42 1 ( ) Vol.42 No.1 2011 1 Journal of Central South University (Science and Technology) Jan. 2011 1, 2 2 3 2 (1. 455002 2. 410083 3. 430071) S S S U416.26 A 1672 7207(2011)01 0170 07 Quantitative analysis of damage evolution as recycled concrete approaches fatigue failure XIAO Jian-qing 1, 2, DING De-xin 2, LUO Xing-wen 3, XU Gen 2 (1. School of Civil Engineering and Architecture, Anyang Normal University, Anyang 455002, China; 2. School of Resources and Safety Engineering, Central South University, Changsha 410083, China; 3. Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China ) Abstract: Advantages and disadvantages of several common damage defined methods were studied with test data of recycled concrete. Secondly, an inverted-s nonlinear fatigue damage cumulative model was proposed based on the three-phase law of fatigue damage evolution and physical meanings and ranges of its parameters were discussed. Eventually, the damage evolution and fatigue life of recycled concrete were investigated using the inverted-s damage model. The results indicate that many methods such as elastic modulus method, ultrasonic velocity method, imum strain and residual strain methods are all able to represent the damage evolution law of recycled concrete. Among them, residual strain method is more suitable for its clear concept and consideration of fatigue initial damage. The fitting damage evolution equation is highly relevant with test data and the theoretically analyzed conclusion on the law of fatigue life of recycled concrete agrees well with the experimental result. Therefore, the inverted-s damage model is very suitable for the description of damage evolution of recycled concrete for its strong adaptability and high accuracy. Key words: recycled concrete; damage variable; damage model; fatigue life 30%~40% 50%~60% [1] 2010 05 062010 07 10 (11002067) (07C652, 08C764) (07-17 07-29) (1958 ) 0734-8282534 E-mail: dingdx@nhu.edu.cn
1 171 [2 8] 1 1.1 [9] E D = 1 (1) E E E E 1 ( ) 20% 0.5 A20-50-6 30% 0.5 A30-50-4 ( n/n n N )[3] 1 A30-50-4 A20-50-6 2 E 1 2 1 A30-50-4 2 A20-50-6 1 Fig.1 Decay curves of elastic modulus 1 Table 1 Static elastic modulus of recycled concrete /% /GPa 0 4.847 10 4.435 15 4.429 20 4.417 25 3.871 30 3.066 2 Table 2 Average loading and unloading elastic modulus of recycled concrete under cyclic loading /% /GPa /GPa 0 6.01 6.45 10 5.64 6.43 15 5.62 6.69 20 5.61 6.82 25 6.43 6.74 30 5.25 6.53 1.2 [10]
172 n f 0 0 ε ε D = (2) ε ε ( ) 42 ε 0 ε n ε f n 2 2 3 1 3 A30-50-4 Fig.3 Damage evolution curve of sample A30-50-4 Obtained by residual strain method [12] 2 A30-50-4 Fig.2 Damage evolution curve of sample A30-50-4 obtained by imum strain method 1.3 [11] n r ε n r f ε r D = (3) ε ε r f n 30% 0.5 A30-50-4 3 0.226 1 1 () 1.4 2 vˆt n 2 vt D = 1 (4) vˆ Tn v T n 0% 0.5 A0-50-4 4 v T [13] a 0 α ε 4 A0-50-4 Fig.4 Decay curve of ultrasonic velocity of sample A0-50-4
1 173 2 2 D 0 D0 = 1 vˆt0 vt ( ˆv T0 ) v T (4)[13] D 0 0 km/s 1 ( ) ( ) [14] 2 S 2.1 [14 18] 5 [19] 6 [19] c a 2 b 2.2 S 5 Fig.5 Evolution law of axial residual strain 6 Fig.6 Classification of three-phase curves 3 [14] [3] S 1/ p β D = D0 + α 1 x (5) β x n n/n D n S 7 8 2.3 S 4 D 0
174 ( ) 42 α (0 1 D 0 ) b 2 β β p α x (1 1) 1 0 β = D p ( ) + 1 (6) α 1 p=2, β=1.25; 2 p=3, β=1.125; 3 p=4, β=1.062 5; 4 p=5, β=1.031 25; 5 p=6, β=1.015 625 7 p (D 0 =0.6, α=0.2) Fig.7 Influence of p to curve 4 S 9 1 α=0.1, β=1.062 5; 2 α=0.15, β=1.140 625; 3 α=0.2, β=1.25; 4 α=0.25, β=1.390 625; 5 α=0.3, β=1.562 5 8 α (D 0 =0.6, p=2) Fig.8 Influence of α to curve [19 20] D 0 D 0 p 7 p S p p [2 8] α 8 α α 1 D 0 =0.7, p=2, α=0.26, β 6.243 6; 2 D 0 =0.6, p=3, α=0.24, β 7.071 4; 3 D 0 =0.55, p=4, α=0.20, β 7.180 2; 4 D 0 =0.5, p=5, α=0.15, β 8.019 5; 5 D 0 =0.4, p=6, α=0.10, β 12.028 2 9 S Fig.9 Inverted-S shaped curves family 3 3.1 S A10-50-6 10 R= 0.999 8 0.000 28 S S 3.2 0% 10% 15% 20% 25% 30% 3 3
1 175 10 A10-50-6 Fig.10 Fitting result of specimen A10-50-6 3 Table 3 Fatigue life of recycled concrete under different displacement ratios /% / A0-50-5 0 86 A10-50-5 10 37 A15-50-4 15 43 A20-50-4 20 55 A25-50-4 25 46 A30-50-4 30 1 171 ( 0%) A30-50-4 S 4 4 11 4 11 S 4 11 Fig.11 Fitting curves of damage evolution under different displacement ratios 4 S Table 4 Fitting results of inverted-s model under different displacement ratios /% D 0 α Β p R / A0-50-6 0 0.371 0.294 1.169 2.399 0.999 2 38 A10-50-6 10 0.454 0.256 1.029 4.732 0.999 8 58 A20-50-6 20 0.220 0.497 1.035 7.433 0.999 7 30 A30-50-4 30 0.226 0.156 1.003 3.749 0.999 9 1 171 11 S ( 4) S S
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