Finite Element Analysis and Design of Suspended Steel- Fibre Reinforced Concrete Slabs

FINITE ELEMENT ANALYSIS AND DESIGN OF SUSPENDED STEEL- FIBRE REINFORCED CONCRETE SLABS OLUGBENGA BABAJIDE SOYEMI A thesis submitted in partial fulfilment of the requirements of the University of East London for the degree of Doctor of Philosophy August 2018 Abstract Over the last 20 years, there has been a rapid expansion in the construction of pile-supported and elevated steel-fibre-reinforced [SFRC] concrete slabs. The use of fibres to replace some or all of the conventional steel reinforcement leads to a significant reduction in construction time. However, current guidance is limited and is dominated by approximate elastic and plastic classical solutions. The design guidelines and construction of the majority of constructed SFRC slabs is almost entirely proprietary (provided by fibre manufacturers and suppliers) and different guidelines from nations (embedded with safety concerns). As a result, designers are unwilling to underwrite current designs in the absence of adequate independent guidance. In this research work, the behaviour of suspended SFRC slabs was studied under concentrated loadings. Available experimental data were used to study the effect of steel fibres on the post- cracking response of concrete. Subsequently, the SFRC constitutive model proposed by Lok and Xiao (1999) was adopted alongside the concrete damaged plasticity model of ABAQUS based on the validation work done. The reliability of the FE numerical model predictions was ensured by calibrating it against existing experimental data. Consequently, additional analyses were carried out examining three main case studies of SFRC slabs namely, single simply supported slabs, 4-panel pile-supported slab (i.e. statically-indeterminate) and 9-panel elevated slab. Parametric studies were carried out covering the full practical range of steel fibre dosages. The results testify that numerically steel fibres can replace rebar in slabs as obtained in the experiment and additional fibres increase the load-carrying capacity, strength and stiffness (thus enhancing response at both the serviceability and ultimate limit states). Ductility was improved by the additional Fibres, and the mode of failure was altered from brittle to ductile. Thus three main parameters were considered in the parametric study, namely increasing the amount of fibres and characteristic strength and at the same time increasing the slab depth. The total removal of conventional reinforcement was achieved mainly by replacing them with steel-fibres. An FE numerical analysis is used to investigate the slab's structural behaviour under different loading conditions leading to transparent and well-defined design guidelines which are urgently needed by industry. Simple design equations were derived using regression analysis to estimate the yield load and the maximum load carrying capacity of the slabs with their corresponding central displacements. These equations were compared with existing design guidelines, and the equations perform better in their estimation. i List of Symbols The following symbols were used in this thesis. Their definition is given where they were first used. Where a symbol has more than one meaning assigned to it, the correct definition will be provided where it appeared. 푙 Length of Fibre 푑 Equivalent diameter of a fibre 휎퐶 Compressive stress in the concrete 푓푐푚 Mean value of concrete cylinder compressive strength 푓푐 Peak stress 푓푦 Characteristic strength in steel 휎푤 Traction applied to the crack surface 퐸푐푚 Modulus of elasticity in compression 퐸푐 Modulus of elasticity of concrete 퐸푠 Modulus of elasticity of steel 푓푐푘 Characteristic compressive cylinder strength of concrete at 28 days 휀푐 Compressive strain in concrete 휀푐1 Compressive strain in concrete at the peak stress 휀푐푢 Ultimate Compressive strain in concrete 휎푤 Stress at crack area 푃 Applied load [maximum load obtained] 퐴푛 Cross-sectional area at the notch 훿 Displacement 푤 Crack width 훿푝 Average displacement at peak stress 푏 퐷퐵푍 Energy absorption capacity [plain concrete] 푓 퐷퐵푍,2 Energy absorption capacity [influences of steel fibres] 푓 퐷퐵푍,3 Energy absorption capacity [influences of steel fibres] ML Moment at mid-span fL Load at the limit of proportionality Py Yield Load Pmax Peak Load L Span of the beam specimen 푏 Width of the failed cross-section ℎ Height of the failed section 푇푏 Flexural toughness 훿푡푏 Deflection of 1/150 of span 푙푐푠 Structural characteristic length 훾푐 Partial safety factor for SFRC in compression 훾푐푡 Partial safety factor for SFRC in tension 푙푥 Shorter side of a slab 푙푦 Longer side of a slab 훼 Moment coefficient [determined by the code] 푞 Applied [action] load ii 푀푝 Positive [sagging] moment 푀푛 Negative [hogging] moment 푞푢 UDL 퐿푒 Effective span 푄푡 Line load 푞푠푤 Self-weight of the pile supported slab 퐿1 Pile to pile centres in x-direction 퐿2 Pile to pile centres in y-direction 퐴 Cross-sectional area of the pile 푙ℎ Effective dimension 푙ℎ of the column head 푙ℎ0 Actual dimension of the column head 푙푐 Column dimension measured in the same direction as 푙ℎ 푑ℎ Drop height 푉푒푓푓 Design effective shear force 푉푡 Design shear transferred to the column 푣 Shear stress on a failure zone 푣푚푎푥 Maximum shear stress at the face of the column 푢0 Perimeter of the column 휏푑 Bond stress 푓푡푢 Flexural Strength 휀푡1 Corresponding strain to the flexural strength 푀푐푟 Crack Moment 푀푢푙푡 Ultimate Moment 푓푢푙푡 Ultimate Load 휎푐 Compressive Strength 퐺푓 Fracture energy 퐸0 Uniaxial initial tangent modulus 푣 Poisson's ratio 훼 Mean coefficient of thermal expansion 휎푡 Uniaxial cut-off tensile stress 휎푡푝 Post-cracking uniaxial cut-off tensile stress 휎푐 Uniaxial maximum compressive stress 푒푐 Uniaxial compressive strain at 휎푐 휎푢 Uniaxial ultimate compressive stress u 푒푢 Uniaxial strain at 휎푢 휉 Constant for tensile strain failure iii Abbreviations ACI America Concrete Institute ADINA Automatic Dynamic Incremental Nonlinear Analysis BSI British Standard Institute CBC Concrete Brittle Cracking CDP Concrete Damaged Plasticity CSC Concrete Smeared Cracking CMOD Crack Mouth Opening Displacement CTOD Crack Tip Opening Displacement ESFRC Elevated Steel Fibre Reinforced Concrete FEA Finite Element Analysis FEM Finite Element Method LFEA Linear Finite Element Analysis LVDT Linear Vertical Displacement Transducers MFRC Metal-Fibre Reinforced Concrete MFRC Metal-Fibre Reinforced Concrete NLFEA Non-Linear Finite Element Analysis SCC Self Compacting Concrete SFRC Steel-Fibre Reinforced Concrete SFRSCC Steel-Fibre Reinforced Self Compacting Concrete SLS Serviceability Limit State UDL Uniform Distributed Load ULS Ultimate Limit State iv List of Figures Figure 1.1: Plain concrete in bending 2 Figure 1.2: (a) Crack Patter in Concrete with No Reinforcement when Load is applied 3 (b) Crack Patter in Concrete with Steel Reinforcement when Load is applied 3 Figure 1.3: Typical Slab Reinforcement laid on [a] Pile Foundation and [b] columns 4 Figure 1.4: A Typical Pile-Supported Slab Layout 5 Figure 1.5: Pile-Supported Floor Slab for Warehouse Partly finished 6 Figure 1.6: Applications of FRC 11 Figure 1.7: Research Outlay 13 Figure 2.1: Sources of Fibres 19 Figure 2.2: Types of Steel-Fibre (The Concrete Society TR63, 2007) 21 Figure 2.3: DramixTM RC-65/35-BN and [b] TABIX-Twincone (Bekaert, 2012, ArcelorMittal, 2011) 21 Figure 2.4: Stress-Strain Relation of concrete in compression (BSI 2004) 23 Figure 2.5: Stress-strain graph adapted from (Kooiman, 2000) 24 Figure 2.6: Setup of [a] Flexural test on notched beam [b] Fracture energy evaluation 25 Figure 2.7: Typical stress distributions in a concrete section subjected to four-point bending (Tlemat et al., 2006a) 26 Figure 2.8: Schematic description of stress-crack opening for [a] plain concrete and [b] SFRC. Adapted from (Löfgren, 2005) 27 Figure 2.9: High performance SFRC. Adapted from (Kooiman, 2000) 28 Figure 2.10: Typical set-up for uni-axial tension testing (RILEM, 2001) 29 Figure 2.11: Crack width Opening w calculation (RILEM, 2001) 30 Figure 2.12: 3-Point bending test set-up (Fall, 2014) 30 Figure 2.13: [a-c] Load – deflection graphs [d] Load-CMOD graph 31 Figure 2.14: 4-point bending test adapted from (Kooiman, 2000) 33 Figure 2.15: Load – deflection Curve (JCI Test) 33 Figure 2.16: Schematic diagram of statically determinate round panel (Bernard, 2000) 34 Figure 2.17: Load-deflection responses of [a] beams and [b] plates (Sukontasukkul, 2003) 35 Figure 2.18: Compressive Stress-Strain of SFRC adapted from BS 8110 38 Figure 2.19: Tensile Stress-Strain Relationship adapted from (Lok and Xiao, 1998) 39 Figure 2.20: Compression stress-strain diagram (Barros and Figueiras, 1999) 42 Figure 2.21: Proposed tensile stress-strain diagram adapted from (Barros and Figueiras, 1999) 43 Figure 2.22: Schematic representation of fracture energy evaluation adapted from (Barros and Figueiras, 1999) 43 Figure 2.23: Stress-Strain Diagram adapted from (RILEM, 2002b) 44 Figure 2.24: 3-Point Bending Test with 25mm Notch adapted from (RILEM, 2002b) 45 v Figure 2.25: Load-Displacement Diagram adapted from (RILEM, 2000) 45 Figure 2.26: Tensile behaviour of SFRC adapted from (Lok and Xiao, 1998) 46 Figure 2.27: Stress-Strain constitutive model adapted from (Lok and Xiao, 1999) 47 Figure 2.28: One and Two-way slabs 51 Figure 2.29: Yield Line Development in 2-way slab 53 Figure 2.30: Folded plate yield line mechanism (The Concrete Society TR34, 2014) 54 Figure 2.31: Folded plate yield line mechanism (The Concrete Society TR34, 2014) 55 Figure 2.32: Fan yield line mechanism at pile (The Concrete Society TR34, 2014) 56 Figure 2.33: Diagrammatic

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