Investigating material characteristics of EPS Geofoam with different laboratory methods

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TRABAJO FIN DE MASTER INVESTIGATING MATERIAL

CHARACTERISTICS OF EPS GEOFOAM WITH DIFFERENT LABORATORY METHODS

AUTOR: MARTÍNEZ MORENO, MARÍA ENCARNACIÓN TUTOR: ALHAMA MANTECA, IVÁN CO-TUTOR: VASLESTAD, JAN MÁSTER EN INGENIERÍA DE CAMINOS, CANALES Y PUERTOS ESCUELA DE INGENIERÍA DE CAMINOS, CANALES Y PUERTOS Y DE

INGENIERÍA DE MINAS UNIVERSIDAD POLITÉCNICA DE CARTAGENA

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ACKNOWLEDGEMENTS

First, I would like to thank Professors Jan Vaslestad and Iván Alhama for supervising this thesis as well as for introducing me in such an interesting topic as EPS; I feel extremely lucky to have been able to develop this project with them. I also feel very grateful to Professors Gonzalo García and José Luis Morales, whose help during the research in geotechnical and construction laboratories in Cartagena University has been essential.

I would also like to thank Calixto Muñoz and Juan Antonio for helping me while carrying out laboratory tests and preparing samples in Cartagena University.

I need to point out the help of Javier Sandoval, Ermias Mijena and Dag Løvstad, from Statens Vegvesen Region Øst, for achieving more knowledge of EPS Geofoam.

Jackon is also gratefully acknowledged for providing EPS samples and allowing the use of its laboratory in Gressvik, Fredrikstad. Especially I would like to thank Hege Karlsen for her help to carry out the tests there.

And last but not least, I feel extremely grateful to my family, especially my parents and brother, my friends and my boyfriend, for supporting me during this adventure, even when the moments were difficult. I could not have carried out this project without them.

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INDEX

1. INTRODUCTION AND AIM OF THE PROJECT ... 9

2. PROPERTIES AND APPLICATIONS OF GEOFOAM IN CIVIL ENGINEERING ... 15

2.1. Lightweight Fill ... 16

2.2. Load Reduction ... 17

2.3. Culverts ... 18

2.4. Energy Absorption ... 18

2.5. Lightweight Culvert Structure ... 19

2.6. Inclusion in Retain Structures ... 20

3. EPS PRODUCTION PROCESS ... 21

3.1. Pre-expansion... 22

3.2. Intermediate ageing... 22

3.3. Moulding ... 23

3.4. Cutting blocks ... 24

4. COMPRESSION TEST ... 27

4.1. Spanish compression test ... 27

4.1.1. Development of the compressive stress test ... 31

4.1.2. Compression Strength tests results ... 32

4.1.2.1. EPS 20 5% Deformation ... 32

4.1.2.2. EPS 20 10% Deformation ... 35

4.1.2.3. EPS 40 5 % Deformation ... 37

4.1.2.4. EPS 40 10% Deformation ... 39

4.1.3. Cycles Load- Unload ... 42

4.1.3.1. EPS 20 5 % Deformation ... 42

4.1.3.2. EPS 20 10% Deformation ... 45

4.1.3.3. EPS 40 5% Deformation ... 48

4.1.3.4. EPS 40 10% Deformation ... 51

4.2. Norwegian compression tests ... 53

4.2.1. Development of Compressive Test... 54

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4.2.1.1. EPS 20 JP 100 5% Deformation ... 55

4.2.1.2. EPS 20 JP 100 10% Deformation... 57

4.2.1.3. EPS 40 JP 300 5% Deformation ... 60

4.2.1.4. EPS 40 JP 300 10% Deformation... 62

4.3. Comparison Spanish and Norwegian EPS Geofoam ... 64

4.3.1. Spanish EPS tested in UPCT and Norwegian EPS tested in Jackon... 64

4.3.1.1. EPS 20 kg/m³ 5% Deformation ... 64

4.3.2. Spanish and Norwegian material tested in Statens Vegvesen (Norwegian Public Roads Administration) ... 67

5. BENDING TEST ... 79

5.1. Spanish bending test ... 79

5.1.1. Test Development ... 81

5.1.2. Test Results ... 83

5.2. Norwegian bending test ... 86

5.2.1. Test Results ... 87

5.3. Comparison of Results ... 90

6. TENSILE TEST... 91

6.1. Spanish tensile test... 91

6.1.1. Following ASTM D1623-03 Standard ... 91

6.1.1.1. Test Results ... 93

6.1.2. Following EN 1607 Standard ... 96

6.1.2.1. Test results ... 96

6.2. Norwegian tensile test ... 106

6.3. Comparison between Spanish and Norwegian Material (with different standards) ... 116

6.3.1. EPS Geofoam 20 kg/m³ ... 116

6.3.2. EPS Geofoam 40 kg/m3 ... 116

6.4. Comparison between Spanish and Norwegian Material (with the same standard) ... 116

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6.4.1. EPS Geofoam 20 kg/m³ ... 116

6.4.2. EPS Geofoam 40 kg/m³ ... 116

6.5. Comparison between Standards testing Spanish Material ... 116

6.5.1. EPS Geofoam 20 kg/m³ ... 116

6.5.2. EPS Geofoam 40 kg/m3 ... 117

7. OEDOMETER TEST ... 119

7.1. Samples ... 119

7.2. EPS 20 kg/m³ oedometer tests ... 124

7.2.1. EPS 20 kg/m³ 12 kPa+12 kPa+25 kPa+50 kPa (Sample 2) ... 124

7.2.2. EPS kg/m³ 20 50 kPa (Sample 6) ... 125

7.2.3. EPS 20 kg/m³ 25 kPa (Sample 7) ... 126

7.3. EPS 40 kg/m³oedometer tests ... 128

7.3.2. EPS 40 50 kPa (Sample 4) ... 129

8. DIRECT SHEAR TEST ... 133

8.1. EPS 20 kg/m³ ... 138

8.1.1. EPS 20 kg/m³ unconsolidated... 138

8.1.2. EPS 20 kg/m³ consolidated ... 139

8.2. EPS 40 kg/m³ ... 142

8.2.1. EPS 40 kg/m³ unconsolidated... 142

8.2.2. EPS 40 kg/m³ consolidated ... 143

8.3. Comparison of results ... 144

9. SHEAR TEST ... 147

9.1. Test Results ... 149

9.1.1. Test results EPS 20 kg/m³ JP 100 ... 150

9.1.2. Test Results EPS 40 kg/m³ JP 300 ... 158

9.2. Comparison of results ... 163

10. CONCLUSIONS... 165

10.1. Compression Tests ... 165

10.2. Bending Tests... 166

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10.3. Tensile Test ... 166

10.4. Oedometer tests ... 166

10.5. Direct shear tests ... 167

10.6. Shear tests ... 167

11. REFERENCES ... 169

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1. INTRODUCTION AND AIM OF THE PROJECT

EPS (the abbreviation for Expanded Polystyrene) is a lightweight material that was initially produced for insulation and packaging purposes. It can be produced in many shapes and densities. However, for civil engineering applications, EPS is used in blocks (called Geofoam blocks), and the most common density is 20 kg/m³, which would have a compression strength of 100 kPa.

Before Geofoam blocks were first used for construction purposes in Norway in 1972, research projects had been carried out, demonstrating that EPS boards could sustain the loads in roads and that its properties did not worsen as time went by.

When settlements of about 20 cm/year occurred in Flåm Bridge, in near Olso, Norway, replacing one metre of the embankment materials with two layers of EPS blocks of fifty centimetres of thickness was decided. This change made the embankment a hundred times lighter, as well as reduced the settlement. In Illustration 1.1, the approximate situation of Flåm Bridge is presented, while in Illustration 1.2, the aspect of this bridge before the application of EPS is shown. Illustration 1.3 shows the aspect of Flåm nowadays.

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Illustration 1.1. Situation of Flåm Bridge, Norway

Illustration 1.2. Picture of the settlement in Flåm Bridge (1972). Source: Statens Vegvesen

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Illustration 1.3. Picture of Flåm Bridge nowadays

Since that very first use of Geofoam blocks in civil engineering, it has become a general practice in many countries all around the world. Moreover, nowadays projects using EPS are known to have been carried out in: Argentina, Australia, Canada, China, Columbia, Czech Republic, Denmark, Finland, France, Germany, Greece, Ireland, Japan, Malaysia, Netherlands, Norway, The Philippines, Poland, Russia, Serbia, South Korea, Sweden, Taiwan, Thailand, Turkey, UK and US. These countries are presented in Illustration 1.4.

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Illustration 1.4. Countries where EPS projects have been carried out.

After this introduction, it can be said that the aim of this project is double:

- One the one hand, different laboratory tests have been carried out in order to obtain a deep knowledge of EPS characteristics, which is useful to create models of behaviour or to introduce parameters in structure or geotechnical computer programmes. Laboratory tests carried out for this project are compression, bending, tensile, oedometer, direct shear and shear. It is expected that the characteristics are different depending on the density of the samples. Therefore, two different densities are tested, 20 kg/m³, which has

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13 been studied in many other different researches, and 40 kg/m³, which would be the highest density that is commonly used.

- On the other hand, a comparison of Spanish and Norwegian EPS results is presented, as this project has been accomplished in both countries. This point of the project is interesting, as EPS is not known to have been used in Spain for civil engineering application yet.

Therefore, the results of the Spanish EPS tests are presented first, followed by the Norwegian tests results, and finally comparison is carried out in chapters from 4 until 9. Firstly, however, an explanation of the different uses of EPS in civil engineering and how it is manufactured is exposed in chapters 2 and 3, respectively.

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2. PROPERTIES AND APPLICATIONS OF GEOFOAM IN CIVIL ENGINEERING

As commented in the Introduction (chapter 1), the first application of EPS blocks in civil engineering took place in Norway, specifically in Flåm Bridge, near Oslo, in order to reduce the excessive settlements that were occurring (about twenty centimetres per year). For the purpose of stopping this soil movement, the embankment material was replaced with EPS blocks, so, as load applied on the ground was a hundred times lower than originally, this new fill could control settlements. In Illustration 2.1, placement of EPS in Flåm Bridge is presented.

Illustration 2.1. Picture of Flåm Bridge Works in 1972. Source: Statens Vegvesen

However, this first use, which could be classified as “Lightweight Fill”, is not the only current application of Geofoam blocks, but other uses have been developed, such as:

- Load Reduction - Culverts

- Energy Absorption

- Lightweight Culvert Structure - Inclusion in Retain Walls

Throughout this point, a small explanation of each of the applications will be presented.

Moreover, the reasons why EPS Geofoam has become so popular during the last forty years are the following:

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16 - It is an extremely light material, as the density of EPS is a hundred times lower

than the average for soils.

- Short construction periods are needed, land usage can be saved, not big amounts of soil have to be dug and the costs of maintenance and overall construction is very law.

- EPS presents good self-sustaining behaviour, as well as Poisson’s ration and a reduction of soil lateral pressure, so it is a suitable material for back fill.

- Its cushion properties have the ability of reducing impact and vibration effects.

- EPS presents good waterproof ability.

All these characteristics make EPS Geofoam a suitable material for different applications in civil engineering works. Nevertheless, it also presents some shortcomings which are necessary to be taken into account whenever planning to use EPS blocks:

- Untreated geofoam is a fire hazard, so if blocks are planned to stay in contact with atmosphere, whether during construction or use, special care is needed. It also may be convenient to order flame- retardant EPS.

- Vulnerable to petroleum solvents, as if geofoam comes in contact with a petroleum compounds, it will immediately turn into a glue-type substance, making it unable to support any load. For that reason, it is necessary to place a geomembrane, in order to protect geofoam from possible oil spills, and it is not suitable to use Geofoam where petroleum solvents are known to be present.

- Forces developed because of buoyancy can result in a dangerous uplift force.

Therefore, higher densities of EPS Geofoam can be considered in those civil engineering projects which present this problematic situation.

- Geofoam blocks should be treated to resist insect infestation. If it is not, insects such as ants can burrow into the EPS blocks, weakening the material.

These negative factors must be considered by civil project designers and managers before placing Geofoam blocks in works, so problems can be avoided or solved in the most efficient way.

2.1. Lightweight Fill

Geofoam blocks are mostly used as a lightweight fill material in road construction, although EPS has also been used in railroads, airfields and other construction projects.

As the weight of EPS in much lower that a common soil (while the mean soil density is around 20 kN/m³, i.e. 2000 kg/m³, Geofoam blocks have a density of 20 kg/m³), the ground underneath the fill has a lower load, which means that construction over soft

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17 soils can be carried out. In Illustration 2.2, an example of this application can be observed.

Illustration 2.2. Example of road section using EPS Geofoam blocks as light weight fill. Source: Geofoam.org

Another important advantage of Geofoam blocks is that one of the sides can be finished vertically, which means less land occupation and, therefore, lower cost for the general project. EPS blocks can also be used as a fill when widening roads, as differential settlements between the old and the new road structure will be avoided.

Also as a lightweight fill material, Geofoam may be also used as a compensating foundation for building as a way to reduce the load on compressible soils and settlements. It can also be useful as fill material for landscaping purpose or sounds barriers to protect the population who resides close to road from noise pollution.

2.2. Load Reduction

As a method to improve bearing capacity of soft soils and, therefore, reduce settlements, Geofoam blocks can be used, as its density is much lower than ordinary soils.

In this way, replacing the proper soil with EPS, the load applied on this soil will be reduced. It is important to keep in mind that the higher density EPS has the higher compression load it can bear, so EPS blocks with different densities may be used depending on the structural demands. However, these different densities and, therefore, weight load, will not be significant when transmitted to the ground, as the previous soil was much heavier.

Moreover, since Geofoam fills can be terminated vertically, low minimal horizontal forces are transmitted to those structures which are connected or next to the fill.

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18 2.3. Culverts

EPS blocks can also be used as a way to reduce soil stress on buried pipes or culverts. In order to protect these pipes, blocks of EPS are located above them, also buried, so a positive arching effect occurs instead of a negative one.

On the one hand, a negative arching effect happens when load of the column of soil above the pipe or culvert is applied on this one, which leads to project thicker pieces in order to resist these loads.

On the other hand, a positive arching effect can be accomplished by placing a compressible material, such as EPS blocks, which absorbs the load due to the column of soil above the structure, leading to a less loaded structure, and therefore thinner pieces.

Illustration 2.3 is a visual example of negative and positive arching.

Illustration 2.3. Negative and positive arching effect without and with EPS. Source: Staten Vegvesen.

2.4. Energy Absorption

In order to reduce the impact loads due to avalanche hazards in mountainous area, EPS is placed over avalanche sheds located on road sections with avalanche activities.

When rock boulders hit the structure, EPS blocks deform and absorb most of the dynamic energy, which leads to a reduction of the dynamic loads applied on the shed.

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19 This idea of absorbing dynamic energy can be used in other fields where protection of structures is needed. In Illustration 2.4 an example of this used can be observed.

Illustration 2.4. Example of EPS used for Energy Absorption. Source: 5^th Conference 5th International Conference on Geofoam Blocks in Construction Applications

2.5. Lightweight Culvert Structure

This application is a new use of EPS that has taken place is Netherlands. In these works, the arching principle is used to design a tunnel without settlements in EPS embankment without foundation. This is an alternative to the standard design with compacted soil around the pipe or culvert.

This option offers various advantages, such as lower building costs and construction time reduction.

In Illustration 2.5, a picture of the construction of this kind of application is shown.

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Illustration 2.5. Construction of corrugated Steel tunnel in EPS fill in Netherlands. Source: InfraDelft

2.6. Inclusion in Retain Structures

It is a very common use of Geofoam blocks to be placed between the retaining structure (i.e. walls or grade beams) and the earth that produces the force against this structure. This inclusion results in a reduction of pressure due to earth, whether static dynamic loads are considered.

As the pressure applied in these structures is lower because of the EPS inclusion, materials are optimised because sections needed are smaller. This means that money can be saved, which is one of the advantages of using EPS in this kind of works. Illustration 2.6 presents two sketches of the application of EPS as Inclusion material.

Illustration 2.6. Examples of EPS Inclusions. Source: The Compressible Inclusion Function of EPS Geofoam

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3. EPS PRODUCTION PROCESS

EPS is obtained by the polymerization of styrene and introduction of small amounts of a blowing agent such as pentane. Both products are hydrocarbons, which mean that EPS only consist of hydrogen and carbon. Illustration 3.1 explains the polymerization of EPS.

lllustration 3.1. EPS obtaining

EPS raw material is found in the market as small round beads or cylindrical pellets, as observed in Illustration 3.2. To get the expanded material, steam process is made. EPS foam has been produced during the last fifty years, and is commonly used for packaging, isolation and, lately, construction.

Illustration 3.2. Raw material and final EPS. Source: Alibaba.com

The production process has the following stage:

- Pre-expansion - Intermediate ageing - Moulding

- Cutting blocks

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22 It is also of high importance the time the polymerization reaction takes, as long times give long molecule chains, and therefore higher strength.

3.1. Pre-expansion

Beads of EPS are expanded at a temperature of about 100 ºC in the “pre- expander”. This high temperature softens beads and the blowing agent, so they expand up to fifty times. Final density depends on temperature and steaming time. An example of pre-expander machine is presented in Illustrations 3.3 and 3.4.

Illustration 3.3. Pre-expander machine. Source: china-epsmachine.com

Illustration 3.4. Example of pre-expander machine in Jackon Factory, Fredrikstad

3.2. Intermediate ageing

When they leave the pre-expander, beads cool down. Inside of the individual cells, a partial vacuum develops by condensation of residual blowing agent. The pressure is equalized by storing the beads to let air diffuse into cells. This is a very slow process.

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23 Beads are storage in silos for about 12 hours to stabilize and make them ready for the rest of the process. These silos are presented in Illustration 3.5.

Illustration 3.5. EPS Silos for intermediate storage. Source: Alibaba.com

3.3. Moulding

Beads are put into a mould made of metal. This mould is closed and steam passes through it. Vacuum is introduced before and after steaming. The residual blowing agent makes beads expand and turns them into a homogenous block. After a fast cooling, the block is removed from the mould and allowed to stabilize. In Illustration 3.6, an example of moulding machine can be observed, and the process of moulding is presented in Illustration 3.7.

Illustration 3.6. Example of moulding machine. Source: Alibaba.com

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Illustration 3.7. EPS moulding process

3.4. Cutting blocks

After some hours, the new blocks may be cut into the needed dimensions with hot wire cutting equipment, as the one presented in Illustration 3.8. Illustration 3.9 shows the final blocks.

Illustration 3.8. EPS cutting machine. Source: hsepsmachine.com

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Illustration 3.9. EPS once produced in Jackon factory, Fredrikstad

The blocks obtained with this process, however, cannot be used immediately after being produced. They can only be placed in works after at least three months, in order to develop all their compression strength.

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4. COMPRESSION TEST

Compressive stress test is the most used test to find out the characteristics of EPS nowadays. The reason of this is that EPS blocks used in different works, such as road embankments or slope stability, are mainly under compressive stress. Therefore, this test becomes a very useful tool when using EPS.

Moreover, because of the importance of this test, different European Standards have been developed in order to give EPS users a common point of view when studying its compression strength. These Standards are EN 826 “Determination of Compression Behaviour of Thermal Insulation Products” and EN 14933 “Thermal insulation and light weight fill products for civil engineering applications- Factory made products of expanded polystyrene (EPS)-Specification”.

On the one hand, the first Standard gives specific information to test EPS samples in order to obtain its compression strength for 10% deformation in the direction of the compressive load.

On the other hand, the second Standard is a compilation of the different standards that can be used in order to achieve more information of this material, and in its Annex B, different graphics to obtain the compression strength according to the density of the material are presented.

In this project, not only compression strength for 10% deformation has been measured, but also for 5% deformation, which gives valuable information too, as this is the test that the Norwegian Public Roads Administration carries out as a way to learn about EPS Geofoam blocks quality.

Furthermore, Spanish and Norwegian EPS blocks have been tested to study compression strength in this material according to their origin. This comparison is shown throughout this chapter.

4.1. Spanish compression test

In order to make a first approximation to cyclic loading, which is very important to understand the behaviour of the EPS (especially if the material is going to take part in road or train embankments) three cycles of load-unload have been carried out, as traffic can be considered a cyclic load. This kind of load is applied when studying Spanish EPS, as the Universal Test machine at “Laboratorio Experimental de Estructuras” (structure laboratory) in UPCT allows to program these cycles.

Tests have been carried out for both of the densities studied in this project, 20 kg/m³ and 40 kg/m³, and for each deformation percentage three samples have been tested, in order to compare results. The samples needed for these tests are cubes of 50 mm of side. The density is calculated with the following equation:

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= ∗ 10

where ρ is the density of the sample, in kg/m³ M is the mass of EPS sample, in g

V is the volume of EPS sample, mm³, and in this case takes a constant value of 50 mm*50 mm*50 mm= 125000 mm³

Therefore, real density of the samples must be measured, as the Annex B of EN 14933 contains both a graphic and an equation in which the average value of compression strength with 10% deformation is obtained from the density of the sample, shown in Illustrations 4.1 and 4.2 respectively.

Illustration 4.1. Graphic compressive stress at 10 % deformation. Source: EN 14933

Illustration 4.2. Regression for average compression strength at 10 % deformation. Source: EN 14933

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29 In order to achieve the needed results, “Micro Test” universal testing machine, which can be found in the Structure Laboratory in UPCT, is used. This machine is shown in Illustrations 4.3 and 4.4.

Illustration 4.3. Micro Test universal testing machine

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Illustration 4.4. Micro Test universal testing machine with a sample to be tested

As a mean to obtain accurate results, this machine is connected to a computer, with which tests can be programmed, as well as save the results and graphic them. In Illustrations 4.5 the programme to control the tests can be observed, while Illustration 4.6 is a sample of the graphic results.

Illustration 4.5. Programme to control the compression strength test

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Illustration 4.6. Example of force- displacement test

4.1.1. Development of the compressive stress test

In order to understand the group of tests that is carried out in point 4.1., the development of the programme that controls them is explained below.

First, it is important to point out that this test is controlled by displacement, i.e. the load cycle goes on until the percentage of deformation (or the equivalent displacement) is reached, while the unload cycle goes on until the displacement is null.

However, as the material may present a residuary deformation, even if the displacement is still changing, the force appears as a negative value, which informs us that the unload cycle is finished.

Another important point is how the change in load-unload happens. Once the searched deformation is reached, five seconds marches before the unload cycle starts.

While this short period of time goes by, the force applied on the sample decreases, getting lower compressive stress for the same sample deformation. The highest stress in this period of five seconds is taken into account as compression strength. This change of stress without changing deformation is marked with a red circle in Illustration 4.7.

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Illustration 4.7. Example of cycling load-unload test where the period of five seconds in marked

Finally, it is also significant to explain that the velocity of both of the cycles, load and unload, is 10% of the thick per minute, i.e. 5 mm per minute. This velocity is the one that appears in EN 826 “Determination of Compression Behaviour of Thermal Insulation Products”.

Nevertheless, in “The Influence of Strain Rate on the Stress-Strain Behavior of EPS Geofoam”, it is possible to observe that velocity gives different results for compressive stress (Negussey, 2018). Moreover, this article also shows that the faster this velocity, the higher compression strength applied for the same percentage of deformation. This means that using the deformation velocity set in the Standard is highly important when results from different projects are going to be compared.

In order to compare this results with the ones obtained from the Norwegian EPS, only the first load is studied, as the three cycles of load-unload could not be performed in the Norwegian laboratories (4.1.2). Once these values are presented, these three cycles of load-unload are studied for both compression strength and Young’s Modulus (4.1.3).

4.1.2. Compression Strength tests results 4.1.2.1. EPS 20 5% Deformation

For this test, no graphics or equations to estimate compression strength according to the density of the samples are presented in the Standards, as EN 14933 just contains this kind of information for 10% deformation. Therefore, for this point, just a study of the results has been carried out. Table 4.1 shows the densities of the samples.

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Table 4.1. Density of the samples EPS 20 5% deformation

Sample (5% deformation) EPS Block Weight (g) Density (kg/m3) Difference (%)

1 20 2.41 19.28 3.6

2 20 2.35 18.8 6

3 20 2.34 18.72 6.4

The results are shown in the Illustrations 4.8-4.10

Illustration 4.8. Results EPS 20 5% deformation. Sample 1

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According to the Illustrations 4.8-4.10, the three samples present a similar behaviour, although the compression strength of the sample 2 is significantly lower than the other two.

An example of this set of tests is presented in Illustration 4.11.

Illustration 4.11. Sample 3 EPS 20 5% deformation while carrying out the test

In addition, the maximum compression strength of each sample is presented in Table 4.2.

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Table 4.2. Maximum compression strength 5% deformation

EPS 20 5%

Sample Compression Strength (kPa)

1 71

2 46

3 71

Mean 62.67

Deviation 14.43

4.1.2.2. EPS 20 10% Deformation

As commented in the previous point, for 10% deformation not only the results of the tests are shown, but also the comparison with the expected compression strength according the Standard EN 14933 (Illustrations 4.1 and 4.2). Therefore, samples density must be calculated, as presented in Table 4.3.

Sample (10% deformation) EPS Block Weight (g) Density (kg/m3) Difference (%)

1 20 2.41 19.28 3.6

2 20 2.35 18.8 6

3 20 2.34 18.72 6.4

An example of one sample of density 20 kg /m³ with a 10% deformation which is tested is shown in Illustration 4.12.

Results are shown in the Illustrations 4.13-4.15.

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37 It is visible in Illustrations 4.13-4.15 that the three samples present a similar behaviour when a deformation of 10% is applied. Compression strength values are also similar for the three samples, as presented in Table 4.4.

EPS 20 10%

1 85

2 86

3 85

Mean 85.33

Deviation 0.577

In order to compare the results of the compression strength to the theoretical one, according to the Standard EN 14933, according to the real density of the samples, this theoretical value is calculated.

For a density of approximately 20 kg/m³, the graphic shown in Illustration 4.1 gives compression strength of 100 kPa, so the equation in Illustration 4.2 is used to obtain more accurate theoretical values. These values are presented in Table 4.5.

Table 4.5. Comparison between theoretical value and real value EPS 20 10% deformation

Density (kg/m³) Theoretical Equation Compression (kPa) Real Compression (kPa)

Sample 1 19.28 111.8 85

Sample 2 18.8 107 86

Sample 3 18.72 106.2 85

As shown in Table 4.5, the real compressive strength is lower than the theoretical one for the three samples.

4.1.2.3. EPS 40 5 % Deformation

As it happened with the tests for EPS 20 5% deformation, the results cannot be compared with theoretical ones. Values of density of the samples that are tested are presented in Table 4.6.

1 40 4.8 38.4 4

2 40 4.6 36.8 8

3 40 4.8 38.4 4

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38 An example of one sample of density 40 kg /m³ with a 5% deformation while being tested is shown in Illustration 4.16.

The results of these tests are shown in Illustrations 4.17-4.19.

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Illustration 4.19. Results EPS 40 5% deformation. Sample3

In this case, the three samples do not show similar behaviour, as the shape of the graphics is different for each of them.

In addition, the maximum compression strength is presented in Table 4.7.

EPS 40 5%

1 237

2 223

3 177

Mean 212.33

Deviation 31.39

For this case, as it was studied for the samples of 20 kg/m³ with 10% deformation in 4.1.2.2, a comparison between the results of compression strength obtained by the tests and the theoretical valued obtained from the equation in Illustration 4.2 is carried out. Therefore, the densities of the sample are needed, as shown in Table 4.8.

1 40 4.8 38.4 4

2 40 4.6 36.8 8

3 40 4.8 38.4 4

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40 An example of one sample of density 40 kg /m³ with a 10% deformation is shown in Illustration 4.20.

The results of the tests are shown in Illustrations 4.21-4.23.

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As it is visible in Illustrations 4.21-4.23, the behaviour of the three samples is similar, although sample 3 presents higher compression strength than the two other ones.

Table 4.9 presents the compression strength of the three samples with 10%

deformation.

EPS 40 10%

1 247

2 234

3 315

Mean 265.33

Deviation 43.50

In order to compare the results of the compression strength to the theoretical one, the Standard EN 14933 is followed, with the formula in Illustrations 4.2. For a density of approximately 40 kg/m³, the graphic in Illustration 4.1 gives a compressive stress of 300 kPa, so the equation is used to obtain more accurate theoretical values.

This comparison is presented in Table 4.10.

Table 4.10. Comparison between theoretical value and real value EPS 40 10% deformation

Density (kg/m³) Theoretical equation compression (kPa) Real compression (kPa)

Sample 1 38.4 303 247

Sample 2 36.8 287 234

Sample 3 38.4 303 315

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42 For the two first samples, it can be observed that the real compressive stress for 10% deformation is lower than the expected, which would mean that these samples could not stand the theoretical stress. The third sample, however, behaves in the opposite way, i.e. the real compressive stress is higher than the theoretical one.

4.1.3. Cycles Load- Unload

As previously explained, three cycles of load-unload are applied to the samples of both densities and deformations. Moreover, a deeper study of Young’s Modulus is carried out in Annex 1, where the different calculations of this property are presented.

4.1.3.1. EPS 20 5 % Deformation

The results of the three cycles load- unload for each of the three densities are shown in the Illustrations 4.24-4.26.

Illustration 4.24. Results EPS 20 5% deformation after three cycles load-unload. Sample 1

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43

Studying the three graphics (Illustrations 4.24-4.26), it can be observed that, while for the three loads the three cycles are different among them, the three unloads have a very similar behaviour.

Moreover, compressive stress for 5% deformation for each load and the residuary displacement after each unload is shown in Tables 4.11 and 4.12.

Table 4.11. Compression strength 5% deformation for the three loads

Compression Strength (kPa) Fist load Second load Third load

Sample 1 71 67 65

Sample 2 46 43 43

Sample 3 71 67 66

Table 4.12. Residuary vertical displacement 5% deformation for the three unloads

Residuary Vertical Displacement (mm) Fist unload Second unload Third unload

Sample 1 0.687 0.805 0.847

Sample 2 0.903 0.998 1.051

Sample 3 0.678 0.774 0.835

In order to develop a preliminary model of stress-deformation, it could be useful to introduce the concept of Young Modulus or Elastic Modulus. This number is a constant which relates the stress with the deformation. As axial compressive stress in these tests has only been applied in vertical direction, the Young equation would follow this equation:

= ∗

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44 where σ is the compressive stress, in MPa

E is the Young Modulus, in MPa ε is the deformation, without units

Therefore, the previous equation is the equation of a line, in which the deformation (ε) is the independent variable and stress (σ) is the dependent one. Young Modulus would be then the slope of the line. This concept is presented in Illustration 4.27.

Illustration 4.27. Graphic of the equation of the line

In this way, Young’s Modulus value would depend on the range of deformation chosen to calculate it. For this reason, in Annex 1 different methods to calculate this property are presented, which are:

a) Dividing each branch of load or unload in different lines and calculating the regression to obtain Young’s Modulus for each of these lines. This method is called

“Graphic”. Moreover, as deformation is presented as a percentage, the results obtained after calculating the lineal regression must be multiplied by 100, so the elasticity modulus has units of kPa.

b) Studying if the whole load or unload branch behaves as a lineal curve.

This method is being called “Lineal regression (1)”.

c) Studying which part of the branch behaves as a lineal curve. This method is named “Lineal regression (2)”.

d) Studying the Young’s modulus as the division of the compression stress by the deformation from “Lineal regression (2)”. This method is called “Δσ/Δε”.

STRESS (kPa)

DEFORMATION

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45 Results of these four methods for the three samples tested are presented in Tables 4.13, 4.14 and 4.15.

Table 4.13. Comparison of results with each method for Sample 1 5% Deformation

Graphic Lineal Regression (1) Lineal Regression (2) Δσ/Δε

Young’s Modulus

(kPa)

Deformation Range (%)

Young’s Modulus (kPa)

(kPa)

Load 1819.6 1.5-5 1387.2 0-5 1822.6 1.5-5 1734.13 1.5-5

Unload 2819.7 5-3.2 1784.2 5-1.4 2707.5 5-3 2699.49 5-3

Load (2) 2083 2.2-5 1738.3 1-5 2032.9 2-5 1968.05 2-5

Unload (2) 2957.3 5-3.45 1803.2 5-1 2715.3 5-3 2664.22 5-3

Load (3) 2292.2 2.7-5 1727.6 1.1-5 2033.33 2-5 1967.89 2-5

Unload (3) 2847.4 5-3.25 1862.9 5-1 2690.7 5-3 2628.69 5-3

(kPa)

Load 1159.1 1.5-5 1121.6 1-5 1181.7 2-5 1154.21 2-5

Unload 1907.7 5-3.2 1307.5 5-2 1812.6 5-3 1805.45 5-3

Load (2) 1251.1 2.2-5 1192.5 1.2-5 1383.8 2-5 1342.68 2-5

Unload (2) 2090.5 5-3.5 1353.7 5-2 1820.1 5-3 1804.28 5-3

Load (3) 1512.7 2.6-5 1182.2 1.2-5 1375.1 2-5 1354.5 2-5

Unload (3) 2251.4 5-3.8 1375.9 5-2 1811.8 5-3 1798.08 5-3

(kPa)

Load 1694.1 1.45-5 1644.2 1-5 1738.7 2-5 1731.3 2-5

Unload 2673.9 5-3.2 1796 5-1 2581.7 5-3 2563.21 5-3

Load (2) 1896.3 2.25-5 1742.6 1-5 1937.8 2-5 1906.8 2-5

Unload (2) 2801.9 5-3.5 1859.1 5-1.5 2582.1 5-3 2542.28 5-3

Load (3) 2061.1 2.7-5 1747.8 1.5-5 1963.1 2-5 1931.31 2-5

Unload (3) 2639.6 5-3.1 1869.6 5-1.5 2578.4 5-3 2538.55 5-3

In Tables 4.13, 4.14 and 4.15, it is visible that “Lineal Regression (1)” is the method that presents lower Young’s Modulus, while the other three have much closer values. It can also be observed that the values are similar for the three unload cycles, while the first load cycles in each sample is significantly different to the following ones.

The results are shown in the Illustrations 4.28-4.30.

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46

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47 Studying the three samples presented in Illustrations 4.28-4.30, it is possible to see that, for each sample, while for the three loads for the three cycles are different among them, the three unloads have a very similar behaviour.

The maximum compression stress and the residuary displacement after unload are shown in Tables 4.16 and 4.17, in order to compare the three samples.

Table 4.16. Maximum compression stress 10% deformation for the three loads

Maximum Compression (kPa)

First load Second load Third load

Sample 1 85 77 76

Sample 2 86 81 77

Sample 3 85 79 75

Table 4.17. Residuary vertical displacement 10% deformation for the three unloads

Residuary Vertical Displacement (mm) First unload Second unload Third unload

Sample 1 2.293 2.501 2.622

Sample 2 2.383 2.608 5.727

Sample 3 2.363 2.551 2.663

In this case, as in the previous point (4.1.3.1), the Young’s Modulus has been calculated with the four different methods and presented in Table 4.18, 4.19 and 4.20.

(kPa)

Load 1433.9 0-5.2 1441.8 1-5 1441.8 1-5 1397.85 1-5

Unload 2112.2 10-7.6 1378.4 10-5 1705.2 10-6 1731.67 10-6

Load (2) 1253.4 3.5-10 1253.4 3.5-10 1253.4 3.5-10 1198.32 3.5-10

Unload (2) 2095.4 10-7.5 1435.5 10-5 1691.8 10-6 1709.57 10-6

Load (3) 1297.4 4-10 1297.8 4-10 1297.8 4-10 1259.56 4-10

Unload (3) 1923.9 10-7 1472.3 10-5 1666.7 10-6 1683.56 10-6

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48

(kPa)

Load 1455.3 0-5.2 1579.2 1-5 1579.2 1-5 1501.18 1-5

Unload 2172.1 10-7.6 1468.3 10-5 1779.3 10-6 1799.2 10-6

Load (2) 1321.4 3.5-10 1332.4 3-10 1355.7 5-10 1359.68 5-10

Unload (2) 2153.3 10-7.5 1543.7 10-5 1757.1 10-6 1771.2 10-6

Load (3) 1363.5 4-10 1380.2 4-10 1419.7 5-10 1426.78 5-10

Unload (3) 1990.2 10-7 1573.6 10-5.5 1732.9 10-6 1749.31 10-6

(kPa)

Load 1600.3 0-4.8 1387.8 1-5 1664.9 1-4 1640.31 1-4

Unload 2003.8 10-7.65 1430.2 10-5 1666.8 10-6 1679.19 10-6

Load (2) 1218 3.45-10 1217.7 3.6-10 1217.7 3.6-10 1220.29 3.6-10

Unload (2) 1991 10-7.5 1467.7 10-5 1645.2 10-6 1658.72 10-6

Load (3) 1259.5 4-10 1261.1 4.1-10 1261.1 4.1-10 1271.07 4.1-10

Unload (3) 1879.2 10-7.1 1486.5 10-5 1624.4 10-6 1641.84 10-6

As in the previous case, the Modulus is similar in the three unload cycles, while the first load cycle is different to the following ones. It can also be appreciated in Tables 4.18, 4.19 and 4.20 that, as for EPS 20 kg/m³ 5%, “Lineal Regression (1)” is the method that presents lower Young’s Modulus, while the other three have much closer values.

The results of the three cycles of load-unload applied on each of the three samples are presented in Illustrations 4.31-4.33.

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49

As it can be observed in the two previous points (4.1.3.1 and 4.1.3.2), for the three samples, the first load behaves differently that the second and the third load, while the three unloads are very similar, as the curves are very close to each other.

Results of the calculation of Young’s modulus for each sample are presented in Tables 4.21, 4.22 and 4.23.

(kPa)

Load 4876.5 0-5 4964.3 1-5 4964.3 1-5 4939.62 1-5

Unload 8145.2 5-3.5 5489.3 5-1.1 6435.6 5-2 6451.61 5-2

Load (2) 5335.2 0.7-5 5403.5 1-5 5403.5 1-5 5392.05 1-5

Unload (2) 8184.7 5-3.5 5615.5 5-1.3 6418 5-2 6434.53 5-2

Load (3) 5423.7 0.8-5 5469.6 1-5 5469.6 1-5 5426.89 1-5

Unload (3) 7928.3 5-3.3 5652 5-1.3 6370.9 5-2 6391.35 5-2