NUMERICAL MODELLING OF REINFORCED CONCRETE MEMBERS UNDER IMPACT LOAD by MD. SHAHARIAR FEROJ HOSSAIN MASTER OF SCIENCE IN CIVIL ENGINEERING (STRUCTURE) DEPARTMENT OF CIVIL ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY DHAKA, BANGLADESH FEBRUARY, 2015 i The thesis titled “NUMERICAL MODELLING OF REINFORCED CONCRETE MEMBERS UNDER IMPACT LOAD” submitted by MD. SHAHARIAR FEROJ HOSSAIN, Roll no: 1009042322P, Session: October 2009; has been accepted as satisfactory in partial fulfillment of the requirement for the degree of Master of Science in Civil Engineering (Structure) on 18 February 2015. BOARD OF EXAMINERS Dr. Tahsin Reza Hossain Chairman Professor Department of Civil Engineering BUET, Dhaka-1000 Dr. A.M.M. Taufiqul Anwar Member (Ex-Officio) Professor and Head Department of Civil Engineering BUET, Dhaka-1000 Dr. Bashir Ahmed Member Professor Department of Civil Engineering BUET, Dhaka-1000 Dr. Sharmin Reza Chowdhury Member (External) Associate Professor Department of Civil Engineering Ahsanullah University of Science and Technology, Dhaka ii DECLARATION It is hereby declared that except for the contents where specific references have been made to the work of others, the study 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 for a Degree, Diploma or other qualification (except for publication) Signature of the Candidate (Md. Shahariar Feroj Hossain) iii ACKNOWLEDGEMENT First of all, I praise and thank Almighty Allah for giving me strength and ability to complete this research work. I would like to gratefully and sincerely thank Dr. Tahsin Reza Hossain, Professor, Department of Civil Engineering, Bangladesh University of Engineering and Technology, BUET, Dhaka, for his guidance, understanding, patience, and most importantly, his friendship during my research work. He helped me by providing necessary references, books and valuable advices. I would also like to thank the Head of the Department of Civil Engineering, BUET for providing all the facilities of the Department in materializing this work. Additionally, I am very gratefully acknowledges the cooperation of all concerned persons and offices of BUET for their helps and advices. Finally, it is also a good opportunity to express my sincere respect and gratitude to my father and mother for their continuous encouragement and blessings in completing the research work. iv ABSTRACT Response due to impact load is different from that caused due to static load. Broadly, the impact load can be classified into i) low velocity large mass impact and ii) high velocity small mass impact. The first category involves collision of vehicle into crash barriers, piers of bridges, drop of an object on slab etc. whereas the second one includes bullet or missile hitting structures, birds hitting airplane etc. Reinforced concrete (RC) members are often subjected to extreme dynamic loading condition due to direct impact. In context of Civil Engineering problem, an investigation into the impact behaviour of RC members subjected to low velocity high mass is very important. The current work deals with low velocity large mass impact on RC structures. Full-scale test of RC member under impact load is very expensive and time-consuming work. The numerical finite element (FE) analysis of RC member has become an effective and reliable solution to overcome this problem. Before carrying out numerical simulation of RC member under impact load, some existing literatures on the relevant field based on experimental, analytical and numerical approaches are thoroughly reviewed. RC members have been modeled by nonlinear FE software ABAQUS (2012). The nonlinearity of RC member has been achieved by incorporating nonlinear effects due to cracking and crushing of concrete and yielding of steel reinforcement. The Concrete Damage Plasticity (CDP) model has been used with appropriate parameters to model the nonlinear behaviour of concrete material and elastic-plastic material has been selected for steel reinforcement. Performance of this numerical simulation has been validated against experimental as well as analytical results for static loads. The numerical simulation is then extended to impact loading. A number of beams and slabs tested by Chan and May (2009) under impact load has been modeled and observed responses have been found to be comparable. The transient impact force histories and crack patterns obtained from FE analysis of these beams and slabs match reasonably well with the test results but a time lag has been observed between peak impact forces for FE analysis. So, CDP model provides consistent results for static as well as impact analysis of RC members. A series of RC beams subjected to low speed high mass impact, tested by Tachibana et al. (2010), has been numerically modeled and analyzed. From the observation of these analyzed beams it is noted that, if only global v damage is under consideration and analyzed RC beam is failed completely due to high mass low velocity impactor‟s load then impulse, total area under time-force curve, only depend upon the momentum of impactor. The duration of impact load varies proportionally with the ratio of momentum of impactor to ultimate bending capacity of beam. The beam fails completely, if the mean impact force exceeds 1.37 times of its ultimate bending capacity. The bending capacity of RC column is also be increased by 1.37 times of its actual capacity, if the failure is governed by tension. But axial capacity will be reduced by 0.91 times when failure is by crushing of concrete before tension yielding. vi CONTENTS DECLARATION .......................................................................................................... iii ACKNOWLEDGEMENT ............................................................................................ iv ABSTRACT .................................................................................................................... v CONTENTS .................................................................................................................. vii LIST OF FIGURES ..................................................................................................... xii LIST OF TABLES ..................................................................................................... xvii NOTATIONS ............................................................................................................... xix Chapter 1: Introduction ................................................................................................. 1 1.1 Background and Present State of the Problem ........................................................ 1 1.2 Objectives with Specific Aims and Possible Outcome .......................................... 2 1.3 Methodology of Work ............................................................................................ 3 1.4 Outlines of the Thesis ............................................................................................. 4 Chapter 2: Literature Review ....................................................................................... 5 2.1 Introduction ............................................................................................................ 5 2.2 Classification of Impact Events Considering Response of Target Structure .......... 5 2.3 Investigation Technique of Impact Events ............................................................. 7 2.3.1 Impact Behaviour of Concrete Beams ............................................................. 7 2.3.2 Failure mode of RC beam under impact load .................................................. 9 2.4 Experimental Investigation of RC Bram under Impact load ................................ 10 2.4.1 Experimental investigation of RC beam carried out by Mylrea (1940) ......... 10 2.4.2 Experimental investigation of RC beam carried out by Feldman et al. (1956, 1958, 1962) ............................................................................................................. 11 2.4.3 Experimental investigation of RC beam carried out by Hughes and Speirs (1982) ...................................................................................................................... 11 2.4.4 Experimental investigation of RC beam carried out by Ando et al. (1999)... 11 2.4.5 Experimental investigation of RC beam carried out by Kishi et al. (2001) ... 12 2.4.6 Experimental investigation of RC beam carried out by Magnusson et al. (2000) ...................................................................................................................... 14 2.4.7 Experimental investigation of RC beam carried out by May et al. (2005, 2006) and Chen and May (2009) ............................................................................ 16 vii 2.4.8 Experimental investigation of RC beam carried out by Saatci and Vecchio (2009a) .................................................................................................................... 17 2.4.9 Experimental investigation of RC beam carried out by Fujikake et al. (2009) ................................................................................................................................. 18 2.5 Analytical Models for Impact Loading on RC Member ....................................... 25 2.5.1 Proposed analytical models carried out by Hughes and Speirs (1982) and Hughes and Beeby (1982) ....................................................................................... 26 2.5.2 Proposed idealizing single degree of freedom system carried out by Comite Euro-International Du Beton (CEB, 1988) ............................................................. 29 2.6 Numerical Model of RC Beam under Impact Load.............................................. 31 2.6.1 Numerical Model of RC Beam under Impact Load carried out by Sangi, A. J. (2011) ...................................................................................................................... 31 2.7 Impact Behaviour of RC Slabs ............................................................................. 33 2.7.1 Impact tests on RC slabs carried out by Sawan and Abdel-Rohman (1986) . 35 2.7.2 Impact tests on RC slabs carried out by Kishi et al. (1997) ........................... 36 2.7.3 Impact tests on RC slabs carried out by Zineddin and Krauthammer (2007) 36 2.7.4 Impact tests on RC slabs carried out by Chen and May (2009) ..................... 37 2.8 Impact Behaviour of Concrete Column ................................................................ 37 2.8.1 Impact tests on RC Column carried out by Leodolft (1989) ......................... 38 2.8.2 Impact tests on RC Column carried out by Feyerabend (1988) ..................... 38 2.8.3 Impact tests on RC Column carried out by Gebbeken et al. (2007) .............. 40 2.9 FE Modelling ........................................................................................................ 40 2.9.1 FE package ..................................................................................................... 41 2.9.2 An overview of ABAQUS (2012) ................................................................. 41 2.9.3 FE modelling of RC ....................................................................................... 44 2.9.4 Contact algorithms ......................................................................................... 47 2.10 Constitutive Concrete Material Models .............................................................. 47 2.10.1 Concrete Damage Plasticity model .............................................................. 48 2.10.2 Material model for reinforcing steel ............................................................ 50 2.11 Damping Coefficients ......................................................................................... 50 2.12 Summary ............................................................................................................. 50 Chapter 3: Nonlinear FE modelling Validation ........................................................ 52 3.1 Introduction .......................................................................................................... 52 viii 3.2 FE Modelling in ABAQUS (2012) ....................................................................... 52 3.3 Validation of FE Model of RC Beam under Static Load with Test Result .......... 54 3.3.1 Dimension of tested RC beam by Saatci (2007) ............................................ 54 3.3.2. Modelling of tested beam by Saatci (2007) .................................................. 56 3.3.3 Response of MS0 beam ................................................................................. 57 3.3.4 Response of MS1 beam ................................................................................. 58 3.3.5 Response of MS2 beam ................................................................................. 58 3.4 Validation of FE Model of RC Slab under Static Load Tested by McNeice (1967) .................................................................................................................................... 60 3.5 Validation of RC Beam Modelling with Theoretical Result ................................ 62 3.5.1 Response of beam .......................................................................................... 65 3.6 Linear FE Analysis of SDOF System under Dynamic Load ................................ 74 3.6.1 Lateral stiffness of the structure ..................................................................... 75 3.6.2 Response to free vibration.............................................................................. 76 3.6.3 Response to step load ..................................................................................... 80 3.6.4 Validation of dynamic equation of equilibrium ............................................. 82 3.7 Response of Nonlinear SDOF System to Free Vibration ..................................... 83 3.8 FE Analysis of SDOF Beam under Impact Load ................................................. 88 3.9 Summary ............................................................................................................... 90 Chapter 4: FE modelling of RC Beam and Slab under Impact ............................... 92 4.1 Introduction .......................................................................................................... 92 4.2 FE Analysis of RC Beam under Impact Load ...................................................... 92 4.3 Simulations of Beam with Plywood Pad at Interface of Beam and Impactor ...... 93 4.3.1 Element‟s modelling ...................................................................................... 93 4.3.2 Parts interaction ............................................................................................. 94 4.3.3 Material property ........................................................................................... 94 4.4 Mesh Sensitivity of Beam with Plywood Pad at Interface of Beam and Impactor .................................................................................................................................... 96 4.4.1 Sensitivity analysis for linear material properties of beam ............................ 97 4.4.2 Sensitivity analysis for nonlinear material properties of beam ...................... 98 4.5 Validation of FE Analysis Results ...................................................................... 101 4.5.1 Transient impact force ................................................................................. 101 4.5.2 Crack patterns and damage .......................................................................... 103 ix 4.5.3 Correlation between transient load and crack development ........................ 104 4.6 Computational Nonlinear Simulations of Beam without Plywood Pad ............. 104 4.7 Validation of FE Analysis Results ...................................................................... 106 4.7.1 Transient impact force ................................................................................. 106 4.7.2 Crack patterns and damage .......................................................................... 107 4.8 FE Analysis of RC Slab under Impact Load ...................................................... 108 4.8.1 Description of slabs tested by Chen and May (2009) .................................. 108 4.8.2 Experimental result of tested slab ................................................................ 109 4.9 Computational Nonlinear FE Analysis of Slab-2 ............................................... 110 4.9.1 Element‟s modelling of RC slab .................................................................. 111 4.9.2 Parts interaction ........................................................................................... 112 4.9.3 Material property ......................................................................................... 112 4.10 Mesh Sensitivity Analysis of Slab .................................................................... 113 4.10.1 Sensitivity analysis for linear material properties of slab .......................... 115 4.10.2 Sensitivity analysis for nonlinear material properties of slab .................... 116 4.11 Comparison of FE Analysis Results of Slab with Test Results ........................ 118 4.11.1 Transient impact force ............................................................................... 118 4.11.2 Crack patterns and damage ........................................................................ 119 4.12 Summary ........................................................................................................... 120 Chapter 5: Behaviour of RC Structure under Impact Load .................................. 121 5.1 Introduction ........................................................................................................ 121 5.2 RC Beam under Impact Load ............................................................................. 121 5.3 Description of Beam Used in Analysis ............................................................... 122 5.3.1 Dimension of beams .................................................................................... 122 5.3.2 Material of beams ........................................................................................ 124 5.3.3 Overview of impactor and respective beam ................................................. 125 5.4 Numerical Modelling of Beam ........................................................................... 126 5.5 Result of Beam Analysis .................................................................................... 129 5.6 Evaluation of Damage Level for RC Beam ........................................................ 136 5.6.1 Result of beam analysis ............................................................................... 136 5.7 RC Column under Impact Load .......................................................................... 140 5.7.1 Dimension and material properties of column ............................................. 141 x