Effect of Size and Shape of Test Specimens on Compressive ...

Effect of Size and Shape of Test Specimens on Compressive Strength of Normal Strength Concrete

S.M. Habibul Ahsan

A thesis submitted to the Department of Civil Engineering of Bangladesh University of

Engineering and Technology, Dhaka, in partial fulfilment of the requirements for the degree

of

MASTER OF SCIENCE IN CIVIL ENGINEERING (STRUCTURAL)

DEPARTMENT OF CIVIL ENGINEERING

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY DHAKA-1000, BANGLADESH

March, 2018

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The thesis titled “Effect of Size and Shape of Test Specimens on Compressive Strength of

Normal Strength Concrete” submitted by S.M. Habibul Ahsan, Roll No.: 0413042335,

Session: April 2013 has been accepted as satisfactory in partial fulfilment of the requirement

for the degree of M.Sc. Engineering (Civil and Structural) on 27th March, 2018.

BOARD OF EXAMINERS ______________________________________ Dr. Mohammad Al Amin Siddique Chairman Associate Professor (Supervisor) Department of Civil Engineering BUET, Dhaka. ______________________________________ Dr. Ahsanul Kabir Member Professor and Head (Ex-officio) Department of Civil Engineering BUET, Dhaka. ______________________________________ Dr. Shameem Ahmed Member Assistant Professor Department of Civil Engineering BUET, Dhaka. ______________________________________ Dr. Md. Tarek Uddin Member Professor (External) Department of Civil and Environmental Engineering IUT, Gazipur.

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D E D I C A T I O N

To Those

Who Are Praised

By

Allah

iv

D E C L A R A T I O N

It is hereby declared that except for the contents where specific reference have been made to

the work of others, the studies contained in this thesis is the result of investigation carried out

by the author. No part of this thesis has been submitted to any other university or other

educational establishment for a Degree, Diploma or other qualification (except for

publication).

_________________________________ S.M. Habibul Ahsan

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A C K N O W L E D G E M E N T

I n t h e n a m e o f A l l a h , M o s t G r a c i o u s , M o s t M e r c i f u l

All praises to the Sustainer of the worlds, and grace, honour and salutations on the Chief of

Apostles and Seal of Prophets, Muhammad Sallallahu Alaihissalam, his family, companions

and those who followed him in an excellent manner and invited mankind towards Allah, till

the Day of Resurrection.

I would like to thank Allah Subha’nahu Wa Ta’ala the Exalted for His blessing that allowed

me to complete this thesis and I pray that He accepts it as a work of sincerity and benefit.

I would like to express my deep and sincere gratitude to my thesis supervisor, Dr.

Mohammad Al Amin Siddique, Associate Professor of Civil Engineering Department of

BUET for his dynamic supervision, continuous guidance, invaluable suggestion, and

enthusiastic encouragement throughout various stages of this research. His active interest in

this topic and valuable advice was the source of author’s inspiration. The author is also

grateful to all personnel of Concrete and SM laboratories of BUET for their excellent support

during carrying out the experimental works.

During this work I have collaborated with many colleagues for whom I have great regard, and

I wish to extend my warmest thanks to all those who have helped me with my work in the

Department of Civil Engineering of BUET.

Finally, I extend my acknowledgement and heartfelt love to my family members who are

always a constant source of inspiration throughout my life.

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A B S T R A C T

Different codes (ASTM, BS etc) specify different size/shape test specimens for quality

assurance testing. Cylinder specimens of 6×12 in. (150×300 mm) or 4×8 in. (100×200 mm)

and cube specimens of 6×6 ×6 in. (150×150×150 mm) or 4×4×4 in. (100×100×100 mm) are

widely used in different countries. In our country, design specifications refer to the

compressive strength obtained from either testing 6×12 in. concrete cylinder or 6 in. concrete

cube and tested as per relevant standards. However, 4×8 in. cylinder specimens are almost

exclusively used in our country nowadays considering testing machine capacity, ease of

handling, cost of materials etc. Therefore, a correlation between concrete compressive

strengths of using cylinders and cube specimens are necessary. L'Hermite equation is widely

used as a conversion factor between the standard cube and cylinder specimens. However, the

applicability of this conversion factor may require to be evaluated in context of concrete as

used in our country. Therefore, the main objective of this research is to study the effect of

size and shape of test specimens on compressive strength of normal strength concrete. The

variability of using L’Hermite equation as a conversion factor of compressive strength is also

evaluated.

An experimental program is carried out to study the size and shape effect of concrete test

specimens on normal strength concrete. A total of 324 nos. samples (90 nos. 6×12 in.

cylinders; 90 nos. 4×8 in. cylinder; 72 nos. 6 in. cube and 72 nos. 4 in. cube) have been

prepared and tested for unit weight, compressive strength, splitting tensile strength, static

modulus of elasticity. In addition, a non-destructive test UPV is conducted to evaluate the

concrete compressive strength. During the experimental study, 06 (six) strength levels

(concrete mix design) i.e., 7 MPa (1000 psi) to 41 MPa (6000 psi) were obtained by mostly

varying water-cement ratio, and other parameters such as maximum size of coarse aggregate,

properties of fine and coarse aggregates and fine aggregate-to-total aggregate ratio were kept

almost the same. 2% air content is considered in all concrete mixes. Parameters like curing

condition, capping method, consolidation and testing method were controlled as per relevant

standards (ASTM and BS) for the entire test program.

From the experimental results, it is observed that the smaller size cylinder specimen (4 × 8

in.) has higher compressive strength than that of larger sizes (6×12 in.) and the same trend is

followed for the cube specimens. The ratio of compressive strength of 4×8 in. cylinder

specimens to that of 6×12 in. specimens is 1.13 on an average with coefficient of variation of

6.2 percent. The average ratio of compressive strength of 4 in. cube specimens to that of 6 in.

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is approximately 1.06 with a coefficient of variation of 6.6 percent. The ratios of compressive

strength between standard cylinder to standard cube are dependent on strength of concrete

and the ratios increases with the increase of strength. Using L’Hermite equation to convert

standard cube strength to cylinder strength is not conservative for strength level between 7

MPa and 41 MPa in case of concrete produced in our country. For the strength range between

41 MPa to 53 MPa, L’Hermite equation yields conservative values. When concrete strength

using cylinder specimens is converted to cube strength according to LGED specification, it

always overestimates the concrete strength for the range of 7 to 40 MPa concrete. For

strength ranges between 10.5 to 62 MPa, REB specification provides better agreement with

the test results.

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T A B L E O F C O N T E N T S Page No.

DEDICATION iii

DECLARATION iv

ACKNOWLEDGEMENT v

ABSTRACT vi

LIST OF FIGURES xii

LIST OF TABLES xvi

LIST OF ABBREVIATIONS xviii

CHAPTER 1 INTRODUCTION

1.1 General 1

1.2 Background of the Study 1

1.3 Objectives of the Present Study 3

1.4 Scope and Methodology of the Study 3

1.5 Organization of the Thesis 3

CHAPTER 2 LITERATURE REVIEW

2.1 Introduction 5

2.2 Size and Shape Effect on Concrete Strength 6

2.3 Factors Affecting Strength of Concrete 9

2.3.1 Water-Cement Ratio 9

2.3.2 Air Entrainment 10

2.3.3 Aggregate/Cement Ratio 10

2.3.4 Coarse Aggregate 11

2.3.5 Curing Condition 12

2.3.6 Mold Material 13

2.3.7 Rate of Load Application 13

2.3.8 Age of Test Specimen 13

2.4 Correlation Between Cylinder and Cube Strength 14

2.4.1 Strength Level 14

2.4.2 Age of Specimen 14

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2.4.3 Aggregate Size 15

2.4.4 Curing Condition 15

2.4.5 Capping Method 15

2.4.6 Consolidation Method 15

2.5 Correlation Between UPV and Compressive Strength 16

2.6 Summary and Discussion 19

CHAPTER 3 EXPERIMENTAL WORK

3.1 Introduction 20

3.2 Sieve Analysis and Aggregate Properties 21

3.3 Mix Design 26

3.4 Material Used in the Present Study 27

3.4.1 Cement 27

3.4.2 Aggregate 27

3.4.3 Water 28

3.5 Methodology 28

3.5.1 Casting of Concrete 28

3.5.2 Compacting & Curing 28

3.6 Test on Fresh Concrete 30

3.6.1 Workability Test 30

3.7 Test on Hardened Concrete 30

3.7.1 Compressive Strength Test 31

3.7.2 Splitting Tensile Strength Test 32

3.7.3 Concrete Density 33

3.7.4 Ultrasound Pulse Velocity Test (UPV) 34

3.7.5 Stress-Strain Diagram and Modulus of Elasticity 35

3.8 Summary 36

CHAPTER 4 RESULTS AND DISCUSSION

4.1 Introduction 37

4.2 Test on Fresh Concrete 37

4.3 Experiment on Hardened Concrete(Non- Destructive) 38

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4.3.1 Hardened Unit Weight of Concrete 38

4.3.2 Ultrasound Pulse Velocity 39

4.4 Experiment on Hardened Concrete (Destructive) 43

4.4.1 Splitting Tensile Strength 43

4.4.2 Compressive Strength Test 45

4.4.3 Correlation between Strength of Cylinders 48

4.4.4 Correlation between Strength of Cubes 52

4.4.5 Correlation between Strength of Cylinder & Cube 55

4.5 Stress-Strain Diagram 62

4.5.1 Static Modulus of Elasticity 62

4.5.2 Static Modulus of Elasticity for Specified

Strength 7 MPa

63


Strength 14 MPa

65


Strength 21 MPa

67


Strength 28 MPa

69


Strength 34 MPa

71


Strength 41 MPa

73

4.6 Failure Pattern 76

4.6.1 Failure Types of Concrete Specimen for Specified

Strength 7 MPa

77


Strength 14 MPa

78


Strength 34 MPa

78

4.7 Summary 80

CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS

5.1 General 81

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5.2 Conclusions 82

5.3 Limitations

83

5.4 Recommendations for the Future Study 83

REFERENCES 85

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L I S T O F F I G U R E S

Page No.

FIGURE 2.1 Wall effect (Neville, 2002) 7

FIGURE 2.2 Water-cement ratio vs. strength of concrete (Neville, 1996)

9

FIGURE 2.3 Influence of the aggregate/cement ratio on strength of concrete (Neville & Brooks, 2007)

10

FIGURE 2.4 Aggregate size, w/c, and compressive strength (Cordon and Gillespie 1963)

11

FIGURE 2.5 Pulse velocity testing equipment 17

FIGURE 2.6 Direct (a), Semi-direct (b), Indirect (surface) transmission (c).

17

FIGURE 3.1 ASTM C 33 gradation chart (upper & lower limit) and sample gradation curve (stone chips-1st phase).

22

FIGURE 3.2 ASTM C 33 gradation chart (upper & lower limit) and sample gradation curve(sand-1st phase).

23

FIGURE 3.3 ASTM C 33 gradation chart (upper & lower limit) and sample gradation curve(stone chips-2nd phase)

24

FIGURE 3.4 ASTM C 33 gradation chart (upper & lower limit) and sample gradation curve(sand-2nd phase).

25

FIGURE 3.5 Natural Sylhet sand 27

FIGURE 3.6 Natural Stone chips 27

FIGURE 3.7 Mixing of concrete ingredients 29

FIGURE 3.8 Placing and compacting of concrete. 30

FIGURE 3.9 Slump test on a fresh concrete 31

FIGURE 3.10 Top and bottom capping of 4×8 in. cylinder 32

FIGURE 3.11 Testing Machine and Test Setup 32

FIGURE 3.12 Typical Splitting tensile strength test set up 33

FIGURE 3.13 Ultrasound Pulse Velocity test 35

FIGURE 3.14 Typical test up with dial gauge for determining modulus of elasticity

36

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FIGURE 4.1 Compressive Strength vs. UPV (6×12 in. Cylinder) 40

FIGURE 4.2 Compressive Strength vs. UPV (4×8 in. Cylinder) 40

FIGURE 4.3 Compressive Strength vs. UPV (6 in. Cube) 41

FIGURE 4.4 Compressive Strength vs. UPV (4 in. Cube) 41

FIGURE 4.5 Tensile Strength vs. UPV 42

FIGURE 4.6 √𝑓′c vs. tensile strength 44

FIGURE 4.7 Water-Cement Ratio vs. Compressive Strength of 6×12 in. Cylinder specimens

47

FIGURE 4.8 Water-Cement Ratio vs. Compressive Strength of 4×8 in. Cylinder specimens

47

FIGURE 4.9 Water-Cement Ratio vs. Compressive Strength of 6 in. Cube specimens

48

FIGURE 4.10 Water-Cement Ratio vs. Compressive Strength of 4 in. Cube specimens

48

FIGURE 4.11 Seven-day strength of standard and small size cylinder specimens

50

FIGURE 4.12 Fourteen-day strength of standard and small size cylinder specimens

51

FIGURE 4.13 Twenty eight-day strength of standard and smaller size cylinder specimens

51

FIGURE 4.14 Seven-day strength of standard and small size cube specimens.

54

FIGURE 4.15 Fourteen-day strength of standard and small size cube specimens

54

FIGURE 4.16 Twenty Eight-day strength of standard and small size cube specimens

55

FIGURE 4.17 Compressive strength vs. conversion factors 56

FIGURE 4.18 Conversion between the cylinder and cube strengths of concrete

58

FIGURE 4.19 Cube strength vs. cylinder/cube ratio (L’Hermite & present study)

59

FIGURE 4.20 Cylinder and cube strength (LGED recommendation and present study)

60

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FIGURE 4.21 Cylinder strength vs cube strength found in the present study

61

FIGURE 4.22 REB cube strength vs cube strength from the present study

62

FIGURE 4.23 Stress-strain diagram for specimen-1 for specified strength 7 MPa

63


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66


66


67


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68


69


70


70


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72


72


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74


74

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FIGURE 4.41 Satisfactory failure patterns for cylinder and cube 77

FIGURE 4.42 Failure pattern of (a) 4 ×8 in. and (b) 6×12 in. cylinders specimen

77

FIGURE 4.43 Failure pattern of 6 in. (a) and 4 in. cubes (b) 77

FIGURE 4.44 Failure type for large and small size cylinder specimens

78

FIGURE 4.45 Shows the failure type of concrete cylinder specimens 79

FIGURE 4.46 Failure pattern is semi-explosive (a) and explosive (b) 79

FIGURE 4.47 Tensile splitting surface for 6×12 and 4×8 in. cylinder

80

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L I S T O F T A B L E S Page No.

Table 3.1 Sieve analysis of stone chips procured at 1st phase 21

Table 3.2 Sieve analysis of Sylhet sand procured at 1st phase 22

Table 3.3 Sieve analysis of stone chips procured at 2nd phase 23

Table 3.4 Sieve analysis of Sylhet sand procured at 2nd phase 24

Table 3.5 Comparison of different properties of Sylhet sand used at 1st and 2nd phases of testing

25

Table 3.6 Comparison of different properties of stone chips used at 1st and 2nd phases of testing

26

Table 3.7 Quantity of materials for different concrete mixes 26

Table 4.1 Slump test results of different concrete mixes 37

Table 4.2 Unit weight of different concrete mixes 38

Table 4.3 Ultrasound Pulse Velocity (m/s) and compressive strength (MPa) of cylinders

39

Table 4.4 Ultrasound Pulse Velocity (m/s) and compressive strength (MPa) of cubes

39

Table 4.5 UPV (m/s) and tensile strength (MPa) for different concrete mixes

42

Table 4.6 Conversion between compressive strength (psi) and splitting tensile strength (psi) for 6×12 in. cylinder

44

Table 4.7 Conversion between compressive strength (psi) and splitting tensile strength (psi) for 4×8 in. cylinder

45

Table 4.8 Compressive strength of cylinder and cube specimens 46

Table 4.9 Conversion factors between cylinder specimens 49

Table 4.10 Conversion factors between 6 in. and 4 in. cube specimens 52

Table 4.11 Conversion factors between 6x12 in. cylinder and 6 in. cube

56

Table 4.12 Conversion factors between 6x12 in. cylinder and 6 in. cube(28-day)

58

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Table 4.13 Conversion factors as recommended by LGED, Bangladesh

59

Table 4.14 Conversion factors between 4x8 in. cylinder and 4 in. cube specimens

60

Table 4.15 Conversion between cylinder to cube strength 61

Table 4.16 Static modulus of elasticity for specified strength 7 MPa

65

Table 4.17 Static modulus of elasticity for specified strength 14 MPa 67




Table 4.21 Static modulus of elasticity for specified strength 41MPa 75

Table 4.22 Summary of findings from stress-strain test data 75

xviii

L I S T O F A B B R E V I A T I O N

ACI American Concrete Institute

AASHTO American Association of State Highway and Transportation Officials

ASTM American Society for Testing and Materials

BS British Standards

IS Indian Standards

UPV Ultrasound Pulse Velocity

PSI Pound Per Square in.

LGED Local Government Engineering Department

REB Rural Electrification Board

PCC Portland Composite Cement

FM Fineness Modulus

1

Chapter 1

INTRODUCTION

1.1 General

Worldwide, over 4.1 billion tons of cement was produced in the year 2017. In the United

States, the annual production is over 86.3 million tons (https://www.statista.com/statistics/).

In Bangladesh, per capita consumption of cement is 120 kg annually, whereas per capita

consumption of cement in Pakistan, Sri Lanka and India are 170 kg, 310 kg and 220 kg

respectively annually (http://www.eblsecurities.com/). Around 32 million tons of concrete

was produced in Bangladesh in 2016-17 compared to 13.9 million tons in 2010-11. If the

demand is considered of other developing countries, Bangladesh has a huge potential in

growth of concrete consumption in the years to come. Concrete is used in many civil

engineering structures such as to build roads, bridges, skyscrapers, airplane runways and

dams etc.

1.2 Background of the study

Concrete is by far the most used building material on earth due to its excellent compressive

strength, mouldability to different predefined shapes and a long service life. In most areas,

concrete takes advantage of inexpensive local materials (sand, brick and stone) and requires

relatively less amount of cement and reinforcing steel which can be transported in from one

to other locations of the country. Concrete in a civil engineering structure mainly resists

compressive stress generated from different load types, and tensile stress is left for

reinforcing steel to take over.

Compressive strength of concrete depends on many factors. The main influencing factors on

strength are taken in practice as: water/cement ratio, degree of compaction, age and

temperature. However, there are also other factors which affect strength: aggregate/cement

ratio, quality of aggregate (grading, surface texture, shape, strength, and stiffness), and the

maximum size of the aggregate. These factors are regarded as of secondary importance when

usual aggregates up to a maximum size 40 mm are used (Neville, 2002).

2

For construction of any concrete structure, compressive strength of concrete is specified

beforehand. Various mix design approaches are available to attain specified strength of

concrete. Among the various methods in use, the method proposed by American Concrete

Institute (ACI 211.1-91) is probably the most popular one. The ACI method requires in total

seven input parameters to design a normal strength concrete mix. These are: coarse aggregate

unit weight, design compressive strength, fine aggregate specific gravity, coarse aggregate

specific gravity, fine aggregate fineness modulus, coarse aggregate maximum size and slump.

Concrete samples as specified by various standards (ASTM, BS and IS etc) are casted and

tested in laboratory to ensure that concrete of specified strength are attained at the

construction site.

It is well established that for a specific mix, compressive strength of concrete varies

depending on shape and/or size of concrete test specimens (Neville, 1996). During

construction works, quality of concrete is ensured by casting concrete samples using various

moulds (6×12 in. (150×300 mm) or 4×8 in. (100×200 mm) cylinders; 6 in. (150 mm) or 4

in.(100 mm) cube) according to different standards in different countries. In our country,

design specifications refer to the compressive strength obtained from either testing 6 × 12 in.

concrete cylinder or 6 in. concrete cube and tested as per relevant standards. However, 4×8

in. cylinder specimens are almost exclusively used in our country nowadays considering

testing machine capacity, ease of handling, cost of materials etc. Also, ASTM C192 and

AASHTO R39 allow the use of 4 × 8 in. cylinders for quality assurance testing. Therefore, a

correlation between concrete compressive strengths of using cylinders and cube specimens

are necessary. A widely used L'Hermite equation gives conversion factors between the

standard cube and cylinder specimens. However, the applicability of these conversion factors

may require to be evaluated in context of concrete as used in our country. Also, government

organizations like LGED, REB etc. have their own conversion factors for different project

specifications. The present study will also evaluate the applicability of the use of these

conversion factors. An experimental program will be conducted to assess the effect of test

specimen sizes and shapes on compressive strength of concrete, to be cured under standard

laboratory controlled conditions and to be tested at 7, 14 and 28 days. In addition, tensile

strength, modulus of elasticity of concrete will be evaluated. A non-destructive test such as

UPV will also be used to assess the variation of different concrete mixes as well as to

correlate the compressive strength.

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1.3 Objectives of the present study

The main objectives of the thesis are as follows:

To determine a correlation between the compressive strength of 4 × 8 in. and 6 × 12

in. cylinders and the variability associated with those results.

To determine a correlation between the compressive strength of 4 in. and 6 in. cubes

and the variability associated with those results.

To evaluate a conversion factor between the compressive strength of cylinders and

cube specimens and the applicability of L'Hermite equation for conversion factors of

cube and cylinder specimens.

1.4 Scope and methodology of the study

An experimental program will be carried out to determine the concrete properties using

different sizes and shape of specimens. Cylinder sizes of 6 ×12 in. and 4×8 in. and cube sizes

of 6×6 in. and 4×4 in. will be used in the study. Specimens with target concrete compressive

strength ranging from 7 MPa (1000 psi) to 41 MPa (6000 psi) will be prepared and tested in

the laboratory. Six different concrete mixes will be prepared. Properties like bulk specific

gravity, unit weight, water absorption capacity, and fineness modulus of coarse and fine

aggregates will be evaluated through different laboratory tests. Portland composite cement

(PCC), Sylhet sand and natural stone aggregates will be used as ingredients of concrete

without any chemical admixture. Concrete compressive strength will be evaluated for

different sizes and shapes at 7, 14, and 28 days. Splitting tensile strength and modulus of

elasticity of concrete will be determined at 28 days. In addition, a non-destructive test such as

Ultrasound Pulse Velocity (Mohammed & Rahman, 2016) will be used to determine the

concrete compressive strength.

1.5 Organization of the thesis

The thesis is organized into five chapters. Chapter 1 is the current chapter, which introduces

the background, objectives and scope of the thesis.

In chapter 2 (literature review), the previous significant works on size and shape effect of

different specimens on concrete strength have been mentioned.

4

Chapter 3 (experimental works) includes complete details about the experiments, which were

performed together with their respective standards.

Chapter 4 (results and discussions) contains the results of experimental program and the

analyses of the obtained results. Explanations and discussions about each of results are made

and were compared with the available literature.

In chapter 5 (conclusions and recommendations), conclusions of the present study are listed

briefly. In addition, a further research scope will be mentioned.

5

Chapter 2

LITERATURE REVIEW

2.1 Introduction

Compressive strength of concrete is determined by testing on hardened concrete samples

which is one of the most important and necessary experiments performed widely for quality

assurance testing. Usually samples of various size and shape according to different standards

are casted in the field/laboratory and crushed them by using relevant testing machines.

Splitting tensile strength, static and dynamic modulus of elasticity, Poisson’s ratio and stress-

strain diagram are evaluated according to relevant testing standards.

However, it is widely known fact that results of the experiment on compressive strength can

be affected by diverse factors, such as specimens’ sizes, their shapes, the moulds used for

casting, curing conditions and rate of load application (Neville, 2002). It is also realized that

the strength of a concrete specimen may also be influenced by other factors, such as modulus

of elasticity of aggregate, its Poisson’s ratio, the aggregate-cement ratio etc. (Neville, 1966).

According to different testing standards (ASTM, BS etc) adopted for compressive and

splitting tensile strengths tests, there are two main shapes for testing concrete specimens:

cubes and cylinders. While cylindrical specimens 150×300 mm (6×12 in.) are used mostly in

Australia, Canada, France, New Zealand and the United States, cubic specimens of 300 mm

(6 in.) and 100 mm (4 in.) are used generally in India and Europe (Yakkali, 2015). Due to two

main shapes and various sizes, testing specimens can easily differ in strengths and may

produce scattered results even if they are from the same batch and tested at the same testing

condition such as age of specimen, curing condition. Of course, in each region, regarding to

the specimens types, there are codes like British and ASTM code, explaining how to perform

the experiment.

One of the differences between cylinder and cube specimens is that before being loaded,

cylinder specimens need capping. The specimens have to be capped by Sulphur mortar,

rubber pad or cement paste in order to have uniform loading surfaces. Unlike the cylinders,

cubes do not require capping as they are turned over on their sides to get plain surface, when

being loaded. Various researches have been conducted and available in literature to

6

understand and clarify the size and shape effect of concrete specimens on the compressive

strength test results. According to Bažant and Planas (1998), size effect can be seen when by

altering the size of a concrete member, its nominal strength also gets changed, even though

their shape is similar to each other. The same definition can be proposed for shape effect as

well, when nominal strength of concrete members is dependent on their shape.

2.2 Size and shape effect on concrete strength

To address size and shape effect on concrete test specimen, conversion factors have been

proposed for different conditions. One of the first investigations about size effect was carried

out in 1925 by Gonnerman, using standard cubes of 6 in. and 8 in. and different sizes of

cylinders. Testing different specimens at different ages, the average cylinder/cube ratio of

0.85 to 0.88 was obtained.

Since concrete is composed of ingredients of variable strength, it is reasonable to assume that

the larger the volume of the concrete, the probability of occurrence of an element of weaker

strength of a given level of strength is higher (Neville, 1966). As a result, for a concrete

specimen of the same batch, it is reasonable to expect that its strength and its variability will

decrease as the specimen size increases. Since the size effect is a result of the non-

homogeneity of the concrete, it follows that the more homogeneous the concrete the smaller

will be the size effect. Lessard and Aitcin (1992) found that the compressive strength of

cylinders of 150 mm dia. by 300 mm height was about 94% that of cylinders of 100 mm dia.

by 200 mm height. Baalbaki et al. (1992) repeated the experiment on a total of 126 cylinders

and found that the strength of the cylinders of 150mm dia. was 93% that of cylinders of 100

mm dia. Neville (2002) suggested that the strength of the 100 mm cubes was about 1.04%

that of the 150 mm cubes.

Size and shape effect and the factors influencing them were also studied by Tokyay and

Ozdemir (1997). They also explained the fact of getting low strength of very small size

specimen compared to large size specimen, which is a contradiction as small size specimen

shall have higher apparent compressive strength. This was explained by the phenomenon of

wall effect (as shown in figure 2.1), according to which, the quantity of mortar required to fill

the space between the particles of the coarse aggregate and the wall of the mold is greater

7

than that necessary in the interior of the mass and therefore in excess of the mortar available

even in a well-proportioned mix. This effect limits the compactibility of specimens and is

more pronounced in specimens with larger lateral surface area-to-volume ratio, and this

phenomenon influences the results of compressive strength, as well as the conversion factors

of different specimens to each other.

Figure 2.1 Wall effect (Neville, 2002)

Size and shape effect for brick aggregate concrete have been studied by Banda et al. (2013).

They compared the results between compressive strength of 6×12 in. cylinder and 6 in. cube

for various water-cement ratio and mix proportion of concrete ingredients. On an average,

cube strength were found 15.12%, 10.63% and 12.00% greater than that of cylinder strengths

for various mix proportions and water-cement ratio. They compared the results between

compressive strength of 6×12 in. cylinder and 4×8 in. cylinder for various water-cement ratio

and mix proportion of concrete ingredients. On an average, small cylinder strengths were

7.40%, 8.03% and 9.70% higher that of larger cylinder strengths for various water- cement

ratios and mix proportions.

Due to different shapes of the testing specimen, measured compressive strengths are different

for cubes and cylinder specimens although they are from the same mix and similar testing

condition. Cylinder specimens are slender compared to that of cubes. The ratio of height-to-

diameter (h/d) of cylinders is 2 while that of cubes is 1. This is one of the causes. It was

found that the cube/cylinder strength ratio decreases by the increase in concrete strength

(Yakkali and Reddy, 2015). This ratio reaches values above 0.9 for high strength concrete. A

8

ratio of 1.15 to 1.25 is expected for normal concrete (25 to 50MPa cube strength), while this

value reaches 1.1 for high strength concrete (55 to 85MPa cube strength) (Yakkali and

Reddy, 2015). Generally, cylinder/cube compressive strength values close to 0.9 and 0.95 for

higher strength concretes. On the other hand, practically, the ratio between cylinder and cube

strength is typically taken equal to 0.8 averagely at a lower to medium strength grades

(Yakkali and Reddy, 2015).

During testing, the platens of the loading machine restrain the lateral expansion of the

concrete in parts of the specimen near its ends. This restraint is dependent on the amount of

friction developed. Under normal conditions, with friction, an element within the specimen is

subjected to a shearing stress as well as to compression. With an increase of distance from the

platen, the magnitude of the shearing stress decreases and the lateral expansion increases.

This shear stress has the confining effect of increasing the axial load for failure. The

restraining effect of the platens of the testing machine extends over the entire height of the

cube but leaves a part of the cylinder unaffected due to this increase in aspect ratio.

Therefore, compressive strengths of cubes are expected to be higher than those of cylinders

made from the same concrete (Yakkali and Reddy, 2015).

In reality, there is no unique relationship among the cube and cylinder made with different

proportions. The interrelation varies also with age factors. Cylinders are believed to give a

higher uniformity of results for similar specimens because their failure is less affected by the

end restraint of the specimen, their strength is influenced by the properties of the coarse

aggregate used in the mix, and the stress distribution on horizontal planes in a cylinder is

more uniform than on a cube specimen. The use of rigid and nonrigid moulds affects their

strength (Yakkali and Reddy, 2015).

As discussed, concrete cubes may be loaded in the direction perpendicular to casting while

cylinders are always loaded in the direction of casting. Since these concrete cubes and

cylinders are casted in multiple layers, their strength will differ based on direction of loading.

Lower the rate of application of load, the lower will be the recorded strength; the reason for

this is probably the effect of creep. If the load is applied slowly, or if the there is some time

lag, the specimen will undergo certain amount of creep which will increase the strain due to

creep will be responsible for failure of sample (Yakkali and Reddy, 2015).

9

The objectives of the present research are to determine correlation between compressive

strength of 6×12 in. cylinder and 4×8 in. cylinder; 6 in. cube and 4 in. cube and 6×12 in.

cylinder and 6 in. cube for normal strength concrete. In the subsequent paragraphs, factor that

affect compressive strength of concrete and factors that may affect correlation of strengths

between cylinder and cube specimens will be discussed.

2.3 Factors affecting strength of concrete

In general, there are many factors that affect the compressive strength of concrete and among

these factors, most of them are interdependent. Some of the important parameters that may

affect the compressive strength of concrete are discussed in the following sections.

2.3.1 Water-cement ratio

In properly compacted concrete, the compressive strength is inversely proportional to water-

cement ratio as shown in figure 2.2.

Figure 2.2 Water-cement ratio Vs strength of concrete (Neville, 1996)

The water-cement ratio is a very important factor in the determination of porosity and

eventually the strength of concrete (Neville 1996). An increase in temperature increases the

rate of the exothermic hydration reaction and also the development of strength with time

(Neville 1996). In practical applications, it is found that the water-cement ratio is usually the

most important factor with respect to strength (Neville 1996).

10

2.3.2 Air entrainment

Air entrainment is the incorporation of air bubbles into the concrete by either using an air-

entraining admixture or air-entraining cement. There are two forms of air found in concrete:

entrapped and entrained air. Entrained air causes a reduction in compressive strength at a

particular water-cement ratio when compared with non-air-entrained concrete. It is found that

as the amount of entrained air increases, the demand for mixing water and sand reduces at a

particular cement content. However, when the cement content increases the reduction in the

demand for mixing water decreases. Thus the reduction in compressive strength associated

with air-entrained concrete can be somewhat compensated by making air-entrained concrete

with lower water-cement ratios (Vandegrift and Schindler, 2006).

2.3.3 Aggregate/cement ratio

It has been found that, for a constant water/cement ratio, a leaner mix leads to a higher

strength. The influence of aggregate/cement ratio on strength of concrete is shown in figure

2.3.

Figure 2.3 Influence of the aggregate/cement ratio on strength of concrete (Neville & Brooks,

2007)

11

The main explanation if this influence lies in the total volume of voids in the concrete.

Clearly if the paste represents a smaller proportion of the volume of concrete (as in the case

of leaner mix) then the total porosity of the concrete is lower, and hence its strength is higher.

The above argument ignores any voids in the aggregate, but with normal aggregates these are

minimal (Vandegrift and Schindler, 2006).

2.3.4 Coarse Aggregate

The strength of concrete is dependent on size, shape, grading, surface texture mineralogy of

the aggregate, strength, stiffness and the maximum size of aggregate as seen in Figure 2.4.

Figure 2.4 Aggregate size, w/c, and compressive strength (Cordon and Gillespie, 1963)

Research studies conducted by Gilkey 1961 and Mehta and Monteiro (1993) suggested that

the effect of aggregate strength on the compressive strength of concrete is not considered in

the case of normal strength concrete, as it is much stronger than the transition zone and

cement paste matrix. Mehta and Monteiro (1993) also explained that the transition zone and

the cement paste matrix would fail before the aggregate and thus nullify the effect of the

12

strength of aggregate. Kosmatka et al. (2002) also suggested that the aggregate strength is

usually not a factor in normal strength concrete as the failure is generally determined by the

cement paste-aggregate bond. Much research has linked the bonding of the aggregate to the

strength of concrete. Neville and Brooks (2007) explained that greater aggregate surface

areas result in better bonding between the aggregate and the cement paste. They also

observed that rough aggregates tend to exhibit better bonding than smooth aggregates. Jones

and Kaplan (1957) made similar observations as Neville and Brooks (2007) but linked the

surface properties to the cracking stress suggesting rough aggregates would crack at a higher

stress compared to smooth aggregates. Figure 2.4 shows the effect of water-cement ratio and

the maximum aggregate size on compressive strength. It can be seen that compressive

strength decreases with an increase in maximum coarse aggregate size especially for

concretes with low water-cement ratios. It should be noted that the compressive strength is

more sensitive to the water-cement ratio than the maximum aggregate size (Vandegrift and

Schindler, 2006).

2.3.5 Curing condition

The reaction of water with cement is called the hydration process and the results are called

the products of hydration. Curing is a process by which moisture loss is prevented at a

particular temperature to enhance the hydration process of cement. The curing process not

only increases strength and durability but also decreases the porosity of the concrete. To

ensure that there is satisfactory development of strength during the hydration process it is

necessary to prevent moisture loss (Kosmatka et al. 2002).

Neville and Brooks (2007) stated that “it must be stressed for a satisfactory development of

strength it is not necessary for all the cement to hydrate and indeed this is rarely achieved in

practice.” Burg (1996) observed that a higher initial curing temperature increases the rate of

hydration process and early-age strength. However, high initial temperatures have been

reported to produce concretes with reduced long-term strengths as per Burg (1996). The

curing temperature is very important with respect to concrete strength because it contributes

towards the rate of hydration. With proper curing the capillary pores get filled up with

hydration products (Neville 1996) and this increases the impermeability and strength

(Kosmatka et al. 2002). To maintain proper hydration during the initial stages of concrete

stiffening, the internal relative humidity should be maintained at 80 percent as per Kosmatka

13

et al. (2002). Neville and Brooks (2007) explained the impermeable nature of adequately

cured concrete by stating that the capillary pores inside concrete get interconnected by pores

formed by the products of hydration after sufficient hydration has taken place (Vandegrift

and Schindler, 2006).

2.3.6 Mold material

It is found that mold material does affect the apparent strength of concrete test specimens. In

general, specimen made with plastic mold has less compressive strength than that made with

steel mold (Vandegrift and Schindler, 2006).

2.3.7 Rate of load application

According to Mali et al. (2015), with the variation of loading, the strength of the specimen

varies proportionately and at higher rate of loading, the compressive strength increases.

However, at lower rate of loading, the reduction in strength of concrete cube compared to its

true strength is insignificant as per Mali et al. (2015).

2.3.8 Age of test specimen

The relationship between strength and porosity is an indicator to extent which the hydration

process is completed and the amount of hydration products present. Different cements require

different lengths of time to achieve a particular strength and the rate of hydration is different

for different types of cement (Neville 1996).

The water-cement ratio influences the rate of the hydration process and consequently the rate

of strength gain in concrete. Meyer (1963) found that when low water-cement ratios are

considered there is a rapid gain in early strength as compared to higher water-cement ratios.

He also found that the rate of strength gain at lower water-cement ratio decreased at later ages

as compared to higher water-cement ratios. Meyer (1963) also showed that the strength of

concrete increases with an increase in the age of concrete.

14

2.4 Correlation between cylinder and cube strength

In general, the factors that may affect the correlation between specimens are: strength level,

age of specimen, aggregate size, capping method, mold material, consolidation method and

curing condition (Vandegrift and Schindler, 2006).

2.4.1 Strength Level

According to Yakalli & Reddy (2015), the value of the ratio of cylinder/cube strength

increases with the increase of strength of concrete. The conclusion can also be drawn from

L’Hermite’s equation that may be used to convert strengths between cylinder and cube

strength. L’Hermite’s equation is written as below:

= 0.76 + 0.2 log10 ( ------------------------ (2.1)

Here, strength is expressed as psi unit.

From the above equation, it is evident that when cube strength increases the ratio

also increases. Units of cube strength and cylinder strength are in psi.

2.4.2 Age of specimen

The relationship between strength and porosity is an indicator to extent which the hydration

process is completed and the amount of hydration products present. Different cements require

different lengths of time to achieve a particular strength and the rate of hydration is different

for different types of cement (Neville 1996). The water-cement ratio influences the rate of the

hydration process and consequently the rate of strength gain. Meyer (1963) found that when

low water-cement ratios are considered there is a rapid gain in early strength as compared to

higher water-cement ratios. He also found that the rate of strength gain at lower water-cement

ratio decreased at later ages as compared to higher water cement ratios. Meyer (1963) also

showed that the strength of concrete increases with an increase in the age of concrete.

15

2.4.3 Aggregate size

According to Sim et al. (2013), the influence of maximum aggregate size on the size effect is

dependent on concrete type. The values of conversion factor for normal weight concrete

slightly increase with the increase of maximum aggregate size. For normal weight concrete,

as maximum aggregate size increased from 8mm to 19mm, the average values of conversion

factor increased by 5.8% in specimen with lateral dimension of 50 mm and by 6.8% in

specimen with lateral dimension of 400 mm.

2.4.4 Curing condition

It has been shown that variation from standard methods of curing conditions can affect the

compressive strength of cylindrical concrete specimens. This is expected as humidity less

than 100% will cause moisture loss from the cylinders and the rate of moisture loss will be

different for cylinders of different sizes (Vandegrift and Schindler, 2006).

2.4.5 Capping method

A study done by Glover and Stallings (2000) at Auburn University found that compressive

strengths from 4 × 8 in. cylinders with neoprene caps were 9.6 % greater than strengths from

sulfur-capped 4 × 8 in. cylinders. It was also found that for 6 × 12 in. cylinders, compressive

strengths from cylinders with neoprene caps were greater by 4.6% than that of strengths from

sulfur-capped cylinders.

2.4.6 Consolidation method

When 6 × 12 in. cylinders compacted with two equal layers and 25 roddings per layer are

compared to 3 × 6 in. cylinders with two equal layers and decreasing number of roddings per

layer, the strength ratio of 3×6 in. cylinder to 6×12 in. cylinder decreases with decreasing

number of roddings per layer for the 3 × 6 in. cylinder (Nassar and Al-Manaseer, 1987).

In the literature review, factors affecting the compressive strength as well as the factors

affecting the correlation between the strengths of test specimens have been discussed. Since

16

the smaller specimen size provides ease in transportation and construction, it is gaining

popularity and is widely used.

The factors that affect the compressive strength as well as the strength ratio are aggregate

size, strength level, and age of specimen. Age of specimen, strength level, and aggregate size

were the three factors that were shown to have the greatest affect on the strength ratio. There

are factors such as compaction, curing conditions, rate of loading etc that can be varied and

will also affect the strength ratio. However, varying these factors will violate AASHTO and

ASTM standards (Vandegrift and Schindler, 2006).

2.5 Correlation between UPV and Compressive strength

UPV (Ultrasound Pulse Velocity) is a nondestructive test done on concrete

specimens/structures. The Non Destructive Testing (NDT) of concrete has a great technical

and useful importance. These techniques have been grown during recent years especially in

the case of construction quality assessment. The main advantage of non-destructive testing

method is to avoid the concrete damage or the performance of building structural

components. Additionally, their usage is simple and quick. Test results are available on the

site and the possibility of concrete testing in structures is demanding in which the cores

cannot be drilled and the use of less expensive equipments.

Recently in Bangladesh, after the collapse of a garments factory that killed more than 3000

workers, it becomes an important task to the civil engineers to assess the safety of the

existing structures. For safety assessment, evaluation of compressive strength of concrete is

an important requirement. Determination of compressive strength by cutting core is not an

easy method. Also, cutting cores from columns may hamper the load carrying capacity of the

columns. On the other hand, UPV through concrete can be evaluated easily for different

structural elements (Mohammed & Rahman, 2016).

The UPV equipment (e.g. PUNDIT) includes a transducer, a receiver and an indicator for

showing the time of travel from the transducer to the receiver (Figure 2.5) (Pundit manual

1998). Ultrasonic pulse uses fast potential changes to create vibration that leads to its basic

frequency. The transducer is firmly attached to concrete surface to vibrate the concrete. The

17

pulses go through the concrete and reach the receiver (ASTM, 2002). The pulse velocity can

be determined from the following equation:

Figure 2.5. Pulse velocity testing equipment. V=L/T ---------------------------------------------------------------------------(2.2)

where V = pulse velocity (km/s), L = path length (cm), T = transit time (μs).

Based on this technique, the velocity of sound in a concrete is related to the concrete modulus

of elasticity:

V = --------------------------------------------------------------------------(2.3)

Where, E = modulus of elasticity, ρ=density of the concrete.

The transducer detects the pulses which reach first and it is usually the leading edge of the

longitudinal vibration. The positions of pulse velocity measurements are categorized in, a:

Opposite faces (direct transmission), b: Adjacent faces (semi-direct transmission) or c: Same

face (indirect or surface transmission) which are shown in Figure 2.6. In this study, the direct

method is used for test specimens.

Figure 2.6. Direct (a), Semi-direct (b) Indirect (surface) transmission (c).

18

A number of studies have been conducted by various authors to correlate UPV and

compressive strength. According to ASTM C597-02, when circumstances permit, a velocity-

strength (or velocity modulus) relationship may be established by the determination of pulse

velocity and compressive strength (or modulus of elasticity) on a number of samples of a

concrete. This relationship may serve as a basis for the estimation of strength (or modulus of

elasticity) by further pulse-velocity tests on that concrete. The accuracy of the measurement

depends upon the ability of the operator to determine precisely the distance between the

transducers and of the equipment to measure precisely the pulse transit time. The received

signal strength and measured transit time are affected by the coupling of the transducers to

the concrete surfaces. Sufficient coupling agent and pressure must be applied to the

transducers to ensure stable transit times. The strength of the received signal is also affected

by the travel path length and by the presence and degree of cracking or deterioration in the

concrete tested.

According to Abo-Qudais (2005), the UPV on test specimen depends on aggregate size

distribution (maximum size of coarse aggregate), water-cement ratio and curing time. The

ultrasonic wave velocity in concrete decrease as the size of used coarse aggregate increase.

This effect is more significant in concrete with higher water–cement ratio. Ultrasound wave

velocity increases with curing time. However, the curing time effect is more significant at

higher water–cement ratios. The concrete strength increases as the size of used aggregate

decreases. This effect is more significant at short age and low water–cement ratio.

According to Al-Nu’man et al. (2015), coarse aggregate contend is a parameter which defines

the relationship between compressive strength and UPV. The equations developed by to Al-

Nu’man et al. (2015) are valid for 18 to 55 MPa concrete with various coarse aggregate

content. They developed the following equations to predict compressive strength of concrete.

fcu = 8.88 e (0.42v) for CA = 1000 kg/m3--------------------------(2.4) fcu = 0.06 e(1.60 v) for CA = 1200 kg/m3 ------------------------- (2.5) fcu = 1.03 e (0.87 v) for CA = 1300 kg/m3 ------------------------ (2.6) fcu = 1.39 e (0.78 v) for CA = 1400 kg/m3 ------------------------ (2.7)

Mohammed & Rahman(2016) carried out an experimental investigation to understand the

variation of ultrasonic pulse velocity (UPV) in concrete with the types of coarse aggregate

19

and sand-to-aggregate volume ratio (s/a). The types of aggregate investigated were brick

chips, crushed stone, round shaped stone and black stone. Sand-to-aggregate ratios were 0.36,

0.40, and 0.44 and W/C ratios were 0.45, 0.50, and 0.55. Concrete specimens were made and

tested for UPV, compressive strength, and modulus of elasticity. They found that UPV in

concrete is significantly influenced by the types of aggregate and s/a ratio in addition to the

compressive strength of concrete. UPV in concrete is reduced with the increase of s/a ratio.

They proposed relationships between UPV and compressive strength, and UPV and modulus

of elasticity for different aggregates and s/a ratio investigated. For sand- to- aggregate ratio of

0.4 the following equation has been developed by the author:

f'c = 1.2003 e(0.000680 UPV) -------------------------------------------------(2.8)

EC = A* e(B*UPV*UPV)---------------------------------------------------------(2.9)

For equation, A & B are coefficient of exponential equation. EC and f'c are modulus of

elasticity and compressive strength in MPa. UPV is Ultrasound Pulse Velocity in m/s.

From the above discussion, it is apparent that UPV in concrete is dependent upon many

factors such as maximum size and type of aggregate, sand-to-aggregate ratio, water cement

ration, curing condition, age of specimen and strength of test specimen. So, no unique

relationship can be developed for all type of concrete mix. However, only varying strength of

concrete keeping other parameter constant, one may develop reliable equation to convert

between UPV and compressive strength.

2.6 Summary and discussion

Size and/or shape effect on compressive strength of concrete has been studied by many

authors; however no unique relationship has been obtained. Their relationship is modified by

many factors such as, strength level, age of specimen, aggregate size, curing condition,

capping method and consolidation method. As already discussed, their relationship is also

modified by wall effect. L’Hermite equation is sometime used to convert compressive

strength between standard cylinder and cube but their applicability in the case of concrete as

produced in Bangladesh needs to be evaluated.

At present there is no major study to convert strength between cylinder and cube in

Bangladesh. Although there are many studies carried out by various authors in different

countries and they did not find any specific relationship for various shapes and sizes. The

results of other authors may not be used in the context of materials as used in our country.

20

Chapter 3

EXPERIMENTAL WORK

3.1 Introduction

The main goal of this study is to figure out the conversion factor between 6×12 in. (150×300

mm) cylinder and 4×8 in. (100×200 mm) cylinder; 6 in. (300 mm) cube and 4 in. (100 mm)

cube; and 6×12 in. cylinder and 6 in. cube. During the experimental study, six mix designs

with concrete target strength ranging from 7 MPa to 41 MPa were prepared and casted in

various shapes/sizes mold. A total of 54 nos. specimen (15 nos. 6×12 in. cylinder; 15 nos.

4×8 in. cylinder; 12 nos. 6 in. cube and 12 nos. 4 in. cube) were prepared for each concrete

mix i.e., total 324 nos. test specimen were prepared for six different strength of concrete. The

specimens were then cured under water in a water tank according to ASTM C 192/C 192M-

02 standard and tested for compressive strength at 7, 14 and 28 days as per ASTM C 39/C

39M standard. The following tests were also done as per relevant testing standard:

1. Slump test as per ASTM C143/C 143M-03.

2. Harden density at 7, 14 and 28 days as per ASTM 127.

3. Ultrasound Pulse Velocity (UPV) at 7, 14 and 28 days as per ASTM C 597-02.

4. Splitting tensile strength test on cylinders at 28 days as per ASTM C 496/C 496M-04.

5. Stress- diagram and static modulus of elasticity at 28 days as per ASTM C 469-02.

For casting concrete specimens, BDS EN 197-1:2003 type II (CEM II/B-M(S-V-L)) cement

of class 42.5 N was used. Stone chips obtained from boulder (from Bholagonj ) crushing as

coarse aggregate and Sylhet sand as fine aggregate and potable water were utilized for each

concrete mix.

Before beginning of casting, the following tests on both the fine and coarse aggregates were

done as per relevant testing standard:

1. Aggregate crushing value as per BS 812 (part 3) 1975.

2. Flakiness index as per BS812; Part1.

3. Sieve analysis as per ASTM C 136.

4. Bulk specific gravity (OD basis) as per ASTM C 127.

5. Apparent specific gravity (OD basis) as per ASTM C 127.

6. Absorption Capacity as per ASTM C 127.

21

7. Dry rodded unit weight as per ASTM C 29.

8. Moisture content as per ASTM C 566-13.

It is mentioned here that initially it was planned to prepare 04 (four) concrete mixes and

materials were procured considering the quantity required for those mix design. However,

later it was extended to 06 (six) concrete mixes, so materials were procured 2nd time.

Adequate care was taken and materials were procured from same source. Therefore, in the 1st

phase of experimental work, target concrete strength ranges from 2000 psi to 5000 psi are

prepared. In the 2nd phase of testing, concrete target strength of 1000 psi and 6000 psi are

casted considering the procured material at the 2nd time.

3.2 Sieve analysis and aggregate properties

Sieve analysis was carried out as per ASTM C 136. This is used primarily to determine the

grading of materials proposed for use as aggregates. The results are used to determine

compliance of the particle size distribution with applicable specification requirements and to

provide necessary data for control of the production of various aggregate products and

mixtures containing aggregates. The results of sieve analysis for coarse aggregate are shown

in the table 3.1 below:

Table 3.1 Sieve analysis of stone chips procured at 1st phase

Sieve Material Percent of Cumulative Percent Fineness Modulus

Size Retained Material Retained % Retained Finer

mm gm % % % 50 0.0 0 0 100

37.5 0.0 0 0 100

25.4 394.0 4 4 96

19.05 5507.0 55 59 41

12.5 3509.0 35 94 6

9.5 444.0 4 98 2 7.41 (Seven Point Four One) 6.3 32.0 0 98 2

4.75 7.0 0 98 2

2.36 0.0 0 98 2

1.18 0.0 0 98 2

0.6 0.0 0 98 2

0.3 0.0 0 98 2

0.15 0.0 0 98 2

0.075 0.0 0 98 2

Pan 107.0 1 99

Total 10000.0

22

Figure 3.1 shows the ASTM gradation limit (upper and lower limit) sample gradation curve

to understand whether the gradation curve of used materials in concrete mixes falls within the

limit as designated by ASTM C 136.

Figure 3.1 ASTM C 33 gradation chart and sample gradation curve(stone chips-1st phase).

It is evident from the above figure that the material gradation chart fall marginally within the

ASTM upper and lower limit. The fineness modulus was calculated using ASTM C 136.

Table 3.2 shows the result of sieve analysis of sylhet sand which has been used fine aggregate

in the concrete mix.

Table 3.2 Sieve analysis of Sylhet sand procured at 1st phase

Sieve Material Percent of Cumulative Percent Fineness Size Retained Material Retained % Retained Finer Modulus mm gm % % % 12.5 0.00 0 0 100 9.5 0.00 0 0 100 6.3 0.00 0 0 100 4.75 0.00 0 0 100 2.93

(Two point nine three)

2.36 35.40 7 7 93 1.18 128.20 26 33 67 0.6 171.50 34 67 33 0.3 104.70 21 88 12 0.15 49.60 10 98 2

0.075 7.60 2 100 0 Pan 3.00

Total 500.0 100

0

10

20

30

40

50

60

70

80

90

100

1 10 100

Pe

rce

nt

fin

er

Sieve size (mm)

Gradation Curve

ASTM Upper Limit

ASTM Lower Limit

23

Figure 3.2 ASTM C 33 gradation chart and sample gradation curve(sand-1st phase)

It is observed from the above figure that gradation curve for Sylhet sand falls within the

gradation curve defined by ASTM upper and lower limit. The fineness modulus was

calculated using ASTM C 136.

Sieve analysis was also done for the materials used in the 2nd phase of experimental work.

Table 3.3 Sieve analysis of stone chips procured at 2nd phase

Sieve Size

Material Retained

Percent of Material Retained

Cumulative % Retained

Percent Finer

Remarks

mm gm % % % 50 0.0 0 0 100

37.5 0.0 0 0 100

25.4 0.0 0 0 100

19.05 5957.0 60 60 40

12.5 3601.0 36 96 4

7.60 (Seven point six zero)

9.5 384.0 4 100 0 6.3 46.0 0 100 0 4.75 0.0 0 100 0 2.36 0.0 0 100 0 1.18 0.0 0 100 0

0.6 0.0 0 100 0

0.3 0.0 0 100 0

0.15 0.0 0 100 0

0.075 0.0 0 100 0

Pan 12.0 0 100

Total 10000.0

0

10

20

30

40

50

60

70

80

90

100

0.01 0.1 1 10

Pe

rce

nt

fin

er

Seive Size (mm)

Gradation curve

ASTM upper limit

ASTM lower limit

24

Figure 3.3 ASTM C 33 gradation chart and sample gradation curve(stone chips-2nd phase).

Table 3.3 shows the result of sieve analysis of stone chips and figure 3.3 shows the gradation

chart compared to the sample used in the current study. It is shown from the figure that the

coarse material gradation chart fall marginally within the ASTM upper and lower limit. The

fineness modulus was calculated using ASTM C 136. Table 3.4 below shows the result of

sieve analysis of sylhet sand.

Table 3.4 Sieve analysis of Sylhet sand procured at 2nd phase

Sieve Material Percent of Cumulative Percent Fineness

Size Retained Material Retained % Retained Finer Modulus

mm gm % % % 12.5 0.00 0 0 100 9.5 0.00 0 0 100 6.3 0.00 0 0 100 4.75 0.00 0 0 100 2.36 20.60 4 4 96 1.18 68.70 14 18 82 2.50 0.6 148.20 30 48 52 (Two point

five zero ) 0.3 174.00 35 83 17 0.15 72.30 14 97 3

0.075 12.90 3 100 0 Pan 3.30 0.7

Total 500.0

0

10

20

30

40

50

60

70

80

90

100

1 10 100

Pe

rcn

t Fi

ne

r

Particle size (mm)

gradation curve

ASTM lower limit

ASTM upper limitr

25

Figure 3.4 ASTM C 33 gradation chart and sample gradation curve(sand-2nd phase).

It is evident from the above figure that gradation curve for Sylhet sand falls within the

gradation curve defined by ASTM upper and lower limit. Tables 3.5 and 3.6 summarized and

provided the comparison of the test results for different aggregate properties used in 1st and

2nd phase of experimental works.

Table 3.5 Comparison of different properties of Sylhet sand used at 1st and 2nd phases of

testing

Sl.

No

Test Name 1st phase 2nd phase

01 Fineness modulus 2.93 2.50

02 Bulk Specific Gravity(OD basis) 2.55 2.55

03 Apparent Specific Gravity (OD) 2.59 2.58

04 Absorption Capacity 1.56% 1.09%

05 Dry Rodded Unit Weight 1560 kg/m3 1590 kg/m3

06 Moisture Content 4.56 % 2.90%

0

10

20

30

40

50

60

70

80

90

100

0.01 0.1 1 10 100

Pe

rce

nt

Fin

er

Particle Size (mm)

Gradation chart

ASTM lower limit

ASTM upper limit

26

Table 3.6 Comparison of different properties of stone chips used at 1st and 2nd phases of

testing

Sl.

No

Test Name 1st phase 2nd phase

01 Fineness modulus 7.41 7.60

02 Bulk Specific Gravity(OD basis) 2.63 2.64

03 Apparent Specific Gravity (OD) 2.65 2.65

04 Absorption Capacity 0.59% 0.46%

05 Dry Rodded Unit Weight 1540 kg/m3 1530 kg/m3

06 Moisture Content 0.60 % 0.14%

07 Aggregate Crushing Value 18% 20%

08 Flakiness Index 11% 13%

3.3 Mix design

Six different concrete strength were considered in the present study. The mix designs were

decided to be different in cement content and water/cement ratio. Table 3.7 shows the

quantity of material used in each of six mix designs. It is observed from the table that

quantity of fine and coarse aggregate was kept almost constant and the variable were water-

cement ratio and cement content. It is also considered 2% air content in all mixes.

Table 3.7 Quantity of materials for different concrete mixes

Mix Target strength (psi)

Cement (kg/m³)

Water (kg/m³) Fine aggregates (kg/m³)

Coarse aggregate (kg/m³)

Mix-1 1000 198 182 796 1186 Mix-2 2000 271 190 753 1130 Mix-3 3000 356 178 734 1102 Mix-4 4000 405 178 717 1075 Mix-5 5000 445 178 727 1090 Mix-6 6000 494 178 689 1034

27

Water to cement ratio of different concrete mixes used as 0.92, 0.70, 0.50, 0.43, 0.40 and

0.36, respectively for mix 1 to 6. A concrete volume of 0.184 m3 was casted for each mix to

get 54 test samples. On a fresh concrete for each mix design, a slump test as a measure of

workability of concrete was done. On a hardened concrete, compressive strength tests at 7,

14, and 28 days and splitting tensile strength test at 28 days were performed. Also, a non-

destructive test such as ultrasonic pulse velocity (UPV) was carried out. Stress-strain diagram

of concrete specimen at 28 days was plotted for each concrete mix and a static modulus of

elasticity was determined for each strength level.

3.4 Material used in the present study

3.4.1 Cement

Portland composite cement widely known as PCC is used in the present study. This cement

complies with technical specification as per BDS EN 197-1:2003, CEM II/B-M (S-V-L), 42.5

N and ASTM C595. According to data provided by the cement manufacturer, the

composition of ingredients of cement used in the present such as Clinker : 65-79%; Slag, Fly

ash & Limestone : 21-35% and Gypsum : 0-5% as per version of the manufacturer.

3.4.2 Aggregate

Coarse aggregate: Natural stone chips were used as coarse aggregate. The stone chips were

obtained by crushing of boulder shipped from Bholagonj. Figures 3.5 and 3.6 show the

aggregates used in the present study.

Fine Aggregate: Natural Sylhet sand was used as fine aggregate.

Figure 3.5 Natural Sylhet Sand Figure 3.6 Natural stone chips

28

3.4.3 Water

Tap water was used for casting all specimens (BS5328: Part 1, 2000).

3.5 Methodology

Six different concrete mixes were designed according to ACI mix design for normal strength

concrete. Considering the aggregate properties and following the method of weight batching,

06 (six) mixes were designed, casted in various shapes and sizes mold.

3.5.1 Casting of concrete

The process of batching, weighting and mixing of necessary materials were performed

according to ASTM standards. By using a concrete mixer machine, first coarse and fine

aggregate were mixed for about two minutes. After that cement was mixed and then water

was added to the blended materials and mixed for approximately 3 minutes. When a test on

fresh concrete (i.e. slump test) had to be performed, necessary sample was taken from fresh

concrete, test was executed and then, the utilized amount of concrete was poured back to the

source, blended once again to make homogeneous mix and then concrete was poured into the

moulds (ASTM C 192/C 192M-02). Due to limitation of mixing machine capacity, half of the

materials were mixed first time and then remaining half of the materials was mixed. Both the

mixes were poured back into the mixing machine again and mixed for 3 minutes. To get

uniform mix, machine-mix concrete was poured on clean, damp platform and remix by

trowel until it appears to be uniform. Figure 3.7 shows the mixing of concrete ingredients.

3.5.2 Compacting and curing

Preparation of satisfactory specimens requires different method of consolidation. The

methods of consolidation are rodding, and internal or external vibration. The selection

method is based on slump of fresh concrete. Rodding or vibration is done when slump of

concrete is greater than or equal to 1 in. Vibration is used when slump of fresh concrete is

less than 1 in.. In this research work, internal vibration was used to consolidate concrete.

4×8 in. cylinders were consolidated in two layers while 6×12 in. cylinders were consolidated

in three layers. For 6 in. cube and 4 in. cube vibration was done in two layers. The insertions

were distributed uniformly in each layer. The vibrator was allowed to penetrate 1 in. in each

layer. After each layer is vibrated, outside of the mold was tapped at least 10 times with the

mallet to close the holes that remain and to release the entrapped air voids (ASTM C 192/C

29

192M-02). Figure 3.7 shows the mixing and 3.8 shows the placement and compaction of

concrete in a cylindrical mould.

Figure 3.7 Mixing of concrete ingredients

The objective of curing at normal temperature is to keep concrete saturated, or nearly

saturated as possible, until the water-filled space in the fresh concrete paste has been

occupied to the desired extent by the products of hydration of cement. The necessity of curing

arises from the fact that hydration of cement can take place only in water filled capillaries.

This is why loss of water by evaporation from the capillaries must be prevented. Adequate

care was taken after casting of concrete into the mold to prevent moisture loss. After being

kept for approximately 24 hours into the molds, the specimens were taken to water tank kept

there until their testing age (ASTM C 192/C 192M-02).

30

Figure 3.8 Placing and compacting of concrete.

3.6 Test on fresh concrete

3.6.1 Workability test

The only test, performed on fresh concrete mixes, was slump test. The experiments were

performed according to ASTM C 143/C 143M-03. In this test, a sample of freshly mixed

concrete is placed and compacted by rodding in a mold shaped frustum of a cone. The mold

is raised, and the concrete allowed subsiding. The vertical distance between the original and

displaced position of the center of the top surface of the concrete is measured and reported as

slump of the concrete. Figure 3.9 shows typical slump test on a fresh concrete.

3.7 Test on hardened concrete

A total of five tests has been conducted to evaluate the hardened properties of concrete for

each concrete mix. Concrete compressive strength, splitting tensile strength, UPV, density

and stress-strain diagram with static modulus of elasticity are determined for each strength.

Details of the test are provided in the next sub-sections.

31

Figure 3.9 Slump test on a fresh concrete

3.7.1 Compressive strength test

In this research, as concrete specimens were chosen from different sizes and shapes, for

executing compressive strength test, different standards were followed. For measurement of

compressive strength of cubes, BS EN 12390-3:2009 was used. Compressive strength test of

cylindrical specimens were carried out according to ASTM C39/C39M– 01. Testing cylinders

in compressive strength has an additional stage of capping. Various types of capping such as

sulphur capping, neoprene rubber pad etc. are widely used around the world. In the present

study, neoprene rubber pad is used as a capping of the tested specimens as typically is shown

in Figure 3.10.

The load was applied at a rate of movement (platen to crosshead measurement)

corresponding to a loading rate on the specimen within the range of 20 to 50 psi/s [0.15 to

0.35 MPa/s]. The designated rate of movement was maintained at least during the latter half

of the anticipated loading phase of the testing cycle. During the application of the first half of

the anticipated loading phase a higher rate of loading was allowed. No adjustment in the rate

of movement of the platen was made at any time while the specimen is yielding rapidly

immediately before failure. The load was applied until the specimen fails, and the maximum

load carried by the specimen was recorded during the test. Type of failure and the appearance

32

of the concrete were noted. Figure 3.11 shows the test set up for determining compressive

strength of concrete.

Figure 3.10 Top and bottom capping of 4×8 in. cylinder

Figure 3.11 Testing Machine and test set up.

3.7.2 Splitting Tensile strength test

Splitting tensile test was also carried out on both the small and large size cylinders at the age

of 28 days. Specimens were properly placed into the machine to be tested. The following

equation was used to calculate splitting tensile strength of concrete specimen:

T = ---------------------------------------------------------------- (3.1)

33

Where,

T = Splitting tensile strength, psi.

P = Maximum applied load indicated by the testing machine, lbf.

l = Length, in..

d = Diameter, in..

The splitting tensile strength test was carried out according to ASTM C 496/C 496M-04.

Figure 3.12 shows the typical tensile strength test up.

Figure 3.12 Typical Splitting tensile strength test set up.

3.7.3 Concrete density

Determination of hardened density was done according to ASTM C 138/C 138M–01a. For a

cylindrical specimen, diameter was measured two times at right angles and average was taken

for calculation. Also length was measured two times and average was taken for calculation.

Volume was then determined. In case of cubic specimen, three dimensions were measured

and volume was then determined. The weight of the tested specimen is measured and the

density of the hardened concrete is determined from the measured volume and weight data.

34

3.7.4 Ultrasound pulse velocity test (UPV)

This test was done following the standard ASTM C 597-02. Ultrasonic pulse velocity test is

one of the non-destructive experiments carried out to assess the uniformity and relative

quality of concrete, to indicate the presence of voids and cracks, and to evaluate the

effectiveness of crack repairs. It is also applicable to indicate changes in the properties of

concrete, and in the survey structures, to estimate the severity of deterioration or cracking.

When circumstances permit (in this research), a velocity-strength relationship may be

established by the determination of pulse velocity and compressive strength on a number of

samples of a concrete. This relationship may serve as a basis for the estimation of strength by

further pulse-velocity test on that concrete (ASTM C 597-02).

Pulses of longitudinal stress waves are generated by an electro-acoustical transducer that is

held in contact with one surface of the concrete under test. After traversing through the

concrete, the pulses are received and converted into electrical energy by a second transducer

located a distance L from the transmitting transducer. The transit time T is measured

electronically. The pulse velocity V is calculated by dividing L by T. Sometimes length of

the specimen can be given as input in the UPV machine, and in this case velocity can be

directly obtained (ASTM C 597-02).

Appropriate coupling agent (ultrasound gel) was used to the transducer faces. The transducers

were then firmly placed against the surfaces of concrete test specimen to get the stable transit

time in micro seconds. Length of the specimen was assigned as input in the UPV machine

and velocity was obtained directly from machine readings. Figure 3.13 presents the typical

arrangements for UPV tests for concrete.

35

Figure 3.13 Ultrasound Pulse Velocity test

3.7.5 Stress-strain diagram and static modulus of elasticity

For each concrete strength, 3 cylinders (4×8 in.) were casted for determining stress-strain

diagram of concrete. For calculating stress-strain diagram, dial gauge of 1 micro meter

precision was used. From the stress-strain diagram, static modulus of elasticity of concrete

was determined in accordance with ASTM C 469-2. Figure 3.14 shows the typical test set up

for determining stress-strain diagram in the elastic range. The following equation as

suggested in ASTM C 469-02 was used for calculating static modulus of elasticity:

E = (S2 – S1) / (ɛ 2 - 0.000050) ----------------------------------------------------------(3.2)

Where,

E= Chord modulus of elasticity.

S2 = Stress corresponding to 40% of ultimate load.

S1 = Stress corresponding to a longitudinal strain, ɛ 1, of 50 millionths, psi and ɛ 2 = Longitudinal strain produced by stress S2.

36

Figure 3.14 Typical test up with dial gauge for determining modulus of elasticity

3.8 Summary

A total of 324 nos. samples (90 nos. 6×12 in. cylinders; 90 nos. 4×8 in. cylinder; 72 nos. 6 in.

cube and 72 nos. 4 in. cube) have been prepared and tested for unit weight, compressive

strength, splitting tensile strength, static modulus of elasticity and UPV to study the effect of

size and shape of test specimens. During the experimental study, 06(six) strength levels (mix

design) i.e., 1000 psi to 6000 psi were obtained by mostly varying water-cement ratio, and

other parameters such as maximum size of coarse aggregate, properties of fine and coarse

aggregate and their quantity and air content (2 percent considered) were almost kept the

same. Parameters like curing condition, capping method and consolidation method and

testing method were controlled as per relevant standards (ASTM and BS) for the entire test

program.

37

Chapter 4

RESULTS AND DISCUSSION

4.1 Introduction

The experiments conducted were briefly explained in the previous chapter. In this chapter,

the outcomes of those mentioned experiments will be shown; graphs and findings from

analyses will be presented, followed by discussions about each of the results.

The experiments carried out were slump test (for fresh concrete), hardened density, ultrasonic

pulse velocity test (PUNDIT) which is a non-destructive test on hardened concrete,

compressive strength, splitting tensile strength test (destructive tests on hardened concrete)

and finally stress-strain diagram of concrete. For each test, results will be presented and

discussed.

4.2 Test on fresh concrete

For each mix design, slump test was performed as workability measure of fresh concrete. The

results are presented in Table 4.1 below.

Table 4.1 Slump test results of different concrete mixes

Mix Design Specified Strength, MPa(psi) Slump, mm(in.)

mix-1 7(1000) 150(6.0)

mix-2 14(2000) 100(4.0)

mix-3 21(3000) 69(2.75)

mix-4 28(4000) 37(1.5)

mix-5 34(5000) 30(1.2)

mix-6 41(6000) 12(0.5)

Specimens with different concrete strength were prepared by mostly varying water-cement

ratio and cement content keeping the water content almost the same. As no chemical

admixture was used in any concrete mix, lower range of water-cement ratio such as mix -6

results higher strength but with lower slump value. On the other hand, the water-cement ratio

was highest for concrete mix-1 and strength obtained was the lowest for the said mix. The

38

gradual low slump is indicative of using lower water-cement ratio of subsequent mixes. The

experiment was performed as per ASTM C 143/C 143M.

4.3 Experiments on hardened concrete (non-destructive)

Hardened properties of concrete such as unit weight and Ultrasound Pulse Velocity (UPV)

through concrete specimen were determined following relevant codes.

4.3.1 Hardened unit weight of concrete

On each concrete strength, hardened concrete unit weight test was performed according to

ASTM C 138. Table 4.2 shows the average hardened density for each experiment’s condition.

Table 4.2 Unit weight of different concrete mixes

Specified

Strength(MPa)

Unit Weight (kg/m3 ) Average unit

weight

(kg/m3) 6×12 in.

(150×300

mm)

4×8 in.

(100×200

mm)

6 in.

cube(150

mm)

4 in.

cube(100mm)

7 2395 2382 2348 2340 2366

14 2371 2357 2335 2332 2348

21 2399 2395 2382 2357 2383

28 2390 2409 2363 2299 2365

34 2387 2343 2365 2314 2352

41 2414 2429 2384 2422 2412

Average 2392 2385 2362 2344

It is shown from Table 4.2 that unit weight of cylindrical specimens is comparatively higher

than that of cube specimen. Also, larger cylinders have higher unit weight than smaller

cylinders. This is due to the fact that three layer of compaction was done for 6×12 in.

cylinders compared to 4×8 in. cylinders in which two layer of compaction was done. Except

few exceptions, the unit weight of cylindrical specimen is higher for each mix design as well

compared to cube specimens.

39

4.3.2 Ultrasound Pulse Velocity (UPV)

Ultrasound Pulse Velocity (UPV) test was performed on each test specimen at 7, 14 and 28

days as per ASTM 597-02. The results are summarized in Table 4.3 and Table 4.4 below for

28-days as most design specification refers to the compressive strength of concrete at 28-

days. UPV vs. splitting tensile strength is summarized at Table 4.5. For sand to aggregate

ratio of 0.4 (0.4 is used in present study) the following equation has been developed by

Mohammed & Rahman (2016) for 4×8 in. cylinder. The applicability of the eq(4.1) is

evaluated in the Table 4.3 below.

f'c = 1.2003 e(0.000680 UPV) -------------------------------------------------(4.1)

where, f'c and UPV are in MPa and m/s respectively.

Table 4.3 Ultrasound Pulse Velocity (m/s) and compressive strength (MPa) of cylinders

Specified

Strength(MPa)

Strength

obtained

(MPa)

6×12 in. cylinder 4×8 in. cylinder

Strength (MPa)

UPV (m/s)

Strength (MPa)

UPV (m/s)

1.2003 e(0.000680

UPV) 7 7.1 7.1 4236 9 4336 22.8

14 11.9 11.9 4292 13 4328 22.8

21 19.3 19.3 4699 19.5 4328 22.8

28 31.2 31.2 4611 35.5 4723 29.8

34 34.3 34.3 4657 38.5 4812 31.6 41 49 49 4712 56 4964 35.1

Table 4.4 Ultrasound Pulse Velocity (m/s) and compressive strength (MPa) of cubes

Specified

Strength(MPa)

Strength

obtained (MPa)

6 in. cube 4 in. cube

Strength (MPa)

UPV (m/s) Strength (MPa)

UPV (m/s)

7 7.1 11.5 4460 12 4426

14 11.9 17.5 4467 18.5 4457

21 19.3 28 4699 26.5 4903

28 31.2 39 4786 45.1 4822

34 34.3 41.5 4736 45.5 4903

41 49 53 4925 55 5230

40

Figure 4.1 Compressive Strength vs. UPV (6×12 in. Cylinder)

Different trends can be seen among different size and shape of test specimens as evident from

Figures 4.1 to 4.4. This difference can be related to size/shape effect, according to which,

different compressive strengths are resulted from different size/shape specimens. Also

coefficient determinations are different for different size/shape specimens. The coefficients of

determination are found as low as 0.64 for 6×12 in. cylinder to as high as 0.94 for 6 in. cube.

Figure 4.2 Compressive Strength vs. UPV (4×8 in. Cylinder)

R² = 0.6429

0

10

20

30

40

50

60

4000 4500 5000 5500

Co

mp

ress

ive

Str

en

gth

(M

Pa)

Ultrasound Pulae Velocity (m/s)

6x12 inch cylinder

R² = 0.9386

0

10

20

30

40

50

60

4000 4500 5000 5500

Co

mp

ress

ive

Str

en

gth

( M

Pa)

Ultrasound Pulse Velocity (m/s)

4x8 inch cylinder

41

Figure 4.3 Compressive Strength vs. UPV (6 in. Cube)

It is evident from the data summarized in Table 4.3 & and Table 4.4 subsequent Figures 4.1

to 4.4 that for the same strength grade different pulse velocities obtained for different

size/shape samples. This indicates that the pulse velocity is not only affected by the strength

grade of the sample but also the size/shape of the test specimen.

Figure 4.4 Compressive Strength vs. UPV (4 in. Cube)

R² = 0.7875

0

10

20

30

40

50

60

4000 4500 5000 5500

Co

mp

ress

ive

Str

en

gth

( M

Pa)


4 in. cube

R² = 0.9402

0

10

20

30

40

50

60

4000 4500 5000 5500

Co

mp

ress

ive

Str

en

gth

( M

Pa)


6 in. cube

42

Table 4.5 UPV (m/s) and tensile strength (MPa) for different concrete mixes

Specified Strength (MPa)

Strength obtained(MPa)

6×12 in. cylinder 4×8 in. cylinder

UPV(m/s) Tensile Strength(MPa)

UPV(m/s) Tensile Strength(MPa)

7 7.1 4277 1.25 4448 1.5

14 11.9 4204 1.5 4274 1.8

21 19.3 4543 2.2 4660 2.1

28 31.2 4628 2.4 4705 3.1

34 34.3 4603 3.0 4737 3.3

41 49 4755 3.5 4964 3.8

In Table 4.5, UPV and their corresponding tensile strength are shown. In general, with the

increase in tensile strength, the value of UPV increases. Figure 4.5 has been plotted both for

6×12 in. cylinder and 4×8 in. cylinder.

Figure 4.5 Tensile Strength vs. UPV

It is evident from above Figures 4.5 that in general with the increase of tensile strength the

value of UPV increases. The coefficient of determination is found to be 0.861 for 6×12 in.

cylinder and 0.780 for 4×8 in. cylinder.

R² = 0.8614 R² = 0.7805

0

0.5

1

1.5

2

2.5

3

3.5

4

4000 4500 5000 5500

Ten

sile

Str

en

gth

(M

Pa)

UPV (m/s)

6x12 inch cylinder

4x8 inch cylinder

43

4.4 Experiments on hardened concrete (destructive)

Splitting tensile strength and compressive strength tests were performed on concrete

specimens. Relationships have been developed between splitting tensile strength and

compressive strength of concrete and are compared with relevant code equations.

Relationship between compressive strength of various shape and size test specimens were

also developed.

4.4.1 Splitting tensile strength

In this experimental investigation, splitting tensile strength test was performed on both 6×12

in. and 4×8 in. cylindrical samples, cured in water, at the age of 28 days. Outcomes of the

experiment are shown in Table 4.5 and 4.6. The Table has several sections showing tensile

strength according to various mix designs for 6×12 in. and 4×8 in. samples and predicting

model considering the baseline equation of ACI (American Concrete Institute). The ACI

equation for predicting tensile strength of a sample is shown as below:

Tensile Strength = 7.5 x c -----------------------------------------------------------------(4.2)

Where f’c is the compressive strength of concrete sample in psi.

However, it is seen from the Figure 4.6 below that the following equation will provide better

agreement with the tensile strength of concrete samples based on obtained compressive

strength of concrete.

Tensile Strength = 5.79 x c ---------------------------------------------------------------(4.3)

Where f'c is the compressive strength of concrete sample in psi.

44

Figure 4.6 c vs tensile strength.

Table 4.6 Conversion between compressive strength (psi) and splitting tensile strength (psi)

for 6×12 in. cylinder

Specified

Strength

(psi)

Mix 6×12 in. cylinder

UPV Tensile

Strength

Compressive

Strength (f’c ) 5.79 x c 7.5x c

1000 Mix-1 4277 180 1030 185 240

2000 Mix-2 4204 225 1720 240 310

3000 Mix-3 4543 320 2790 305 395

4000 Mix-4 4628 345 4530 390 505

5000 Mix-5 4603 430 4980 408 530

6000 Mix-6 4755 500 7110 488 630

y = 5.7908x R² = 0.9822

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90

Ten

sile

Str

en

gth

(p

si)

√ f'c

Series1

45

Table 4.7 Conversion between compressive strength (psi) and splitting tensile strength (psi)

for 4×8 in. cylinder

Specified

Strength

(psi)

Mix 4×8 in. cylinder

UPV Tensile

Strength(psi)

Compressive

Strength (f’c ) 5.79x c 7.5 x c

1000 Mix-1 4448 210 1280 205 270

2000 Mix-2 4274 260 1880 250 325

3000 Mix-3 4660 310 2870 310 400

4000 Mix-4 4705 445 5150 415 540

5000 Mix-5 4737 475 5500 429 555

6000 Mix-6 4964 562 8160 525 680

It is evident from Table 4.6 and 4.7 that eq.(2) predict more closely the tensile strength of

stone aggregate concrete usually produced/used in construction in our country. The variation

from ACI recommended equation may be due to the fact that various ingredients used to

produce concrete in our country are different than that used in USA.

4.4.2 Compressive strength test

The most extensive experiment was compressive strength test during this study. A total of

three factors were investigated to figure out their influence on the compressive strength. The

factors are three different ages, six different concrete mixes and finally, moulds’ shapes and

sizes. The employed moulds were 2 different cubes (4 in. and 8 in.) and two different

cylinders (4×8 in. and 6×12 in.). Three samples were casted for each batch of testing in order

to minimize scatters and errors in results and analyses.

In addition, three samples (4×8 in.) from each concrete mix, stress-strain curves are plotted

by using Universal Testing Machine and dial gauge.

46

Table 4.8 Compressive strength of cylinder and cube specimens

Specified

strength

(MPa)

W/C Slump

(mm)

Age

(day)

Compressive Strength (MPa) Mode of

Failure at

28 days 6×12 in.

cylinder

4×8 in.

cylinder

6 in.

cube

4 in.

cube

7 0.92 150 7 3.5 5.7 7.2 5.8 Mortar 14 5.8 7.4 8.9 9.3 28 7.1 8.8 11.3 12.1

14 0.70 100 7 8.1 8.4 13.3 11.7 Mortar 14 9.9 10.9 15.4 15.6 28 11.9 12.9 17.5 18.6

21 0.50 69 7 12.7 12.8 16.3 18.9

Combined

14 16.3 17.3 22.1 19.4 28 19.3 19.8 28.2 26.5

28 0.43 37 7 19.8 22.9 27.8 33.3 14 26.4 29.3 33.5 34.5 28 31.2 35.5 39 45.1

34 0.40 30 7 27.5 31.4 33.6 29.8 14 26 30.8 38.4 41.3 28 34.3 38.5 41.5 45.7

41 0.36 12 7 39.9 45 43.8 47.8 14 43 50.6 47.7 52.1 28 49 56.3 53 54.9

A common observation from many experimental works on the size effect in the strength of

concrete is that the specimen of smaller size has the higher compressive strength (Neville,

1966). From the above Table 4.8, it is evident that the smaller size cylinder specimen has

higher compressive strength than that of larger size cylinder, and also the smaller cube has

comparatively higher compressive strength than that of larger cube. It is generally true that

cubes with same lateral dimension or smaller have higher compressive strength than that of

cylinders for the similar mix and lateral dimension, which can also be visualized from above

Table 4.8. In few cases, the results are not in accordance with common observation on the

size effect in the strength of concrete. For example, the bold marks on the strength of small

cube actually have lesser strength than their counterpart i.e. 6 in. cube. This may be attributed

to improper placing /compacting/curing /testing/strength gain with age /wall effect of the said

specimens. Figures 4.7 to 10 show water-cement ratio vs compressive strength of various size

specimens tested at 28-day. From the figures, it is apparent that the compressive strength

47

decrease exponentially with the increase of water cement ratio. From regression analysis, the

coefficients of determination are found to be 0.948, 0.878, 0.974 and 0.946, respectively.

Figure 4.7 Water-cement ratio vs. compressive strength of 6×12 in. cylinder specimens

Figure 4.8 Water- cement ratio vs. compressive strength of 4×8 in. cylinder specimens

R² = 0.948

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)

Water cement ratio (W/C)

6x12 in cylinder

R² = 0.878

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)


4x8 inch cylinder

48

Figure 4.9 Water-cement ratio vs. compressive strength of 6 in. cube specimens

Figure 4.10 Water-cement ratio vs. compressive strength of 4 in. cube specimens

4.4.3 Correlation between strength of cylinders

In our country, design specifications refer to the compressive strength obtained from either

testing 6×12 in. concrete cylinder or 6 in. concrete cube and tested as per relevant standards.

However, 4×8 in. cylinders are almost exclusively used in our country nowadays considering

testing machine capacity, ease of handling, cost of materials etc. Also, ASTM C192 and

R² = 0.974

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)


6 inch cube

R² = 0.946

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)


4 inch cube

49

AASHTO R39 allow the use of 4×8 in. cylinders for quality assurance testing. Therefore, a

correlation between concrete compressive strengths of using cylinders and cube specimens

are necessary. The subsequent tables and figures will illustrate the conversion factors

between 6×12 in. cylinder and 4×8 in. cylinder. The conversion factors will be evaluated

with respect to 6×12 in. cylinder.

Table 4.9 Conversion factors between cylinder specimens

Specified

strength

(MPa)

Age (day) Compressive Strength

(MPa)

Conversion

factors

7-day &

14-day

strength as

percentage

of 28-day

strength

(4×8 in.)

7-day & 14-day strength as percentage of 28-day strength (6×12 in.)

6×12 in.

cylinder

4×8 in.

cylinder

7 7 3.5 5.7 1.60 64.5% 50.2% 14 5.8 7.4 1.28 83.9% 81.8% 28 7.1 8.8 1.25 - -

14 7 8.1 8.4 1.04 64.5% 67.9 14 9.9 10.9 1.10 83.9% 83.6 28 11.9 12.9 1.09 - -

21 7 12.7 12.8 1.01 54.2% 65.8 14 16.3 17.3 1.06 87.4% 84.4 28 19.3 19.8 1.03 - -

28 7 19.8 22.9 1.16 64.6% 63.4 14 26.4 29.3 1.11 82.4% 84.5 28 31.2 35.5 1.14 - -

34 7 27.5 31.4 1.14 81.5% 80.1 14 26 30.8 1.18 80.0% 75.8 28 34.3 38.5 1.12 - -

41 7 39.9 45 1.12 80.0% 81.5 14 43 50.6 1.18 89.8% 87.7 28 49 56.3 1.15 - -

It is useful to determine conversion factor at 28-day as most of the specification indicate 28-

day strength of concrete is specified as design strength and is used for quality assurance

testing. From the above Table 4.9, it is also apparent that the conversion factors do not follow

a specific pattern i.e. the conversion factor is not dependent of age and compressive strength

50

of concrete specimen. If we consider 28-day strength to determine conversion factor, the

average value of conversion factor is 1.13 with a standard deviation and coefficient of

variation are 0.07 and 6.2%, respectively. Another way to say that small size cylinder

strength will be 13% more than that of standard cylinder strength in an average.

It is also interesting to note the strength gain at 7-day and 14-day as a percentage of 28 day

strength. Sometime it is required to predict 28-day strength form early strength data for

acceptance of a batch of concrete. From Table 4.9, it is apparent that up to 31 MPa concrete

7-day strength may be taken as 65% of 28 day strength and 14-day strength may be taken as

85% of 28-day strength. For 31 to 49 MPa, 7-day strength may be taken as 81% of 28 day

strength and 14-day strength may be taken as 87% of 28-day strength.

Figure 4.11 Seven-day strength of standard and small size cylinder specimens

From the above Figure 4.11, it is shown that for larger water-cement ratio, the difference in

strength between the standard and smaller size cylinder strength is comparatively smaller

than that of lower water-cement ratio.

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)


6x12 inch cylinder

4x8 inch cylinder

51

Figure 4.12 Fourteen-day strength of standard and small size cylinder specimens

From the above Figure 4.12, it is observable that for larger water cement ratio, the difference

in strength between standard and small cylinder strength is smaller than that of lower water

cement ratio. Both graphs almost merge at water/cement ratio of 0.5. After that the difference

in strength increases again.

Figure 4.13 Twenty eight-day strength of standard and smaller size cylinder specimens

From the above Figure 4.13, it is observable that for larger water cement ratio, the difference

in strength between standard and small cylinder strength is comparatively smaller than that of

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)


6x12 inch cylinder

4.8 inch cyinder

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)


6x12 inch cylinder

4.8 inch cyinder

52

lower water cement ratio. Both graphs almost merge at water/cement ratio 0.5. After that the

difference in strength increases again.

4.4.4 Correlation between strength of cubes

In our country, design specifications refer to the compressive strength obtained from either

testing 6×12 in. concrete cylinder or 6 in. concrete cube and tested as per relevant standards.

However, 4 in. cubes are sometimes prepared for quality assurance testing. Therefore,

correlations between concrete compressive strengths of using different size cube specimens

are necessary. The subsequent Tables and Figures will illustrate the conversion factors

between 6 in. cube and 4 in. cube. The conversion factors will be evaluated with respect to 6

in. cube.

Table 4.10 Conversion factors between 6 in. and 4 in. cube specimens

Specified

strength

(MPa)

Age (day) Compressive Strength

(psi)

Conversion

factors

7-day &

14-day

strength as

percentage

of 28-day

strength (4

in. cube)

7-day & 14-day strength as percentage of 28-day strength (6 in. cube)

6 in. cube 4 in. cube

7 7 7.2 5.8 0.82 48.1% 63.4% 14 8.9 9.3 1.05 76.6% 78.7% 28 11.3 12.1 1.07 - -

14 7 13.3 11.7 0.88 63.1% 76.2% 14 15.4 15.6 1.02 84.1% 88.1% 28 17.5 18.6 1.06 - -

21 7 16.3 18.9 1.15 71.1% 57.9% 14 22.1 19.4 0.88 73.3% 78.4% 28 28.2 26.5 0.94 - -

28 7 27.8 33.3 1.20 73.9% 71.3% 14 33.5 34.5 1.03 76.5% 85.9% 28 39 45.1 1.15 - -

34 7 33.6 29.8 0.89 65.3% 80.9% 14 38.4 41.3 1.07 90.0% 92.5% 28 41.5 45.7 1.10 - -

41 7 43.8 47.8 1.09 87.1% 82.7% 14 47.7 52.1 1.09 94.8% 90.0% 28 53 54.9 1.04 - -

53

It is useful to determine conversion factor at 28-day as most of the specification indicate 28-

day strength of concrete is specified as a design strength and is used for quality assurance

testing. From the above Table 4.10, it is also apparent that the conversion factors do not

follow a specific pattern i.e. the conversion factor is not dependent of age and compressive

strength of concrete specimen. If we consider 28-day strength to determine conversion factor,

the average value of conversion factor is 1.06 with a standard deviation and coefficients of

variation are 0.07 and 6.6%, respectively. Another way to say that small cube strength will be

6% more than standard cube strength on an average.

It is also interesting to note the strength gain at 7-day and 14-day as a percentage of 28 day

strength. Sometime it is required to predict 28-day strength form early strength data for

acceptance of a batch of concrete. From the Table, it is apparent that strength gain does not

follow specific pattern. 7-day and 14-day strength gain as a percentage of 28-day strength

vary from 63% to 87% for small size cube.

It is apparent that for specified strength of 7 MPa, 7-day strength of small cube is only about

48% of 28-day strength which is unusual and may be attributable to improper

placing/compacting/curing/testing of the sample. It is apparent from the Table 4.10 that for

larger cube and for specified strength of 34 MPa and 41 MPa, 7-day and 14-day strengths

may be taken as 80% and 90% of 28-day strength, respectively. However, for lower strength

level the data does not fit well in any pattern.

54

Figure 4.14 Seven-day strength of standard and small size cube specimens.

From the above Figure 4.14, it is observed that for larger water-cement ratio up to 0.6, the

standard cube (6 in.) strength is higher. Both graphs almost merge at water/cement ratio of

0.6. After that the strength of smaller cube is higher that standard cube. It is observed from

the above graph that strength of small cube actually decrease when water cement ratio

decreases from 0.43 to 0.40 which is an exception. The anomaly may occur due to improper

placing/compaction/curing/testing of said concrete samples.

Figure 4.15 Fourteen-day strength of standard and small size cube specimens

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)


6 inch cube

4 inch cube

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)


6 inch cube

4 inch cube

55

From the above Figure 4.15, it is shown that for larger water-cement ratio up to 0.7, the

difference of strength between standard cube and smaller cube is small compared to other

water cement ratios. It is interesting to note that at a water-cement ratio 0.5, the standard cube

strength is higher. This anomaly may be explained by improper placing/curing/compacting/

wall effect /testing of said samples.

Figure 4.16 Twenty Eight-day strength of standard and small size cube specimens

From the above Figure 4.16, it is shown that for larger water-cement ratio up to 0.7, the

difference of strength between standard cube and smaller cube is small compared to other

water cement ratios. It is interesting to note that at water cement ration 0.5, the standard cube

strength is higher. This anomaly may be explained by improper placing/curing/compacting/

testing/wall effect of said samples.

4.4.5 Correlation between strength of cylinder and cube

Correlation coefficient between compressive strength of standard cylinder (6×12 in.) and

standard cube (6 in.) will be determined in the subsequent section. Coefficients are

determined with respect to standard cube (as denominator). It is observed from previous

Table 4.10 that strength gains with respect to age are not consistent in case of cube specimens

(both standard and small cube), so conversion factor will be evaluated on the basis of 28-day

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Co

mp

ress

ive

Str

en

gth

(M

Pa)


6 inch cube

4 inch cube

56

strength. It is also evident from the below Table 4.10 that the conversion factors at 14-day

and 7-day do not follow any specific pattern. Figure 4.17 has been plotted considering all the

Table 4.11 Conversion factors between 6x12 in. cylinder and 6 in. cube

Specified

strength

(MPa)

Age (day) Compressive Strength (MPa) Conversion factor

6×12 in. cylinder 6 in. cube

7 7 3.5 7.2 0.50 14 5.8 8.9 0.65 28 7.1 11.3 0.62

14 7 8.1 13.3 0.60 14 9.9 15.4 0.64 28 11.9 17.5 0.68

21 7 12.7 16.3 0.77 14 16.3 22.1 0.73 28 19.3 28.2 0.68

28 7 19.8 27.8 0.71 14 26.4 33.5 0.78 28 31.2 39 0.80

34 7 27.5 33.6 0.82 14 26 38.4 0.68 28 34.3 41.5 0.83

41 7 39.9 43.8 0.91 14 43 47.7 0.90 28 49 53 0.92

Figure 4.17 Compressive strength vs. conversion factors

R² = 0.763

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60

Co

nve

rsio

n f

acto

r

Compressive strength of standard cube (MPa)

Conversion factor

57

conversion factors. From the above Figure 4.17 the coefficient of determination is found to be

0.763. Due to inconsistent strength gain at 7-day and 14-day, this low value of coefficient of

determination is observed. In the subsequent section, 28-day strength will be considered for

evaluation of conversion factors and applicability of widely used L’Hermite’s equation.

This problem of finding conversion factor has been studied by many authors notably

L’Hermite and Adam M. Neville. L’Hermite proposed below equation for evaluating the

conversion factors:

= 0.76 + 0.2 ------------------------ (4.4)

Adam M. Neville proposed following equation irrespective of strength of cube specimen. He

finds a fixed conversion factor which is 0.81. His generalized equation is as below:

= 0.56 + 0.687 ( ) ------------------------ ---------- (4.5)

Where, h = height of 6×12 in. cylinder

And V = Volume of 6×12 in cylinder.

Cylinder strength and cube strength are in psi unit.

As fixed ratio was not obtained in this research, so applicability of widely used L’Hermite

equation will be considered in the subsequent section. Also, LGED/REB has their own

conversion factors to convert cylinder strength to cube strength. Applicability of these

conversion factors will also be considered. It is hypothesized that due to difference in

concrete constituents in Bangladesh compared to other countries where those equations were

developed, the conversion factor will be different than that predicted by L’Hermite equation.

The below Table 4.12 is prepared to depict comparative scenario. Figure 4.18 below

represent the ratio (cylinder/cube) vs cube strength as predicted by L’Hermite equation and as

found from present study.

58

Table 4.12 Conversion factors between 6×12 in. cylinder and 6 in. cube (28-day)

Specified

strength (psi)

Age

(day)

Compressive Strength

(psi)

Conversion factor Conversion factor

6×12 in.

cylinder

6 in. cube Predicted by

L’Hermitte equation

1000 28 1030 1640 0.63 0.71 2000 28 1720 2540 0.68 0.75 3000 28 2790 4090 0.68 0.79 4000 28 4530 5660 0.80 0.82 5000 28 4980 6020 0.83 0.83 6000 28 7110 7690 0.92 0.85

Figure 4.18 Conversion between the cylinder and cube strengths of concrete

y = 1.1866x R² = 0.9361

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60

Cu

be

Str

en

gth

(M

Pa)

Cylinder Strength (MPa)

Cube Strength

Linear (Cube Strength)

59

Figure 4.19 Cube strength vs. cylinder/cube ratio (L’Hermite & present study)

The following equation as obtained from Figure 4.18 above with coefficient of determination

0.983 will be used to convert cylinder strength to cube strength.

fcu = 1.186 fcyl --------------------------------------------- (4.6)

Where fcu and fcyl are 6 in. cube strength and 6×12 in. cylinder strength in MPa respectively.

LGED, Bangladesh has a comprehensive chart to convert cylinder strength to cube strength.

The comparative scenario is depicted in the Table 4.13 below.

Table 4.13 Conversion factors as recommended by LGED, Bangladesh


Proposed by LGED

Cube strength (MPa)

Proposed by LGED

Cube strengths from

present study (MPa)

Percent

variation 7 9 8.3 8.4%

10 13 11.9 9.2%

15 19 17.8 6.7%

20 25 23.7 5.5%

25 31 29.7 4.3%

30 37 35.6 4%

35 44 41.5 6%

40 50 47.5 5.3%

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2000 4000 6000 8000 10000

Cyl

ind

er/

Cu

be

Cube Strength (psi)

PresentStudy(Cylinder/Cube)L'Hermite Equation(Cylinder/Cube)

60

Figure 4.20 Cylinder and cube strength (LGED recommendation and present study)

From the above Table 4.13 and Figure 4.20, it is evident that LGED overestimates cube

strength for concrete ranges from 7 to 40 MPa. The percent variation ranges from 4% to 9.2%

and again the variation is not significant.

Table 4.14 Conversion factors between 4×8 in. cylinder and 4 in. cube specimens

Specified

strength

(MPa)

Age

(day)

Compressive Strength

(MPa)

Conversion

factor from

present study

Conversion factor

4×8 in.

cylinder

4 in. cube Proposed by REB

7 28 8.8 12.1 1.38 1.20 for less than 28 MPa 14 28 12.9 18.6 1.44

21 28 19.8 26.5 1.34 1.15 between 28 to 49 MPa 28 28 35.5 45.1 1.27

34 28 38.5 45.7 1.19 1.10 for more than 49 MPa 41 28 56.3 54.9 0.98

0

10

20

30

40

50

60

0 10 20 30 40 50

Cu

be

Str

en

gth

(M

Pa)


Cube strength (MPa)Proposed by LGED

Cube strengths frompresent study (Mpa)

61

In the above Table 4.14, conversion factor with respect to 4×8 in. cylinder has been shown as

obtained in the present study. Correspondingly REB recommended values have been shown

in the right most column. In Figure 4.21, cylinder strength vs cube strength has been plotted

to find the trend line and following conversion equation is obtained:

fcu = 1.118 fcyl ----------------------------------------------------------(4.7)

Where fcu and fcyl are 4 in. cube strength and 4×8 in. cylinder strength in MPa respectively.

Figure 4.21 Cylinder strength vs. cube strength found in the present study

Table 4.15 Conversion between cylinder to cube strength


Proposed by REB

Cube strength (MPa)

Proposed by REB

Cube Strengths from present

study (psi) 8.8 10.5 9.8 12.9 15.5 14.4 19.8 23.8 22.0 35.5 40.8 39.7 38.5 44.3 43.0 56.0 62.0 63.0

y = 1.1183x R² = 0.9029

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60

Cu

be

Str

en

gth

(M

pa)


4 inch cube

62

Figure 4.22 REB cube strength vs. cube strength from present study

Comparison between the cube strength as proposed by REB and from the present study has

been shown in Figure 4.22. It is evident that for cylinder strengths between 8.8 to 56.0 MPa,

there is not much difference between REB cube strength and strength of cube found from

present study.

4.5 Stress-Strain diagram

For each concrete strength level, 3 cylinders (4×8 in.) were casted for drawing stress-strain

diagram. For drawing stress-strain diagram dial gauge of 1 micro meter precision was used.

From the stress-strain diagram, static modulus of elasticity of concrete was determined in

accordance with ASTM C 469.

4.5.1 Static modulus of elasticity

The following equation as suggested in ASTM C 469 was used for calculating static modulus

of elasticity:

E = (S2 – S1) / (ɛ 2 - 0.000050) ----------------------------------------------------------(4.8)

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60

Cu

be

Str

en

gth

(M

pa)


Cube strength (MPa)Proposed by REB

Cube Strengths frompresent study (psi)

63

Where,

E= Chord modulus of elasticity.

S2 = Stress corresponding to 40% of ultimate load.

S1 = Stress corresponding to a longitudinal strain, ɛ 1, of 50 millionths, psi and ɛ 2 = Longitudinal strain produced by stress S2.

4.5.2 Static modulus of elasticity for specified strength 7 MPa

For each concrete mix, three specimens were casted for drawing stress-strain diagram. The

following stress-strain diagrams are chronologically for specimen-1, specimen-2 and

specimen-3 as shown in figures 4.23 to 4.25, respectively. Table 4.16 shows the summarized

values for three specimens.

Figure 4.23 Stress-strain diagram for specimen-1 for specified strength 7 MPa

0

100

200

300

400

500

600

700

0 0.00005 0.0001 0.00015 0.0002 0.00025

Stre

ss (

psi

)

Strain (in/in)

64



0

100

200

300

400

500

600

0 0.00005 0.0001 0.00015 0.0002 0.00025

Stre

ss (

psi

)

Strain (in/in)

0

100

200

300

400

500

600

700

0 0.00005 0.0001 0.00015 0.0002 0.00025

Stre

ss (

psi

)

Strain (in/in)

65


Specimen ID Compressive

strength (psi)

S2 (psi) S1 (psi) ɛ 2(in/in) Modulus of

Elasticity

(ksi)

Predicted by

57000x c

(ksi)

Specimen-1 832 333 159 0.00011 2900 1600

Specimen-2 1140 456 186 0.00014 3000 1900

Specimen-3 832 333 150 0.000112 2900 1600


For each mix, three specimens were casted for drawing stress-strain diagram. The following

stress-strain diagrams are chronologically for specimen-1, specimen-2 and specimen-3 as

shown in figures 4.26 to 4.28, respectively.


0

200

400

600

800

1000

1200

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004

(str

ess

(p

si)

Strain (in/in)

66



Table 4.17 presents the modulus of elasticity values for specified strength of 14 MPa for all

the three specimens.

0

100

200

300

400

500

600

700

800

900

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007

Stre

ss (

psi

)

Strain (in/in)

0

100

200

300

400

500

600

700

800

900

1000

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035

Stre

ss (

psi

)

Strain (in/in)

67



strength (psi)

S2 (psi) S1 (psi) ɛ 2(in/in) Modulus of

Elasticity

(ksi)

Predicted by

57000x c

(ksi)

Specimen-1 2150 860 105 0.000302 3000 2600

Specimen-2 1473 589 57 0.00058 1000 2200

Specimen-3 1828 731 123 0.000253 3000 2400

4.5.4 Static modulus of elasticity for specified strength 21MPa




0

200

400

600

800

1000

1200

1400

1600

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 0.00045

Stre

ss (

psi

)

Strain (in/in)

Figure 4.29 Stress-strain diagram for sample-1 for specified strength 21 MPa

68





0

200

400

600

800

1000

1200

1400

1600

0 0.0001 0.0002 0.0003 0.0004 0.0005

Stre

ss (

psi

)

Strain (in/in)

0

200

400

600

800

1000

1200

1400

1600

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035

Stre

ss (

psi

)

Strain (in/in)

69



strength (psi)

S2 (psi) S1

(psi) ɛ 2(in/in) Modulus of

Elasticity

(ksi)

Predicted by

57000x c

(ksi)

Specimen-1 2570 1028 280 0.0003 3000 2900

Specimen-2 2688 1075 294 0.00031 3000 3000

Specimen-3 3029 1211 413 0.00021 5000 3100






0

500

1000

1500

2000

2500

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006

Stre

ss (

psi

)

Strain (in/in)

70





0

500

1000

1500

2000

2500

0 0.0002 0.0004 0.0006 0.0008 0.001

Stre

ss (

psi

)

Strain(in/in)

0

500

1000

1500

2000

2500

0 0.0001 0.0002 0.0003 0.0004 0.0005

Stre

ss (

psi

)

Strain (in/in)

71



strength (psi)

S2 (psi) S1


Elasticity

(ksi)

Predicted by

57000x c

(ksi)

Specimen-1 4199 1679 311 0.000393 4000 3700

Specimen-2 4362 1744 306 0.00053 3000 3800

Specimen-3 4667 1867 360 0.000353 5000 3900






0

500

1000

1500

2000

2500

3000

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008

Stre

ss (

psi

)

Strain (in/in)

72





0

500

1000

1500

2000

2500

3000

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008

Stre

ss (

psi

)

Strain (in/in)

0

500

1000

1500

2000

2500

3000

0 0.0002 0.0004 0.0006 0.0008

Stre

ss (

psi

)

Strain (in/in)

73



strength (psi)

S2 (psi) S1


Elasticity

(ksi)

Predicted by

57000x c

(ksi)

Specimen-1 5394 2157 153 0.00055 4000 4200

Specimen-2 5342 2137 103 0.00072 3000 4200

Specimen-3 5466 2186 353 0.000508 4000 4200

4.5.7 Static modulus of elasticity for specified strength of 41MPa





0

500

1000

1500

2000

2500

3000

3500

4000

0 0.0002 0.0004 0.0006 0.0008 0.001

Stre

ss (

psi

)

Strain (in/in)

74





0

500

1000

1500

2000

2500

3000

3500

4000

0 0.0002 0.0004 0.0006 0.0008 0.001

Stre

ss (

psi

)

Strain (in/in)

0

500

1000

1500

2000

2500

3000

3500

4000

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Stre

ss (

psi

)

Strain (in/in)

75



strength (psi)

S2 (psi) S1


Elasticity

(ksi)

Predicted by

57000x c

(ksi)

Specimen-1 7527 3010 289 0.00073 4000 5000

Specimen-2 7939 3175 300 0.000625 5000 5100

Specimen-3 7634 3053 341 0.00095 3000 5000

Table 4.22 Summary of findings from stress-strain test data

Specified

Strength(psi)


Strength (psi)

Modulus of

Elasticity

(ksi)

Predicted by

57000x c

(ksi)

% variation

1000 Specimen-1 830 2900 1600 44.82%

Specimen-2 1140 3000 1900 36.66%

Specimen-3 830 2900 1600 44.82%

2000 Specimen-1 2150 3000 2600 13.33%

Specimen-2 1470 1000 2200 -120%

Specimen-3 1830 3000 2400 20%

3000 Specimen-1 2570 3000 2900 3.33%

Specimen-2 2690 3000 3000 0.0%

Specimen-3 3030 5000 3100 38%

4000 Specimen-1 4200 4000 3700 7.5%

Specimen-2 4360 3000 3800 -26.66%

Specimen-3 4670 5000 3900 22%

5000 Specimen-1 5390 4000 4200 -5%

Specimen-2 5340 3000 4200 -40%

76

Specified

Strength(psi)


Strength (psi)

Modulus of

Elasticity

(ksi)

Predicted by

57000x c

(ksi)

% variation

Specimen-3 5470 4000 4200 -5%

6000 Specimen-1 7530 4000 5000 -25%

Specimen-2 7940 5000 5100 -2%

Specimen-3 7630 3000 5000 -66.66%

From the Table as shown 4.22 above, modulus of elasticity may be taken equal to

57000x c as mentioned by ACI code. From the above Table, few results are not in

accordance with ACI projected values which may be due to experimental errors.

4.6 Failure pattern

Figure 4.41 below shows the different satisfactory failure pattern for Cylinder and cube as

described in ASTM C39/ C39M and BS 1881-116: 1983.

Figure 4.41 Satisfactory failure patterns for cylinder and cube

77

4.6.1 Failure types of concrete specimen for specified strength 7 MPa

(a) (b)

Figure 4.42 Failure pattern of (a) 4 ×8 in. and (b) 6×12 in. cylinders specimen

From the above Figure 4.42, it is evident that the crack pattern is columnar type. Cement

paste which binds the aggregate together is very low strength type, so mortar failure is

observed with columnar cracking.

(a) (b)

Figure 4.43 Failure pattern of 6 in. (a) and 4 in. cubes (b)

From the above Figure 4.43, it is evident that the crack pattern is non explosive type. Cement

paste which binds the aggregate together is very low strength type, so mortar failure is

observed with non explosive cracking.

78


Figure 4.44 Failure type for large and small size cylinder specimens

From the above Figure 4.44, it is evident that the crack pattern is columnar type. Cement

paste which binds the aggregate together is very low strength type (specified strength of

concrete is 2000 psi), so mortar failure is observed with columnar cracking. Also cracking

lines are more densely spaced that the specimen of specified strength 1000 psi as shown in

Figure 4.46.


The failure type is different for higher strength concrete. The cement paste that binds the

aggregate together is of higher strength and this type of failure is always combined and

explosive in nature. Figure 4.45 shows the failure type of cylindrical specimen both 6×12 in.

and 4×8 in..

79

Figure 4.45 Shows the failure type of concrete cylinder specimens

From the figure, it is evident that the failure type is shear and explosive as well as the failure

is combined in nature. The cylinder take load gradually upto a pick and then sudden

explosion would occur during the failure. For concrete of specified strength of 6000 psi

similar pattern of failures were observed.

From Figure 4.46, failure pattern is semi explosive (left) and explosive (right) in nature

(a) (b)

Figure: 4.46 Failure pattern is semi-explosive (a) and explosive (b)

80

From the Figure 4.47, it is shown below, the failure is obtained combined.

Figure: 4.47 Tensile splitting surface for 6×12 and 4×8 in. cylinder

4.7 Summary:

In this chapter, the effect of specimen size and shape on concrete compressive strength have

been evaluated using the test results found in Chapter 3. From the study, it is found that

smaller size cylinder specimen has higher compressive strength than that of larger sizes and

the same trend is followed for the cube specimens. The ratio of compressive strength of 4×8

in. cylinder specimens to that of 6×12 in. specimens is 1.13 on an average with coefficient of

variation of 6.2 percent. The average ratio of compressive strength of 4 in. cube specimens to

that of 6 in. is approximately 1.06 with coefficient of variation of 6.6 percent. The ratios of

compressive strength between standard cylinder to standard cube are dependent on strength

of concrete and the ratios increases with the increase of strength. Using L’Hermite equation

to convert standard cube strength to cylinder strength is not conservative for strength level

between 7 and 41 MPa in case of concrete produced in our country. For the strength range

between 41 MPa to 53 MPa, L’Hermite equation yields conservative values. LGED

overestimates cube strength for concrete ranges from 7 to 40 MPa. The percent variation

ranges from 4% to 9.2% and again the variation is not significant. For strength ranges

between 10.5 to 62 MPa, there is not much difference between REB cube strength and

strength of cube found from the present study.

6×12 in. cylinder

4 x8 in. cylinder

81

Chapter 5

CONCLUSIONS AND RECOMMENDATIONS

5.1 General

The effect of size and shape of test specimens on compressive strength of normal strength

concrete and correlating the strength of concrete considering different size and shape of

specimens used in Bangladesh were the main objectives of this study. Most of the design

specification of Bangladesh refers to either the strength of 6×12 in. cylinder or 6 in. cube.

However, smaller cylinder/cube are used for quality assurance testing in laboratory

considering the testing machine capacity or ease of handling. For this reason, relationship is

required to be developed between various size samples. In this research, various relationships

have been proposed: UPV versus compressive strength of various size/shape test specimens;

correlation coefficient among various size/shape test specimens’ strengths; UPV versus

splitting tensile strength. The applicability of widely used L’Hermite equation to convert

standard cube strength to cylinder strength was also evaluated in this research. In addition,

government organizations such as LGED, REB etc. have used their own conversion factors to

convert standard cube strength to cylinder strength in technical specification of various

projects. The applicability of this conversion factor is evaluated as well. From the ACI

proposed equation, it is known that splitting tensile strength of concrete is dependent on

compressive strength of concrete and ACI proposes equation to determine splitting tensile

strength from compressive strength of concrete. The applicability of ACI equation in the

context of materials used in our country was evaluated in this study. ACI also proposes

equation to get static modulus of elasticity from compressive strength of concrete. The

viability of this equation is evaluated in this study. From the literature review, it is known that

correlation coefficient between compressive strengths of different shapes/sizes specimen is

dependent on strength level of specimens, age of specimen, maximum aggregate size,

capping method, mold material consolidation method and curing condition. However,

varying these factors such as capping method, mold material, consolidation method and

curing condition will violate AASHTO and ASTM standards. In this research, these were

done as per ASTM standards. Only variable was strength level and age of specimen as

maximum size of aggregate was also kept the same throughout the experimental study.

Strength of concrete was varied by mostly varying water-cement ratio keeping the other

ingredients to be the same.

82

5.2 Conclusions

Based on the experimental work done on various shape/size concrete test specimens and

correlation study among them, the following conclusions can be drawn for size and shape

effects including other general findings:

1. Unit weight of cylindrical specimens is comparatively higher than that of cube

specimens. Also, larger size cylinder specimens have higher unit weight than that of

smaller size specimens. This is due to the fact that three layer of compaction was done

for 6×12 in. cylinder specimens compared to 4×8 in. cylinder specimens in which two

layer of compaction was done.

2. For the same strength grade, different pulse velocities obtained using UPV tests for

different size/shape samples. This indicates that the pulse velocity is not only affected

by the strength grade of the sample but also the size/shape of the test specimen.

3. The relationship between the splitting tensile strength and compressive strength may

be expressed using the obtained results as 5.79 x c in comparison to 7.5 x c as

proposed by ACI.

4. The smaller size cylinder specimen has higher compressive strength than that of the

larger size specimen for the same concrete mix. The same trend is obtained for cube

specimens.

5. The ratio of compressive strength of 4x8 in. cylinder specimen to that of 6x12 in.

cylinder have been determined at 28-day. The average value of conversion factor is

1.13 with a standard deviation and coefficient of variation are 0.07 and 6.2%,

respectively. Another way to say that smaller size cylinder specimen results 13%

higher strength than that of standard cylinder strength in an average.

6. The ratio of compressive strength of 4 in. cube specimen to that of 6 in. specimen

have been determined at 28-day. The average value of conversion factor is 1.06 with a

standard deviation and coefficients of variation are 0.07 and 6.6%, respectively. That

83

means, smaller size cube strength will have only 6% higher strength results than that

of the standard cube specimens.

7. Correlation coefficients between compressive strength of standard cylinder (6 ×12 in.)

and standard cube (6 in.) have been determined at 7, 14 and 28 days. Coefficients are

determined with respect to standard cube (as denominator). It is observed that at 28-

day strength, the ratios increase with the increase of strength of standard cube. Using

L’Hermite equation to convert standard cube strength to cylinder strength is not

conservative for strength level between 7 MPa and 41 MPa in case of concrete

produced in our country. For the strength range between 41 MPa to 53 MPa,

L’Hermite equation yields conservative values.

8. LGED overestimates cube strength for concrete ranges from 7 to 40 MPa. The percent

variation ranges from 4% to 9.2% and again the variation is not significant. For

strength ranges between 10.5 to 62 MPa, there is not much difference between REB

cube strength and strength of cube found from the present study.

9. The static modulus of elasticity as predicted by the ACI equation 57000x c is

shown good agreement with the test results.

5.3 Limitations

1. The materials were carried in two phases and the grain size distribution of coarse

aggregate marginally fall with the lower limit.

2. For all sample sizes ¾ inch downgraded coarse aggregate was used. For this reason

impact of maximum size of coarse aggregate on shape and size effect was not

incorporated in this study.

3. Only standard size samples have been studied.

5.4 Recommendations for the Future Study

It is recommended that the study can be extended further in the following fields:

84

1. The conversion ratios vary with the maximum size of coarse aggregate. So, future

study may be carried out to find the effect of different size coarse aggregate on the

size/shape effect (conversion ratios).

2. Effect of type of coarse aggregate (Brick chips, rounded stone aggregate, black stone

chips etc) may be considered to assess the size/shape effect on strength of concrete.

3. Different Prism shape may be considered for the preparation of test specimens.

4. UPV in concrete is dependent upon many factors such as maximum size and type of

aggregate, sand-to-aggregate ratio, water-cement ratio, curing condition, age of

specimen and strength of test specimens. Future study may look into those factors.

85

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