Technical Manual

www.radmix.com

47

Index CONTENT PAgE # Introduction 3 World Leaders in Fibre Reinforcing 4 Structural Synthetic fibres 5 Fibre Reinforcement of Shotcrete 6 Product Range and Performance Characteristics 7- 15 Radmix Box Dowel 16 Concrete Fibre Composite Behaviour 17 Radmix Fibre Reinforced Concrete 18 Radmix Fibre Applications 26 Radmix Pavement Design 28 Precast 33 Shotcrete 34 Toppings 35 Bored Piers 37 References 38

Structural Synthetic Fibre - RAD 45S 5 Fibre Reinforcement of Shot-crete 6

Radmix Fibre Applications Radmix SFRC Applications � 1 Shot-crete � Toppings � 9

41

Fibres are playing a significant role as the reinforcing medium of choice for concrete construction. Fibre Reinforced Concrete (FRC) uses have now expanded beyond pavement applications, into areas where the reinforcing specification has historically been bars or fabric. With developments in fibre technology, FRC performance characteristics include significant ductile and structural behaviour and enhanced tensile, shear and flexural strengths.

Compared to conventional reinforced concrete, FRC exhibits greater crack resistance, durability, fatigue life, resistance to impact and gauging, shrinkage stresses, thermal shock and seismic ductility characteristics.

Comprehensive research into FRC has placed Radmix in a position as one of the world’s most efficient and technologically advanced steel and synthetic suppliers and manufacterers. Focusing on innovation and flexibility in the development of fibres, Radmix is able to provide the optimum fibre type for a variety of applications.

This technical manual is set out to educate and assist professional design consultants in the design and construction of structures using FRC.

With over �5 years of experience and training in construction technology, the engineers at Radmix continue to provide the most appropriate solution to concrete reinforcing.

Introduction

World leaders in fibre reinforcing Radmix International Pty Ltd combines comprehensive research into the latest reinforcing fibre technology from Australia, Europe, Korea, China and the USA with in-house development of fibre design and production technology. This investment has placed Radmix as one of the world’s most efficient and technologically advanced synthetic and steel fibre manufacturers.

As a result, new types of fibres for different applications have been produced from synthetic, wire and slit sheet. Radmix stands as one of the few companies, world wide, to provide a complete range of fibres and technical expertise at competitive prices.

Radmix’s philosophy of fibre design has at its core the focus of maximum user friendliness in all stages of construction, including construction technology effects and cost effectiveness. This focus compliments a “fracture mechanics” approach to ductility and crack propagation in SFRC in the recommendation of fibre specification for a particular end use. The Radmix computer-aided design program provides the interface with Consulting Engineers and also the Design and Construction Industry.

A commitment to, and investment in research has led the expertise developed by Radmix being sort after by engineers and construction companies around the globe.

Historical developments of fibres As the structural use of concrete developed in the second half of the 1800’s, interest was focused on reinforcements to enhance its low tensile capacity. The first patent for steel fibre reinforced concrete was filed in California by A. Bernard in 1874. A patent by H. Alfsen in France, 1918 was followed by G.C. Martin in California, 19�7 for SFRC pipes and H. Etheridge, 19�1 who examined the use of steel rings to address the anchorage of steel fibres.

The Second World War and later years saw G. Constantinesco taking patents out in England, 194� and USA, 1954. This was followed by numerous patents, but the widespread use was hindered by high costs, poor testing facilities and the parallel rapid development of concrete reinforced with steel bar and wire systems. It was not until the experiments by James Romualdi in 196� at the Carnegie Institute of Technology that a clearer understanding of the properties of SFRC emerged.

Fibre Reinforced Shotcrete has been a later extension of this understanding, with the first application being to stabilise the rock slope of a tunnel portal, Idaho in 197�. The development of SFRC continues and in more recent years extensive R&D has been focused heavily on structural synthetic fibres. Synthetic fibres now play a major roll in reinforcing throughout the world in areas such as tunnel lining, underground support, pre-cast and general concrete pavements. The development of structural synthetic fibres has revolutionised the use of fibres with increased performance over it's predesessor steel fibres. Extensive research and development throughout the world continues...

The macro structural synthetic fibre has been embraced and readily accepted in the construction industry as end users recognise the benefits of replacing reo-bar and mesh with synthetic fibre. Structural synthetic fibre is superior to more conventional reinforcement as it can outperform, give greater cost savings, is easier to use and safer to handle. Rad mix has uniquely packaged the RAD47s, RAD55s & RAD65s fibres in water soluble bio degradable materials. The entire packaging is placed in the concrete mix which dissolves within seconds, leaving the fibres to disperse evenly throughout the matrix. It has been demonstrated in the round determinate panel (RDP) tests, that by using structural synthetic fibres at a dosage rate of only 5kg to 9kg per cubic metre of concrete is required to obtain higher energy absorption compared to a steel fibre dose rates of 30kg to 50kg, for the application of structural concrete such as ground slabs, pre-cast and shotcrete.

The beam test show slabs on grade and pre-cast concrete predominately require a dosage rate of between 20kg to 45kg of steel fibres per cubic metre, in comparison, using between 3kg to 9kg of structural synthetic fibres per cubic metre of concrete. Synthetic fibres achieve greater strength and ductility in applications for pavements, roads pre-cast and overlays.

, pre-cast and overlays.

Structural Synthetic Fibre:

Fibre Reinforcement of Shotcrete Concrete is essentially a mixture of cement, blended sand and aggregate, water and various property-enhancing admixtures. Shotcrete can be considered both as a means of placing a concrete type of product and the product itself, which is equivalent to a concrete with aggregate up to 10mm in size, with a relatively high cement content and often with additional cementitious components, such as silica fume. Plastic Shotcrete commonly has low water:cement ratio, which accounts for high compressive strengths in the hardened state, but this can also lead to a brittle engineering material.

Reinforcement is added to shotcrete in order to give some pseudo-ductility as well as post-crack load-bearing capacity, especially in high deformation applications, such as those encountered in the mining industry. Welded wire mesh has been used to reinforce Shotcrete, but stiffness compatibility and placement difficulties has meant that a continuous metallic reinforcement has been dropped in favour of discreet fibres that cross incipient cracks to add toughness and ductility.

The round determinate panel test uses an 800mm diameter Shotcrete panel, 75mm thick that has three supports around the periphery of the panel. The panel is supported horizontally in a frame and loaded vertically from above. The load/deflection curves are developed as the specimen is loaded, up to first crack and beyond. Commonly , the centre point deflection is taken to 40mm, although when testing for a prototype where very high deformation might be expected, deflections of up to 100mm can be used. The resultant load/deflection curves in Joules can be used to compare different reinforcing elements compared to a non-reinforced control specimen at different ages, different deflections and different dosages, etc.

It appears that the addition of any fibre does little to enhance the first crack of a shotcrete matrix, but the fibres start to work as soon as the crack attempts to open. Fibres bridging the crack start to take load and resist flexural deformation giving added energy absorption capacity. Steel fibres provide beneficial efforts immediately after first crack but do not maintain their superiority as central deformation proceeds past about 5mm. The post-crack load- bearing capacity of macro synthetic structural fibres has been found to provide increasing benefit over steel fibres with further increasing benefit as the Shotcrete matrix ages.

Many studies and construction projects from the 1980’s to the end of the �0th century focused on the use of steel macro fibres to reinforce shotcrete. Geometric variables such as aspect ratio, fibre cross-section shape, as well as the characteristics of steel stock used to form the fibre and the manufacturing process to shape the fibre were all evaluated in an attempt to refine and improve upon the engineering character of the hardened product. Trials using high performance, macro synthetic structural fibres started in �000, around the same time as the rock engineering industry was accepting the results of round determinate panel testing under what is now ASTM C1550- 04 “Standard Test Method for Flexural Toughness of Fibre Reinforced Concrete (Using Centrally Loaded Round Panel):. It was found that relatively low mass addition rates of the synthetic fibres outperformed the standard steel energy panels by up to 100%.

For deflection in the order of 40mm, most steel fibres have pulled out of the matrix and there is no further residual load-bearing capacity. On the contrary, macro synthetic structural fibres have been found to provide increasing levels of cumulative energy absorption to deflections of up to 100mm.

At “Shotcrete: More Engineering Development”, the second international conference on engineering development in shotcrete held in Cairns, Queensland, �004, papers were presented that showed cumulative energy absorption values of around 600 Joules for synthetic fibres at a deflection of 40mm and an age of 100 days, compared to around �00 Joules for steel fibres under identical conditions. Macro synthetic structural fibres have become the dominant reinforcement in shotcrete projects, especially where relatively large-scale deformations may be expected, such as in mining engineering environment.

1.0 Radmix Fibres

RADmIx RAD47s (STRuCTuRAL SYNTHETIC) FIBRE

uCT CODE PERFORmANCE CHARACTERISTICS

RAD47s Width = 1.2820 Thickness = 0.49333 Length = 47mm

Gives optimum performance in highly corrosive environments. Is ideally suited in ground slabs and pre-cast products.

PROFILE

RAD45S

RAD25CR

RAD35CR

RAD835UW

RAD1050UW

Product Range and Performance Characteristics

PRODUCT DESCRIPTION Macro Structural Synthetic Polypropylene Fibre, minimum tensile strength 550 MPa.

These fibres show very defined ductile behaviour characteristics.

Flexural Toughness and First-Crack Strength of Fiber-Reinforced Concrete REPORT CERTIFICATE - ASTM C 1018

1 of 1 CLIENT : Radmix International Pty Ltd WG JOB NO : 1212-70-1326 PROJECT : Radmix Fibre Trials LOCATION : Welshpool Sample Id : Concrete Beam, 180408 - 1 Lab No. : 180408 - 1 Casting Date: Date Tested : Age of Specimens: 30 Specimen Condition : Moulded Sample, Wet

Deflection Method : Third Point-Loading

Details of Specimens : Widths (b), (mm) : 101 Depths (d), (mm) : 105 Fibre Type : RAD 47 S Length (l), (mm) : 360 Beam Span, (mm) : 300 Dosage, (kg/m3) : 6 Specimen Dry Mass, gram: 8320

Flexural Toughness and First-Crack Strength

First Crack Load, (N) 12245 Maximum Load, (N) 16144 I5 - 4.3

First Crack Deflection, (mm) 0.036 Toughness Indices I10 - 8.4 First Crack Strength, (MPa) 3.33 I20 - 15.5

Flexural Tensile Strength, (MPa) 4.39 Residual Strength R5,10 - 82.3

R10,20 - 71.2 COMMENT: Equivalent Flexural Ratio Re,3 (%) : 79 (Note: Re,3 additional information is not a requirement of the test method.)

Certificate No. : 180408 - 1 Approved Signatory : ___________________________ ( T. Mansour ) Date : ______

Kalgoorlie Laboratory Port Hedland Laboratory Karratha Laboratory

Tel (08) 9091 4718 Tel (08) 9172 3135 Tel (08) 9144 0624

Fax (08) 9091 6682 Fax (08) 9172 3135 Fax (08) 9144 2904

18-Apr-08 18-May-08

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Load

(KN

)

LOAD DEFLECTION CURVE

Deflection, (mm)

Western Geotechnics Pty Ltd 36 Railway Parade WELSHPOOL WA 6106

(ABN 91 105 324 436) Tel 1300 781 744 Fax (08) 9458 3700 perth@westerngeo com au www westerngeo com au

QMS.Forms.Concrete.WG084.04.A

Product Range and Performance Characteristics

1.2 Radmix Fibres

RADmIx RAD55s (STRuCTuRAL SYNTHETIC) FIBRE

PRODuCT DESCRIPTION

Macro Structural Synthetic Polypropylene Fibre, minimum tensile strength 550 MPa. These fibres show very defined ductile behaviour characteristics.

PRODuCT CODE PERFORmANCE CHARACTERISTICS

RAD55s Width = 1.4820 Thickness = 0.4611 Length = 55mm

PROFILE

RAD45S

RAD25CR

RAD35CR

RAD835UW

RAD1050UW

Suitable for all types of concrete reinforcing

RAD55s is an all purpose fibre suited for most applications.

Product Range and Performance Characteristics

RADMIX RAD65s (STRUCTURAL SYNTHETIC) FIBRE

PRODUCT DESCRIPTION

Macro Structural Synthetic Polypropylene Fibre, minimum tensile strength 550 MPa. These fibres show very defined ductile behaviour characteristics. Performance levels are excellent in shotcrete.

PRODUCT CODE PERFORMANCE CHARACTERISTICS

RAD65s Width = 1.6825 Thickness = 0.4822 Length = 65mm

Generates a very high energy absorption rate when used in the concrete mix for shotcreting, enabling the matrix to provide greater flexural toughness.

PROFILE

RAD45S

RAD25CR

RAD35CR

RAD835UW

RAD1050UW

1.3 Radmix Fibres

Page 1 of 1

CLIENT : XXXcrete Australia Pty Ltd JOB No. : 08-01-584 PROJECT : Jetcrete (Radmix) Lab No. : 08-WG-3120 LOCATION : Raleigh Casting Date :

Sample Id : QA 05345 Date Tested :

Type of Fiber : Synthetic RADMIX 65mm Age at Testing :

Specimen Details : Condition of specimen: Excellent Average Diameter of Panel, mm : 795 Average Thickness of Panel , mm : 76 Standard Deviation of Thickness, mm : 1.3 Number or Radial Cracks : 3 Energy Absorption at the Following Central Deflection:

Direct Absorption

Energy Absorption at 5 mm Deflection, (Joules) = 89 Energy Absorption at 10 mm Deflection, (Joules) = 191 Energy Absorption at 20 mm Deflection, (Joules) = 377 Energy Absorption at 40 mm Deflection, (Joules) = 598 COMMENTS:

1. Sprayed sample supplied by client & delivered to the Laboratory on

2. Sample tested as received. 3. Laboratory Curing Conditions : Standard moist temperate zone (acc. To AS 1012.8.1 cl. 9.3)

Average Fibre Count / 200mm: 38 (Additional information - Not a requirement of the Test Method) Certificate No. : 08-WG-3120 / C400

Approved Signatory : _________________________________ ( J.Reid ) Date : _____________ SN 2411

373 593

36 Railway Parade Welshpool WA 6106 Phone 1300 781 744 Fax (08) 9458 3700

14/03/2008

13/03/08

Flexural Toughness of Fiber Reinforced Concrete - Round Panel

ASTM C 1550

88 188

10-Feb-08 13-Mar-08 32 Days

Corrected Absorption

LOAD - DEFLECTION CURVE

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35 40 Net Deflection (mm)

Lo

ad

(K

N)

0

100

200

300

400

500

600

700

800

En

erg

y A

bs

orp

tio

n,

(Jo

ule

s)

Failure Diagram

This document is issued in accordance with NATA’s accreditation requirements

Accreditation No. 2418

C400.RDP.cert.06.A

Product Range and Performance Characteristics 1.4 Radmix Fibres

RADmIx “FW” (FLATTENED WIRE) FIBRE DESCRIPTION

PRODuCT DESCRIPTION

Flattened hard-drawn wire fibres, conforming to the provisions of ASTM A8�0 Type 1 (Drawn Wire), minimum tensile strength 900 MPa.

Flattened Wire Fibres, due to the positive mechanical anchorage characteristics of the undulation and high tensile strength are specially suited to applications where the risk of stresses on the concrete exceeding its tensile strength is clearly defined. That is, post-crack performance (toughness) is excellent.

PRODuCT CODE PERFORmANCE CHARACTERISTICS

RAD40FW Diameter 0.9 x length 40mm; Aspect Ratio = 44.44 Excellent fibre for ground slabs and pre-cast. Other sizes available on order.

1.5 Radmix Fibres

PROFILE

RAD45S

RAD25CR

RAD35CR

RAD835UW

RAD1050UW

Product Range and Performance Characteristics

RADmIx “HW” (HOOKED

WIRE) FIBRE PRODuCT DESCRIPTION

Hooked end hard-drawn wire fibres, conforming to the provisions of ASTM A8�0 Type 1 (Drawn Wire).

1.6 Radmix Fibres

RAD45S

RAD25CR

RAD35CR

RAD835UW

RAD1050UW

PROFILE

RAD45S

RAD25CR

RAD35CR

RAD835UW

RAD1050UW

RAD45S

RAD25CR

RAD35CR

RAD835UW

RAD1050UW

Product Range and Performance Characteristics

PRODUCT CODE RAD6535HW

PERFORMANCE CHARACTERISTICS

Glued Hooked End Fibre, Diameter 0.5mm x length 37mm Aspect Ratio = 74 Tensile Strength = 1300 MPa. Ideal for shotcrete.

PROFILE

PRODUCT CODE RAD7535HW

PERFORMANCE CHARACTERISTICS

Diameter 0.75 x length 35mm Aspect Ratio = 46.6 Tensile Strength = 1100 MPa.

General purpose fibre also suited for shot-crete.

PROFILE

PRODUCT CODE RAD6560HW

PERFORMANCE CHARACTERISTICS

Glued Hooked End Fibre Diameter 0.9mm x length 60mm Aspect Ratio = 66.66 TTensile Strength; 1ensile Strength; 1100 MPa100 MPa Ideal for ground slabs, giving a high Re3 value.

PROFILE

PRODUCT CODE RAD8060HW

Glued Hooked End Fibre PERFORMANCE Diameter 0.75 x length 60mm CHARACTERISTICS Aspect Ratio = 80 TTensile Strength; 1ensile Strength; 1100 MPa100 MPa

Ideal for concrete slabs under constant loads.

PROFILE

PRODUCT CODE RADPAVE 35 . PERFORMANCE Diameter 0.85 x Length 30mm Aspect Ratio = 35CHARACTERISTICS Tensile Strength = 1100

Ideal for medium and heavy industrial pavements with large bay sizes and high post loading conditions.

PROFILE

RADmIx “uW” (uNDuLATED WIRE) FIBRE

PRODuCT DESCRIPTION

Undulated hard-drawn wire fibres, conforming to the provisions of ASTM A8�0 Type 1 (Drawn Wire), minimum tensile strength 1000 MPa.

1.7 Radmix Fibres

Available on order.

PRODuCT CODE PERFORmANCE CHARACTERISTICS

RAD835uW Diameter 0.8 x length �5mm aspect ratio = 4�.75

A robust fibre that suits most applications.

RAD1050uW Diameter 1.0 x length 50mm aspect ratio = 50

Ideal for medium and heavy industrial pavements with large bay sizes and high post loading conditions.

PROFILE

RAD45S

RAD25CR

RAD35CR

RAD835UW

RAD1050UW

PROFILE

RAD45S

RAD25CR

RAD35CR

RAD835UW

RAD1050UW

Product Range and Performance Characteristics

Radmix Box Dowel

Radmix has revolutionised the dowel joint with a simple and effective system that provides greater load transfer at control and construction joints in concrete slabs.

The Box Dowel provides a system (Ribflex) which while maintaining a level slab surface over joints, allows movement sideways plus back and forth when expansion and contraction occurs in the concrete.

Curling is a significant problem in concrete slabs. The Box Dowel helps in restraining slab curling by restricting vertical movement, thus maintaining a level slab.

The Radmix Box Dowel is a cost effective system allowing for a greater load transfer over slab joints. This gives the client a better system at a lower cost.Specifying a Box Dowel is specifying a dowel joint with the reassurance of exact dowel placement.

The Radmix Box Dowel is available in two sizes (16mm & �0mm) to compliment the load transfer at slab joints in pavements ranging from thinner (light duty) to thick (heavy duty) concrete slabs. Each Radmix Box Dowel system is supplied with one box and bars.

BENEFITS: • Greater load carrying capacity over slab joints• Ease of movement between slabs• Reduction of slab curling• Fast installation• Wider spacing between dowels• Cost saving

DOWEL TYPE 125 150 175 200 225 250 PlusBD16 650 650 550 450 �50 N/A

BD20 N/A N/A 600 600 450 400

SLAB THICKNESS (mm)

Box Dowel spacing for ground slabs

Installation

Step One:

Nail the Dowel Box on the inside of the formwork at a height that is central to the slab thickness.

Step Two:

The concrete is then poured between formwork, encasing the dowel boxes.

Step Three:

Formwork is then stripped, leaving the front of the Dowel Box exposed, ready for the insertion of the dowel bars.

Step Four:

Dowel bars are placed into the holes provided by the Dowel Box previously cast into the slab. Concrete is then poured for the new slab, incasing the protruding ends of the dowel bars.

Box Dowel

Formwork Formwork

Box Dowel

Dowel Bar Box Dowel

Concrete

Dowel Box

Concrete

Dowel Bar

RIBFLEX

Concrete

�. Concrete Fibre Composite Behaviour

2.1 Mechanism of concrete - fibre interaction

Plain concrete is a non-homogeneous mixture of cement, water, coarse aggregates, fine aggregates and admixtures. The hydration reaction between the cement and water results in a net shrinkage in the hardened cement paste. The function of the coarse aggregate is a duality of economically reducing the volume of the cement paste, and to provide a restraint mechanism against the autogenous (hydration) shrinkage.

Hsu, Slate, Sturman & Winter in their paper "Microcracking of Plain Concrete and the Shape of the Stress- Strain Curve" [Journal of the ACI Feb 196� pp�09] showed that there are incipient microcracks at the surface of the larger coarse aggregate particles. These cracks exist in a zero load condition.

As concrete is stressed due to various loading conditions, including fatigue, the microcracks are propagated along the faces of the aggregate and under appropriate conditions propagate through the concrete matrix to adjacent coarse aggregate particles. These cracks exist in a zero load condition.

As the matrix consists of cement paste and the finer aggregate, it is the matrix into which the steel fibres are mixed and are ‘randomly’ aligned, though modified by the relative positioning of the larger aggregate.

The matrix thus becomes a composite mixture, reinforced by the fibres. The fibres change the tensile stress level required for a crack to initiate through it, depending on the number and effectiveness of the fibres in the crack tip zone.

2.2 Advantages of fibres in concrete

As the crack tip progresses through the matrix, as discussed above, the width of the propagating crack increases. For fibres passing through and resisting the microcrack widening, the development of the required stress in the fibre is provided by both; • Surface bond effects between the cement paste and the fibre; and • Mechanical anchorage mechanisms due to fibre shape, which enhance the effect of surface bond or act as an alternative should stress levels in the matrix exceed the surface bond effects, which have been estimated to be in the order of 3 MPa. For straight fibres, the length of fibre required to provide sufficient surface area for bond to develop the tensile strength of the fibre results in fibre length being excessive, in terms of adversely affecting the plastic state properties of the concrete. This can result in undesirable ‘balling’ of fibres and / or difficulties in placing, compacting and finishing of the concrete.

Fibre manufacturers have addressed the challenges presented by straight fibres through providing various mechanical anchorages in the fibre shape. These can be classified into two distinct types: continuously deformed and end-anchored.

Continuously deformed fibres provide a defined mechanical anchorage mechanism close to the position of any propagating crack, leading to greater restraint and stress redistribution into the surrounding matrix. A number of fibre manufactures have elected to provide mechanical anchorage effects by the end anchorage technique through providing deformed ends.

These fibres, under the developing stress from the propagating microcrack, progressively loose surface bond dependant on the effectiveness of the end anchorage. They then bridge the developed crack over the length of the debonded fibre. The published literature by the purveyors of this type of fibre shows diagrams of the bridged crack with the stressed fibre.

2.2 Advantages of fibres in concrete (continued)

When the stress in the concrete exceeds this ‘balanced’ macro crack condition the end anchorage is lost and the deformed ends either slide through the void cast into the cement paste in a straightening mode, or alternatively slip by local crushing the matrix as the end pulls through. The purveyors of these end anchorage fibres define that this is a preferred failure mechanism. The fibre stress at which fibre pull-out occurs, relative to the tensile capacity of the fibre is not defined.

Radmix Pty Ltd has taken the philosophy that it is more appropriate to restrain the propagating crack and disperse the stress into the surrounding matrix by a combination of surface bond and closely spaced mechanical anchorages along the length of the continuously deformed fibre.

�.� Fracture Mechanics vs. Crack Management.

The approach by Radmix Pty Ltd to the dispersion of propagating cracks in the matrix as described above, leads to a fundamental differing of philosophy of SFRC behaviour relative to some other fibre purveyors. It is more appropriate to adopt the ‘fracture mechanics’ approach of the fibre matrix, acting as a composite material, being able to withstand higher tensile stresses before gross crack initiation, rather than one which relies on ‘bridged’ macro cracks (crack management).

This ‘crack management’ approach has as its basis that the developed stress in the unbonded fibre allows the concrete element to continue to take load at high deflection. This approach includes the consideration of the global performance in the constant deflection rate flexural beam or ‘toughness’ test up to �mm deflection over a 450mm span, irrespective of the formation of cracks which may be more than the durability limiting crack width of 0.1mm.

�. Properties of Radmix Fibre Reinforced Concrete

Radmix fibres provide concrete with exceptional material properties. Concrete is considered a brittle material primarily due to its low tensile strength and low tensile strain capacity prior to fracture. In many applications, poor tensile performance of the concrete is compensated for by the inclusion of steel reinforcing bars in the tensile zones of the concrete structure to carry tensile stresses. Concrete can be modified to perform in a more ductile manner by adding a random distribution of Radmix fibres in the concrete.

This results in a composite or two-phase system of brittle concrete and fibres to form an elastic-plastic system. The primary advantage of this system is the development of a pre-crack and post-crack load carrying capacity in concrete members rather than a catastrophic failure following the initiation of the first crack.

In the majority of pavements, shotcrete and pre-cast applications, stresses in the concrete are randomly distributed and influenced by the dynamic loading conditions. It is, therefore, almost impossible to determine a true stress pattern and place one or two layers of reinforcement at fixed locations while stresses vary from the top to the bottom of the element. Loading conditions such as cyclic loading, thermal shock, shear, impact and shrinkage develop random stress distributions in the concrete.

The random distribution of Radmix fibre reinforcement in the concrete ensures that the stress is redistributed throughout the concrete matrix. Micro-cracks that increase in size through normal stress development are subjected to a fibre barrier in all parts of the composite system. Thus small cracks are intercepted before propagating further into larger cracks that might impair the structure.

It should be understood however, that the design of the fibre is an important factor. Radmix fibres are a crucial factor to the success of the concrete structure’s design.

The capacity of Radmix fibres to uniformly transfer loads throughout a matrix is a representation of the ductility that can be achieved with SFRC compared to plain concrete. The brittleness of plain concrete is therefore eliminated.

Depending on the specification of the concrete and the dosage rate of Radmix fibres, the various physical properties of concrete may be modified by the following degree, as shown in Table �.1.

TABLE 3.1 PHYSICAL PROPERTIES mODIFIED BY RADmIx FIBRES.

PHYSICAL PROPERTY BENEFICIAL EFFECT

Modulus of Rupture 1 to � x plain concrete

Shear Strength 1.�5 to � x plain concrete

Torsional Strength 1.�5 to � x plain concrete

Impact Energy Absorption � to 15 x plain concrete

Fatigue Resistance 1.� to � x plain concrete

Cavitation & Erosion Resistance 1 to 1.4 x plain concrete

Restrained Shrinkage Cracks Reduced Crack Widths

Corrosion Resistance No Cathodic Corrosion Observed

The average values of concrete Compressive Strength ( F’c ) and Static Modulus of Elasticity ( Ec ) for different concretes with varying percentages of fibre are shown in Table �.�.

The compressive strength of plain concrete was for a characteristic strength of 48.5 MPa, whereas for the fibrous concrete with 0.5% and 1.0% by volume fibre contents, the compressive strength decreased slightly. For higher quantities of fibres (1.5% and �.0% by volume) there was an appreciable reduction in compressive strength.

The decrease in strength is due to the increase in yield with a consequent reduction in cement factor and an increase in water demand associated with increased wetted surface area of the added fibres. If optimum mix proportions are maintained the compressive strengths can be maintained.

It is also interesting to note the level of ductility produced during failure under compression induced stresses. A compression test cylinder, instead of exhibiting a characteristic brittle failure of plain concrete, yields and then progressively crushes. This ductility, which is seen graphically in the load deflection curve of toughness testing, can be induced at low volume addition levels of 0.�5% by volume or �0 kg/m�.

�.1 Compressive Strength and Static Modulus of Elasticity

TABLE 3.2 - COmPARISON OF SFRC PROPERTIES FOR INCREASINg FIBRE CONTENT

FIBRE CONTENT F’c Ec Pulse Velocity Fr

% of volume Dosage (MPa) (kPa) (m/s) (MPa) kg per cu. m

Plain Concrete 0 48.5 �4.55 4,46� 4.�7

0.5% 40 47.1 �4.41 4,4�6 5.�4

1.0% 80 41.9 ��.�0 4,�0� 5.65

1.5% 1�0 �8.8 �0.1� 4,195 7.�4

�.0% 160 �8.1 �1.0� 4,��1 7.7�

Legend: F’c -Characteristic Compressive Strength at �8 days Ec -Static Modulus of Elasticity at �8 days Fr -Modulus of Rupture [Static Flexural Strength] for controlled deflection rate at �8 days.

20

A more economic way to achieve high characteristic static flexural strength values is by improving the concrete mix design, typically by increasing the cement content or by lowering the water/cement ratio. The beneficial effect of fibres on static flexural strength is of a marginal improvement.

Increases in concrete Static Flexural Strength ‘Fr’ values are typically quite small at economic fibre dosage rates less than 1% by volume. Table �.� illustrates the dosages and the effect on Static Flexural Strength. To benefit from the use of fibres, it is necessary to take into account the strength after cracking, above the stress levels of elastic behaviour on the load-deflection graph and examine the ramifications of utilising the plastic or hinge forming behaviour. With redistribution of stresses, this is defined as the toughness of Radmix SFRC.

�.� Static Flexural Strength (Modulus of Rupture)

Table �.� - Static Flexural Strength and Compressive ratios.

Fibre Content Fr Fr+√F’c Ffc Ffc+√F’c % of volume

Dosage (mPa) (mPa) kg per cu. m 0.5% 40 5.34 9.38 5.17 9.08 1.0% 80 5.65 10.41 5.14 9.56 1.5% 1�0 7.34 14.19 6.07 11.73 �.0% 160 7.72 15.06 6.14 12.51

Legend: Fr - Modulus of rupture F’c- Characteristic Compressive strength Ffc- Flexural strength at first crack

A significant difference in the performance of concrete with and without Radmix Fibre is seen in the load deflection curves, first crack strengths and toughness indices. Load deflection curves are a standardised method of quantifying the energy a beam absorbs during its load induced flexural deflection. The area under the curve represents the energy absorbed by the beam and is often referred to as the toughness.

Toughness is calculated according to ASTM C1018 and JSCE4, using load deflection data taken from third point loading as applied to beams in the static flexural test. Deflection is measured at the mid-point using electronic dial gauges. The test is deflection controlled and a plot of both the elastic and plastic regions of failure recorded. The test rig is shown in Figure A, with a JSCE Japanese yoke.

Unlike plain concrete, Radmix fibre reinforced concrete does not fail in a brittle catastrophic manner at the formation of the first crack with a clearly identifiable maximum load. This ductile behaviour is illustrated in the load-deflection curve in figure B, reference ASTM C1019-97. Well before signs of significant material distress are visible, the load deflection curve becomes non-linear, and microscopic examination of the specimen reveals fine cracks. An increase in the fibre concentration correlates with a slight increase on the first crack strength. Compared to plain concrete, the reduction in the value of flexural rigidity with increased deflection is not as severe when using fibre reinforced concrete. In other words, the rate of degeneration of moment of inertia is slowed down as the fibres resist the propagation of crack growth.

3.3 Load Deflection Behaviour (Toughness)

FIg A. C-1018 TEST APPARATuS WITH JAPANESE YOKE

LOAD CELL

ACTuATOR

LVDT

Spherical Seating

Steel Beam

Specimen

6”6” 6” 6”

Steel Beam

Roller Seating

FIg B. ImPORTANT CHARACTERISTICS OF THE LOAD – DEFLECTION CuRVE

The toughness index, ‘I(x)’ determined by ASTM C1018 is a dimensionless parameter which defines or fingerprints the shape of the load-deflection curve. Indices have been defined on the basis of service levels, identified as multiples of the first crack deflection. This index is computed by dividing the total area under the load deflection curve (up to the given service level deflection) by the area under the same curve, (up to the first crack deflection).

Based on the ideal shape for a perfectly elastic material, the toughness index I5 is calculated for a deflection of � times the first crack deflection. Likewise, I10 and I�0 are the indices up to 5.5 and 15.5 times the first crack deflection respectively. The toughness index for plain concrete is equal to 1.0 because all the plain concrete beams fail immediately after first crack. The toughness indices for fibre concrete vary greatly depending on the type of fibre, aspect ratio, volume fraction and the distribution of fibres.

�.4 Toughness Indicies

TABLE 3.4 - TOugHNESS INDICES FOR 50mm CORRugATED STEEL FIBRE.

Fibre Content I5 I10 I30 I10 ÷ I5 I30 ÷ I10

% of volume Dosage kg per cu. m

Plain Concrete 0 1.0 1.0 1.0 1.0 1.0 0.5% 40 4.46 8.05 15.62 1.82 1.87 1.0% 80 4.83 8.22 16.03 1.70 1.95 1.5% 120 5.48 9.39 17.28 1.73 1.85 2.0% 160 5.37 9.59 21.62 1.78 2.14

Legend: Fr - Modulus of rupture

F’c- Characteristic Compressive strength

Ffc- Flexural strength at first crack

This can be expressed in many different forms, an example would be the endurance limit expressed as a percentage modulus of rupture of plain concrete. The endurance limit, EL, is defined as the maximum flexural fatigue stress at which a beam could with stand � million cycles of non-reversed fatigue loading, as a percentage of the modulus of rupture of plain concrete.

For beams reinforced with 0.5% and 1.0% by volume corrugated fibre there is an appreciable increase in the endurance limit expressed as a percentage of the Modulus Of Rupture of plain concrete. The endurance limit is 71% for the mix with a 0.5% by volume fibre concentration (Figure C) and is 86% for the mix with 1.0% by volume fibre content, whereas the endurance limit for plain concrete was 65%.

All beams which had withstood � million cycles were further tested for an additional � million cycles at the same load range as previously used. With the exception of one beam containing 1.0% by volume of steel fibre, all the beams withstood 4 million cycles without showing any signs of additional distress or cracking. In other words, when a beam is subjected to a stress lower than its fatigue stress, then the beam may never fail in fatigue.

This means Radmix fibres can be added to concrete in high fatigue components such as ground slabs, to give extended life or a reduced section thickness.

�.5 Fatigue / Endurance Limit

�50 750 1�50 1750 ��50 �750 ��50 �750 0 500 1000 1500 �000 �500 �000 �500 4000

1.0000.9500.9000.8500.8000.7500.7000.6500.6000.5500.500

FIg C. RATIO OF FATIguE STRESS TO FLExuRAL STRESS VS THE NumBER OF LOAD CYCLES

No Failure

Source: V.Ramakrishnan, Transportatiion Research Board, January ��-�6, 1989, Washington, D.C..

Number of Loads Cycles (in thousands)

ffmax/fr

101 10� 10� 104 105 106

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

Steel FiberReinforced Concrete

maximum Fatigue Stress

Static Cracking Stress

Number of Loads Cycles to Failure

Steel fibres

PCA AirportPavement Design Curve

FIg E. FATIguE STRESS VS. LOADINg CYCLES TO FAILuRE

FIg D. 50mm STEEL FIBRE FATIguE DESIgN DATA

�6 �4 4� 50 58 66 74 8� 90 98 106 114 1�0 1�6

.95

.90

.85

.80

.75

.70

.65

.60

Stre

ss R

atio

Quantity of 50mm Steel Fibre per cubic metre of concrete

When concrete is subjected to a drying environment, shrinkage occurs and can be followed by cracking. The extent of shrinkage depends on many factors. These include the properties of the concrete material, temperature and humidity of the environment, the age when concrete is subjected to the drying environment, and the size of the structure. If the concrete is restrained from shrinkage, tensile stresses that exceed the tensile strength of the concrete may develop and the concrete will crack. The addition of Radmix fibres has proven to considerably reduce the widths of cracks resulting from restrained shrinkage.

Tests have been conducted using a ring type specimen to simulate restrained shrinkage cracking (figure F). Concrete was cast around a steel mandrel and observations made as the sample shrank, crack widths and times were recorded. Using the specimen the effects of steel fibres 0.�5% to 1.5% by volume were studied to determine the fibres effect on restrained shrinkage cracks

�.6 Shrinkage Cracking

Source: Shrinkage Cracking of Fibre Reinforced Concrete, ACI Materials Journal, March-April, 1990.

FIg F. TEST SET uP TO mEASuRE CRACK WIDTH WITH mICROSCOPE

In figure G one can observe that a quantity of 0.�5% by volume ( �0 kg/m�) of steel fibres reduces the largest crack width in the specimen by over 70%. This concentration represents 0.15% cross-sectional area of steel and is most commonly specified to replace shrinkage wire mesh.

With Radmix SFRC, the fibres bridging the crack will provide resistance to crack widening, which will provide tensile stress to the un-cracked portion of the concrete. As a result, the measured strain values exhibit a reversal in trend as indicated in figure I, which plots the results for a specimen reinforced with 0.�5% steel fibres.

If these additional tensile stresses exceed the current concrete tensile strength, another crack may form. As the concentration of fibre is increased, the largest crack width the microscope can detect is dramatically reduced.

0

0.2

0.4

0.6

0.8

1.0

1.2

1.2 1.410.80.60.40.20.0

Aver

age

Cra

ck W

idth

(mm

)

Steel Fibre Volume (%)Source: Shrinkage Crack Width Vs. Steel Fibre Volume, ACI, Mar-Apr ‘90.

Theoretical Analysis Experimental Results

FIg g. AVERAgE CRACK WIDTH VS. STEEL FIBRE VOLumE (RESTRAINED SHRINKAgE)

Fibres have the ability, even at moderate addition levels, to improve punch and shear. Table is a summary of the results from punch and shear tests of flat plates measuring 150mm thick x � metres wide x � metres long, and subjected to centre point loading (Figure J). The tests have been done to compare punch and shear behaviour of plain, polypropylene, mill cut, � layers of welded wire mesh and high tensile deformed steel fibres.

It can be observed that the values of punch and shear are improved by the addition of relatively small quantities of fibres.

�.7 Punch and Shear

FIg K. COmPARATIVE SLAB TESTS

Plate1 Plate � Plate � Plate 4 Plate 5 Plate 6

100

80

60

40

�0

0

Load at First Crack & Failure

Load

in K

ips

No

Rei

nfor

cem

ent

8x8-

W4.

5 @

Top

8x8-

W6.

0 To

p &

Bot

tom

Mill

Cut

Fib

er

��#/

CY

�.0”

50#/

CY

�.0”

First Crack Ultimate Failure

FIg J. COmPARISON OF PERFORmANCE IN PuNCH AND SHEAR: PLATE TESTS — THAmES POLYTECHNIC, 1989.

Slab Load at First Crack Load at Failure Comments Reinforcement (kN) (kN)

No reinforcement 180 �00 Cracks through full depth and punching

� Layers of �80 �80 Cracks through full depth and punching WWM(�00x�00x7mm)

High Strength Deformed �80 �95 Cracks through full Steel Fibre depth (50mm long �0 kg/m�) and no visible punching

�.5 7.5 1�.5 17.5 ��.5 �7.5 ��.5 �7.5 0.0 5 10 15 �0 �5 �0 �5 40

0

-100

-�00

-�00

-400

-500

0.25 % Steel Fiber

Time (days)Stra

in M

easu

rem

ents

Frequency of measurements every �4 hours

FIg I. CRACK WIDTH DEVELOPmENT VS. TImE

�.6 Shrinkage Cracking (Continued)

The corrosion resistance of Radmix steel fibres are governed by the same factors that influence corrosion resistance of conventionally reinforced concrete. As long as the matrix maintains its alkalinity and remains un- cracked, deterioration is not likely to occur. Should the matrix protection be lost, the small cross section of the fibres means that even with complete conversion of the fibres to corrosion products, the development of disruptive stresses does not occur.

One of the major advantages of steel fibres over mesh or bar reinforcing in severe exposure environments is that it will not support classic galvanic corrosion cells which are often the cause of corrosion and deterioration in mesh and bar. The fibres being unique and discrete are protected by the alkaline matrix, so no mechanism for the propagation of corrosion activity exists. Hence Radmix steel fibres can be used to advantage in extremely aggressive environments.

�.8 Durability

The drop weight test (ACI Committee 5��) is a very simple test that can give a comparative example of the performance of steel fibres in concrete. Figure L shows the number of blows for first crack and full failure. The impact strength increased considerably with the increase in fibre content. Compared to plain concrete, the increase in impact strengths were significant, a 0.5% addition by volume increasing impact by 10 fold. The results illustrate that the addition of Radmix fibres significantly increase impact resistance. As there are few, if any fibres in the trowelled surface layer of a pavement, this can be worn away by abrasion and gouging before fibres can be of benefit. After the surface has been lost to abrasion the course aggregate will resist the abrasion, but the steel fibres assist in the stability of the large aggregate particles.

�.9 Impact Resistance

FIg L. ImPACT RESISTANCE

�.10 Impact Resistance

Gouging resistance can be significantly enhanced with the use of Radmix fibres. Typically a high dosage of fibres is recommended.

Figure M. shows the typical pull-out behaviour of a 50mm, high tensile deformed fibre similar to Radmix UW fibres. In general, the longer the steel fibre, the greater the contact area between the fibre-matrix interface and the higher resistance to pullout. As the resistance to pullout increases, the load capacity of the concrete increases.

High pullout strength can be achieved by using a high tensile steel fibre. Other performance criteria such as concrete workability must be also considered in fibre selection.

�.11 Pull-Out

FIg m. TYPICAL LOAD PuLL - OuT DISTANCE CuRVE WITH SLIPPINg FIBERS

(Crimped, High Tensile Wire)Average Tensile Strength = 1�41 MPa (180,000 PSi)

Load

(N) (

LBS)

0.5 1.5 �.5 �.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 0.0 1.0 �.0 �.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0

500(���4)

450

400(1779)

�50

�00(1��4)

�50

�00(890)

150

100(444)

50

0

Source: Single fiber pull out tests on steel fibers embedded in cement mortar by Yves-R La Palme, Louis-Paul Hebert

Pull Out Distance (mm)

Pulse velocity is given in Table �.�. The average pulse velocity shows very little variation. This indicates that the fibre content has little or no effect on the pulse velocity. This result indicates that the addition of Radmix fibres to concrete does not affect the elastic wave transmitting property of concrete.

�.1� Pulse Velocity

4. Radmix Fibre Applications General

Radmix is a primary and secondary reinforcing medium and is most suited to thin sections and plates where stresses are highly variable. These typically occur in pavement, shotcrete, bored piers and pre-cast elements. Other applications include its use in decking systems with toppings, refractory applications, seismic and explosive resistant structures, machinery bases, chemical containment, mine blocks and other suited areas.

4.1 Pavements

Fibres have been successfully used for pavement applications in many hundreds of thousands of square metres of concrete. It has been used as the primary reinforcement for commercial and industrial pavement projects such as, heavy duty workshop floors, heavy duty tiles, roads, roundabouts, airport runways, timber bridge and jetty overlays, boat and barge ramps, hardstand areas, bike paths, factory and warehouse floors.

The use of Radmix fibres reduces labour and material costs because it allows rapid site preparation and speedier concrete placement with the elimination of conventional reinforcing. All of these features combine to make Radmix SFRC more economical both during construction and over the life of the pavement.

4.� Shotcrete

Fibre reinforced shotcrete has now become an accepted method of ground control around the world. Major mining, infrastructure and capital works using shotcrete have a large component that is fibre reinforced.

Radmix fibre reinforced shotcrete offers the client a product which is easier and safer to apply, cost effective and superior in strength and toughness than conventional forms of reinforcing. Some key applications for Radmix reinforced shotcrete are embankment stabilisation tunnel and cavern linings, erosion control, dam and water course lining, pipeline coatings and architectural features.

Significant cost savings result from productivity improvements, as there are none of the delays commonly encountered by placing conventional mesh reinforcement. Other obvious benefits are the more efficient use of concrete as the shotcrete follows the natural surface contours of the ground, this results in a reduction of cross- section as steel cover is no longer an issue.

4.� Precast Products

With precast products, Radmix SFRC has a special place in thin walled products. There is no mesh to place, and often mesh can not be placed where it is required or it needs greater cover, which increases the section size.

SFRC is used in numerous precast products which range from drainage pits, TBM tunnel segment liners, grease arrestors, cattle troughs, mine blocks, septic and water tanks, tank baffles, tilt up wall panels, sound barriers, refractory castables, manhole covers, pontoons and junction pits just to name a few. The elimination of conventional reinforcing and in some cases the reduction in section thickness can contribute to significant productivity improvements, this together with reduced material volume can deliver significant cost savings. Radmix is approved for use under AS/NZS 1546.1: 1998 On site Domestic Waste Water Treatment Units.

4.4 Bored Compression Piers

Significant time and cost savings can be made by replacing the conventional shrinkage cage with Radmix fibres, significant projects in Europe, the Americas and Australia have been completed using this construction method.

4.5 Toppings & Decking Systems

Radmix fibre reinforcement can be used in toppings to replace conventional reinforcing which traditionally is used for shrinkage and thermal crack control. As fibres do not have a specific cover requirement it can be extremely cost and time effective in toppings for industrial and commercial projects. These savings are also a vailable for proprietary concrete and metal deck systems.

4.6 Refractory Applications

In high temperature applications steel fibres significantly reduces cracking caused by thermal shock. Thermal spalling is also reduced as the fibres improve matrix interlock in the concrete. Steel fibre reinforcing has significant applications in metalliferous manufacturing facilities.

4.7 Explosion Resistant Structures

Radmix can be used on its own or combined with other reinforcement to improve energy absorbing capabilities and spalling resistance. Typical applications are in security products such as safes and vaults. Certain military applications will also benefit from the properties of SFRC.

4.8 Chemical Containing Facilities

For this application, prevention of chemical attack will be concrete property dependent. Improving the quality of the concrete by the addition of Radmix fibres will protect against the likelihood of structural degradation caused by expansive corrosion from chemical attack at depth because of lack of crack control.

4.9 Mine Blocks

By comparison to non-fibrous concrete blocks, Radmix SFRC blocks offer significant advantages in load bearing and post failure toughness, catastrophic failure risk is significantly reduced with fibre reinforced mine blocks. 5.0 Pathways The use of Radmix SFRC in walkways, driveway cross-overs and hardstands allow for flexible design while providing maximum crack control.

5. Radmix Design Program 5.1 Pavements — Industrial, Commercial and Heavy Duty

Radmix Ltd. prides itself in its ability to be able to provide full support in regards to slab design for industrial, commercial and heavy duty applications. The procedures are based on established design methods and are derived from first principles, the material properties are those accepted by testing under world wide recognised standards.

The comprehensive method for pavement design is the Radmix Design Program. This allows for a rigorous analysis to be performed to optimise the design. Many different parameters can be analysed and the program allows for interaction to enable comparison of designs and optimisation of performance.

The Radmix Design Program is simple to use and very interactive. Design parameters are inbuilt but can also be modified or overridden to suit the particular circumstance. Should the Radmix Design Program™ not be suitable for the relevant analysis Radmix recommend the PCA Airport Program™. This is available directly from the PCA in America. The PCA Airport Program is an internationally respected and easily available program.

This information is based on knowledge and performance of the material, every precaution is taken in manufacture of the product and the responsibility is limited to the quality of supply, with no warranty in the field as there is no control over site conditions or execution of the work. For warranty of work please contact Radmix Pty Ltd. to assess your particular project.

5.� Computer Aided Design Methods

PAVEMENT THICKNESS DESIGN PARAMETERS The following parameters need to be considered in the determination of the pavement thickness requirements: MODULUS OF SUBGRADE REACTION (K)The Modulus of Subgrade Reaction (k) was devised by Westergaard as an empirical parameter to characterise the support provided to concrete pavements by the under lying foundation.

The ‘k’ figure must be quoted for all calculations. In the absence of performing the physical test there are many available references that provide correlations between typical soil tests, such as CBR and a relevant ‘k’ value.Concrete Properties.

CONCRETE PROPERTIES The Design Flexural Strength, Modulus of Elasticity and Poisson’s Ratio are important factors that form the basis of the Radmix Design Programs. For the Radmix Design Program these properties are resident by default but can be overridden if desired. Please see Appendix 1. LOAD PARAMETERS — RADMIX DESIGN PROGRAM™ The following different load conditions can be modelled to give a thickness design for Radmix fibres:

• Uniform Distributed Loads • Wheel Loadings – Single and Dual Wheel • Point Loads • Line Loads • Racking Loads

RADMIX DESIGN PROGRAM™ The thickness design method is based on the work of Westergaard, developed by Chandler and by Chandler and Neal. This theoretical analysis, simplified, assumes that the slab acts as a homogenous, isotropic, elastic solid in equilibrium and that the reaction of the soil is vertical and proportional to the deflections of slab.

The stresses obtained from the characteristic loads, suitably factored by 1.5 to �.0, should not exceed the Modulus of Rupture of the concrete. Tests on ground supported slabs indicate that the use of Westergaard’s equations and their derivatives for thickness design will give very conservative results. Hence, a Eisenman modification is applied to bring the design back in line with observations of full scale plate tests performed by Beckett.

For a more sophisticated design, only relating to Racking Loads the Meyerhof Alternative is used. The Meyerhof Method is the most up-to-date approach and is fully accepted for particular racking loads. The Meyerhof Method relies on Yield Line Theory and fibre dosage must be significant enough to allow for a yield capacity to be developed by the Radmix fibre that is being used. This design method has been further developed by Losberg.

Meyerhof allowed a approximate moment distribution in a steel fibre reinforced slab on a elastic subgrade due to a concentrated load. There is a fundamental change after the slab has passed into the plastic stage. In this plastic stage a yield capacity can be assigned and by using Meyerhof an appropriate design determined. Losberg found that the elastic properties of floors with a yield capacity are different to unreinforced floors.

5.� Computer Aided Design Methods (Continued)

5.� Westergaard Analysis Component

UNIFORM LOADINGS The design of floor slabs for warehouses and pavements must consider the interaction between the slab and foundation. When a floor slab is being designed to support a uniformly loaded area on either side of open aisles the slab can be treated as a beam on an elastic foundation. It is assumed that the uniform loading extends a considerable distance and that the slab is supported by a suitable foundation material whose Modulus of Subgrade Reaction is known or can be estimated. The critical quantities affecting the design of the aisles areas are the Flexural Stresses at the top of the slab caused by the negative moment, and the Uplift Pressure that may tend to separate the slab from the subgrade.

The maximum negative moment occurs at the centre of the aisle when there is no joint in the slab, except at the column ties. This moment can be computed by the following equation:

Where: q = Live Load �a = Aisle Width

Where E = Young’s Modulus I = Moment of Inertia k = Modulus of Subgrade Reaction B = Width of "beam"(1 mm for analysis)If the ratio, b/a is larger than �, then part of the equation becomes insignificant. The maximum negative moment can then be expressed:

Where the aisle width is unknown, the calculation can be carried out for the critical aisle width, which will give the maximum negative moment for any given slab/subgrade system. The critical aisle width can be given by:

WHEEL AND POINT LOADS The tensile stresses in a ground supported slab for given applied loads may be computed using the Westergaard - Eisenman Equation as follows:

where: µ = Poisson’s ratio h = Depth of the slab q = Applied load E = Young’s Modulus b* = Dispersed radius of contact

5.� Westergaard Analysis Component (continued)

Although various methods may be used to determine edge and corner stresses in a slab, it has been found that the use of internal condition load factors, such as those recommended in the Concrete Society’s Technical Report �4, give extremely good correlation with Kelley’s modification of Westergaard, for example.

Tied joints and those maintaining fibre/aggregate interlock 00% Dowelled joints opening between 1-6mm ��% Free edges and other joints having no load transfer 85%

The Radmix Design Program™ uses this approach for simplicity, whilst offering the user the flexibility to choose the type of joint system during the evaluation process.

When designing for racking systems, if possible, effort should be made to provide a joint layout that will allow the critical load to be maintained in the internal position. If this can not be achieved, an appropriate analysis should be carried out according to the joint type. Warning – although it may be possible to keep centre legs of the back to back rack system in an internal position, a single outer leg placed over a free edge may prove to be the critical load.

For forklift trucks and other wheeled traffic, the analysis should be carried out with due regard to the joint layout. For instance a slab constructed using large bay method of construction with regular grid of saw induced joints, may be assumed to allow internal conditions to apply over the majority of the slab. However, there may be construction joints which being dowelled, will be the critical component. RADIUS OF CONTACT AREA For back to back racking systems, the critical load is that applied by the two centre-most legs. In accordance with the Concrete Society TR�4 recommendations, the combined load of both legs is taken over the combined area of both base plates and the gap in between. The equivalent radius of contact area may therefore be given as: B = √([A(B + Z)] / π)

Where: A = Width of base plate B = Length of base plate Z = Distance between centres of base plates

For more sophisticated analysis another input made modification can be made, the testing of Beckett showed this analysis to be extremely conservative and a modification can be input called ‘Mid-depth’ and ‘Full-depth’ dispersion, see Figure M. The base plates can be artificially enlarged in the program to give greater bearing area and it is quite acceptable to use ‘mid-depth dispersion’ in reasonable ground. For high loads on good ground ‘full-depth dispersion’ is acceptable.

noisrepsiD htped diM

balSbalS

Base Plat ffective Base Plate Base Plate 45º Degree Angle

FIg m.

htpedlluF noisrepsiD

e E

For wheel loads, the area loaded by a wheel is taken as the wheel load divided by the contact pressure. Contact pressure is assumed as 0.7N/mm� for pneumatic tyres, 1.�5N/mm� for cushion tyres, and 1.7N/mm� for solid wheels:

where: q = Wheel load pc = Tyre contact pressure

For dual wheel trucks, the combined load is taken over an equivalent radius of contact area of 1.7�h. Although several simplifications are made using the above procedure, including no account being taken for tangential stress influence from nearby loads, the resultant stresses computed compare very well with the more advanced methods of analysis, such as those employed by the PCA Airport ProgramTM.

LINE LOADSAs a quick check to determine if the given line load may be accommodated by given slab/sub-grade system, assuming the load to be "Knife edge", Winkler’s equation may be used:

Where:

k = Modulus of Subgrade Reaction P = Load over width b E = Young’s Modulus I = Moment of inertia = Distance from the load

WARPING STRESSFor external slabs which are subjected to significant temperature variations, warping stresses due to temperature gradients, warping should be taken into consideration. Theoretically, warping stresses for slabs longer than 8 times the radius of relative stiffness can be calculated. For the purpose of simplification the warping stress is assumed to be swarp = 5 kPa

5.4 Meyerhof Analysis Component of the Radmix Design Program Meyerhof offers a more refined design for back to back racking loads, this must only be used for pavements with no warping stresses (i.e. internal), fibre dosages of �5Kg/m� and greater with good sub-base conditions, as it relies on yield theory. No mid-depth dispersion is allowed.

Radius of relative stiffness of slab L is defined as:

Where: E = Modulus of Elasticity h = Slab thickness m = Poisson’s ratio k = Modulus of sub grade reaction

FLEXURAL CAPACITY

For flexure Meyerhof gives the following simple and conservative formulae for the collapse load of slabs under a single concentrated load.

Central Load P0 = 6(1 + 2a/L)M0

Edge Load P0 = 3.5(1 + 3a/L)M0

Corner Load P0 = 2(1 + 4a/L)M0

For a plain concrete slab, the value of M0 is taken as:

Where: P0 = Collapse load a = Contact radius load L = Radius of relative stiffness of the slab M0 = Limit moment of resistance of the slab b = Unit width of the slab h = Slab thickness fct = Flexural strength of concrete

The complete formulae for steel fibre reinforced concrete and details are outlined in Concrete Society TR�4. A typical print result for the Radmix Design Program is shown in Appendix 1.

5.5 PCA Airport — Concrete Thickness Design for Airport and Industrial Pavements Program The PCA Airport “Concrete thickness Design for Airport and Industrial Pavements" program is a competent, reliable and conservative program for use in design of Radmix SFRC slabs where the parameters exceed or are outside the analysis spectrum of Westergaard or Meyerhof.

5.4 Meyerhof Analysis (Continued)

7. Precast Radmix fibres have a special place in thin walled precast products. As there is no mesh to place, this resolves the challenge when mesh cannot be placed where it is required and as the mesh needs protection by the concrete cover, this usually increases the thickness.

Fibre reinforced concrete is used in numerous precast products which range from drainage pits, TBM tunnel segment liners, grease arrestors, cattle troughs, mine blocks, septic and water tanks, tank baffles, tilt up wall panels, sound barriers, refractory castables, pontoons and junction pits just to name a few.

The elimination of conventional reinforcing and in most cases the reduction in section thickness can contribute to significant productivity improvements, this together with the reduced material volume can provide significant cost savings. The reduced weight of a precast unit can be a factor in transport and related handling costs.

Reduced product damage and resultant wastage is a significant advantage when using Radmix fibres in a factory environment. Due to the three dimensional nature of the reinforcing, the Radmix fibres reinforce the edges and corners of precast products. Impact and demoulding damage in thus reduced.

Radmix fibre reinforced concrete has the advantage of being able to assist in the absorption of impact loads which frequently occur during on-site installation.

Radmix fibres are approved for use under AS/NZ 1546.1: 1998 “On-site Domestic Waste Water Treatment Units”. Many manufacturers are using the Radmix system as the standard allows for a reduction in the concrete thickness.

�7

6. ShotcreteOver recent years, the use of shotcrete for tunnel, rock and slope stabilisation has increased substantially. Its principal advantages are in the reduction in material use, greater speed, safety in application and lower costs.

The use of fibre as reinforcement has taken over from mesh. Fibres offers significant reduction in costs, saves time and is technically superior.

Radmix fibre reinforced shotcrete out perform mesh reinforced shotcrete with improved crack resistance, ductility, energy absorption and impact characteristics. Properly designed, Radmix Fibre Reinforced Shotcrete will reduce or eliminate cracking and allow for deformation with ductile stress redistribution.

TYPICAL APPLICATIONSFibre reinforced shotcrete (SFRS) has found typical applications in: • Tunnel developments • Tunnel final linings • Tunnel repairs • Slope stabilisation • Retaining walls and soil nailing • Cavern developments • Channel linings • Swimming pools

In these applications the Radmix SFRS has a structural requirement. The typically asked question is; “what is the comparison to wire mesh?” Comparative studies of load/deformation tests on large plates by Morgan and Mowat, and Little showed SFRS to be superior in residual load carrying capacity at small deformations after first crack and equivalent in performance at large deformations.

ADVANTAGES OF RADMIX FIBRE REINFORCED SHOTCRETE Radmix fibres allows shotcrete to follow the contours of the rock or ground, giving a consistent thickness, which provides a significant reduction in shotcrete consumption.

Elimination of the need to install mesh and the reduction in the time for which the lifting equipment is needed results in reduction of cycle times and overall costs.

Elimination of the difficult and dangerous job of installing mesh considerably increases safety on the work site.

PERFORMANCEAs Radmix Pty Ltd has a large range of fibres, different approaches for their use is important.

8. Toppings Bonded and Unbonded Fibre Reinforced Overlays Two types of overlays can be used to either increase the load capacity of an existing pavement or to provide improved surface finish, abrasion resistance or general rehabilitation. When the overlay is to be placed over a existing slab which is structurally sound and is relatively level, clean and undamaged, a bonded overlay should be considered.

In other circumstances and particularly where significant increases in slab load carrying capacity is required, a unbonded overlay should be used.

Bonded Overlays

The success of bonded overlays is dependent on achieving a good and uniform bond between the existing slab and the overlay. Careful control of construction procedures and high quality workmanship is required to ensure a satisfactory result. It should be noted that a risk does exist in achieving this method of construction and it should be assessed with this knowledge of this risk.

To provide bonding, the slab should be roughened by high pressure water cutting or milling and be in a clean, dust free condition (note that scabbling is a process which is not as effective as the other nominated surface preparations). Many proprietary epoxy bonding agents for wet to dry exist and applicators must follow suppliers recommendations.

The jointing pattern in the underlying slab needs to be reproduced to avoid reflective cracking. It is recommended that joints in the topping do not exceed 4 metre centres.

Curing of the slab is of utmost importance, if the slab is allowed to prematurely dry, shrinkage and curling will occur which can destroy the bond.

Bonded overlays can be up to 50mm thick, with a recommended aggregate size no more than 1/4 the slab thickness. The concrete mix should be designed for low shrinkage and with a relatively high fibre dosage

(recommended minimum �0 kg/m� for steel fibres and 6kg/m3 for structural synthetic fibres), dependant on other performance criteria for example impact.

The thickness design of bonded overlays is based on the difference between the required thickness for the particular loading application and the equivalent thickness of the existing slab.

The following empirical design procedure developed by the Corps Of Engineers as reported by Mellinger and related to the performance of fibre concrete by Parker

For bonded overlays: ho = hd – he

Where: ho = Thickness of overlay hd = Design thickness required for a single fibre slab on grade he = Existing equivalent thickness of slab

For:

hb = thickness of base slab Fb = Flexural strength of base F1 = Flexural strength of fibre concrete overlay mo = Poisson’s ratio of fibre concrete = 0.15 m1 = Poisson’s ratio of base slab concrete, normally = 0.15

Unbonded Overlays

Unbonded overlays are constructed in a similar fashion to conventional floors and pavements, bonding sould not occur to the existing slab. The existing slab should be level and any projections removed or depressions filled. Unbonded toppings are typically required when the surface of the existing slab is contaminated, for example by oil and grease which prevent bond. The rule of thumb test is that if the surface is sprayed with water, beads of water should not be seen.

Debonding can be achieved through a membrane such as asphalt, crushed rock, or polythene sheeting.

Careful attention is required to have good compaction and curing, to prevent early shrinkage or curling.

Since there is no bond, there is no need to reproduce the existing joint pattern. The joint pattern is not recommended to exceed 4m centres for overlays less than 100mm thick. The minimum thickness recommended for unbonded toppings is 75 mm.

The thickness design for unbonded overlays takes into account the condition of the existing slab through the use of a Condition Factor, C, with recommended values as follows:

C = 1.00 where the existing slab is structurally sound C = 0.75 where the slab has minor cracks and the cracks are non working C = 0.50 Where the existing slab has extensive cracks and surface damage C = 0.�5 where the existing slab is badly cracked and shattered

For unbonded overlays: ho = √ { [hd � – (Che)� }

Where:

hd = Determined from appropriate design chart for assumed Modulus of Subgrade Reaction he = From bonded equation previously Toppings for Proprietary Suspended Floor Systems

Radmix fibres can be used as a substitute for shrinkage steel in compression components of proprietary decking systems.

9. Bored Piers Fibre Reinforced Compression Bored Piers

RADMIX™ FIBRE ALTERNATIVE Radmix range of fibres are a strong alternative for reinforcing bar for shrinkage steel in Compression Bored Piers. In addition, Radmix fibres can easily save time and money by replacement of the reinforcing cage.

Advantages

Time Saving: No on-site fabrication is required, no time wasted placing and positioning cages. Cost savings: Radmix fibres save money. Confidence: Radmix fibres are uniformly distributed in the concrete and there are none of the problems associated with accurately placing cages. Corrosion Performance: Radmix fibres have excellent corrosion performance, which gives peace of mind.

The following outline of the characteristics of Radmix fibres relating to compressively loaded Bored and Auger Flight Piers.

BENDING / FLEXURAL FORCES In the pre-crack initial stages of bending flexural forces, neither fibres nor steel bar have any effect on load capacity. However in the post cracking stage, fibres will allow progressive ductile failure as they bridge a crack and progressively withdraw. In a high moment area at the top of a pier or with eccentric loading, a cage can be included in the top 1m to 1.5m length of the pier.

DIRECT TENSION In direct tension, multi or single fibre tests have displayed a progressive withdrawal as a ductile failure occurs. The Radmix fibres mix homogeneously in the concrete such that across any failure plane, fibres will be present.

COMPRESSION Obviously load capacity will not exceed concrete strength. Radmix fibres do not increase compressive strength but they do provide ductile failure.

STEEL REPLACEMENT Radmix fibre is a replacement for conventional reinforcement and provides equivalent cross sectional steel area replacement.

CORROSION Extensive field trials in Australia and overseas has shown the superior performance of fibres in corrosive environments. The fibres are unique and discrete in the concrete mix, hence no corrosion can occur outside carbonated areas in the concrete.

RESEARCH AND DEVELOPMENT Work undertaken locally and overseas with Bored and Continuous Flight Piers show the ability of fibres in full scale testing. Please ask for technical report details.

ADVANTAGES A quick calculation from appendix � will show the cost savings available. The saving in time, reduced difficulty and peace of mind are the advantages of Radmix fibres.

10. ReferencesRadmix International Pty Ltd Technical Manual �006

“macro Structural Synthetic Fibres”, David Wood – Canada �004.

“State-of-the-Art Report on Fibre Reinforced Concrete” ACI Manual of Concrete Practice, ACI 544.IR – 96, ACI Committee 544, November 1996.

“measurement of Properties of Fibre Reinforced Concrete” ACI Manual of Concrete Practice, ACI 544.�R - 89, ACI Committee 544.

“guide for Specifying, Proportioning, mixing, Placing and Finishing Steel Fibre Reinforced Concrete” ACI Manual of Concrete Practice, ACI 544.�R - 9�, ACI Committee 544, May 199�.

“The mechanical Properties of Steel Fibre Reinforced Concrete” A Materials Symposium on Concretes for the 1990’s, Ohio State University, Columbus, Ohio. R.E. Smith, April 1994.

“Shotcrete for underground Support in mines - Engineering Principles” Shotcrete - Techniques, Procedures and Mining Applications, Kalgoorlie, Western Australia. D.F. Wood, October 1996.

“Fibre Reinforced Concrete: An Overview” Aberdeen’s World of Concrete ‘96, Seminar 19-�9, ‘Fibre Reinforced Concrete.’ R.F. Zollo, January 1996.

“Steel Fibre Reinforced Concrete and Shotcrete” Aberdeen’s World of Concrete ‘96, Seminar 19-�6, ‘Fibre Reinforced Concrete.’ P.C. Tatnall, January 1996.

“method of tests for Flexural Strength and Flexural Toughness of Fibre Reinforced Concrete” JCI-SF4, Japanese Concrete Institute.

“Standard Specification for Steel Fibres for Fibre Reinforced Concrete” ASTM A8�0 - 96, American Society for Testing and Materials, 1996.

“Standard Test method for Flexural Toughness and First Crack Strength of Fibre Reinforced Concrete” ASTM C1018 - 97 American Society for Testing and Materials, 1997.

“Steel Fibre Reinforced Piles at Horse mEsa Dam”, Concrete International, June 1995, Page ��, Z.K. Baysai Downey, 1995.

“Portland Cement Paste and Concrete” Technion - Israel Institute of Technology, Haifa, Israel, ISBN 0-���-�4��1-9, I.Soroka, 1979.

NOTE: There is a large body of references available on the subject of Fibre Reinforced Concrete. For example, the ACI Committee 554 “State of the Art Report ACI544.IR - 96 has some 157 references and the reader is referred to in this body of work.

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