SIZE EFFECT IN NORMAL AND HIGH-STRENGTH CONCRETE CYLINDERS SUBJECTED TO STATIC AND DYNAMIC AXIAL COMPRESSIVE LOADS

ABSTRACT

Concrete structures have traditionally been designed on the basis of strength criteria.  This implies that geometrically similar structures of different sizes should fail at the same nominal stress.  However, this is not quite true in many cases because of the Size Effect, which may be understood as the dependence of the concrete structure on its characteristic dimension.  The actual concrete strength of relatively larger structural members may be significantly lower than that of the standard size.  By neglecting the Size Effect, predicted load capacity values become increasingly less conservative as a member size increases.  Also, very large structures such as dams, bridges, and foundations are too large and too strong to be tested at full scale in the laboratory.  In recent years, major advances have been made in understanding of scaling and Size Effect.  However, these advances remain only in the static domain (i.e., slow loading rates), and none of the previous studies have addressed the effect of higher loading rates or high-strength concrete (HSC) on the Size Effect.  Structural concrete can be subjected to high loading rates, such as those associated with impact and explosion incidents.  Such load conditions are generated by dropped objects, vehicle collision into structures, accidental industrial explosions, missile impacts, military explosions, etc.  The Size Effect in normal strength concrete (NSC) is a phenomenon explained by a combination of plasticity and fracture mechanics, and it is related to the energy balance during the damage/fracture process which causes a change in the mode of failure of the concrete member with the increase in its size, thus causing a reduction in its strength. Although structural response and damage evolution are expected to be size-dependent, it is not clear how time or the material strength affect this phenomenon.  In this study, the Size Effect phenomenon was investigated under   compressive static and impact loads for both normal and high-strength concrete cylinders.  This study was conducted by performing 127 compressive static and impact tests on both normal and high-strength concrete and 192 numerical simulations. The tests provided data whose analysis produced evidence on the effect of loading rate and material strength on the Size Effect for structural concrete in compression. Parallel pre- and post-test computational simulations were used to perform ‘numerical tests’ of the same specimens, and to explore the role of the time dimension on the physical phenomena that contribute to the Size Effect. Comparisons between test and numerical data assisted and guided the investigators in identifying the governing parameters that define the physical phenomena. In addition, the precision test data assisted in validating the computational tools used for the study.  This thesis describes this multinational collaborative study (with experimental tests performed at three different locations: Penn State University, USA; the National Defense Academy, Japan; and the University of British Colombia, Canada), and it presents data from both the unique impact tests and the related numerical simulations. Two material models were developed to simulate the dynamic Size Effect that was proved to exist in this study.  The study also proved the existence of Size Effect in parameters other than strength such as the modulus of elasticity and the strain at maximum stress.  This necessitated modifying the existing Size Effect which was mainly confined to the strength parameter only.  Use of high-speed photography enabled the detection of several modes of failure experienced by concrete cylinders subjected to axial impact.     TABLE OF CONTENTS LIST OF FIGURES………………………………………………………………………………………….. viii LIST OF TABLES……………………………………………………………………………………………. xii NOMENCLATURE………………………………………………………………………………………….. xiv ACKNOWLEDGMENTS…………………………………………………………………………………. xvi    

CHAPTER ONE INTRODUCTION………………………………………………………………………………………………..1

1.1        Research Significance………………………………………………………………………………… 1 1.2       Objective and Scope…………………………………………………………………………………… 2 1.3 Thesis Layout……………………………………………………………………………………………. 3  

CHAPTER TWO LITERATURE REVIEW……………………………………………………………………………………..4

2.1        Introduction………………………………………………………………………………………………. 4 2.2 Classical Definition of Size Effect……………………………………………………………….. 4 2.3 Proposed Modification to the Definition of Size Effect ………………………………….. 5 2.4       Background ………………………………………………………………………………………………. 5 2.5       Evidence of Size Effect………………………………………………………………………………. 7 2.5.1 Theoretical Evidence……………………………………………………………………………………………………………7 2.5.2 Experimental evidence…………………………………………………………………………………………………………9 2.5.2.1 Size Effect in Concrete Compressive Strength…………………………………………………………………9 2.5.2.2 Size Effect in Concrete Tensile Strength………………………………………………………………………….9 2.5.2.3 Size Effect in Strain Gradient and Cracking Strain ………………………………………………………..10 2.5.2.4 Size Effect in Ultimate Shear Strength…………………………………………………………………………..10 2.5.2.5      Size Effect in Diagonal Shear Failure of Beams without Stirrups………………………………….10 2.5.2.6 Torsional failure ……………………………………………………………………………………………………………..11 2.5.2.7 Punching shear failure of slabs……………………………………………………………………………………….11 2.5.2.8 Pull-out failures………………………………………………………………………………………………………………11 2.5.2.9 Compression failure of tied columns………………………………………………………………………………11 2.5.2.10 Three-point bending of beams ………………………………………………………………………………………..11 2.5.2.11 Influence of Specimen Size on Elastic Modulus of Concrete…………………………………………12 2.6 Explanation of Size Effect ………………………………………………………………………… 12 2.6.1 Statistical Theory ……………………………………………………………………………………………………………….12 2.6.2 Energy Theory and the Size Effect Law…………………………………………………………………………….14 2.6.3 Boundary Layer Effect……………………………………………………………………………………………………….19 2.6.4 Diffusion Phenomena…………………………………………………………………………………………………………20 2.6.5          Hydration Heat or Other Phenomena Associated With Chemical Reactions……………………..22 2.6.6     Influence of aggregate size on Size Effect …………………………………………………………………………22 2.7        Size Effect in High-Strength Concrete (HSC)……………………………………………… 23 2.8       Size Effect in the Dynamic Domain …………………………………………………………… 24 2.9       Design and Code Issues ……………………………………………………………………………. 25 2.10      Summary of Key Issues for this Study……………………………………………………….. 27  

CHAPTER THREEMETHODOLOGY……………………………………………………………………………………………..28

3.1       Pre-test Simulations …………………………………………………………………………………. 29 3.1.1      Description of the Concrete Constitutive Models………………………………………………………………32 3.2       Tests ………………………………………………………………………………………………………. 37 3.2.1       Tests on Normal-Strength Concrete (NSC) Cylinders……………………………………………………….37 3.2.2 Tests on High-Strength Concrete (HSC) Cylinders……………………………………………………………41 3.2.3 Data Obtained From the Tests……………………………………………………………………………………………42 3.3       Post-test simulations ………………………………………………………………………………… 43 3.4 Statement of Work …………………………………………………………………………………… 49  

CHAPTER FOURINSTRUMENTATIONS AND TEST SETUP……………………………………………………..51

4.1        Introduction…………………………………………………………………………………………….. 51 4.2 Drop Hammers………………………………………………………………………………………… 52 4.2.1 Drop hammer at Penn State University………………………………………………………………………………52 4.2.2    Drop hammer at NDA, Japan…………………………………………………………………………………………….58 4.2.3    Drop Hammers at UBC, Canada………………………………………………………………………………………..61 4.3       Response Measurement…………………………………………………………………………….. 63 4.3.1 Background………………………………………………………………………………………………………………………..63 4.3.2 Sensors and Transducers……………………………………………………………………………………………………65 4.3.3 Sensor selection………………………………………………………………………………………………………………….65 4.3.3.1 Load Cells ………………………………………………………………………………………………………………………66 4.3.3.2 Accelerometers……………………………………………………………………………………………………………….67 4.3.3.3 Strain Gages……………………………………………………………………………………………………………………69 4.4 High-Speed Data Acquisition Systems……………………………………………………….. 71 4.4.1 Data Acquisition System at Penn State University (PSU)………………………………………………….72 4.4.2         Data Acquisition System at the National Defense Academy (NDA)…………………………………76 4.4.3         Data acquisition system at the University of British Colombia (UBC)………………………………77 4.5 High-Speed Photography………………………………………………………………………….. 78  

CHAPTER FIVERESULTS AND DISCUSSION – HIGH-STRENGTH CONCRETE…………………..80

5.1 Pre-test Simulations …………………………………………………………………………………. 80 5.2 Tests ………………………………………………………………………………………………………. 84 5.3       Comparison of Test and Pre-Test Simulation Results …………………………………… 89 5.4 Post-test simulations ………………………………………………………………………………… 92 5.5 Results……………………………………………………………………………………………………. 95 5.6        Discussion of Results……………………………………………………………………………….. 97 5.7 Summary of main achievements………………………………………………………………… 99  

CHAPTER SIXRESULTS AND DISCUSSION – NORMAL-STRENGTH CONCRETE………….101

6.1 Pre-test Simulations ……………………………………………………………………………….. 102 6.1.1 Hard Impact Pre-Test Simulations……………………………………………………………………………………103 6.1.2    Soft Impact Pre-Test Simulations…………………………………………………………………………………….103 6.2 Tests …………………………………………………………………………………………………….. 108 6.2.1 Static Tests Results…………………………………………………………………………………………………………..109 6.2.2 Dynamic Tests Results……………………………………………………………………………………………………..110 6.2.2.1   Dynamic Tests Performed at Penn State University……………………………………………………..110 6.2.2.2   Dynamic Tests Performed at the NDA, Japan………………………………………………………………121 6.2.2.3 Dynamic Tests Performed at UBC, Canada………………………………………………………………….126 6.3 Study of Tests Results…………………………………………………………………………….. 130 6.4 Comparison of Test and Pre-Test Simulation Results …………………………………. 133 6.5       Post-test simulations ………………………………………………………………………………. 138 6.5.1       Results of Post-Test simulations of Penn State Tests……………………………………………………….139 6.5.1.1 Hard Impact Tests…………………………………………………………………………………………………………139 6.5.1.2 Soft Impact Tests………………………………………………………………………………………………………….140 6.5.2      Results of Post-Test simulations of NDA Tests……………………………………………………………….142 6.5.2.1 Hard Impact Tests…………………………………………………………………………………………………………142 6.5.2.2 Soft Impact Tests………………………………………………………………………………………………………….143 6.5.3      Results of Post-Test simulations of UBC Tests………………………………………………………………..144 6.6 Summary of Results……………………………………………………………………………….. 145 6.7 Discussion of Results……………………………………………………………………………… 148 6.8 Summary of main achievements………………………………………………………………. 149  

CHAPTER SEVENRESULTS AND DISCUSSION – COMPARISON OFNORMAL-STRENGTH AND HIGH-STRENGTH CONCRETE RESULTS…………………………………………..151

7.1 Static Test Results………………………………………………………………………………….. 151 7.1.1 Static Tests Data and the Size Effect Law………………………………………………………………………..151 7.1.2 Modulus of Elasticity……………………………………………………………………………………………………….154 7.1.3 Strain at Maximum Stress………………………………………………………………………………………………..155 7.2 Dynamic Test Results …………………………………………………………………………….. 156 7.2.1 Modes of Failure ………………………………………………………………………………………………………………157 7.2.2 Strength Criteria ……………………………………………………………………………………………………………….166 7.2.3 Loading Rate Effect………………………………………………………………………………………………………….168 7.2.4   Strains at Maximum Stress……………………………………………………………………………………………….168 7.3       Models performance ………………………………………………………………………………. 172 7.4 Summary of main achievements………………………………………………………………. 179  

CHAPTER EIGHTCONCLUSIONS AND RECOMMENDATIONS………………………………………………181

8.1       Conclusions …………………………………………………………………………………………… 181 8.2       Recommendations ………………………………………………………………………………….. 183  BIBLIOGRAPHY…………………………………………………………………………………………….185  APPENDIX ONE FLOW CHARTS OF WORK DATA ………………………………………………………………..193  APPENDIX TWO SAMPLE OF RAW TEST RESULTS……………………………………………………………..202  APPENDIX THREE SAMPLE OF PROCESSED TEST RESULTS………………………………………………..205  APPENDIX FOUR SAMPLE OF COMPARISON OF STRESS-TIME HISTORY OBTAINED FROM TEST AND FROM MODEL…………………………………………………………………………….212

LIST OF FIGURES

CHAPTER ONE

INTRODUCTION

1.1 Research Significance

Concrete structures have traditionally been designed on the basis of strength criteria.  This implies that geometrically similar structures of different sizes should fail at the same nominal stress.  However, this is not quite true in many cases because of the Size Effect, which may be understood as the dependence of the concrete structure on its characteristic dimension.   To civil engineers, the Size Effect is of paramount importance.  Concrete structures are designed based on the strength of a standard specimen size.  The actual concrete strength of relatively larger structural members may be significantly lower than that of the standard size.  By neglecting Size Effect, predicted load capacity values become increasingly less conservative as a member size increases.  Also, very large structures such as dams, bridges, and foundations are too large and too strong to be tested at full scale in the laboratory.   In recent years, major advances have been made in understanding of scaling and Size Effect.  However, these advances remain only in the static domain (i.e., slow loading rates), and none of the previous studies have addressed the effect of higher loading rates or high-strength concrete (HSC) on the Size Effect.  Structural concrete can be subjected to high loading rates, such as those associated with impact and explosion incidents.  Such load conditions are generated by dropped objects, vehicle collision into structures, accidental industrial explosions, missile impacts, military explosions, etc.   The Size Effect in normal strength concrete (NSC) is a phenomenon explained by a combination of plasticity and fracture mechanics, and it is related to the energy balance during the damage/fracture process. Although structural response and damage evolution are expected to be size-dependent, it is not clear how time or the material strength affect this phenomenon.

1.2 Objective and Scope

The objective of this study is to assess the effect of time on the Size Effect for both normal-strength concrete (NSC) and high-strength concrete (HSC) cylindrical specimens under compressive severe dynamic loading conditions (loading rates of 10^-3 sec). The study was conducted by performing both static and dynamic tests and parallel numerical simulations. The tests provided data whose analysis produced evidence on the effect of loading rate and material strength on the Size Effect for structural concrete in compression. Parallel pre- and post-test computational simulations were used to perform ‘numerical tests’ of the same structural/material specimens, and to explore the role of the time dimension on the physical phenomena that contribute to the Size Effect. A comparison between test and numerical data was done to assist and guide the investigator in developing a better understanding of the Size Effect phenomenon (with emphasis on short duration dynamics).  In additions, the precision impact test data assisted in validating the computational tools used for the study.   The dissertation describes the outcome of the experimental and numerical investigation, and it presents data from both the impact tests and the related numerical simulations.  Discussions of the findings lead to conclusions and recommendations for future research and possible implementation of these findings into the design of impact and blast resistant structural concrete buildings and systems.

1.3 Thesis Layout

Chapter One of this thesis is an introduction that lists the scope and objective of the thesis.  Chapter Two is a background of the Size Effect phenomenon and the current state of knowledge in this area.  Chapter Three outlines the methodology of the study.  Chapter Four is a description of the test setup and the instrumentations used in the three different test locations.  Chapters Five and Six present the results of the tests and the simulations for the high-strength and normal strength concrete cylinders respectively, theses chapters also include a discussion of the results obtained.  The results for the high-strength and normal-strength concrete are compared in Chapter Seven, and conclusions and recommendations for future work are given in Chapter Eight. Flow charts of work data and samples of the results of the tests and the simulations are given in the Appendices.

SIZE EFFECT IN NORMAL AND HIGH-STRENGTH CONCRETE CYLINDERS SUBJECTED TO STATIC AND DYNAMIC AXIAL COMPRESSIVE LOADS