Under complex seismic forces, the failure characteristics of the plastic hinge region at the bottom of the pier column and the methods improving the ductility have attracted extensive attention. In this study, steel fiber-reinforced concrete with fine aggregate (SFRC-FA) was applied to locally replace the conventional concrete in the potential plastic hinge region at the bottom of the pier column. Five SFRC-FA pier column specimens with different stirrup ratios and different replacement lengths and one conventional reinforced concrete pier column specimen were produced. Using the seismic behavior tests under the combined bending-shear-torsion-axial force, the failure mode, torsional bearing capacity, energy dissipation, and the torsional plastic hinges of the pier columns were investigated. In addition, an equation for calculating the torsional bearing capacity of the new composite pier columns was proposed. The results showed that (1) compared with the reinforced concrete pier column, the plastic hinge was shifted from the bottom of the pier column to the middle of the height of the pier column due to the application of SFRC-FA at the bottom of the pier column, which improved the torsional bearing capacity; (2) the effect of reducing the stirrup ratio of the SFRC-FA replacement region on the torsional bearing capacity, cracking mode, energy dissipation, and ductility was not obvious; (3) the accuracy of the new equation based on the space truss model proposed in this article was verified by comparison with the experiments of this study and other researches.

The earlier research on bridge piers mainly focused on axial, bending, shear forces, and related seismic performance [

Against this background, Qiu et al. [

FRC and ECC are efficient cement-based composites that can compensate for the drawbacks of quasibrittleness of conventional concrete and has better structural performance than conventional concrete [

However, the above-mentioned research of FRCs materials in the plastic hinge region mainly focused on the seismic performance of structural members subjected to compression-bending-shear (CBS) loads. Moreover, due to the large coarse aggregate, conventional SFRC is likely to cause pouring difficulties in significant reinforcement congestion zone of joints. In order to have the characteristics of superhigh ductility, ECCs materials have the disadvantages of excessive fiber content, many raw materials, high cost, and unsatisfactory workability in the fresh state. Therefore, it is necessary to reduce the coarse aggregate size of SFRC and improve the workability in the fresh state and focus on the seismic behavior and failure mode for strengthening pier columns in the case of compression-bending-shear-torsion.

The aim of this work was to evaluate the effect of the application of steel fiber-reinforced concrete with fine aggregate (SFRC-FA) on the torsional seismic behavior of solid square piers through the comparative analysis of one conventional RC specimen and five SFRC-FA specimens. All the specimens were subjected to combined reversed cyclic lateral torsion and constant axial loading. The reinforcement stirrup ratio, axial compression ratio, and height of the SFRC-FA at the plastic hinge region were considered to better understand their influences on the seismic behavior of bridge piers, including failure pattern, torsional load-rotation angle hysteretic characteristics, envelope curves, torsional bearing capacity, ductility, and energy dissipation. Furthermore, a new equation based on the space truss model was proposed in this article.

Five specimens of RC pier columns locally replaced with SFRC-FA and one specimen of ordinary RC pier column were constructed and tested at Zhejiang University to investigate the influence of SFRC-FA replacement length, stirrup ratio, and axial-torsional loading on the seismic behavior of pier columns.

As shown in Figure _{r}) and stirrup ratios (_{s}) of six specimens. The stirrups applied to the replacement length are spaced at 120, 180, and 240 mm on the center vertically (Figure _{s} = 0.686%, 0.432%, and 0.343%, respectively. The pier column specimens were tested in a lateral reverse cyclic manner until severe damage occurred at the potential plastic hinges.

Specimen configuration. (a) C1 specimen. (b) Top view of specimen. (c) SF1∼SF5 specimens.

Parameters of the specimens on replacement region.

Column | C1 | SF1 | SF2 | SF3 | SF4 | SF5 |
---|---|---|---|---|---|---|

_{r} (mm) | 0 | 800 | 800 | 800 | 500 | 300 |

_{s} (%) | 0.686 | 0.686 | 0.432 | 0.343 | 0.686 | 0.686 |

_{r}: the locally replaced length using SFRC-FA; _{s}: the stirrup ratio of _{r}.

As one of the purposes of this study is to clarify the influence of the SFRC-FA replacement length and the stirrup ratio on the seismic behavior of pier columns under combined action of axial force and torsion, all the specimens were designed to fail under torsional loading, in accordance with the 2008 Guidelines for seismic design of highway bridges [

Table

Sectional dimension and reinforcement arrangement.

Pier column | Loading beam | Foundation | |
---|---|---|---|

Section | |||

Dimension | 300 × 300 | 600 × 300 | 1000 × 400 |

Main bar | 6D22 + 2D10 | 10D22 | 12D16 |

Stirrup | D8@120 | D8@150 | D8@150 |

Reinforcement material properties.

Diameter (mm) | Yield strength (MPa) | Ultimate strength (MPa) | Young’s modulus (GPa) |
---|---|---|---|

8 | 365 | 490 | 180 |

10 | 571 | 644 | 189 |

16 | 562 | 631 | 183 |

22 | 559 | 627 | 194 |

Concrete and SFRC-FA material properties.

Type | Compressive strength (MPa) | Flexural strength (MPa) | Young’s modulus (GPa) |
---|---|---|---|

Concrete | 54.5 | 6.1 | 34.1 |

SFRC-FA | 52.2 | 12.0 | 40.8 |

Mixture of SFRC-FA.

Cement (kg/m^{3}) | Water (kg/m^{3}) | Fly ash (kg/m^{3}) | Aggregate (kg/m^{3}) | River sand (kg/m^{3}) | Steel fiber volume ratio (%) | Superplasticizer (kg/m^{3}) |
---|---|---|---|---|---|---|

373 | 242 | 205 | 462 | 993 | 2 | 5 |

Indexes of steel fiber.

Diameter (mm) | Length (mm) | Tensile strength (MPa) | Young’s modulus (GPa) | Density (g/cm^{3}) |
---|---|---|---|---|

0.2 | 13 | 1500 | 2700 | 7.8 |

Steel fibers.

A photograph of experimental setup and the details of the loading system are shown in Figures

Photograph of the test model installed on the facility.

Schematic diagram of the test setup.

It can be seen in Figure _{1}∼_{9}) were used for measuring the displacements of each specimen. The displacement transducers, _{1}∼_{4}, were installed at the centerline of the loading beam to record the displacement data, which was used to calculate the rotation angle of the pier column (_{1} − _{2})/_{5}∼_{9} were installed at the centerline of the pier column to measure the relative displacement at different heights. Figure

Arrangement of LVDTs.

Locations of strain gauges embedded in stirrups and longitudinal bars (/mm). (a) Stirrups. (b) Longitudinal bars.

Loading was mainly controlled by measured displacement in terms of the rotation angle _{max} or the specimen experienced a significant loss of torsional load. Therefore, instrumentations were used to monitor the applied loads, deformation of the pier column, and strain of the reinforcing bars. And, during the selected loading steps in the tests, the observed damage was recorded with photographs and sketches. The location of cracks, spalling, and any buckled reinforcing bars were documented.

Lateral loading history of experimental program.

The crack patterns at the end of tests of six specimens are shown in Figure

Crack propagation at the end of tests.

Figures _{y}) was determined when the area enclosed by the torsion-rotation angle curve is equal to that surrounded by bilinear curve when rotation angle ranges from 0 to _{u} [_{max} to indicate the maximum torque of positive load and −_{max} to indicate the maximum torque of negative load. The symbols “+” and “−” indicate the difference in the loading direction.

Damage and hysteresis curves of specimen C1.

Damage and hysteresis curves of specimen SF1.

Damage and hysteresis curves of specimen SF2.

Damage and hysteresis curves of specimen SF3.

Damage and hysteresis curves of specimen SF4.

Damage and hysteresis curves of specimen SF5.

Torsion and rotation angle at the critical loading stage.

Specimen | Initial crack occurred | Yielding point | Maximum load | ||||
---|---|---|---|---|---|---|---|

Torsion (kN·m) | Rotation angle (10^{−3} rad) | Torsion (kN·m) | Rotation angle (10^{−3} rad) | Torsion (kN·m) | Rotation angle (10^{−3} rad) | ||

C1 | Positive | 21.09 | 1.77 | 30.06 | 3.69 | 34.58 | 7.16 |

Negative | −21.01 | −1.65 | −42.97 | −5.50 | −55.34 | −9.33 | |

SF1 | Positive | 39.22 | 3.54 | 49.82 | 4.85 | 55.84 | 5.78 |

Negative | −40.24 | −2.94 | −53.89 | −4.59 | −59.30 | −6.08 | |

SF2 | Positive | 45.70 | 4.66 | 56.23 | 5.88 | 60.15 | 6.77 |

Negative | −44.93 | −3.36 | −59.35 | −4.64 | −62.62 | −5.05 | |

SF3 | Positive | 42.54 | 4.31 | 51.43 | 5.28 | 57.76 | 6.12 |

Negative | −44.71 | −2.76 | −55.12 | −4.87 | −62.43 | −6.33 | |

SF4 | Positive | 45.24 | 4.47 | 54.97 | 5.76 | 60.75 | 6.87 |

Negative | −47.16 | −4.41 | −54.88 | −5.24 | −59.71 | −7.10 | |

SF5 | Positive | 38.15 | 3.91 | 52.41 | 5.78 | 56.83 | 6.82 |

Negative | −41.25 | −2.48 | −61.32 | −3.45 | −62.73 | −4.23 |

Equivalent elastic-plastic energy method (_{1} = _{2}) and _{1}, _{2}, _{3} stand for the area of the regions in the torsion-rotation angle curve [

In the case of specimen C1, the initial cracks occurred at the height of 300 mm on A and D surfaces of the pier column when the load reached 35% of the maximum negative torque (−_{max}). The positive and negative cracks then gradually extended upward to the height of 1100 mm and downward to the bottom of the pier column. These cracks eventually met in an area between 200 mm and 600 mm in height, and they formed the angle of about 40–60°, as shown in Figure

As shown in Figure ^{−3} rad and −5.50 × 10^{−3} rad, while the stirrup bar yielded 9.81 × 10^{−3} rad followed by cover concrete spalling at 300 mm height of surface C and surface D. As loading continued, the torsion reached the maximum value of −55.34 kN·m (−_{max}) at the rotation angle of −9.33 × 10^{−3} rad followed by a long stage of deterioration. Finally, the torsion deteriorated to 77% × (−_{max}) at the rotation angle of −19.43 × 10^{−3} rad, at which the loading was terminated. The experimental results of specimen C1 were used as a benchmark for analyzing the seismic performance of other specimens with different SFRC-FA replacement lengths.

In the cases of specimens SF1, SF2, and SF3, the crack morphology and the crack distribution were similar, although the stirrup ratios in the SFRC-FA replacement section were 0.686%, 0.432%, and 0.343%, respectively (Figures _{max} in a loading cycle; in the third stage, as the rotation angle increases, the torsion bearing capacity decreases slowly, which showed well ductility.

Due to replacement by SFRC-FA at the bottom of the pier column, no cracks observed until the torque of SF1, SF2, and SF3 reached 39.2 kN·m, −44.9 kN·m, and 42.5 kN·m, which were 70%, 72%, and 74% of their maximum torsion (±_{max}), respectively. Obviously, their cracking torque was much high than that of specimen C1 (−35% _{max}). Taking SF1 for example, cracks quickly extended through surfaces C and D from the initial one at 1050 mm height with a 60-degree angle relative to the horizontal direction. Subsequently, the crack width gradually became larger and the torque of SF1 reached _{max} of 55.84 kN·m at a rotation angle of 5.78 × 10^{−3} rad, which was smaller than the rotation angle of C1 at the maximum torque. Moreover, the torsional bearing capacity of SF1 decreased suddenly after _{max}, unlike C1. After that, as the torsional bearing capacity slowly decreased, the conventional concrete on the upper part of the pier column gradually cracked and spalled, forming a concentrated region of cracks and large rotational deformation near the mid-height of the upper column, which was assumed to be a torsional plastic hinge. As shown in Figure ^{−3} rad, while in the SFRC-FA replacement region, neither did the stirrups yield nor did cracks occur on the surface. Although some of the stirrups in the SFRC-FA region yielded in the final failure mode, there were almost no cracks on the four surfaces of the SFRC-FA replacement region, which showed that SFRC-FA improved the torsional bearing capacity and deformation capacity of the pier column.

In the cases of specimens SF4 and SF5, the crack morphology and the crack distribution were similar to those of SF1, SF2, and SF3, as shown in Figures

For the specimen SF4, when the rotation angle reached 4.47 × 10^{−3} rad (45.24 kN·m), the initial diagonal cracks occurred, and they expanded rapidly in the range of 500 mm to 1000 mm on all four surfaces. However, when the rotation angle of specimen SF5 reached 3.91 × 10^{−3} rad (38.15 kN·m), the initial diagonal cracks occurred on the surface of C and D, and they expanded rapidly in the range of 300 mm to 400 mm height. Both SF4 and SF5 reached the maximum torsional bearing capacity soon after cracks occurred. Afterward, the cracks of SF4 and SF5 expanded at 60 degrees in the range of 450–1300 mm and 250–1400 mm, respectively.

The theoretical equations for plastic hinges in various codes [

There are many damage indexes [_{p} was proposed taken as the average cracked length of these six specimens:_{e} is the height of the pier column.

The length of the severely damaged plastic hinge _{ph} which has the approximate length in the range of 0.5_{cor}–1.5_{cor} [_{cor} is the core side length of the square concrete section.

The torsional envelop curves under different torque levels and constant axial compression are shown in Figure ^{−3} rad, 34.6 kN·m, whereas the hysteresis envelopes of SF series specimens were linear up to 55.8–62.7 kN·m with rotation angle at ^{−3} rad, which were the rotation angles relative to their torsional strength. This showed that the torsional rigidities and peak strength of pier columns have been greatly improved when locally replaced with SFRC-FA at the bottom of pier columns, with 11–26% and 60–76%, respectively. In addition, there were three obvious deterioration stages of SF series specimens: (1) a steep drop of about 15% _{max} following the torsional peak; (2) a moderate strength-decreasing platform between 85% _{max} to 75% _{max} and even 70% _{max}; (3) quick failure. Compared to SF series specimens, C1 only went through two obvious deterioration stages: a typical yielding platform under nearly double _{max} and 85% _{max} and a quick failure afterward. On the other hand, few differences in envelop curves were found between SF1 and SF5 with the SFRC-FA replacement length of 300–800 mm, meaning that increasing the replacement length had little effects on peak strength and torsional hysteresis behavior when the length exceeds the section size of members.

Envelop curves. (a) Envelop curves of six specimens. (b) Deterioration of C1 and SF1.

The limit rotation is usually defined as the corresponding rotation when the load decreases to 85% of the peak load or when the specimen is not capable of carrying the load [_{max} and 75% _{max}, as marked in Figure _{max}, the ductility coefficient _{max}.

Table _{max}∼75% _{max} deterioration stage. Although SFRC-FA strengthening may lead to a 1/3 ductility decrease in positive loading, the reinforcing method brings about general fortification in the negative loading condition in rotation ductility, especially in SF1. On the other hand, due to the “lock and unlock” effect [

Ductility coefficient of specimens.

Specimen | _{y} (10^{−3} rad) | _{y} (kN·m) | _{85} (10^{−3} rad) | 85% ± _{max} (kN·m) | _{85} | _{75} (10^{−3} rad) | 75% ± _{max} (kN·m) | _{75} | |
---|---|---|---|---|---|---|---|---|---|

C1 | Negative | −6.8 | −40.0 | −11.8 | −47.0 | 1.7 | −14.4 | −41.5 | 2.1 |

Positive | 3.7 | 30.1 | 11.8 | 29.4 | 3.2 | 12.1 | 25.9 | 3.3 | |

SF1 | Negative | −4.6 | −53.9 | −20.9 | −50.4 | 4.6 | −25.3 | −44.5 | 5.5 |

Positive | 4.8 | 49.8 | 6.4 | 47.5 | 1.3 | 14.1 | 41.9 | 2.9 | |

SF2 | Negative | −4.6 | −59.3 | −8.4 | −53.2 | 1.8 | −15.7 | −47.0 | 3.4 |

Positive | 5.9 | 56.2 | 9.5 | 51.1 | 1.6 | 11.7 | 45.1 | 2.0 | |

SF3 | Negative | −4.9 | −55.1 | −15.1 | −53.1 | 3.1 | −16.0 | −46.8 | 3.3 |

Positive | 5.3 | 51.4 | 7.2 | 49.1 | 1.4 | 10.9 | 43.3 | 2.1 | |

SF4 | Negative | −5.2 | −54.9 | −15.6 | −50.8 | 3.0 | −18.9 | −44.8 | 3.6 |

Positive | 5.8 | 55.0 | 7.6 | 51.6 | 1.3 | 10.2 | 45.6 | 1.8 | |

SF5 | Negative | −3.4 | −61.3 | −9.8 | −53.3 | 2.8 | −13.0 | −47.0 | 3.8 |

Positive | 5.8 | 52.4 | 11.1 | 48.3 | 1.9 | 12.0 | 42.6 | 2.1 |

Ductility coefficient at _{85} and _{75} of six specimens.

Figure

Loading-displacement curve.

As shown in Figure _{Tmax} and _{75%Tmax} of SF series specimens was much larger than that of specimen C1, which may also result in better energy dissipation capacity due to the good toughness of SFRC-FA materials.

Coefficient

The space truss model developed by Hsu [_{sv} is the area of one stirrup section; _{yv} is the yield stress of stirrup bars; _{0} is the area enclosed by the centerline of the shear flow zone;

In order to study the combined action, torsion _{0}, _{0}, _{0}, _{0} mean the strength under single action of torsion, shear, bending moment, and axial compression, respectively.

Equation (

Equation (

The JTG 3362-2018 specification [_{t} is the concrete tensile strength; _{t} is the torsional plastic moment of resistance. Furthermore, the torsional reinforced effect was not taken into consideration in the Caltrans code [

As shown in Table _{0}, _{1}, _{2}, and _{3} represent the experimental result and the calculated results by equations (_{2} of this study and other studies in the literature by equation (_{1} by equation (_{3} by equation (

Comparison of calculation methods of torsion bearing capacity (kN·m).

Specimens | _{0} | _{0} | Calculated results (kN·m) | |||||
---|---|---|---|---|---|---|---|---|

_{1} | _{2} | _{3} | _{1}/_{0} | _{2}/_{0} | _{3}/_{0} | |||

C1 | 0.60 | 43.38 | 38.44 | 35.73 | 52.69 | 0.89 | 0.82 | 1.21 |

SF1 | 0.60 | 57.57 | 38.44 | 35.73 | 52.69 | 0.67 | 0.62 | 0.92 |

SF2 | 0.60 | 61.39 | 38.44 | 35.73 | 52.69 | 0.63 | 0.58 | 0.86 |

SF3 | 0.60 | 60.10 | 38.44 | 35.73 | 52.69 | 0.64 | 0.59 | 0.88 |

SF4 | 0.60 | 60.23 | 38.44 | 35.73 | 52.69 | 0.64 | 0.59 | 0.87 |

SF5 | 0.60 | 59.78 | 38.44 | 35.73 | 52.69 | 0.64 | 0.60 | 0.88 |

P1 [ | 0 | 72.90 | 72.51 | 50.22 | 83.70 | 0.99 | 0.69 | 1.15 |

P2 [ | 0.22 | 81.60 | 72.51 | 62.39 | 95.87 | 0.89 | 0.76 | 1.17 |

C2 [ | 0 | 82.30 | 67.60 | 45.66 | 76.10 | 0.82 | 0.55 | 0.92 |

C3 [ | 0 | 77.20 | 67.60 | 45.66 | 76.10 | 0.88 | 0.59 | 0.99 |

C4 [ | 0 | 95.50 | 95.60 | 64.58 | 107.63 | 1.00 | 0.68 | 1.13 |

C5 [ | 0 | 100.70 | 95.60 | 64.58 | 107.63 | 0.95 | 0.64 | 1.07 |

C6 [ | 0.52 | 109.70 | 87.27 | 71.88 | 111.18 | 0.80 | 0.66 | 1.01 |

C7 [ | 0.52 | 96.30 | 67.60 | 58.59 | 89.03 | 0.70 | 0.61 | 0.92 |

R1 [ | 1.33 | 37.93 | 24.27 | 0.64 | 27.43 | 0.72 | 35.25 | 0.93 |

R2 [ | 1.33 | 33.46 | 24.27 | 0.73 | 27.43 | 0.82 | 35.25 | 1.05 |

R3 [ | 1.24 | 31.31 | 23.87 | 0.76 | 27.43 | 0.88 | 34.84 | 1.11 |

R4 [ | 1.86 | 35.73 | 24.91 | 0.70 | 27.43 | 0.77 | 35.89 | 1.00 |

R5 [ | 1.73 | 31.38 | 24.47 | 0.78 | 27.43 | 0.87 | 35.44 | 1.13 |

R6 [ | 2.27 | 38.34 | 25.32 | 0.66 | 27.43 | 0.72 | 36.30 | 0.95 |

R7 [ | 2.00 | 31.00 | 24.45 | 0.79 | 27.43 | 0.88 | 35.42 | 1.14 |

R8 [ | 2.17 | 40.35 | 27.81 | 0.69 | 32.46 | 0.80 | 40.80 | 1.01 |

R9 [ | 1.14 | 52.10 | 35.19 | 0.68 | 44.76 | 0.86 | 53.10 | 1.02 |

Statistical analysis | Numbers of specimens | 23 | Average | 0.80 | 0.67 | 1.01 | ||

Mean square error | 0.013 | 0.006 | 0.012 | |||||

Coefficient of variation | 0.144 | 0.112 | 0.107 |

The seismic behavior tests and theoretical studies on the pier columns of SFRC-FA replacing conventional concrete in the potential plastic hinges were carried out subject to torsion combined with axial compression. The major conclusions drawn from the above studies are as follows:

The evolution process of the rotation angle and the crack patterns of the test specimens indicated that the torsional seismic failure mode of the pier columns was obviously dependent on the SFRC-FA replacement length. With the increase of the SFRC-FA replacement length at the bottom of the pier column, the plastic hinge was shifted up to the conventional concrete region in the middle of the height of the pier column. Although the plastic hinge length of SF series specimens was basically the same as that of the conventional concrete specimen, it improved the torsional bearing capacity and ductility of the pier column.

In the tests of the SF1∼3 pier columns, the change of the stirrup ratio (0.343–0.686%) had little effect on the torsional bearing capacity, ductility, cracking pattern, energy dissipation, and other seismic behaviors, which indicated that the application of SFRC-FA material in the potential plastic hinge region could reduce the stirrup ratio.

Based on the space truss model, a new equation for calculating the torsion bearing capacity was proposed, taken into account the effect of axial force and the application of SFRC-FA. Compared with the equations proposed by various international codes, the equation proposed herein did not underestimate the torsion bearing capacity, whose coefficient of variation was better.

In total, the experimental results proved that the application of SFRC-FA in the potential plastic hinge region changed the failure mode and improved the torsional bearing capacity of the pier column. Certainly, further rigorous studies are wanted to understand the interactions between the SFRC-FA and the conventional concrete and their effect on the seismic behaviors of the composite pier columns. In addition, testing SFRC-FA pier columns under combined cyclic bending-torsion loads with larger torsion-bending ratios may be a focus for further research.

The raw/processed data required to reproduce these findings cannot be shared at this time as the data are also part of an ongoing study. The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

The authors declare that they have no conflicts of interest.

This study was supported by the National Natural Science Foundation of China (51578495) and Zhejiang Provincial Natural Science Foundation of China (LY16E080002). The authors appreciate the great assistance of Xiao-Hua JI and Yu Peng in the execution of experiments.