Size dependent mechanical behavior of ultra high performance fiber reinforced concrete

Ultra-high-performance fiber-reinforced concrete UHPFRC is one of promising engineered construction materials for the purpose above mentioned owing to the very high strength, ductility a

Size dependent mechanical behavior of ultra-high-performance fiber-reinforced

Size dependent mechanical behavior of ultra-high-performance fiber-reinforced

concrete

Duy Liem NGUYEN

A dissertation submitted to the Faculty of the Sejong University in partial fulfillment of the requirements for the degree of Doctor of

Philosophy in Civil & Environmental Engineering

February 2015

Approved by Major Advisor Dong Joo KIM

I would like to dedicate this dissertation to my parents and my wife who have

supported me all the way

Firstly, I would like to express my deep gratitude to my Advisor, Professor Dong Joo KIM, for his supporting my doctoral program at Korea, for his enthusiasm and great knowledge The encouragement, experience and advice from him helped me have more confidence and energy to complete the work

I sincerely would like to thank the rest of my dissertation committee for useful comments and questions in addition to encouragements

I also thank my Korean labmates giving me many supports and help when I was studying at Sejong University Specially thank my Vietnamese friends studying or working in Korea We have shared weal and woe, encouraged each other to overcome much obstacle in the period of overseas study

Finally, I would like to express my wholehearted thanks to my parents and my family for their supports, patience and encouragement

Korea, November 2014

Duy Liem NGUYEN

There has been much interest on enhancing the robustness, toughness and durability of civil infrastructure under severe mechanical and environmental loadingconditions Ultra-high-performance fiber-reinforced concrete (UHPFRC) is one of promising engineered construction materials for the purpose above mentioned owing

to the very high strength, ductility and durability of UHPFRC based on its unique tensile strain-hardening behavior and extremely densified microstructure Thus, many structural engineers are trying to apply various types of UHPFRCs including DUCTAL, CERACEM, Multi-scale Cement Composites (MSCC), CEMTECmultiscaleand CARDIFRC into various civil infrastructure, e.g., bridge, high rise building and other military structures However, the application of UHPFRCs is still not popular because current UHPFRCs are still expensive in comparison with normal concrete In addition, there is no design code for the application of UHPFRCs yet and this situation

is really an obstacle for its practical application In order to propose the design codefor UHPFRCs, all the mechanical performances of UHPFRCs should be clearly understood Among their mechanical performances, size effects on the tensile and flexural behaviors of UHPFRCs are not fully understood yet

Thus, in this dissertation, the size dependent mechanical behaviors of UHPFRCsunder direct tension and flexure was systematically investigated In addition, the correlation between tensile and flexural behaviors of UHPFRC is also discovered This dissertation contains three parts as follows

First, the size effects on the flexural behavior of UHPFRCs were investigated Three types of flexural specimens with different sizes, but identical shape, were used

in four-point bending tests Two types of steel fiber volume content were used in a mortar matrix: one included 1.0% long twisted steel fibers and 0.5% short smoothsteel fibers and the other contained 1.0% long twisted steel fibers and 1.0% short

smooth steel fibers The UHPFRCs showed clear specimen size effects on the flexural strength, normalized deflection, and normalized energy absorption capacity The UHPFRCs with lower fiber volume content produced lower strain capacity and highersize effect The source for the observed size dependent flexural behavior of UHPFRCs were discussed.

Second, the specimen size and geometry effects on the direct tensile stress versus strain responses of UHPFRCs were experimentally discovered Six series of specimens with different geometries were designed to investigate the effect of different gauge length, thickness, section area and volume on the tensile responses of UHPFRCs The UHPFRCs in the experimental program contained 1.0% long twisted steel fibers and 1.0% short smooth steel fibers Although the different sizes and geometries of specimens did not generate significant influence on the post-cracking strength of the UHPFRCs, they produced clear effects on its strain capacity, energy absorption capacity and multiple cracking behavior

Finally, the correlation between the tensile and flexural behavior of the UHPFRCswas analytically investigated The models for compressive and tensile stress versus strain responses of UHPFRCs were proposed One model was proposed for thecompressive behavior of the UHPFRCs while three different models were proposed for the tensile behavior of the UHPFRCs Section analysis were carried out by using the proposed models and discovered the influence of tensile response on the predictedflexural behavior, including the condition for generating deflection-hardening behavior

초고성능 섬유보강 콘크리트 (Ultra High Performance Fiber Reinforced Concrete, UHPFRC)는 등의 우수한 역학적 특성과 치밀한 조직을기반으로 높은 내구성이 기대되는 차세대 건설재료이다 하지만, 현재UHPFRC 의 압축, 인장 그리고 휨인장 거동에 대하여 보고된 결과들은 대부분실험실에서 소규모 실험체에 대하여 실험을 수행한 결과를 바탕으로 하고

있다 또한, 시멘트 기반의 복합재료들은 대부분 취성적인 특성을 나타내고

있어 실험체 크기가 커짐에 따라, 강도가 저하하는 실험체 크기 효과에 대하여

많이 보고된 바 있다 UHPFRC 또한 시멘트 기반의 복합재료이고 섬유를보강하지 않은 초고성능 콘크리트 (Ultra High Performance Concrete,

연성적인 거동을 보인다고 하더라도, 실험체 크기가 UHPFRC 의 역학적거동에 미치는 영향을 정확하게 조사하여 설계에 반영할 필요가 있다 논문의연구결과는 UHPFRC 의 설계기준을 만들기 위해 유용한 정보와 기본적인이해를 제공 할 것으로 기대된다 이를 위해 아래와 같은 세 가지 세부연구목표들이 달성되었다.

1) UHPFRC 의 휨인장 거동은 시험체의 크기 변화에 따라서 영향을 받는다

즉, 시험체의 크기가 커질수록 휨강도, 처짐능력, 그리고 에너지흡수능력이 분명하게 저하하는 경향을 나타내었다 하지만, UHPFRC 의

크기효과가 미치는 영향이 감소하였다 이러한 UHPFRC 의 휨 거동에영향을 미치는 시험체의 크기 효과는 시험체가 휨 하중을 받아 최대휨인장 강도를 보일 때 휨 인장 시험체의 하단에 유발되는 최대 휨인장변형률과 밀접한 관계를 가지고 있다 또한 UHPFRC 의 크기효과를보여주는 그래프를 제시하였다

나타내지 않았지만, 직접 인장 하중 하에서 UHPFRC 의 인장 변형능력, 에너지 흡수능력 그리고 다수의 균열 생성 능력 등에는 명확하기 그

크기 및 시험체 형상에 따른 영향을 나타내었다

3) UHPFRC 의 직접 인장거동은, 해석적 그리고 실험적인 연구결과들에근거하여, 그 휨 인장 거동과 매우 밀접한 상관관계를 가진다

UHPFRC 의 단면 변형률과 응력 분포가 그 UHPFRC 의 최대 모멘트저항강도와 그 점에서의 처점에 어떠한 영향을 미치는지 상세히조사하였다.

주요어 : 초고강도 섬유보강 콘크리트; 시험체 크기의 영향; 최종균열강도;

최대 휨 하중점; 변형 경화; 처짐 경화.

TABLE OF CONTENTS

TABLE OF CONTENTS i

LIST OF FIGURES iv

LIST OF TABLES vii

CHAPTER I: INTRODUCTION 1

1.1 Motivation 1

1.2 Literature review of UHPFRC 2

1.3 Goal and objectives 5

1.4 Organization of dissertation 7

CHAPTER II: SIZE EFFECT ON FLEXURAL BEHAVIOR OF ULTRA-HIGH-PERFORMANCE FIBER-REINFORCED CONCRETE 13

2.1 Introduction 13

2.1.1 Background 13

2.1.2 Size effect on fiber-reinforced concrete 14

2.2 Theoretical review of size effect 15

2.2.1 Theoretical review of size effect 15

2.2.2 Flexural behavior of UHP-HFRC 18

2.3 Materials and test methods 25

2.3.1 Specimen characteristics 25

2.4.2 Size effect on flexural behavior of UHP-HFRCs 33

2.4.3 Influence of material ductility on the size effect 38

2.4.4 Parameters of size effect: Weibull modulus m and Bažant parameters B and D0 41

2.5 Conclusions 45

CHAPTER III: SIZE AND GEOMETRY EFFECT ON TENSILE BEHAVIOR OF ULTRA-HIGH-PERFORMANCE FIBER-REINFORCED CONCRETE 52

3.1 Introduction 52

3.2 Size dependent mechanical properties of cement-based materials 54

3.3 Strain-hardening tensile behavior of UHPFRC 56

3.4 Experimental program 58

3.4.1 Materials and specimen preparation 60

3.4.2 Test setup and procedure 62

3.5 Result and discusion 63

3.5.1 Distribution of fibers within the cross-section 69

3.5.2 Effects of size and geometry of specimens on the tensile response of UHPFRC 71

3.6 Conclusions 86

CHAPTER IV: CORRELATION BETWEEN TENSILE AND FLEXURAL BEHAVIOR OF ULTRA-HIGH-PERFORMANCE FIBER-REINFORCED CONCRETE 94

4.1 Introduction 94

4.2 Predicting flexural behavior of UHPFRCs based on their tensile behaviors 95

4.2.1 Proposed model for predicting flexural behavior of UHPFRCs 95

4.2.2 Section analysis 97

4.3 Difference between gauge length dependent tensile and flexural behavior of

UHPFRC 111

4.3.1 Experimental test 111

4.3.2 Discussion 112

4.4 Conclusions 115

CHAPTER V: SUMMARY, CONCLUSIONS AND FUTURE WORKS 120

5.1 Summary and conclusions 120

5.1.1 Conclusions related to the size effect on flexural behavior of UHPFRC 121

5.1.2 Conclusions related to the size and geometry effect on tensile behavior of UHPFRC 122

5.1.3 Conclusions related to the correlation between tensile and flexural behavior of UHPFRC 123

5.2 Recommendations for future research 124

LIST OF FIGURES

Fig 1.1 – Compressive behavior of UHPFRC using 1% twist fiber blended with 1%

short smooth fiber by volume (Nguyen and Kim [23]) 4

Fig 1.2 – Classification of FRCCs (Naaman and Reinhardt [13]) 5

Fig 1.3 – Structure of the dissertation 7

Fig 2.1 – Size effects on the strength of brittle material [33] 18

Fig 2.2 – Typical deflection–hardening flexural behavior of UHP–HFRC 19

Fig 2.3 – Relationships between moment and curvature (a) and shear force and shear strain (b) [38] 22

Fig 2.4 – Distribution along beam of moment–curvature (M–) and shear force–shear strain (V–) 22

Fig 2.5 – Distribution of moment, shear, and cracks along beam 23

Fig 2.6 – Photo of specimen with multiple cracks 24

Fig 2.7 – Photos of fibers 27

Fig 2.8 – Three types of flexural specimen 29

Fig 2.9 – Test setup for bending test 30

Fig 2.10 – Average load (P) versus deflection ( ) curve of UHP–HFRCs for various specimen sizes 32

Fig 2.11 – Average equivalent bending stress ( f ) versus normalized deflection ( L) curve of UHP–HFRCs for various specimen sizes 32

Fig 2.12 – Multiple–cracking behavior of UHP–HFRCs 33

Fig 2.13 – Size effect on equivalent bending strength 34

Fig 2.14 – Size effect on normalized deflection at MOR 36

Fig 2.15 – Size effect on normalized toughness at MOR 37

Fig 16 – Size effect on cracking behavior of UHP–HFRCs 38

Fig 2.18 – Weibull distribution for UHP–HFRCs 42

Fig 2.19 – General graph of size effect law of UHP–HFRCs 44

Fig 3.1 – Tensile behavior of UHPFRC and investigated size parameters 57

Fig 3.2 – Shape of tensile specimens and molds 60

Fig 3.3 – Tensile test set-up and external load cells used 63

Fig 3.4 – Average tensile stress versus strain response of UHPFRC according to different geometry and size 65

Fig 3.5 – Multiple cracking behavior of UHPFRC according to different geometry and size 66

Fig 3.6 – Typical fiber distribution at section near the major crack 70

Fig 3.7 – Effects of gauge length on tensile parameters of UHPFRC 73

Fig 3.8 – Effects of section area on tensile parameters of UHPFRC 75

Fig 3.9 – Effects of volume on tensile parameters of UHPFRC 77

Fig 3.10 – Effects of thickness on tensile parameters of UHPFRC 79

Fig 3.11 – Modeling specimen as a chain in comparison of different gauge lengths 80

Fig 3.12 – Influence of pcon complementary energy 81

Fig 3.13 – Volume effect under bridging comparison 82

Fig 3.14 – Assumed distribution of defects 82

Fig 3.15 – Sensitivity of size parameters in illustration 84

Fig 3.16 – Effects of normalized size parameters on normalized tensile parameters of UHPFRC 85

Fig 4.1 – Proposed models for compressive and tensile behavior of UHPFRCs 96

Fig 4.4 – Assumed strain and stress distribution along the depth of section for softening behavior of UHPFRC with a clear sudden load drop, pc cc 99Fig 4.5 – Typical moment versus curvature response of UHPFRC

strain-(Kim et al [15]) 101Fig 4.6 – Condition for tensile models to surely produce deflection-hardening of UHPFRCs and the flexural stress and strain at beam bottom at MOR 102Fig 4.7 – Effect of softening slope E2on flexural parameters of tensile strain-

hardening UHPFRCs 104Fig 4.8 – Effect of softening slope E1 on flexural parameters of tensile strain-

softening UHPFRCs with no sudden load drop 106Fig 4.9 – Effect of pc/ ratio on flexural parameters of tensile strain-softening ccUHPFRCs with sudden load drop 107Fig 4.10 – The assumed strain and stress distribution at section and three cases of UHPFRCs 108Fig 4.11 – The flexural behavior of UHPFRC obtained from prediction and from experimental test .110Fig 4.12 – Geometry of tensile and flexural specimens 112Fig 4.13 – Effects of gauge length on the tensile and flexural behavior of

UHPFRC 113Fig 4.14 – Influence of tensile strain capacity ( ) of UHPFRC on flexuralpc

strength (f MOR) 115

LIST OF TABLES

Table 2.1 – Composition and compressive strength of matrix [36,37] 25

Table 2.2 – Properties of fibers 26

Table 2.3 – Test specimens used in this study 26

Table 2.4 – Average value of parameters describing flexural behavior of UHPFRCs 31

Table 2.5 – Average number of cracks and average crack spacing 40

Table 2.6 – Average value of parameters describing tensile behavior of UHPFRCs 41

Table 2.7 – Ratio of strength, normalized deflection, and normalized toughness at LOP 43

Table 2.8 – Ratio of strength, normalized deflection, and normalized toughness at MOR 43

Table 3.1 – Test series of specimens according to different size and geometry 59

Table 3.2 – Composition and compressive strength of matrix (Park et al [29]) 61

Table 3.3 – Properties of fibers 61

Table 3.4 – Tensile parameters of UHPFRCs according to different size and geometry 66

Table 3.5 – Multiple micro-cracking behavior of UHPFRC according to different size and geometry 68

Table 3.6 – Average number of fibers within a unit area of 100 mm2 69

Table 3.7 – Slope of normalized tensile parameter versus normalized size parameter response (referred to Fig 3.15, 3.16) 86

CHAPTER I INTRODUCTION

1.1 Motivation

The rapid deterioration of civil infrastructure is an urgent problem Constructions become structurally deficient or functionally obsolete in addition to increasing maintenance cost Destroying useless constructions also produces environmental issue, specially for cement-based materials that are almost not recyclable To enhance the robustness, toughness and durability of civil infrastructure under severe mechanical and environmental loads, structural engineers and material scientists have intensively explored stronger and more durable materials Among advanced cement-based

materials achieved recently, Ultra-high-performance fiber-reinforced concrete

(UHPFRC) is one of promising engineered construction materials with its very high toughness and cracking resistance under outstanding behavior: strain- or deflection-hardening behavior accompanied by multiple micro-cracks However, the application

of UHPFRC has still been limitative so far and no design code for UHPFRC is one of reasons Because it causes much difficulty for structural designer and construction owner in project economic evaluation related to reliable factor in design

Size effect is a well-known phenomenon occurring in quasi-brittle material or concrete: the strength of material would change (often decrease) as the specimen size increased (Weibull [1,2], Bažant [3], Bažant and Kazemi [4], Rossi et al [5], Zhou et

al [6], Kim et al [7], Malaikah [8], Wu et al [9]) Although UHPFRCs containing steel fibers are much more ductile than their original mortar matrices, the effects of different sizes on the mechanical properties of UHPFRCs are still questionable, not

of UHPFRCs should be investigated to properly design structural members (e.g., to predict the prototype strength) as well as minimize the size effects.

In a design code of a cement-based material, the mechanical properties of material are usually performed under the uniaxial test: compression and direct tension Specially for UHPFRCs, they are classified according to their tensile behaviors: strain-hardening and strain-softening performance (Marshal and Cox [10], Li at al [11,12], Naaman and Reinhardt [13,14]) However, flexural member has been known as one of the most common structures in a civil construction Therefore, the influences of direct tensile behavior of UHPFRCs on their flexural behavior should be studied: firstly, for predicting flexural behavior from tensile and compressive behavior, and secondly, for enhancing moment resistance capacity of UHPFRCs

The such situation is the motivation for this dissertation focusing on investigating

size dependent mechanical behavior of UHPFRC It is highly expected that the study

results will provide to research community much useful information and fundamental understanding of UHPFRC, finally contribute to the design code of UHPFRCs

1.2 Literature review of UHPFRC

There is great achievement in developing cement-based materials Normal concretewas very early produced, about twelve million years ago, under form of cement deposit resulted from reactions between limestone and oil shale during natural combustion [15] Up to now, normal concrete has still been the most popularly used man-made material After normal concrete, fiber-reinforced cementitious composite (FRCC) was developed as a considerably advanced cement-based material Compared with normal concrete, FRCC has demonstrated higher compressive strength (90 MPa),

UHPFRC was lastly developed with its superior mechanical and material properties as detailed below.

There are two principle components producing UHPFRC: the one is motar matrix (ultra-high-performance concrete, UHPC) and the other is reinforcing fiber added A UHPC itself has an extremely densified microstructure resulting its ultra-high compressive strength (more than 150 MPa), high durability (due to low porosity) and brittle nature The brittleness of UHPC is one of main obstacles for its practical application To improve the nature of UHPCs from brittle to ductile, much research has been reported using steel fibers added to UHPC matrices to form UHPFRC (Chanvillard and Rigaud [17], Maeder et al [18], Rossi et al [19], Benson and Karihaloo [20], Farhat et al [21], Wille et al [22]) It is obviously that the mechanical behaviors of UHPFRC are much dependent on fiber properties such as fiber volume content, fiber type, fiber geometry (aspect ratio, length, shap of cross section) or fiberstrength… Under compression, UHPFRC still showed brittle failure with sudden load drop beyond the limit of proportionality, as illustrated in Fig.1.1 (Nguyen and Kim [23]), although the ductility of the composite was enhanced owing to addition of steel fibers The compressive strength of UHPFRC is ordinarily from 150-200 MPa with modulus of elasticity 40-45 GPa (Nguyen and Kim [23], Graybeal [24]) UHPFRC with a proper fiber content can perform strain-hardening behavior and multiple micro-cracks under direct tension It is observed that UHPFRC showed high post-cracking strength (18 MPa), high ductility (strain capacity 0.6%) and high energy absorption capacity (Park et al [25]) Similar to FRCC, a tensile strain-hardening response of UHPFRC always generate a deflection-hardening behavior, while a tensile strain-softening response may generate a deflection-hardening or a deflection-softening behavior of UHPFRC as described in Fig 1.2(Naaman and Reinhardt [13]) It means that producing a deflection-hardening is easier than producing a tensile strain-hardening The reason is that the cross-section of beam comprises two states of stress: compression and tension, whereas whole tensile cross-section includes only tension

To enhance both the tensile strength and ductility of UHPFRCs by using a small amount of fibers with no difficulty in workability, a hybrid system of fibers, including macro and micro fibers was successfully discovered (Park et al [25]).In the hybrid system, the macro fibers were discovered to be high effective in enhancing ductility while the micro fibers were effective in improving tensile strength Furthermore, the limit in amount of fibers owing to workability for mono macro fibers and mono micro fibers are different Mono macro fibers are limited at about 2% volume content whereas mono micro fibers can be used up to 6% Thus, the use of hybrid fibers can increase the fiber content in composites for enhancing mechanical resistance of UHPFRC.

Generally compared with conventional concrete, UHPFRC is approximately five times higher in compressive strength (200 MPa / 40 MPa), six times higher in direct tension (18 MPa / 3 MPa), higher ductility (ductile failure) and higher durability

Fig 1.2 – Classification of FRCCs (Naaman and Reinhardt [13])

1.3 Goal and objectives

The overall goal of this research is to provide the valuable information about the size dependent mechanical properties of UHPFRC as well as correlation between tensile and flexural behavior of UHPFRC To approach the goal, three major objectives and relative tasks have been conducted as follows:

Objective 1: Investigating the size dependent flexural behavior of UHPFRC The specific tasks for attaining this objective are: 1) carry out an experimental program under bending with different-sized specimens and two types of fiber volume content, 2) evaluate the influence of specimen size on the flexural behavior of UHPFRCs, and

Objective 2: Investigating the size and geometry effect on tensile behavior of UHPFRC The specific tasks for attaining this objective are: 1) carry out an experimental program under direct tension with different sizes and geometries, 2) evaluate the influence of gauge length, 3) evaluate the influence of section area, 4) evaluate the influence of volume, and 5) evaluate the influence of thickness on tensile behavior of UHPFRC.

Objective 3: Investigating correlation between tensile and flexural behavior of UHPFRC The specific tasks for attaining this objective are: 1) propose models of compressive and tensile stress versus strain response for predicting flexural behavior

of UHPFRC, 2) determine condition for a tensile strain-softening of UHPFRCs to produce a deflection-hardening, 3) determine the state of stress and strains at beam bottom at maximum moment resistance of UHPFRCs, and 4) investigate the influence

of tensile strength and strain capacity of UHPFRCs on the moment resistance capacity

of beam

Fig 1.3 – Structure of the dissertation

1.4 Organization of dissertation

This dissertation includes five chapters as shown in Fig 1.3 Chapter I is for introduction of the dissertation while Chapter V is for summary of the work Three middle chapters are about three main objectives mentioned in previous section and related to journal and proceeding papers as follows:

 Chapter II is corresponding to the journal paper: Nguyen D.L., Kim D.J., Ryu G.S, Koh K.T Size effect on flexural behavior of ultra-high-performance

 Chapter III is corresponding to the journal paper: Nguyen D.L., Ryu G.S, Koh K.T, Kim D.J Size and geometry dependent tensile behavior of ultra-high-performance hybrid fiber-reinforced concrete Composites: Part B 58, 2014, pp 279-292.

 Chapter IV is based on two proceeding papers: i) Nguyen D.L and Kim D.J Predicting flexural behavior of ultra-high-performance fiber-reinforced concrete based on uniaxial tensile behavior Proceeding of the 9th Korea-Japan Joint Seminar on Bridge Maintenance, Japan, July 24-27, 2013, pp 77-79 and ii) Nguyen D.L., Kim D.J., Koh K.T, Ryu G.S Gauge length dependent tensile and flexural behavior of ultra-high-performance fiber reinforced concrete The 22nd International Conference on Structural Mechanics in Reactor Technology, San Francisco, California, USA, August 18-23, 2013, Pap-513-ver-1

PUBLICATIONS FROM DISSERTATION

 Nguyen D.L., Kim D.J., Ryu G.S, Koh K.T Size effect on flexural behavior of ultra-high-performance hybrid fiber-reinforced concrete Composites: Part B 45,

2013, pp 1104-1116

 Nguyen D.L., Ryu G.S, Koh K.T, Kim D.J Size and geometry dependent tensile behavior of ultra-high-performance fiber-reinforced concrete.Composites: Part B 58, 2014, pp 279-292

 Nguyen D.L and Kim D.J Predicting flexural behavior of performance fiber-reinforced concrete based on uniaxial tensile behavior Proceeding of the 9th Korea-Japan Joint Seminar on Bridge Maintenance, Japan, July 24-27, 2013, pp 77-79

ultra-high- Nguyen D.L., Kim D.J., Koh K.T, Ryu G.S Gauge length dependent tensile and flexural behavior of ultra-high-performance fiber reinforced concrete The 22nd International Conference on Structural Mechanics in Reactor Technology, San Francisco, California, USA, August 18-23, 2013, Pap-513-ver-1

[7] Kim J K., Yi S.T and Yang E.I Size effect on flexural compressive strength of concrete specimens ACI Structural journal, 2000, Title no 97-S32.

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[14] Naaman A.E., Reinhardt H.W Characterization of high performance fiber reinforced cement composites, in: A.E Naaman, H.W Reinhardt (Eds.), High performance fiber reinforced cement composites: HPFRCC 2 Proceedings of 2nd internationalworkshop on HPFRCC, Chapter 41, RILEM, No 31, E.& FNSpon, London, 1996, pp 1–24

[15] Department of Materials Science and Engineering, University of Illinois, Champaign The History of Concrete, retrieved 8 January 2013

Urbana-[16] Nguyen D.L., Song J., Manathamsombat C., Kim D.J Comparative electromechanical damage-sensing behavior of six strain-hardening steel-fiber-reinforced cementitious composites under direct tension, Composites: Part B 69, 2015,

pp 159-168 (Accepted and online)

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to retrofitting Eng Fract Mech, 2007, 74(1–2):151–67

[22] Wille K., Kim D.J., Naaman A.E Strain hardening UHP-FRC with low fiber contents Mater Struct , 2011, 44:583–98

[23] Nguyen D.L and Kim D.J Compressive behavior of ultra-high-performance fiber-reinforced concretes with steel fibers Conference of Korea Concrete Institute, Jeju, Spring 2014, pp 945-946

[24] Graybeal B Compressive behavior of ultra-high-performance fiber-reinforced concrete ACI Materials Journal, Vol 104, No 2, Mar.-April 2007, pp 146-152.[25] Park S.H., Kim D.J., Ryu G.S., Koh K.T Tensile behavior of ultra high performance hybrid fiber reinforced concrete Cem Concr Compos 2012, 34:172–184

CHAPTER II SIZE EFFECT ON FLEXURAL BEHAVIOR OF ULTRA-HIGH-PERFORMANCE FIBER-

Wille et al [11, 42] recently produced strain-hardening behavior with 14.0–14.9 MPa post-cracking strength and 0.45%–0.61% strain capacity by using only 2% (by volume) high-strength deformed steel fibers in an ultra-high-performance concrete (UHPC) Park et al [12] blended long, deformed steel fibers and short, smooth steel fibers in a UHPC and successfully developed an UHPFRC with 18.6 MPa tensile post-

and 1.5% small, smooth (SS-) fiber by volume The superior tensile properties of UHPFRC using deformed steel fibers are widely expected to increase the practical application of these innovative construction materials.

Although the superior properties of UHPFRC are very attractive to structural engineers who wish to design civil infrastructure and buildings and utilize the advantages of new construction materials, the material properties of UHPFRC used in various sizes might be different due to size effect This factor should be considered in the design code to serve structural engineers obtaining right design Although the test results of structural members would provide the most exact values, the geometry of structural members are various and the testing of them requires huge space, equipments, high cost and much time Thus, the understanding of the size dependent mechanical performance of UHPFRC is highly expected to help the prediction of their performance in large structural members

This situation was the motivation for the experimental study reported in this chapter, which focuses on the flexural response of UHPFRC in different-sized specimens with low fiber contents (1.5%–2.0% by volume), made by blending 1% T-fibers and either 0.5% or 1% SS-fibers The aim of this research is to investigate thesize effect on the behavior of UHPFRCs The specific objectives are to investigate 1) the influence of specimen size on the flexural behavior of UHPFRCs, and 2) the influence of the tensile ductility of UHPFRCs on the size effect

2.1.2 Size Effect on Fiber-Reinforced Concrete

While the size effect on concrete or concrete structural members has been

three types of fibers including twisted steel, spectra, and polyvinyl alcohol The fibers were investigated independently with various volume contents; the researchers reported that the maximum post-cracking strength was less sensitive to size than the strain capacity in tension However, they observed a significant size effect on the flexural behavior of HPFRCC, specifically in flexural strength, deflection, and resulting toughness Lepech and Li [27] investigated the size effect on the flexural behavior of engineered cement composites (ECC), and reported that the size effect on the flexural strength of ECC members was negligible when compared to reinforced concrete specimens due to its high ductility However, they did not discuss the size effect on the flexural ductility Kim et al [28] also carried out bending tests for fiber-reinforced cementitious composites (FRCC) with three different sizes They found that both the flexural strength and normalized deflection capacity increased as the size of the specimens decreased; i.e., there was a clear size effect on the flexural behavior of FRCC However, there is still little information about the size effect on the mechanical and cracking behavior of UHPFRC Reineck at al [29] investigated the influence of specimen size on both tensile and flexural strength of UHPFRC; they reported that the ratio between the width and the depth of the section was also one of the key parameters influencing the tensile and flexural strength For thin flexural members, Spasojevic et al [30] discovered that UHPFRC characterized by a strain capacity of 0.2% to 0.3% showed a reduced size effect on flexural response Overall, the size effect on the mechanical behavior of UHPFRC is still not clearly understood and requires further investigation.

2.2 Theoretical review of size effect

2.2.1 Theoretical review of size effect

There are two major approaches to explain the size effect on the strength of

approach is Weibull’s theory, while the representative deterministic approach is Bažant’s theory based on fracture mechanics Both theories propose that material parameters indicating the brittleness (or ductility) of materials can be used to inform the mechanical properties of materials according to different sizes

Weibull’s theory is well known because it is simple and easy to understand, even though it does not explain the sources of size effect and consider the structural geometry as well as the failure mechanism According to Weibull’s theory, a larger specimen has a weaker strength because it has a higher possibility of having larger and more-severe flaws or defects in specimens Considering the fracture strength of two

different sizes of specimens, S 1 and S 2, with effective volumes V E1 and V E2,respectively, there is a correlation between them [31]:

1

1 2

2 1

m E

where VE is the effective volume of the specimen according to loading condition,

and m (larger than 0) is the Weibull modulus that characterizes the flaw distribution in the material The Weibull modulus m is considered to be a material parameter

describing the size effect

As described in Eq [1], if V E1 is smaller than V E2 , the strength S 1 of the smaller

specimen is higher than the strength S 2of the larger specimen In addition, the Weibull

modulus m indicates the brittleness (or ductility) of material; i.e., the material with the lower value of m is more brittle The probability of failure P f S in Weibull’s theory was provided by Weibull [32] in Eq [2]

where S is the maximum failure strength and S0 is the scale parameter.

Bažant [14] proposed the theory of size effect from a deterministic approach by using fracture mechanics for concrete and quasibrittle materials, described as follows:

2 0

where N is the nominal strength, f t' is the tensile strength of the material, D 0is a

parameter depending on structural geometry, D is the size of the structural member, and B is a parameter characterizing the solution according to plastic limit analysis

based on the strength concept

As illustrated in Fig 2.1 using a logarithmic scale, there are two parts to the dashed line: a horizontal line and an inclined line with a slope of -1/2 The nominal strength

N

 of the material is described by the horizontal dashed line if the material fails by yielding, without any size effect on the strength of the material The inclined line describes the case where the nominal strength is inversely proportional to the square root of the specimen sizeD, based on linear elastic fracture mechanics The nominal strength of concrete according to specimen size is illustrated by a solid curve in Fig 2.1 The curve approaches the horizontal line if the size of the structure or specimen is very small and the inclined line if the member size is very large UHPFRC in this research produced multiple micro-cracks during hardening performance and then eventually failed with a localized major crack which is correlated with deterministic aspect of Bažant’s theory Whereas Weibull’s theory is based on probability of failure, not related to cracking behavior, so it certainly can be used for analysis Thus, this research has been applied both Bažant’s and Weibull’s theory together

Fig 2.1 – Size effects on the strength of brittle material [33]

2.2.2 Flexural behavior of UHPFRC

2.2.2.1 Flexural parameters of UHPFRC

The typical deflection-hardening behavior of UHPFRC is illustrated in Fig 2.2 [13, 34] In Fig 2.2, two points important in describing the flexural behavior are identified

in the equivalent bending stress ( f ) versus normalized deflection by span length ( L) curve: 1) the limit of proportionality (LOP), and 2) the modulus of rupture (MOR) The LOP is defined in this study as the limit of the linear elastic region due to first-cracking while the MOR is defined as the point where the maximum equivalent bending stress occurs [34] The deflection-hardening behavior can be obtained if the maximum equivalent bending strength at the MOR, f MOR , is higher than the equivalent bending strength, f , at the LOP In this research, the first-cracking

the size effect on the flexural behavior of UHPFRC, the f versus  L curve is used

in Fig 2.2, instead of the load (P) versus deflection ( ) curve suggested in [35]

Fig 2.2 – Typical deflection-hardening flexural behavior of UHPFRC

The parameters used in analyzing the size effect on the flexural behavior are the equivalent bending strength (flexural strength f ), normalized deflection ( L), and normalized toughness (normalized energy absorption capacityT ) obtained from the

f versus  L curve, as shown in Fig 2.2

The normalized deflection ( L) is defined as the ratio of the midspan deflection

to the span length, and the normalized toughness (T) is the area under the f versus

L

 curve up to a certain normalized deflection point The equivalent bending stress

f under the four-point bending test (4PBT) is calculated from the equation suggested

2.2.2.2 Deflection-curvature relation at LOP and MOR

The measured deflection of UHPFRC specimens during the flexural test includes the deflection due to moment (M ) and the deflection due to shear (V ) The deflection due to shear (V) is generally negligible in comparison with the deflection due to moment (M) if the ratio between the span and the depth of the specimen is large, otherwise both moment and shear must be considered for analysis Thus, in this study, the deflection measured at the middle of the span was generated from both flexural moment and shear force as described in Eq [5]

M dx  V dx

L L

V M

total    

0

0 0

a unit load at the middle of the span to obtain the deflection at this point

The relationships between moment and curvature as shown in Fig 2.3a and between shear force and strain as shown in Fig 2.3b, proposed by Elsaigh for deflection-hardening FRC [38], are assumed and used for UHPFRC since the typical deflection-hardening of UHPFRC is similar to that of FRC When the specimen is

post crack (BC) Based on these relationships, the diagram of curvature and shear strain can be set up along the beam as shown in Fig 2.4 In the Fig 2.4, the shape of non-linear AB was simplified to be approximately linear (section from LOP to MOR)

in calculating deflection using Eq [5] The midspan deflection at the LOP and MOR can be drawn using Eqs [6] and [7]:

23

1361216

23

L

h k

MOR MOR MOR MOR

LOP LOP

M are the curvature and moment at the MOR, k is the shear coefficient,  is

Poisson’s ratio, and h and L are the depth of the section and the span length,

respectively

M MOR

M LOP

MOR LOP

shear force and shear strain (b) [38]

MOR LOP Due to M

LOP

L/3

P L/3 L/3

L/2 L/2

M

M PL/6 Diagram M due to P

P 1 Zone 2 Zone 1 Zone 2 Zone 2 Zone 1 Zone 2

L/3

2.2.2.3 Cracking behavior of UHPFRCs under four-point bending

Fig 2.5 shows the typical multiple-cracking behavior of UHPFRCs under 4PBT The flexural specimen under 4PBT can be divided into two zones, zone 1 and zone 2,according to the load condition shown in Fig 2.5 Zone 1 is the middle one-third of the span where multiple cracks are generated only by constant moment The multiple cracks generated in zone 1 are uniformly distributed; thus, the length of zone 1 can be considered as the flexural gage length similar to the gage length in a direct tensile test Zone 2 includes the two-thirds of the span (one-third each at either side of zone 1) where the cracking behavior is influenced by shear as well as moment The magnitude

of the shear force in zone 2 is constant while the magnitude of the moment increases linearly from the support to zone 1 Consequently, the cracks in zone 2 are non-uniform and gradually increased from the support to zone 1 Under 4PBT for UHPFRC, multiple densely spaced cracks develop in zone 1, while relatively few sparsely spaced cracks develop in zone 2

Fig 2.5 – Distribution of moment, shear, and cracks along beam