An experimental study of the validity of the round panel test method for shotcrete

DEGREE PROJECT IN

CIVIL ENGINEERING AND URBAN MANAGEMENT STOCKHOLM, SWEDEN 2018

An experimental study of the validity of the round panel test method for shotcrete

NADIA EL ZAIN

An experimental study of the validity of the round panel test method for shotcrete

NADIA EL ZAIN

Master Thesis in Concrete Structures June 2018

TRITA-ABE-MBT-18381

Abstract

Shotcrete (sprayed concrete) was used for the first time in 1914 and has become of growing importance in stabilizing the excavated tunnel sections over the past century. Even though the technology develops, there are some difficult tasks such as the design of a bolt anchored tunnel lining made of shotcrete. A proven and established design method does not exist today;

instead the design of tunnel linings are based on trial and error or experience from similar projects. One method used today, to determine the actual structural behavior of fiber reinforced shotcrete, is the standard beam test method. Previous studies have shown that the beam method gives scattered results since the testing volume are relatively small and the fibers might be unevenly distributed.

In 1998, an alternative to determine the actual structural behavior of reinforced shotcrete was proposed, based on using round determinate panels. In 2004 this method became a part of the American Society for Testing and Materials, ASTM, standards. The method has the potential of becoming a major, reliable test procedure that better reproduce the behavior of reinforced shotcrete in situ, compared to test beams.

An experimental test series was performed to compare the different testing methods in terms of data variability and validity, in the laboratory of Vattenfall in Älvkarleby. The experiment was performed on 30 specimens in total, with five different concrete recipes. The difference in the recipe was the fiber and cement content. The round panels are designed according to ASTM C-1550 and the beams according to SS-EN14488-3. The results from the experiment is here presented and evaluated, and also including the data variability and validity for the proposed method. The two basic testing methods of using beams and round panels are investigated, compared and evaluated, and their advantages and disadvantages discussed.

Keywords: Shotcrete, sprayed concrete, yield line theory, tunnel lining, steel fibers, round determinate panels, test beams

Sammanfattning

Sprutbetong användes första gången år 1914 och har under det gångna århundradet blivit allt viktigare för att stabilisera utsprängda tunnelsektioner. Trots att tekniken utvecklas finns det svårigheter med att exempelvis utforma bultförankrade tunnelbeklädnader av sprutbetong. En beprövad och etablerad metod att konstruera sprutbetongbeklädnad existerar inte idag. Istället används erfarenhetsåterföring från tidigare projekt och/eller experimentella försök. En testmetod som används idag för att återskapa beteendet hos sprutbetong är balkförsök.

Tidigare studier har däremot visat att resultaten från försöken oftast har stor spridning vilket kan bero på att brottytorna är små areor där fibrerna kan vara ojämnt fördelade vilket påverkar resultaten.

År 1998 föreslogs en alternativ metod för att fastställa de mekaniska egenskaperna hos sprutbetong, baserat på användning av runda plattor. År 2004 blev denna metod en del av the American Society for Testing and Materials, ASTM, standarder. Metoden har potential att bli en viktigt och tillförlitligt testmetod som mer realistiskt efterliknar beteendet hos fiberarmerad sprutbetong jämfört med balkprovning.

En experimentell försöksserie har genomförts hos Vattenfall i Älvkarleby, för att jämföra de två metoderna med avseende på mätosäkerhet. Försöksserien är på totalt 30 prover, där fem olika betongrecept använts. Cementmängden och fiberhalten varierade mellan de olika recepten. De runda plattorna är utförda enligt ASTM C-1550 och balkarna enligt SS- EN14488-3. Resultaten från försöken har redovisats och utvärderats, och en mätosäkerhersanalys presenteras för metoden ASTM C-1550. Korrelationen mellan resultaten från de två metoderna är beräknad och varianskoefficienten presenteras. För- och nackdelar mellan båda testmetoderna diskuteras.

Nyckelord: Sprutbetong, tunnelbeklädnad, runda plattor, fiberarmerad sprutbetong, böjdraghållfasthet, mätosäkerhet, balkar

Preface

The research presented is written for the Department of Civil and Architectural Engineering at KTH Royal Institute of Technology. The work has been performed in collaboration with Vattenfall Research and Development in Älvkarleby during the spring term 2018.

I would like to thank my supervisor Prof. Anders Ansell for his support, advice and guidance throughout this work, Holger Ecke for his useful advice, Per-Erik Thorsell for his help during the laboratory experiments, Peter Skärberg and Patric Strand for their help to execute the experiment.

Stockholm, June 2018 Nadia El zain

Table of Contents

1 INTRODUCTION ... 1

1.1 Background ... 2

1.2 Aims and goals ... 3

1.3 Limitations ... 3

1.4 Outline ... 3

2 SHOTCRETE ... 5

2.1 Additives and accelerators ... 6

2.2 Fiber reinforced shotcrete ... 8

2.3 Application of shotcrete ... 11

2.4 Shotcrete use ... 14

2.5 Flexural strength ... 16

2.5.1 Yield line theory for beams ... 17

2.5.2 Yield line theory for round panels ... 19

2.5.3 Previous studies ... 22

3 BEAM METHODS ... 25

3.1 Method according to ASTM C1018 ... 25

3.2 Swedish Concrete Association Method ... 27

3.3 Method according to SS-EN-14651 ... 28

3.4 Method according to SS-EN14488-3 ... 29

4 ROUND PANEL METHOD ... 31

4.1 Experimental method validation ... 31

4.2 Method according to ASTM C-1550 ... 33

5 EXPERIMENTAL INVESTIGATIONS ... 35

5.1 Test series ... 35

5.2 Concrete mixing and casting ... 37

5.3 Set-up for beam test ... 40

5.4 Set up for round-panel testing ... 42

5.5 Data variability and validity for ASTM C1550 ... 45

6 RESULTS ... 49

6.1 Round panels ... 49

6.2 Beams ... 51

6.3 Comparison ... 52

6.4 Data variability and validity for ASTM C1550 ... 55

7 DISCUSSION AND CONCLUSIONS ... 59

7.1 Experimental results ... 59

7.2 Yield line theory ... 60

7.3 The data variability and validity of the round determinate panel test ... 61

7.4 Conclusions ... 61

7.5 Further research ... 62

BIBLIOGRAPHY ... 63

APPENDIX ... 67 A – EXPERIMENTAL RESULTS FROM THE BEAM TEST

B – EXPERIMENTAL RESULTS FROM THE ROUND PANEL TEST

1 Introduction

Shotcrete, also called sprayed concrete, was used for the first time in 1914 and has during the last century become increasingly important in stabilizing excavated tunnel sections over the past century (Höfler et al., 2011). It has replaced the traditional methods of lining tunnel profiles and today, tunneling without shotcrete is inconceivable. Shotcrete is today a new complete technology which can be defined with three components:

 Shotcrete as a material

 Shotcreting as a placing process

 Shotcrete as a construction material

The concrete mix design for shotcrete is determined based on specified parameters and the requirements of application. The technology has a huge potential for further innovation and a great future. Shotcrete has been permanently developed and improved since it was used for the first time (Höfler et al., 2011).

Even though the technology develops, there are some difficult tasks such as the design of a bolt anchored tunnel lining made of shotcrete. A proven and established design method does not exist today, instead the design of tunnel lining are based on trial and error or experience from similar projects. The reason for this is that the understanding of the mechanical properties of reinforced shotcrete and how the structure interacts with the rock when loaded is still limited

.

Figure 1.1 Shotcrete used for tunnel lining (Kooley, 2010)

1.1 Background

To obtain the flexural properties of shotcrete, beam tests are usually performed. There are different types of tests, depending on which standard is used. An experimental study performed by Minelli & Plizzari (2010) has shown that the standard beam testing method performed to obtain the properties of shotcrete gives scattered results. One reason can be the small cross-section of the beam (Minelli & Plizzari, 2011).

For structures, with a high degree of redundancy, fiber reinforced shotcrete with low volume fraction is more commonly accepted and suitable. If stress redistribution may occur, large fracture areas will appear, and the structural behavior will consequently be governed by the mean values of the material properties. However, structural tests of full scale slabs give remarkably lower scatter in the results compared to the beam tests due to the larger fracture area (Minelli & Plizzari, 2011).

By using test elements, where stress redistribution may occur, more realistic values for fiber reinforced shocrete will be obtained. One suggestion is to use square panels as described in EN 1488-4 (2014). However, square panels are simply supported along the edge which is not realistic because of the shrinkage effect. Shrinkage will cause deformation of the specimens.

Thus, the crack pattern is therefore hardly predictable and the use of constitutive laws for cracked concrete becomes difficult since the location for the supports are randomly distributed along the four edges. As a solution, a round determinate panel test method was proposed by the American Society for Testing and Materials, ASTM, in 2004 (Minelli &

Plizzari, 2011). The idea of the method was put forth by Bernard (1998) but at first, the method was only used in in Australia. The proposed method is based on a round panel supported on three pivots and exposed to a centric load, see Figure 1.2. The background to the method is further described in chapter 4.

1.2 Aims and goals

The aim for this project is to evaluate alternative testing methods to determine the material properties of fiber reinforced shotcrete, such as the flexural strength. Laboratory experiments are performed where the round determinate panels are tested and compared with the traditional beam method. The results from the two methods are evaluated and discussed. The goal is to see if the proposed method can give a better understanding of the design of reinforced shotcrete e.g. in tunnel linings. The yield line theory for the beams and round panels will be presented for a better understanding of the behavior of the specimens when subjected to loads. Since fibers are used in the mixture, the flexural strength is harder to calculate because of the unknown fiber distribution. Therefore, the theory and the equations behind it are presented for a better understanding of the presented methods and results.

1.3 Limitations

 To avoid errors because of irregular surfaces from spraying the shotcrete, the specimens in this experiment was cast, not sprayed.

 The theoretical values based of the yield line theory is not calculated for the specimens since the compressive strength is not measured.

 The data variability and validity analyses are based on the accuracy of the obtained peak loads from the experiments.

1.4 Outline

The content of this report is presented below to give an overview of the structure of this project.

Chapter 2, includes general theory and background

Chapter 3, contains description of the methods used for bending tests of beams

Chapter 4, contains background history and a brief description of the round panel method.

Chapter 5, describes the experimental procedures and the equipment used.

Chapter 6, presents the results from the experimental tests.

Chapter 7, give conclusions from this study, followed by suggestions for further work.

2 Shotcrete

Shotcrete is a cement-based type of concrete that often contains more cement, smaller aggregate fractions than normal, cast concrete. Today, shotcrete is often fiber reinforced.

Furthermore, shotcrete is usually mixed with accelerators when used for linings and shells.

The application is of course also different since shotcrete is sprayed onto a surface or into a mold, instead of poured in place. The history of shotcrete started in the early 20^th century.

Carl Akeley is seen to be the inventor of shotcrete from when in 1907 he presented the

“plastergun” that was used to paint walls, see Figure 2.1. The equipment forced dry plaster mix through a hose with the help of compressed air, towards a noozle. Here, a water spray was connected so that water could be added in the mix (Teichert, 2002). The method was patented in 1911 by the Cement Gun Company who changed the name of the equipment to

“Cement Gun” and the sprayed material to “Gunite”. The method has today different names, such as “sprayed concrete” and “shotcrete”. In the USA, “shotcrete” is defined as a mix where the size of aggregate is less than 10 mm. The first process of this invention was the dry mix method while the process of the wet mix method came in the 1950’s, but was first fully developed in the 1970’s. The processes for both methods are described in section 2.3 in this thesis.

In the beginning, shotcrete was mainly used for reinforcing concrete repair work. Compared to concrete, shotcrete has lower water/cement ratio, high density and low permeability in order to obtain low surface cracking and most importantly high final strength with rapid strength growth. Because of the characterized properties, shotcrete has become of great importance for the construction field, especially for the tunnel and underground industry.

Furthermore, shotcrete does not require formwork since it is sprayed directly onto the subsurface of the construction. Instead, the interaction between machine, concrete and the operator is important since the application requires technical skills. The angle of the nozzle and the velocity of the shotcrete also have a big impact on the material properties since it affect e.g. the fiber distribution (Lawrence, 1999).

Figure 2.1 - Shotcrete sprayed into a round mold (ASTM C1550, 2012)

2.1 Additives and accelerators

In the 2000’s, additives were introduced for the shotcrete mixture. The additives could accelerate the mixture, make it smoother, control air content, etc. (Neville & Brooks, 2010).

In other words, they can improve or change the properties of the shotcrete in a way that cannot be done through the mix of water, aggregate and cement only. Additives make the concrete a complex multi-material system and are added at a fraction of the binder or cement weight with an approximate range of 0.5-7.0%. The additives must be added when the cement is wet since they otherwise can react with the cement which can have a negative effect. The effect of different additives is presented in Table.2.1. Air reducer and water reducer additives are used in experiment in this thesis.

Table 2.1 - Additives and their different effects on properties of the shotcrete (Höfler et al., 2011)

When spraying shotcrete, accelerators are added to the mixture which make the shotcrete bond to the target surface. There are three different types of accelerators:

 Sodium silicate-based (“water-glass”) accelerators

 Aluminate based accelerators

 Alkali-free accelerators

The accelerators affect the strength of the shotcrete depending on what type and the amount of accelerator used. The first two types affect the pH value of the mixtures which has an impact on the strength and the handling of the shotcrete. The sodium-based accelerator give shotcrete a more solid consistency. However, the early strength of the shotcrete does not increase since the hydration of the cement is not affected. On the other hand, the aluminate-based accelerator

The disadvantage is that the strength of the shotcrete decreases somewhat over time and the accelerator also give the shotcrete a pH-value over 12 which can harm the eyes and skin of workers and equipment operators (Höfler et al., 2011). Figure 2.2 shows how the strength of the shotcrete is affected with accelerators added to the mixture.

Today, alkali-free accelerators are used more widely since they increase the strength of shotcrete rapidly without affecting the strength negatively over time and since the pH value does not excess 12. The alkali-free accelerators are often based on aluminum hydroxide or aluminum sulfate. Figure 2.3. illustrates the strength of shotcrete from day one to 28 days after casting. As shown, the strength of the shotcrete is not affected negatively when using alkali-free accelerators compared to with Aluminate Sodium silicate-based accelerators (Lukas et al. 1995).

Figure 2.2 - The development of the strength when Aluminate based accelerator is added in the mixture (Lukas et al. 1995)

Figure 2.3 – The development of the strength when Alkali free accelerator is added in the mixture (Lukas et al. 1995)

2.2 Fiber reinforced shotcrete

In 1874, Anders Berard obtained a patent for steel fibers concrete but this was not developed until the Second World War. To improve and make pavements more resistant against bombing, these were reinforced with fibers. Steel fibers has been used for over more than 50 years in Sweden, usually to reinforce tunnels constructed in hard and jointed rock. The most common shotcrete used is fiber reinforced shotcrete (FRS) (Holmgren & Silfwerbrand, 2017).

With steel fibers, welded wire mesh could be replaced as the mean to provide ductility and flexural strength to the shotcrete linings. Steel fibers are easier to use in shotcrete on rough or irregular excavation surfaces, which is difficult with wire mesh fastened by bolting. It is also faster to apply since the installation of the wire mesh is eliminated (Goodwill, 2011). The steel fibers increase the flexural strength, by delaying the crack growth, and prevents post- cracking when shrinkage and over-stressing occurs. Steel fibers also exhibit low creep which lead to stress relaxation with time (Neville & Brooks, 2010).

Figure 2.4 - Spraying shotcrete on welded wire mesh (Concrete institute of Australia, 2010)

Today, the development of varying types of materials, qualities and design has been improved for fiber reinforced concrete structures. The fibers can be of e.g. glass, polymer and carbon (Neville & Brooks, 2010). The dominating material used today, and the one used in shotcrete, is steel in different shapes and sizes. The fibers can be provided with different end anchors and cross sections, see Figure 2.5. Shotcrete often reach failure by pull-out of the fibers when subjected to a flexural test and the fibers with hooked ends will therefore have improved bond and are more effective (Goodwill, 2011).

Figure 2.5 - Different types of fibers (Holmgren & Silfwerbrand, 2017)

For practical reason, fibers with the length 𝑙_𝑓 = 35 to 60 mm and diameters 𝑑_𝑓 = 0.5 to 1 mm with bent ends is usually used. The fibers can also be categorized by a slenderness ratio 𝜆_𝑓 with the variation of 60 to 80. The slenderness ratio can be calculated by the equation;

𝜆_𝑓 = ^𝑙𝑓

𝑑𝑓 (2.1)

The fiber content is recommended to be expressed as a percentage by volume, the volume of fibers per m³. The amount of fibers in the concrete mix has to be chosen carefully since applying a large amount of fibers can lead to difficulties in pumping and spraying the shotcrete and applying a smaller amount will decrease the flexural (Holmgren &

Silfwerbrand, 2017). The frequently used amount of fibers is 40 – 60 kg/m³ (Sika, 2018a).

To determine the properties of fiber reinforced shotcrete, a beam test can be performed, see Figure 2.6. There are two possible different modes of action which occurs when the fibers concrete cracks after being subjected to loading. For strain softening, the fibers in the concrete must take up all the tensile forces. The load must decrease after the first cracks if the fibers cannot take the full tension, see Figure 2.8. This depends on if the amount of fibers is too small or too ineffective and as a consequence, there will be no additional cracks other than the first crack. The durability is only at risk if the structure is subjected to an environment where corrosion is possible, since the cracks widens at larger deflections. This behavior is common for shotcrete and is here illustrated in Figure 2.7 (Holmgren & Silfwerbrand, 2017).

For strain hardening, when the first crack appears, the fibers are not effective enough to take up the full tension force but still withstand a load increase after cracking. Additional cracks will therefore be developed and there will not be any durability risk for the structure, see

Figure 2.6 - Beam subjected to four-point loading (Holmgren, & Silfwerbrand, 2017)

Figure 2.7 – Common load/deflection curve for shotcrete (Holmgren & Silfwerbrand, 2017)

Figure 2.8 - Load-deflection curves for strain hardening and softening (Holmgren & Silfwerbrand, 2017)

The steel fibers used in shotcrete needs to meet the guidelines according to EN 14889-1 (2006). The guideline according to the standard divides steel fibers into five groups depending on the production method:

1. Cold-drawn wire 2. Cut sheet

3. Melted extracted

4. Shaved cold drawn wire

The tensile strength for the steel fibers is determined according to EN 10002-1. However, there are some exceptions in the regulation and therefore the guideline proposed according to EN 14889-1 (2006) should be followed.

The tensile strength for cold-drawn wire steel fibers should be determined, from the source wire, before deformation. The tensile strength for an individual fiber can only allowed to become 15 % lower than the declared tensile strength. Moreover, 95 % of the used fibers must meet the specified tolerance according to the standard.

The tensile strength for cut sheet steel fibers should be determined, from the source plate, before deformation. The tensile strength for an individual fiber can only be 15 % lower than the declared tensile strength. Moreover, 95 % of the used fibers must meet the specified tolerance according to the standard.

The melted extracted, shaved cold drawn and milled from blocks fibers has an irregular cross- section and the tensile strength must be determined with a testing machine. The length of the fibers must be at least 20 mm. Since the cross-section is irregular, the fibers will break at the minimum cross-section. The tensile strength is determined by distribute the maximal load through the cross-section. For these fibers, at least 90 % must fulfill the minimum tensile strength.

Another method to evaluate the effectiveness of fibers in concrete is by the method proposed in ASTM C1018 (1997). This is done by a third-point load beam test and where the residual and maximum flexural strength are determined from a load/deflection curve.

2.3 Application of shotcrete

The oldest process for application of shotcrete is the dry mix method. The dry ingredients, cement and aggregate, are blended in a machine before air pressure with high velocity is applied which pushes the mix through a hose. The water is added later at the work face through the nozzle and there the consistency of the shotcrete can be instantaneously adjustable. Generally, the water/cement ratio, wct, for shotcrete is around 0.4 (Lawrence, 1999). The use of shotcrete did not reach Sweden until after World War I. The dry mix method was presented in Sweden in the 1930’s and was used to reinforce concrete constructions such as railways for Statens Järnvägar (SJ). The use of the dry shotcrete mix method increased during the 1950’s and in the 1960’s a new technology to reinforce the mix with fibers was developed.

The dry mix method did have some problems in the beginning since the old machines could be blocked if the moisture content of the mixture was more than 3 %. However, the machines today are of rotor type where the dry mix is fed into an open hopper before revolving in a barrel and lastly compressed air is added through the nozzle, making the mixture to drive forward in order to be blended with water. The new machines have a capability to handle mixtures with moisture content up to 10 % (Lawrence, 1999). The dry mix method is usually used in tunneling, repair work, for swimming pools and new construction in housing. The advantage with the dry method is simpler transport of materials and that the equipment is of relative light weight. The disadvantage is that since the mixture is dry, the environment around can get dusty and the degree of rebound is also high (Neville & Brooks, 2010).

Figure 2.9 - The process of dry mix method (Goodfellow, 2011)

In the later introduced method, the wet mix method from the 1950’s, the dry mixture is blended with water prior to being pumped through the hose. The first equipment used for the wet mix method was called “True gun” (Lawrence, L. 1999). The mixture is well blended with air before being pumped with high air pressure through the nozzle. The wet mix can be applied in different ways, but it should be noted that for smaller operations such as repairs, pre-blended dry mixture in bags is preferred. The water/cement ratio for the wet mixture should usually be below 0.45. If the water/cement ratio is higher than 0.45, it can be reduced with plasticizers (Lawrence, L. 1999).

Additions can be made to the mixture, e.g. accelerating admixture can be added at the nozzle to stiffen the shotcrete quickly and to prevent the shotcrete from falling from the receiving surface (Holmgren, 2015). The benefit with the wet mix method is higher capacity and lower rebound. The mixture needs to be mixed during the time it is not sprayed, thus it requires another type of equipment which is heavier than the equipment used for the dry mix method.

The wet-mix method was fully introduced in Sweden in the 1970’s, initially used in construction of hydropower plants (Neville & Brooks, 2010).

Figure 2.11 - Process of wet mix method (Goodfellow, 2011)

To summarize, compared to the dry-mix procedure, the advantages of the wet mix method are;

 Lower rebound.

 Less dust wastes.

 Generally a higher output capacity can be achieved.

Furthermore, larger volumes of shotcrete can be placed on the receiving surface. In other words, the wet mix method is known to be faster, simpler and more economical for larger work compared to the dry-mix method and has gradually taking over the market. In Sweden and Norway, this method has been the most frequently used since the 1980’s. However, for smaller works and under special conditions such as in areas of difficult access, the dry mix method is still used (Swedberg, 2013).

2.4 Shotcrete use

Shotcrete linings in hard rock are sometimes unreinforced. The unreinforced shotcrete will have two different effects in tunnels. The mortar effect is used to fill up cracks in caves and to bind the rock mass together. Due to velocity of the projected shotcrete, the mix penetrates cracks and joints and act as a mortar. Since this effect is not yet proven, it is hard to determine to which degree it is effective (Holmgren, 2015). The sealing effect helps the rock to carry itself and by applying the shotcrete early, the risk of key stone falling is prevented. Even the risk for clay filled joints to be washed off or dried out decreases when the surface is sealed with shotcrete. Unlike with the mortar effect, the sealing effect is proven to exist through experiments, even though it is still difficult to quantify the effect (Holmgren, 2015).

Shotcrete has a wide use, for example;

 Stabilizations in tunnels and underground constructions

 Sealing works

 Concrete repairs

 Trenching and slope stabilizations

 Swimming pools

However, the most common areas are tunneling, mining and concrete repairs. Furthermore, shotcrete is used in all areas of tunnel construction where the load-bearing properties and stability of the substrate tunnel determines the construction method

.

Thus, the stresses will be distributed around the excavation face and section (Höfler et al., 2011).

Shotcrete can be used as temporary support or for the final lining in tunnels. When shotcrete is used for final linings, it is usually reinforced with steel fibers or wire mesh. Rock bolts are also used to hold up the load from the rocks in the tunnels. The thickness of shotcrete often varies between 50 – 500 mm, sprayed in one or several layers. Shotcrete is perfect for stabilization of excavations because of the application thickness, material formulation, early strength development, and the possibility to re-spray the shotcrete on the treated area. When using shotcrete as temporary support in tunnels, the shotcrete is used as structural support and should be designed to obtain the properties required for this. Since the technology has developed, shotcrete today in tunnel construction is sometimes designed with a waterproofing system. This waterproofing system can be built by e.g. having the surface coated by a polymer waterproofing membrane or by having a water drainage system built behind the tunnel shell, see Figure 2.12 (Goodfellow, 2009).

Figure 2.12 - Shotcrete applied in tunnel with a remotely-controlled machine (Höfler et al., 2011).

Figure 2.13 - Forming a swimming pool using shotcrete (Concrete institute of Australia, 2010)

As mentioned before, shotcrete is also used for constructing swimming pools, see Figure 2.13.

The shotcrete is sprayed on the excavated soil, which eliminates the cost for form and the pools can thus also be constructed with different advanced shapes. The advantage of using shotcrete is the elimination of the cost for the formwork is that it is watertight and economical (Concrete institute of Australia, 2010). Shotcrete is an effective method in civil engineering construction and in the mining industries since it is easily and rapidly applied and therefore is cost-effective. The process of placement is quicker, formwork is generally eliminated, and the placement and compaction are carried out as one operation.

2.5 Flexural strength

The strength of a specimens depends on the material used in the mixture. When a specimen is subjected to a load, the stress increases until the specimen cracks and the failure stress is reached. When the crack extends during the increasing load, elastic energy stored in the crack is released until failure is reached. The maximum tensile strength in the bottom of the specimen is the modulus of rupture. This value depends on the dimension of the specimens and can be obtained by a flexural test (Neville & Brooks, 2010). When the specimen is subjected to a flexural test under bending, tensile stresses will appear below of the neutral axis and compressive stresses above the axis, see Figures 2.14 and 2.15. The corresponding load obtained when failure is reached is used to calculate the flexural strength of the material. The cracks develop underneath the beam, which makes the specimens fail in tensile portion. Thus, the stress is equal to the tensile strength.

Figure 2.14 Tension and compression stress when subjected to a load (XYZTEC, 2018)

Figure 2.15 Beam subjected to a bending test

2.5.1 Yield line theory for beams

By performing a beam test the flexural failure of fiber reinforced shotcrete can be obtained.

The beam method is used to obtain the characterized mechanical properties of the concrete by peak load 𝐹_𝑚𝑎𝑥, first crack load 𝐹_{𝑓𝑙𝑐𝑟}, the associated crack deflection 𝛿_𝑐𝑟 and the residual flexural load 𝐹_𝑟𝑒𝑠. By calculating the residual flexural load, the flexural strength can be determined (Malmgren, 2007). As shown in the Figure 2.16, for a four-point loading test the moment for the beam can be expressed as:

𝑀 =^𝐹𝐿₆ (2.2)

where F is the load and L the length of the beam. The bending stress over the beam height is assumed to vary linearly, thus the flexural stress can be determined as:

𝜎 =_𝑏ℎ^𝐹𝐿₂ → 𝑓_𝑟𝑒𝑠 =^𝐹_𝑏ℎ^𝑟𝑒𝑠₂^𝐿 (2.3) where b is the width of the beam and h is the height of the cross-section. From the first crack load, 𝐹_{𝑓𝑙𝑐𝑟}, the crack strength can be obtained with:

𝑓_{𝑓𝑟𝑐𝑙} =^{𝐹𝑓𝑟𝑐𝑙}_𝑏ℎ2^𝐿 (2.4)

Figure 2.16 - Load-displacement curve from a typical beam test (Malmgren, 2007).

The load carrying capacity of a beam, the upper boundary load method can be used. The method is based on the yield line theory and used to minimize the risk of underestimation of the load carrying capacity by identifying of the lowest load which gives geometrically possible deformation pattern. Thus, the yield line theory is a design method on the safe side

by using safety factors

.

The yield line theory is based on the principle of virtual work and here it is assumed that the internal work ,𝑊_𝑖, is carried out within the beam, or slab, as a result of a virtual deformation, δ, and assumed to be equal to the work, 𝑊_𝛾, by external forces F, see Eq (2.5) and and Figure 2.17 (Nilsson et al., 2012).

Figure 2.17 - External work (Nilsson et al., 2012).

The external work is calculated as:

𝑊_𝛾= 𝑝𝛿𝑏 (2.5)

where 𝑝 is the external load, 𝛿 the virtual deformation and b the width of the beam b, as shown in Figure 2.17.

Figure 2.18 - Internal work (Nilsson, Olofsson, & Johansson, 2012)

The internal work is calculated with the equation above

𝑊_𝑖 = 2𝑚𝜃𝑏 = 4𝑚𝛿 (^𝑏_𝑎) (2.6) where 𝑚 is the moment capacity calculated per unit length, a the length of the beam and 𝜃 the angular deformation, as in Figure 2.18.

By looking at the stress-strain relationship for a material, it can be classified as ductile, brittle or quasi-brittle. When a brittle material reaches failure, the stress capacity decreases fast compared to for a ductile material that will reach a plastic zone where the material will strain under constant stress. When a quasi-brittle material reach failure, a gradual strain-behavior is shown after the maximum load is obtained. The most importing aspect for the design is the consideration of the nonlinear materials behavior at failure. Figure 2.19 show different types of stress-strain diagrams where the curves represents elastic-brittle material, elastic-quasi- brittle material and elastic-plastic material, where the latter is seen as the idealized stress- strain relation (Nilsson, 2000). One presumption, for a design based on the yield line theory, is that the material exhibits an idealized stress-strain behavior, as shown in Figure 2.18. To determine the ultimate load capacity for a shotcrete lining, a yield line analysis can then be performed.

Figure 2.19 - Stress-strain diagram for different type of materials

2.5.2 Yield line theory for round panels

For round panels supported at three points and subjected to a centric load (see chapter 4), a simplified yield line theory can be used, based on the following assumptions:

 The material is ideally plastic

 Ignore the friction

 Small angles (less than 10°)

The yield-line pattern for the round panels does only have one yield pattern and it occurs where the fiber dosage is between low and medium (Salo et al., 2013), see Figure 2.20 and 2.21.

Elastic-plastic material Elastic-brittle material Elastic-quasi-brittle material

Figure 2.20 The yield line theory for round panels (Martin et al., 2001).

Figure 2.21 - The yield line for round panels with a low to medium fiber dosage (Salo et al., 2013)

To calculate the virtual work of the round panels, the following equations are used.

𝑊_𝑖𝑛𝑡 = 3√3𝑚 (2.7)

𝑊_𝑒𝑥𝑡 = 𝐹𝛿 (2.8)

With these equations, the force can be calculated:

𝐹 = 3√3𝑚(^𝑅_𝑟) (2.9)

where R is the radius of the round panel, r the reactant radius and m is the cracking moment that can be calculated using the elastic theory:

𝑚

_𝑒𝑙

=

^{𝑓𝑡,𝑓𝑙ℎ}

2

(2.10)

where 𝑓_𝑡is the flexural tensile strength and h the thickness of the slab. For the plastic moment, the following equation can be used:

𝑚

_𝑝𝑙

=

^{𝑓𝑡,𝑓𝑙ℎ}

2

4 (2.11)

By using the equations from EN 1992-1-1 (2004), the flexural strength can be calculated by insertion of the compressive cylinder strength.

If

𝑓_𝑐𝑘 ≤ 50 𝑀𝑃𝑎 → 𝑓_𝑐𝑡𝑚 = 0,3𝑓_𝑐𝑘(²

3) (2.12)

or if

𝑓_𝑐𝑘 > 50 𝑀𝑃𝑎 → 𝑓_𝑐𝑡𝑚 = 2.12(1 +^{𝑓𝑐𝑘+8}

10 ) (2.13)

where 𝑓_𝑐𝑘 is characteristic compressive cylinder strength of concrete at 28 days in MPa. By using the following equation, the characteristic (with fractile = 5%) value can be obtained from the mean strength:

𝑓_{𝑐𝑡𝑘0,05}= 0,7𝑓_𝑐𝑡𝑚 (2.14)

The flexural tensile strength is given by:

𝑓_{𝑐𝑡𝑚,𝑓𝑙} = 𝑚𝑎𝑥 {(1.6 − ^ℎ

1000) 𝑓_𝑐𝑡𝑚; 𝑓_𝑐𝑡𝑚} (2.15) 𝑓𝑐𝑡𝑘,0.05,𝑓𝑙 = 𝑚𝑎𝑥 {1.6 − ^ℎ

1000)𝑓_{𝑐𝑡𝑘0.05}; 𝑓_{𝑐𝑡𝑘0.05} } (2.16)

The load-carrying capacity can also be expressed as a sum of moments, positive and negative, along the radial and tangential yield-lines. The positive radial yield-line is on the upper edge while the negative tangential yield-line is on the lower edge of the slab (Nilsson, 2000).

The relation is:

𝑃 = 2 ∙ 𝜋 ∙ (𝑚_𝑟+ 𝑚_𝑡)

∙

^tan(

𝜑 2) 𝜑

2

(2.17)

where P is the centric force subjected to the beam, 𝜑 the angle between the cracks, 𝑚_𝑟 the radial moment and 𝑚_𝑡 the tangential moment.

2.5.3 Previous studies

A study that contained an experimental part to obtain the strength of beams and round test panels is presented by Nilsson (2000). The variation between the test specimens were the amount of fibers. The obtained results show that the calculated values, obtained with the yield line theory, is much lower than the experimental results.

The results for a fiber content of 60 kg/m³ are presented in Figure 2.24, with results from round panel testing, and in Figure 2.25 from beam testing. Each graph compares results from the laboratory tests and calculations based on the yield line theory for the reference panels and beams. The results show a generally lower value for the calculated results compared to the experiment made. The explanation for this phenomenon is the dome action, which is the main load carrying mechanism for the specimens (Nilsson, 2000).

Figure 2.22 - Comparison between test result, for the round panels, and numerical solutions according to yield line theory based on reference and beam tests (Nilsson, 2000)

Figure 2.23 - Comparison between test result, for the beams, and numerical solutions according to

Another study that contained an experimental part to obtain the strength of beams and round test panels is presented by Oliveira et al. (2018). The residual strength for the beams and the energy absorption for the round panels was obtained and evaluated. The variation between the test specimens were the amount of fibers. The obtained results from the experiments showed that the coefficient of variation for the round panel test was lower than the obtain value from the beam test. The variance for the round panels was calculated to 10-11 % while the variations for the beams were calculated to approximate 15 %.

3 Beam methods

To determine the flexural strength of shotcrete, a beam test can be performed. The properties obtained are relevant for the structural design where the common structural element used is a slab. For fiber concrete, the ductility parameters according to a modified version ASTM C1018 (1984) has previously been used in Sweden (Holmgren & Silfwerbrand, 2017).

3.1 Method according to ASTM C1018

The main function of the fibers in the shotcrete is to provide ductility by keeping cracks together and increasing the deformation capacity. The most common test type is beam bending which is relatively easy to set up. The test is normally performed with a four-point loaded beam for which a load-deflection curve is recorded. In accordance with ASTM C1018 (1984), the loads are placed with a spacing of one third of the span, as shown in Figure 3.1.

The test is commonly performed 28 days after casting. While increasing the intensity of the load, the displacement are recorded (Holmgren & Silfwerbrand, 2017).

Figure 3.1 - Four-point loaded beam test (Holmgren & Silfwerbrand, 2017).

The method is independent of beam dimensions since the area under the load-deflection curve divided by the area up to crack is defined as the ductility index. To obtain the average strength of the beam, residual stress factors are needed. The ductility indices 𝐼₅, 𝐼₁₀, 𝐼50 and the residual strength factors 𝑅₅, 𝑅10,50 are determined from:

𝐼

₅

=

^{𝐴𝑟𝑒𝑎 0𝐴′𝐵′𝐵𝐴0}

𝐴𝑟𝑒𝑎 0𝐴^′𝐴0 (3.1)

𝐼

₁₀

=

^{𝐴𝑟𝑒𝑎 0𝐴}_{𝐴𝑟𝑒𝑎 0𝐴}^{′𝐵′𝐶′𝐶𝐵𝐴0}_′𝐴0 (3.2)

𝐼

₅₀

=

^{𝐴𝑟𝑒𝑎 0𝐴′𝐵′𝐶′𝐷′𝐷𝐶𝐵𝐴0}

𝐴𝑟𝑒𝑎 0𝐴^′𝐴0 (3.3)

𝑅_5,10 = 100 ∙^{𝐼10−𝐼5}

5 (3.4)

𝑅_10,50 = 100 ∙^𝐼50₄₀^−𝐼10 (3.5)

The shaded area in Figure 3.2 defines the area 0𝐴′𝐴0. The other areas expressed in Eqs. (3.2 – 3.5) are the areas limited by the curve 0𝐴′𝐵′𝐶′𝐷′ , without approximations. By giving all ductility indices values which are given by their subscript, i.e. so that for 𝐼₅ = 5 and 𝐼₂₀ = 20 the material can be seen as an ideal elastoplastic material, leading to that the residual strength factors become 100 %.

Figure 3.2 - Load/deflection curve to obtain (Holmgren & Silfwerbrand, 2017)

Furthermore, to indicate how much “superior” or “inferior” the fibers concrete is to an ideally elastoplastic material, the ductility index is used. By using a certain interval, the size of the fraction of the crack stress can be defined by the residual strength factors. The crack strength𝑓_{𝑓𝑙𝑐𝑟}, the residual strength 𝑓_{𝑓𝑙𝑟𝑒𝑠} and the failure strength 𝑓_𝑓𝑙𝑢 are calculated as:

𝑓

_{𝑓𝑙𝑐𝑟}

=

^𝐹_{𝑏 ∙ ℎ}^{𝑓𝑙𝑐𝑟 ∙ 𝑙}₂ (3.6)

𝑓

_𝑓𝑙𝑢

=

_𝑏∙ℎ^{𝐹𝑢∙𝑙}₂ (3.7)

𝑓

_{𝑓𝑙𝑟𝑒𝑠}

= 𝑓

_{𝑓𝑙𝑐𝑟}

∙

^𝑅5,10₂₀₀^+𝑅10,50 (3.8)

The maximum load 𝐹_{𝑓𝑙𝑐𝑟} and the crack load 𝐹_𝑓𝑙𝑢 are recorded when performing the test. To accept the results from testing, the cracks cannot lie 25 mm outside an area with a constant moment, thus the test must be rejected.

The elastic modulus can be calculated with the equation:

𝐸 =

²³

108

∙

_{𝛿^{{𝐹2−𝐹1}𝑙3}

2−𝛿₁}𝑏ℎ³ (3.9)

where 𝛿₂ and 𝛿₁ are the deflections at midpoint when

𝐹

₁

=

^{𝐹𝑐𝑙𝑟}₄ ^and

𝐹

₂

=

^{3𝐹𝑓𝑙𝑐𝑟}₄

.

3.2 Swedish Concrete Association Method

The previously used test method described by the Swedish Concrete Association (1997) is based on ASTM C1018 (1984) presented above. The difference between the standards are mainly:

1. The height of the beam shall still be ℎ = 75 mm. However, if the real member dimension differs from 75 mm, other height can be used if the ratio between span length l and height is still 𝑙/ℎ = 6

2. A detailed procedure is defined in order to improve the values on the mid-span deflection at cracking, 𝛿_𝑐𝑟, and crack load 𝐹_{𝑓𝑙𝑐𝑟}.

3. Residual strength factors 𝑅_10,𝑋 for any arbitrary ductility demand X are defined.

If the residual strength𝑓_{𝑓𝑙𝑟𝑒𝑠} is defined as:

𝑓_{𝑓𝑙𝑟𝑒𝑠} = 𝑓_{𝑓𝑙𝑐𝑟}∙^𝑅₁₀₀^10,𝑋 (3.10)

It can be proven that 𝑓_{𝑓𝑙𝑟𝑒𝑠} is the average flexural stress obtained at the beam test between the midspan deflections 5.5 𝛿_𝑐𝑟 and (𝑋 + 1) ∙ 𝛿_𝑐𝑟/2. However, this method is no longer practically used today.

3.3 Method according to SS-EN-14651

The standard according to SS-EN-14651 (2007) determines the flexural strength of concrete through use of the European notched fibers concrete beam. The dimension of the beam is given by a span to height ratio of l/h = 150/550, as shown in Figure 3.3, and is tested after 28 days with a three-point bending test.

By measuring the load value at a certain predefined crack mouth opening displacement (CMOD) over the notch, the residual strength value can be determined from the following:

𝑓

_𝑅,𝑖

= (

³

2

) ·

^{(𝐹𝑅,𝑖·𝑙)}

𝑏·ℎ_𝑠𝑝

;

i = 1,2,3,4 (3.11) where ℎ_𝑠𝑝 is the ligament height and set to ℎ_𝑠𝑝= 125 mm according to the standard. The values of CMOD used to determine the strength value 𝑓_𝑅,𝑖 is at CDOM equal to 0,5; 1,5; 2,5;

and 3,5 mm, as shown in Figure 3.4.

Figure 3.3 - Three-point load test performed on a notched beam (Holmgren & Silfwerbrand, 2017)

Figure 3.4 - Load/CDOM curve (Holmgren & Silfwerbrand, 2017).

The strength values determined from the test method SS-EN-14651 (2007) can be used to determine the strength values from the test method according to Swedish Concrete Association (1997) since there is a relationship between these two methods, given by:

𝑓

_𝑟,1

= (

^𝑅₁₀₀^10,20

) ∙ 𝑓

_{𝑓𝑐𝑙𝑟} (3.12)

3.4 Method according to SS-EN14488-3

The standard SS-EN14488-3 (2006) is for bending tests of fiber reinforced shotcrete and is a part of the Eurocode package. The tests carried out within the thesis will follow this standard.

The testing method were notched beams are used is usually not requested since the method has some uncertainty with the predicted crack that appears at the notch and is more time consuming. The shotcrete is sprayed in a prism shaped mold (“spray box”) before it will rest for 28 days. When the shotcrete has hardened, it will be sawn to three beams with dimension as in the modified ASTM C1018 (1984) before it will be subjected to a four-point bending test. The first residual flexural strengths are obtained by observing the load/deflection response from the deflection-controlled experiment. Overall, the residual strength 𝑓_𝑟𝑛 are determined in a simpler way than for the ASTM C1018 method:

 The smallest load from when the midpoint deflection of the beam is between 0,5 mm − 1,0 mm is used to determine 𝑓_𝑟1

 The smallest load from when the midpoint deflection of the beam is between 0,5 mm − 2,0 mm is used to determine 𝑓_𝑟2

 The smallest load from when the midpoint deflection of the beam is between 0,5 mm − 4,0 mm is used to determine 𝑓_𝑟3

The moment capacity can be obtained when the ductility has been determined from:

𝑚 = 𝑓_𝑟𝑛 ∙ ^𝑑₆² (3.13)

By using a four-point bending test, the bending moment between the load points is constant which makes the maximum stress occur in the span between the load points. The crack will therefore occur in this span.

4 Round panel method

An alternative method to test the flexural properties of fiber reinforced concrete and shotcrete has been developed by Bernard (1998). The method is based on round panels, supported on three symmetrically arranged pivots, and subjected to a central point load. The load is applied through a hemispherical-ended steel piston advanced at a prescribed rate of displacement. The machine records the development of the cracks due to the increasing force.

4.1 Experimental method validation

The experiment Bernard (1998) executed was a comparison of different specimens of round panels with different fixtures for determinate supports. The diameter of the specimens was set to 300, 600 and 850 mm. The diameter of the supports was set to 500, 800 and 980 mm to permit the specimens to be seated on the supports. The thickness of the panels differed as well, with an interval of 25, 50 and 75 mm. The specimens were tested on a displacement-controlled Instron 8506 Universal testing machine to failure (Bernard, 1998). The three different fixtures for the slab supports are described below.

Most of the round panels with determinate support failed with three radial cracks with an angle close to 120°, see Figure 4.1. After the first crack, the panels were rapidly unloaded, indicating that the energy absorptions produced is the highest and most consistent for the determinately supported specimens. The test panels failed in a flexural mode in every test and thus, tension occurred and shear stresses were less significant. Therefore, the determinate mode of support is attractive when the effect of shear is not wanted (Bernard, 1998).

Figure 4.1 – Determinate support test panel (Bernard, 1998)

The crack pattern for simply supported panels was less consistent compared to the determinately supported panels, see Figure 4.2. The simply supported restraint panels showed between 4 and 8 cracks, but the majority of the panels exhibited 5-6 cracks. For this case, the unloading took longer time than for the panels with determinate supports. Instead, greater residual load capacity is consequently given for a central displacement. Otherwise, the behavior of the simply supported panels is comparable to that of the determinately supported panels (Bernard, 1998).

Figure 4.2 – Simply supported test panel (Bernard, 1998)

The specimens with fully clamped edge failed with 10 to 18 fine radial cracks followed by punching through at the center, see Figure 4.3. The fully clamped and quasi-continuous edge is dominated by a shearing behavior which is not satisfying for investigation of flexural and membrane capacity in specimens of small to medium size. results in general showed failure of the panels in two distinctly different modes involving shear or flexural action. The shear dominated behavior led to a rapid drop in load carrying capacity and the total energy absorbing capacity decreased because of shearing within the panel. When shearing commenced, the residual load capacity dropped to zero. The two modes of supports are similar, and the only difference is the width of the clamped area surrounding the failed central region. These modes are undesirable since the performance variability increases when the test induces high shear stresses and sometimes a punching failure. Furthermore, the research has shown a strong influence from variation in thickness of the panels while the diameter has shown a minor influence on the performance (Bernard, 1998).

Figure 4.3 – Fully clamped edge test panel (Bernard, 1998)

The most important conclusion of these experiments is that the determinate mode of support, compared to the alternative methods, offer substantial experimental advantages such as consistent mode of failure. Furthermore, the total energy absorption and the peak load carrying capacity was lower compared to the alternative methods. The panels from the simply and determinate support all showed flexural modes of failure while shear behavior played a more significant role during failure for the fully clamped and quasi-continuous edge restraint panels. Therefore, for routine performance assessment, the determinate and simply support conditions are more suitable compared to the rigid modes of restrain. However, in terms of consistency of the failure pattern, the determinate support is preferred (Bernard, 1998). The use of this procedure presents several advantages over alternative methods for post-crack performance assessment for fiber reinforced concrete beam and panel specimens, including simplicity in specimen production and testing, low cost, and high reliability (Bernard 1999).

4.2 Method according to ASTM C-1550

The standard ASTM C-1550 (2012) describes a method for testing circular slabs to determine the flexural strength of shotcrete. The shotcrete will be sprayed in a circular mold with a diameter of 800 ± 10 mm and a thickness of 75 -5/+15 mm. The thickness of the panel represents the commonly used thickness lining in mines. The dimensions are important to maintain regardless of the size of aggregates or fiber length used in the mixture. It is important to have the surface of the specimen as smooth as possible which can be obtained by screeding the surface before the shotcrete has hardened (ASTM C1550, 2012).

The specimens should be hardened for 28 days before testing. The testing machine used for the testing has three supports with an angle of 120° between them. The circular slab will later be subjected to a centric point-load with a constant velocity of 4 mm/minute. The load and deflection will be registered continuously through the testing. Three main cracks will appear on the circular slab before reaching failure (ASTM C1550, 2012). By using three pivoted supports, the load distribution at the start of testing will be determinate. Since the tangential moment, between each of the supports, is higher along the radial bisector, the panel will almost always break into three segments when failure is reach. Occasionally, the panel can break in two segments. This happens when the rotation angle in the crack is higher than the given central displacement and is characterized by low energy absorption (Salo et al., 2013).

If this occurs, the test is failed (ASTM C1550, 2012). By measuring the energy absorption or the load capacity at the first crack and the selected central displacements, the performance of the panel can be determined. The central displacements are set to 5, 10, 20 and 40 mm (Morgan et al. 1999). The energy absorption can be obtained by integrating the area under the load/deflection curve (Salo et al., 2013).

5 Experimental investigations

This chapter gives a brief description of the experimental investigations carried out, including the test specimens, instrumentation and procedure. The experiments were performed at Vattenfalls research and development concrete laboratory in Älvkarleby. The main purpose with the experiment was to compare the two tests techniques, for beam and round determinate panels, in terms of data variability and validity. The experiment was performed on a total of 30 specimens based on five different concrete recipes. The bending tests performed on beams were according to SS-EN14488-3 (2006) and the round determinate panel tests to ASTM C- 1550 (2016). Since imperfections can occur when spraying, such as uneven surfaces and undistributed fibers, the specimens here are instead cast. The beams can be sawn if uneven surfaces occur, but since the round panels are not sawn the panel can be rejected for testing since the dimensions of the panels are important. If the round panels are sawn, the results may be affected since the fibers will be cut. Since the aim is to study the reliability of the new testing method, and not the effects from spraying, using cast instead of sprayed samples will minimize these errors.

5.1 Test series

The shotcrete mix design used for the experiments is close to a typical shotcrete recipe generally used in e.g. tunnels. Three different recipes were used with a variation in the amount of cement and steel fibers. The experiment was performed on 14 beams and 14 round panels, thus 28 specimens in total. The beams have the length 500 mm, the height 125 mm and a width of 75 mm. The round panels had a diameter of 800 mm and a thickness of 70 mm.

The additive Sika Viscocret EVO 36 (Sika, 2018b) and Sika Perfin-300 (Sika, 2018c) where used in the mixture to avoid air content and to make it smooth. The recipes of the shotcrete mix are given in Tables 5.1-5.2. Recipes was chosen according to Figure 5.1. By having this variation, the effect of the fibers and the cement can be studied and compared.

Table 5.1 - Shotcrete mixture for beams

Specimen Water

[kg/m³]

Cement [kg/m³]

Steel fibers [kg/m³]

Water cement ratio w/c

Aggregates [kg/m³] 0-8 mm 0-2 mm

Beam 1-3 246.75 525 40 0.44 1046.0 448.3

Beam 4-6 246.75 525 60 0.44 1046.0 448.3

Beam 7-9 223.25 475 40 0.47 1119.5 479.8

Beam 10-12 223.25 475 60 0.47 1119.5 479.8

Beam 13-15 220.00 500 50 0.44 1110.6 476.0

Table 5.2 Shotcrete mixture for round panels

Specimen Water

[kg/m³]

Cement [kg/m³]

Steel fibers [kg/m³]

Water cement ratio w/c

Aggregates [kg/m³] 0-8 mm 8-16 mm

Round panel 1-3 246.75 525 40 0.44 1046.0 448.3

Round panel 4-6 246.75 525 60 0.44 1046.0 448.3

Round panel 7-9 223.25 475 40 0.47 1119.5 479.8

Round panel 10-12 223.25 475 60 0.47 1119.5 479.8

Round panel 13-15 220.00 500 50 0.44 1110.6 476.0

Figure 5.1 The variation of the cement and fiber content 470

485 500 515 530

35 45 55 65

Cement content [kg/m3]

Fiber content [kg/m³]

5.2 Concrete mixing and casting

The blender used to mix the concrete is shown in Figure 5.2. The dry mixture was mixed for about one minute before water was added and then for further two minutes while the additives were added. After adding the fibers, the mixture was blended for about three more minutes.

Figure 5.2 Mixture blender at Vattenfall laboratory

An air gauge was used to measure the amount of air in the mixture, see Figure 5.3. The goal was to have an air content less than 5 %. A vibrator was used to blend the mixture in the molds.

Figure 5.3 Air gage at Vattenfall laboratory