Experimental and numerical investigations of the seismic performance of columns with fiber-reinforced concrete in theplastic hinge region

Abstract

Fiber-reinforced concrete materials have high tensile toughness and exhibit multiple micro-cracking behavior and strain-hardening property in direct tension loads. To improve the seismic performance and damage tolerance of reinforced concrete columns, nine columns using fiber-reinforced concrete in the lower 300-mm end region and one conventional reinforced concrete column were designed and tested under lateral cyclic loading. The test parameters included the axial load ratio and the shear span ratio. The cracking and failure modes, hysteretic behavior, deformation capacity, energy dissipation capacity, and stiffness degradation of all specimens were analyzed in detail. In addition, a finite element model was established, and a parametric analysis was conducted. The test results showed that the fiber-reinforced concrete columns with a shear span ratio of 2.0 experienced bending failure, and that the strength and stiffness degraded at a lower rate compared to the normal concrete counterpart. The axial load ratio and shear span ratio had a significant effect on the deformation capacity and energy dissipation capacity of the columns. Fiber-reinforced concrete columns with just shear-resisting stirrups can satisfy the deformation and energy dissipation requirements.

Keywords

column fiber-reinforced concrete finite element simulation quasi-static test seismic performance shear span ratio

Introduction

Post-earthquake reconnaissance and experimental research have indicated that sufficient load-carrying capacity and ductility of frame columns are critical to ensure that structures do not collapse during a major earthquake. To improve the seismic performance of reinforced concrete (RC) columns, a number of experimental studies and theoretical analyses have been conducted and several effective measures have been proposed, such as the use of high-strength stirrups and high-strength concrete (ACI-ASCE Committee, 1997), closely spaced stirrups, and different stirrup forms (Essawy and El-Hawary, 1998; Hwang and Yun, 2004; Li and Park, 2004). However, high-strength concrete cannot change the inherent brittleness of ordinary concrete. Therefore, it cannot improve the ductility of columns. Furthermore, closely spaced stirrups are difficult to construct, and the construction quality is often poor.

A significant number of recent earthquakes have caused serious damage to structures. To ensure post-earthquake serviceability, attention has been drawn to the development and implementation of innovative materials in new and existing structures to improve their performance under seismic loads. Fiber-reinforced concrete (FRC) is a high-toughness concrete. Numerous studies (Fischer and Li, 2003; Li, 2003; Li et al., 2001; Lin et al., 1999) have indicated that FRC materials have high tensile toughness and exhibit multiple micro-cracking behaviors and strain-hardening properties in direct tension loads. FRC materials also have good crack-width control ability with increasing deformation that can be used by shear-critical members, such as beam–column joints (Parra-Montesinos et al., 2005; Qudah and Maalej, 2014), squat walls, and coupling beams (Canbolat et al., 2005), and flexural members subjected to high shear stress reversals, even when little or no transverse steel reinforcement is used. FRC materials increase the shear strength, deformation, energy dissipation capacity, and damage tolerance of the flexural and shear members.

To improve the seismic performance of RC columns, Fischer and Li (2002) were the first to investigate the effect of the ductile deformation behavior of engineered cementitious composite (ECC) on the response of steel-reinforced columns under reversed cyclic loading conditions. Their results indicated that the ductile behavior of ECC allowed for the high deformation of steel reinforcement, which significantly enhanced the dissipated energy and resulted in the full utilization of the plastic deformation capacity of the steel reinforcement. Billington and Yoon (2004) showed that using ductile fiber-reinforced cement-based composites (DFRCCs) allowed bridge pier systems to dissipate more hysteretic energy than traditional concrete up to drift levels of 3%–6%. Furthermore, DFRCC maintained its integrity better than RC did under high cyclic tensile compressive loads. Saiidi et al. (2009) showed that the application of ECC and superelastic shape-memory alloy within the plastic hinge region of a column resulted in a much higher drift capacity and much less residual displacement compared to conventional RC columns. Cho et al. (2012) applied high-performance fiber-reinforced cementitious composites (HPFRCs) instead of concrete locally in the plastic hinge region of a column to improve the seismic performance of RC columns. The results showed that this HPFRC column not only improved cyclic lateral load and deformation capacities but also minimized the bending and shear cracks in the flexural critical region of the RC columns. Aviram et al. (2014) studied the seismic performance of HPFRC bridge columns under bidirectional cyclic loading. The results demonstrated the considerable benefits of using tensile strain-hardening FRC in typical highway overpass bridge columns.

Based on the above studies, FRC materials were used in the potential damage region of RC columns, and ordinary concrete was used in the remaining regions to improve the seismic performance of RC columns in this study. Nine columns using FRC in the lower 300-mm end region and one conventional RC column were designed and tested under lateral cyclic loading. The influence of the shear span ratio and the axial load ratio on the hysteretic behavior, the deformation capacity, energy dissipation capacity, and stiffness degradation of the columns was investigated and evaluated.

Experimental programs

Test specimens

A total of 10 1/2-scaled columns with the same cross section of 250 mm × 250 mm were designed and fabricated based on the orthogonal experiment design method. The design parameters primarily included the axial load ratio and the shear span ratio. The cross section for all of the specimens had main longitudinal reinforcements as four units of D16 bars. The dimensions and reinforcement details of specimens are shown in Figure 1, where the shaded regions represent the FRC materials and h represents the height of the column-loading point to the column base. The height of the FRC materials in the column bottom region was 300 mm, and they were embedded 100 mm into the bottom beam. During the preparation of the specimens, the FRC columns were separated into different casting parts using a plywood formwork. The FRC parts in the plastic hinge region were cast first, and the FRC materials were vibrated mechanically to avoid honeycombs and holes. The plywood formwork was removed within a day of casting, and the surface of the FRC material was chiseled roughly, so that it could bond well with the ordinary concrete. Then, the ordinary concrete in the bottom beam and the rest of the column was cast. Specimen RC10 was cast in whole. Specimen details are shown in Table 1.

Figure 1.

Dimensions and reinforcement details of the specimens (units: mm).

Table 1.

Parameters of the specimens.

Specimen	Loading point height (mm)	Shear span ratio	Strength of matrix material (MPa)	Test axial load ratio	Axial load (kN)
FRC1	625	2.5	62.00	0.091	270.0
FRC2	750	3.0	62.00	0.122	362.8
FRC3	500	2.0	62.00	0.152	450.0
FRC4	750	3.0	63.26	0.088	263.0
FRC5	500	2.0	63.26	0.157	470.0
FRC6	625	2.5	63.26	0.197	590.0
FRC7	500	2.0	65.80	0.131	410.0
FRC8	625	2.5	65.80	0.178	555.0
FRC9	750	3.0	65.80	0.208	650.0
RC10	625	2.5	48.32	0.235	540.0

FRC: fiber-reinforced concrete; RC: reinforced concrete.

Material properties

FRC materials were mixed with gelatinizing materials (cement and fly ash), sand, fibers, water, and water-reducing agents. The maximum diameter of the sand was 1.18 mm. Ordinary Portland cement with a grade of 42.5R was used. The grade of the fly ash was level I. A naphthalene-type water-reducing agent was added during the mixing process to maintain an acceptable workability. Polyvinyl alcohol (PVA) fibers in 2.0% volume fractions were used as the cement-based reinforced material. The basic parameters of the PVA fibers are shown in Table 2. The compressive strength of the FRC and concrete was determined by averaging the results of three 100 mm × 100 mm × 100 mm and 150 mm × 150 mm × 150 mm cubes that were fabricated using the same concrete mix and cured under the same conditions as the companion specimens. The measured cube compressive strengths are given in Table 1. A typical tensile stress versus strain response for the FRC materials with PVA fibers obtained from a dumbbell-shaped specimen is shown in Figure 2. The longitudinal reinforcement of the columns was 16-mm diameter hot rolled ribbed bars, the transverse reinforcement of the columns was 6-mm diameter hot rolled plain bars, and the mechanical properties are shown in Table 3.

Table 2.

Performance indicators of the PVA fibers.

Fiber name	Length (mm)	Diameter (µm)	Tensile strength (MPa)	Young’s modulus (GPa)	Elongation ratio (%)
PVA	12	39	1600	40	7

PVA: polyvinyl alcohol.

Figure 2.

Typical tensile stress versus strain response of the FRC material.

Table 3.

Mechanical properties of the steel reinforcement.

Steel grade	Diameter (mm)	Yield strength (MPa)	Ultimate strength (MPa)	Elastic modulus (×10⁵ N/mm²)
HRB400	16	440	609	1.93
HPB235	6	273	427	2.14

Instrumentation and test procedures

The horizontal displacement of the loading point was measured using a linear variable differential transducer (LVDT) with a capacity of 100 mm in the positive and negative direction. Two LVDTs with a range of 25 mm were mounted in the lower end of the column to measure the tensile and compressive deformation. Two LVDTs with a range of 25 mm were also arranged crosswise in the plastic hinge region to measure the oblique deformation of the column, as shown in Figure 3. Electrical resistance strain gauges were installed on the longitudinal reinforcements and stirrups, as shown in Figure 1. Test data were automatically collected by the static and dynamic strain measurement systems.

Figure 3.

Schematic arrangement of test setup.

The axial load was applied using a 1000-kN vertical hydraulic jack. Horizontal cyclic loads were applied using a 300-kN horizontal actuator. The test setup is shown in Figure 3. The axial load was applied first and kept constant during the test. Then, the horizontal cyclic loads were applied. The lateral loading procedure included load-controlled and displacement-controlled, which is illustrated in Figure 4.

Figure 4.

Cyclic loading program.

Test results and analysis

Test observations and analysis of the failure modes and mechanisms

The failure modes of the nine FRC columns and the RC column are shown in Figure 5. When the lateral load was small, none of the specimens had cracks, and the lateral deformation was small. As the load increased, minor horizontal cracks with a length of 2–6 cm first appeared at the bottom of the columns, and the cracking load was about 60–120 kN. Subsequently, a small number of horizontal cracks and diagonal cracks appeared in the plastic hinge region. The crack-closure phenomenon was observed, and the residual deformation was small when the column was unloaded. The yield load was approximately 100–200 kN, and the mean drift ratio (the ratio of the top horizontal displacement to the height of the loading point, θ = Δ/h) of the nine FRC columns was 1.37%. The drift ratio of the RC column (specimen RC10) was 1.22%.

Figure 5.

Failure modes of the specimens: (a) FRC1, (b) FRC2, (c) FRC3, (d) FRC4, (e) FRC5, (f) FRC6, (g) FRC7, (h) FRC8,(i) FRC9, and (j) RC10.

As the load continued to increase, the cracks at the bottom of the column widened and extended, the crack width reached 1–2 mm, and the crack length was 5–10 cm. Simultaneously, new horizontal and diagonal cracks appeared in the plastic hinge region. With the gradual increase in the horizontal displacement, the horizontal loads increased slightly. The drift ratios of the nine FRC columns at the peak loads (140–230 kN) ranged from 1.95% to 3.0%, and the mean value was 2.38%, whereas that of the ordinary RC column (specimen RC10) was 1.92%. Compared to specimen RC10, the drift ratio of specimen FRC6 increased by 33.33%. The horizontal cracks at the bottom of the columns widened and extended and then became the main cracks and the crack widths reached 2–3 mm. The diagonal crack width of specimen RC10 reached 2 mm, and the length was 18 cm at the peak load. Vertical cracks appeared in the end region of the column. However, the cracks in specimen FRC6 were minor, and its diagonal cracks were short and not obvious.

When the horizontal displacement reached 2Δ_y, the horizontal cracks in the FRC specimens at the column end widened to 3–5 mm. A plurality of horizontal cracks developed, and several vertical cracks appeared in the range of 8 cm from the bottom of the column. The horizontal cracks at the bottom of the column and the diagonal cracks in the plastic hinge region of the RC column continued to expand, the concrete in the four corners of the lower region of the column was in compression, and a small portion of the concrete spalled. When the displacement of specimens FRC1–FRC9 reached (3–7)Δ_y, vertical cracks appeared along the longitudinal reinforcement position, there were multiple small cracks in the lower region of the column, the main crack widened, and its length extended into the entire column section. The FRC materials in the lower region of the column were bulged under compression, showing obvious bending failure characteristics. The horizontal crack width of the FRC specimens at the bottom of the columns reached 6–15 mm at failure loads. When the top horizontal displacement of specimen RC10 reached 3Δ_y, the horizontal and diagonal cracks in the range of 20 cm from the bottom of the column widened to 2.5 mm, and the vertical cracks widened to 1.5 mm. The corner concrete spalled significantly, the reinforcements were exposed, and the specimen suddenly failed after reaching the peak load. The drift ratios of the nine FRC columns at the failure loads were from 7.07% to 8.60%, and that of the RC column were 3.62%.

As shown in Figure 5, the appearance and the number of the diagonal cracks are different for the different shear span ratios (from 2.0 to 3.0), indicating that the shear span ratio has a significant effect on the failure modes of the FRC columns. FRC materials were used in specimens FRC1–FRC9; because of the bridging effect of fibers in the crack interface, there were some cracks in the region of the use of FRC materials; however, the FRC did not fall off, but instead relied on the fibers to remain together. Therefore, the FRC columns have good deformability and delay the occurrence of damage. The cracks in the regions using FRC at the failure loads are small, except for the main crack, avoiding suddenly brittle failure and ultimately producing a certain type of bending ductility characteristic. The shear span ratio of specimen FRC7 was 2.0, and obvious diagonal and horizontal cracks appeared in the plastic hinge region under horizontal loads. The axial load of specimen FRC7 was relatively small in the three specimens with a shear span ratio of 2.0 (specimens FRC3, FRC5, and FRC7), which could not restrain the development and expansion of cracks. Moreover, the strain gauge was installed on the longitudinal reinforcement at the column end, and the strain gauge was coated by gauze and epoxy adhesive, which decreased the bond strength of the FRC materials and the reinforcements; therefore, the cover FRC spalled, the entire specimen exhibited a greater damage deformation at the failure load.

Hysteretic curves and skeleton curves

The measured horizontal load–displacement hysteresis curves of the 10 specimens are shown in Figure 6, where the upper and lower horizontal coordinates represent the drift ratio θ and horizontal displacement Δ at the top of the column, respectively. The ordinate represents the horizontal load F. The different markers represent the positions of the cracking load point, yield load point, peak load point, ultimate load point, and failure load point, respectively.

Figure 6.

Horizontal load–displacement hysteresis curves of the specimens.

The values of the load and displacement of each specimen at the characteristic points are listed in Table 4. The yield displacement Δ_y is determined when the strain of the longitudinal reinforcement reaches the yield strain. The ultimate load is defined as the peak load descends to approximately 85%, and the relative displacement is the ultimate displacement Δ_u. Comparisons of the skeleton curves are shown in Figure 7, where λ represents the shear span ratio.

Table 4.

Load and displacement of each specimen at the characteristic points.

Specimen	Cracking		Yield		Peak		Ultimate
Specimen	Δ_cr (mm)	P_cr (kN)	Δ_y (mm)	P_y (kN)	Δ_p (mm)	P_p (kN)	Δ_u (mm)	P_u (kN)
FRC1	1.76	40.69	8.30	119.54	15.81	137.42	29.42	117.18
FRC2	3.10	59.62	11.00	119.75	17.50	129.59	38.94	111.62
FRC3	3.34	120.90	7.01	198.93	12.30	221.65	25.91	188.86
FRC4	3.26	60.27	8.36	99.88	22.50	118.75	45.51	102.28
FRC5	2.25	81.50	7.05	198.78	9.76	225.38	27.00	190.01
FRC6	2.74	79.95	8.95	159.64	16.01	174.50	32.50	148.87
FRC7	2.90	99.68	8.95	200.04	11.51	203.05	25.49	176.62
FRC8	1.85	61.20	7.49	159.59	13.76	186.66	31.00	153.77
FRC9	3.16	79.56	9.05	138.76	15.50	151.69	36.57	126.94
RC10	1.49	60.04	7.60	159.69	11.98	177.00	20.80	150.33

FRC: fiber-reinforced concrete; RC: reinforced concrete.

Figure 7.

Comparison of skeleton curves: (a) Effect of the shear span ratio and the axial load ratio (f_cu = 62 MPa); (b) Effect of the shear span ratio and the axial load ratio (f_cu = 65.80 MPa); (c) Effect of the material; (d) Effect of the shear span ratio; (e) Effect of the small axial load ratio; (f) Effect of the axial load ratio (λ = 2.0); (g) Effect of the axial load ratio (λ = 2.5); and (h) Effect of the axial load ratio (λ = 3.0).

The following observations can be made based on Figures 6 and 7:

Before reaching the yield loads, the hysteresis curves are basically linear. Before reaching the peak loads, the shapes of the hysteresis curves of each specimen are similar and do not suffer significant stiffness degradation. As the loads exceed the peak values, with the increase in the loads, the hysteresis loop of specimen RC10 is relatively narrow, and there is a clear degradation in the load-carrying capacity and stiffness, indicating that its plastic deformation and energy capacity are poor. The hysteresis loops of specimens FRC1–FRC9 are all relatively full, and the degradations of the load-carrying capacity and stiffness are relatively slow. Figure 7(c) compares the skeleton curves of specimens FRC6 and RC10. It is obvious that the FRC columns have better deformation and energy dissipation capacities than the ordinary concrete column does.

Figure 7(a) and (b) compares the skeleton curves when the strength level of the FRC remains constant. It can be seen that FRC columns with smaller shear span ratios and relatively larger axial load ratios have a larger load-carrying capacity and smaller ultimate displacement. This is primarily due to the larger axial load. The extension and expansion of cracks have been restrained, and the load-carrying capacity of the columns has increased, however, this results in a decrease in the displacement ductility. Therefore, the axial load ratio of the columns should be limited in designs to ensure that the columns have good ductility. When the axial load ratios and the measured strengths of the FRC are similar (Figure 7(d)), smaller shear span ratios have higher load-carrying capacity and smaller ultimate displacement.

When the shear span ratios are the same and there is little difference in the FRC strength (Figure 7(f) to (h)), the load-carrying capacity increases and the deformation capacity decreases with increasing axial load ratio. For different shear span ratios, when the axial load ratio is small (0.091–0.122), although the shear span ratios are different, the skeleton curves coincide with each other (Figure 7(e)), showing that the shear span ratio has little influence on columns with small axial load ratios. This is primarily because the restriction of the column is weakened when the axial load ratio is relatively small.

Energy performance

The energy dissipation capacity of a structure or structural component reflects its seismic energy absorption ability. The cumulative energy consumption and energy consumption ratio are used to describe the energy performance in this study. On the load–displacement hysteresis curves, the area surrounded by loading curves reflects the energy absorption ability of the structure under cyclic loading, and the area surrounded by unloading curves reflects the energy release ability of the structure. The shortfall is the energy dissipation E_i, which is the area surrounded by the hysteresis curves. The cumulative energy consumption is E = ∑E_i, where i represents the cycle number of loading and unloading. The energy consumption ratio is β_E = E/(V_yΔ_y). The cumulative energy consumption of each characteristic point and the energy consumption ratios of the 10 columns under cyclic loading are presented in Table 5.

Table 5.

Cumulative energy consumption and energy consumption ratio of the columns.

Specimen	Cumulative energy consumption (kN m)				β_E
Specimen	Yield load	Peak load	Ultimate load	Failure load	β_E
FRC1	0.34	5.68	33.16	127.37	220.67
FRC2	0.24	5.49	34.77	90.2	68.47
FRC3	0.37	7.33	45.25	146.18	104.83
FRC4	0.34	11.18	82.02	111.38	133.39
FRC5	0.42	2.05	44.72	168.23	120.04
FRC6	0.69	8.72	56.23	141.63	99.13
FRC7	0.92	3.52	40.12	106.94	59.73
FRC8	0.43	7.13	52.8	142.5	119.22
FRC9	0.66	7.45	62.9	175.21	139.52
RC10	0.57	3.22	20.02	24.27	19.99

FRC: fiber-reinforced concrete; RC: reinforced concrete.

The cumulative energy consumption and energy consumption ratio of specimen FRC6 are 5.84 and 4.96 times than that of specimen RC10, respectively. Overall, the energy dissipation capacity of the FRC column is much larger than that of the RC column. When the strength of FRC is the same (specimens FRC7, FRC8, and FRC9), there is an increasing trend in the cumulative energy consumption and energy consumption ratio with the increase of the axial load ratio and the shear span ratio. For specimen FRC7, the shear span ratio is 2.0 and the axial load is relatively small, the specimen cannot restrain the development and expansion of the cracks. The loads of specimen FRC7 decline quickly when the load exceeds the peak load, and the number of loading cycles is less when reaching the failure load, therefore, the cumulative energy consumption is smaller. Compared to specimens FRC3 and FRC5, the yield displacement of specimen FRC7 has increased by 27.67% and 26.95%, respectively, because of the small difference in the yield load. Therefore, the energy consumption ratio of specimen FRC7 is significantly lower than those of the other FRC specimens according to the definition of the energy consumption ratio.

Deformation performance

In the seismic design of structures, ductility is an important indicator for the plastic deformation of structures or members. It is also an indicator that measures the seismic performance of structures. The displacement ductility factor is defined as µ = Δ_u/Δ_y. The ultimate drift ratio is θ_u = Δ_u/h. Table 6 lists the displacement ductility factor and the ultimate drift ratio for each specimen.

Table 6.

Displacement ductility factor and ultimate drift ratio of the specimens.

Specimen	FRC1	FRC2	FRC3	FRC4	FRC5	FRC6	FRC7	FRC8	FRC9	RC10
µ	3.54	3.54	3.70	5.44	3.83	3.63	2.85	4.14	4.04	2.74
θ_u	4.71%	5.19%	5.18%	6.07%	5.40%	5.20%	5.10%	4.96%	4.88%	3.33%

FRC: fiber-reinforced concrete; RC: reinforced concrete.

The following conclusions can be obtained from Table 6 and Figure 6:

The average value of the displacement ductility factor and the ultimate drift ratio of specimens FRC1–FRC9 are 3.86% and 5.19%, respectively. Compared to specimen RC10, the displacement ductility factor and the ultimate drift ratio of specimen FRC6 improved by 32.48% and 56.16%, respectively, indicating that the displacement ductility factor and the ultimate drift ratio of columns can be greatly improved using FRC materials in the plastic hinge region, and the FRC columns have good plastic deformation capacity.

Compared to the RC column, the average yield displacement, peak displacement, and ultimate displacement of the FRC columns increased by 11.4%, 24.9%, and 56.2%, respectively. When these specimens were fabricated, the FRC materials in the lower end of the column were stretched into the bottom beam. Therefore, FRC materials play a role in improving the yield displacement. After the yield of the reinforcements, the deformation of the specimens occurred primarily in the FRC regions of the column end, and the peak displacement and ultimate displacement were improved significantly.

When the shear span ratio is 2.0 (specimens FRC3, FRC5, and FRC7), the relationship of the axial load ratio is n₅ > n₃ > n₇ (where n₃, n₅, and n₇ are the test axial load ratios of specimens FRC3, FRC5, and FRC7, respectively, the same below), and the relationship of the ultimate drift ratio is θ_u₅ > θ_u₃ > θ_u₇ (where θ_u₃, θ_u₅, and θ_u₇ are the ultimate drift ratio of specimens FRC3, FRC5, and FRC7, respectively, the same below). The axial load ratio of specimen FRC7 was relatively small, which weakened the restraint on the column, and the yield displacement increased. There was little difference in the ultimate displacement of specimens FRC3, FRC5, and FRC7; therefore, the displacement ductility factor of specimen FRC7 was significantly lower. When the shear span ratio is 2.5 (specimens FRC1, FRC6, and FRC8), the relationship of the axial load ratio is n₆ > n₈ > n₁, and the relationship of the ultimate drift ratio is θ_u₆ > θ_u₈ > θ_u₁. When the shear span ratio is 3.0 (specimens FRC2, FRC4, and FRC9), the relationship of the axial load ratio is n₉ > n₂ > n₄, and the relationship of the ultimate drift ratio is θ_u₄ > θ_u₂ > θ_u₉. It can be seen that the ultimate drift ratio is related to the shear span ratio and the axial load ratio, further analysis is given in the following sections.

Stiffness degradation

The stiffness of a structure or a component decreases with the increase in cycle number and the displacement in the low cyclic loading test, which is a major cause of reduced seismic performance of structures and components. Figure 8 shows the degradation curves of the secant stiffness of the columns versus the lateral displacement at the top of the columns under reversed cyclic lateral loading.

Figure 8.

Curves of stiffness degradation: (a) Effect of the shear span ratio and the axial load ratio (f_cu = 62 MPa); (b) Effect of the shear span ratio and the axial load ratio (f_cu = 65.80 MPa); (c) Effect of the material; (d) Effect of the axial load ratio (λ=2.0); (e) Effect of the axial load ratio (λ=2.5); and (f) Effect of the axial load ratio (λ=3.0).

When the strength of the FRC is the same (Figure 8(a)), the relationship of the axial load ratio is n₃ > n₂ > n₁, and the relationship of the shear span ratio is λ₂ > λ₁ > λ₃ (where λ₁, λ₂, and λ₃ are the shear span ratios of specimens FRC1, FRC2, and FRC3, respectively). The stiffness degradation of specimen FRC3 is rapid, and specimens FRC2 and FRC1 have the same downward trend before the displacement reaches 40 mm. This is primarily because the column is prone to shear failure, and the stiffness degradation is faster when the shear span ratio is relatively small. When the horizontal load exceeds the peak load, the larger axial load quickens the failure of the column; thus, the ductility decreases, and the stiffness degradation is faster. From the curve of stiffness degradation shown in Figure 8(b), it is evident that the trend in the stiffness degradation curves of the three specimens is almost the same when the axial load ratio and the shear span ratio are gradually increased, indicating that the axial load ratio and the shear span ratio influence the stiffness degradation to some extent.

Figure 8(c) illustrates the influence of using FRC in the plastic hinge region on the stiffness degradation of the columns. It is obvious that the stiffness degradation of specimen RC10 is faster and the ultimate displacement is smaller, whereas that of specimen FRC6 is slow and its displacement ductility is much larger than that of the ordinary concrete column.

Figure 8(d) to (f) shows the influence of the axial load ratio on the stiffness degradation of the columns. In summary, the stiffness of the columns decreases as the displacement increases, the stiffness degradation is faster when the displacement is relatively small, and the stiffness degradation rate is relatively smooth when the displacement is relatively larger. When the other conditions remain constant, the stiffness degradation of the columns is obvious with the increase in the axial load ratio, and the stiffness degradation rate is larger as the shear span ratio decreases.

Numerical simulations and parametric analysis

Numerical simulations

A numerical model of the columns was developed using the Open System for Earthquake Engineering Simulation (OpenSees) (Mazzoni et al., 2009) platform using the flexibility-based fiber section approach.

In the numerical model of the columns, the Concrete01 uniaxial material in OpenSees was used to simulate the ordinary concrete. The monotonic response was based on the work of Kent and Park (1971) and modified by Scott et al. (1982), and the tensile strength of concrete was ignored. For the unconfined concrete, the compressive strength f_c was determined by material tests, the elastic modulus E_c was determined according to the Chinese Code GB50010 (2010). The peak compressive strain $ε_{0}$ and ultimate compressive strain $ε_{u}$ were determined based on OpenSees recommendations. For the confined concrete, the compressive strength f_cc, the peak compressive strain $ε_{c 0}$ , and the ultimate compressive strain $ε_{c u}$ were calculated as follows

f_{c c} = (1 + \frac{ρ_{s} f_{y h}}{f_{c}}) f_{c}

(1)

ε_{c 0} = 2 (1 + \frac{ρ_{s} f_{y h}}{f_{c}}) \frac{f_{c}}{E_{c}}

(2)

ε_{c u} = ε_{u} + 0.9 ρ_{s} (\frac{f_{y h}}{300})

(3)

where $ρ_{s}$ and $f_{y h}$ are the volumetric ratio and the yield strength of the transverse reinforcement, respectively. The ultimate strength was set to 0.2 f_cc for the confined part and 0 for the concrete cover.

FRC materials exhibit strain-hardening behavior with multiple cracking under uniaxial tensile loading. Due to the high tensile strength of FRC, the peak strength is increased and the stiffness degradation rate is reduced under reversed cyclic loading. Therefore, Concrete02 material was used to simulate the FRC material, which was used to construct a uniaxial material object with tensile strength and linear tension softening. For the unconfined FRC, the compressive strength $f_{c}$ was obtained from tests, and $E_{c} = f_{c u}^{0.596} \times 10^{3} (MPa)$ was the elastic modulus, where $f_{c u}$ is the cube strength of FRC, which was proposed by Li (2011). The peak strain was $ε_{0} = 2 f_{c} / E_{c}$ , and the ultimate strain $ε_{u}$ was set to 0.03. For the confined FRC, the calculation of the relevant parameters of FRC $(f_{c c}, ε_{c 0}, and ε_{c u})$ was the same as that of the ordinary concrete, except the values for FRC were adopted.

FRC materials have high tensile strength. A uniaxial tensile stress versus strain relation was proposed by Kanda et al. (2000). For the sake of the simulations, the ultimate tensile strength $σ_{t u}$ was necessary and was calculated as $σ_{t u} = 3.683 f_{c u}^{0.174}$ , which was obtained from trial fitting by Li (2011). The tensile-softening stiffness was taken to be 0.125 times the elastic modulus of FRC.

The Giuffré–Menegotto–Pinto constitutive model (Menegotto and Pinto, 1973) which accounted the Bauschinger effect and isotropic strain hardening was used to simulate the steel in the columns and can simulate the behavior of the stiffness degradation well. Steel yield strengths were based on tensile tests of the reinforcement.

A nonlinear beam–column element with fiber section was used to simulate the columns. The fiber section was discretized into smaller regions for which the material stress–strain response was integrated to give the resultant behavior. Because the fiber section cannot account for the influence of shear, for the columns with small shear span ratios, the hysteretic material model was used to simulate the shear deformation relationship of the column section, and the shear deformation was combined into the fiber section using the section aggregator command in OpenSees.

Figure 9 compares the experimental and simulated hysteretic curves. The horizontal displacement of the simulated and experimental values at positive and negative loading is in basic agreement, and the maximum difference between the test results and predicted horizontal displacement is 6.1%, which is acceptable. However, there are larger errors in the peak loads, especially, the positive loads of specimens FRC3, FRC5, and FRC7. This is primarily because the positive and negative loads of the test are not the same, whereas those of the simulation are the same. A comparison of the experimental and simulated peak loads of the specimens indicates that the errors of the specimens are relatively small, and the average error is 12.3%. For this article, when the simulation using OpenSees was conducted, the program’s internal material model was used to simulate the FRC materials, and the material was defined by the input parameters of the corresponding feature points instead of the constitutive model of FRC material. Therefore, the initial stiffness of the simulation was larger than that of the test results. A fiber model was adopted for the simulation, which is based on the plane section assumption. The column members do not remain in the plane in the test, which increases the constraints and improves the stiffness of columns. Therefore, there are some differences between the simulated and experimental results. In general, the error of the peak load and the ultimate drift ratio of the specimens are small and acceptable, and the model and parameters of the materials can be used for the following parametric analysis.

Figure 9.

Comparison of the experimental and simulated hysteretic curves.

Parametric analysis

To further determine the influence of the shear span ratio, the axial load ratio, and the strength of FRC on the seismic performance of the FRC columns, the FRC columns were simulated using OpenSees, and the influence of the main test parameters on the seismic performance of the columns was analyzed.

Effect of the shear span ratio

Figure 10 shows the effects of the shear span ratio on the peak load and the ultimate drift ratio when the axial load ratio, the strength of the FRC, and the volumetric ratio of the transverse reinforcement are the same. It can be seen that the peak load decreases gradually by approximately 31.75%, 26.66%, 22.24%, and 18.68% when the shear span ratio is increased from 1.0 to 1.5, 1.5 to 2.0, 2.0 to 2.5, and 2.5 to 3.0, respectively. However, there is an increasing trend in the ultimate drift ratio, and the rate of increase becomes small with the increase in the shear span ratio. This is primarily due to the reduction in the shear deformation as the deformation capacity of the column increases.

Figure 10.

Effect of the shear span ratio.

Effect of the strength of the FRC

The effect of the strength of the FRC was simulated by varying the values from 40 to 80 MPa while keeping the other parameters constant. The results shown in Figure 11 confirm that the peak load increases and the ultimate drift ratio slightly decreases at a lower rate with an increase in the strength of the FRC.

Figure 11.

Effect of the strength of the FRC.

Effect of the axial load ratio

When the shear span ratio, the strength of the FRC, and the volumetric ratio of the transverse reinforcement are the same, the effect of the axial load ratio on the peak load and the ultimate drift ratio can be seen in Figure 12. With the increase in the axial load ratio, the peak load increases and the ultimate drift ratio decreases. It can therefore be concluded that the axial load ratio of the columns has a large impact on the peak load and the ultimate drift ratio.

Figure 12.

Effect of the axial load ratio.

Effect of the volumetric ratio of the transverse reinforcement

When the axial load ratio, shear span ratio, and strength of the FRC remain constant, the effect of the volumetric ratio of the transverse reinforcement on the peak load and the ultimate drift ratio is shown in Figure 13. It can be seen that, with the increase in the volumetric ratio of the transverse reinforcement, the peak load does not change significantly and that the ultimate drift ratio increases slightly, in the range of 2%. It is shown that the volumetric ratio of the transverse reinforcement has no significant effect on the specimens using FRC materials, and the number of stirrups can be appropriately reduced in FRC columns.

Figure 13.

Effect of the volumetric ratio of the transverse reinforcement.

Conclusion

Results from a research program that aimed at improving the seismic performance and damage tolerance of RC columns using strain-hardening FRC materials were reported. According to the results of the quasi-static test and numerical simulations of nine FRC columns and an ordinary concrete column, the failure modes and seismic performance of FRC columns were analyzed. The following conclusions can be made on the basis of the experimental and numerical results:

The 10 columns showed bending failure after the yield of the longitudinal steel, especially, the FRC columns with a shear span ratio of 2.0. The FRC columns still experienced bending failure with good ductility on the condition that the number of stirrups was designed only to meet the requirements of the shear. This demonstrates that there is no need to configure many multiple stirrups to achieve the ductile failure mode for a FRC column. It is recommended that ordinary concrete is replaced with FRC materials with respect to the unavoidable short columns and other shear-critical members in RC structures.

The RC column suddenly failed after reaching the peak load and the concrete spalled significantly at the lower end of the column. However, because of the role of fiber bridging in the crack interface, the cracks at the corners of the FRC columns were mostly small, and the FRC was damaged but did not fall off. The FRC columns have good resistance to damage and can reduce post-earthquake repair costs.

The displacement ductility factor and the cumulative energy consumption of the columns with FRC in the plastic hinge region have been improved, and the strength and stiffness degradations of the FRC column are relatively slow. This result indicates that using FRC can greatly improve the deformation capacity and energy dissipation capacity of the column.

Numerical analysis demonstrated that the shear span ratio and the axial load ratio have large effects on the load-carrying capacity and ultimate drift ratio. The effect of the strength of the FRC on the load-carrying capacity is obvious; however, its effect on the drift ratio is small. The effect of the volumetric ratio of the transverse reinforcement on the load-carrying capacity and the ultimate drift ratio is not significant; therefore, the number of stirrups can be reduced in FRC columns.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was funded by the National Natural Science Foundation of China (grant numbers 51078305 and 51278402), whose support is gratefully acknowledged.

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