Graduate Member School due to of Heat Environmental of Hydration Studies Nagoya University Maruyama Laboratory Numerical Prediction of Crack Width in Massive Concrete Ingi Jang * 1 Ippei Maruyama* 1 * 1 Nagoya university Presented by Ingi Jang
2 Today s talk will explain about three points What is the originality point of the proposed model Time-dependent fracture energy Effect of tension stiffening - Time-dependent RC-zone - Linear decay in the post-cracking range How to verify the validity of the proposed model Comparisons between numerical analysis and experiments are performed. Parametric study of beam structure To investigate the influence of three parameters : reinforcement ratio, length of structure, temperature history.
How to control the thermal crack width & How to predict by numerical analysis 3 For crack controlling, the allowable maximum crack width and the stress-strength ratio are used. Even though statistical and theoretical analysis support this idea, this index is still skeptical and not straightforward. When the cracking characteristics of a reinforced concrete member are evaluated by a numerical method, the fracture characteristics of plain concrete and reinforced concrete have been identified as the most important factors. T ( ) t Crack width (mm) Allowable maximum crack width Architectural Institute of Japan, Recommendations for Practice of Thermal Cracking Control of Massive Concrete in Building, Japan : 28, pp. 36-37 Stress-strength ratio
How to control the thermal crack width & How to predict by numerical analysis 4 For crack controlling, the allowable maximum crack width and the stress-strength ratio are used. Even though statistical and theoretical analysis support this idea, this index is still skeptical and not straightforward. When the cracking characteristics of a reinforced concrete member are evaluated by a numerical method, the fracture characteristics of plain concrete and reinforced concrete have been identified as the most important factors. T ( ) t f t σ??? ε crack ε Architectural Institute of Japan, Recommendations for Practice of Thermal Cracking Control of Massive Concrete in Building, Japan : 28, pp. 36-37
How can we predict the thermal crack by numerical analysis? 5 Time-dependent fracture energy and effect of tension stiffening are taken into account in FEM for predicting thermal crack width in massive concrete members. The subdivision of areas into a plain concrete zone and bond effect area called RC-zone has been proposed. Plain concrete zone Reinforcement concrete zone f t σ c W 1 =.75 G f / f t W c =5. G f / f t.25f t w c w 1 1/4 softening function w Linear tension stiffening model Xuehui AN, Koichi MAEKAWA, and Hajime OKAMURA, Numerical simulation of size effect in shear strength of RC beams, J. of Material, Concrete Structures and Pavements, JSCE, Vol. 35, May, 1997, pp. 297-316
Time-dependent stress-strain relation of plain concrete zone The fracture energy is treated as a time-dependent property. 6 Plain concrete element G f (t e ) = 1 (d max f c (t e )) 1/3 where, t e : temperature adjusted concrete age (days), G f (t e ) : fracture energy (N/m), d max : maximum size of aggregate (mm), f c (t e ) : compressive strength of concrete at te (N/mm 2 ) Just after initiation of crack t=t i Hardening of concrete Elapse of time after moment of crack initiation t=t i+1 σ c ε cr (t i ) G f (t i ) f t (t i+1 ) σ c ε cr (t i ) G f (t i+1 ) f t (t i ) σ c (t i-1 ) σ c (t i ) σ c (t i ) σ c (t i+1 ) ε ε Δε c (t i ) Δε c (t i+1 ) Japan Society of Civil Engineers, Standard Specification for design and Construction of Concrete Structures, Japan : 22, pp. 27
Time-dependent stress-strain relation of plain concrete zone Just after initiation of crack t=t i 7 σ c ε cr (t i ) f t (t i ) σ c (t i-1 ) σ c σ c (t i ) Hardening of concrete Δε c (t i ) Elapse of time after moment of crack initiation t=t i+1 ε σ c (t i ) f t (t i+1 ) σ c σ c (t i ) σ c (t i+1 ) ε cr (t i ) Δε c (t i+1 ) ε σ c (t i+1 ) ε ε c (t i ) ε c (t i+1 ) Point where the stress and strain are zero at t i+1 Point where the stress and strain are zero at t i
Time-dependent stress-strain relation of reinforcement concrete zone The maximum area of RC-zone depends on the tensile strength of concrete, yielding strength of rebar, and section area of rebar. Reinforcement concrete element h cc,mmmmmm tt ii = AA cc.mmmmmm tt ii AA cc,mmmmmm tt ee σ c (t i-1 ) = AA ss ff ssss ff tt tt ee σ c (t i ) Just after initiation of crack t=t i σ c ε cr (t i ) 8 Δε c (t i ) ε Xuehui AN, Koichi MAEKAWA, and Hajime OKAMURA, Numerical simulation of size effect in shear strength of RC beams, J. of Material, Concrete Structures and Pavements, JSCE, Vol. 35, May, 1997, pp. 297-316
Time-dependent stress-strain relation of reinforcement concrete zone Reinforcement concrete element h cc,mmmmmm tt ii+1 Plain concrete element Just after initiation of crack t=t i Hardening of concrete Elapse of time after moment of crack initiation t=t i+1 σ c ε cr (t i ) 9 σ c ε cr (t i ) σ c (t i ) σ c (t i+1 ) σ c (t i-1 ) σ c (t i ) Δε c (t i+1 ) ε Δε c (t i ) ε σ c ε cr (t i ) σ c (t i ) σ c (t i+1 ) Xuehui AN, Koichi MAEKAWA, and Hajime OKAMURA, Numerical simulation of size effect in shear strength of RC beams, J. of Material, Concrete Structures and Pavements, JSCE, Vol. 35, May, 1997, pp. 297-316 Δε c (t i+1 ) ε
1 Comparison of the proposed model with experiment 153 5 15 5 5 A:135 B:75 55 Wall structure C 75 75 C Base structure 15 (mm) The three cases of experiments which is purposed to investigate about thermal crack characteristics and influence of reinforcement in massive concrete structures were selected. The base structure was located underground after hardening enough. The longitudinal reinforcement ratio of base structure is.2%. The comparison with experiment is performed by focusing three points. - Stress history at C - Maximum crack width at A and B - Number of cracks, Spacing of cracks Japan Concrete Institute, Guideline of massive concrete for control crack, Japan : 28, pp. 148-174
11 Comparison of the proposed model with experiment Unit cement content Reinforcement ratio Parameters No.1-2 No.2 No.3-2 Type of cement No. 1-2, No. 2 1 91 869 C = 32kg/m 3 Ordinary Portland Cement C = 38kg/m 3 P =.27% P =.65% No. 3-2 1 91 869 9 7 6@22=132 15 9 16@85=136 15 7 14D19 p =.27% 34D19 p =.65% Japan Concrete Institute, Guideline of massive concrete for control crack, Japan : 28, pp. 148-174
12 Comparison result of No.1-2 (C=32kg/m 3, p=.27%) 7.25m 7.75m Temperature ( ) 5 4 3 2 1 ANALYSIS EXPERIMENTAL (a) experiment 4.2m 2.8m 1.m 2.8m 4.2m Stress of concrete (kgf/cm 2 ) 2 1 σ c =f t -1 2 4 6 8 1 Time (days) Location from the bottom of wall structure (mm) 15 12 9 6 3 (b) numerical analysis Analysis Experiment Numerical analysis.1.2.3.4.5.6 Maximum crack width (mm) Experiment
13 Comparison result of No.2 (C=38kg/m 3, p=.27%) 3.8m 3.8m 2.4m 2.8m 2.2m Temperature ( ) Stress of concrete (kgf/cm 2 ) 6 4 2 2 1-1 σ c =f t ANALYSIS EXPERIMENTAL 2 4 6 8 1 Time (days) Location from the bottom of wall structure (mm) 3.8m 3.m 1.4m 3.m 3.8m 15 12 9 6 3 (a) experiment (b) numerical analysis Analysis.1.2.3.4.5.6 Maximum crack width (mm) Experiment Experiment Numerical analysis
14 Comparison result of No.3-2 (C=38kg/m 3, p=.65%) 5.2m.8m 1.9m 1.6m 5.6m Temperature ( ) Stress of concrete (kgf/cm 2 ) 5 4 3 2 1 2 1-1 σ c =f t ANALYSIS EXPERIMENTAL 2 4 6 8 1 Time (days) Location from the bottom of wall structure (mm) (a) experiment 4.6m 1.8m 2.2m 1.8m 4.6m 15 12 9 6 3 (b) numerical analysis Analysis.5.1.15.2 Maximum crack width (mm) Experiment Experiment Numerical analysis
15 Parametric study of beam structure The parametric study is performed by proposed model to investigate the influence of three parameters for the risk of cracking. - Unit cement content / Length of structure / Reinforcement ratio L=?? m Parameter Symbol Unit cement content (kg/m 3 ) Length of structure (m) Reinforcement ratio (%) Standard 35 25.45 ρ=?? % Base structure Ground Beam structure T.1 25 25.45 T.2 45 25.45 L.1 35 1.45 L.2 35 4.45 R.1 35 25.635 R.2 35 25.85 Xuehui AN, Koichi MAEKAWA, and Hajime OKAMURA, Numerical simulation of size effect in shear strength of RC beams, J. of Material, Concrete Structures and Pavements, JSCE, Vol. 35, May, 1997, pp. 297-316
16 Parametric study of beam structure D16 Beam structure Base structure Ground 8 1 1 5@16 1 The reinforcement ratio of the base structure is.2% in the longitudinal and it is assumed to be composed of the same concrete as the beam. The underlying ground is considered as large as the base structure. 1 1 1 1 175 9@25 175 (mm) 1 3
17 Influence of unit cement content 45kg/m 3 Temperature ( ) Stress of concrete (N/mm 2 ) 7 6 5 4 3 2 1 2 1-1 -2 35kg/m 3 25kg/m 3 25kg/m 3 35kg/m 3 45kg/m 3-3 2 4 6 8 1 12 14 Time (days) Crack Width (mm).6.5.4.3.2.1 maximum average 5 6 7 Maximum Temperature ( ) (a) 25kg/m 3 (b) 35kg/m 3 (c) 45kg/m 3
18 Influence of length of structure Temperature ( ) Stress of concrete (N/mm 2 ) 7 6 5 4 3 2 1 2 1 35kg/m 3-1 1m 1m -2 25m 25m 4m -3 2 4 6 8 1 12 14 4m Time (days) Crack Width (mm).4.3.2.1 maximum average 1 2 3 4 Length of structure (m) (a) 1m (b) 25m (c) 4m
19 Influence of reinforcement ratio Temperature ( ) Stress of concrete (N/mm 2 ) 7 6 5 4 3 2 1 2 1 35kg/m 3-1 -2.45%.635%.85% -3 2 4 6 8 1 12 14 Time (days) Crack Width (mm).4.3.2.1.4.5.6.7.8.9 Reinforcement ratio (%) maximum (a).45% average (b).635% (c).85%
2 Conclusion In this study, the time-dependent fracture energy and the effect of the tension stiffening are taken into account in the FEM for predicting the thermal crack width. The proposed model is preilminarily validated through a comparison of the calculated results with the experimental results. Good agreement was confirmed in the case of rather higher reinforcement ratio range. The parametric study was performed to investigate the influence of the unit cement content, length of the target RC member, and the reinforcement ratio. From this parametric study, a shorter length of the target member and reducing of the maximum peak temperature seem efficient methods to control the crack width under the criterion.
21 Thank you very much for your kind attention
22 Effect of high temperature history Based on experiments 1), it has been reported that the compressive strength of concrete, which has experienced a high temperature history in the early age, shows a slow progression in a long-term view. Fig.4 shows the relationship between compressive strength ratio and temperature adjusted concrete age based on experiment results 1). The compressive strength ratio is defined by compressive strength at any temperature adjusted concrete age t divided by compressive strength at 365 days in temperature adjusted concrete age. 1) Hisachi SUGIYAMA, and Yoshihiro MASUDA, Strength development of concrete cured under high temperature conditions in an early age, Journal of Structural and Construction Engineering, No.515, 1999, January, pp.23-3
23 Effect of high temperature history In case that the maximum temperature of temperature history is higher than 45 C, the compressive strength of concrete is included in range of α between.7 and.9. In this study, the coefficient of temperature history (α) is divided in two cases. When the maximum temperature that concrete has been experienced is under 45 C, α is 1.. In case of above 45 C, α is.8. ff cc tt ee = eeeeee ss αα 1 28 tt ee ss ff TT 1 2 ff cccc αα Fig.4 Relationship between compressive strength ratio and temperature adjusted concrete age 1) Hisachi SUGIYAMA, and Yoshihiro MASUDA, Strength development of concrete cured under high temperature conditions in an early age, Journal of Structural and Construction Engineering, No.515, 1999, January, pp.23-3
24 Crack width calculation The crack width is calculated from distribution of crack strain (ε cr ). The distribution of crack strain is obtained at location where the crack initiation is assumed, like A-B line. Through integration of crack strain between A and B, the crack width can be calculated 1). ε cr = ε - ε e - ε sh - ε T - ε creep A B ε cr XX BBεεcccc WW cccc = xx dddd XX AA 1) σ c f t ε cr x A x B x.25f t ε crack ε c ε 1) Yasuaki Ishikawa, Hironari Ohashi, and Tadaaki Tanabe, Proposal of calculation method for crack widths using smeared crack model, Proceedings of the Japan Concrete Institute, Vol. 31, 29, pp. 1555-156
25 Evaluation equation of material properties Temperature adjusted concrete age is calculated by 1) n [ ] t = t exp 13.65 4/(273 + T( t ) / T ) e i i i= 1 where, t e : temperature adjusted concrete age (days), Δt i : number of days where a temperature T( C) prevails, T =1 C. Compressive strength 1) ff cc tt ee = eeeeee ss 1 28 tt ee ss ff TT 1 2 ff cccc Tensile strength 2),3) ff tt tt ee =.18 ff cc tt ee.75 Young s modulus 4) EE cc tt ee = 3.35 1 4 kk 1 kk 2 γγ 2.4 2 ff cc tt ee 6 where, t : 1 day, f c,28 : compressive strength of concrete at 28 days in temperature adjusted concrete age (N/mm 2 ), s : coefficient of cement type, s f : correction term for starting point of hardening, α : coefficient of temperature history, γ : air-dried mass per unit volume of concrete (t/m 3 ), k 1, k 2 : coefficients according to aggregate and admixtures. 1) CEB-FIP, Model code 199, Bulletind Information, CEB, Lausanne, 199 2) Toru KAWAGUCHI, Yasumichi KOSHIRO, Masanori TSUZUKI, and Nagao HORI, Analytical study on the effect of thermal stress in massive concrete : Part1. Method of analytical study, Proceedings of the Japan Concrete Institute,Vol. A-1, September, 26, pp. 113-114 3) Ippei MARUYAMA, and Ryoichi SATO, Prediction of stress-strength ratio in slab-type mass-concrete, Proceeding of the Japan Concrete Institute, Vol. A-1, September, 26, pp. 117-118 4) Construction Ministry of Japan, Report of project of general technology development : Development of advanced reinforced concrete buildings using high-strength concrete and reinforcement, 1993 1 3