Examples of fibre-only pile-supported slabs.

Hull 10,000 200 50 B e ~ k e t t ( ~ ~ )

Chesh t re 52,000 3 6 x 3 6 400 45 Eddy(zz)

Poole, Dorset 3 5 x 3 0 220 40 ~ i t t l e ( ~ ~ )

Thurrock, Essex 46,000 3 0 x 3 0 230 45 Bouhon & Ale~andre@~)

Waltham Abbey, Essex 55,000 3 0 x 3 0 250 45 Eddy(26)

Peterborough 85,000 4 0 x 4 0 270or310 50 Eddy(z7)

10

Overview of typical applications

An example of the use of a combination of steel fibres with conventional reinforcement was the 6300m2 floor of a factory in Lancashire(28). The 325mm thick floor was supported on a 3.3 x 2.8m grid of piles. Prefabricated cages of reinforcement were used to form virtual beams between the pile heads. The concrete contained 45kg/m3 of steel fibres, with polypropylene micro fibres to improve the resistance to plastic cracking and settlement.

Hedebratt and Silf~erbrandc~~l reported that more than 300,000m2 of pile-supported floors with combined reinforcement had been constructed in Sweden between 2001 and 2005.

3.2.3 Elevated suspended A recent development arising from experience with pile-supported slabs has been the use of steel fibres for elevated suspended slabs, i.e. slabs fully supported by columns. Tests have that steel fibres can be used to replace all the conventional flexural and shear reinforcement for slabs with column spacings in the range 5-8m. Figure 7 shows the slab under test. A limited amount of bar reinforcement is provided between the column heads to satisfy the requirements in BS 8110 and other design codes for horizontal ties to ensure robustness. The fibre dosages used are 100kg/m3 or more, which is significantly higher than those used in pile-supported floors, and thus outside the scope of the design approaches discussed in this Report.

On the basis of the results of the trials, there have been a number of actual applications. In the UK the first was for the initial floor slabs of four blocks for two-storey apartments in Walmley, Birmingham.The slabs, which had a total plan area of 770m2, were 180- 200mm thick and spanned about 6m between supports. The fibre dosage was 100kg/m3, which replaced al l the structural reinforcement except the bars required for robustness. Figure 8 shows one of the slabs being cast. There have been other applications in Belgium and the Baltic States.

Belowleft Figure 7 Testing elevated suspended slab.

Belowright Figure 8 Construction of steel-free elevated suspended

slab inwalmley, Birmingham.

3.3 In-situ concrete

Bebwleft Figure 9 Construction of basement using insulating

concrete formwork.

Be/owright Figure 10 In-situ concrete wall.

A paper by Vitt(31) suggests that steel fibres can be combined with conventional reinforcement to help control cracking, thereby reducing the amount of bars or fabric required.This approach would be particularly suitable for applications such as water retaining structures, where the design is dominated by the need to control the width of early thermal cracks. Vitt suggests that a reduction of 50% in the amount of reinforcement is possible in some applications, while still maintaining the same crack width. The paper includes five examples of the approach being used in practice.

Steel fibres have been used to replace the nominal reinforcement in concrete walls cast in-situ, in applications such as Insulating Concrete Formwork. Traditional reinforcing bars are still required for structural purposes, such as in lintels over windows and doors and to connect the wall to the foundations. Figure 9 shows the technique being used for the construction of a basement.

Derssland and Kan~tad(~~) reported briefly on the use of steel-fibre-reinforced self-compacting concrete for the construction of the walls, floor slab and the roof of a house in a military training camp. Load tests were carried out in-situ on areas of slab fully or partially reinforced with fibres and comparisons made with the behaviour of conventionally-reinforced areas of slab. In parallel with the construction, full-scale beam trials were carried out. The authors concluded that fibres were capable of replacing all the ordinary reinforcement in this type of application. In Austria and Germany, steel fibres are often used to replace the traditional reinforcement in the foundations and basement walls of low-rise houses. Typical dosages are in the region of 20-35kg/m3.

Figure 10 shows a 2lOm long, 6m high, 300mm thick retaining wall in Beringen, Belgium. Here the fibre dosage was 80kg/m3, and fibres replaced al l the reinforcement in the wall with the exception of starter bars a t the base.

Figure 11 shows a steel-fibre-reinforced concrete safety barrier on the A10 motorway in Austria, with a noise barrier mounted on top. The loads from vehicle impact on the barrier are carried by prestressing tendons embedded in the concrete. The steel fibres, a t a dosage of 40kg/m3, were included in the concrete to control cracking and to accommodate the wind loads on thenoise barrier.

12

Figure 12 shows steel-fibre-reinforced concrete being used for the lining of a water supply channel.

Right Figure 11 Motorway barrier in

Austria.

Farright Figure 12 Lining water supply

channel.

3.4 COmpOSite slabs On

steel decking Steel fibres can be used for the reinforcement of the concrete in composite slabs constructed with light gauge profiled steel decking (see Figure 13).The use of fibre-reinforced concrete offers advantages in terms of speed of construction, site safety and a more reliable distribution of reinforcement over the full thickness of the concrete layer.

During the construction process the need to place fabric on the steel deck is avoided, speeding the construction operations and reducing the health and safety risks associated with manual handling of the sheets. On busy sites, crane time is often a t a premium and avoiding the need to crane bundles of fabric into position should be advantageous. Opera- tives involved in placing the concrete do not have to contend with tripping hazards on the deck and the reinforcement is not affected by site operatives having to tread on it. Evat-~s(~~) gives a brief overview of the advantages of the approach and includes some of the background research carried out to prove the system.

Examples of the use of steel fibres in composite slabs include the Goldbound building, a mixed retail and residential development in Manchester. Martin(34) describes a call centre in Thanet and a production facility in Burton on Trent. T h o m ~ o n ( ~ ~ ) outlines other projects including a retail development in Broadstairs, student accommodation in Salford and the conversion of a Victorian hospital building in Glasgow into luxury homes. Figure 14 shows a retail development that incorporated composite slabs in its construction.

13

3.5 Precast units 3.51 Tunnel lining Segments Precast concrete segmental linings have been produced traditionally in both reinforced

concrete and plain (unreinforced) concrete. The use of unreinforced concrete, and the beneficial cost savings in omitting the reinforcement, generally results in other compro- mises being made in the design. Commonly, this includes the need for more segments in a ring to limit flexural stresses for both temporary conditions (transportation and handling loads) and for permanent loads. Unreinforced concrete also has severe limitations where indirect tensile stresses may develop in a structure that is predominantly influenced by compression loads. This includes the performance of the lining at the longitudinal joints for transfer of the load between segments, and at the circumferential joints where tunnel boring machine (TBM) propulsion ram pressures act on the lining, both cases resulting in bursting stresses.

The use of steel-fibre-reinforced concrete in segmentally-lined tunnels has resulted in designs with fewer segments in a ring than for an unreinforced concrete solution. Steel fibre reinforcement provides a ductility and robustness in the material that is suited to the manufacturing process, the forces imparted during construction, and the long-term loading experienced by a tunnel lining, but which is lacking in unreinforced concrete.

There have been several utility tunnels designed and built with steel fibres. One of the first examples of the large-scale use of steel-fibre-reinforced precast tunnel linings was on the 1.4km long Heathrow Baggage Tunnel, built in 1995(36). Steel fibres were also selected for the reinforcement of the precast linings for the 24km of the Second Phase of the Channel Tunnel Rail Link (CTRL), to improve their resistance to cracking and damage during handling and transport (see Figure 15). Polypropylene micro fibres were added to improve performance in a fire(37). An additional consideration was their durability, particularly in saline or aggressive environments, mainly due to the good crack control. It was reported(38) that there was a small cost saving over conventionally-reinforced segment units. Steel-fibre- reinforced precast tunnel linings were also used for the extension of the Jubilee Line and the Docklands Light Railway, both in London. Figures 16 and 17 show the trial assembly of a tunnel lining ring and a completed tunnel lining. Be/ow/eft Figure l5

Precast tunnel Lining units for the Channel Tunnel Rail Link.

Be,owright ~i~~~~ 16 Trialassembly oftunnel Lining ring.

King and Alder(39) list a number of other projects that used steel-fibre-reinforced precast tunnel linings including various water supply and disposal applications.

-.., ,-

e,,-. . _.. -

14

Figure 17 Completed tunnel lining.

3.5.2 Storage tanks, pipes, etc.

Precast storage tanks, both for use above and below ground, can be made with steel-fibre- reinforced concrete. For example, one UK manufacturer produces circular and elliptical tanks with the walls and bases reinforced simply with steel fibres, although some conventional bar reinforcement is used in the roof and when loadings are particularly high. Steel fibres are also used for some smaller rectangular tanks. The manufacturer claims that the units are lighter than their conventionally-reinforced counterparts, are more durable and have improved fatigue resistance. One manufacturer in Australia produces septic tanks reinforced only with steel fibres.

Steel fibres are used for standard precast units such as pipes and manholes.

3.5.3 PreCaSt beams and Strobach reported on the development of prestressed precast beams with steel fibres in place of the conventional shear links and unstressed main reinforcement. Four full-scale beams were tested under short-term and long-term loads (see Figure 18), which demonstrated that fibres could provide sufficient shear capacity in the span and also resist the local bursting stresses near the ends of the beams where the prestressing force was introduced. Subsequently, this type of beam has been used as the main roof support structure for a paper mill and two large stores in Germany (see Figure 19).

panels

Right Figure 18 Long-term test on precast

beam with fibre reinforcement.

Farright Figure 19 Precast roof beams for

distribution centre in Erfurt, Germany.

15

Figure 20 shows precast steel-fibre-reinforced concrete wall panels

Precast Figure 20

wall panels.

16

Full-scale trials have been carried out in Norway on the use of steel-fibre-reinforced concrete for prestressed hollow core units, to improve the shear capacity.

3.6 Sprayed concrete (s ho t c re te)

3.6.1 General Since the first recorded field application a t Ririe Dam, Idaho in 1972(41), steel fibres have been used increasingly in both dry and wet sprayed concrete (or shotcrete) in mining, tunnelling, slope stabilisation and repair work, replacing the traditional single or double layers of steel fabric reinforcement. Typically, rock faces excavated by blasting are rough and irregular. In such cases, the absence of fabric reinforcement leads to much reduced volumes of fibre-reinforced sprayed concrete being required for rock support and stabilisation work. In general this is because the sprayed concrete can follow the excavated profile more closely without the need to infill behind and/or cover the fabric that inevitably bridges across a rough excavated profile. In addition, the use of fibre rather than fabric reinforcement reduces the amount of material lost due to rebound and eliminates the creation of voids or spraying 'shadows' that can occur behind fabric.

Spraying may be carried out using a hand-held 'gun' (see Figure 21) or with a robotic spraying arm (see Figure 22). The latter improves construction safety because it is no longer necessary for operatives to work under unsupported tunnel roofs, freshly excavated areas or below high rock faces to fix fabric or to apply the sprayed concrete.

Fibre-reinforced sprayed concrete has been shown by several studies to be a t least equivalent to fabric reinforcement in terms of its structural performance for similar However, toughness (ductility) is generally recognised as the property most enhanced by the use of steel fibre reinforcement in sprayed concrete, with the material able to accommodate sometimes significant ground movements in mines and tunnels without sudden brittle failure. Bond between the sprayed concrete and rock substrate is also generally improved by the use of fibre. Usually, this is attributed to the absence of fabric reinforcement that can impede spraying and compaction of the sprayed concrete. Fabric may cause voids and shadows that will provide access for water which could cause long-term durability problems. # .

Rght Figure 21 Sprayed concrete using hand-held 'gun'.

Farrfght Figure 22 Spraying concrete using robotic arm.

Steel fibre contents in sprayed concrete are typically in the range 25-60kg/m3, depending on the required toughness and type of fibre. Generally, steel fibres in sprayed concrete have lengths of 20-40mm and aspect ratios of between 50 and 80. The higher the fibre aspect ratio and volume concentration, the better the performance of the hardened sprayed concrete, but the greater the impact on production as it becomes more difficult to mix, pump and spray the concrete due to the fibres becoming entangled(43). Normally, it is recommended that the length of the fibre should not exceed 0.7 of the internal diameter of the delivery pipe or hose.

A comprehensive description of al l aspects of sprayed concrete technology and typical applications is provided by Austin and together with an extensive reference list for further reading. Concrete Society Technical Report 56(43) also provides a useful overview of construction and repair using modern wet-process sprayed concrete.

3.6.2 Tunnel linings Steel-fibre-reinforced sprayed concrete, or FRS, has been used worldwide for many years as part of the short-term (sometimes referred to as 'temporary' or 'primary') support systems for underground excavations in rock. The principal reasons for this have been discussed above. High rates of production can be achieved in comparative safety using the wet mix process and modern remotely controlled plant. In such cases, typically in road, rail and water tunnels, the sprayed concrete will be used only to stabilise the excavation during construction, with a cast concrete lining providing the long-term or permanent support. However, in some countries, particularly Scandinavia, but increasingly elsewhere, FRS is used to provide both the primary and long-term support of tunnels. In many cases the sprayed concrete may be left exposed and visible; alternatively, non-structural linings may be provided in, for example, some road tunnels. Caverns for hydroelectric power genera- tion and other uses are commonly left with permanently exposed sprayed concrete surfaces; an early example was the Kotmale Hydroelectric Project in Sri Lanka constructed in the mid-1980s. If required, sprayed concrete can be pigmented or painted to provide aesthetically acceptable finishes. FRS may be covered with a thin finishing coat of plain

17

sprayed concrete; this is often done to minimise the risk of minor injury due to exposed fibre protruding from the surface of the FRS. However, this is not usually a significant risk because in well applied sprayed concrete the amount of protruding fibre is relatively small and any protruding ends tend to quickly corrode and disappear, (such corrosion usually stops a t a short distance below the surface, as discussed elsewhere in this Report).

S~annellc~~) provides a review of the use of sprayed concrete for permanent tunnel linings. In addition, Morgan and Hee~e(~~1 give various examples of permanent linings including the headrace tunnels of the Stave Falls hydroelectric scheme in British Columbia and stations on the Stockholm Metro in Sweden, see Figure 23.

Figure 23 Stockholm Metro with permanent shotcrete

linings.

3.6.3 Slope and rock sta bi lisat ion

Figure 24 Stabilised rock face.

C A

18

Steel-fibre-reinforced sprayed concrete is an effective form of rock slope stabilisation (see Figure 24). Normally, FRS is used to provide surface protection and/or membrane action in conjunction with rock anchors or rock dowels (sometimes referred to as 'soil nails' in very weak rock conditions) and slope drainage measures. Steel fibres are used increasingly in place of fabric reinforcement, although much slope stabilisation work is sti l l carried out using hand-sprayed dry mix sprayed concrete and fabric. Generally, this is because slope work tends to be on a relatively small scale that does not justify the use of high-capacity mechanised plant to apply wet mix sprayed concrete. However, this is becoming less of a constraint as more plant becomes available worldwide. Dry mix is preferred for hand spraying because the weight of the hoses tends to be too great for manual application of wet mix.

Durability and bond can be of more importance than structural strength in these applications.

3.6.4 Repairs Sprayed concrete is an efficient technique when large areas of concrete need to be reinstated or added to an existing structure. The approach has been successfully used on many types of structures, including bridges, buildings, tunnels, cooling towers and marine structures. Austin and and Concrete Society Technical Report 56(43) provide overviews of a wide range of applications and techniques.

Sprayed concrete incorporating steel fibres was used for the repair of the ChannelTunnel following the fire in 1996. Al l the fire-damaged material was removed back to sound concrete; a t times, damage extended through the complete thickness of the original precast segments. The damaged area, amounting to 5700m2 in total, was filled with fibre-reinforced sprayed concrete followed by a final layer of plain sprayed concrete.

S ~ a n n e l U ~ ~ ~ ~ ~ ) notes the increasing use of sprayed concrete for tunnel asset management while Knight and Richard~on(~*) describe repairs carried out on a Victorian railway tunnel in Wales, where a series of sprayed concrete arches were constructed to provide additional support in weak areas. A thinner layer was sprayed over the remainder of the tunnel to eliminate water ingress.

The Highways Agency BD27/86(49) currently limits the use of fibres in sprayed concrete to 25mm melt extract, with a maximum fibre content of 5% by weight. The use of other fibres should be acceptable but would require a ‘departure from standard’. The Standard requires a 5-13mm thick over-coating of sprayed concrete not containing fibres.

3.7 Structures subjected to blast and ballistic loading

Conventional hardened reinforced concrete has a tendency to scab and spall when it is subjected to blast or impact loading. This occurs as a result of the interactions of the reflected waves transmitted in the concrete. Steel or composite antiscabbing plates can be installed to reduce the hazards from the concrete fragments but these do not prevent material deterioration occurring. SFRC can minimise spalling and scabbing and can make an important contribution to the integrity and resistance of blast-resistant structures. Lok & X i a ~ ( ~ ~ ) tested SFRC model structural elements, exposing panels to the air blast over- pressure generated from high explosives, with charge weights ranging from 8 to 40kg. They found that a nominal addition of steel fibres can overcome breaching and severe damage. A single degree of freedom model was used to predict the response.

The Swedish Defence Research Agency conducted penetration tests on a range of concretes, in which projectiles ranging in diameter from 43mm to 152mm were fired from an artillery piece a t concrete targets. The diameter of the entrance crater was reduced in those concretes with steel fibres(5’).

Penetration tests with smaller (25mm diameter) projectiles were carried out by Dancygier and Yankele~ky(~~) who found that specimens with steel fibres had reduced front and rear damage compared to similar specimens without fibres. From observations it was concluded that the fibres action under impact load was based primarily on their bond to the matrix.

19

4. Test methods to estab properties of SFRC

ish material

4.1 General Fibres have no effect on the mechanical material properties of plain concrete before cracking unless the fibre dosage exceeds around 80kg/m3. The design of such high performance composites is not covered in this Report. For the purposes of structures within the scope of this Report, the material properties of uncracked SFRC can be estimated by treating it as plain concrete (e.g. applying the formulae given in Eurocode 2(12)). Only the material properties of SFRC in tension are discussed below.

The axial tensile strength and flexural strength of SFRC are the same as for plain concrete and are determined as summarised in Sections 4.1.1 and 4.1.2 below. Tests specific to SFRC relate to the quantification of the material ductility and take the form of:

Beam tests to determine residual flexural strength, and in some tests a measure of

Plate tests to determine toughness in terms of energy absorption capacity, as discussed toughness, as discussed in Section 4.2.

in Section 4.3.

The results from the two forms of test are not directly comparable in terms of specifying ductility and designers should be careful not to specify possibly demanding requirements that may not be directly relevant to a particular design. Normally, residual strength is required where the concrete characteristics are used in a structural design model, whereas energy absorption is more relevant to situations, such as rock bolting in conjunction with sprayed concrete, where energy has to be absorbed during deformation under service conditions. Plate tests are also often considered to model more realistically the biaxial bending that can occur in some applications such as in pile caps or rock support. The relative merits of beam and slab tests are discussed further in Section 4.3.5, and some suggested correlations between equivalent flexural strength from beam tests and energy absorption from determinate round panel tests a t low deflections are discussed in Section 7.5.

The material factor of safety for SFRC, yc, is set a t 1.0 for the serviceability limit state and should be taken as 1.5 a t the ultimate limit state, to be consistent with the factors in Eurocode 2 for concrete without fibres.

411 Axial tensile strength O f

SFRC The design tensile strength of SFRC is the same as that for plain concrete.The apparent tensile strength of concrete depends on the type of test specimen used. The 'true' tensile strength of concrete can be determined in direct or indirect tension (splitting) tests. Eurocode 2 defines the tensile strength of concrete as follows:

The lower characteristic tensile strength of concrete is given in Eurocode 2 as:

(Equation 1)

20

and the mean tensile strength of concrete is given as:

fctm = 0.3fc,2’3 (Equation 2)

where: ‘c k = characteristic cylinder strength in compression

41.2 Flexural strength O f

SFRC The flexural strength of SFRC is the same as that for plain concrete. It is calculated from the failure load in standard beam tests, making the usual assumption that the stress distribution is linear over the depth of the section.The assumption of a linear stress distribution is reasonable up to first cracking but not a t the peak load, which corresponds to the flexural strength. Eurocode 2 defines the flexural strength of concrete in terms of the tensile strength as follows:

The lower characteristic flexural strength is given by:

(Equation 3)

where: h = section depth in mm.

The mean flexural strength is given by:

(Equation 4) fcrm,fl = max{(l.6 - h/1000)fC,,; fctm}

4.2 Beam tests to determine residual flexural

strength 4.21 Introduction The residualflexural strength of SFRC after crackingdepends on the fibre type and dosage.

It is determined experimentally since it cannot be calculated reliably in terms of the properties of the plain concrete matrix and the steel fibres. Standard test methods are available to determine the residual strength in bending and tension and its toughness. Standard flexural test procedures have been proposed by organisations including RILEM, the Japanese Concrete Institute (JCI), ASTM and EFNARC (the European Federation of Producers and Applicators of Specialist Products for Structures) for both beams and slabs as described below. Historically, theJapanese beam test JCI-SF4 has been widely adopted by steel fibre manufacturers in the UK. Recently, the RILEM beam test has been incorporated almost totally into BS EN 14651: 2005@) and the EFNARC beam test has been incorporated into BS EN 14488(53).

Theoretically, uniaxial tension tests are preferable to beam tests since they can be used to characterise the stress-crack opening (0-w) response of SFRC, which is needed in advanced design methods. Commonly, in practice, beam tests are carried out because they are simpler to execute than tension tests and simulate the conditions in many practical applications.

21

h material properties of SI-KC

4.2.2 BS EN 14651: 2005

Figure 25 Vpk.1 graph of Load against CMOD for SFRC.

22

BS EN 14651(*) specifies a method for measuring the flexural-tensile strength of metallic fibre reinforced concrete in moulded test specimens. The testing method is intended for metallic fibres no longer than 60mm. (Although the test is specifically for steel fibres, the method should be equally appropriate for combinations of metallic and other fibres.) The method provides for the determination of the limit of proportionality (LOP), which corresponds to the flexural strength, and of a set of residual flexural-tensile strength values. The Standard does not specify the number of specimens that should be tested.Typically, a minimum of six beams should be tested. The test is similar to the RILEM beam test (see Section 4.2.3).

The test beams, which are centrally loaded, measure 150mm square in cross-section and are simply supported over a span of 500mm. The specimens are notched at mid-span. The performance is specified in terms of the relationship between the applied load and the crack mouth opening displacement (CMOD), which can be either measured directly or calculated in terms of the central deflection.The LOP is defined as the highest load (FJ up to a CMOD of 0.05 mm.The centre-point load is also recorded at the following CMOD:

FL is the load corresponding to the LOP F, at CMOD, = 0.5mm (corresponding central deflection 6,, = 0.47mm) F2 at CMOD, = 1.5mm (6R2 = 1.32mm) F, at CMOD, = 2.5mm (6R3 = 2.17mm) F4 at CMOD, = 3.5mm (6, = 3.02mm)

Figure 25 shows typical graphs of load, F, against the CMOD for SFRC. The flexural strength of the SFRC test beam, fL, is calculated in terms of the centre-span load, FL, as follows:

fL = 6ML/bh2, = 3FLL/2bh,,’

where:

h,, = b = sectionwidth 1 = span.

depth of the beam above the notch = 125 f Imm

(Equation 5)

1

I I 1. I I I I t I I I I t 1 I I CMOD(mm)

b I & I

0 CMODl= 0,s CMOD, = 1,5 CMOD, = 2.5 CMOD. E 3,s

The residual flexural strenzths of the SFRC test beam are calculated in terms of the centre-span load, FR,, as follows:

= 6M,/bhZsp = 3FR{/2bhS: (Equation 6) fRj

Tensile strengths are based on an assumed linear stress distribution. In reality, the true shape of the stress distribution is non-linear and defined by the stress-strain response of the concrete. The residual flexural strengths are greater than the maximum tensile stress in the beam which occurs near the neutral axis after cracking.

4.2.3 RlLEM TC-162 TDF RILEM have developed a standard beam test(’) recently, which has been adopted by BS EN 14651: 2005, and a uniaxial test for the basic stress-crack width (0-w) relationship that is used in advanced design procedures, whereas the beam test is ideal for development work on fibres and for assessing the influence of fibre type and dosage in the laboratory. The specimens are notched in both these tests, which has the advantage that the crack forms in a predefined position and not a t the weakest section. The RlLEM beam test forms the basis of the RILEM stress-crack width (a-w) design method and stress-strain (0-E) design methods.

The uniaxial test is ideal for determining

4.2.4 JCI-SF4 tes t The Japanese beam test is widely used in the UK currently, but it is likely to be superseded by BS EN 14651: 2005 in due course. In the Japanese Concrete Institute Standard test JCl- SF4(55) (also published by the Japan Society of Civil Engineers and known as the JSCE-SF4 test), a minimum of six 150 x 150 x 600mm long beams are loaded to failure under third point loading across a span of 450mm. The test is only valid if specimens fai l due to the formation of a flexural crack in the middle third of the beam. The outputs from the JCl test

are the toughness and the equivalent flexural strength, which is calculated from the average failure load up to a deflection of 3mm. The toughness, T,,,, which corresponds to the energy absorbed by the beam, is given by the area under the load displacement diagram up to a prescribed mid-point deflection of 6,,, = span/l50 = 3mm. The equivalent flexural strength a t a deflection of 3mm (fctflea3) is defined as:

where: L = test span b = section width h = sectiondepth

23

The equivalent flexural ratio, Re,,, is expressed as:

(Equation 8)

where:

fctrn.n = mean concrete flexural strength which is calculated from the maximum

load P indicated by the testing machine before failure.

= PU(bh2) (Equation 9)

A disadvantage of the JCl test is that the load is not related to the crack width. Therefore, the crack width corresponding to a mid-span deflection of 3mm can vary significantly dependent on the position of the crack. Furthermore, the shape of the load deflection curve is not fully defined by the toughness and equivalent flexural ratio

4.2.5 EFNARC beam test For sprayed concrete, the EFNARC Specification(56) contains details of tests on beams cut from panels positioned vertically and sprayed with the same equipment, technique, etc. as for the actual work. The beams are tested in four-point bending on a 450mm span up to a central deflection of 4mm. The plot of deflection against load is used to determine the flexural strength and also the residual strength class, which is determined from the stress a t specified deflections of 0.5, 1.0, 2.0 and 4.0mm.

4.2.6 BS EN 14488 beam test Part 3 of BS EN 14488(53) largely adopts the EFNARC beam test to provide first peak, ultimate, and residual flexural strengths for sprayed concrete. The residual flexural strengths derived from this test correspond to the deformation and residual strength classes for sprayed concrete defined in BS EN 14487(57), as discussed further in Section 7.5.

4.2.7 DIN beam test The German DIN 1048(58) includes a beam test that may be used in connection with the German guidelines for the design of sprayed concrete for rock support, as discussed in Section 7.5. The standard describes both three-point and four-point loading on 150 x 150mm beams, 600mm between the outer supports. The four-point test is recommended generally and is similar to the JSCE-SF4 test described earlier.

4.2.8 ASTM beam tests ASTM C 1399(59) uses a 150 x 150 x 350mm long test beam, tested in four-point bending on a 300mm span. Initially the beam is supported on a steel plate in the test rig and loaded to a deflection of OSmm, so that it cracks. The beam is then unloaded, the plate removed and the load reapplied. The average residual strength is determined from the loads a t four specified deflections (0.5,0.75,1.0 and 1.25mm).

24

ASTM C 1609(60) uses 150 x 150mm beams (although smaller ones may be used when testing short fibres). Again, they are loaded in four-,point bending, on a span equal to three times the specimen depth. However, in this case, the loading is continuous. The peak load and the residual load a t deflections (span/600 and span/l50, i.e. 0.75mm and 3.0mm for 150mm deep specimens) are determined. From these loads the peak and residual strengths a t the specified deflections are calculated. If required, the toughness is determined from the area under the load-deflection curve up to a deflection of span/l50.

4.3 Slab tests to determine toughness

4.31 EFNARC For sprayed concrete, the EFNARC Specification(s6) contains details of a test on a square panel 600x600x100mm thick. This is simply supported on all four sides, with a span of 500mm, and a central point load is applied. Energy absorption is measured up to a deflection of 25mm and is used to determine the toughness. The test cannot be used to determine the basic material properties. Similar tests are included in some national Standards, for example in France and Switzerland. The tests will be replaced by Part 5 of EN 14488(s3) in due course.

4.3.2 BS EN 14488 plate test Part 5 of BS EN 14488(s3) largely adopts the EFNARC square plate test to provide energy absorption up to a central deflection of 25mm.The energy absorption measured in this test corresponds to the energy absorption classes defined in BS EN 14487(57), as discussed further in Section 7.5.

4.3.3 ASTM tests An alternative is the ASTM C 1550(61) Round Determinate Panel test, in which a point load is applied to the centre of a 800mm diameter round panel 75mm thick, supported on three symmetrically arranged pivots located on a 750mm diameter circle. The loading piston is advanced a t a constant rate of 4mm/min. The test proceeds to a total central deflection of 40mm after which the energy absorbed by the specimen is obtained as the area under the load-deflection curve. The round panel test offers designers, contractors, and clients several important advantages over alternative forms of post-crack performance assessment. The most important of these is the low within-batch variability in results due to the repeatability of the cracking pattern, but other advantages include the elimination of saw-cutting from the process of specimen production and the use of easy-to-prepare formwork. Lambrechts(62) found that the coefficient of variation in the equivalent flexural strength, fe,so, was significantly less for round plate tests than for beam tests. Only five RDP plate tests, compared with 15 beam tests, were required to get a mean value for fe3 that lay within +/- 10% of the true value. In addition, the f,,,, values derived from RDP tests were around 15% higher than the values determined from beam tests.

4.3.4 StatiCally indeterminate

S ta nda rds

Some fibre manufacturers use round indeterminate plate tests to determine the flexural strength of SFRC for incorporation in their design approaches. These tests, which are not covered by Standards, should be seen as part of the design assisted by testing route (see Section 5.3) rather than a method of determining the fundamental properties of SFRC. It is difficult therefore t o compare the results from such tests with the properties determined by other methods, such as beam tests and round determinate panel tests.

slab tests not covered by

4.3.5 Discussion The respective merits of beam and plate tests t o determine the flexural capacity of SFRC are keenly debated by steel fibre suppliers. Some, but not all, fibre suppliers believe that beam tests do not model the structural response of SFRC in pile-supported slabs since multiple cracks do not develop in beam tests with fibre dosages below around 80kg/m3. In practice, some fibre suppliers determine the flexural resistance of SFRC for the design of pile-supported slabs from statically indeterminate round plate tests. This approach is currently used for pile-supported slabs and suspended flat slabs, and is based on load tests on full-scale sub-assemblies. Guidance on interpreting the results of such tests is given in Section 5.3.

The design moment of resistance can be determined from plate tests by yield line analysis. Tests show that the resulting moment of resistance is greater than that given by beam tests for reasons discussed below. It follows that a fair comparison can only be made between the flexural strengths of SFRC quoted by different suppliers if the same test method is used t o determine flexural strength in each case.

The main advantages claimed for statically indeterminate plate tests are: a) Multiple cracks develop at failure. b) There is less scatter in the results than for beam tests. c) They are more representative of real slabs than beam tests.

Point a) is subject t o debate between fibre suppliers and is only relevant for structures like pile-supported slabs where multiple cracks and stress redistribution develop over point supports. Point b) applies to standard and non-standard plate tests and is substantiated by research (Marti

The disadvantage of statically indeterminate plate tests is that the flexural resistance is not related to crack width. The results of round plate tests are commonly interpreted using yield line analysis in which the flexural resistance is assumed to be constant along yield lines. The flexural resistance derived from statically indeterminate plate tests depends on the assumptions made in the analysis. The true moment of resistance can only be determined if the analysis accounts for the observed crack pattern at failure and the dimensions of the loaded area. In reality, the flexural resistance varies with crack width that, in turn, varies along the yield lines. Therefore, it is not possible to rigorously determine the relationship between flexural resistance and crack width from statically indeterminate plate tests. Ideally, the structural response should be predicted from rigorous material models rather than the other way round. In practice, this is not always feasible since the resulting models may be unnecessarily complex for practical design.

26

Tests used by various fibre suppliers are not discussed here but attention is drawn to the comments in Section 5.3. Designers should critically review the interpretation of test

results, design methodology and project references when recommending the design assistedby testing approach.

The alternative view encapsulated in the RILEM 0-E design method is that load redistribution should be excluded in the determination of material properties. According to this approach, material properties should be determined from statically determinate beam or plate tests in which the crack pattern is clearly defined. Any stress redistribution within a structure should be taken into account in the structural analysis and only there.

27

5. Overview of design processes

5.1 General As discussed in previous Chapters, there are many different applications in which steel fibres are used. Various design approaches are adopted that fall broadly into three different categories, as outlined below. All three are equally valid, but each may have its limitations.

5.2 Design on the basis of material properties

In this approach, material properties such as residual tensile strength are determined from standard small beam or statically determinate slab tests (see Chapter 4). These properties are then inserted into equations defining the performance of the concrete element to determine the load capacity. This is the approach adopted by design codes such as BS 8110(64) and Eurocode 2(12) for conventionally-reinforced concrete, and the equations may be determined mathematically or empirically. In general, the design equations will be linked to properties determined from a specific test; as discussed in Chapter 4. One advantage of this approach is that the equations are general and are not specific to any particular material. This approach is discussed in detail in Chapter 6 and some specific applications are given in Chapter 7.

5.3 Design assisted by testing

Design entirely based on testing is not common in reinforced concrete building structures. Generally, codes of practice permit design assisted by testing only where adequate calculation models are not available. Tensile strength of concrete is low and unreliable, and test results exhibit a large scatter. For this reason, it is universal practice to neglect the tensile strength in the calculation of resistance. However the same will not be possible in tests. Additional confidence in test results can be found through reference projects successfully completed using this design approach.

Test programmes should be designed in such a way that an appropriate design strength can be established, which includes proper allowance for the uncertainties covered by the partial safety factors in conventional design. Generally, it will be necessary to establish the influence of material strengths on the behaviour and their variability so that a characteristic (and thus design) response can be derived. When testing is carried out on elements smaller than the prototype, size effects should be considered in the interpretation of results. The tendency of fibres on the form faces to align themselves parallel to the face can give enhanced properties in this zone. This effect will be less significant for larger members. The effects of variations in linear dimensions as well as thickness should be considered. The statistical uncertainty due to the limited number of tests should also be taken into account. BS EN 1990(65), Basis ofstructural design, provides some guidance on this.

In the context of the design of steel fibre reinforced concrete slabs designed by the specialist designer on the basis of tests, the consultant advising the client should be satisfied that the principles noted above and in Section 4.3.4 have been followed, and that the various geometric and loading parameters are within the range of validity of the tests. The consultant should check that any design method based on relatively small-scale testing allows for factors such as the effects of restrained contraction and the effects of non-structural

28

cracks. Attention should be paid t o behaviour at both ultimate limit state (strength) and serviceability limit state (crack widths and deflections). Reputable steel fibre suppliers will be able to provide relevant information to support their design.

Such an approach has been used widely for the design of pile-supported slabs. More recently, i t has been used for fully suspended of the concrete in small beam tests, while satisfactory for linear elements, is not representative of the performance of elements such as slabs. This assertion is not universally accepted. In theory, it should be possible to accurately predict the structural response of suspended slabs from material properties measured in the standard beam tests described in Chapter 4. Thus, the process consists of testing round indeterminate slabs t o determine the design flexural resistance. The slab can then be designed by yield line theory. This design procedure is justified by the results of load tests on large-scale sub-assemblies of suspended slabs. The validation procedure involves determining the capacity of the developed yield lines from the observed failure pattern and collapse load. One limitation of the approach is that the plastic moment capacities so determined are specific to the particular type of fibre, dosage and yield line pattern tested; the results cannot be extrapolated to other types and dosages of fibres or other yield line patterns without further large-scale testing. In practice, designs based on testing are restricted to the use of a single fibre type and dosage rate. The consequences of differences in spans and loads between prototype sub-assemblies and full-scale structure should also be carefully evaluated when considering the design by testing route. Particular attention should be given to size effects and differences in crack widths that govern the residual flexural capacity after cracking.

The basic premise is that the performance

A partial application of this approach is the design of composite slabs on steel decking where tests t o determine the local performance of fibre-reinforced concrete, e.g. around stud shear connectors, have been used to demonstrate that the performance is adequate. Slabs with fibre-reinforced concrete can thus be designed in accordance with the Standards for composite slabs with fabric reinforcement, see Section 7.4.

The designer should also be satisfied that the requirements for fire resistance, allowable deflections, allowable crack widths and reinforcement for robustness have been met.

5.4 Design on the basis of Design by performance testing, or proof testing, is an approved method contained in all - performance structural codes. It is applicable t o repetitive units, where a large number of items are

required for a particular purpose. The element’s dimensions, fibre content, etc. will be determined on the basis of judgement or experience. Representative completed units will be tested to demonstrate their ability t o carry specified loads. Section 7.6 outlines the requirements for some precast units given in British and European Standards.

One limitation of this approach is that, generally, the testing will simply indicate that the element is capable of carrying the required load and not derive i ts ultimate capacity. Hence, there is only limited scope for extrapolating the results t o other sizes or types of elements. In addition, the approach does not permit a change from one dosage of a particular type of fibre to a different dosage or type of fibre.

29

General design approaches

6.1 Background 61.1 General

6. General design approaches

This Report is concerned with the design of SFRC with fibre dosages below around 80kg/m3, in which case the flexural resistance reduces after cracking as shown in Figure 26.

Figure 26 Typical load: deflection response for SFRC in a

beam test. I Load at

first crack

Average load under plot to

3mm

I I I I I

Deflection 3 mm

The residual flexural strength after cracking depends on the fibre type and dosage. The type of load deflection response shown in Figure 26 is known as strain softening since the flexural resistance reduces with increasing deformation after cracking. This type of behaviour differs from that of reinforced concrete where the flexural resistance increases after cracking, provided that the minimum amount of reinforcement specified in structural design codes is provided. The strain softening response invalidates many of the simplifying assumptions conventionally made in the design of reinforced concrete.

The structural response of SFRC at failure depends on whether the loading is load or displacement controlled. Load control arises when loads are increased to failure. Displace- ment control arises when displacements rather than loads are imposed on a structure. In this case, the internal actions are governed by the stiffness of the structure that reduces after cracking. Difficulties arise in the analysis of SFRC since it is a strain softening material in which the flexural strength reduces with increasing crack width. The consequence of this is that the curvature is not uniquely defined in terms of the applied bending moment. Therefore, the true ultimate load of a statically indeterminate member can only be calculated with non-linear structural analysis. In practice, it is common to make Simplifying assumptions and to design SFRC structures using conventional design methods. Table 3 indicates the level of confidence in current design methods for SFRC.

Current state Table 3

of the art.

Linear elastic analysis with no redistribution OK

Linear elastic analysis with redistribution OK and plastic analyses

Flexure OK

Shear OK

Minimum reinforcement to control cracking OK

Crack width calculation OK

OK

OK

OK

Limited test evidence available, in many applications flexural failure will be critical 7

7

The effect of the reduction in flexural capacity of SFRC after cracking can be seen by considering the behaviour of a simply supported beam loaded a t its third points.The beam cracks at the weakest section within i ts central third where the moment is sensibly uniform. Subsequently, the load reduces as indicated in Figure 26, if the loading is displacement controlled, and no further cracks form. The strain softening response differs significantly from the response of reinforced concrete, which is typically strain hardening as shown in Figure 27.

1 Figure 27 Idealised momentcurvature diagram for

strain hardening material. I t M

The load-deflection response in Figure 26 is analogous to the response of slabs with less reinforcement than the minimum prescribed in Codes of Practice for the design of reinforced concrete structures. No significant difference in behaviour would be noted in a load-controlled test between a plain concrete and a SFRC simply supported beam. The benefit of steel fibres arises solely from the ductility they impart after cracking, which is advantageous in statically indeterminate structures such as continuous beams and pile-supported slabs. The benefit of steel fibres can be seen by examining the behaviour of a beam that is built in (i.e. vertically and rotationally restrained) a t each end.

Consider two uniformly loaded geometrically identical concrete beams, one made from SFRC and the other from plain concrete, which are built in a t each end. Both beams would behave virtually elastically until the support moment reached the flexural moment of resistance, which would be almost the same for each beam. The corresponding uniformly distributed load, q, is given by:

q = 12Mfl/L2 (Equation 10)

where:

Mfl =

L = span. flexural resistance, assumed to be the same for both beams

31

~ ~ ---------- -

c;enerai design approaches -___

The plain concrete beam would fail immediately after first cracking since i ts moment capacity would rapidly reduce to zero a t the supports causing the span moment to increase above the section’s flexural capacity The fibre-reinforced concrete beam would not fail a t

q , provided it had sufficient ductility to redistribute the excess moment from the support to the span to maintain equilibrium The SFRC beam would fail when the moment reached the flexural moment of resistance, M,, in the span at a load, q,,, given by:

where:

Msup(8) = residual moment a t the support when the section reaches M, which depends on the hinge rotation, 8.

The residual moment a t the support at failure is governed by the hinge rotation as shown below. After cracking, the slope a t the support is given by:

8 = qL3/(24E/) - MsUp(8)V(2€/) (Equation 12)

Assume for simplicity that:

M SUP = M(8) = PMfl-a8 (Equation 13)

Hence,

8 = (qL3 - 12pM,L)/(24€/ - 12aL) (Equation 14)

The span moment is given by:

The beam fails in a load-controlled test when the moment a t mid-span reaches the flexural capacity, i.e. when Mspan = M, and:

q,, = 8[(1 + p)M, - a81/L2 (Equation 16)

The collapse load, q,,, can be found by substituting for 8 from Equation 14 into Equation 16 and rearranging, to give:

q, = 1 2Mfl [4€/(l + p) - 2aLl/[L2(6€/ - aL)] (Equation 17)

The collapse load, q,,, depends on the moment rotation response of the non-linear hinge at

the support which is governed by the fibre type, dosage and section depth. Concrete Society Technical Report 34 (TR 34)@) uses a simple method for the design of ground- supported slabs which is equivalent to assuming that a = 0 and P = Re,3 in Equation 17, in which case:

4, = 8M,(1 + Re,,)/L2 (Equation 18)

32

compared with:

4, = 12M,,/L2 (Equation 19)

for a plain concrete beam. It follows that the strength and ductility of the beam is only predicted to increase if Re,, is greater than 0.5. By definition, the maximum possible value of Re,, for SFRC is 1 for which the failure load q, is increased by 4/3 over that of a corresponding plain concrete beam. It follows that SFRC can only be used to replace all the reinforcement bars in lightly stressed members such as statically indeterminate slabs where significant moment redistribution occurs on cracking. The moment capacity of highly stressed sections can be enhanced as required with conventional reinforcement. The benefits of using SFRC are most apparent for ground floor slabs and for pile-supported slabs where the bending moment distribution is highly peaked a t supports or concentrated loads. In this case, stresses are redistributed to uncracked areas after cracking allowing multiple cracks to develop a t failure.

61.2 Elastic design Linear elastic analysis is appropriate for predicting the response of SFRC structures a t the serviceability limit state and can be used for design a t the ultimate limit state. In particular, it is important to examine the effects of pattern loading, which commonly occur in warehouse use. Piles supporting ground floor slabs are generally not built into them (see Section 7.3.5) and therefore any risk of uplift a t pile locations will need to be carefully examined by the analysis.

Elastic analysis can be used to estimate whether cracking is likely at the SLS (serviceability limit state).Theoretically, the maximum crack width can be estimated in terms of the internal actions taking account of shrinkage. In practice, it is not possible to make accurate predictions of crack widths in complex structures such as pile-supported slabs. Elastic design is inefficient a t the ULS (ultimate limit state), unless moment redistribution is permitted, since the flexural resistance of SFRC is unchanged by the addition of fibres.The benefit of adding fibres is only realised if localised moment redistribution is permitted after cracking by designing for average rather than peak moments over point supports. The draft Dutch CUR guidelines(3) permit maximum support moments to be redistributed to the span by up to 20% but moment redistribution over point supports is not permitted. The application of elastic analysis to the design of pile-supported slabs is discussed in Section 7.3.2.

61.3 Yield line design Yield line theory is a powerful technique for calculating collapse loads in flexure for ductile statically indeterminate slabs where internal moment redistribution occurs after cracking. However, the application of classical theory to SFRC requires caution since it is open to question whether the design moment can be sustained a t large rotations. The method is an upper bound method in which a collapse mechanism is assumed. The slab is assumed to be divided into rigid regions bounded by yield lines that act like hinges. The moment of resistance is assumed to be constant along yield lines, which is not the case for SFRC where

33

6.2 Design recommendations for

flexure

6.2.1 Design in terms of Re,3: Sections without convent i ona I

steel rein force men t

the residual flexural resistance reduces with increasing CMOD which is not computed in yield line analysis. Generally, there is no accepted method for calculating the plastic moment of resistance to be used in yield line analysis. It can be calculated from material properties as described in Section 6.2. The collapse load corresponding to an assumed collapse mechanism can be found by equating internal and external work. Theoretically, every possible mechanism should be examined to find the most critical. In practice, critical mechanisms can usually be defined for structures like pile-supported slabs.

Yield line theory is widely used for the design of SFRC ground-bearing and pile-supported slabs but has the following limitations: 0 No information is given on support reactions or deflections. 0 The adverse effects of pattern loading, such as uplift a t piles, are not considered. 0 The method is an upper bound one, which means that the design may be unsafe if not

a l l the critical mechanisms have been investigated. 0 The method is only valid if slabs have adequate ductility for the assumed yield lines to

develop. It is not possible to verify whether this is the case since the analysis provides no information on slab deformations.

Despite these theoretical objections, there is considerable experimental evidence to justify the use of yield line analysis for the design of SFRC slabs. Yield line analysis often under- estimates the failure loads measured in tests since it does not account for the beneficial effects of compressive membrane action. Commonly, yield line analysis is used for the design of SFRC piled slabs but a separate elastic analysis should be made to check stresses and crack widths a t the SLS. The application of yield line theory to the design of pile- supported slabs is discussed in Section 7.3.3.

The bending moments to be used in the design of SFRC can be derived using either elastic or plastic analysis as described in Section 6.1. The design moment of resistance is calculated in terms of residual tensile strengths derived in standard beam tests. Design equations are presented in terms of residual strengths derived using both the Japanese beam test (Re,3) and BS EN 1465W (fK, and fKJ.

The simplified stress block shown in Figure 28 is recommended for the preliminary design of fibre-reinforced concrete sections without conventional reinforcement if Re,3 is available.

34


Figure 28 Simplified stress block for SFRC.

I

The corresponding design ultimate moment of resistance is given by:

M, = 0.8fcdf,bhz[0.5 + 0.1 t;d(0.8fc, + f;,)]/[0.8(d + Cd1

where: fcd = design compressive strength of concrete (cylinder) ftd = design residual tensile strength of the concrete

= 0.37Re*, fctdYc

(Equation 20)

(Equation 21)

where: fctM = characteristic flexural strength which should be calculated using Equation 3, with

y, = material partial safety factor for SFRC, taken as 1.5 in this Report. h equal to the member (not test beam) depth in mm

Re,, is derived in the Japanese beam test (see Section 4.2.4) and can be estimated from the results of the BS EN 14651: 2005 or the RILEM notched beam test using the following Equation taken from the draft CUR guidelined3).

Re,3 = 1 .5[D3d3.01 L /(bh,,ZfcM) (Equation 22)

where: D,, = total area under the load deflection relationship to a deflection of 3.0mm L = span h,, = depth of the beam above the notch.

In pile-supported slabs, it is reasonable to use the mean rather than characteristic flexural strength in Equation 21.

Combined flexure and axial load Sections can also be analysed for combined flexure and axial load using the stress block in Figure 28. The depth to the neutral axis can be found by considering axial equilibrium. The flexural resistance is found by taking moments about the centroid of the uncracked section.

1 6.2.2 Sections with convent i ona I s tee[

rein fo rcernen t

The analysis described in Section 6.21 is readily modified to incorporate the effect of conventional reinforcement. The corresponding strain diagram and stress block at the ultimate limit state are shown in Figure 29.

Figure 29 SimpUfkd stress block for SFRC with

rupplemontary reinforcement.

Strain

The only difference from the analysis for conventional reinforced concrete is that the tensile stress in the concrete is assumed to be Cd, which is given by Equation 21. The depth to the neutral axis is found by considering axial equilibrium and the design moment of resistance is found by taking moments about the tension reinforcement.

Axial equilibrium

(Equation 23)

where: C, = 0.8bxf,, (Equation 24)

(Equation 25)

(Equation 26)

L; = fdsc

= A&

Moment of resistance

(Equation 27) M = C,(d - 0.4x)+C5(d - d') - b(h - x)Cd(d - 0.5h - 0.5~)

The procedure can be readily adapted to include the effect of axial load if required. In this case, the strain in the extreme compressive fibre of the concrete, E,", should be calculated in accordance with Eurocode 2.

36


6.2.3 Design in terms of BS The moment-crack width (M-w) response of a section can be derived in terms of the

EN 14651 (8) - Moment:crack residual strengths fR, and fR4 derived in the BS EN 14651 beam test using the procedure given in the RILEM o--E design guidelines or more simply with the stress block shown in Figure 30.

width response

Figure 30 Simplifird stress Mock for d h i n g M-w

response for SFRC.

A Eb

Strain

The EC2 rectangular parabolic stress block can also be used for concrete in 1 compression.

fb = 9 - ( 0 2 - aa)(w - 0.5)/3 where w=(h -X)Q

The compressive stress blocks are based on the recommendations given in Eurocode 2. The simplified triangular stress block is valid for concrete compressive strains up to 0.00175 for fck less than 50MPa. The depth to the neutral axis is found by considering axial equilibrium and the design moment of resistance is found by taking moments.

Axial equilibrium

C, = T, = 0.5b(h - x)(o, + fb) (Equation 28)

where: b = sectionwidth

fb = CJ] - (a2 - CJJW - 0.5)/3 (Equation 29)

( = (f,,/0.00175) ~ ~ x / ( h - x ) (for triangular compressive stress block) (Equation 30)

C, = O.Sbx( (for triangular compressive stress block) (Equation 31)

w = (h -x)Eb (Equation 32)

= strain at extreme tension fibre (see Figure 30)

o2 = 0.45fR,k, (Equation 33)

= 0.37fR4k, (Equation 34)

37

,

f,, and fR4 are the characteristic residual strengths a t CMOD of 0.5 and 3.5mm respectively derived in the BS EN 14651 beam test.

k, = max[(l.6 - h/l000)/1.475, 0.68) but <I (Equation 35)

Moment of resistance M = O.Sf,b(h -x)(h + ~ / 3 ) + b(0, - fJ(h -x ) (h + ~ ) / 6 (Equation 36)

The M-w response of the section can be computed by: 0 Solving Equation 28 for x, the depth to the neutral axis, for crack widths between 0.5

0 Calculating the moment of resistance with Equation 36. and 3.5mm and

The procedure can be readily adapted to include the effects of reinforcement and axial load if required. Figure 31 shows a typical M-w diagram from such a calculation for a section in flexure. The maximum moment of resistance generally occurs before the maximum strain in the extreme compressive fibre reaches the limitingvalue defined in EC 2 (i.e. 0.0035 for pure flexure). In plastic design, the design ultimate moment should be taken as the moment of resistance corresponding to the limiting extreme fibre compressive strain defined in EC 2. In elastic design, the maximum moment of resistance can be used.

Figure 31 Typical M-w response for SFRC section. 20 I

4

15

E z ; 10

5 r 5

0

+ fR1=3.6MPa, fR4=3MPa

0 0.5 1 1.5 2 2.5 3 3.5 4

Crack width w mm

The RlLEM 0-E guidelines limit the crack width to 3.5mm at the ULS to ensure sufficient anchorage capacity for the steel fibres. The corresponding design ultimate moment can readily be calculated with the procedure described above. It should be noted that the hinge rotation corresponding to a given crack width reduces significantly with section depth since it is given by:

e = w/(h -XI (Equation 37)

where: w = crack width.

38

If x is assumed t o be 0.1 h:

e = I . I I W / ~ (Equation 38)

which reduces inversely in proportion with member depth, h. Yield line analysis is only valid if the structure has sufficient ductility to develop the assumed yield lines. Equation 38 suggests that yield line analysis should be used with caution in thick slabs (h>600 mm) which may have insufficient ductility to develop the assumed collapse mechanism.

I '

6.2.4 Flexural Size effects The flexyral strength of SFRC is size dependent as explained in Appendix B.2 but there is little consensus on the magnitude of the size effect. The influence of size effects is complex since it depends on crack width as well as section depth. The influence of size effects is greatest at first cracking and progressively reduces with increasing crack width. The design moment of resistance fs commonly related t o the average flexural strength measured in beam tests, which is size dependent. The size effect included in the equations for flexural resistance in this Section are in accordance with the recommendations of Eurocode 2(12)

for plain concrete.

\

,

6.3 Shear strength 6.31 Beam shear There is no agreed method for calculating the design shear strength of fibre-reinforced

concrete without conventional reinforcement. Currently used resistance models assume the presence of longitudinal reinforcement. Most recent design recommendations (e.g. RILEM) are based on the ENV version of Eurocode 2(2), which has been superseded. The published Eurocode 2'12) gives the following equation for the shear resistance of reinforced concrete without web reinforcement:

V,,,, = [C,,,, k( 1 OOp, fCk)'I3 + k,O, Jb,d 2 0.035k3/2f,,"2bwd (Equation 39)

where: C,,, and k , are nationally determined parameters with recommended values of 0.I8/yc and 0.15 respectively

p, = bw= width of web d = effectivedepth.

A/bwd 50.02 where AS is the area of tensile flexural reinforcement

oCp = N,,/A, c 0.2fc,

where: I Ne, = axial force due t o load or prestress (Ned>O for compression)

k = 1 + 4(200/d) 5 2 with d i n mm (Equation 40)

39

Fibres increase the shear strength if longitudinal reinforcement bars are provided. The RlLEM design recommendations are broadly adopted in this Report but have been updated to be in line with Eurocode 2(12) as appropriate. The design shear strength of SFRC with supplementary steel flexural reinforcempnt is given by:

where: vrd = 0.7k,k~, (Equation 42)

where:

k, = =

n =

T , ~ =

factor taking into account the contribution of flanges in aT-section 1 + n(h@,)(hdd) and 421.5 (b, - bw)/h, 5 3 and n I 3bw/h, design value of the increase in shear strength due to steel fibres

= 012fRk4 -012 Re,3 fctkO

where: fRk4 = residual flexural strength measured in BS EN 14651: 2005 at a crack width of 3.5 mm fctk,” = characteristic flexural strength of plain concrete Vw, = contribution of the stirrups to shear strength

= (A,,/s)0.9dfw,

where: 5

fwd = design yield strength of the stirrups. = stirrup spacing measured along the longitudinal axis

Equation 41 is only valid for SFRC sections with longitudinal reinforcement bars for flexure. In the absence of appropriate test evidence, it is suggested that the design shear strength of SFRC slabs without reinforcement bars for flexure, with Re,4 t 0.4, is calculated using the lower bound to Equation 39, in which case:

V,, = 0.035k3’2f~/2bwd (Equation 43)

where k is defined in Equation 40 and d = 0.75h

The RlLEM 0-E guidelines state that minimum shear reinforcement is not required in SFRC beams but it must be guaranteed that the fibres have a significant influence on the shear strength.

40

.

6.3.2 Punching shear It is recommended that the design rules for punching shear given in Eurocode 2 are only used for SFRC with conventional longitudinal reinforcement. The design shear stress (as defined in Clause 6.38 of Eurocode 2) should not exceed vmax a t the face of the contact area irrespective of the amount of reinforcement in the slab. The value of v,,, is given by:

vmaX = 0.5 v fcd (Equation 44)

where:

fcd = v = 0.6 (1 - f c , / 2 5 0 )

design concrete compressive strength (cylinder) = fck / y,

where:

fck = characteristic compressive strength (cylinder).

Hence, the maximum design punching shear resistance, Pp,max, is given by:

where:

U, = perimeter of the loaded area.

The shear stress is checked on the critical shear perimeter at a distance 2dfrom the edge of the loaded area. The corresponding design shear strength for slabs without links is given by:

where: vRd,, = shear strength in MPa

All the terms in Equation 46 are defined below Equation 39. It is suggested that in the absence of appropriate test data, pI should not be taken as greater than 0.003 in Equation 46 unless the term T~~ is neglected.

In the absence of appropriate test evidence, it is recommended that the design punching shear strength of SFRC sections without reinforcement bars for flexure, with 0.4, is calculated using the lower bound to Equation 46, in which case:

V,, = 0.035k3/2fc,'/2~,d (Equation 47)

where:

U , = d =

length of the shear perimeter a t 2dfrom the face of the loaded area effective depth - 0.85h.

The design punching shear strength of SFRC slabs with supplementary steel reinforcement bars over point supports (e.g. piles) and stirrups can be obtained as described in Eurocode 2 with vRdc given by Equation 46.

41

6.4 Serviceability limit state

Deflections and crack widths need to be controlled a t the SLS

6.41 Deflections Deflections will be less in SFRC slabs than reinforced concrete slabs with the same area of bar reinforcement since tension stiffening in cracked concrete is significantly enhanced by steel fibres which bridge cracks. Deflections can be estimated in uncracked SFRC slabs with elastic analysis using an effective elastic modulus to account for creep. A more complex non-linear analysis is required to calculate deflections in cracked SFRC slabs without longitudinal reinforcement. The procedure involves introducing non-linear hinges at critical sections as described in the RlLEM design guidance for the 0-w methods4 which is discussed in Appendix BA.

6.4.2 Cracking Crack control in SFRC can be provided by: 0 The presence of conventional steel reinforcement bars 0 Prestressing 0 The surrounding structure in statically indeterminate slabs and beams

The designer should agree the allowable crack limits with the client at the start of any job since it may have a significant impact on the design solution and methodology. Crack control is required in al l structures. Crack widths cannot be controlled in statically determinate members reinforced with only steel fibres unless sufficient fibres (typically more than 80kg/m3) are provided to give a strain hardening response.The design of such composites is outside the scope of this Report. Thus, it is suggested that statically determinate SFRC beams and slabs should not be designed using the recommendations given in this Report unless supplementary steel reinforcement bars are provided for flexure.

Although there is no suitable design approach for estimating crack widths in structures reinforced with fibres only (see Section 6.4.4), experience has shown that fibres can be beneficial in limit the widths of cracks.

6.4.3 Causes Of cracking Cracks can arise in slabs due to the combined effect of restrained early-age thermal contraction, restrained shrinkage and loading. Any cracks that occur a t an early age are likely to increase in width, with time, due to shrinkage. The extent of cracking can be reduced by minimising shrinkage through using well designed concretes with low watercement ratios. In ground-supported and pile-supported slabs it is also beneficial to minimise friction by providing a slip membrane between the concrete and sub-base, which should be continuous over the supporting piles and tops of ground beams. Sandaker(69) states that:

’ “It is almost impossible to give a general answer to the question of how to avoid or reduce the friction problem between concrete and subgrade”.

42

He goes on to suggest that a double layer of polythene can favourably limit friction. An alternative approach is to cast the slab directly onto the sub-base in which case cracking is likely a t the SLS. It can be shown (RILEM o-w method) that the resulting crack spacing is governed by factors including the stress-crack opening relationship, ground roughness and the concrete tensile strength.

6.4.4 Crack COntfO[ It is only possible to realistically calculate crack widths in statically indeterminate structures without conventional reinforcement by carrying out a non-linear analysis, which is impractical for design. The most critical location for cracking in slabs is usually over columns and piles where flexural and punching stresses are greatest. Usually, it is impossible to reliably predict crack widths in SFRC structures without conventional reinforcement since the crack widths are not related to stresses given by elastic analysis once the section capacity is exceeded and softening develops. In some circumstances, it may be necessary to control crack widths to prescribed limits. In this case, consideration should be given to providing conventional reinforcement in addition to steel fibres to control crack widths. Moreover, crack widths can be estimated using the method given in the RlLEM o-E design guideline.

6.4.5 Minimum reinforcement

Codes of Practice for reinforced concrete require a minimum area of reinforcement to be provided in al l members to ensure multiple cracking. The minimum area of reinforcement required to develop multiple cracking in reinforced concrete tension members is found by equating the yield capacity of the reinforcement to the cracking load. If less than the Code specified minimum area of reinforcement is provided, only a single crack forms. In this case, the crack width is equal approximately to the imposed displacement. The response of SFRC members with conventional reinforcement is similar to that described above but the minimum area of reinforcement, and crack widths, are reduced by the fibres that bridge cracks and, consequently, increase the residual tensile stress in the concrete after cracking. The RILEM o-E design method gives the following formula, (which has been updated in this Report to be consistent with Eurocode 2), for calculating the minimum area of reinforcement required to limit the design crack width to approximately 0.25mm:

ASIAct = (kkcfctef - 0.45fRm,/l .4)/(fy, / I .4) (Equation 48)

where:

fRm, = the average residual tensile strength of the SFRC a t the moment when a crack is

AS = arda of reinforcement within tensile zone which satisfies the design crack width

Act = area of concrete in the tensile zone (the area of concrete in tension just before

fctef = tensile strength of the concrete a t the time cracks are first expected to occur.

expected to occur as defined in BS EN 14651: 2005 (see Section 4.2.2).

(mm'); ifA, is less than zero only steel fibres are necessary.

the first crack forms).

fctef = fctm or lower, fctm(t), if cracking is expected to occur before 28 days. In some cases dependent on ambient conditions this may be within 3 to 5 days of casting.

43

_-

c h w a i design 8pproaches

kc = coefficient which takes account of the shape of the stress distribution in the concrete immediately before cracking The relevant stress distribution IS that resulting from the combination of effects of loading and imposed deformations k, = 1 for pure tension For bending combined with tensile axial forces k, = 0 4(1 + 3oc/2fcieR) c l for rectangular sections with h<l Om (5, is the axial tensile stress induced by restrained shrinkage For other cases refer to Eurocode 2

defined in EC 2 k

tk

= coefficient that allows for the effect of non-uniform self-equilibrating stresses as

= characteristic yield strength of reinforcement (MPa)

It is assumed in Equation 48 that the maximum stress permitted in the reinforcement immediately after the formation of the first crack is o,=fyJ1.4.

Multiple cracking only develops in statically indeterminate SFRC slabs such as piled rafts since stress is redistributed to uncracked sections after cracking. Crack widths are only uniquely governed by the stress resultant a t a crack if the resistance (e.g. flexural capacity) increases with increasing generalised strain (e.g. curvature), which is not the case for SFRC. Therefore, it is difficult to assess the effectiveness of steel fibres in controlling cracks in the absence of conventional reinforcement since the crack width is largely dictated by the overall structural response that can only be determined with non-linear analysis, which is not practical a t present.

6.5 Durability Where SFRC is placed in a corrosive environment, consideration should be given to ignoring the structural contribution of the fibres in the surface zone. Further limited information is given in Section 9.1.

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7. Design for specific applications

7.1 Fire design For many of the current applications of steel fibres, fire will not be a significant design consideration but there may be situations in which the load capacity of the element will be affected. Steel-fibre-reinforced concrete is not covered by either BS 8110(64) or Part 1-2 of Eurocode 2(12), but a similar approach should be adopted. For the fibre dosages commonly used, the thermal conductivity of the concrete is unaffected. In the absence of other guidance, it should be assumed that steel-fibre-reinforced concrete experiences the same loss of strength with increasing temperature as conventional concrete. Eurocode 2 gives temperature profiles for different elements subjected to fire for different periods, from which the residual strength of the concrete a t various locations can be determined and, hence, the load capacity of the element in the fire situation. It has been found that steel fibres do not significantly affect explosive spalling; for high strength concrete, polypropylene fibres should be included in the concrete, in line with the guidance in the Eurocode.

The fire design of composite slabs on steel decking, using specific combinations of fibres and decking, has been determined by full-scale testing and a fire engineering model. This is outlined in Section 7.4.

7.2 Ground-supported slabs 7.2.1 Industrial floors Guidance on the design of concrete ground-supported slabs reinforced with steel fibres is

given in the Third Edition of Concrete Society Technical Report 34, Concrete industrial floors - A guide to design and ~ons&tion(~~). The design equations are based on plastic analysis, and assume the use of steel fibres (or correctly located steel fabric reinforcement) in the concrete. The bending moment capacity of a steel-fibre-reinforced slab is a function of the Re,3 value determined from the Japanese JCI-SF4 beam test [see Section 4.2.4) and has been confirmed by testing.

The design formulae in TR 34 are similar to those in Eurocode 2(l2) and the National Annex. For steel fibres, the formulae have been calibrated against test results and the resulting slab thicknesses are similar to those determined by established methods for industrial floors, which have been shown to be satisfactory in service. The design approach is based on plastic analysis, which leads to the requirement that the slab behaves in a ductile manner after it cracks. This cannot be fulfilled by plain concrete alone and, hence, sufficient fibres must be used to provide an adequate moment capacity when the slab is in a cracked state.

Experience indicates that significant tensile strains can be generated in large area ground- supported slabs due to shrinkage and that cracks can occur if the slabs are restrained, for example by early-age loading. TR 34 gives some guidance on how such tensile stresses may need to be considered in the design of slabs.

45

-~ ~ ~ _ _ _ _ _ - _ ~ - - - ~ - ---- -

Design for specific appkations -

Roesler eta/ (67) tested two ground-supported slabs with steel fibres The design strengths were determined using the TR 34 design approach, and compared with the actual failure

A partial safety factor for loads of 1.2 is used for permanent loads (e.g. racking in a warehouse) and 1.6 for dynamic loads (e.g. materials handling equipment and equipment subject to vibration). A materials partial safety factor of 1.5 is applied to the concrete properties.

Appendix A gives a summary of the design approach; for further information seeTechnical Report 34, which also includes a worked example.

7.2.2 External paving An unpublished TRL report by Chandler and Hassan(16) has reviewed the use of steel-fibre- reinforced concrete for pavements. Although there have been various trials most of the results reported appear to be qualitative rather than quantitative. However, there is some in-service evidence that pavement thicknesses can be reduced. ] o h n ~ t o n ( ~ ~ ) reported reductions to about 70% when using about 40kg/m3 steel fibres, but this will presumably depend on the fibre type. At a higher dosage, 80kg/m3, the slab thickness could be reduced to 50-60% of the plain concrete thickness. An example quoted by Kul~hrestha(~*) for an airfield pavement compares a 300mm fibre-reinforced slab (96kg/m3 fibres) with a 400mm unreinforced slab. Fibres gave an enhanced fatigue life, from 43,500 to a t least 105,000 cycles.

Although TR 34 is specifically for internal industrial floors, it has been suggested that the same approach could be applied to the design of external paving, applying the factor of 1.6 to the vehicle loading to account for repeated applications. This approach has been adopted for a number of contracts but has not yet been calibrated against traditional design approaches, which are largely empirical and based on observed behaviour of roads. External paving slabs are subjected to a more aggressive environment than internal slabs. Hence, one area of difference in the design approach may be the transfer of loads across joints; the work reported by Galloway and Gregory(18) would suggest that fibres may corrode rapidly a t relatively small crack openings (about Imm).

7.3 Pile-supported slabs 7.33 Background It is assumed conventionally that no support is provided by the ground since piles are used

in poor quality ground that is likely to settle relative to the piles leaving a void under the slab. The most highly stressed sections in slabs are over supports and under concentrated loads. For pile-supported slabs, the critical locations for cracking are over internal supports with the worst case occurring a t the first internal support from the edge. Both elastic and plastic design methods are used for the design of pile-supported slabs. Plastic design methods tend to give more economic designs a t the ultimate limit state but additional

46

7.3.2 Elastic design methods

checks are required a t the serviceability limit state. As indicated previously, design may be on the basis of material properties or may be assisted by testing. This Section only gives details of the first approach.

The latest draft Dutch elastic moments a t the design ultimate limit state. The design moments can be calculated using the elastic moment coefficients given in the Dutch Code NEN 6720(73) for flat slabs, or elastic finite element analysis. The slab is divided into column and middle strips as in BS 8110 which implies lateral redistribution of moment a t supports since the design moment within the column strip is significantly less than the peak elastic moment. The width of the column strip is equal to one half of the shorter span. The design method is similar to that of a conventionally reinforced slab designed using the moment coefficients given inTable 312 of BS 8110,ThisTable is not applicable to industrial floors since it is only valid if the characteristic imposed load is less than 5kN/m2 and the ratio of the characteristic imposed load to the characteristic dead load is less than 1.25. For square panels, NEN 6720 gives the maximum support moment in the column strip over interior columns as:

require pile-supported SFRC slabs to be designed for

M = aqL2 kNm/m (Equation 49)

where: q = applied load L = span a = 0132 for internal panels

0190 for corner panels 0178 for edge panels.

No moment redistribution is allowed to the moments given by Equation 49. BS 8110 requires the column strip to be designed for 75% of the hogging moment, which can be calculated using Table 3.12 provided the simplification of loading arrangements described in Clause 3.5.2.3 is valid. BS 8110 requires two thirds of the flexural reinforcement in the column strip to be placed in half its width centred over the support, which has the effect that the slab is designed to resist twice the average moment in the column strip over the support. The resulting peak moment coefficients for the column strip corresponding to Table 3.12 in BS 8110 are 0.126 at interior supports and 0172 at first interior supports. These coefficients compare favourably with the coefficients given in the Dutch code and are suggested for use in the UK for the design of pile-supported slabs (other than for industrial applications) a t the ultimate limit state. An elastic analysis should be carried out for industrial floor slabs with pattern loading. The slab can be divided into panels in each orthogonal direction, as for a flat slab. The design ultimate moments can be calculated with tabulated moment coefficients, an equivalent frame analysis with the piles modelled as point supports or finite element analysis. In the case of an elastic finite element analysis, the peak moments can be averaged over the central half of the column strip as recommended in BS 8110 for flat slabs. It is beneficial to limit the hogging design ultimate moments over supports as described in BS 8110 or otherwise.

47

In Holland, the slab thickness is usually chosen to ensure that no conventional reinforcement is required in the bottom of internal spans. Conventional reinforcement is placed over piles and in the bottom of external spans to locally increase the design moment of resistance of the slab as required. Alternatively, the external spans can be reduced below the internal spans to make the moments in internal and external spans equal.

7.3.3 Yield line desigr O f piled rafts

Yield line design can be used to design piled rafts a t the ultimate limit state but a separate elastic design check is required a t the serviceability limit state. Tests show that the failure load of slabs can be increased significantly by membrane action, in which case yield line analysis gives very conservative estimates of failure loads. The process of yield line design involves identifying the critical collapse mechanisms and calculating the corresponding moments of resistance.

48

It is informative to compare the yield line design of reinforced concrete flat slabs and SFRC slabs without supplementary steel reinforcement. For this purpose, it is convenient to examine the critical collapse mechanisms for a square interior panel supported on circular columns for which two mechanisms need to be considered. The first collapse mechanism is a wide beam failure where, conventionally, yield lines are assumed to form a t the face of the columns. The collapse load corresponding to the wide beam failure mode is given by equating the internal and external work.

External work = 0.5qL(L - h,) = Internal work = 8m (Equation 50)

m = qL(L-hJA6 (Equation 51)

where: q = uniformly distributed load L =

h, = diameter of support m =

span between centrelines of supports

required moment of resistance, which is assumed to be equal for hogging and sagging.

The second yield line pattern that needs to be considered is a fan of radius, R, centred on the support. The perimeter of the fan is assumed to displace downwards by unity along with the remainder of the slab. Kennedy and Cood~hild(~~1 show that the required moment of resistance corresponding to the fan mechanism can be given by:

rn + rn' - qL2{l - (A/Lz)1/31/2n (Equation 52)

where: A = area of the column cross-section m'= hogging moment of resistance rn = sagging moment of resistance.

If h i 1 = 0.1 and m = m’(no conventional reinforcement), rn = 0.064qL2 kNm/m. The corresponding design moment of resistance for the wide beam collapse mechanism, (i.e. with h/L = 0.1) is M = 0.056q12 kNm/m. Therefore, the fan is critical in this example since the corresponding design moment is greater than for the wide beam mechanism. The critical plastic design moment of 0.064~71~ is less than half the corresponding elastic design moment of O.132qL2 given by Equation 49.

Kennedy and Coodchild recommend that all the reinforcement required to resist the hogging moment should be placed in the column strip to control cracking. This recommendation has the effect of locally increasing the moment of resistance by a factor of 2 in the column strip, which makes the wide beam mechanism critical. The resulting moment of resistance in the column strip is 0.112~71~ kN/m, which is close to the elastic design moment of 0.132qL2 kNm/m given by Equation 49. Experience shows that crack widths in conventionally-reinforced flat slabs designed using elastic moment coefficients may exceed the Code limit of 0.3mm over columns but are usually acceptable in reality. In practice, SFRC piled-supported slabs are frequently designed in the UK using yield line analysis without any steel reinforcement being placed over the piles. Consequently, the design ultimate flexural resistance of the slab in the column strips over the piles is around half that of a flat slab detailed in accordance with the recommendations of BS 8110 or Kennedy and Coodchild. This is acceptable a t the ultimate limit state, if the fan mechanism is not critical, but requires closer examination a t the serviceability limit state.

The behaviour of SFRC slabs a t the SLS is better than implied above if the material factor of safety for SFRC is taken as 1.0 for the SLS and 1.5 at the ULS as recommended in Section 4.1. In this case, the design ultimate moment of resistance is less than two thirds of the flexural resistance a t the SLS. It follows that the ratio of the mean flexural resistance to the design ULS elastic moment (given by Equation 49) is approximately:

MRn/lLIElasticdesignuls = 1.5 x 0.064/0.132 = 0.73<1 (Equation 53)

Cracking is of concern in service when the loading is less than 70% of the design ultimate load. It should be remembered that the peak elastic design moment within the column strip may be significantly greater than the average value given by Equation 49, dependent on the pile diameter. The peak moment will be less than the elastic moment due to moment redistribution after cracking. The analysis also neglects the effect of tensile stress induced by restrained shrinkage. The corresponding ratio MR,,/ME,ast,cdeslgn uIs for a conventionally- reinforced concrete slab designed with Equation 51 and detailed according to the recommendations of Kennedy and Coodchild is:

MRn/MEiasticdeslgnuls = 115 x 2 x 0.056/0.132 = 0.98 (Equation 54)

where 1.15 is the material factor of safety for the reinforcement. Comparison of Equations 53 and 54 suggests that cracking may be more severe in SFRC slabs designed with yield line analysis than in reinforced concrete slabs detailed in accordance with the recommendations of Kennedy and Coodchild. Tests show that crack widths are significantly reduced in SFRC slabs if supplementary conventional reinforcement is provided over the piles to

49

help control cracking. Tests also show that the number of cracks increases significantly when conventional reinforcement is provided in SFRC slabs over piles with a consequent reduction in crack width. It is a matter of judgement whether it is acceptable to omit steel reinforcement over piles in SFRC slabs. Many SFRC slabs without steel reinforcement have performed satisfactorily over the years but problems with cracking over piles have occasionally arisen.

7.3.4 Serviceability l imi t State check

Slabs should be checked a t the SLS using characteristic design loads with mean material properties taking the effect of restrained shrinkage into account. The design SLS moments can be estimated with elastic plate theory or elastic finite element analysis. Restrained shrinkage can induce significant tensile stresses, which can be partially relieved by cracking at the serviceability limit state. Silf~erbrandc~~) identifies two different principles for avoiding uncontrolled shrinkage cracking in ground-supported slabs. Firstly, to minimise the causes of cracking by a) reducing the free shrinkage strain of SFRC through appropriate concrete specification, and b) reducing restraint with an effective slip membrane. Secondly, the consequences of cracking can be limited by reinforcing the slab and providing joints. Frequently, it is assumed that it is unnecessary to consider the effect of restraint a t the ultimate limit state in SFRC. This assumption is justified with Losberg’s hypothesis(76), which states that restrained stresses vanish as soon as the reinforcement yields. The hypothesis is reasonable for SFRC slabs, with adequate ductility, if critical sections are designed as cracked a t the ULS. In this case, Losberg’s hypothesis is reasonable and it is only necessary to consider the effect of shrinkage a t the SLS.

Realistically, it is difficult to estimate the stresses induced by restrained shrinkage due to uncertainties in assessing the degree of restraint and the long-term concrete material properties. If the slab is fully restrained, the shrinkage stress can be expressed as:

(Equation 55) fshfu,l = ‘cmEsh -k

where: cp = creep coefficient E,, = shrinkage strain.

Typical values of fcm, E,, and cp are Ecm = 30CPa, cp = 2 and E,, = 500 x 10-6, which gives = 5MPa. Traditionally, the restraint factor for a slab cast on grade is assumed to vary

from zero a t the edges to a maximum mid-way between joints. Concrete Society Technical Report 34@) states that this approach significantly overestimates the stresses and suggests that Table 3.3 in BS 8110-2, which gives Values ofrestraintrecordedin various structures, is relevant. For a massive pour cast on to existing blinding, Table 3.3 recommends a restraint factor of between 0.1 and 0.2. TR 34 recommends a restraint factor of 0.2, which gives:

f+ = 0.2 x 5 = 1.0 MPa (Equation 56)

50

TR 34 does not give any guidance on dealing with restrained shrinkage in pile-supported slabs where additional lateral restraint may be provided by the piles. It is not clear to what extent restraint stresses are alleviated by a carefully detailed slip membrane which, to be effective, should be continuous over piles and ground beams. Slabs can be designed as either cracked or uncracked a t the SLS. If slabs are designed to be uncracked, the elastic flexural stresses should be limited to fnm - fsh a t the SLS. This approach is likely to lead to uneconomic designs. The alternative approach is to allow limited cracking in the slab over piles.

In this case, it is difficult, and perhaps impossible, to reliably predict maximum crack widths since significant moment redistribution occurs on cracking. The problem is exacerbated by the uncertain effects of restrained shrinkage that can only be eliminated by creating a void below the slab and allowing it to move freely laterally relative to the supports, which may not be practicable. Therefore, some degree of cracking should be accepted in practice. Despite these theoretical concerns, there is considerable evidence that SFRC slabs usually perform satisfactorily in reality.

7.3.5 COIlStrUCtiOt l details In pile-supported slabs, a slip joint is commonly introduced a t the interface between the top of the piles and the slab to minimise the risk of cracking caused by restrained movements including shrinkage. This is a departure from the traditional detail of building the top of the piles 75 mm or so in to the slab. The attention of the piling sub-contractor should be drawn to this feature, and the designer should take this detail into account in assessing the overall stability of the structure and the design of the piles.

7.4 Composite f\oors on steel decking

Steel-fibre-reinforced composite slab solutions, using specific combinations of steel decking and fibres, have been developed by a number of fibre manufacturers working in partnership with manufacturers of profiled steel decking. The Steel Construction Institute (SCI) was commissioned by these manufacturers to investigate the performance of their fibre- reinforced solutions. Composite slabs perform two structural functions, as load-bearing members spanning between the supporting beams and as the compression flange of composite beams. The scope of the investigations made by SCI cover these two structural functions, for both normal and fire design.

Traditionally, composite slabs constructed using light gauge profiled steel decking have incorporated a layer of fabric reinforcement for the purpose of crack control. This is not assumed to contribute to the load-carrying capacity of the slab in normal design, which is developed purely from the composite action between the concrete and the profiled steel deck.

I

51

Typically, composite floor slabs are supported on steel beams with welded shear studs providing the shear interaction between the steel section and the concrete slab. The capacity of the shear studs will be affected by the fibre-reinforced concrete, and appropriate design values need t o be developed for shear studs embedded in fibre concrete. In order to mobilise the concrete in the slab and maximise the effective width of the concrete flange the slab’s resistance to transverse shear is also important.

Before omitting a l l the fabric, the designer should be satisfied that adequate provision has been made for all structural aspects. Generally, fibres are only used to replace the nominal fabric; any additional reinforcement required in the edge beams, in the troughs and/or for continuity over supports may still be required.

The design is in accordance with Part 4 of BS 5950(77) or Eurocode 4(78). It is important to note that the design guidance is currently for a specific steel decking system and a specific type of fibre. There is no generic design guidance available and, hence, substitution of alternative fibres or alternative decking is not possible. At present, the results from the testing described below are confidential to the decking supplier and are not in the public domain.

To justify the use of fibres, tests have been carried out t o determine their effect on the transverse shear resistance of composite slabs and the capacity of the welded shear studs. For a given type of fibre, the shear resistance has been determined experimentally using the type of specimen originally developed by Hoffbeck with a range of fibre dosages and concrete strengths. For concrete reinforced with fibres, i t is difficult t o apply the current design recommendations given in Part 3 of BS 5950 for transverse reinforcement without a significant revision to the design equation. As a consequence of this, a completely new design model was developed for the concrete flange of a composite beam that is reinforced with fibres. Hoffbeck-style tests were used to investigate the shear performance of concrete reinforced with fibres, in particular, whether the presence of fibres would reduce, or eliminate, the amount of conventional transverse reinforcement needed t o control longitudinal splitting in composite beam applications.

From the results, the transverse shear resistance of fibre-reinforced concrete can be determined using the lower-bound plasticity model given in Eurocode 2(12). This new resistance equation does not include the resistance of the steel deck. Due t o the fact that there is a large sample of data from these investigations, the design equations developed have been assessed using the requirements given in Annex D of BS EN 1990: 2002(65). This procedure is used to ensure that the design model satisfies the target level of reliability demanded in modern British and European Standards.

To determine the capacity of welded studs in fibre-reinforced concrete, standard push-off tests conforming to the general requirements of Eurocode 4 were carried out. To eliminate any artificial restraint along the slab edges, the edge trim (used t o form the edge of the slabs) was removed prior to testing.

52 I

7.5 Sprayed concrete for rock support

7.5 I I n t rod u ct i o n

Current standards define the resistance of studs in slabs on decking as the resistance of studs embedded within a solid slab multiplied by a reduction factor. Thus, tests were carried out on specimens incorporating the standard decking profile as well as on solid slab specimens. This enabled appropriate reduction factors to be determined rather than simply relying on code-defined values. Generally, the capacity of the studs is better than conventionally-reinforced specimens.

In order to determine the performance in fire, tests were carried out on full-scale specimens. The range of application of the results has been extended t o other slab thicknesses and spans by the use of a fire engineering model, allowing suppliers to provide appropriate design tables for 60, 90 and 120 minutes fire resistance.

Common uses of steel-fibre-reinforced sprayed concrete, or FRS, are for rock support in underground excavations and as part of stabilisation works for rock slopes. As noted in Section 3.6, fibre is used in FRS mainly to increase the toughness of the concrete, i.e. to increase the ability to sustain load in flexure or bending beyond the onset of cracking of the concrete matrix. However, toughness as such is not easily assimilated directly into structural design. There has been a general move away from attempts to establish ‘toughness indices’ in recent years towards ‘toughness characterisation’ and the use of equivalent residual flexural-tensile strengths in design (see Austin and Robins(41)). Papworth(80) has provided correlations between toughness characterisations and FRS design requirements that give direct guidance to design engineers, as will be discussed further below, although considerable judgement and experience are still necessary to achieve safe and efficient designs. He also discusses situations, usually involving large ground displacements in corrosive conditions, where synthetic fibre may be more cost effective and/or technically acceptable than steel fibre.

The suggested approach to the design of FRS is to specify the concrete, usually in terms of its characteristic cube or cylinder compressive strength, and toughness parameters; then to determine the sprayed concrete thickness, or thicknesses, and the type and amount of fibre required, t o comply with these specified material requirements and achieve the particular design requirements. This approach allows FRS material(s) to be specified in the first instance which the designer can be reasonably confident will achieve the specified requirements consistently during construction, and at reasonable cost.

The design requirements, and the method by which the sprayed concrete thickness and amount of fibre are determined, may differ between projects depending on factors such as ground conditions, excavation geometry, construction sequence, type of support proposed and design method. The design may be based on semi-empirical, toughness characterisation, or deterministic and analytical approaches, depending on the particular project requirements.

53

For particular projects, it is often necessary for a single specified FRS concrete to meet different design requirements and to perform under a range of differing conditions; flexural capacity, toughness, and fibre content may be only some of the factors to be considered.

BS EN 14487(57) provides Standards for definitions, specifications, conformity and execution of sprayed concrete in general, including FRS.

7.5.2 %Tli-empiriCal approach

A widely used semi-empirical approach for tunnel and cavern support is the Norwegian ‘Q System’ of rock mass classification and support prediction(8’J82). This approach predicts the rock support required for a wide range of rock mass conditions and excavation sizes, ranging from intact rock requiring no support to extremely poor conditions requiring closely spaced rock bolts with thick layers of FRS or possibly cast concrete arches. The system also allows a number of other parameters to be predicted, including deformation.

Initially, the system gave no guidance on the amount of fibre to be included in the sprayed concrete for the different support classes. However, Crimstad more recently provided recommendations on the energy classes required based on EFNARW square panel tests.

EFNARC energy classes are assigned to support classes where deformation of the excavation is predicted by the Q System to be such that significant energy absorption may be required. It is assumed that these recommendations were made as a matter of judgement based on experience and consideration of the predicted deformation.

Where no energy class is indicated, it is assumed that only nominal amounts of fibre are required, or that plain sprayed concrete is adequate as indicated on the chart.

Vander~allec~~) summarises suggested energy levels, based on the results of comparative EFNARC panel tests using fibre and proven mesh reinforcement, as follows:

500 Joules -for sound groundhock conditions 0 700 Joules - for medium ground/rock conditions

1000 Joules -for difficult groundhock conditions.

These recommendations are qualitative, but are generally consistent with those of Crimstad They are also the energy absorption classes adopted by BS EN 14487(57).

Papworth(80) derives more detailed, but similar, recommendations in respect of Q System support classes, as discussed further below.

54

7.5.3 Use of toughness characterisation

Figure 32 EFNARC residual strength and deformation

Table 4 EFNARC residual strength class definition

points.

An alternative method for deciding on the quantity of fibre required is to consider the toughness characterisation suggested by, for example, EFNARC(56), which draws on earliei work by the Norwegian Concrete Association, and Chan Toughness characterisatior sets out classes of equivalent flexural strengths a t specified central deflections in a beam test.

EFNARC proposes five ‘residual strength classes’, and three ‘deformation classes’ related to the residual strength classes, as indicated in Figure 32. Similar residual strength and deformation classes are adopted by BS EN 14487(57).

4

3

2

1

0 0 0.5 1 2 3 4

Beam deflection (mm)

I 05 1 5 2 5 ‘ 3 5 I 4 5 I

Low I 1 3 2 3 3 3 4 3

i Normal 2 10 2 0 3 0 4 0

0 5 1 5 2 5 3 5 - ___ - ~ _. _ _ .-

4

The purpose of the deformation classes is to give designers flexibility in the choice of deformation required under service conditions. However, no guidance is given on the choice of deformation class, other than the general terminology of low, normal and high deformation. Although it is stated that, for the purpose of design, the deflection limit for i deformation class can be considered in terms of the equivalent angular rotation or nomina crack width for a beam cracked at mid-span. (BS EN 14487(57) includes guidance on the angular rotation corresponding to each deformation class.) Considerable experience is required, therefore, to select the appropriate toughness characterisation for a project

5

It is suggested here that an EFNARC residual strength Class 2 and a ‘normal’ deformation class are appropriate for general initial (or ‘temporary’) support use where no specific design requirements arise. This should be achievable with modest steel fibre dosages (say approximately 40kg/m3), and a concrete matrix having a characteristic compressive cube strength of 30MPa. However, each project should be assessed individually before assuming that there are no specific requirements which might lead to a more demanding specification. For a permanent lining constructed after significant ground movements have ceased, a residual strength Class 1 and a ‘low’ deformation ciass would usually be considered as an adequate long-term provision.

Having chosen the toughness characterisation required, the type and amount of fibre needed to achieve the requirements can be determined by experimentation and beam testing. It may be necessary to increase the strength of the concrete in order to achieve the more demanding classes. Alternatively, Bernard(86) provides a methodology for relating the requirements of equivalent flexural strength measured in beam tests with the results of round panel tests t o ASTM C 1550. This is discussed further below.

Chan and Heere and M ~ r g a n ( ~ ~ ) discuss the Toughness Performance Level (TPL) approach to characterisation. In this approach, the load-deflection response of a beam tested in accordance with ASTM C 1609(60) (superseding ASTM C 1018(88) in the original papers) is matched against a series of templates that are expressed as a percentage of the design flexural strength measured at deflections of 1/600 and V I50 of the beam span. This template matching process allows the toughness of a fibre-reinforced sprayed concrete to be characterised as one of five performance levels (TPL I to V). In the example shown, the templates are for a 4MPa flexural strength, and the tested concrete would be assessed as TPL Level 1 1 1 .

Papworth(80) suggested the guidance on the required TPL for certain tunnel conditions shown in Table 4. He also presents a very useful overall correlation between TPL, Q System rock support classes (as indicated on Figure 31), and the required energy absorption classes from both EFNARC panel tests (at 25mm central deflection) and ASTM C 1550 round panel tests (at 40mm and 80mm central deflection). The round panel test is discussed further below.

Table 5 Toughness Performance Levels for different

tunnel conditions.

IV Appropriate for situations involving severe ground movement with an expectation of cracking of the sprayed concrete, which squeezes ground in tunnels and mines, and where additional support in the form of rock bolts, and/or cable bolts may be required.

Suitable for relatively stable rock in hard rock mines or tunnels where relatively low rock stress and movement is expected, and the potential for cracking of the sprayed concrete is expected to be minor.

Should be used where the potential for stress and movement-induced cracking is considered low (or the consequences of such cracking are not severe), and where the fibre is providing mainly thermal and shrinkage crack control and, perhaps, some enhanced impact resistance.

Ill

I1

56

IV F > 1400 > 560 > 840 55

E > 1000 > 400 > 600 40

111 D > 700 > 280 > 420 27 5

I t C

I B

0 A 0

> 500 > 200 > 300 20

0 0 0

Table 6 summarises Papworth’s proposed correlations, together with some indicative dosage requirements for commercially available steel and synthetic fibres. Importantly, he notes that for sprayed concrete work, dosages must be estimated taking into account fibre rebound and suggests assuming approximately a maximum of 20% for wet process sprayed concrete and 40% for dry process sprayed concrete, and this was done in proposing Table 6.

Table 6 implies that a range of sprayed concretes should be available on a project. In many cases this may be considered to be impractical with the preference being for only one or two separate concretes being specified that can meet a wide range of requirements.

TheTable also suggests using 80mm deflection in the round panel test for establishing high deflection criteria, although many laboratories may not be able to test to such high deflections. However, Papworth notes that steel fibre may not be economic for this type of application. The high deflection criteria are most likely to be applicable only to deep mines or possibly to some deep mountain tunnels where high deflections can be expected and tolerated. Design criteria for most other applications have been or are being developed in terms of the standard deflection criteria, although Papworth discusses the use of low deflection testing where cracking is of particular concern.

7.5.4 Deterministic design Essentially, the addition of fibre to sprayed concrete is related to the performance of the composite material in bending. Bending can occur in a layer of FRS as a result of:

Bending moments generated in a continuous arch lining or ‘shell’ due to asymmetrical

Bending moments generated in a layer of FRS used to support individual blocks of ground deformation following excavation

rock, or zones of loose fractured rock, that are kinematically free to fall or slide into an excavation.

Bending moments in a continuous FRS lining or shell may be calculated using numerical modelling techniques, such as finite element or finite difference methods. This form of support action would usually be associated with poor ground conditions, and may occur in conjunction with other support measures such as rock reinforcement or structural steel arch ribs.

57

D

Figure 33 Rock block or zone of looso rock loading

rprayod concroto (from Barrott and McCr~rth('~)).

In better rock conditions, the support action is more likely to be related to the second alternative of supporting individual rock blocks, or zones of fractured loose rock. In this case, the bending moments in the FRS arise as a result of slab action. A sprayed concrete slab may either span between sprayed concrete that is well-adhered to the rock surface beyond the extremities of the block or fractured rock to be supported, or more likely will be designed to span between a pattern of rock bolts that support the FRS slab, which, in turn, supports the rock, as indicated in Figure 33.

Barrett and M~Creath@~) and Maidlcgo) discuss the range of support models applicable to sprayed concrete support design in blocky rock. Barrett and McCreath identify six potential modes of sprayed concrete failure, as shown on Figure 34, of which adhesive, flexural, direct shear and punching shear are identified as the most likely modes in blocky ground.

The deterministic approach of Barrett and McCreath presents some anomalies when compared with the predictions of rock support classification systems and should be used with appropriate consideration given to relevant precedent practice. The approach often depends on rock bolt spacing, and in such cases the rock load on the sprayed concrete will increase as the bolt spacing increases, assuming the same geometry of the rock pyramid to be supported. Although this is intuitively correct if designing support in a consistent ground type, it can present difficulties in the more usual situation of differing ground conditions in a tunnel. In such cases, support in the better rock conditions should have wider bolt spacing and thinner sprayed concrete than in poorer rock conditions, and the rock load on the sprayed concrete can be expected to decrease with the increased bolt spacing, rather than increase as the approach of Barrett and McCreath may imply.

Once the appropriate support action has been identified, the critical bending moments can be calculated either from numerical modelling in the case of a continuous lining or shell, or by using conventional structural theory in the case of block support. It is necessary then to establish the relevant design stresses in the FRS using an appropriate stress block, and in particular the flexural-tensile stresses that ultimately determine the fibre requirements.

Design f o r specific a pp li ca t ions

Figure 35 Stress block for steel-fibre-reinforced sprayed C0IIQ.t. tunnel kings &ved hwn DBV

gddelhm (AKh. and BUnd"2').

Adhesive failure

Direct shear failure

Compressive failure

Flexural failure

Punching shear failure

Tensile failure

At present, no English-language design codes exist covering the specific use of FRS in tunnel construction. However, guidelines are available from the German Concrete Society, Deutscher Beton-Verein (DBV)(91) for construction using steel fibre and these have been used on a recent project in Australia reported by Asche and Barna~d(~~). The DBV recommended stress block for FRS as used on that project is indicated in Figure 35. The flexural capacity of the section is calculated by summing the moment contributions of concrete acting in compression and fibre acting in tension across the cracked portion of the lining.

Compression

Tension

59

The critical tensile stresses in the DBV stress block are taken t o be as follows: 0 The equivalent residual flexural-tensile strength measured between cracking and a

total post-crack central beam deflection of 0.5mm, measured in a DIN 1048 beam test(s8), for the tensile stress closest to the neutral axis. The equivalent residual flexural-tensile strength measured between cracking and a total post-crack central beam deflection of 3.0mm, measured in a DIN 1048 beam test, for the tensile stress reemotefrom the neutralaxis.

Asche and Be~nard (~~) provide further details of the methodology and design assumptions.

An alternative stress-strain model for more general application to FRS, and based on three- point testing of notched beams, is provided by RILEM, and is described and discussed by Vander~a l le (~~) .

The type and amount of fibre required to meet the requirements of the chosen stress block can be found by a process of experimentation and testing using the appropriate beam test. Alternatively, Bernard(86) provides a methodology for relating the requirements of equivalent residual flexural strength measured in beam tests with the results of round panel tests to ASTM C 1550. This is discussed further below.

7.5.5 Use O f ASTM c 1550 round panel tests

As discussed elsewhere in this Report, there have been concerns for some years over the repeatability of beam tests, as reported by Austin and R~bins(~’).This led t o a detailed study by Barnard of the use of round panel tests in particular as an alternative approach to the assessment of toughness by the energy absorption approach. (These tests are occasionally referred to alternatively as round determinate panel or RDP tests.) This research indicated that round panel testing of sprayed concrete gave much improved within-batch variability and several other advantages, including cost, compared with beam testing. ASTM C 1550 was published in 2003 to provide a standard test method using round panels, and the method is becoming widely adopted for the testing of FRS.

The larger deflections of round panel tests compared with beam tests reflects the intended main application of tunnel and mining support; the small deflections of beam tests related originally t o the design of ground slabs. However, there is no direct correlation inferred in either case between the test deflections and the ground deformations to be expected in construction.

In 2004, Bernard(86) published correlations between the minimum level of energy absorption or residual load capacity in the ASTM C 1550 round panel test (and the central panel deflection at which these should be measured, typically 40mm), and the equivalent selected minimum level of post-crack performance based on beam tests, i.e. the required equivalent flexural-tensile stress or strength and the central beam deflection at which these should be measured. As the available design methods for FRS are in terms of beam testing criteria, as discussed above, these correlations allow the results of the more reliable and cheaper round panel tests t o be used in the design process.

60

Table 7 Correlation between EFNARC beam tests and

ASTM C 1550 round panel tests by energy equivalence (from Bernard(86)).

Note:

* Including friction

The correlations are in the form of graphical plots o f 0 Post-crack energy a t a specific central panel deflection against the equivalent residual

0 Post-crack load capacity a t a specific central panel deflection against the residual stress in an EFNARC beam test a t a selected central beam deflection, and

strength in an EFNARC beam test a t a selected central beam deflection.

The designer can choose which of the round panel parameters, i.e. post-crack energy absorption or post-crack load capacity, is most appropriate for a particular project, although energy criteria appear to be most commonly used.

The results are also presented in tabular form, and those for the energy correlation are reproduced in Table 7. The Table gives the levels of average post-crack energy absorption in ASTM C 1550 panels for a nominal post-crack equivalent residual strength of 1MPa for EFNARC beams; performance a t greater equivalent residual strengths can be found as a multiple of these values.

05 1 0 0 731 4 58 5 2 1136

1 0 10 1693 10 6 12 2 1151

2 0 1 0 3 618 22 6 26 6 1174

3 0 1 0 5 542 34 7 41 6 1199

4 0 1 0 7 469 46 8 57 5 1230

As an example, an EFNARC residual strength of 2.5MPa (i.e. within EFNARC residual strength Class 2) and normal deformation class (say 2mm central beam deflection) would be equivalent to a post-crack energy of say 2.5 x 25 = 62J a t 3.618mm central panel deflection in an ASTM C 1550 panel test.

Asche and Berr~ard(~~) give an example of the application of round panel testing to the design of FRS for a recent tunnel project in Australia.

Finally in this section, it is useful to note that Bernard(94) suggests an approximate correlation between the results of EFNARC panel tests with 25mm central deflection and ASTM C 1550 round panel tests with 40mm central deflection as follows:

EFNARC,,,, (Joules) = 2.5 x ASTM C 1550,,,, (Joules)

and that Papworth(*O) suggests good correlations between the results of round panel tests carried out at low deflection (lomm) and the equivalent flexural strength a t 3mm deflection in a JSCE SF4 four-point beam test, as shown in Table 8, and which may be applicable to low-deflection situations. See also Section 4.2.4.

61

Table 8 Correlation between equivalent flexural strength and energy absorption for low

deflection situations (from Papworth@o)).

150

200

250

300

350

7.6 Precast products 7.61 General design approach

7.6.2 Tunnel lining segments

In many cases, the design of precast products will be on the basis of their performance. Some examples are given in the following Sections.

Section 9 of Part 2 of BS 8110(64) gives some limited guidance on the testing of precast units. It contains a requirement that the performance should be in accordance with that expected from the design calculations, e.g. that the unit should not fail in an unexpected manner. In general, the ultimate strength should exceed the design ultimate load by a margin of a t least 5%.

There are no internationally recognised design codes for tunnel linings, whether traditionally- reinforced or steel-fibre-reinforced. Generally, the design of precast concrete segmental linings tends to follow the recommendations provided in appropriate national design codes and standards for traditionally-reinforced concrete. However. strict adherence to all code requirements is not always observed where it can be demonstrated to be unimpor- tant to the loading conditions experienced by the lining. Partial factors of safety from the codes are usually adopted, but particular care needs to be exercised in their application. This is especially so in relation to the beneficial effects of some loads, such as water pressure, which improve some aspects of the design (uniform compression and reduced bending effects), while making others worse (indirect tensile stresses a t joints).

Precast concrete segmental linings are loaded and stressed in different ways through their life history. The potential stresses experienced by segmental linings are summarised in Table 9, taken from King and Alder(39).

62

Table 9 Precast concrete segment loading history

(from King and Alder(39)). Removal from mould Low Flexural Flexural strength

Turning, stacking, storing Low Flexural 1 Flexural strength

Transportation to site/face 28 day Flexural Flexural strength

Handling/erection at face 28 day Flexural Flexural strength

Handling/erection at face 28 day Tensile bursting (Tunnel Boring Indirect tensile strength

Handling/erection at face 28 day Compressive (TBM rams) , Compressive strength

Permanent loads 28 day + Flexural at ultimate and Flexural strength

Machine (TBM) rams)

serviceability limit states (ULS & SLS)

Permanent loads 28 day t Compressive Compressive strength

Permanent - loads 28 day + Tensile bursting (joints) ~ - Indirect tensile strength

This illustrates the predominant flexural stress conditions experienced by the lining in the temporary loading situations, from removal from the mould, until erection of the segment a t the tunnel face It is also evident that indirect tensile stresses may be present in both the temporary and permanent conditions, and that the designer needs to take particular care in the detailing of all joints to achieve a balance between the resultant bending moments in the main segment body, and the tensile stresses a t the joints

For the permanent loading condition, precast concrete segmental linings are influenced generally by the dominant compression loads in the ring. Commonly, bending stresses are low and counterbalanced by the high compression loads, with the result that there are often no, or extremely low, tensile stresses in the main body of the segment. As noted in Section 3.5.1, unreinforced linings are a possible design solution in many cases, but impose other limitations on the logistical approach to the whole tunnelling process.The use of steel-fibre-reinforced concrete mitigates some of these issues. In particular, the use of steel fibres is reported to significantly reduce the amount of handling damage experienced by a lining, compared to unreinforced and traditionally reinforced concrete elements.

For steel-fibre-reinforced concrete to be considered as a design option for a segmental lining, there are a range of design prerequisites to limit flexural stresses that need to be met These can be summarised as follows (11 Suitable handling system to remove the segment from the mould

Suitable stacking arrangement during storage and transportation Suitable lifting system to erect the segment in the tunnel Resultant combined axial and bending stresses within the section capacity

The capacity of the steel-fibre-reinforced concrete section may be derived from the methods discussed in Chapter 6. It is considered important from a safety point of view, that residual (post-cracking) stresses are considered in the design for each stage, as previous mishandling or unexpected loading may have taken the element past i ts first crack flexural strength without the damage being physically visible. A t the design stage, flexural and tensile strengths of the steel-fibre-reinforced concrete may be based upon the relationships provided in Appendix B. However, extensive testing on previous projects suggests that these can be considered as the lower bound values that can be achieved, and higher

63

values may be achievable with appropriate materials and design. In addition, it is important that whatever values are adopted for the design, they are fully validated and continuously checked by appropriate testing during lining manufacture.

King(95) has suggested that, typically, steel-fibre-reinforced concrete for segmental linings would include the following attributes and properties to achieve desirable design properties, although other considerations may alter particular project decisions: 0 Hooked, or deformed end, fibres that tend to exhibit higher ductility and higher tough-

ness characteristics than straight fibres. 0 Longer fibres that tend to exhibit higher toughness characteristics. Long fibres can also

cause more problems with mixing and balling within the concrete, and fibre aspect ratios of between 60 and 80 are likely to perform satisfactorily.

0 Low water:cement ratios improve durability by reducing the free moisture available to aid chloride transportation and increase electrical conductivity. This will also reduce shrinkage strains and creep strain.

0 High fibre strengths (1000MPa to 1200MPa) to improve ductility. Failure by the gradual pull-out of the fibres is the preferred failure mechanism, rather than the sudden snapping of the fibre. The bond between fibre and concrete matrix will increase with age and the fibre dosage and strength need to be sufficient to compensate for this.

0 High fibre dosages will cause mixing difficulties and low dosages minimal performance enhancement post-crack. For segmental tunnel linings, a dosage of between 30 and 50kg/m3 is likely to be appropriate, although further enhancement can be obtained with higher dosages; up to 100kg/m3 have been produced under laboratory conditions.

7.6.3 Pipes and ancillary products

BS 5911(96) covers the requirements for the design of concrete pipes, for drainage and water supply, and associated products such as manholes and inspection chambers. The scope of this Standard refers to unreinforced steel fibre and reinforced pipes. The various parts of the Standard give the loading requirements. For example, Part 1 gives the minimum crushing load per metre run for various sizes and shapes of concrete pipe, and Part 3 gives the patch loads to be carried by cover slabs. Durability requirements are covered in the Standard by the specification of cement types and minimum cement contents.

BS 5911 will be replaced in due course by BS EN 1916(97), covering pipes and fittings, and BS EN 1917(98), covering manholes and inspection chambers. Both codes cover the use of unreinforced and reinforced concrete as well as steel-fibre-reinforced concrete. As with BS 5911, design is based on proof testing.

64

8. Construction aspects 8.1 Cast in-situ or precast

concrete 8.1 .1 Specification The basic concrete should be specified in accordance with BS 8500(99) to ensure adequate

durability. In aggressive situations where the appearance of the concrete is a primary concern, it may be necessary to specify stainless steel fibres to eliminate rust staining due to the corrosion of exposed fibres. Alternatively, galvanised fibres may be used, although these require the use of an inhibitor in the concrete and are not suitable for situations in which the coating on exposed fibres may be subject to abrasion.

The amount and type of fibre to be used will be determined by the supplier on the basis of the required design parameters (e.g. the required with an appropriate allowance for batching tolerances, see Section 81.2. Generally, designing concretes with steel fibres does not require special consideration beyond that of normal quality-controlled concrete. The main exception may be that some modification to the consistence may be needed to improve handling and placing. This may necessitate adjusting the aggregate grading, for example, especially a t higher fibre dosages or where longer fibres are used.

Fibres alter the rheology of the concrete and can give rise to an apparent loss of consistence as measured by the slump test. However, the compaction energy required to place the concrete is no greater than for plain concrete. Workability as measured by the Vebe compaction tes t shows little change due to the addition of fibres. (There is a requirement in BS EN 14889-1(5) for the fibre supplier to declare the change in consistence of a reference concrete that complies with BS EN 14845-1(7) when using the minimum amount of fibres needed to obtain the required strength, as described in Section 21.) The loss of consistence will be more apparent in a concrete containing sharply angular aggregate. A plasticiser or superplasticiser may be used to adjust the consistence to a level better suited to the construction method. To ensure that the consistence is appropriate for the construction method, liaison between the concrete producer and the contractor is recommended.

In addition, liaison between the ready-mixed concrete producer and the contractor is essential to ensure that the concrete is correctly proportioned for the method of delivery, handling and finishing on site.

81.2 Adding fibres to the concrete

Most commercially available steel fibres can be added to the fresh concrete a t any stage (see Figures 36 and 37). They may be dispersed on to the aggregate conveyor or into the weigh hopper at the batching plant or be added on site via the hopper of the concrete truck mixer. However, most best practice guidelines for ready-mixed concrete advise against adding any materials to the concrete on site unless under controlled conditions. In every case it is essential that the fibres are added in accordance with an agreed quality assurance (QA) procedure, and by operatives who are fully trained in the use of steel fibres. Where ready-mixed concrete is supplied as part of a nationally accepted QA scheme (e.g. QSRMC in the UK), the use of steel fibres should form part of that scheme, with clearly defined responsibilities for al l parties.

65

Following a QA procedure will ensure that the correct quantity of fibres is added and that proper mixing takes place to ensure that they are uniformly distributed throughout the batch. BS EN 14650(100) requires that, for concrete to be used in precast products, the batching tolerance should not exceed *5% of the specified value. It has been reported that equipment installed in batching plants will dispense fibres to an accuracy of G'kg/m3.

Currently, the most common method of adding steel fibres is directly to the back of the ready-mixed concrete truck on site. Special equipment, such as pneumatic blast machines or vibrating screens, can also be used to introduce the fibres into the concrete.Typica1 mixing time is 5 minutes at full drum speed (12 rev/min). As long as the aspect ratio of the fibre is less than 50, the fibres may be dispensed directly without any risk of balling. With higher aspect ratios, some manufacturers employ special packaging techniques to reduce the risk. For example, the fibres may be formed into bundles using water-soluble glue that dissolves during mixing, or they may be parallel packed rather like a box of matches.

66

I b i. 8.1.3 Pumping Pumping fibre concrete does not require specialist equipment. Concrete containing short

steel fibres should cause few problems. Longer (5060mm) steel fibres, commonly used in floor construction, require careful attention, particularly a t higher dosages of more than 25kg/m3, although concrete with up to 50kg/m3 is frequently pumped. (Kitching(*O) gives details of the successful pumping of concrete containing 50kg/m3 of 60mm-long fibres.) In some cases, concrete with dosages of 80-100kg/m3 has been successfully pumped for elevated slabs and for foundation rafts. Recently, concrete has been successfully pumped for the slabs of a 10 storey building, see Figure 38.

Discussions between the supplier and the contractor prior to the use of high aspect ratio steel fibres and steel fibre concrete with high fibre dosage rates are advisable. In some cases pumping trials may be appropriate. Generally, concrete designs need to be adjusted so as to reduce the proportion of coarse aggregate thereby increasing the fines content. This produces a concrete in which the fibres can be distributed more easily. During the mixing process the fibres should not be allowed to agglomerate into balls and so special precautions may be necessary to introduce the fibres into the concrete.

Construction aspects I

Figure 38 Pumping steel fibre concrete for slabs of a 10

storey building.

8.1.4 Placing Any standard placing technique may be used. As mentioned, it may be necessary to adjust the consistence to optimise handling. With higher concentrations of steel fibre, it may be easier to move the concrete around with a rake rather than a shovel. For floors and paving, the fact that the reinforcement is distributed evenly throughout fibre-reinforced concrete is well suited to modern large bay methods of construction.

8.1.5 COI'TlpaCting and finishing

All conventional concrete compacting and finishing techniques can be used. As well as materials and equipment, the experience of the concrete placing gang has a great effect on the quality of the surface finish. The type of finish (e.g. power floated, trowelled, brushed) will depend on the particular application and the client's requirements. Fibre-reinforcedconcrete should be cured as for concrete reinforced with steel bars or fabric.

Some specific guidance for floors and slabs is given below.

Internal floors For floors, the timing of floating and trowelling operations should be fitted to the prevailing weather. As with any concrete, problems such as differential setting caused by inconsistent concrete delivery can be avoided by careful control. The surface mortar (or 'fat') produced as a result of compacting the concrete and initial power floating is usually sufficient to cover most surface fibres. It should be noted that floors constructed with fibre dosages over 20-25kg/m3, especially of the longer wire-drawn fibres, may require a dry-shake topping to

. I

further reduce the number of surface fibres. Generally, an occasional fibre a t the surface is not considered to pose a problem. Experienced flooring contractors should be able to provide evidence of existing slabs that are performing well.

The ability to produce a ‘fibre-free’ floor surface finish depends on several factors: U Fibre type. While high-quality surfaces can be achieved with any fibre type, small slit

sheet fibres tend to be easier to finish. Also, as a result of their lower tensile strength, any fibres protruding directly through the surface are cut flush normally by the power trowel blades.

0 Compaction method. Compaction must be applied from the surface, by means such as a laser screed, razor-back or vibrating beam. This is required to ‘settle’ the fibres below the surface. Poker vibrators do not give sufficient uniformity and should not be employed to reduce fibres at the surface. However, poker vibrators should be used to compact the lower layers of concrete in thick slabs as surface applied vibration is unlikely to be sufficient.

0 Screed method. Very high quality finishes have been achieved by following the laser screed with a vibrating highway float before trowelling. On flood pours, a vibrating highway float should be used to provide the necessary surface vibration. Discharge/placement. The quantity of concrete discharged from the mixer or pump should not be so great that the laser screed or screeding beam has to remove excessive amounts of surcharge. This over-pour should be no greater than 50mm above the required thickness. The concrete slump should not be too low, as this will cause uneven discharge and increase the risk that the screeding equipment will tear the surface as it passes.

A few cosmetically unacceptable steel fibres may st i l l be present a t the surface. The usual remedy is to snip the loose ends with wire cutters and fill any surface blemish with a proprietary resin mortar.

Unless a high-build coating is being applied, shot-blasting the surface of a steel fibre concrete floor is not recommended normally because of the risk of exposing surface fibres. Other techniques that have been used to remove loose steel fibres from the plastic concrete surface include brooms and magnetic rollers.

External paving The requirements for the finish for external paving (e.g. for roads, hard standings and storage areas) will be less onerous than for internal floors, with a lightly tamped or floated surface being sufficient. A brushed finish should be avoided generally as fibres near the surface fibre may be dislodged. Fibres exposed on the surface of the paving are usually of little concern and will be worn away by traffic.

68

81.6 Health and Safety As indicated above, where fibres are added directly to the truck mixer on site, this should be done with due regard to Health and Safety regulations for access, working a t height, etc. An appropriate method statement should be developed. Staff should be suitably trained and under the supervision of technical/production personnel.

All operatives involved with placing, compacting and finishing the concrete should wear appropriate personal protective equipment, e.g. gloves and boots. The presence of fibres in the fresh concrete should not present any increased risk.

81.7 Testing for fibre quantity and distribution

Although visual inspection will normally be sufficient to determine when homogeneous dispersion has been achieved, a more accurate assessment may sometimes be required.

For determining the fibre content of fresh concrete, the draft CUR recommendation^(^)

suggest the following:

“Two samples of at least 8 litres shall be taken for each mixer truck to be checked; a t least three mixer trucks shall be checked, and the quantity of fibres shall be measured by washing out. The mean fibre dosage, measured over at least six samples, shall not be lower than the intended value minus 10% and shall not be lower than the intended value minus 4kg/m3. No individual result shall be lower than the intended value minus 20%, nor lower than the target value minus 9kg/m3.”

The Recommendation requires that the fibre-reinforced concrete be supplied under a quality assurance scheme, to ensure that the properties are as assumed in the design Alternatively, it requires the fabrication and testing of beam specimens, two for each casting day and a minimum of six specimens for the project as a whole At least one cube should be cut from each specimen after testing to check the compressive strength

BS EN 14721(101) gives a method for measuring the fibre content of concrete used in precast applications. As indicated earlier, BS EN 14650(100) requires that the batching tolerance should not exceed *5% of the specified value. (The equivalent European Standards for concrete cast in-situ are in the process of being developed. In the meantime, it is suggested that the precast codes should be used for both applications.)

For precast concrete tunnel lining segments, King and Alder(39) suggest that a set of three 5 litre samples should be taken per mixing unit every 24 hours. The average fibre content from the set of three samples should exceed the design fibre content and no individual sample should have a fibre content less than 80% of the design fibre content.

8.2 Sprayed concrete 8.21 General guidance A comprehensive description of a l l aspects of sprayed concrete technology, including

equipment, construction practice, quality control and site safety considerations, is provided by Austin and Robind4’). Concrete Society Technical Report 56(43) provides a useful overview of construction and repair using modern wet-process sprayed concrete. EFNARC(56) provides a model specification for sprayed concrete, with guidelines published separately for the information of specifiers and contractors. MaidUgo) includes discussion of both sprayed and cast concrete construction using steel fibre reinforcement.

Several major suppliers of sprayed concrete and fibres produce their own guidelines and detailed product support, and may be contacted as necessary. Much of the guidance given in Section 8.1 for cast concrete is also applicable to sprayed concrete. A European standard on testing sprayed concrete, EN 14488(53), is currently being developed; most parts have been published as British Standards.

8.2.2 Testing for fibre quantity and distribution

Fibre Steel fibre for sprayed concrete will usually be subjected to compliance testing for tensile strength, diameter and minimum and maximum length, as for cast concrete applications.

A typical requirement would be for at least one tensile test, consisting of 10 randomly selected finished fibres, t o be performed for each 4.5 tonnes of material supplied or for each shipment if less than 4.5 tonnes. The average value of tensile strength in these tests should not be less than the specified minimum. The tensile strength of any one of the ten specimens shall not be less than the specified minimum less an appropriate margin.

Bending tests of fibre can be carried out in accordance with ASTM A 820: 96(6).

Fibre quantity and distribution The EFNARC Specification(56) and BS EN 14488(53) include tests on samples of sprayed concrete to determine the fibre content. (The same approach could be used for conventionally cast concrete.) Three samples, each l-2kg, are taken from freshly sprayed concrete in the works or from a test panel sprayed with the same equipment, technique, layer thickness per pass, spraying distance, etc. as the actual work. The samples are weighed and placed in filter equipment where the cement and fine materials can be washed out so that the fibres can be separated from the mass and weighed t o determine the amount per m3 of sprayed concrete.

Alternatively, cores may be cut from hardened concrete. The cores are crushed so that the fibres can be separated out, possibly by magnet. Recommendations for the frequency of testing are included in BS EN 14487(57).

70

Flexural toughness testing As noted in Section 4, BS EN 14488(53) specifies a square panel test for flexural toughness testing and BS EN 14487(57) inchdes recommendations for the frequency of testing. How- ever, as also discussed in Chapter 4, round panel tests to ASTM C 1550 are becoming widely adopted internationally for the specification and control of fibre-reinforced sprayed concrete work in particular. In Europe, the EFNARC plate test is extensively used. Typical requirements are for one test (meaning the results of tests on 3 panels from the same sprayed concrete batch) for each 150m3 of each type of FRS placed in the works.The sprayed concrete shall be acceptable if the results from at least 2 out of 3 panels tested for each test exceed the minimum specified requirements. Bernard@) discusses the coefficients of variability tc be expected from this test method.

Beam testing BS EN 14488(53) specifies a beam test for determining residual strength and deformation classes and BS EN 14487(57) includes recommendations for the frequency of testing.

Other works tests Other works tests for sprayed concrete are normally independent of fibre content and are therefore beyond the scope of this Report. General guidance on quality control for al l aspects of sprayed concrete construction may be found in Austin and

8.2.3 Health and safety The spraying process is potentially dangerous as it involves sprayingdense particles a t high velocity onto generally hard surfaces which, in the case of hand spraying, may be only a short distance from the operator (optimum nozzle to substrate distances are of the order of 1 to 1.5m maximum). To minimise the risks to operatives, modern high production application of fibre-reinforced sprayed concrete should be undertaken using remote controlled robotic sprays, which are available in a range of sizes; manufacturers should be contacted for details. Remote controlled spraying allows the operator to control the process from a position of safety. Generally, the wet mix process produces considerably less rebound and dust than the dry mix process. However, appropriate personal protective equipment will usually be required, including gloves, head protector, safety shoes, eye protectors and dust masks. Usually, design risk assessments will indicate that wet mix sprayed concrete applied by robotic sprays should be specified wherever possible in preference to hand applied dry mix sprayed concrete.

In the case of the wet mix process, fibre can be batched automatically at the batching plant or directly by hand into the mixer unit before discharge into the robotic spray. Normally, fibre is not considered to increase the hazard associated with sprayed concrete, provided that al l necessary precautions are taken in accordance with an appropriate risk assessment.

Austin and on safety related to the use of sprayed concrete, and with particular reference to plant and equipment, materials, personnel, training and certification, and site operations.

and Concrete Society Technical Report 56(43) provide general guidance

71

9. I n -service performance

9.1 Durability Steel fibres in concrete are protected from corrosion by the background alkalinity of the cement paste. The steel, being discontinuous in nature, is not capable of giving rise to galvanic corrosion. Also, even if they do corrode, the small volume of each fibre is insufficient to create the bursting stresses associated with corrosion of larger diameter reinforcement. Thus, there are no minimum cover requirements. There may be some partially embedded or loose fibres on the surface of the concrete that will corrode rapidly in exposed conditions. The resulting rust staining may only be of concern for high quality visual concrete.

King and Alder(39) reviewed a number of durability studies, specifically in relation to the use of steel-fibre-reinforced concrete in tunnels. Their conclusions were that:

“Steel-fibre-reinforced concrete will provide a material a t least as durable as normal reinforced concrete. Carbonation does not pose a significant threat, and although fibres a t the immediate surface layer corrode to a depth of surface carbonation, the fibres in the body of the specimen do not corrode ... The restriction of crack widths to that normally recommended in conventional reinforced concrete will lead to a satisfactory design with much of the flexural strength retained.”

Bernard(lo2) tested sprayed concrete specimens reinforced with steel fibres. Pre-cracked specimens were stored in coastal or inland sites for up to two years and the effects assessed by examining the residual energy absorption capacity using panel tests. He concluded that:

“Corrosion and performance loss for fibre-reinforced shotcrete reinforced with steel fibres was substantial, even after only seven months exposure. Crack width was found to influence the degree of deterioration ... cracks greater than O.lmm width led to significant rates of deterioration.”

Lambrechts reported on notched, pre-cracked beam specimens that were exposed to a variety of wetting and drying environments for up to 18 months. A t the end of the period, only the fibres very close to the surface were found to be corroded. No corrosion was observed in the body of the concrete even for those specimens that were fully saturated by chlorides. The specimens were load tested after exposure. In all cases the maximum load achieved was a t least equal to the load after pre-cracking, indicating again that no significant corrosion of the fibres had occurred.

9.2 lnSpeCti0tl and repair In line with al l structures, concrete reinforced with steel fibres should be inspected regu- larly for signs of damage or The most likely causes of damage are over- loading, impact and abrasion. As there are no significant deterioration mechanisms for the fibres, visual inspection should be al l that will be required (unlike structures reinforced

72

with conventional steel reinforcement where it may be necessary to carry out electro- chemical tests to assess the risk of corrosion). If there is concern about the effects of a corrosive environment, it may be prudent to take a core to confirm the depth of any loss of fibres, particularly where there are cracks.

Clearly, after a significant fire there will be a need to carry out a full inspection and appraisal of the concrete in the affected areas. Damaged concrete will have to be removed and replaced(105). The colour of the concrete after it has cooled down will give an estimate of the actual temperatures reached during the fire. It should be assumed that the steel fibres will loose al l their strength a t the rate indicated for steel reinforcement in Eurocode 2(12).

If required for structural purposes, affected areas will have to be removed and replaced.

Repairs will be no different from those for any concrete structure. Loose or damaged areas should be cut back to sound material. The surface of the concrete should be roughened to ensure that the new concrete bonds well. Replacement concrete may be placed by hand in small areas. Larger areas can be reinstated by casting additional concrete or by spraying.

9.3 Surface appearance As indicated earlier, there may be some staining on the surface of the concrete due to local rusting of the fibres. In heavily trafficked areas, the surface laitance on slabs will be worn away fairly rapidly, which will expose fibres that will not have been visible initially. The finishing process should ensure that they will be lying in the exposed surface, rather than a t an angle to it. (Where the slab has been finished with a rotating screed, such as a Bunyan roller, the rotation will tend to align the fibres a t right angles to the roller.) Exposed fibres will be progressively worn away as the surface is slowly abraded.

9.4 Demolition and Because of their good record in service, there is little experience of demolition and recycling recycling of steel-fibre-reinforced concrete.

It has been suggested that concrete with a low fibre dosage can readily be broken up using standard equipment, e.g. pneumatic or hydraulic breakers. It can then be crushed and the fibres extracted as scrap metal using magnets; it is unlikely that the extracted fibres could be reused. The aggregate could be recycled, subject to the usual restrictions on use, see Part 2 of BS 8500(99).

Demolishing concrete containing fibres a t higher dosages and/or higher aspect ratios could be more problematic because of their toughness and ductility. Standard breakers would be unlikely to have much effect. It would probably be necessary to cut the structure into appropriately sized pieces, for example using a diamond saw, which could be fed into a crushing plant. It is unlikely that the steel fibres could be recovered from the crushed concrete and, hence, the resulting material would probably only be suitable for sub-bases and not as aggregate for concrete.

73

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Vol. 6,1976, pp 773-782.

Appendix A. Design of ground-supported slabs

This Appendix gives a summary of the design approach in Concrete Society Technical Report 34@) for the design of ground-supported slabs. TR 34 also includes a worked example.

Note that this design approach is only applicable if the (equivalent flexural strength ratio, determined from the JCI-SF4 beam test) is greater than 0.3. If the Re,, is less than 0.3 the slab should be considered as being unreinforced and designed by elastic methods.

A.l Bending For the ultimate limit state of bending, the requirements a t the upper and lower surface of the slab are different. Cracking is permitted on the underside of the slab but not a t the upper surface. Hence, the full plastic bending moment capacity can be developed a t sagging yield lines but only the moment to cause cracking a t hogging yield lines. There must be sufficient rotation at the sagging yield lines to develop the hogging moment capacity.

Three load locations are considered in design as follows: 0 Internal - the centre of the load is located more than ( I+ a) from a slab edge (i.e. a

Edge -the centre of the load is located a from a free edge or joint and more than ( I + a)

Corner - the centre of the load is located a from both edges forming a corner.

free edge or a joint).

from a corner (i.e. a free corner or the intersection of two joints).

where: a =

I = radius of relative stiffness, given by: equivalent contact radius of the load

I = [E,, x 103 h3 12 (I - v 2 ) 4,b]0.25 (Equation AI)

where:

E,, = h = slabdepth (mm) v =

Ksub =

short-term modulus of elasticity of concrete (CPa)

Poisson’s ratio for concrete (dimensionless, usually taken as 0.2) modulus of subgrade reaction (N/mm3).

Linear interpolation can be used for loads a t intermediate positions.

For each load location, a pair of equations is given to estimate the ultimate load capacity (P,) of ground-supported slabs subjected to a single concentrated load. The first equation of each pair is for a true point load (a = 0). The second is for a concentrated load and is valid for a / I > 0.2. Linear interpolation can be used for values of a / I between 0 and 0.2.

79

For an internal load with:

a l l = O

P, = 2n (MP + M,,)

a l l 2 0.2

P,=4n(Mp+M,)/ 1 - - [ :j For an edge load with:

a / l = 0

P, = [IT (MP + M,,) 121 + ZM,,

a I I 2 0.2

PU=[~(Mp+Mn)+4M,, ] / 1 - - [ .?I For a free corner load with:

a / l = 0

P, = 2Mn

a l l 2 0.2

P, = 4Mn I [I - (U I I)]

(Equation A2a)

(Equation A2b)

(Equation A3a)

(Equation A3b)

(Equation A4a)

(Equation A4b)

It should be noted that: These are ultimate limit state equations and, hence, P, is equal to the applied load

These equations deal with flexure; it is essential to check for punching shear. times the appropriate partial safety factor for actions.

In the above equations:

MP = ultimate positive (sagging) resistance moment of the slab =

(fctk." 1 Yc ) %.3 h2 1 6

Mn = ultimate negative (hogging) resistance moment of slab =

(fctk,fl 1 Y, 1 h2 1 6

(Equation ASa)

(Equation ASb)

80

where:

fCtk," =

h = slabdepth (mm)

Re,3 =

characteristic tensile strength of concrete (MPa) (Equation A6) = 1' + (200 )"'I fctk(005) ' fctk(0.05)

equivalent flexural strength ratio.

The use of Equation A6 is discussed further in Appendix B, where it appears as Equation B6).

A.2 Punching shear Design against punching shear a t concentrated loads is based on the approach in the Eurocode for suspended slabs. This means that designs are conservative because no account is taken of transfer of load directly through the slab to the ground beneath.

Punching shear capacity is determined in accordance with Eurocode 2 by checking the shear at the face of the contact area and at the critical perimeter situated at a distance 2d from the face of the contact area, where d is the effective depth of the slab, taken as 0.75h for fibre-reinforced slabs, where h is the overall slab depth. Generally, it is the shear on the critical perimeter that governs load-carrying capacity.

The shear stress a t the face of the contact area should not exceed vmax irrespective of the amount of reinforcement in the slab. The value of vmax is given by:

vmaX = 0.5 k, fcd (Equation A7)

where: fcd = design concrete compressive strength (cylinder) = fck v c

k, = 0.6 (1 - fck / 250)

where:

fck = characteristic compressive strength (cylinder)

Hence, maximum load capacity in punching, Pp,max, is given by:

(Equation A8)

where:

uo = perimeter of the loaded area

The shear stress is checked on the critical shear perimeter a t a distance 2dfrom the edge of the loaded area. The slab ultimate load capacity for punching shear (plain concrete only) is given by:

Pp = (0 .035k3/* fC~/* )u,d (Equation A9)

where: k I 1+(200/d)05

U , = length of the critical shear perimeter.

81

RlLEM guidance@) suggests that the presence of steel fibres will increase the design shear capacity over that of plain concrete by an amount vf given by:

Vf = 0.1 2 %3 fctk fl (Equation A10)

where:

fctk," = characteristic flexural strength of plain concrete

The guidance depends on the presence of conventional reinforcement, but tests on large- scale steel fibre-only reinforced ground-supported slabs have shown that application of the above guidance gives conservative results. Thus, for steel fibre-reinforced concrete the slab load capacity, Pp, is given by:

Pp = (0.035k3"fC,"* + 0.12Re,, fc,k,fl)u,d (Equation A l l )

Note that the above are ultimate limit state equations and, hence, Pp should be greater than the applied load times the appropriate partial safety factor for actions.

A.3 Other design considerations

Equations are also given in TR 34 for combinations of loads, line loads and uniformly distributed loads. It also gives guidance on serviceability considerations.

A.4 Comparison Of test results with the design

approach in TR 34

In order t o check the validity of the design equations in Technical Report 34(68), comparisons have been made with the results of tests by Roesler four ground-supported slabs, two with synthetic fibres and two with steel fibres. Only the ones with steel fibres are considered here.

They tested

The comparisons are made on the basis of the quoted cylinder compressive strengths and flexural strengths, with partial safety factors set initially t o 1.0. Note that the values were measured at 56 days so will be higher than the 28 day values used in the TR 34 design approach .

Both slabs were 131.8mm thick and were loaded through a 203mm square steel plate.

Thus, a = 114.5mm

Average modulus of sub-grade reaction quoted as k = 0.1.

Following the procedure outlined above, the comparisons were carried out as summarised in Table Al .

82

barison between strengths of

I rneasui ground,

Table A1 Ped and predicted -supported slabs.

Thus, using the quoted actual cylinder strengths and flexural strengths, wi th partial safety factors set to 1.0, all failures occurred below the characteristic values. This may be due t o an overestimate of flexural tensile concrete strength (see Section B.2). Nonetheless, if comparisons are made including a materials partial safety factor o f 1.5, i.e. comparing with the predicted design strengths, the slabs failed at 25% above the predicted value, indicating that the approach is safe.

83

B.1 Design for flexure

Appendix B. Design

Figure B1 Structural modo1 for Olrron

U-w mrthod.

Various methods have been proposed for calculating the moment of resistance of SFRC sections, which can be classified as follows: 1. Discrete crack non-linear finite element analysis 2. Smeared crack non-linear finite element analysis 3. The stress-crack width method o-w 4. The stress-strain method o-E 5. Plastic analysis.

The first two of these methods are specialised and will not be discussed further. Of the remainder, the o-w method is the most rigorous but is overly complex for normal use. Methods 4 and 5 are widely used in practice and are described in Section 6.2. Only the o-w method is discussed in this Appendix.

The o-w method is a simplified method for modelling the hinge rotation at a crack in SFRC.The RILEM o-w is a useful introduction to the method. Figure B1 shows an idealised o-w structural model and corresponding o-w relationship for SFRC proposed by 0leson(lo6). In SFRC, stress is transferred across cracks by the combined contribution of the concrete and fibres.The crack can be modelled using the fictitious crack model (see Figure 82) that Hillerborg er al.(lo7) developed to model fracture in plain concrete. The tensile stress at the top of the crack is assumed to equal the concrete tensile strength. The crack is subdivided into a fictitious crack of length a with width I w, (see Figure B2) across which tensile stress is transferred in accordance with the o-w diagram. The length of crack below the fictitious crack is referred to as a true crack since it is stress free.

crack

a) Geometry, loading and deformation of crack b) Geometry, loading and deformation of cracked incremental horizontal strip of hinge

- w W l w2 c) Definition of parameters of bilinear stress-crack opening

relationship; parameters a, and a, are negative slopes of left and right-line segments respectively

84

Appendix B - Design

Figure B2 Fictitious crack model.

I 4. x- 4 b--

traction free aggregate process crack interlock zone

4 b fictitious crack

Concrete crack

-- aggregate process interlock zone

' I

4 b fibre bridging

I I I I I

I' fictitious crack

Crack in SFRC

The essence of the o-w method is shown in Figure B1, which shows the geometry, loading and deformation of the cracked hinge proposed by Oleson('O'j). The non-linear response is assumed to be concentrated within the cracked hinge. The moment capacity of the hinge is related to the hinge rotation, which, in turn, is related to the crack width. It is possible to derive the moment-rotation response of a hinge directly from the stress-crack opening relationship, which can be idealised as shown in Figure B1. It should be noted that it is necessary to assume the length of the hinge in the o-w method. The length of the hinge can be derived from calibrating the method with non-linear finite element analysis. Ulfkjaer have shown that the length of the hinge is approximately half the depth of the beam. Oleson gives closed form equations that define the moment-rotation response corresponding to his cracked hinge model with the o-w relationship shown in Figure B1.

8.2 Flexural size effects 8.23 Size effects in plain

concrete beams Flexural size effects need to be considered in the design of plain and fibre-reinforced concrete. The flexural strength of concrete is defined as:

fd=6M,,l(bh2)

where: M,= peak moment in a 4 point bending test.

(Equation BI)

85

~-

I- --?#

Tests show that the flexural strength of concrete is size dependent. The size dependency of fctfl is widely recognised but there are significant variations in the concrete flexural strengths adopted in published design guidance as noted below:

Eurocode 2 (ENV)

(Equation B2)

where:

fctk(0051 = lower characteristic tensile strength of concrete = 0.21fc;'3 (Equation B3)

Dramix Guideline and RlLEM o-E method

Eurocode 2

TR 34

(Equation B4)

(Equation 85)

(Equation B6)

The size effect terms used in Eurocode 2 and TR 34 are compared in Figure B2, which shows that Eurocode 2 gives significantly lower strengths than TR 34. The TR 34 equation was taken from a draft of Eurocode 2 that was subsequently amended to give the current Euro- code 2 equation. The draft equation was used in an extensive calibration process during the drafting of TR34, which set appropriate safety factors, etc. It is recommended that theTR 34 equation is only used in designs for ground-bearing slabs in strict accordance with TR 34.

The size dependency of the flexural strength can be explained with non-linear fracture mechanics. Experimental research shows that concrete is a strain-softening material in tension. In plain concrete, stress is transferred across micro-cracks by crack bridging for crack widths up to around 0.05mrn. The strain-softening behaviour can be characterised by plotting the residual tensile strength against the crack width in a displacement controlled tensile test. Figure B3 shows an idealised o-w diagram for plain concrete. The area under the o-w diagram is equal to the fracture energy, C,.The strain-softening behaviour of plain concrete was first explained by Hillerborg using the fictitious crack concept. The tensile stress a t the top of the crack is assumed to equal the concrete tensile strength. The fictitious crack model can be used to explain why the flexural strength of concrete is greater than its strength in direct tension. Section analysis shows that the peak moment corresponding to the o-w relationship in Figure B3 occurs after the stress reaches the tensile strength a t the extreme tension fibre. Figure 84 shows a load displacement curve for a plain concrete beam in a displacement controlled test and the corresponding stress blocks that change shape after cracking due to the strain-softening response of the concrete in tension.

86

Appendix B - Design

Figure B3 Idealised U-w relationship for plain concrete.

Figure 84 load displacement response of plain concrete

beam and associated stress blocks.

Stress o

Crack width w

Q (-1 a(+) o(-1 0 (+I -3 0 +3 -3 0 +3

I

2

3 4 n F/b (MN/rn)

E =30,00OMPa

50 100 150 Deflection (pm)

87

Appendix E3 - Design

The presence of a size effect is also explained by the fictitious crack model. Consider the two cracked beams shown in Figure B5.The larger beam has the same width but twice the length and depth of the smaller. The crack in the larger beam is twice as long as that in the smaller. Assume that the stress distribution a t the crack in the smaller beam corresponds to the peak moment and, furthermore, that the crack in the larger beam is twice as wide as that in the smaller beam. Assume that the o-w response is as shown in Figure B3. Therefore, the stress a t the bottom of the fictitious crack is reduced by a factor of 0.5 in the larger beam. It follows that the flexural strength is size dependent. The magnitude of the size effect can be quantified experimentally or numerically using non-linear Finite Element Analysis.

Figure B5 Influence of doubling beam length and depth

on flexural strength.

1

t 0.5 aft t

B.2.2 Size effects in fibre- reinforced concrete

There is l i tt le consensus on size effects in fibre-reinforced concrete beams in flexure. For example, size effects are included in some design methods such asTR 34 and the RlLEM o-E design recommendations but not others. The influence of size effects on SFRC varies with loading due to the relative contributions of the concrete and the fibres. The concrete contribution is the stress-crack opening relationship for plain concrete while the fibre contribution consists of an ascending part followed by a softening part as illustrated in Figure B6, which is adapted from the RlLEM o-w design guideline. Figure B6 shows that the concrete contribution dominates a t very small crack widths but is insignificant a t crack widths greater than 0.1-0.2mm.

88

Appendix B - Design

Figure 86 Re la th contributions of fibre and concrete to

a-w response of SFRC.

Figure 87 Influence of beam d q t h a d crack width on

flexural resistance for Oleson e w ddonship with ba P 0.75.

Stress (MPa) 4.00

3.00

2.00

1.00

0.00

i Concrete contribution -

0.01 0.10 1.00 10.00

w (mm)

The influence of fibres on the moment-rotation response of the hinge a t a crack can be modelled using the 0-w method described in Appendix BI. The ratio between the peak moment and the first cracking moment (M, = {bh2/6}fc,) depends significantly on the G-w relationship, which is fibre and concrete dependent. Figures 87 and 88 show the results of a parametric study on the series of beams described in Table 81. The analysis was carried out using the cracked hinge model of Oleson(’06) with the material properties he adopted. A bilinear G-w relationship was used as shown in Figure B1 with b, = 0.75 and 0.5. The moment of resistance was normalised with respect to M, = (bh2/6)fc,.

1.0 . I - Ir

--C Nofibres * Maxb2=0.75

+ w=3.Smm b2=0.75 4 w=l.Smm

+ w=0.5mm b2=0.75 0.5 ~

0 1 I I I I I I

0 100 200 300 400

Section depth (mm)

500 600 700

89

Hppenaix tj - Design I

Figure B8 Influence of barn depth and crack width on

flexural resistance for Oleson 0-w relationship with ba = 0.5.

Table B1 Material properties assumed in Figures 87 and

B8.

2.0

1.8

1.6

1.4 $ $ 1.2

r, 1.0 - \

0.8

0.6

0.4

0.2

0

m = I -f Max b2pO.5 Max no fibres

+ wr3.5mmb24.5

I I I I I I I

0 100 200 300 400 500 600 1

L88 3 15 0.2 1 0.75 I

I 20 0.5 = Figures 87 and 88 show that the influence of beam depth on the peak moment depends significantly on the U-w relationship. The Re,3 value was calculated for the o-w relationship assumed in Figure B1 by analysing a beam with the same loading arrangement and geometry as used in the Japanese beam test. The hinge was assumed to form a t mid-span. The corresponding Re,3 value was 0.75. Figures B7 and 88 show that the influence of size effects on the residual moment of resistance after cracking reduces with increasing crack width. This suggests that size effects arise since the design flexural resistance is defined typically as an average flexural resistance up to a prescribed crack width.

8.2.3 Size effects in RlLEM a-E method

The stress block used in the RILEM U--E design method is shown in Figure B9.The design ultimate moment is the least corresponding to either a maximum crack width of 3.5mm or an extreme fibre strain of 25%. In practice, the 3.5mm crack width usually governs for section depths greater than 150mm. The stress block used in the RILEM U--E design method can be simplified as shown in Figure 6.5 with litt le error. Figures 87 and B8 suggest that size effects are likely to be most significant at CMOD of 0.5mm (corresponding to f R , )

and least significant at CMOD of 3.5mm (corresponding to fR4). The origin of the size effect in the RILEM U--E method (which is almost equal to k,,=I.O - 0.6(h - 12.5)/47.5 for all CMOD where h is in cm) appears to be related to the definition of u2, which is defined in terms of fR, as illustrated in Figure BIO. The background to the size effect is given in Section 3.1.1 of the RlLEM guideline, which states:

~~

Appendix B - Design I

Figure B9 RILEM a-r design method.

I factors. A comparison of the predictions of the design method and of the experimental results of structural elements of various sizes revealed a severe overestimation of the carrying capacity by the design method. In order to compensate this effect, size dependent safety factors have been introduced. It should be noted that the origin of this apparent size effect is not yet fully understood.”

tb E2

1

Ec[%O]

3[

2.0A7+ . E3

I

I E

o1 = 0.7 fctm,fe (1.6 -d) (d in m) 02 = 0.45 fR1 kh 03 = 0.37 fR4 kh E, = 9500 ( f c tm)”3

kh : size factor

(N/mm2) =ol /E, (N/mm2) (N/mm2) = 25 %o (N/mm2)

e2 = E, + 0.1 %

h [cm] - 12.5 kh = 1.0 - 0.6 I 12.5 s h 460 [cm] I 47.5

I 0.2 - I

I I

I I I I I 1 I . 10 20 30 40 50 60 70

h [cml

1 I I t t I I I I I I 1

E % I I I I 4 , I I 1

I I I I 25 0 -2.0 -3.5

91

Figure B10 Stress Mocks used in derivation of RlLEM 0-a

method.

OSh,

OSh,

bh' Ml = YfR.1 Mz= b 0.66h, 0.5h, Of7

M 7 = y f R . 4 bh2 M2=b0.9hq OSh, Of4

B.2.4 Size effects in TR 34 A size effect is incorporated in both design methods given in TR 34 since the design strength is assumed to be proportional to the flexural strength given by Equation 12. TR 34 defines the design moment of resistance as an average moment of resistance related to Re,, in Equation A5a. Figures 87 and B8 suggest that it is conservative to apply the size factor for plain concrete to the equivalent flexural strength fctkeq300 derived in the Japanese beam test.

92

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