Study on Seismic Performance of Steel Fiber Reinforced Concrete Pier Under Bending–Torsion Coupling

Abstract

To systematically study the mechanical behavior of a steel fiber-reinforced concrete (SFRC) pier under bending–torsion coupling, three pier specimens with a clear height of 1200 mm, a diameter of 300 mm, and an SFRC height of 300 mm in the plastic hinge region were designed and fabricated. Quasi-static tests were carried out to observe the damage patterns and failure modes of the specimens. On this basis, multiple finite element models were established using the ABAQUS 2018 software to study the influence of the torsion–bending ratio and SFRC height on the seismic performance of the pier. The results show that the bending–torsion coupling effect leads to a decrease in the bending and torsion capacities of the pier. The presence of torque causes the plastic hinge position to move up and the plastic hinge area to expand. Adding SFRC at the bottom of the pier can effectively improve the bearing capacity of the pier under earthquake action. The optimal height of SFRC is half of the clear height of the pier under the common torsion–bending ratio, which can not only improve the seismic performance of the structure but also avoid material waste.

1. Introduction

The number of curved girder bridges is increasing with the rapid development of transportation. Due to the influence of curvature, the center of gravity of the curved girder bridge deck deviates from the pier. The pier is typically subjected to complex forces such as compression, bending, shear, and torsion due to earthquakes [1,2]. Deng [3] carried out quasi-static tests on RC piers under the coupled effects of compression, bending, shear, and torsion, and the different failure modes of the piers under various loading conditions were determined. Jiao [4] found that the damage of the piers was increased and the energy dissipation and load-bearing capacities of the piers were weakened due to torsional and shear effects. Zhu [5] performed a series of tests to study the mechanical properties of RC piers under various loading cycles. The results showed that an increase in the number of loading cycles accelerated damage accumulation and led to the cyclic degradation of RC piers, which resulted in bending–shear failure. In order to improve the seismic resistance of piers, Zahn [6] proposed the theory of ductile seismic design, emphasizing the formation of plastic hinges through structural plastic deformation to resist seismic forces. Some scholars have aimed to improve the ductility of piers by increasing the stirrup reinforcement and optimizing the section dimensions [7,8,9]. However, these measures might result in increased costs and greater construction difficulty.

In recent years, technological innovation in bridge engineering has been promoted by new materials. The seismic performance of RC piers has been improved by several scholars through the use of high-ductility concrete, replacing ordinary concrete at the pier ends [10]. Zhang [11] studied the seismic performance of prefabricated piers with ultra-high-performance fiber-reinforced concrete (UHPFRC)-enhanced bottom segments and found that prefabricated piers with UHPFRC bottom segments had higher lateral strength and residual displacement compared to those with ordinary reinforced concrete segments. Pang [12] compared the seismic performance of piers constructed from different fiber-reinforced concrete materials, including steel fiber-reinforced concrete (SFRC), polypropylene fiber-reinforced concrete (PFRC), and high-performance fiber-reinforced concrete (HySPFRC). The results showed that all types of fibers effectively improved the seismic performance of the piers. Xu [13] carried out uniaxial cyclic compression tests on steel fiber-reinforced concrete specimens and found that the specimens had obvious ductility characteristics. Zhang [14] studied the effect of fiber-reinforced cement-based composite materials on the mechanical properties of RC piers, and the results showed that the seismic performance of the RC piers was significantly improved after reinforcement. Yu [15] used a glass fiber-reinforced polymer (GFRP) and aramid fiber-reinforced polymer (AFRP) to strengthen the plastic hinge regions of piers, and the test results showed that the specimen reinforced with AFRP had the best seismic performance. Shi [16] found that adding polyvinyl alcohol (PVA) fibers in the concrete could effectively improve the spalling at the base of precast circular hollow piers. Osman [17] established a determination method for the drift ratio limit state and the corresponding strength of an RC circular pier with GFRP. Guerrero [18] reinforced the wall panel joints using SFRC, and it was indicated that SFRC could delay crack propagation and enhance the deformability of the wall.

In summary, while research has been conducted by numerous scholars on the seismic performance of SFRC piers under bending–torsion coupling effects, a systematic analysis of the influence of the component parameters and external load parameters on the mechanical behavior of SFRC circular piers has not been performed. Therefore, in this work, quasi-static tests and numerical simulations were conducted to study the influence of using SFRC in the plastic hinge region on the seismic performance of piers. On this basis, a parameter analysis was conducted to explore the most effective method to improve the seismic resistance of piers.

2. Overview of the Experiment

2.1. Specimen Design

Three cylindrical piers were created according to the geometric similarity ratio of 1/3, and the geometric dimensions and reinforcement situations of the three specimens were exactly the same. The effective height of the pier was 1400 mm (clear height 1200 mm), and the size of the base was 1000 mm (length) × 1000 mm (width) × 400 mm (height). The diameter of the pier was 300 mm, and the height of the SFRC in the plastic hinge region was 300 mm. The strength grade of the concrete was C40, and the type of steel bar was HRB400. The diameter of the longitudinal steel bar was 16 mm, and the diameter of the spiral stirrup was 8 mm. In the SFRC region at the bottom of the pier, the volume ratio of steel fibers was 1%. The axial compression ratio is an important parameter in quasi-static tests. According to the relevant specifications and literature [3,19,20], the axial compression ratio of the three specimens was set to 0.2. The torsion–bending ratios were 0, 0.17, and 0.36, respectively, labeled as SFRC-1, SFRC-2, and SFRC-3. The specific dimensions and reinforcement details of the SFRC bridge piers are shown in Figure 1, and the testing parameters of the three specimens are listed in

Table 1. Testing parameters of specimens.

Specimen Number	SFRC Height/mm	Axial Compression Ratio	Torsion–Bending Ratio
SFRC-1	300	0.2	0
SFRC-2	300	0.2	0.17
SFRC-3	300	0.2	0.36

.

2.2. Mechanical Properties of Materials

In this work, steel fibers with a length of 30 mm and a length–diameter ratio of 55 were used. As shown in Figure 2, the shape of the steel fibers was end-hooked, and the tensile strength grade was 1000. Before the quasi-static tests, the mechanical properties of the concrete and steel bar were measured using reserved samples. The cube compressive strengths of the concrete are listed in

Table 2. Cube compressive strength of concrete.

Material	Sample Number	Compressive Strength/MPa
Ordinary concrete (C40)	Sample 1	46.5
	Sample 2	47.8
	Sample 3	46.2
Steel fiber-reinforced concrete	Sample 1	56.2
	Sample 2	60.2
	Sample 3	56.5

, and the yield strength and ultimate strength of the steel bar are listed in

Table 3. Strength of steel bars.

Diameter/mm	Sample Number	Yield Strength/MPa	Ultimate Strength/MPa
16	Sample 1	435	625
	Sample 2	441	619
	Sample 3	437	626
8	Sample 1	430	614
	Sample 2	422	620
	Sample 3	424	615

. The strength of the materials met the design requirements of the test.

2.3. Loading Plan

The axial force was applied by an MTS vertical actuator. Torque was applied by adjusting the eccentric displacement of the MTS horizontal actuator and the specimen. The greater the eccentric displacement, the stronger the torsional effect of the pier. In the experiment, the horizontal actuator was used to apply reciprocating displacement to the specimen, and the displacement was loaded based on drift ratios of 0.25%, 0.5%, 1%, 1.5%, 2%, 2.5%, etc. When the bearing capacity of the specimen decreased to 85% of the peak load, the loading was stopped. The loading site is shown in Figure 3, and the experimental loading system is shown in Figure 4.

2.4. Experimental Phenomenon

For the no-torsion pier SFRC-1, several horizontal fine cracks were generated on the front of the pier base during the initial stage of loading. As the loading displacement increased, the horizontal cracks were continuously developed and extended. When the longitudinal steel bar firstly reached yield, short horizontal cracks were observed in the middle of the pier. Moreover, the first through crack, with a width of 2–3 mm, was formed 10 cm above the pier base. As the loading displacement continued to increase, the horizontal cracks in the middle of the pier extended laterally, and short vertical cracks developing upwards appeared in the middle and lower parts of the pier sides. The second through crack, with a width of 1 mm, was formed 17 cm above the pier base, accompanied by the sound of steel fibers being pulled out. When the horizontal bearing capacity was reduced to 85% of the peak load, two through cracks were formed within 25 cm of the pier base, and the height of the crack reached 75 cm. At this moment, the concrete at the bottom of the pier was crushed, and partial concrete near the main cracks was peeled off. It could be seen that the main cracks on the specimen were horizontal cracks, showing obvious bending failure characteristics. Due to the presence of SFRC, the failure mode of the specimen was different from that of an ordinary concrete pier. The addition of steel fibers improved the tensile strength of the concrete and the flexural bearing capacity of the bottom of the pier, which was subjected to the maximum load. The pier body was kept relatively intact until failure, with no significant areas of concrete spalling and no loss of vertical bearing capacity. The final failure mode of SFRC-1 is shown in Figure 5a.

Compared with SFRC-1, SFRC-2 and SFRC-3 suffered different degrees of bending–torsion damage due to the different torsion–bending ratios. As the experiment progressed, diagonal cracks firstly appeared in the middle and upper parts of SFRC-3, which had a higher torsion–bending ratio. Under cyclic bending–torsion action, the diagonal cracks in the middle and upper parts of the two piers gradually increased, forming an ‘X’-shaped intersecting crack network. As the loading displacement increased, the diagonal cracks continued to extend upwards and downwards, forming a spiral that traversed through the entire cross-section. The cracks on SFRC-3 were wider and longer than those on SFRC-2. In the later stage of loading, the steel bars at the crack section of SFRC-3 yielded, and the cracks in the pier developed rapidly, with a length of 95 cm. The concrete at 20–50 cm from the top of the pier bulged and fell off extensively, resulting in the exposure of the spiral stirrups and longitudinal bars. For SFRC-2, the crack length reached 90 cm. Some intersecting diagonal cracks with a width of 7 mm and a height of about 25 cm were formed at 20 cm from the top of the pier, and the concrete protective layer bulged but did not fall off. According to the experimental phenomena, it can be seen that the presence of torque causes the main cracks on the specimen to be diagonal cracks, and shear failure becomes the main failure mode. The greater the torque, the more serious the damage of the specimen. In addition, the change in the failure mode caused the plastic hinge position to move up from the bottom of the pier, and the length of the plastic hinge was greater than that in specimen SFRC-1 without torsion. The final failure modes of SFRC-2 and SFRC-3 are shown in Figure 5b,c.

Considering the limited length of this paper, the relevant experimental data of the three specimens (hysteresis curves, skeleton curves, etc.) will be introduced in the following sections in comparison with the results of the numerical simulations.

3. Numerical Simulations

3.1. Model Parameters

In order to better simulate the mechanical properties of SFRC, the Umat subroutine is used to randomly generate steel fibers in the concrete, and the relevant parameters are listed in

Table 4. Relevant parameters of steel fiber.

Material Type	Elastic Modulus /GPa	Tensile Strength /MPa	Cross-Sectional Area/mm2	Density /(g·cm−3)	Poisson’s Ratio
Steel fiber	200	2000	0.23	7.85	0.3

. In terms of model elements, concrete is simulated using the eight-node hexahedral reduced integration solid element (C3D8R), while steel fibers and rebars are simulated using the truss element (T3D2). In terms of material properties, the ideal elastoplastic model is used to simulate the constitutive behavior of steel fibers. The concrete damage plasticity model is used to simulate the constitutive behavior of concrete, and the damage factors in this model have a good simulation effect on the mechanical properties of concrete under cyclic loading [21]. The relevant parameters of the concrete are listed in

Table 5. Relevant parameters of concrete.

Material Type	Elastic Modulus /MPa	Poisson’s Ratio	Dilation Angle/°	Eccentricity	fb0/fc0	K	Viscosity Parameter
Concrete	32,500	0.2	30	0.1	1.16	0.667	0.005

Note: f_b0/f_c0 represents the ratio of biaxial compressive strength to uniaxial compressive strength; K represents the influence parameter of the yield surface.

. Considering the damage of concrete, the stress–strain curves are as shown in Figure 6, and the specific parameters are determined based on a material performance test and relevant specifications [22].

In Figure 6, ${\sigma }_c$ and ${\epsilon }_c$ represent compressive stress and compressive strain; ${\epsilon }_c^{in}$, ${\epsilon }_{0c}^{el}$, ${\epsilon }_c^{pl}$, and ${\epsilon }_c^{el}$ represent the inelastic strain, elastic strain (undamaged), plastic strain, and elastic strain (damaged) under compression; ${\sigma }_{c0}$ and ${\sigma }_{cu}$ represent the yield stress and ultimate stress under compression; $E_0$ represents the initial elastic modulus; $d_c$ represents the compressive damage factor; ${\sigma }_t$ and ${\epsilon }_t$ represent tensile stress and tensile strain; ${\epsilon }_t^{ck}$, ${\epsilon }_{0t}^{el}$, ${\epsilon }_t^{pl}$, and ${\epsilon }_t^{el}$ represent the cracking strain, elastic strain (undamaged), plastic strain, and elastic strain (damaged) under tension; ${\sigma }_{t0}$ represents the ultimate stress under tension; and $d_t$ represents the tensile damage factor.

To simulate the bond-slip phenomenon between the concrete and rebar under cyclic loading, the rebar material model developed by Fang [23] is used in ABAQUS (2018 version). The numerical model of the specimen is shown in Figure 7.

3.2. Model Reliability Verification

The damage cloud pictures, hysteresis curves, and skeleton curves of the three piers obtained by numerical simulations are compared with the experimental phenomena and data to verify the reliability of the simulation method.

The comparisons between the damage cloud pictures and test failure modes are shown in Figure 8, Figure 9 and Figure 10. It can be seen that the area with significant damage obtained from the numerical simulation is basically consistent with the failure area observed in the experiment. The numerical simulation results are in good agreement with the experimental phenomena.

The hysteresis curves and skeleton curves of the three piers from the tests were compared with the numerical simulation results, as shown in Figure 11 and Figure 12. It can be observed that the numerical simulation and the quasi-static test are in good agreement in terms of the peak load and ultimate displacement. However, differences exist in the unloading process.

The reason is that the subroutine used in this study simulates the slip between the rebar and concrete by reducing the stiffness of the rebar in the later stages. This results in an excessive reduction in the rebar stiffness during the later stages of loading, leading to a decrease in the overall stiffness. Consequently, the unloading stiffness obtained from the numerical simulation is smaller than that obtained from the experiment, but the overall error is less than 15%. The comparison of the hysteresis curves and skeleton curves indicates that the numerical model and analysis method used in this work are relatively reliable and can be used for subsequent analysis.

4. Parametric Analysis of Seismic Performance

To further investigate the influence of the distribution range of SFRC and the loading parameters on the mechanical behavior of SFRC bridge piers, a parametric analysis was conducted. Twenty-five numerical analysis models were established by changing the height of the SFRC in the plastic hinge region and the torsion–bending ratio. Other structural parameters (sectional dimensions, reinforcement, etc.) and material parameters (steel fibers, concrete, etc.) were consistent with the models in Section 3. The specimen numbers and specific parameters are shown in

Table 6. Specific parameters of numerical analysis models.

Specimen Number	SFRC Height/mm	Torsion–Bending Ratio
RC-0	0	0
SFRC300-0	300	0
SFRC600-0	600	0
SFRC900-0	900	0
SFRC1200-0	1200	0
RC-0.09	0	0.09
SFRC300-0.09	300	0.09
SFRC600-0.09	600	0.09
SFRC900-0.09	900	0.09
SFRC1200-0.09	1200	0.09
RC-0.17	0	0.17
SFRC300-0.17	300	0.17
SFRC600-0.17	600	0.17
SFRC900-0.17	900	0.17
SFRC1200-0.17	1200	0.17
RC-0.27	0	0.27
SFRC300-0.27	300	0.27
SFRC600-0.27	600	0.27
SFRC900-0.27	900	0.27
SFRC1200-0.27	1200	0.27
RC-0.36	0	0.36
SFRC300-0.36	300	0.36
SFRC600-0.36	600	0.36
SFRC900-0.36	900	0.36
SFRC1200-0.36	1200	0.36

.

4.1. Influence of Torsion–Bending Ratio

Keeping the height of the SFRC in the plastic hinge region constant, the skeleton curves of the piers under different torsion–bending ratios were compared, as shown in Figure 13a–e. To quantitatively analyze the influence of the torsion–bending ratio on the maximum bearing capacity of the specimens, the reduction ratio of the maximum bearing capacity of the specimens under the bending–torsion coupling effect compared to the no-torsion specimens was determined, as listed in

Table 7. The reduction ratio of the maximum bearing capacity compared to no-torsion specimens.

Torsion–Bending Ratio	Reduction Ratio of Bearing Capacity/%
	RC	SFRC300	SFRC600	SFRC900	SFRC1200
0	—	—	—	—	—
0.09	0.21	0.74	2.56	1.1	0.44
0.17	6.52	3.73	3.92	3.54	3.67
0.27	22.47	25.24	9.12	9.61	8.95
0.36	28.62	27.12	23.26	15.95	15.93

.

It can be observed that, under the bending–torsion coupling effect, the torsion effect on the bridge pier is more obvious as the torsion–bending ratio increases. The presence of torque will increase the strain demand on the pier section, resulting in the insufficient deformation capacity of the pier under shear and bending moments. The reduction ratio of the maximum bearing capacity of the bridge pier is accelerated as the torsion–bending ratio increases, while the trend of the decrease in bearing capacity is delayed by the addition of steel fibers.

When the torsion–bending ratio is 0.09, the reduction ratio of the maximum bearing capacity for both SFRC and RC piers is relatively small. When the torsion–bending ratio is 0.17, the reduction ratio of the maximum bearing capacity of the RC pier is larger than that of the SFRC pier, indicating that SFRC materials can effectively improve the structural bearing capacity and reduce the decrease ratio in the structural bearing capacity under low torsion–bending ratios. When the torsion–bending ratio is 0.27, the bearing capacities of the RC pier and the pier with an SFRC height of 300 mm decrease obviously, while the bearing capacities of other specimens decrease by less than 10%. When the torsion–bending ratio is 0.36, the reduction ratio of the maximum bearing capacity of the RC pier and the piers with SFRC heights of 300 mm and 600 mm is about 20–30%, while that of piers with SFRC heights of 900 mm and 1200 mm is about 16%.

It can be seen that the bending–torsion coupling has a significant effect on the bending and torsion bearing capacities of piers. When the SFRC reaches a certain height, the bearing capacity of the pier cannot be obviously improved by increasing the height of the SFRC.

4.2. Influence of SFRC Height

Keeping the torsion–bending ratio constant, the skeleton curves of the piers with different heights of SFRC in the plastic hinge region were compared, as shown in Figure 14a–e. To quantitatively analyze the influence of the SFRC height on the maximum bearing capacity of the specimens, the improvement in the maximum bearing capacity of the specimens with different heights of SFRC compared to the RC pier was determined, as listed in

Table 8. The increase ratio of the maximum bearing capacity compared to the RC specimen.

Torsion–Bending Ratio	Increase Ratio of Bearing Capacity/%
	RC	SFRC300	SFRC600	SFRC900	SFRC1200
0	—	9.54	16.37	17.66	18.95
0.09	—	8.96	13.62	16.09	18.68
0.17	—	12.81	19.60	21.41	22.58
0.27	—	5.63	36.99	37.19	39.70
0.36	—	11.84	25.11	38.56	40.10

.

It can be observed that, when the torsion–bending ratio is the same, the maximum bearing capacity increases with the increase in the height of the SFRC in the plastic hinge region. In the early stage of loading, there is no significant attenuation in the stiffness of the piers. The maximum bearing capacities of the piers with SFRC are all larger than those of RC piers. After the peak load, the skeleton curves of RC piers decrease more steeply, and the larger the torsion–bending ratio, the more obvious the decrease in the bearing capacity. Due to the addition of steel fibers, the bearing capacities of the piers with SFRC decrease relatively slowly.

When the torsion–bending ratio does not exceed 0.17, the addition of SFRC improves the maximum bearing capacity of the pier to a certain extent, and the maximum increase ratio is about 23%. When the torsion–bending ratio exceeds 0.17, the maximum bearing capacity of the SFRC pier is significantly improved.

Considering the presence of torque, the bending–torsion coupling has a great influence on the bearing capacity of the pier. The larger the torsion–bending ratio, the more obviously the maximum bearing capacity of the SFRC pier is improved. The addition of SFRC material at the bottom of the pier increases its tensile strength and toughness, delays crack development, and significantly improves the maximum bearing capacity of the bridge pier. Under the common bending–torsion coupling effect (the torsion–bending ratio is less than 0.3), when the height of SFRC is 600 mm (half of the clear height of the pier), the pier already has a high bearing capacity, and the material can be fully utilized. If the height of SFRC continues to increase, the impact on the maximum bearing capacity is not significant. Under the action of a higher torsion–bending ratio, there will be a certain benefit when further increasing the height of the SFRC.

5. Discussion

There are many parameters that affect the seismic performance of SFRC piers, such as the size of the specimen, the material properties, the reinforcement, the action mode of external loads, and so on.

Considering the structural construction, this paper focuses on the parameters of the torsion–bending ratio and SFRC height, while the other parameters of the analysis models remained unchanged. Therefore, the optimal SFRC height proposed above is only applicable to piers similar to the analysis models considered in this paper, but the research results can provide a reference for the design of other forms of piers.

In terms of the external load, the maximum torsion–bending ratio of the analysis models considered in this work is 0.36, and the research results can be applied to the design of most bridge piers. In special engineering, when the bridge structure is very irregular, the torsion–bending ratio of the external load on the pier may exceed 0.36. Under a higher torsion–bending ratio, the seismic performance and optimal SFRC height of piers need to be further studied.

6. Conclusions

In this study, three piers with an SFRC height of 300 mm at the bottom were designed, and quasi-static tests under different torsion–bending ratios were carried out. On this basis, a parameter analysis was conducted using the ABAQUS software to study the influence of the torsion–bending ratio and SFRC height on the seismic performance of piers. The conclusions are as follows.

• The bending–torsion coupling effect leads to a decrease in the bending and torsion capacities of the pier, and the greater the torsion effect, the more rapidly the bearing capacity of the pier decreases. The presence of torque causes the plastic hinge position to move up and the plastic hinge area to expand.
• Adding SFRC at the bottom of the pier can reduce the attenuation rate of the bearing capacity, delay stiffness degradation, control the cracking of concrete, and effectively improve the bearing capacity of the pier under earthquake action.
• For the pier model considered in this paper, the optimal height of SFRC is half of the clear height of the pier under the common torsion–bending ratio. This type of pier can not only improve the seismic performance of the structure but also avoid material waste.

The research results in this paper can provide a reference for the design of bridge piers. The seismic performance of SFRC piers under higher torsion–bending ratios, as well as the design capacity and bearing capacity of SFRC piers, need to be further studied.