Luận án: Hành vi cơ học phụ thuộc kích thước của bê tông cường độ cực cao cốt sợi UHPC

Size dependent mechanical behavior of ultra-high-performance fiber-reinforced concrete Duy Liem NGUYEN February 2015 Department of Civil & Environmental Engineering The Graduate School Sejong University 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 DEDICATION I would like to dedicate this dissertation to my parents and my wife who have supported me all the way ACKNOWLEDGEMENTS 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 Abstract There has been much interest on enhancing the robustness, toughness and durability of civil infrastructure under severe mechanical and environmental loading conditions.

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), CEMTECmultiscale and CARDIFRC into various civil infrastructure, e., 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 code for 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 UHPFRCs under 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 smooth steel 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 higher size 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 UHPFRCs was analytically investigated.

The models for compressive and tensile stress versus strain responses of UHPFRCs were proposed. One model was proposed for the compressive 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 predicted flexural behavior, including the condition for generating deflection-hardening behavior. Keywords: ultra-high-performance fiber-reinforced concrete; size effect; post cracking strength; modulus of rupture; strain hardening; deflection hardening.

국문초록 시험체 크기에 따른 초고강도 섬유보강 콘크리트의 역 학적 거동 건설환경공학과 세종대학교 대학원 Duy Liem NGUYEN 초고성능 섬유보강 콘크리트 (Ultra High Performance Fiber Reinforced Concrete, UHPFRC)는 등의 우수한 역학적 특성과 치밀한 조직을 기반으로 높은 내구성이 기대되는 차세대 건설재료이다. 하지만, 현재 UHPFRC 의 압축, 인장 그리고 휨인장 거동에 대하여 보고된 결과들은 대부분 실험실에서 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 섬유를 보강하지 않은 초고성능 콘크리트 (Ultra High Performance Concrete, UHPC)의 경우 매우 취성적인 거동을 나타내어, 섬유를 보강한 UHPFRC 가 연성적인 거동을 보인다고 하더라도, 실험체 크기가 UHPFRC 의 역학적 거동에 미치는 영향을 정확하게 조사하여 설계에 반영할 필요가 있다.

논문의 연구결과는 UHPFRC 의 설계기준을 만들기 위해 유용한 정보와 기본적인 이해를 제공 할 것으로 기대된다. 이를 위해 아래와 같은 세 가지 세부 연구목표들이 달성되었다. 1) UHPFRC 의 휨인장 거동은 시험체의 크기 변화에 따라서 영향을 받는다. 즉, 시험체의 크기가 커질수록 휨강도, 처짐능력, 그리고 에너지 흡수능력이 분명하게 저하하는 경향을 나타내었다.

하지만, UHPFRC 의 연성도, 즉 섬유보강량이 증가할수록 휨인장 거동에 시험체의 크기효과가 미치는 영향이 감소하였다. 이러한 UHPFRC 의 휨 거동에 영향을 미치는 시험체의 크기 효과는 시험체가 휨 하중을 받아 최대 휨인장 강도를 보일 때 휨 인장 시험체의 하단에 유발되는 최대 휨인장 변형률과 밀접한 관계를 가지고 있다. 또한 UHPFRC 의 크기효과를 보여주는 그래프를 제시하였다. 2) UHPFRC 의 직접 인장 강도는 시험체 크기에 따른 뚜렷한 경향을 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 연구결과들에 근거하여, 그 휨 인장 거동과 매우 밀접한 상관관계를 가진다. UHPFRC 의 휨 거동 예측을 위해, UHPFRC 의 압축과 직접인장 거동을 단순화한 해석 식들을 제안하였다. 또한, 변형경화 거동을 나타내기 위한 조건 식들에 대한 검토를 수행하였으며, 최대 휨 강도 점에서의 UHPFRC 의 단면 변형률과 응력 분포가 그 UHPFRC 의 최대 모멘트 저항강도와 그 점에서의 처점에 어떠한 영향을 미치는지 상세히 조사하였다. 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.2 Literature review of UHPFRC .3 Goal and objectives .4 Organization of dissertation .7 CHAPTER II: SIZE EFFECT ON FLEXURAL BEHAVIOR OF ULTRA- HIGH-PERFORMANCE FIBER-REINFORCED CONCRETE .2 Size effect on fiber-reinforced concrete.2 Theoretical review of size effect .1 Theoretical review of size effect.2 Flexural behavior of UHP-HFRC .3 Materials and test methods .2 Materials and specimen preparation .3 Test setup and procedure .4 Results and discusion .1 Deflection-hardening behavior of UHP-HFRCs.2 Size effect on flexural behavior of UHP-HFRCs.3 Influence of material ductility on the size effect.4 Parameters of size effect: Weibull modulus m and Bažant parameters B and D0. 45 CHAPTER III: SIZE AND GEOMETRY EFFECT ON TENSILE BEHAVIOR OF ULTRA-HIGH-PERFORMANCE FIBER-REINFORCED CONCRETE .2 Size dependent mechanical properties of cement-based materials.3 Strain-hardening tensile behavior of UHPFRC.1 Materials and specimen preparation .2 Test setup and procedure .5 Result and discusion.1 Distribution of fibers within the cross-section.2 Effects of size and geometry of specimens on the tensile response of UHPFRC. 86 CHAPTER IV: CORRELATION BETWEEN TENSILE AND FLEXURAL BEHAVIOR OF ULTRA-HIGH-PERFORMANCE FIBER-REINFORCED CONCRETE .2 Predicting flexural behavior of UHPFRCs based on their tensile behaviors.1 Proposed model for predicting flexural behavior of UHPFRCs .3 Comparison with experimental test .3 Difference between gauge length dependent tensile and flexural behavior of UHPFRC .115 CHAPTER V: SUMMARY, CONCLUSIONS AND FUTURE WORKS .1 Summary and conclusions.1 Conclusions related to the size effect on flexural behavior of UHPFRC .2 Conclusions related to the size and geometry effect on tensile behavior of UHPFRC.3 Conclusions related to the correlation between tensile and flexural behavior of UHPFRC .2 Recommendations for future research.124 iii LIST OF FIGURES Fig.1 – Compressive behavior of UHPFRC using 1% twist fiber blended with 1% short smooth fiber by volume (Nguyen and Kim [23]).2 – Classification of FRCCs (Naaman and Reinhardt [13]).3 – Structure of the dissertation .1 – Size effects on the strength of brittle material [33].2 – Typical deflection–hardening flexural behavior of UHP–HFRC .3 – Relationships between moment and curvature (a) and shear force and shear strain (b) [38].4 – Distribution along beam of moment–curvature (M–) and shear force–shear strain (V–).5 – Distribution of moment, shear, and cracks along beam .6 – Photo of specimen with multiple cracks .7 – Photos of fibers .8 – Three types of flexural specimen .9 – Test setup for bending test .10 – Average load ( P ) versus deflection (  ) curve of UHP–HFRCs for various specimen sizes .11 – Average equivalent bending stress ( f ) versus normalized deflection (  L ) curve of UHP–HFRCs for various specimen sizes.12 – Multiple–cracking behavior of UHP–HFRCs.13 – Size effect on equivalent bending strength .14 – Size effect on normalized deflection at MOR.15 – Size effect on normalized toughness at MOR. 16 – Size effect on cracking behavior of UHP–HFRCs.17 – Tensile behavior of UHP–HFRCs.18 – Weibull distribution for UHP–HFRCs.19 – General graph of size effect law of UHP–HFRCs .1 – Tensile behavior of UHPFRC and investigated size parameters .2 – Shape of tensile specimens and molds .3 – Tensile test set-up and external load cells used .4 – Average tensile stress versus strain response of UHPFRC according to different geometry and size .5 – Multiple cracking behavior of UHPFRC according to different geometry and size.6 – Typical fiber distribution at section near the major crack.7 – Effects of gauge length on tensile parameters of UHPFRC.8 – Effects of section area on tensile parameters of UHPFRC .9 – Effects of volume on tensile parameters of UHPFRC .10 – Effects of thickness on tensile parameters of UHPFRC .11 – Modeling specimen as a chain in comparison of different gauge lengths.12 – Influence of  pc on complementary energy.13 – Volume effect under bridging comparison .14 – Assumed distribution of defects.15 – Sensitivity of size parameters in illustration .16 – Effects of normalized size parameters on normalized tensile parameters of UHPFRC.1 – Proposed models for compressive and tensile behavior of UHPFRCs .2 – Assumed strain and stress distribution along the depth of section for strain- hardening behavior of UHPFRC .3 – Assumed strain and stress distribution along the depth of section for strain- softening behavior of UHPFRC with no clear sudden load drop,  pc   cc .4 – Assumed strain and stress distribution along the depth of section for strain- softening behavior of UHPFRC with a clear sudden load drop,  pc   cc .5 – Typical moment versus curvature response of UHPFRC (Kim et al.6 – Condition for tensile models to surely produce deflection-hardening of UHPFRCs and the flexural stress and strain at beam bottom at MOR.7 – Effect of softening slope E2 on flexural parameters of tensile strain- hardening UHPFRCs.8 – Effect of softening slope E1 on flexural parameters of tensile strain- softening UHPFRCs with no sudden load drop .9 – Effect of  pc /  cc ratio on flexural parameters of tensile strain-softening UHPFRCs with sudden load drop .10 – The assumed strain and stress distribution at section and three cases of UHPFRCs.11 – The flexural behavior of UHPFRC obtained from prediction and from experimental test .12 – Geometry of tensile and flexural specimens .