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Frontiers of Structural and Civil Engineering

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Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (4) : 888-906    https://doi.org/10.1007/s11709-020-0637-0
RESEARCH ARTICLE
Novel empirical model for predicting residual flexural capacity of corroded steel reinforced concrete beam
Zhao-Hui LU1,2, Hong-Jun WANG2, Fulin QU3, Yan-Gang ZHAO1, Peiran LI3, Wengui LI3()
1. Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China
2. School of Civil Engineering, Central South University, Changsha 410075, China
3. School of Civil and Environmental Engineering, University of Technology Sydney, NSW 2007, Australia
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Abstract

In this study, a total of 177 flexural experimental tests of corroded reinforced concrete (CRC) beams were collected from the published literature. The database of flexural capacity of CRC beam was established by using unified and standardized experimental data. Through this database, the effects of various parameters on the flexural capacity of CRC beams were discussed, including beam width, the effective height of beam section, ratio of strength between longitudinal reinforcement and concrete, concrete compressive strength, and longitudinal reinforcement corrosion ratio. The results indicate that the corrosion of longitudinal reinforcement has the greatest effect on the residual flexural capacity of CRC beams, while other parameters have much less effect. In addition, six available empirical models for calculating the residual flexural strength of CRC beams were also collected and compared with each other based on the established database. It indicates that though five of six existing empirical models underestimate the flexural capacity of CRC beams, there is one model overestimating the flexural capacity. Finally, a newly developed empirical model is proposed to provide accurate and effective predictions in a large range of corrosion ratio for safety assessment of flexural failure of CRC beams confirmed by the comparisons.
Keywords CRC beams      flexural capacity      steel corrosion      database      empirical models     
Corresponding Author(s): Wengui LI   
Just Accepted Date: 29 May 2020   Online First Date: 13 July 2020    Issue Date: 27 August 2020
 Cite this article:   
Zhao-Hui LU,Hong-Jun WANG,Fulin QU, et al. Novel empirical model for predicting residual flexural capacity of corroded steel reinforced concrete beam[J]. Front. Struct. Civ. Eng., 2020, 14(4): 888-906.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0637-0
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I4/888
literature specimen concrete strength (MPa) b (mm) h (mm) rl (%) fy (MPa) l hwt (%) hsn (%) Mfx,exp
(kN·m)		 Pfx,exp (kN)
Jin and Zhao [18]
(17 tests)		 BD1 22.13 150 150 1.33 427 2.65 0.47 1.76 10.27 34.23
BD2 22.13 150 150 1.33 427 2.65 0.54 1.83 9.53 31.77
BD3 22.13 150 150 1.33 427 2.65 1.21 2.49 9.92 33.07
BD4 22.13 150 150 1.33 427 2.65 1.24 2.52 9.32 31.07
BD5 22.13 150 150 1.33 427 2.65 1.24 2.52 10.27 34.23
BD6 22.13 150 150 1.33 427 2.65 1.27 2.55 9.53 31.77
BD7 22.13 150 150 1.33 427 2.65 2.15 3.42 9.53 31.77
BD8 22.13 150 150 1.33 427 2.65 2.82 4.08 9.07 30.23
BD9 22.13 150 150 1.33 427 2.65 2.83 4.09 9.53 31.77
BD10 22.13 150 150 1.33 427 2.65 2.88 4.14 8.69 28.97
BD11 22.13 150 150 1.33 427 2.65 3.45 4.71 9.53 31.77
BD12 22.13 150 150 1.33 427 2.65 4.14 5.39 8.20 27.33
BD13 22.13 150 150 1.33 427 2.65 5.20 6.43 8.69 28.97
BD14 22.13 150 150 1.33 427 2.65 6.05 7.27 7.89 26.30
BDU1 22.13 150 150 1.33 427 2.65 0.47 1.76 9.91 33.03
BDU2 22.13 150 150 1.33 427 2.65 4.85 6.09 8.56 28.53
BDU3 22.13(fcu,150) 150 150 1.33 427 2.65 5.58 6.81 8.32 27.73
Hui et al. [6]
(24 tests)		 A01 39.4 151 252 0.90 397 3.1 0.00 0.00 26.14 37.34
A02 39.4 158 251 0.89 397 3.2 0.00 0.00 26.49 37.84
A21 39.6 154 255 0.92 383 3.2 7.11 8.32 21.84 31.20
A22 39.6 158 257 0.87 378 3.1 10.17 15.65 22.19 31.70
A31 38.1 176 250 0.79 381 3.2 4.60 5.84 22.40 32.00
A32 38.1 176 253 0.80 382 3.2 8.49 9.68 24.21 34.59
B01 39.4 153 251 1.19 402 3.2 0.00 0.00 33.70 48.14
B02 39.4 156 253 1.15 402 3.1 0.00 0.00 33.74 48.20
B11 35.0 160 254 1.14 495 3.2 3.60 4.85 30.20 43.14
B12 35.0 156 252 1.20 410 3.3 2.20 3.47 30.90 44.14
B21 36.6 173 250 1.10 395 3.3 4.49 5.73 28.45 40.64
B22 36.6 154 254 1.20 396 3.2 3.99 5.24 29.78 42.54
B31 31.4 166 253 1.12 396 3.2 5.40 6.63 30.55 43.64
B32 31.4 158 251 1.18 393 3.2 4.20 5.45 29.50 42.14
C01 39.4 168 252 1.40 381 3.3 0.00 0.00 38.95 55.64
C02 34.6 159 254 1.45 381 3.2 2.33 3.60 36.85 52.64
C21 34.4 156 253 1.52 376 3.3 3.33 4.59 31.95 45.64
C22 34.4 166 256 1.40 380 3.2 4.65 5.89 35.45 50.64
D01 39.4 163 251 0.85 297 3.2 0.00 0.00 23.20 33.14
D02 39.4 164 250 0.83 297 3.1 0.00 0.00 23.20 33.14
D21 34.4 172 252 0.80 293 3.1 10.99 16.42 17.74 25.34
D22 34.4 158 252 0.90 303 3.2 9.68 10.85 17.95 25.64
E01 35.6 155 249 0.63 494 3.0 0.00 0.00 26.00 37.14
E02 34.4(fcu,150) 172 255 0.58 494 3.1 8.82 10.01 21.45 30.64
Cao et al. [34]
(12 tests)		 RCBD12(1) 34.4 120 200 1.08 470 2.78 0.00 0.00 20.53 41.06
RCBD12(2) 34.4 120 200 1.08 470 2.78 2.16 3.43 18.50 37.00
RCBD12(3) 34.4 120 200 1.08 470 2.78 4.19 5.44 17.34 34.68
RCBD12(4) 34.4 120 200 1.08 470 2.78 6.72 7.93 15.18 30.36
RCBD12(5) 34.4 120 200 1.08 470 2.78 9.31 10.49 14.50 29.00
RCBD12(6) 34.4 120 200 1.08 470 2.78 13.05 18.35 12.90 25.80
RCBD14(1) 34.4 120 200 1.48 500 2.78 0.00 0.00 26.73 53.46
RCBD14(2) 34.4 120 200 1.48 500 2.78 2.36 3.63 24.60 49.20
RCBD14(3) 34.4 120 200 1.48 500 2.78 4.47 5.71 22.40 44.80
RCBD14(4) 34.4 120 200 1.48 500 2.78 6.29 7.51 20.70 41.40
RCBD14(5) 34.4 120 200 1.48 500 2.78 9.58 10.76 19.50 39.00
RCBD14(6) 34.4 (fcu,150) 120 200 1.48 500 2.78 12.34 17.69 18.10 36.20
Xia et al. [35]
(20 tests)		 BAI-0 25.9 150 200 1.49 425 2.06 0.00 0.00 22.68 64.80
BAI-1 25.9 150 200 1.49 425 2.06 1.80 3.25 22.24 63.54
BAI-2 25.9 150 200 1.49 425 2.06 3.09 4.5 21.63 61.80
BAI-3 25.9 150 200 1.49 425 2.06 3.80 5.19 20.65 59.00
BAI-4 25.9 150 200 1.49 425 2.06 5.64 6.97 20.84 59.54
BAI-5 25.9 150 200 1.49 425 2.06 6.07 7.39 21.37 61.06
BAI-6 25.9 150 200 1.49 425 2.06 7.08 8.37 20.00 57.14
BAI-7 25.9 150 200 1.49 425 2.06 8.67 9.91 20.84 59.54
BAI-8 25.9 150 200 1.49 425 2.06 8.85 10.08 19.22 54.91
BAI-9 25.9 150 200 1.49 425 2.06 10.36 11.55 18.34 52.40
BBII-0 35.6 150 200 1.72 575 2.06 0.00 0.00 38.50 110.00
BBII-1 35.6 150 200 1.72 575 2.06 1.45 2.91 36.75 105.00
BBII-2 35.6 150 200 1.72 575 2.06 1.84 3.28 35.00 100.00
BBII-3 35.6 150 200 1.72 575 2.06 2.64 4.06 34.48 98.51
BBII-4 35.6 150 200 1.72 575 2.06 3.75 5.14 35.04 100.11
BBII-5 35.6 150 200 1.72 575 2.06 5.26 6.6 35.88 102.51
BBII-6 35.6 150 200 1.72 575 2.06 5.84 7.16 33.08 94.51
BBII-7 35.6 150 200 1.72 575 2.06 7.37 8.65 34.39 98.26
BBII-8 35.6 150 200 1.72 575 2.06 7.76 9.03 34.48 98.51
BBII-9 35.6 (fcu,150) 150 200 1.72 575 2.06 8.98 10.21 32.13 91.80
Azad et al. [26]
(36 tests)		 B1-1 28 200 215 1.26 593 2.2 3.50 4.75 31.50 90.00
B1-2 28 200 215 1.26 593 2.2 6.00 7.22 28.18 80.51
B1-3 28 200 215 1.26 593 2.2 4.13 5.38 18.38 52.51
B1-4 28 200 215 1.26 593 2.2 15.85 20.98 22.40 64.00
B1-5 28 200 215 1.26 593 2.2 2.95 4.21 30.98 88.51
B1-6 28 200 215 1.26 593 2.2 15.83 20.96 17.33 49.51
B2-1 28 200 265 0.96 593 1.67 11.82 17.20 36.58 104.51
B2-2 28 200 265 0.96 593 1.67 9.86 11.03 40.95 117.00
B2-3 28 200 265 0.96 593 1.67 18.74 23.70 24.33 69.51
B2-4 28 200 265 0.96 593 1.67 17.53 22.56 26.95 77.00
B2-5 28 200 265 0.96 593 1.67 25.53 35.14 26.60 76.00
B2-6 28 200 265 0.96 593 1.67 25.81 35.38 20.48 58.51
B3-1 28 200 315 0.78 593 1.35 13.34 18.63 37.63 107.51
B3-2 28 200 315 0.78 593 1.35 17.85 22.86 36.05 103.00
B3-3 28 200 315 0.78 593 1.35 6.02 7.24 52.50 150.00
B3-4 28 200 315 0.78 593 1.35 5.84 7.06 55.30 158.00
B3-5 28 200 315 0.78 593 1.35 26.29 35.80 35.70 102.00
B3-6 28 200 315 0.78 593 1.35 4.63 5.87 57.58 164.51
B4-1 28 200 215 1.61 575 2.2 5.28 6.51 33.60 96.00
B4-2 28 200 215 1.61 575 2.2 9.40 10.58 22.23 63.51
B4-3 28 200 215 1.61 575 2.2 11.27 16.68 22.75 65.00
B4-4 28 200 215 1.61 575 2.2 12.26 17.61 23.10 66.00
B4-5 28 200 215 1.61 575 2.2 20.09 30.40 18.73 53.51
B4-6 28 200 215 1.61 575 2.2 21.06 31.24 16.10 46.00
B5-1 28 200 265 1.22 575 1.68 9.10 10.28 31.15 89.00
B5-2 28 200 265 1.22 575 1.68 9.53 10.71 38.15 109.00
B5-3 28 200 265 1.22 575 1.68 9.53 10.71 29.75 85.00
B5-4 28 200 265 1.22 575 1.68 5.76 6.99 40.95 117.00
B5-5 28 200 265 1.22 575 1.68 14.18 19.42 25.55 73.00
B5-6 28 200 265 1.22 575 1.68 17.80 22.81 25.20 72.00
B6-1 28 200 315 0.99 575 1.36 5.67 6.90 58.98 168.51
B6-2 28 200 315 0.99 575 1.36 1.39 2.67 65.98 188.51
B6-3 28 200 315 0.99 575 1.36 4.69 5.93 57.40 164.00
B6-4 28 200 315 0.99 575 1.36 10.08 15.57 36.93 105.51
B6-5 28 200 315 0.99 575 1.36 3.37 4.63 48.48 138.51
B6-6 28(fcyl,75) 200 315 0.99 575 1.36 20.02 30.34 35.00 100.00
Azad et al. [25]
(24 tests)		 BT1-2-4 38.91 150 150 0.92 520 3.10 5.40 6.63 10.68 30.51
BT1-3-4 36.89 150 150 0.92 520 3.10 14.20 19.43 10.15 29.00
BT1-2-6 45.77 150 150 0.92 520 3.10 15.20 20.37 10.46 29.89
BT1-3-6 46.45 150 150 0.92 520 3.10 21.40 31.54 9.15 26.14
BT1-2-8 33.40 150 150 0.92 520 3.10 21.50 31.63 7.82 22.34
BT1-3-8 46.45 150 150 0.92 520 3.10 31.00 44.73 6.48 18.51
BT2-2-4 39.94 150 150 1.33 590 3.10 5.50 6.73 12.76 36.46
BT2-3-4 35.68 150 150 1.33 590 3.10 8.80 9.99 11.97 34.20
BT2-2-6 44.45 150 150 1.33 590 3.10 21.10 31.28 10.43 29.80
BT2-3-6 44.21 150 150 1.33 590 3.10 14.00 19.25 10.55 30.14
BT2-2-8 44.69 150 150 1.33 590 3.10 22.90 32.85 8.88 25.37
BT2-3-8 37.66 150 150 1.33 590 3.10 25.50 35.11 8.49 24.26
BT3-2-4 40.18 150 150 1.06 520 3.54 8.00 9.20 10.92 31.20
BT3-3-4 35.68 150 150 1.06 520 3.54 9.10 10.28 10.19 29.11
BT3-2-6 33.40 150 150 1.06 520 3.54 10.10 15.58 9.88 28.23
BT3-3-6 44.21 150 150 1.06 520 3.54 17.60 22.63 9.28 26.51
BT3-2-8 33.40 150 150 1.06 520 3.54 21.40 31.54 9.12 26.06
BT3-3-8 33.40 150 150 1.06 520 3.54 34.80 47.77 6.60 18.86
BT4-2-4 36.89 150 150 1.54 590 3.57 7.90 9.10 12.03 34.37
BT4-3-4 46.49 150 150 1.54 590 3.57 10.90 16.34 10.93 31.23
BT4-2-6 46.49 150 150 1.54 590 3.57 13.40 18.68 10.02 28.63
BT4-3-6 40.94 150 150 1.54 590 3.57 18.60 23.57 8.98 25.66
BT4-2-8 40.94 150 150 1.54 590 3.57 18.00 23.00 9.00 25.71
BT4-3-8 37.66 (fcyl,75) 150 150 1.54 590 3.57 20.70 30.93 7.57 21.63
Shang [36]
(8 tests)		 L10 42.78 151 200 1.61 321 3.64 0.00 0.00 21.37 35.62
L11 42.78 150 200 1.61 321 3.59 7.21 8.42 17.82 29.70
L12 42.78 150 200 1.61 321 3.61 9.63 10.80 17.51 29.18
L13 42.78 152 200 1.61 321 3.57 16.23 21.34 14.98 24.97
L20 44.90 151 200 0.89 313 3.57 0.00 0.00 11.21 18.68
L21 44.90 151 200 0.89 313 3.53 6.47 7.69 11.53 19.22
L22 44.90 150 200 0.89 313 3.59 12.42 13.56 11.26 18.77
L23 44.90 (fcu,150) 151 200 0.89 313 3.55 19.32 29.73 9.21 15.35
Rodriguez et al. [4]
(16 tests)		 1 52.60 150 200 0.92 585 4.88 11.81 17.19 17.8 22.25
111 62.62 150 200 0.63 575 4.85 0.00 0.00 15.1 18.88
112 62.62 150 200 0.63 575 4.85 0.00 0.00 15.7 19.63
115 42.58 150 200 0.63 575 4.85 8.29 13.88 11.6 14.50
114 42.58 150 200 0.63 575 4.85 11.81 17.19 10.5 13.13
113 42.58 150 200 0.63 575 4.85 13.35 18.64 10.1 12.63
121 60.11 150 200 1.84 585 4.88 0.00 0.00 36.1 45.13
122 60.11 150 200 1.84 585 4.88 0.00 0.00 38.3 47.88
126 43.82 150 200 1.84 585 4.88 9.2 10.38 29 36.25
211 62.62 150 200 1.84 585 4.88 0.00 0.00 38.4 48.00
212 62.62 150 200 1.84 585 4.88 0.00 0.00 39.4 49.25
311 61.36 150 200 1.84 585 4.88 0.00 0.00 38.1 47.63
312 61.36 150 200 1.84 585 4.88 0.00 0.00 38.8 48.50
313 46.34 150 200 1.84 585 4.88 8.56 9.75 28.2 35.25
314 46.34 150 200 1.84 585 4.88 9.86 15.36 28.5 35.63
316 46.34(fcyl,150) 150 200 1.84 585 4.88 7.89 13.51 27.5 34.38
Chen [37]
(7 tests)		 1 30 120 200 0.83 335 2.55 0.00 0.00 7.88 19.70
2 30 120 200 0.83 335 2.55 0.5 1.79 8.82 22.05
3 30 120 200 0.83 335 2.55 1 2.29 8.02 20.05
4 30 120 200 0.83 335 2.55 3 4.26 7.23 18.08
5 30 120 200 0.83 335 2.55 6 7.22 5.78 14.45
6 30 120 200 0.83 335 2.55 12 17.37 5.11 12.78
7 30(fcu,150) 120 200 0.83 335 2.55 24 33.80 2.84 7.10
Zhang [38]
(13 tests)		 1 23.56 120 180 0.87 335 3.44 0.00 0.00 6.40 12.30
2 23.56 120 180 0.87 335 3.44 0.00 0.00 6.84 13.15
3 23.56 120 180 0.87 335 3.44 0.00 0.00 6.68 12.85
4 23.56 120 180 0.87 335 3.44 0.00 0.00 6.55 12.60
5 23.56 120 180 0.87 335 3.44 1.23 2.51 6.97 13.40
6 23.56 120 180 0.87 335 3.44 1.77 3.05 7.05 13.55
7 23.56 120 180 0.87 335 3.44 2.43 3.70 7.10 13.65
8 23.56 120 180 0.87 335 3.44 2.92 4.18 6.99 13.45
9 23.56 120 180 0.87 335 3.44 3.57 4.82 6.08 11.70
10 23.56 120 180 0.87 335 3.44 5.08 6.31 6.44 12.39
11 23.56 120 180 0.87 335 3.44 5.94 7.16 6.34 12.20
12 23.56 120 180 0.87 335 3.44 6.72 7.93 6.47 12.45
13 23.56(fcu,150) 120 180 0.87 335 3.44 6.91 8.12 6.53 12.55
Tab.1  Experimental data of flexural tests for CRC beams
different strength of concrete strength values (MPa)
fcyl, 150 12 16 20 25 30 35 40 45 50 55 60 70 80 90
ft 1.6 1.9 2.2 2.6 2.9 3.2 3.5 3.8 4.1 4.2 4.4 4.6 4.8 5.0
fcu, 150 15 20 25 30 37 45 50 55 60 67 75 85 95 105
fck 10.0 13.4 16.7 20.1 24.8 30.2 33.5 36.9 40.2 44.9 50.3 56.9 63.4 70.4
Tab.2  The conversion relationship among fcyl,150, ft, fcu, 150 and fck [41,33]
Fig.1  Ultimate flexural stress (sfx,exp) with respect to the corrosion ratio of longitudinal reinforcement (hwt).
Fig.2  Ultimate flexural stress (sfx,exp) with respect to width of beam section (b).
Fig.3  Ultimate flexural stress (sfx,exp) with respect to effective depth of beam section (h0).
Fig.4  Normalized ultimate flexural stress (sfxn,exp) with respect to cylinder compressive strength of concrete (fcyl,150).
Fig.5  Ultimate flexural stress (sfx,exp) with respect to ratio of strength between longitudinal reinforcement and concrete (rlfy/fcyl,150).
Fig.6  The relations between the ratios (Mfx,exp/Mfx,cal) and weight loss ratio of the longitudinal reinforcement (hwt) of the existing models. (a) Zhang et al.’s model [22]; (b) Xu’s model [23]; (c) Sun’s model [24]; (d) Azad et al.’s model [25]; (e) Azad et al.’s modified model [26]; (f) Torres-Acosta et al.’s model [27].
literature the ratios of test results to the predictions of existing models and new model
mean standard deviation maximum minimum maximum-minimum
Zhang et al. [22] 1.118 0.246 2.221 0.564 1.657
Xu [23] 1.250 0.310 2.682 0.597 2.085
Sun [24] 0.998 0.208 1.895 0.497 1.398
Azad et al. [25] 1.394 0.375 3.197 0.824 2.373
Azad et al. [26] 1.294 0.329 2.979 0.722 2.257
Torres-Acosta et al. [27] 1.509 0.917 5.501 0.683 4.818
The new proposal 1.030 0.171 1.653 0.626 1.027
Tab.3  Comparisons on residual flexural capacity of CRC beams from tests and predictions of existing empirical models and the new proposal
Fig.7  The experimental flexural capacity versus the predictions of the existing models. (a) Zhang et al.’s model [22]; (b) Xu’s model [23]; (c) Sun’s model [24]; (d) Azad et al.’s model [25]; (e) Azad et al.’s modified model [26]; (f) Torres-Acosta et al.’s model [27].
Fig.8  Comparisons between experimental results and the predictions of the new proposal. (a) The relationship between Mfx,exp/Mfx,cal and hwt; (b) The test results versus the predictions.
Fig.9  Sensitivity analysis of the new empirical model.
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[1] Behnam VAKHSHOURI, Shami NEJADI. Empirical models and design codes in prediction of modulus of elasticity of concrete[J]. Front. Struct. Civ. Eng., 2019, 13(1): 38-48.
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