Experimental and numerical investigations on cyclic behaviors of precast segmental bridge piers with the hybrid of high-strength bars and unbonded prestressing tendons

Abstract

Precast segmental piers are gaining increasing attentions in low-medium seismic-risked regions. In this paper, cyclic behaviors of two precast segment piers reinforced with the hybrid of high-strength energy dissipation (“H” ED, ≥500 MPa) bars and unbonded tendons were experimentally investigated, accompanied with another two piers reinforced with merely “H” ED bars for the comparative study. It was observed that unbonded tendons benefitted the segmental piers in rising the lateral strength and mitigating the residual drift. On the other aspect, the tendons also made concrete prone to damage. Alongside, the finite element (FE) model is constructed for the four tested segmental piers, discritized with the displacement-controlled beam-colum element with a fiber section. With the bond-slip behavior of the “H” ED bars being incorporated, the numerical model accurately reflects the piers’ seismic behaviors.

Keywords

precast segmental pier cyclic loading fiber finite element high-strength bar unbonded prestressing tendons

Introduction

Precast concrete technique significantly accelerates construction speed, reduces on-site construction activities, and alleviates adverse disturbances on the environment and the public traffic (FHWA, 2009). Moreover, the agreed quality of precast concrete members guarantees a structure’s long-term serviceability and lowers its life-cycle cost (Hewes and Priestley, 2002).

For bridges, precast members have already been extensively adopted in the superstructure (Liu, 2010), for example, precast pretensioned concrete girders, precast segmental box girder bridges, etc. Comparatively, precast concrete technique in the bridge substructure attracts lesser attentions. Nevertheless, after being first applied in the JFK Causeway in Texas in the 1970’s, the bridge community realizes that precast piers also display apparent advantages. In comparison with cast-in-place (CIP) piers, segmental piers are weak in dissipating input earthquake energy (Ou et al., 2010), and therewith are not preferred in high-seismicity regions. On the other aspect, segmental piers are gaining widespread applications in low-medium seismic-risked regions, as they exhibit mitigated concrete damage and reduced residual drift, which are important quantitative indices for seismic resilience.

For a precast segmental pier, longitudinal ED bars remain continuous across the segmental joints, and consume the majority of input earthquake energy (Bu et al., 2016). Therefore, mechanical properties of the ED bars greatly affect a precast segmental pier’s seismic behaviors. For the engineering practice, HRB400 is the widely-adopted ED bars in segmental piers (Hose, 2001; Lehman et al., 2004). Until very recently, high-strength (denoted as “H” hereafter) reinforcements with yield strength ≥500 MPa gain applications in bridge engineering (Barbosa et al., 2016; Wang et al., 2015). Wang et al. (2015) pointed out that the amount of “H” ED bars could be significantly reduced compared to the conventional HRB400 ED bars, whereas the seismic performance of the columns were maintained. Ou et al. (2010) revealed that piers with “H” ED bars exhibited higher strength, greater ductility, and larger energy dissipation than the counterparts with HRB400 ED bars. On the other aspect, it is demonstrated that cutting-edge bridge design is focusing on seismic resilience, which requires smaller residual drift and concrete damage for the purpose of post-earthquake fast rehabilitation. To this end, unbonded prestressing tendons are further introduced into bridge piers to provide a considerable restoring force at a larger drift (Sun et al., 2016). The post-tensioning technique gains initial attention in CIP piers and is soon extended to segmental piers (Ou et al., 2010; Wang et al., 2008). Nevertheless, researches regarding the segmental piers reinforced with “H” ED bars and unbonded tendons, or their hybrid, are still far from sufficient, according to the authors’ knowledge.

Besides experimental investigations, finite element (FE) models for bridge piers are continuously proposed and improved, mainly involving solid finite element (FE) models (Li et al., 2017; Wang et al., 2008) and fiber-based FE models (Tazarv and Saiidi, 2016). A fiber-based FE model discretizes a cross-section into a bundle of fibers. By assigning each fiber a unique uniaxial material model (Priestley et al., 1996) and assuming that the cross-section remains plane, mechanical behaviors of concrete structures can be derived (Huang and Kwon, 2015; Pan et al., 2017). The predefined moment-curvature relationship is not required for concrete members, as fiber-based FE model can automatically capture instantaneous interaction of axial load and moment. Compared to a solid FE model, the fiber-based FE model does not require the expensive computational cost and the high-level modeling strategy (Tazarv and Saiidi, 2016; Wu and Pantelides, 2018). It should be pointed out that the fiber-based FE model is effective in predicting seismic responses of CIP piers (Guerrini et al., 2014), but precast segmental piers, as the segmental joint is discontinuous and hard to be captured. Accurate fiber-based FE models for precast segmental piers are still pursued.

This invesitgation focuses on seismic responses of two segmental piers reinforced with the hybrid of “H” ED bars and unbonded tendons. Moreover, another two segmental piers reinforced with merely “H” ED bars were also tested for the comparative study. Furthermore, fiber-based FE models for are proposed and can well predict their seismic responses. This paper is organizned as follows. Details of the segmentally-erected piers and cyclic loading scheme are presented in Sect. 2. Seismic performances of these piers are compared in Sect. 3, in terms of damage evolution, lateral strength and ductility, unloading stiffness, residual drift, and energy disspation. Finally, the fiber-based FE model intended for segmental piers is presented and validated in Sect. 4.

Experimental program

Specimens fabrication

Table 1 summarizes details of the four 1:2 scaled precast segmental piers. Among them, two piers were reinforced with merely “H” ED bars (denoted as “PRC” hereafter), and the other two piers were reinforced with the hybrid of “H” ED bars and unbonded tendons (denoted as “PPC” hereafter). Eight and Fourteen “H” ED bars were embedded in piers PRC-H-8/PPC-H-8 and piers PRC-H-14/PPC-H-14, respectively, leading to 0.89% and 1.56% longitudinal reinforcement ratios. All the four piers adopted the 8 mm-dia. circular normal-strength spirals at the 50 mm spacing. Piers PPC-H-8 and PPC-H-14 were additionally reinforced with seven 15.2 mm-dia. unbonded tendons.

Table 1.

Details for tested piers.

Pier	ED bars	Tendons	$\frac{N}{{f'}_{c} A}$ (%)	$\frac{P}{{f'}_{c} A}$ (%)	$\frac{N + P}{{f'}_{c} A}$ (%)
PRC-H-8	Eight or fourteen20 mm-dia. bars	—	8	—	8
PRC-H-14		—	8	—	8
PPC-H-8		Seven 15.2 mm-dia.tendon	8	7	15
PPC-H-14			8	7	15

N: external axial load; P: prestressing force; N–P: total axial load; $f'_{t}$ : cylindrical strength of concrete; A: cross-section area.

All the four piers shared the same nominal design, and their specimen configurations and cross-sections are shown in Figure 1. The 0.6 m-dia. (D) circular shaft consisted two 1.175 m deep segments. The 0.6 × 1.5 × 2.0 m reinforced concrete (RC) footing was fixed to the ground during test. Lateral load was exerted at the middle of the 0.6 m thick precast cap beam. Effective height (H) of the tested piers was (1.175 × 2 + 0.3) = 2.65 m and their height-to-diameter (H/D) ratio was 2.65/0.6 = 4.42 > 3. As a consequence, flexural-dominated failure mode was expected for the tested piers (Colomb et al., 2008; Parghi and Alam, 2016).

Figure 1.

Specimen configurations and cross-sections.

Before casting the RC footing, the shaft, and the top cap, corrugated plastic pipes were placed for further place of ED bars and unbonded tendons, see Figure 2(a). These precast segments were transported to the laboratory for assemblage, see Figure 2(b). After the “H” ED bars were placed in the corrugated plastic pipes, mortar was poured to bond the “H” ED bars to the shaft, see Figure 2(c). Special attention was paid that a 200 mm length of ED bars was debonded from the shaft at the interface between the RC footing and the shaft by wrapping ED bars with soft plastic pipes, see Figures 1 and 2(d). The purpose was to mitigate the stress concentration resulting from the opening and closing of the joint during lateral loading. The two PPC piers were soon post-tensioned with vertical unbonded tendons, see Figure 2(e).

Figure 2.

Construction sequences: (a) Segment prefabrication, (b) Segment assemblage, (c) Grouting mortar, (d) ED bars with a 200mm debonded length, and (e) Prestressing unbonded tendons.

Following test procedures in the Chinese code (GB 50010, 2010), the mean cylindrical strengths for concrete ( $f'_{c}$ = 35.2 MPa) and mortar ( $f'_{c, g}$ = 48.6 MPa) were obtained. The 20 mm-dia. HRB600 bars (SU JG/T054, 2012) served as the “H” ED bars. Mechanical properties of three HRB600 samples were measured and were summarized in Table 2, following ASTM (ASTM A615/A615M-20, 2020). The typical stress-strain relationship is characterized by the solid line in Figure 3. The definition of parameters in Figure 3 is listed below Table 2. The 8 mm-dia. HRB400 bars (GB 50010, 2010) were adopted as the normal-strength stirrups. The yield strength of unbonded tendons was 1860 MPa.

Table 2.

Tensile testing of 20 mm-dia. “H” ED bars.

ED bar	$E_{s}$ (GPa)	$f_{sy}$ (MPa)	$f_{su}$ (MPa)	$ε_{su}$ (%)
H	197	626	823	20.0
	204	625	826	20.5
	195	631	826	19.5

$E_{s}$ : young’s modulus; $f_{sy}$ : yield strength; $f_{su}$ : ultimate tensile strength; $ε_{su}$ : ultimate strain.

Figure 3.

Tested and fitted uniaxial stress-strain relationships for “H” ED bar.

Test setup and loading scheme

Before the initiation of cyclic lateral loading, approximately 8% of the piers’ compressive strength ( $N$ = 0.08 $f'_{c} A$ , see Table 1) was exerted axially and vertically at the top of the cap beam by two prestressed thread bars, representing the superstructure’s self-weight. All these specimens were bolted to the ground by four thread bars through the footing.

For the two PPC piers, unbonded tendons provided extra prestressing force to the piers. Guerrini et al. (2014) quantitatively recommended the value of prestressing force, for the purpose of mitigating residual drift. Considering that the axial load ratio of a RC bridge pier in practice was generally less than 0.15 $f'_{c} A$ , the effective prestressing force of the piers was selected as $P$ = 0.07 $f'_{c} A$ , see Table 1. To this end, seven 15.2 mm-dia. tendons were initially tensioned to 800 MPa, with the short-term prestressing loss being taken into account.

Figure 4(a) schematically shows the test setup. The RC footing was fixed to the laboratory floor during lateral loading. An ASTM digital hydraulic actuator system was applied on the cap beam to pull/push these piers. The external axial load $N$ was realized through pre-tensioned thread bars. Of special attention was that the two thread bars titled with the increasing lateral displacement, which resulted in a small horizontal restoring force. The hysteretic curves presented in Sect. 3 already eliminated this disturbance (Tong et al., 2019).

Figure 4.

Schematical illustration of the test: (a) Test setup (b) Loading scheme.

The displacement-control loading scheme is presented in Figure 4(b). The increment of displacement amplitude was 5 mm, before the displacement amplitude reached 50 mm. This increment was then amplified to 10 mm. At each loading amplitude, the identical lateral displacement was repeated three times. The test of a precast segment pier lasted around 5 h, and was terminated at the failure of one or more ED bars.

Test results and discussions

Damage evolution and hysteretic response

All the tested PRC and PPC piers displayed the ductile, flexural-dominated failure mode. Their failure patterns are illustrated in Figure 5, emphasizing on the plastic hinge zone.

Figure 5.

Failure patterns: (a) Pier PRC-H-8, (b) Pier PPC-H-8, (c) Pier PRC-H-14, and (d) Pier PPC-H-14.

The height of concrete spalling and crushing of the PRC and PPC piers is marked in Figure 5. The height grew from 200 mm for pier PRC-H-8 (see Figure 5(a)) to 440 mm for pier PPC-H-8 (see Figure 5(b)). The difference was more notable between pier PRC-H-14 (220 mm, see Figure 5(c)) and pier PPC-H-14 (1050 mm, see Figure 5(d)). It can be seen that PPC pier presented weaker while damage was realized at larger loads. Therefore, the PPC pier was prone to concrete damage, with the introduction of unbonded prestressing tendons. The reason was straightforward and could be attributed to the lager axial load ratio (0.15 $f'_{c} A$ ) of the two PPC piers, which was only 0.08 $f'_{c} A$ for the two PRC piers.

Four damage levels (DL) are defined in Table 3 to quantitively evaluate the damage evolution of a precast segmental pier, and they are: DL1—Minor/Slight damage, DL2—Moderate damage, DL3—Major/Extensive damage, and DL4—Failure/Collapse. It is noted that the symbol for DL4 is the fracture of ED bars or tendons, or the degradation of lateral strength to 80% of the peak strength ( $0.8 F_{\max}$ , Paulay and Priestley, 1992), whichever occurs first.

Table 3.

Damage level (DL) definitions for a precast segmental pier.

Damage Level	Threshold values	Quantitative description
DL1	$\min {\begin{matrix} ε_{s} ⩽ ε_{sy} \\ ε_{c} ⩽ 0.004 \end{matrix}$	First yielding of ED bars;
		Barely visible of concrete cracks and joint opening.
DL2	$min {\begin{matrix} ε_{c} > 0.004 \\ ε_{s} > 0.015 \end{matrix}$	Spalling of cover concrete;
		1–2 mm crack width;
		Visible joint opening.
DL3	$min {\begin{matrix} ε_{c} ⩾ 0.004 + 1.4 ρ_{w} \frac{f_{yw}}{f_{cc}} \\ ε_{s} > 0.06 \end{matrix}$	Crushing of core concrete;
		First hoop fracture;
		Buckling of ED bars;
		> 2 mm crack width;
		Apparent joint opening.
DL4	$min {\begin{matrix} F < 0.8 F_{\max} \\ ε_{s} > 0.075 \\ ε_{s, p} > 0.05 \end{matrix}$	80% of peak strength;
		Fracture of ED bars or unbonded tendons.

$ε_{c}$ : strain of concrete; $ε_{s}$ : strain in the ED bar; $ε_{s, p}$ : strain in the unbonded tendon; $ρ_{w}$ : volumetric transverse reinforcement ratio; $f_{yw}$ : yield stress of transverse reinforcement; $f_{cc}$ : strength of core concrete; $F$ - lateral force; $F_{max}$ : peak lateral force.

The evolution of damage with the lateral drift is summarized in Table 4. It was found that the unbonded tendons increased the threshold drift for level DL1, which benefitted a precast segmental pier to remain quasi-elastic behaviors. More specifically, this threshold value increased from 1.08% for pier PRC-H-8 to 1.29% for pier PPC-H-8, and from 1.10% for pier PRC-H-14 to 1.41% for pier PPC-H-14. Nevertheless, it was demonstrated that threshold drift for other three levels (DL2, DL3, and DL4) was not improved apparently by the unbonded tendons.

Table 4.

Threshold drifts (%) for four different damage levels.

	DL1	DL2	DL3	DL4
PRC-H-8	1.08	3.40	4.80	5.18
PPC-H-8	1.29	3.21	4.58	4.96
PRC-H-14	1.10	3.77	4.45	4.83
PPC-H-14	1.41	3.21	5.18	5.38

The hysteretic curves for PRC and PPC piers are shown in Figure 6, characterizing the lateral force versus the drift. The initiations of the first ED bar yielding and the ED bar fracture are also marked.

Figure 6.

Tested hysteretic curves: (a) Pier PRC-H-8, (b) Pier PPC-H-8, (c) Pier PRC-H-14, and (d) Pier PPC-H-14.

Strength and ductility

The following variables are employed to quantify the strength and ductility of the tested piers, namely yield force $F_{y}$ , yield drift $Δ_{y}$ , peak force $F_{\max}$ , ultimate drift $Δ_{u}$ , and ductility factor $μ_{Δ}$ ( $μ_{Δ} = Δ_{u} / Δ_{y}$ ). The $Δ_{y}$ is defined as the intersection point of the following two lines: the line connecting origin and the point of the skeleton curve with 0.75 $F_{\max}$ , and tangent line of the skeleton curve at $F_{\max}$ (Sun et al., 2016). The $Δ_{u}$ is defined when the strength of the descending branch reaches 0.80 $F_{\max}$ (Paulay and Priestley, 1992), or the fracture of ED bars/unbonded tendons.

In Figure 7, the measured skeleton curves categorized by the quantity of ED bars are plotted. The mean values of aforementioned variables in the first and third quadrants (see Figure 7) are summarized in Table 5. It was indicated that both $F_{y}$ and $F_{\max}$ were enhanced by the unbonded tendons. For the piers with 8 ED bars, pier PPC-H-8 exhibited a higher value of $F_{y}$ ( $F_{\max}$ ) than pier PRC-H-8, which was $F_{y}$ =195.6 kN ( $F_{\max}$ =229.2 kN) for pier PPC-H-8, and was $F_{y}$ =143.6 kN ( $F_{\max}$ =169.9 kN) for pier PRC-H-8, respectively. Similar trend was found for the piers with 14 ED bars, with $F_{y}$ =244.0 kN ( $F_{\max}$ =285.7 kN) for pier PPC-H-14, and $F_{y}$ =225.0 kN ( $F_{\max}$ =256.1 kN) for pier PRC-H-14.

Table 5.

Strength and ductility variables.

Pier	$F_{y}$ (kN)	$Δ_{y}$ (%)	$F_{\max}$ (kN)	$Δ_{u}$ (%)	$μ_{Δ}$
PRC-H-8	143.6	1.1	169.9	5.18	4.80
PPC-H-8	195.6	1.0	229.2	4.96	4.98
PRC-H-14	225.0	1.2	256.1	4.83	4.03
PPC-H-14	244.0	1.3	285.7	5.38	4.14

Figure 7.

Tested skeleton curves: (a) Piers PRC-H-8 andPPC-H-8 (b) Piers PRC-H-14 and PPC-H-14.

On the other aspect, unbonded tendons displayed insignificant effects on the ductility. Both $Δ_{u}$ and $μ_{Δ}$ showed a little variation for the piers. All the piers had similar ductile behaviors as $μ_{Δ}$ ≥ 3 (Caltrans SDC, 2019).

Unloading stiffness degradation

Unloading stiffness in this study is defined as the slope of the line connecting the points of the unloading branch at the 20% and 80% of the peak strength of that cycle (Wang et al., 2017). Furthermore, the ratio of initial stiffness to unloading stiffness is named as $η_{un}$ . The value of $η_{un}$ is illustrated in Figure 8 using the hysteretic curve of pier PPC-H-8 in the first quadrant (see Figure 6(b)).

Figure 8.

Illustration of the $η_{un}$ for pier PPC-H-8.

Figure 9(a) shows the $η_{un}$ of segmental piers with 8 ED bars. Before 2% drift, the $η_{un}$ was almost the same for piers PRC-H-8 and PPC-H-8. However, the difference of $η_{un}$ became apparent for the two piers at ≥2% drift. Pier PPC-H-8 degraded more apparently in terms of unloading stiffness. Figure 9(b) shows the $η_{un}$ of the segmental piers with 14 ED bars. Interestingly, the $η_{un}$ did not witness too much difference for the two piers, either with or without unbonded tendons.

Figure 9.

Unloading degradation parameter $η_{un}$ : (a) Piers PRC-H-8 and PPC-H-8 (b) Piers PRC-H-14 and PPC-H-14.

Residual drift

Residual drift is an important measurement of post-earthquake functionality of a bridge. In Japan, the bridges with >1.75% residual drift were demolished, even though they survived in the Hyogo-Ken NanBu earthquake in 1995 (Kawashima et al., 1998). After this earthquake, the allowable residual drift was set as 1% for highway bridges in Japan (Japan Road Association, 2012). Nevertheless, it should be noted that not all specifications put forward limit on the residual drift (Caltrans SDC, 2019).

The residual drift of the first cycle at each drift level was compared in Figure 10. Obviously, the residual drift was negligible (<0.25%) for either a PRC or a PPC pier if the lateral drift varies within (–2%, +2%), see Figure 10. Within this stage, there was no substantial benefit in mitigating the residual drift brought out by the unbonded tendons.

Figure 10.

Residual drift evolutions: (a) Piers PRC-H-8 and PPC-H-8 (b) Piers PRC-H-14 and PPC-H-14.

Nevertheless, vertical prestressing tendons benefited reducing the residual drift when subjected to >2% lateral drift. At 5.29% lateral drift, unbonded tendons decreased the residual drift from 2.94% for pier PRC-H-8 to 2.17% for pier PPC-H-8 (see Figure 10(a)), and from 2.30% for pier PRC-H-14 to 1.93% for pier PPC-H-14 (see Figure 10(b)). The mitigation of excessive residual drift, originated from the unbonded tendon, was more apparent when approaching the fracture of ED bars. Specifically, pier PRC-H-8 exhibited 3.66% final residual drift, compared to 2.27% of its counterpart - pier PPC-H-8. Furthermore, pier PRC-H-14 had 3.65% final residual drift, compared to 2.32% of its counterpart—pier PPC-H-8.

Residual drift was closely related to the amount of unbonded tendons. It is demonstrated that more tendons were necessary to bring the residual drift back to the targeted value, for example, 1.0% in Japanese code (Japan Road Association, 2012).

Energy dissipation

Figure 11(a) depicts energy dissipation per loop at different lateral drifts for piers PRC-H-8 and PPC-H-8. It seems that unbonded tendons did not increase the capacity of energy dissipation for pier PPC-H-8, compared to pier PRC-H-8. Consequently, the area of concrete’s spalling and crushing for pier PPC-H-8 (Figure 5(b)) was similar to that for pier PRC-H-8 (Figure 5(a)).

Figure 11.

Energy dissipation per loop: (a) Piers PRC-H-8 and PPC-H-8 (b) Piers PRC-H-14 and PPC-H-14.

For the piers with 14 ED bars, Figure 11(b) suggests that the energy dissipation per loop was enhanced significantly with unbonded tendons (pier PPC-H-14), especially for the loops with >3.5% lateral drift. The area of concrete spalling and crushing for pier PPC-H-14 (Figure 5(d)) was much bigger than pier PRC-H-14 (Figure 5(c)), indicating more energy consumed by pier PPC-H-14.

Numerical simulation

A reliable fiber-based FE model for a precast segmental pier can reveal its hysteretic behaviors, predict its seismic performances, optimize the design, etc. In the study, numerical simulations are carried out within the framework of the open-source finite element code OpenSees (Mazzoni et al., 2009). The proposed fiber-based FE model takes the special mechanical behaviors at the joints into account and is validated by the experimental results.

Description of numerical model

The pier is discretized into five different element types, see Figure 12. For the elements above the plastic hinge zone, the elasticBeamColumn element object in OpenSees is assigned for Type I elements in Figure 12. This element object does not consider any plastic or damage behaviors and can save the computational cost. It is demonstrated that the opening and closing of the joint between two shaft segments (inside Type I elements) was not apparent during lateral loading. Therewith, this joint is not considered in the model, and only the other joint between the shaft and footing (between Type II and III elements) is modeled. Effective stiffness $E I_{eff}$ , rather than gross stiffness $E I_{g}$ , is assigned to Type I elements (Li, 2010). The $E I_{eff}$ combines the influences from axial load ratio, reinforcement slippage, longitudinal reinforcement ratio, concrete cracking, and is expressed as (Li, 2010):

\frac{E I_{eff}}{E I_{g}} = 0.29 + 0.48 \frac{N + P}{A {f'}_{c}} - 0.31 \frac{f_{sy} d_{b}}{H \sqrt{{f'}_{c}}} + 6.1 ρ_{l}

(1)

where $d_{b}$ is the diameter of a ED bar, and $ρ_{l}$ is the longitudinal reinforcement ratio.

Figure 12.

The fiber FE model for pier PPC-H-8.

Elements located in the plastic hinge zone are critical to capture concrete cracking, spalling and crushing, as well as the damage accumulated in ED bars. The disBeamColumn element object, with the fiber section type fiberSec, is assigned for Type II elements in Figure 12. The cross-section with the fiberSec attribute is divided into numerous fibers. For the piers with 8 ED bars, the cross-section consists of 408 fibers, including 320 fibers for core concrete, 80 fibers for cover concrete and 8 fibers for ED bars, see Figure 12. The elements length is set as the plastic hinge length $L_{p}$ (Caltrans SDC 2019), which yields:

L_{p} = 0.08 H + 0.022 d_{b} f_{sy} (mm, MPa)

(2)

The RC footing in this fiber-based FE model is divided into the one with 200 mm unbonded ED bars (see Type III in Figure 12), and the one with bonded ED bars (see Type IV in Figure 12). The disBeamColumn element object with the fiberSec attribute is assigned for Type III and IV elements.

The “truss” element object is assigned for vertical unbonded tendons, see Type V elements in Figure 12. The unbonded tendons and the pier share the identical mesh scheme. The deformation compatibility condition requires that the element representing the unbonded tendons share the same horizontal displacement with the surrounding element representing the shaft, but the vertical displacement. To this end, the horizontal and rotation DOFs of the unbonded tendons are coupled with the shaft, whereas their vertical DOF is released, except the two end points standing for the anchorage zones.

Material properties

Uniaxial material model Concrete01 in OpenSees is employed to describe the constitutive law of core concrete and cover concrete of the elements located in the plastic hinge zone, named Type II elements in Figure 12. Concrete01 neglects the tensile behavior of concrete and only compressive behavior is considered (Park et al., 1972, Scott et al., 1982). The degraded linear unloading/reloading stiffness of concrete can also be embraced in Concrete01. This material model consists of a parabolic ascending part, a linear descending part and a horizontal part, as:

σ_{c} = {\begin{matrix} K {f'}_{c} [2 (\frac{ε_{c}}{ε_{c 0}}) - (\frac{ε_{c}}{ε_{c 0}})^{2}] ε_{c} ⩽ ε_{c 0} \\ K {f'}_{c} [1 - Z (ε_{c} - ε_{c 0})] ε_{c 0} ⩽ ε_{c} ⩽ ε_{cu} \\ 0.2 K {f'}_{c} ε_{c} > ε_{cu} \end{matrix}

(3)

where $K$ is strength enhancement coefficient of core concrete, due to confinement of transverse reinforcements; $ε_{c 0}$ is the strain at the point of maximum stress (0.002 in the study); $ε_{cu}$ is the strain when stress drops to 20% of peak stress; and $Z$ is the strain softening slope. The detailed definitions of these variables can be found in Park et al. (1972) and Scott et al. (1982).

Concrete01 is also employed for Type III and Type IV elements. Of special attention is that a high compressive strength (10 $f'_{c}$ ) is assigned for Concrete01 of the RC footing. In addition, no degraded strength ( $Z = 1.0$ in equation (3)) is assumed. The purpose is to avoid the possible concrete damage in the RC footing, which remained elastic during the test.

Uniaxial material model ReinforcingSteel in OpenSees is capable of considering the damage accumulation, stiffness degradation, and strength reduction, and is employed for the “H” ED bars. The stress-strain relationship of the “H” ED bars is (Esmaeily and Xiao, 2005):

σ_{s} = {\begin{matrix} E_{s} ε_{s} for 0 < ε_{s} ⩽ ε_{sy} \\ f_{sy} for ε_{sy} < ε_{s} < k_{1} ε_{sy} \\ k_{3} f_{sy} + \frac{E_{s} (1 - k_{3})}{ε_{sy} {(k_{2} - k_{1})}^{2}} (ε - k_{2} ε_{sy})^{2} for k_{1} ε_{sy} < ε_{s} < k_{2} ε_{sy} \end{matrix}

(4)

where $E_{s}$ is 204 GPa; $f_{sy}$ is 625 MPa; $ε_{sy}$ is 0.0031. $k_{1}$ , $k_{2}$ , and $k_{3}$ are applied to define the shape of the stress-strain curve and their definitions and values are illustrated as the dash line in Figure 3.

For the ED bars in the Type II and Type IV elements, the ReinforcingSteel material defined in Figure 3 and equation (4) is utilized.

Nevertheless, the default stress-strain relationship, see Figure 3 and equation (4), is modified for the 200 mm unbonded ED bars in Type III elements, to take the bond-slip behavior into account. Specifically, the deformation of the 200 mm unbonded ED bar consists of (see Figure 13(a)): (1) the elongation due to the stress increment; (2) the slippage of the ED bar in the plastic hinge zone; and (3) the slippage of the ED bar in the RC footing. In this study, the item (2) is equivalent to item (3). The elongation of 200 mm unbonded ED bars $δ_{bar}$ is given as:

\begin{matrix} δ_{bar} = ε_{s} (L_{d 1} + L_{un}) for ε_{s} ⩽ ε_{sy} \\ δ_{bar} = ε_{s} L_{un} + ε_{sy} L_{d 1} + (ε_{s} + ε_{sy}) L_{d 2} for ε_{s} > ε_{sy} \end{matrix}

(5)

where $ε_{s}$ is the strain of the ED bar; $L_{un}$ is the unbonded length; and $L_{d 1}$ ( $L_{d 2}$ ) is the length along which average bond shear stress ${\bar{τ}}_{b 1}$ ( ${\bar{τ}}_{b 2}$ ) is assumed. The bond transfer lengths $L_{d 1}$ and $L_{d 2}$ are defined as (see Figure 13(b)):

\begin{matrix} L_{d 1} = \frac{f_{s} d_{b}}{4 {\bar{τ}}_{b 1}} ⩽ \frac{f_{sy} d_{b}}{4 {\bar{τ}}_{b 1}} \\ L_{d 2} = \frac{(f_{s} - f_{sy}) d_{b}}{4 {\bar{τ}}_{b 2}} \end{matrix}

(6)

where $f_{s}$ is the stress of the ED bar corresponding to the strain $ε_{s}$ . A simplified bond shear stress distribution is adopted, where ${\bar{τ}}_{b 1} = 1.0 \sqrt{f_{c, g}^{'}}$ for $ε_{s}$ ≤ $ε_{sy}$ , and ${\bar{τ}}_{b 2} = 0.5 \sqrt{f_{c, g}^{'}}$ for $ε_{s}$ > $ε_{sy}$ (Ou et al., 2010).

Fiure. 13.

The mechanical behaviors of ED bar at the joint: (a) Joint opening (b) Strain of ED bar.

To embrace the bond-slip behavior of the unbonded ED bars in the fiber-based FE model, the elastic modulus is delibratively decreased from $E_{s}$ to $E'_{s}$ . The expression of $E'_{s}$ can be obtained as:

\begin{matrix} σ_{sy} = E_{s} \cdot ε_{sy} = E_{s} \cdot \frac{δ_{bar}}{L_{un} + L_{d 1}} = {E'}_{s} \cdot \frac{δ_{bar}}{L_{un}} \\ {E'}_{s} = \frac{L_{un}}{L_{un} + L_{d 1}} E_{s} = \frac{E_{s}}{{k'}_{0}} \end{matrix}

(7)

where $E_{s}$ is the Young’s modulus of the steel; and $k'_{0} = 1 + \frac{f_{sy} d_{b}}{4 {\bar{τ}}_{b 1} L_{un}}$ .

Following the similar procedure, the modified stress-strain relationship for the unbonded ED bar is expressed as:

σ_{s} = {\begin{matrix} E_{s} ε_{s} / {k'}_{0} for 0 < ε_{s} ⩽ {k'}_{0} ε_{sy} \\ f_{sy} for {k'}_{0} ε_{sy} < ε_{s} < {k'}_{1} ε_{sy} \\ k_{3} f_{sy} + \frac{E_{s} (1 - k_{3})}{ε_{sy} {({k'}_{2} - {k'}_{1})}^{2}} (ε - {k'}_{2} ε_{sy})^{2} for {k'}_{1} ε_{sy} < ε_{s} < {k'}_{2} ε_{sy} \end{matrix}

(8)

where $k'_{1}$ and $k'_{2}$ are defined as:

\begin{matrix} {k'}_{1} = k_{1} + \frac{f_{sy} d_{b}}{4 {\bar{τ}}_{b 1} L_{un}} \\ {k'}_{2} = k_{2} + \frac{f_{sy} d_{b}}{4 {\bar{τ}}_{b 1} L_{un}} + \frac{f_{sy} d_{b}}{2 {\bar{τ}}_{b 2} L_{un}} (k_{3} - 1) (\frac{2}{3} k_{1} + \frac{1}{3} k_{2}) \end{matrix}

(9)

By the employment of equation (9) for the unbonded ED bars, the ReinforcingSteel material model can consider the bond-slip behavior.

For the unbonded vertical prestressing tendons (Type V elements), the uniaxial material model Steel02 in OpenSees with the initial stress being employed.

Comparison of numerical and experimental results

Hysteretic curves, skeleton curves, residual drifts, and energy dissipation per loop from numerical simulations are compared with the experimental ones to validate the proposed fiber FE model.

Figure 14 illustrates the comparison between the experimental (solid lines) and numerical (dashed lines) hysteretic curves. In order to clearly illustrate the results, only the curve of the first cycle for each loading phase is plotted for both the numerical and test results. It can be seen that the numerical curves generally coincide well with the experimental curves.

Figure 14.

Experimetal and numerical hysteretic curves. (replace with a clear one): (a) Pier PRC-H-8, (b) Pier PPC-H-8, (c) Pier PRC-H-14, (d) Pier PPC-H-14.

Detailed comparisons are plotted from Figures 15 and 16, in terms of residual drift versus total drift, and energy dissipation per loop. It shows that the numerical results agree well with the test results.

Figure 15.

Experimetal and numerical residual drifts:(a) Pier PRC-H-8, (b) Pier PPC-H-8, (c) Pier PRC-H-14,(d) Pier PPC-H-14.

Figure 16.

Experimetal and numerical energy dissipation per hysteretic loop: (a) Pier PRC-H-8, (b) Pier PPC-H-8, (c) Pier PRC-H-14, (d) Pier PPC-H-14.

Conclusion

Cyclic responses of precast segmental piers with the hybrid of high-strength bars and unbonded tendons were experimentally investigated, along with the fiber-based FE models. The following conclusions can be drawn:

The unbonded tendons are beneficial in increasing a PPC pier’s lateral strength and mitigating the residual drift. In addition, a PPC pier is more potential to exhibit quasi-elastic behaviors under a small-to-medium earthquake.

The unbonded tendons apparently increase the energy dissipation capacity for a PPC pier with a high quantity of “H” ED bars, at the cost of enlarged the zone of concrete spalling and crushing.

Energy dissipation capacity of a PRC or PPC pier increased with the quantity of “H” ED bars. Nevertheless, the residual drift is also enlarged.

With the bond-slip behavior of “H” ED bars being accounted for, the fiber-based FE model is capable of capturing seismic behaviors of either a PRC pier or a PPC pier.

With greater lateral strength and mitigated residual drift, precast segmental piers reinforced with the hybrid of high-strength bars and unbonded tendons are recommended in enhancing seismic resilience. It is demonstrated that the ratio of “H” ED bars to unbonded tendons should be optimized to balance the residual drift and the concrete damage zone.

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 research is supported by the National Natural Science Foundation (51778137, 51978161), and Shanghai Engineering Research Center of High Performance Composite Bridges (19DZ2254200).

ORCID iDs

Teng Tong

Zhao Liu

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