Fatigue behaviour of steel fibre reinforced concrete in direct compresion

FATIGUE BEHAVIOUR OF STEEL FIBRE REINFORCED CONCRETE IN DIRECT COMPRESSION

By

RAFEEQ AHMED S.

月

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Degree of

DOCTOR OF PHILOSOPHY

DEPARTMENT OF CIVIL ENGINEERING :NDIAN:NSTITUTE OF TECHNOLOGY HAUZ KHAS,NEW DELHI-110 016,INDIA

MARCH 1996

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CERTIFICATE

This is to certiか that thesis entitled 'Fatigue Behaviour of Steel Fibre Reinforced Concrete in Direct Compression',being submitted by Mr. Rafeeq Ahmed S. to the Indian Instimre of Technology, Delhi, India, for the award of ihe Doctor of P皿osophy in Civil Engineering. is a record of bonaffide research work carried out by him under my guidance and supervision.

To the best of my knowledge the thesis has reached1 the requisite standard. The material presented in this thesis has not been submitted in part or full to any other university or institution for award 、） f a degree or diploma.

Dr. Ashok Gupta Supervisor

Asst. Professor

Dept. of Civil Engineering Indian Institute of Technology New Delhi,India

ACKNOWLEDGEMENTS

I am one oj訪。紀few fort厚na tes> 励o could get an opportuniりto 如rk 刀nder Proj S. Krishnamoor吻 and Dr. 月訪ok Gupta. i am indebted to 乃OJ S.

K市みnamoort勿，Pr可ressor 依etired), D叩arement oj Civil E昭in如ng, IJT De/bらfor s智estion of功isルId ofresearch, conti加ed gu泌nce and encour'収ement thro婦out 訪is invest如tion. I am also grateful to Mrs. Savitri Krishna moo吻碗o has a/wa声 been kind andaectionate to me.

Iwi訪 to express niソ凌叩sense ofgratitude and sincere thanks to niソsupervisor, Dr.A訪ok Gupta，月ssL Professor, D卿rtment of Civil Engineering, /IT De乃i, for 'ns val町ble gui山nce and encou聖ement山ring this invest卿tio n.

I am also greatly inde彪dtoル B. 助atta訪aァe, Asst. Professor, D叩artment of Civil Engineering, IlT Delhi, for h方encour'碧口刀ent山ring訪is stu力．

I am grateful to Mr. Baんsuんman以n and 入leeなm怨ham, 品ientists, SER C,, Aたdras for extending the郵se of訪eir library to me.

乃esuppoけingな加ratoクs嶋房ルた Venna, CL.，乃訪，n, G. S., Choudhary Badle Ram, Bαなn Sin帥，Shriめandルndit, Siya Ram, Bみagwan Singみ，乃叩a, Anu and 訪ivなId町ervi:平ccなI訪anks for their active help in the laboratories.

J am 訪』nk/ui to Proj R如，G.V and Saみ， R.K. for 加l/ping me 切切rk 面th んstron 刀iachine.

My sin一んnks are必。ムe toみof Panめ」R.K. and Prem Sin帥ofApplied 腕めanics D叩artmentfor allo切ing me to utilise訪e MTS machine.

I ackno勿lei柳 w励 gratitude, the help ルndered り my co堀gues, Ra卿na吃R.V,Nage訪，M, Rakesh庖mar> Shamsad月hrn ed and M冗 Sowmini Ravi 山ring功e co郵rse oftみis investigation.

I am thankful to mソ声en活 Harsha, P.H.，月vanti, Mufti, Aiなz, Rais and Asな77' for the 伽ne加I timeやent toge功グduring my tenure it ZIT Dell,i.

I owe mソ sincere gratitude to rn）・grand mother, 戸ther and mother 動。

encouraged me in tみis endeavour. I also express n:ソgratitude 1 o I ny bro功erらsist町・Zn・ la鴫sister and伽訪er-zn－なw for their encouragement throug加ut.

I an: thankful to my parents_・in-law _励o supported and encouraged me during 功effinal s甥es of功is stuみ．

Finally, I wish to express my love and gratitude to my 加loりed _切fe, Ayesha 品ltana, forみer concern andfor a/wa〕・， being the肥励en J neededみer the most.

ABSTRACT

This study based on a detailed experimental investigation presents the influence of fibres on the fatigue behaviour of plain concrete in direct compression. Both the S-N behaviour and strain behaviour have been investigated and analysed using mathematical regression fits and neural network modelling.

The fibre parameters were, type, namely, straight and hooked and volume, namely, i%o可y for straight fibres and I and 2%for hooked fibres.

The maximum stress level was varied from 95%to about 55%ot the static ultimate strength of the specimens. The minimum stress level was 10% of the static ultimate strength. The cycling was carried upto one million cycles・

Strains of specimens have been measured using electrical resistance strain gauges or crosshead movement as appropriate.

The investigations showed that fibres enhanced the fatigue strength of concrete ar all stress levels significantly though not very greatly. Larger the fibre content higher the fatigue strength and hooked fibres were better than straight fibres. More important, fibres reduced the variability in fatigue life, at any stress level, and 5%

defectile characteristic strength of concrete was notably enhanced by incorporation of fibres・

The strains at failure of fibre reinforced concretes were higher than those of plain concrete and the strain behaviour on fatigue cycling showed that fibres aLso increase the strain-sufference capability of concrete at both the stages of dilation and failure・

A neural network based on backpropagation modelled both the S-N and strain behaviours extremely well and it could take into account the static ultimate strength as well in the modelling-a feature usually missing in the mathematical fits proposed by many earlier investigators. Neural network could also extrapolate the S-N behaviour beyond the experimental region (i.e. beyond one million cycles) and as such can be used to predict fatigue life of concrete at very high cycle and super high cycle fatigue. The neural network was also used on the data of S・N and strain behaviour of a few research workers and it demonstrated its applicability vei..vell.

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CONTENTS

List of Figures List of Tables List of Plates

List of Symbols and Abbreviations

Chapter

INTRODUCTION

I.i Fatigue of concrete

i .2 Behaviour of concrete under fatigue I .3 Fibre reinforced concrete

i .4 Fibre reinforced concrete under fatigue i .5 Mathematical modelling

i .6 Need for further research 1.7 Objectives of this study 1.8 Scope

i .9 Thesis organisation

Chapter 2

LITERATURE REVIEW Introduction 舞 Fatigue of ductile materials Fatigue of brittle materials Fatigue of plain concrete

2.4. i Investigation under direct compression 2.4.1.i Effect 醸rate of loading 2.4.1.2 Effect6 fstress range 2.4. 1 .3 Effect of stress ratio 2.4. 1 .4 Effect of concrete strength 2,4. 1 .5 Effect of aggregate type

2.4. 1 .6 Mathematical representation of S-N behaviour 2.4. 1 .7 Evaluation of strains

2.4. 1 .8 Crack growth under fatigue

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2.4. 1 .9 Energy absorption under fatigue 33 2.4.1.lo Effect of variable amplitude loads 33 2.4.2 Investigation under flexure 34 2.4.2. 1 Effect of stress ratio 34 2.4.2.2 Effect of moisture conditions 36 2.4.2.3 Effect of rest periods 41 2.4.2.4 Effect of concrete strength 43 2.4.2.5 Effect of air content, water/cement ratio

and aggregate type 44

2.4.2.6 Effectofsize 45

2.4.2.7 Mathematical representation of S-N behaviour 47 2.4.3 A Summary on fatigue of plain concrete in compression

and fatigue 49

2 . 5 Fatigue of reinforced concrete and prestressed concrete members 49 2.5. 1 Fatigue of reinforced concrete structures 49 2.5.2 Fatigue behaviour of prestressed concrete members 52 2.5.3 A summary on fatigue of reinforced and prestressed

concrete structures 55

2.5.3.i Reinforced concrete 55 2.5.3.2 Prestressed concrete 56

2.6 Fibre reinforced concrete 56

2.6.1 Introduction 56

2.6.2 Mechanism of fibre reinforcing 57 2.6.2.1 The strengthening mechanism 57 2.6.2.2 The toughening mechanism 57 2.6.3 Static properties of fibre reinforced concrete 58 2.7 Fatigue of steel fibre reinforced concrete 59 2.7. 1 Investigations u耐er direct compression 嘱59 2.7.2 Investigations under flexure 65 2.7.3 A summary on fatigue of fibre reinforced concrete

in compression and flexure 69 2.8 Neural network material modelling 70 Chapter 3

NEURAL NETWORKS 3 Introduction

3.1.1 Definitions of neural networks 3.i .2 Salient features of neural networks

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The biological analogue

3.3

The artificial neural network

3.3.I The basic components of an artificial neural network 3.3.I.i A single processing element

3.3.1.2 Inputs and outputs 3.3. 1 .3 Weighing factors 3.3.I .4 Neuron functions 3.3.i .5 Activation functions 3 . 3 . 1 . 6 Learning functions 3.3.2 Combining elements

3.3.3 Combining layers 3.3.4 Connectivity options 3.3.5 Learning mechanism

3.3.5,i Learning rate 3.3.5.2 Learning laws

3.4

The backpropagation neural network 3.4.1 Introduction

3.4.2 Backpropagation training

3.5

Neural network used in this investigation 3.5,i Introduction

3.5.1.i Translation part

3.5.I .2 Learning and testing part 3.5. 1 .3 Potential rule adding part 3.5.2 Limitations of the package

Chapter 4

EXPERIMENTAL INVESTIGATION 4.1 Intr

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4.2 Experimental programme 4.2.I Materials used 4.2.2 Mix proportion

4.2.3 Types of specimens cast

4.2.3.i Specimens for fatigue tests

4.2.3.2 Specimens for compressive strength tests 4.2.3.3 Specimens for split tensile tests

4.2.4 Casting 4.2.5 Curing

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4.3 Testing machines used

4.3.i Machines for fatigue testing 4.3.i.i Instron machine 4.3.i .2 MTS machine 4.3.2 Machines for static testing 4.4 Testing

4.4.i Fatigue testing 4.4.2 Static testing 4.5 Observations during testing

4.5.i During the fatigue testing 4.5.2 During the static testing

Chapter 5

RESULTS AND DISCUSSIONS: S-N BEHAVIOUR Experimental data

5.i'i Mean fatigue strength curves

Effect of rate of loading on the S-N behaviour 5.2. 1 Modiffied S-log N relationships

5.2.2 Characteristic curves

Variability of S-N behaviour as influenced by fibre addition Neural network modelling

Effect of ffibre content on the fatigue life of concrete Statistical analysis of fatigue data

Neural network modelling of data of other research workers

Chapter 6

RESULTS AND DISCUSSIONS: STRA永/DEFORMATION BEHAVIOURS

Plain concrete in Flexure i%SFRC

i%HFRC 2%HFRC

Deformation behaviour of run-out specimens Neural network modelling

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225 238 6.7 Effect of fibre content on the failure strain 178 6.8 Effect of fibre content on the fatigue life at the commence

of stage ill of strain development 202

6.9 Strain at the commencement of stage 1H 202 6.10 Neural network modelling of data of an earlier research worker 204 Chapter 7

CONCLUSIONS AND SCOPE FOR FURTHER RESEARChl

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Conclusions

7.1.I S-N Behaviour 7.1.2 Strain behaviour 7. 1 .3 Other observations Scope for further research

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REFERENCES APPENDIX A APPENDIX B APPENDIX C