This paper investigates the cyclic stress-strain behavior of steel-polypropylene-blended fiber-reinforced concrete (BFRC) under uniaxial cyclic compression. A total of 48 prism specimens were tested for different fiber volume fractions and aspect ratios. The results show that the introduction of blended fibers has synergetic effects on improving the cyclic behavior of concrete in terms of peak strength, postpeak ductility, hysteretic energy dissipation, and stiffness degradation. Moreover, the increase in the volume fractions of both steel and polypropylene fibers can lead to a remarkable decrease in plastic strain accumulation. Furthermore, the stiffness degradation ratio as well as the stress deterioration ratio of BFRC can be significantly alleviated in comparison with those of plain concrete, notwithstanding that the degradation amount is insensitive to the variations of fiber parameters. Subsequently, based on the test results, a constitutive model is developed to generalize the cyclic stress-strain responses of BFRC, with the contributions of blended fibers taken into account. The developed model is then verified by independent experimental results and other test data reported in the literature. It is observed that the prediction yields a close estimation of the cyclic compressive behavior of BFRC with varying fiber parameters.
Concrete has been well acknowledged as one of the most widely used construction and building materials in civil engineering field. It is witnessed nowadays that a number of practical applications for large-scale concrete structures have emerged, such as high-rise buildings, large-span bridges, and nuclear power plants. However, plain concrete demonstrates explicitly its disadvantages that hinder its further application, e.g. susceptibility to cracking, low deformation threshold, and limited ductility, which at times have been the key determinants resulting in the selection of other alternative materials [
It has to be mentioned that the cyclic stress-strain relation of BFRC plays an important role in the elastoplastic analysis of concrete members and directly determines the ductile and hysteretic behaviors of concrete structures subjected to seismic, explosive, and fatigue loads [
The objective of this paper is to study the stress-strain relation of steel-polypropylene-blended fiber-reinforced concrete (BFRC) subjected to uniaxial cyclic compression. The influences of volume fraction and aspect ratio of blended fiber on the stress-strain responses and parameters of cyclic mechanical behavior were studied. Based on the experimental results, an empirical constitutive model was developed to generalize the cyclic compressive stress-strain responses of BFRC, with the effects of blended fiber taken into consideration.
Prismatic specimens with a dimension of 150 mm × 150 mm × 300 mm were employed in this study. The mix proportions of plain concrete designed according to the code JGJ 55-2011 [
Designed concrete mix proportions (kg/m3) [
Cement | Sand | Gravel | Water | Superplasticizer | Water-cement ratio |
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417 | 724 | 1086 | 175 | 2.1 | 0.42 |
Grading curves for fine and coarse aggregates.
Two different types of fibers were considered in this study, namely, steel fiber (SF) and polypropylene fiber (PF), as shown in Figure
Respective features of (a) SF and (b) PF.
Major properties of fibers.
Fiber species | No. | Aspect ratio | Equivalent diameter (mm) | Fiber type | Density (g/cm3) | Tensile strength (MPa) |
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Steel fiber | SA | 30 | 0.55 | Corrugated type | 7.8 | ≥600 |
SB | 60 | |||||
SC | 80 | |||||
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Polypropylene fiber | PA | 167 | 0.048 | Monofilament type | 0.91 | ≥400 |
PB | 280 | |||||
PC | 396 |
All the specimens were fabricated following the Chinese Standard CSCE 38:2004 [
Details of specimens.
No. | Specimens | SF | PF |
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1 | S000P000 | — | — | — | — | 47.53 | 2.75 |
2 | SB10P000 | 1.00% | 60 | — | — | 51.75 | 3.96 |
3 | SB15P000 | 1.50% | 60 | — | — | 52.91 | 4.47 |
4 | S000PA15 | — | — | 0.15% | 167 | 48.80 | 3.47 |
5 | S000PC15 | — | — | 0.15% | 396 | 50.65 | 3.58 |
6 | SB10PA10 | 1.00% | 60 | 0.10% | 167 | 53.71 | 3.99 |
7 | SB10PA15 | 1.00% | 60 | 0.15% | 167 | 55.2 | 4.13 |
8 | SB15PA10 | 1.50% | 60 | 0.10% | 167 | 58.05 | 4.61 |
9 | SA15PB15 | 1.50% | 30 | 0.15% | 280 | 54.65 | 4.19 |
10 | SB15PA15 | 1.50% | 60 | 0.15% | 167 | 53.35 | 4.25 |
11 | SB15PB15 | 1.50% | 60 | 0.15% | 280 | 52.35 | 4.36 |
12 | SB15PC15 | 1.50% | 60 | 0.15% | 396 | 51.15 | 4.50 |
13 | SC15PA15 | 1.50% | 80 | 0.15% | 167 | 53.70 | 4.76 |
14 | SB15PA20 | 1.50% | 60 | 0.20% | 167 | 50.91 | 3.76 |
15 | SB20PA15 | 2.00% | 60 | 0.15% | 167 | 56.22 | 5.36 |
16 | SB20PA20 | 2.00% | 60 | 0.20% | 167 | 54.65 | 5.07 |
The cyclic tests were performed on a universal electrohydraulic servo-rock testing machine-INSTRON-1346 with a 2000 kN load capacity, as shown in Figure
Schematic diagram of experimental setups.
A preload of approximately 10% of the ultimate strength was applied at the beginning of each test. A hierarchical loading method with a controlled displacement load was used, as shown in Figure
Schematic diagram of cyclic loading procedure [
Figure
Typical failure modes for concrete specimens.
The typical axial stress-strain relations of BFRC for various fiber volume fractions and aspect ratios under cyclic compression are illustrated in Figure
Cyclic stress-strain relations of BFRC specimen for various fiber volume fractions and aspect ratios. (a) Effect of fiber types. (b) Effect of volume fraction of SF. (c) Effect of aspect ratio of SF. (d) Effect of volume fraction of PF. (e) Effect of aspect ratio of PF.
Figure Elastic stage (Path OA). The initial microcracks are restrained by the randomly distributed fibers. The contributions of blended fiber on the mechanical behavior of BFRC at this stage are negligible. Initial crack propagating stage (Path AB). Visible fine cracks can be observed on the specimen at this stage. The internal crack distributions and the degree of crack propagation are determined by the volume fraction of PF [ Stable crack propagating stage (Path BC). Macrocracks can be seen when the load reaches the ultimate strength, and at the peak stress, a sudden increase in the width of cracks can be observed, which is induced by the events of steel fiber pull-out, matrix cracking, and debonding between the aggregate and matrix. Fracture-occurring stage (Path CD). The cracks in specimens propagate and coalesce into a main crack. The deformation of PF increases continuously or PF fractures. At this stage, steel fiber debonding occurs continuously with increasing loads and loading cycles. Continuous failure stage (Path DE). The width of the main cracks becomes larger, and the partial SFs are completely pulled out, with small pieces of concrete peeled off. Convergence stage (Path EF). The tensile stress between the two sides of a crack is undertaken by SFs, and when the increasing amount of fibers is pulled out, the concrete specimen collapses into failure.
Ideal schematic of cyclic compressive process of BFRC specimen. (a) Schematic of stress-strain curve and the corresponding morphologies of typical specimen surface for each loading stage. (b) The schematic drawing showing propagation of a crack.
In addition, Path GH is the unloading stage, where the stress is diminishing and the elastic deformation is recovered, with partial cracks closure. Path HI is the first reloading stage. The axial stress has not reached the last unloading stress, and therefore, the width of cracks almost remains as a constant. Path IJ is the second reloading stage. At this stage, the cracks propagate continually until the next unloading strain.
In order to analyze the effects of blended fiber on the mechanical behavior of concrete, the envelope curves referenced as the upper boundary of a cyclic response are plotted for each specimen, as shown in Figure
Envelope curves of BFRC specimens for different fiber volume fractions and aspect ratios. (a) Effect of volume fraction of SF. (b) Effect of aspect ratio of SF. (c) Effect of volume fraction of PF. (d) Effect of aspect ratio of PF.
Based on the above descriptions, it can be concluded that the synergistic effect of blended fiber is positive on the concrete strength, despite that the effect of PF has a small fluctuation. However, adding PF into concrete matrix has insignificant effects on the ductility of concrete specimens when subjected to cyclic loading in this study, which can be interpreted that initial damages such as microcracks and weak interfaces increase with increasing volume fraction of PF.
The plastic strain is the accumulated residual axial strain of concrete when the load is unloaded to zero [
Relations between plastic strain and envelope unloading strain. (a) Effect of fiber type. (b) Effect of volume fraction of SF. (c) Effect of aspect ratio of SF. (d) Effect of volume fraction of PF. (e) Effect of aspect ratio of PF. (f) Comparisons of plastic strain between fitting and predicted results.
Fitting parameters for the relation between plastic strain and envelope unloading strain.
Specimens |
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S000P000 | 0.00 | 0.000 | 0.589 | 1.000 |
S000PA15 | 0.00 | 0.251 | 0.527 | 0.870 |
SB15P000 | 0.90 | 0.000 | 0.533 | 0.880 |
SB10PA15 | 0.60 | 0.251 | 0.528 | 0.871 |
SB15PA15 | 0.90 | 0.251 | 0.459 | 0.758 |
SB20PA15 | 1.20 | 0.251 | 0.497 | 0.820 |
SA15PA15 | 0.45 | 0.251 | 0.496 | 0.818 |
SC15PA15 | 1.20 | 0.251 | 0.497 | 0.821 |
SB15PA10 | 0.90 | 0.167 | 0.502 | 0.829 |
SB15PA20 | 0.90 | 0.334 | 0.496 | 0.819 |
SB15PB15 | 0.90 | 0.420 | 0.493 | 0.813 |
SB15PC15 | 0.90 | 0.594 | 0.467 | 0.770 |
Note:
It is seen from Figure
The above analysis could be explained by the effective fiber bridging effect of fiber reinforcing index, which is proportional to the fiber volume fraction and aspect ratio [
In this work, two reinforcing indexes
Thus, the fitting parameters
Figure
Elastic stiffness degradation is a key aspect to reflect the damage evolution, which can be quantified by the variations of elastic reloading modulus during cyclic loading. In the present study, as a simplified calculation rule, the slope between the unloading point and ultimate unloading point is defined as the unloading elastic modulus, as shown in Figure
Key parameters’ definition of cyclic stress-strain of BFRC.
Elastic stiffness versus unloading strain for concrete specimens.
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0.00 | 53.86 | 0.00 | 71.35 | 0.00 | 67.62 | 0.00 | 75.34 | 0.00 | 75.06 | 0.00 | 84.00 |
1.02 | 33.28 | 0.99 | 50.20 | 1.01 | 50.13 | 1.03 | 57.82 | 0.92 | 70.85 | 0.96 | 74.21 |
1.82 | 22.70 | 2.43 | 34.50 | 3.46 | 20.60 | 3.51 | 36.46 | 2.46 | 29.99 | 2.48 | 29.92 |
2.82 | 15.92 | 4.68 | 15.30 | 4.50 | 19.16 | 4.58 | 25.53 | 3.54 | 20.57 | 3.54 | 23.46 |
4.05 | 8.51 | 5.79 | 10.49 | 5.54 | 15.57 | 5.61 | 21.26 | 4.62 | 13.71 | 4.60 | 19.02 |
5.10 | 6.34 | 6.84 | 8.35 | 6.58 | 13.82 | 6.65 | 18.42 | 5.68 | 10.77 | 5.65 | 17.22 |
6.15 | 4.54 | 7.88 | 7.00 | 7.62 | 12.35 | 7.68 | 15.59 | 6.72 | 8.86 | 6.69 | 15.15 |
7.20 | 3.97 | 8.90 | 5.83 | 8.65 | 11.14 | 8.69 | 13.62 | 7.75 | 7.66 | 7.72 | 13.78 |
8.23 | 3.03 | 9.91 | 5.18 | 9.69 | 10.20 | 9.73 | 12.01 | 8.80 | 6.62 | 8.74 | 12.78 |
9.24 | 2.56 | 10.94 | 4.86 | 10.69 | 9.37 | 10.75 | 10.82 | 9.81 | 6.05 | 9.77 | 12.08 |
10.26 | 2.25 | 11.95 | 4.29 | 11.73 | 8.67 | 12.78 | 10.22 | 10.82 | 5.69 | 10.78 | 11.35 |
11.28 | 1.96 | 12.95 | 3.85 | 12.74 | 8.13 | 13.78 | 8.56 | 11.85 | 5.15 | 11.79 | 10.85 |
12.27 | 1.89 | — | — | 13.77 | 7.81 | — | — | 12.86 | 4.91 | 12.81 | 10.46 |
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0.00 | 61.29 | 0.00 | 66.04 | 0.00 | 59.00 | 0.00 | 58.07 | 0.00 | 68.49 | 0.00 | 65.02 |
1.02 | 42.40 | 1.00 | 57.39 | 1.10 | 27.48 | 1.19 | 33.48 | 1.04 | 51.33 | 1.00 | 49.74 |
2.38 | 30.29 | 2.44 | 30.67 | 2.44 | 31.26 | 2.44 | 31.98 | 2.42 | 32.29 | 2.42 | 33.70 |
3.49 | 21.85 | 3.48 | 24.72 | 3.54 | 21.77 | 3.52 | 23.46 | 3.48 | 24.52 | 3.51 | 22.21 |
4.56 | 14.59 | 4.55 | 21.30 | 4.56 | 17.08 | 4.58 | 16.44 | 4.56 | 19.84 | 4.59 | 14.79 |
5.64 | 11.68 | 5.60 | 17.48 | 5.62 | 14.26 | 5.64 | 12.06 | 5.63 | 14.71 | 5.67 | 11.26 |
6.70 | 9.87 | 6.64 | 14.79 | 6.65 | 12.70 | 6.70 | 9.50 | 6.69 | 11.40 | 6.71 | 9.06 |
7.75 | 8.67 | 7.69 | 12.53 | 7.68 | 11.59 | 7.73 | 7.79 | 7.71 | 9.51 | 7.75 | 7.79 |
8.76 | 7.85 | 8.73 | 10.65 | 8.71 | 10.62 | 8.77 | 6.52 | 8.74 | 8.15 | 8.79 | 6.72 |
9.20 | 10.21 | 9.76 | 9.38 | 9.74 | 9.70 | 9.80 | 5.58 | 9.77 | 7.10 | 9.80 | 5.89 |
10.82 | 6.45 | 10.79 | 8.04 | 10.74 | 9.07 | 10.82 | 4.91 | 10.81 | 6.29 | 10.83 | 5.27 |
11.84 | 5.92 | 11.80 | 7.31 | 11.79 | 8.44 | 11.84 | 4.40 | 11.82 | 5.73 | 11.85 | 4.78 |
12.84 | 5.52 | 12.82 | 6.47 | 12.79 | 7.92 | 12.85 | 4.07 | 12.84 | 5.21 | 12.88 | 4.55 |
13.86 | 5.45 | — | — | 13.82 | 7.46 | 13.87 | 3.64 | 13.85 | 4.90 | 13.89 | 4.21 |
Figure
Relations between elastic stiffness degradation and envelope unloading strain. (a) Effect of fiber type; (b) effect of volume fraction of SF; (c) effect of aspect ratio of SF; (d) effect of volume fraction of PF; (e) effect of aspect ratio of PF; and (f) schematic diagram of typical elastic stiffness degradation process of BFRC.
In comparison with plain concrete, the elastic stiffness degradation of FRC is moderate. The stiffness ratios of FRC are larger than that of plain concrete (see in Figure
Research results on the stress deterioration of uniaxial cyclic compression have shown that the stress of a reloading branch is less than the envelope unloading stress at the same unloading strain [
The relations between the stress deterioration ratio and nondimensionalized envelope unloading strain (
Relations between stress deterioration ratio and envelope unloading strain. (a) Effect of steel fiber volume fraction; (b) effect of steel fiber aspect ratio; (c) effect of polypropylene fiber volume fraction; and (d) effect of polypropylene fiber aspect ratio.
With respect to the fiber effects, the results indicate that the influences are insignificant, especially when the nondimensionalized unloading strain exceeds 3.0. However, a fluctuant fiber effect can still be seen when the nondimensionalized unloading strain is less than 3.0, which can be ignored according to the conclusions in the literature [
Relation between stress deterioration ratio and nondimensionalized unloading strain for BFRC.
This section presents a cyclic constitutive model for BFRC based on the experimental results in the current study. The proposed model consists of three components: (1) a monotonic stress-strain model to describe the envelope curve, (2) a power expression for the unloading path, and (3) a broken line for the reloading path, as shown in Figure
Previous experimental studies have shown that the monotonic stress-strain curve can be generally assumed as the envelope curve of concrete material under cyclic compression [
The
Comparisons of parameters between experimental and predicted results. (a) Parameter
In addition, the
Comparisons of mechanical parameters between experimental [
Considerable research results have shown that the unloading path from the envelope curve to the plastic strain point is nonlinear, which becomes significant when the unloading path intersects the strain axis. In addition, the shape of the unloading curve depends on the initial unloading point and ultimate unloading point [
Variation of
As aforementioned, the reloading path of a full cycle consists of a linear segment and a parabolic segment. At present, many equations have been proposed to simulate the reloading path, from linear function to nonlinear approximation. However, the predictions exhibit remarkable deviations in particular when the reloading path is approaching to the intersection point with the unloading curve. To tackle this problem, a sectional model [
The first linear portion of the reloading path is defined by the following equation:
The second linear portion of the reloading path is expressed by the following equation:
For incomplete unloading, the unloading path of the stress-strain curve is interrupted at the point (
In order to facilitate better understanding and implementation, a step-by-step process for generating the stress-strain curves of BFRC under cyclic compression is summarized in Figure
Flowchart describing the generation of stress-strain curves under cyclic compression.
Figure
Typical comparisons of experimental results and proposed models for concrete.
However, it should be noted that the model for PFRC and BFRC is only validated based on the current test results due to the lack of test data in the literature.
The introduction of blended fibers into concrete matrix has positive influences on improving the mechanical behavior of concrete under cyclic loading, reflected in that an improvement on peak strength and postpeak ductility can be observed, notwithstanding that PF has an insignificant effect for ductility. The failure pattern of BFRC is ductile, while that of plain concrete is brittle. Obvious degradation on elastic stiffness and strength with increasing loading cycles is observed, especially on the postpeak region. The capacity of FRC in hysteretic energy dissipation is stronger than that of plain concrete. With respect to SFRC and BFRC, the energy dissipation remains active owing to the steel fiber sliding and pull-out mechanisms. In comparison with plain concrete, the increase in volume fractions of both fibers can lead to a remarkable decrease in plastic strain accumulation. The stiffness degradation ratio as well as the stress deterioration ratio of BFRC is significantly alleviated in comparison with those of plain concrete, despite the degradation degrees being insensitive to the variations of fiber parameters. A semiempirical constitutive model for BFRC under uniaxial cyclic compression is developed to generalize the cyclic stress-strain response, with the contributions of blended fiber taken into consideration. The predictions are found in satisfactory agreement with the results in this study and other literature.
All the data underlying the findings of the study can be found in the tables in the article.
The authors declare that they have no conflicts of interest.
The present work was supported by the Chinese National Natural Science Foundation (Grant nos. 51608397 and 51478367). The financial support is gratefully acknowledged.