Seismic Performance of the PVA Fiber Reinforced Concrete Prefabricated Hollow Circular Piers with Socket and Slot Connection

Abstract

The seismic performance of prefabricated hollow circular piers with socket and slot connection was evaluated through model tests and numerical simulations. The quasi-static tests with cyclic lateral load and constant axial load were conducted on three large pier specimens. The piers of these three specimens were cast by polyvinyl alcohol (PVA) fiber concrete, and the piers were connected to the cover beams by slotted connections and to the bearing platform by socketed connections. The seismic performance of the specimens was investigated in terms of failure modes, hysteresis curves, skeleton curves, stiffness degradation, energy dissipation, and residual deformation. The test results showed that, within a certain range, increasing the axial compression ratio is able to enhance the shear bearing capacity of prefabricated hollow piers and increase the cumulative energy dissipation, but it is not beneficial to the ductility. In addition, the increase in the shear span ratio significantly reduces the shear bearing capacity of piers and increases the residual deformation of the specimen, but the ductility is significantly improved. In addition, the numerical model of the prefabricated hollow pier was established by ABAQUS. The result of the numerical simulation was consistent and similar to the experimental result in terms of damage modes and load–displacement curves. Finally, the parametric analysis of the prefabricated hollow piers was carried out on the basis of the numerical model.

1. Introduction

In the recent past, with the rapid development of transportation construction, various urban viaducts, sea-crossings, and river-crossing bridges have been vigorously constructed, and prefabricated assembly technology is widely used in these fields. One of the most widely used prefabricated components is bridge piers. The prefabricated bridge pier technology is a rapid construction technology method [1,2,3]. Compared with the conventional integral poured-in-place pier components, the prefabricated pier technology has many advantages during construction, such as shortening construction time, reducing traffic disturbance, minimizing the effect on the surrounding environment, and controlling the bridge construction quality [4,5,6].

In addition, prefabricated piers also have obvious advantages compared to integral cast-in-place piers in terms of mechanical properties. Studies have shown that the damage of segmental piers is mainly due to the opening of the joints at the bottom of the pier, and the overall damage and residual displacement of the pier are smaller than those of traditional cast-in-place piers, and the recovery ability of prefabricated piers is also stronger after unloading [7,8]. The different forms of joints will affect the seismic performance of prefabricated piers. The connection form between the pier body of the prefabricated bridge pier and the cover beam and bearing platform is generally socket type and slot type. Han et al. [9,10] conducted model tests on bridge piers and concluded that the seismic performance indexes such as bearing capacity, ductility, and energy dissipation capacity of prefabricated piers were significantly enhanced as the depth of pier embedment increased (more than 1.5 times the column diameter). Mashal et al. [11] designed a socketed prefabricated bridge pier and conducted a quasi-static test, which showed that the hysteresis curves of socketed joint specimens were more pronounced than the pinching phenomenon of cast-in-place piers. Matsumoto [12], on the other hand, completed a reduced-scale test model experiment, and the test results showed that the ductility and deformation capacity of the bridge pier with slotted connections were higher.

Some new structural materials are also used in the grouting of prefabricated piers to achieve better seismic performance and prevent the structure from major damage during earthquakes. Motaref et al. [13] and Youm et al. [14] found that compared with ordinary reinforced concrete (RC) piers, the use of fiber reinforced polymer (FRP) material in prefabricated segmental columns reduces the damage and residual deformation of the plastic hinge zone. Willian et al. [15] used hybrid fiber reinforced concrete (HYFRC) to reinforce the lower part of the bridge pier. The test results showed that the reinforced bridge pier was only slightly damaged after many earthquakes. Mohebbi et al. [16] conducted shaking table tests on a new post-tensioned precast bridge column (integrally precast) using ultra-high-performance fiber-reinforced concrete (UHPFRC) in the plastic hinge zone. The experimental results indicated that UHPFRC not only helps to avoid reinforcements buckling and eliminates low circumferential fatigue failure, but also improves the seismic performance of prefabricated segmental bridge columns (PSBC) and reduces structural damage. Su et al. [17] investigated four PVA fiber-reinforced ultra-high-performance concrete solid rectangular cross-section short columns and showed that PVA fiber can improve the ultimate elastoplastic displacement angle of the concrete pier, and the energy dissipation capacity was also enhanced. Tarfan et al. [18] and Huang et al. [19] renovated three reinforced concrete buildings of different heights using pre-tensioned aramid fiber reinforced polymer AFRP materials and showed that prestressed AFRP reinforcement can improve the overall ductility of the structure.

It is hollow piers that can effectively reduce the seismic response of bridges, while providing higher efficiency and economic benefits compared to solid sections [20]. Therefore, it is of great engineering significance to study the seismic performance of prefabricated hollow piers. However, previous studies on the seismic performance of prefabricated piers have mainly focused on solid piers, and there is a relative lack of research on hollow piers. The effect of PVA fiber concrete on the seismic performance of prefabricated hollow circular piers also needs further study.

Three new structural types of piers were designed in this experiment. The pier body and the cover beam are connected by slot type, while the pier body and the cap are connected by socket type. The purpose of this study is to evaluate the seismic performance of the prefabricated PVA concrete hollow circular piers with this connection form under the influence of different axial compression ratios and shear span ratios. The quasi-static cyclic loading method was adopted to compare and analyze the failure mode, hysteretic curve, skeleton curve, stiffness degradation, energy dissipation, and residual displacement of the specimens, and to evaluate the seismic performance of each specimen. Then, the finite element model of a prefabricated hollow pier was established, and the applicability and accuracy of the model were verified by test results. On this basis, parametric analysis was carried out to further study the influence of the shear span ratio and axial compression ratio on the shear capacity of the prefabricated hollow pier.

2. Experimental Program

2.1. Test Specimens

The fabrication and loading of the test specimens were carried out at Yancheng Engineering Institute (Yancheng, Jiangsu, China). Three precast hollow pier specimens were cast with three different types of concrete, of which the pier part was made of PVA fiber concrete, and the pier cap and bearing cap were made of ordinary concrete, both of which had a design strength grade of C60, while the part at the junction of bearing and pier was made of grouted concrete with a design strength grade of C50. The specific mix of the two types of concrete is shown in

Table 1. The concrete mix of test specimens.

Concrete Type	Cement (kg/m3)	Water (kg/m3)	Admixtures (kg/m3)	Stone (kg/m3)	Sand (kg/m3)	PVA Fiber (%)
C50	385	150	120	1077	660	0
C60	410	151.2	130	1121.5	630.8	0
C60 PVA	410	151.2	130	1121.5	630.8	0.5

Notes: strength grade of C50 Admixtures = Slag powder (75 kg/m³); Expansion agent (40 kg/m³); Additives (5 kg/m³); strength grade of C60 Admixtures = Slag powder (102 kg/m³); Silicon powder (20.5 kg/m³); NF (7.5 kg/m³).

. The PVA fibers (Figure 1) used in this test are bundled monofilament with a diameter of 15 μm and a length of 10 mm, which were purchased from the Kuraray Company (Shanghai, China); the properties of PVA fiber are listed in

Table 2. Properties of PVA fiber.

Properties	Elastic Modulus (GPa)	Density (g/mm3)	Fiber Length (mm)	Fiber Diameter (mm)	Tensile Strength (MPa)
PVA fiber	61	1.26	10	0.015	510

.

The dimensions and reinforcement details of the three prefabricated hollow pier specimens are the same. First, the longitudinal reinforcement is of HRB400 grade. The internal and external longitudinal reinforcement consisted of 13 φ12 and 13 φ6, respectively, so the calculated longitudinal reinforcement rate was ρ = 0.093%. Then, the hoop reinforcement of the specimen is composed of φ6 low carbon steel wire. According to the spacing of the stirrups, the interior of the pier body is divided into an encrypted area and a non-encrypted area. While adjusting the height of the pier body for the S3 specimen, the height of the non-encrypted area in the inner stirrup was adjusted to 117 cm. The rest of the tie bars are of HPB300 grade. The yield strength and elastic modulus of steel bars at all levels are shown in

Table 3. Mechanical parameters of reinforcing steel (MPa).

Steel Type	Yield Strength fy	Ultimate Strength fst	Elastic Modules Es
HRB400	360	630	2.0 × 105
HPB300	270	510
Low carbon steel wire	400	650

.

The dimension of the cushion cap of the three specimens is all 150 × 150 × 70 cm, and the dimensions of the cover beams are all 70 × 70 × 40 cm. The geometric parameter changes in the pier body are shown in Figure 2. The layout of the internal reinforcement of the pier is shown in Figure 3. The parameters of the dimensions and reinforcement of each specimen are listed in

Table 4. Design parameters of circular prefabricated hollow pier test specimens.

Specimen Number	Outer Diameter D (cm)	Wall Thickness (cm)	Stirrup Reinforcement Ratio ρsv (%)	Effective Height H (cm)	Axial Compression Ratio n	Shear Span Ratio λ
S1	50	11	0.56	120	0.05	2.4
S2	50	11	0.56	120	0.10	2.4
S3	50	11	0.56	170	0.10	3.4

Notes: n is axial compression ratio; λ is shear span ratio, λ = H/D; H is the effective height of pier, H = H₁/2 + H₂.

. The cross-sectional dimensions and reinforcement are the same for all three specimens. There are two test variables of axial compression ratio and shear span ratio for the experiment, and it should be noted that specimen S2 is used as the reference specimen. Specimen S1 and specimen S2 were tested with the axial compression ratio as the test variable, and specimen S2 and specimen S3 were tested with the shear span ratio as the test variable. The respective effects of the axial compression ratio and the shear span ratio on the seismic performance of bridge piers were investigated by comparison between the two groups.

2.2. Construction Process

The assembly process of the specimen is illustrated by taking the typical member S2 as an example: I. According to the size of the scaled model and the relevant parameters of the reinforcement configuration, the three parts of the internal reinforcement cage of the cover beam, the pier body, and the cap were respectively bound (Figure 4a). II. Put the reinforcement cage of the cap and the pier body into the template for positioning, and use the PVA concrete prepared for on-site pouring. Then, insert the hollow section of the lower part of the pier body into the positioning block set inside the cap, and fill the remaining part of the cap with C50 grouted concrete. Then, put the cover beam reinforcement cage into the built formwork to complete the preliminary positioning, and pour the C60 normal concrete into the cap formwork. At the same time, pipelines were reserved on the top of the cover beam, and the galvanized corrugated sleeve prepared in advance is inserted into it (Figure 4b,c). III. Finally, use high-strength non-shrinkage grouting cement to pour into the galvanized corrugated steel pipe to complete the whole production of prefabricated high-strength piers (Figure 4d).

2.3. Specimen Loading Scheme

Before the test loading, the strain of concrete and steel bars and the displacement of the pier were monitored by pasting strain gauges and linear variable differential transducers (LVDTs). The loading equipment in this test mainly includes a vertical loading device and a horizontal loading device, as shown in Figure 5. During the test, the vertical force was applied by a 3000 kN hydraulic jack. The pressure value of the jack is controlled by the oil pump. The jack is connected to the reaction beam by a rotating hinge, and its purpose is to ensure that the jack is always in contact with the loading surface during the loading process. The horizontal force is applied by a 1000 kN electro-hydraulic servo horizontal actuator, which is fixed on the reaction wall to provide a cyclic horizontal force for the specimen. During the horizontal loading process, the axial pressure jack will move with the movement of the column top under the action of the roller, and the pressure of the axial pressure jack will fluctuate to a certain extent. Therefore, when the deviation is greater than 5% of the design value, the pressure of the vertical jack should be adjusted in time.

The loading sequence of the specimens is shown in Figure 6. In the early stage of cyclic loading, force loading control is used first. Take 10~30 kN as a load step and load three times in the east–west direction, respectively, until cracks appear on the surface of the specimen. After the pier body of the specimen is cracked, the average value of the cracking displacement in the two directions is calculated as the control value in the displacement loading stage. Each displacement loading stage consists of three cycles, each of which applies positive and negative loads in turn. When each section is loaded to the maximum displacement, the load is held for 2 min, so that the cracks on the specimen are fully developed, and the specimen is observed. When the bearing capacity of the specimen drops to 85% of the maximum bearing capacity, the loading ends.

3. Test Results and Analysis

3.1. Failure Patterns

The behavior of three specimens, including crack development and concrete spalling, was recorded in each cyclic loading displacement. To facilitate the detection and recording of concrete cracks, we drew 10 cm × 10 cm grid lines on the pier of each specimen before the test.

The failure process of the three specimens in the cyclic loading process can be divided into three stages, namely, the development stage of horizontal crack, oblique crack development stage, and failure stage. First of all, when the lateral loading displacement is small, no cracks appear in the specimens, and the bridge pier is still in the elastic stage. With the rise of lateral displacement, the pier body in the horizontal displacement loading direction (E, W direction) began to show the first horizontal crack. In addition, with the increase in loading displacement, the number of horizontal cracks increases along the height direction and grows along the circumference direction of the pier. Compared with specimen S2, specimen S1 has a lower axial compression ratio, so the first horizontal crack of specimen S1 appears earlier with a height of about 20 cm, as shown in Figure 7. The pier height of specimen S3 is taller than specimen S2, so the first horizontal crack can appear only at a greater displacement level, and the height of the tallest horizontal crack reaches 80 cm.

When the lateral displacement is further increased, the horizontal cracks on the E and W sides develop on the N and S sides along the circumferential direction. In addition, horizontal cracks begin to show a slanting downward development trend and then turn into slanting fractures. At this moment, the development of fractures enters the slanting fracture stage, as shown in Figure 8. Subsequently, oblique cracks on both sides intersect at side N and side S, respectively. Compared with specimen S2, specimen S3 has more dense horizontal cracks, and the included angle between oblique cracks and the horizontal direction is smaller. Furthermore, while the oblique crack develops, the higher position along the pier body continues to appear with new horizontal cracks.

As the lateral loading displacement continues to increase and the lateral load exceeds the peak load, cracks stop extending along the length direction and their number does not increase. At the same time, the crack width continues to increase, and at this time the piers enter the failure stage, as shown in Figure 9. It is worth noting that the horizontal crack width at the bottom of the pier increases obviously, and in each specimen finally appears a large width of the main crack. For the final failure patterns, specimen S1 with a low axial compression ratio showed good ductility, only peeling phenomenon occurred on both sides of loading, and no obvious concrete spalling. Part of concrete spalling occurred in specimen S2 and specimen S3 specimens, and the failure of specimen S3 was accompanied by the cracking sound of concrete. This is due to the internal reinforcement buckling under compression, and the reinforcement and concrete extrusion staggered, resulting in the sound of broken concrete. In addition, in tests of super-strength fiber-reinforced concrete columns using PVA fiber concrete, Nozawa et al. [21] found significant peeling and spalling in normal concrete columns under cyclic loading. However, in the failure pattern of the PVA concrete column, a slight spalling of the concrete at the bottom of the column only occurred near failure, which is consistent with the concrete failure phenomenon of the specimens in this study. This is due to the fibers limiting the spalling of the concrete cover.

3.2. Hysteresis Curve

The pier top displacement and corresponding load were recorded under cyclic loading, and the horizontal load–displacement hysteresis curves of specimens S1~S3 were drawn accordingly, as shown in Figure 10.

Using specimen S2 as an example, the hysteresis curve was evaluated. When the lateral horizontal load is small, the hysteresis loop is narrow and overlaps, and the relationship between load and lateral displacement is approximately linear. During reloading and unloading, the curve almost overlaps the intersection of the horizontal axis, which means that the structure mostly recovers after each unloading. Subsequently, when the displacement amplitude of the lateral loading increases, cracks begin to appear near the bottom of the bridge pier body. Then, the crack gradually extends to the central position of the pier body, and the crack is further widened. The concrete cracks at the joint of the pier body are serious and the reinforcement yields. In addition, the stiffness of the specimen decreases gradually during loading and unloading, and the bearing capacity of the specimen soon reaches its peak. Finally, when the load drops to about 85% of the peak load, horizontal main cracks appear at the bottom of the pier body, the crack width increases continuously, and the specimen has obvious residual displacement, which means that the specimen has been destroyed.

The hysteresis curves of specimen S1 and specimen S2 were similar in shape and size, while the hysteresis curve of specimen S3 is fuller than those of the other two specimens. First of all, specimens S1 and S2 reach the load peak value (207.6 kN and 243.75 kN) at a similar displacement level (about 24 mm). At a higher axial compression ratio, specimen S2 showed better bearing performance by increasing the peak load by 17.4% compared to S1. However, under the same shear span ratio, the ultimate displacement of specimen S1 with a lower axial compression ratio (n = 0.05) was close to 40 mm, which was significantly larger than that of specimen S2 (n = 0.10). In short, the increase in the axial compression ratio can improve the bearing capacity of the specimen but will reduce the ductility of the specimen.

Compared with specimen S2, the hysteresis curve of specimen S3 is fuller and the pinch effect is obvious. The good deformation performance of specimen S3 reflects its good energy dissipation and seismic performance. However, the peak load of S3 was only 169.17 kN, 30.6% lower than specimen S2. It means that the shear span ratio is an important factor affecting the seismic performance of the specimen. The improvement in the shear span ratio can significantly improve the ductility of the specimen but also reduce the bearing capacity of the specimen.

3.3. Skeleton Curve

Figure 11 shows the skeleton curves of the three specimens, which are extracted from the hysteresis curves of the lateral displacement of the load. According to the skeleton curve, the bearing performance and ductility indexes of each specimen are summarized in

Table 5. Load-bearing capacity and displacement ductility of each specimen.

Specimen	Py (kN)	Δy (mm)	Pp (kN)	Δp (mm)	Pu (kN)	Δu (mm)	μΔ	Δu
S1	190	17.37	207.66	24.6	172.13	39.6	2.28	3.30%
S2	226.01	15.45	243.75	24.1	207.48	34	2.21	2.83%
S3	143.64	13.67	169.17	24.5	143.79	41	3.01	2.41%

Annotation: P_y is yield load; Δ_y is yield displacement; P_p is peak load; Δ_p is peak displacement; P_u is ultimate load; Δ_u is ultimate displacement; μ_Δ is displacement ductility coefficient.

. Since no obvious yield point can be observed in the skeleton curve obtained from the test, the yield load and ultimate load of the specimen are determined by the energy method [22], as shown in Figure 11. The ultimate load is defined as the corresponding load when the load drops to 85% of the peak load [23]. The ductility and plastic deformation capacity of the specimen are reflected by the displacement ductility coefficient μ_Δ and the ultimate drift ratio Δ_u, which is calculated according to Equations (1) and (2).

$${\mu }_{\mathsf{\Delta }}=\frac{{\mathsf{\Delta }}_{\mathrm{u}}}{{\mathsf{\Delta }}_{\mathrm{y}}}$$

(1)

$${\delta }_{\mathrm{u}}=\frac{{\mathsf{\Delta }}_{\mathrm{u}}}{H}\times 100\%$$

(2)

where Δ_u and Δ_y represent the displacement corresponding to the ultimate load and the displacement corresponding to the yield load. H is the effective height of the specimen, where S1 and S2 are 120 cm and S3 is 170 cm.

As shown in Table 5, the bearing performance and ductility indexes of different specimens were compared. In the case of the same shear span ratio, the bearing performance of specimen S2 is higher than that of specimen S1, reflecting that the improvement in the axial compression ratio can effectively improve the bearing capacity. Under the same axial compression ratio, the bearing capacity of specimen S3 is significantly lower than that of specimen S2. In addition, the yield displacement Δ_y of specimen S3 was 13.67 mm, which was less than that of specimen S2, 15.45 mm, reflecting that specimen S3 entered into yield earlier. However, the ultimate displacement Δ_u of specimen S3 was 7 mm later than that of specimen S2, indicating that the yield stage of specimen S3 was longer. This is also reflected in the fact that the displacement ductility coefficient of specimen S3 is significantly greater than that of the other two specimens. In conclusion, from the test results, on the one hand, the improvement in the axial compression ratio is beneficial to the bearing capacity and has a slight negative impact on displacement ductility. On the other hand, the increase in shear span ratio significantly decreases the bearing capacity of the specimen, but effectively improves its ductility.

3.4. Stiffness Degradation

The stiffness of the structure is a reflection of the deformation capacity of the structure.

The tangent stiffness K_s = P/u of the specimen under any load–displacement pair (P, u) is obtained from the skeleton curve. The ratio of K_s to the initial stiffness K₀ of the bridge pier reflects the stiffness degradation of the specimen, and the stiffness degradation curve is shown in Figure 12. The stiffness degradation trends of specimen S1 and specimen S3 are similar, both of them experience a gradual change from rapid degradation of stiffness to a slow decrease in stiffness. At the early stage of loading, the initial stiffness degradation is faster due to a large number of cracks and their development. At the later stage of loading near the damage, the number of cracks almost stops increasing and the stiffness degradation curve tends to smooth out. However, the stiffness degradation curve of specimen S2 remains approximately straight, and the degradation rate in the initial stage is smaller. When the ultimate displacement is reached, the stiffness of specimen S2 degrades to 0.33 K₀, which is higher than 0.25 K₀ of specimen S1 and 0.16 K₀ of specimen S3. The increase in axial compression restrains the deformation of the specimen to a certain extent and limits the development of cracks, thus effectively improving the stiffness of the bridge pier. Therefore, increasing the axial compression ratio and decreasing the shear span ratio can not only reduce the degradation of stiffness at ultimate load but also effectively reduce the degradation rate of stiffness at the initial stage.

3.5. Energy Dissipation

The area enclosed by the load–displacement hysteresis curve represents the energy absorbed by the bridge pier during cyclic loading. The relationship between the cumulative energy dissipation of each specimen and the corresponding displacement level is shown in Figure 13. At the beginning of loading, the specimens are in the elastic or local plastic state. At this time, the energy dissipation of each specimen is at a low level, and the cumulative energy dissipation curve grows slowly. With the increase in cyclic displacement, the steel and concrete enter plasticity. At this time, the degree of pier damage gradually increased, and the energy dissipation curve began to grow steadily. The cumulative energy dissipation curves of specimen S2 and specimen S1 before approaching the yield displacement are almost the same. However, after yielding displacement, the cumulative energy dissipation of specimen S2 with a larger axial compression ratio is significantly higher than that of specimen S1. The final cumulative energy dissipation of specimen S2 is 38.9% higher than that of specimen S1. It can be seen that the increase in axial compression ratio can increase the energy dissipation capacity of the bridge pier under cyclic loading. This is because specimens with a large axial compression ratio have a higher load capacity and thus a larger area enclosed by the hysteresis curve. Before the lateral displacement reached 20 mm, the cumulative energy dissipation of specimen S3 was slightly larger than that of specimen S2 for the same displacement, and the cumulative energy dissipation of specimen S2 exceeded that of specimen S3 for the subsequent loading process. However, the final cumulative energy dissipation of the specimen was greater for the specimen with a larger shear span ratio, and the cumulative energy dissipation of specimen S3 increased by 18% compared with that of specimen S2. The hysteresis curve of specimen S3 was fuller than that of specimen S2, and thus the cumulative energy dissipation was greater.

3.6. Residual Displacement Ratios

Residual deformation refers to the deformation of the pier body that is not recovered when the horizontal force of the top of the pier falls to zero. The smaller the residual deformation of the pier, the stronger the self-centering ability of the pier, which can continue to work better after the earthquake and is conducive to repair. In order to eliminate the influence of the height of the test piece piers, the residual displacement ratio is used to reflect the residual deformation, and the residual displacement ratio is defined as shown in the following equation.

$${\delta }_{\mathrm{r}}=\frac{D_{\mathrm{r}}^{+}+D_{\mathrm{r}}^{-}}{2}\times \frac{1}{L}\times 100\%$$

(3)

where D_r⁺ and D_r⁻ represent the positive and negative residual displacements of the specimen, respectively, which correspond to the intersection of the horizontal axes of the hysteresis curve. For three cycles in each displacement level, only the residual displacement of the first cycle is taken for the calculation of Δ_r.

The relationship curve between the residual displacement ratio and the drift ratio of each specimen is shown in Figure 14. It can be seen that the residual displacement ratio of the specimen gradually increases with the increase in the loaded displacement. It can be seen that the residual displacement ratio of the specimen gradually increases with the increase in the loaded displacement. When the loading displacement is small, the residual deformation of the specimen is not obvious, and the deformation of the bridge pier can be recovered better after unloading. When the loading displacement exceeded the yield displacement, the residual deformation of the specimen began to have a significant elevation. As the load continued to increase, the cracking of concrete increased and the yielding of reinforcement led to the increase in plastic deformation of the specimen, and the residual deformation after unloading was even larger. It can be seen that the curves corresponding to specimen S1 and specimen S2 almost overlap, indicating that the axial compression ratio is not an important factor affecting the residual deformation of the specimen when the axial compression ratio does not exceed 0.10. In addition, it can be seen that the residual displacement ratio curve of specimen S3 is obviously always above the residual displacement curve of specimen S2. When the drift ratio reaches 2.0%, the residual displacement ratio of specimen S3 increases by 77% compared with that of specimen S2. The residual displacement ratio Δr of specimen S3 occurs at the stage of a rapid increase in residual deformation earlier than the drift ratio. Therefore, an increase in the shear span ratio significantly increases the residual deformation of the specimen.

4. Numerical Analysis

In this study, for prefabricated hollow piers, a numerical model was established based on ABAQUS, and model verification was completed. Secondly, the seismic behavior of a prefabricated hollow pier at different levels of axial compression ratio and shear span ratio was analyzed and compared.

4.1. Model Description

Figure 15 shows the finite element numerical analysis model of the prefabricated hollow bridge pier. The concrete part of the model includes the cap beam, pier body, and cushion cap, all of which are simulated by solid elements. Corresponding to the actual construction, the cushion cap is divided into the prefabricated block and the post-cast block. The longitudinal reinforcement and the spiral stirrup inside the pier body and the internal reinforcement of the cushion cap are all simulated by truss elements. The contact relationship between different concrete parts is established by defining the friction coefficient between them. Regardless of the slip of reinforcement and concrete, the reinforcement is embedded into the concrete to form a whole. According to the loading system in the test, the cyclic load is applied to the cap beam in the way of force first and then displacement.

4.2. Constitutive of Materials

The concrete plastic damage (CDP) model in ABAQUS is extensive to the structure and loading mode of the numerical model, so it is applied to study the nonlinear behavior of prefabricated hollow bridge piers in this study [24]. The ideal elastic–plastic model was adopted for the reinforcement in the pier, and the Von Mises yield criterion was adopted for the yield criterion. The unloading and reloading paths adopt the most general assumption that the stiffness of unloading and reloading is the same. The yield stress and elastic modulus of reinforcement are obtained from the material property test, as shown in Table 3. The research conclusion of Zhang et al. [25] shows that there is little difference between concrete mixed with fiber and normal concrete in the compressive stress–strain curves. Therefore, based on research [26] and the material characteristics of PVA concrete, the compressive and tensile constitutive models of PVA concrete are given, as shown in Equations (4)–(6).

$$y=\{\begin{array}{cc}\alpha x+\left(3-2\alpha \right)x^2+\left(\alpha -2\right)x^3& 0\le x\le 1\\ \frac{x}{\beta {(x-1)}^2+x}& x>1\end{array}$$

(4)

where $y=\frac{\sigma }{{\sigma }_{c,r}},x=\frac{\epsilon }{{\epsilon }_{c,r}},\alpha =E_{\mathrm{c}}/E_{\mathrm{p}},E_{\mathrm{p}}=\frac{{\sigma }_{c,r}}{{\epsilon }_{c,r}}$, ${\epsilon }_{c,r}=\left(700+172\sqrt{{\sigma }_{c,r}}\right)\times {10}^{-6}$; and ${\sigma }_{c,r}$ is peak compressive stress, taking the concrete uniaxial compressive strength representative value; ${\epsilon }_{c,r}$ is peak compressive strain; α is the control parameters of rising part of the concrete stress–strain curve under uniaxial compression; E_c is the initial elastic modulus of concrete; E_p is peak secant modulus of concrete; β is the control parameters of falling part of the concrete stress–strain curve under uniaxial tensile.

$$y=\{\begin{array}{cc}\frac{E_{\mathrm{t}}}{E_{\mathrm{p}}}x+\left(1.5-1.25\frac{E_{\mathrm{t}}}{E_{\mathrm{p}}}\right)x^2+\left(0.25\frac{E_{\mathrm{t}}}{E_{\mathrm{p}}}-0.5\right)x^4& 0\le x\le 1\\ \frac{x}{{\alpha }_f{(x-1)}^{1.7}+x}& x>1\end{array}$$

(5)

$${\alpha }_f=\frac{0.312f_{\mathrm{t}}^2}{1+3.58{\rho }_f\frac{l_f}{d_f}}$$

(6)

where E_t is the initial tensile modulus of fiber reinforced concrete; E_p is the peak secant modulus of fiber reinforced concrete; f_t is the representative value of the uniaxial compressive strength of concrete; ρ_f and are fiber volume fraction and aspect ratio, respectively.

4.3. Validation of the Model

Specimen S2 was used as the reference group for comparison, based on which the finite element model was established for seismic analysis and compared with the test results to verify the validity of the model. Figure 16 shows the comparison between the numerical results and the experimental results for the damage model of specimen S2. From Figure 16, it can be seen that the concrete Mises stress in the numerical model is large at the bottom of the pier near the bearing, which is consistent with the occurrence of concrete crushing at the bottom of the pier in the test. It can be seen that the failure pattern of specimen S2 in the test is similar to the results of the numerical model. In addition, Figure 17 shows that the external longitudinal reinforcement of the pier in the numerical model exceeds the yield strength near the bottom of the pier, which is also consistent with the flexural buckling of the reinforcement in the experiment.

The numerical simulation results of cyclic loading of specimen S2 are presented in Figure 18. The solid lines represent the experimental data, and the dotted lines represent the numerical results. Figure 18a is the hysteresis curve obtained from the experimental results and numerical simulation. First of all, the hysteretic curve is in good agreement with the experimental results on the whole, with a similar shape and close peak load. However, there is a large difference in unloading stiffness and residual displacement after yield, which may be due to the failure of reinforced concrete slip. Figure 18b is the simulation result of the skeleton curve, and it can be seen that the overall trend is relatively consistent. The stiffness of the elastic stage is similar to that of the test, and the peak load and ultimate load obtained by numerical simulation are slightly smaller than the test results.

Table 6. Comparison of parameters between numerical simulation and experimental results.

Specimen	Yield Load (kN)			Peak Load (kN)			Ultimate Load (kN)
	Exp.	Num.	Error (%)	Exp.	Num.	Error (%)	Exp.	Num.	Error (%)
S2	207.44	226.01	9.0	229.13	243.75	6.4	194.65	207.48	6.6

provides the comparison of important parameters and errors between the numerical simulation results and the experimental results for specimen S2. In conclusion, the finite element model of the prefabricated hollow bridge pier established in this paper can effectively reflect the bearing capacity level and stiffness degradation trend of the bridge pier under cyclic loading.

4.4. Parametric Study

Based on the established finite element model, the effects of the axial compression ratio and the shear span ratio on the seismic performance of prefabricated hollow bridge piers were investigated. The axial compression ratio varies from 5% to 15% on the basis of 2.5%, with five levels in total. The shear span ratio varies from 1.9 to 3.9 on the basis of 0.5, and there are also five levels. It should be noted that in the finite element model, the shear span ratio of specimens can be changed by changing the height of the pier body and keeping the pier body section unchanged. In addition, the shear span ratio λ in the finite element model of the bridge pier was maintained at 2.4 when studying the variation in the axial compression ratio parameter. The axial compression ratio n of the finite element model of the bridge pier was maintained at 0.1 when studying the variation in the shear span ratio parameter.

The analysis results of finite element parameter changes are shown In Figure 19. As shown in Figure 19a, in the initial elastic stage, the increase in the axial compression ratio will be beneficial to the improvement of stiffness, but the effect is not apparent. The larger the axial compression ratio in terms of bearing capacity, the greater the peak load of the prefabricated hollow pier. When the axial compression ratio is increased from 5% to 15%, the ultimate load of the pier is increased by 25.1%. However, in terms of ductility, the larger the axial compression ratio, the faster the decreasing rate of the stiffness of the pier in the failure stage, and the lower the ultimate displacement and displacement ductility. In conclusion, increasing the axial compression ratio is an effective method to enhance the bearing capacity of prefabricated hollow bridge piers, but its negative impact on displacement ductility should be considered.

Figure 19b shows the skeleton curves of the hollow pier at different shear span ratios. Firstly, the increase in the shear span ratio has a significant negative effect on the peak load and ultimate load of the hollow pier, which is the same as that of the solid pier. Compared with a low shear span ratio (λ = 1.9), the peak load of the hollow pier with high shear span ratio (λ = 3.9) is reduced by 36.1%. In addition, the influence of the shear span ratio on the displacement ductility is related to its magnitude. When the shear span ratio is small, the increase in the shear span ratio has an obvious effect on the displacement ductility. However, when the shear span ratio is large, its influence on the displacement ductility is small. In conclusion, the improvement of the shear span ratio has a negative effect on the shear bearing capacity of hollow bridge piers, but it can improve the deformation capacity of hollow bridge piers, which is beneficial to the energy consumption of components and the seismic resistance of structures.

5. Conclusions

Quasi-static tests and numerical simulations were performed to obtain the response of bridge piers under cyclic loads to study the seismic performance of prefabricated circular hollow piers. The effects of the axial compression ratio and shear span ratio factors on the seismic performance of bridge piers were analyzed by comparing the seismic performance of three pier specimens in terms of fail patterns, hysteresis curve, and skeleton curve. The conclusions are as follows:

(1) In the test phenomenon, the concrete crack development pattern was similar for the three bridge pier specimens. The specimens all showed a main crack with a large crack width at the bottom of the pier when they finally failed. Spalling of concrete at the bottom of the pier occurred in both specimens S2 and S3, but specimen S1 had only peeling of concrete. The presence of PVA fibers restrained the spalling of the protective layer of concrete.

(2) Under the cyclic load, the hysteresis curves of the three specimens have an obvious pinching effect, among which the hysteresis curve of specimen 3 is relatively full. From the comparison of the skeleton curves, it can be seen that the increase in the axial compression ratio can effectively improve the bearing capacity, and the increase in the shear span ratio can improve the ductility of the specimens.

(3) From the test results, the increase in the axial compression ratio and the shear span ratio can improve the cumulative energy dissipation of the bridge pier, but they will lead to more significant stiffness degradation at the final failure. The residual displacement ratio curves of Specimens S1 and S2 almost overlap, but the residual deformation of specimen S3 with a large shear span ratio is significantly larger.

(4) The seismic performance of the prefabricated hollow piers was well modeled using ABAQUS software. The parametric analysis shows that: the increase in the axial compression ratio can effectively improve the bearing capacity of the bridge pier; the increase in the shear span ratio, especially when the shear span ratio is small, will significantly reduce the bearing capacity of the bridge pier, but at the same time it will improve the displacement ductility of the bridge pier.