1. Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA 2. Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China 3. Key Laboratory of Geotechnical and Underground Engineering (Tongji University), Ministry of Education, Shanghai 200092, China
The tensile behavior of hybrid fiber reinforced concrete (HFRC) is important to the design of HFRC and HFRC structure. This study used an artificial neural network (ANN) model to describe the tensile behavior of HFRC. This ANN model can describe well the tensile stress-strain curve of HFRC with the consideration of 23 features of HFRC. In the model, three methods to process output features (no-processed, mid-processed, and processed) are discussed and the mid-processed method is recommended to achieve a better reproduction of the experimental data. This means the strain should be normalized while the stress doesn’t need normalization. To prepare the database of the model, both many direct tensile test results and the relevant literature data are collected. Moreover, a traditional equation-based model is also established and compared with the ANN model. The results show that the ANN model has a better prediction than the equation-based model in terms of the tensile stress-strain curve, tensile strength, and strain corresponding to tensile strength of HFRC. Finally, the sensitivity analysis of the ANN model is also performed to analyze the contribution of each input feature to the tensile strength and strain corresponding to tensile strength. The mechanical properties of plain concrete make the main contribution to the tensile strength and strain corresponding to tensile strength, while steel fibers tend to make more contributions to these two items than PVA fibers.
strain corresponding to tensile strength of plain concrete
components of HFRC
weight of the cement
weight of fly ash
weight of slag powder
weight of water
weight of coarse aggregate
weight of fine aggregate
water binder ratio
Tab.1
cementitious material
fiber volume (%)
fiber length (mm)
fiber diameter (mm)
Ref.
steel fiber
PVA fiber
steel fiber
PVA fiber
steel fiber
PVA fiber
cement+fly ash+slag powder (HFRC)
0.5
0.5
38
12
0.677
0.039
[9]
0.5
1.0
0.5
1.5
1.0
0.5
1.0
1.0
1.0
1.5
1.5
0.5
1.5
1.0
1.5
1.5
cement (HFRC)
0.8
0.1
35/50
8/12
0.55/0.75
0.04
[10]
0.8
0.2
1.3
0.1
1.3
0.2
cement (HFRC)
0.05
0.15
38
12
1.10
0.04
[33]
0.1
0.3
0.3
0.6
0.03
0.17
0.06
0.34
0.11
0.69
0.02
0.18
0.04
0.36
0.08
0.72
cement (HFRC)
0.25
0.07
12/15
30/60
0.5/0.73
0.015
[34]
0.25
0.14
0.51
0.07
0.51
0.14
cement +GGBS*+silica fume (HFRC)
0.25
0.25
20
6
0.4
0.12
[35]
0.5
0.25
0.75
0.25
1
0.25
1.25
0.25
0.25
0.25
Tab.2
Fig.4
type
feature
mean
median
standard deviation
output
tensile stress
2.40
2.47
0.97
tensile strength
4.10
4.02
0.20
strain corresponding to tensile strength
0.000253
0.000168
0.000172
input
strain
0.002542
0.001309
0.003017
fiber volume of steel fiber
1.04
1.00
0.38
weight of steel fiber
81.84
78.50
29.79
length of steel fiber
39.53
38.00
4.54
diameter of steel fiber
0.68
0.68
0.05
aspect ratio of steel fiber
58.51
56.13
4.13
reinforcement index of steel fiber
0.61
0.56
0.22
fiber volume of PVA fiber
0.81
1.00
0.52
weight of PVA fiber
10.56
13.00
6.81
length of PVA fiber
11.59
12.00
1.21
diameter of PVA fiber
0.04
0.04
0.00
aspect ratio of PVA fiber
295.53
307.69
32.32
reinforcement index of PVA fiber
2.48
3.08
1.64
elastic modulus of plain concrete
35915
35369
1135
tensile strength of plain concrete
3.28
3.41
0.21
strain corresponding to tensile strength of plain concrete
0.000087
0.000088
0.000019
weight of the cement
282
225
98
weight of fly ash
56
75
33
weight of slag powder
56
75
33
weight of water
174
165
16
weight of coarse aggregate
1019
1024
8
weight of fine aggregate
756
785
50
water binder ratio
0.443
0.440
0.004
Tab.3
Fig.5
Fig.6
Fig.7
mix ID
MAE
????R2
ANN
equation
ANN
equation
no-processed
mid-processed
processed
no-processed
mid-processed
processed
S0.5P0.5
0.047
0.046
0.075
0.119
0.992
0.994
0.986
0.973
S0.5P1.0
0.045
0.050
0.094
0.199
0.996
0.995
0.977
0.929
S0.5P1.5
0.041
0.045
0.068
0.482
0.996
0.995
0.987
0.561
S1.0P0.5
0.077
0.076
0.109
0.234
0.982
0.984
0.968
0.918
S1.0P1.0
0.048
0.065
0.092
0.485
0.996
0.992
0.983
0.569
S1.0P1.5
0.068
0.059
0.143
0.692
0.989
0.992
0.955
0.350
S1.5P0.5
0.124
0.123
0.239
0.688
0.953
0.964
0.882
0.354
S1.5P1.0
0.048
0.049
0.132
0.571
0.997
0.997
0.977
0.622
S1.5P1.5
0.052
0.032
0.080
1.139
0.997
0.998
0.990
0.139
Tab.4
Fig.8
Fig.9
Fig.10
Fig.11
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