Seismic performance of precast hollow bridge piers with different construction details

Abstract

Currently the design scheme of precast hollow concrete bridge piers will be adopted in bridge design in China, but there is no code including specific design details of precast segmental piers in high seismic risk area. For comparative study of seismic performance of the hollow bridge piers which had different design details, six specimens of hollow section bridge pier were designed and tested. The specimens consist of the monolithic cast-in-place concrete bridge pier, precast segmental prestressed pier with cast-in-place joint and precast segmental concrete bridge pier with dry joints. Results show that all specimens have good displacement capacity. The bridge pier with bonded prestressed strands exhibits better energy dissipation capacity and higher strength. The un-bonded prestressed strand bridge pier displays less residual plastic displacement and energy dissipation capacity. The bridge pier with both bonded prestressed strands at the edge of the section and un-bonded in the center of the section not only exhibits more ductility capacity and less residual plastic displacement, but also shows better energy dissipation capacity. Compared with experimental results of prestressed bridge columns, analytical result demonstrates the developed numerical analysis model would provide the reasonable and accurate results.

Keywords

hollow pier / seismic performance / cyclic load / precast concrete / bridge columns

Introduction

The precast segmental construction technology of bridge superstructure and piers has been applied recently to some long sea-crossing bridges, such as Shanghai Yangzi River Bridge, East Sea Bridge, Hangzhou Bay Bridge, Hong Kong-Zhuhai-Macao Bridge, and various urban viaducts in China. Compared with traditional cast-in-place bridge, the use of precast components can accelerate on-site construction operations, because precast segmental construction technology shifts the location of time-consuming tasks to precast factories and allows other construction in sequential order to be performed in parallel. These changes reduce on-site construction time; minimize traffic disruptions, environmental impact and construction noise; improve work zone safety, especially in busy city and with limit operation platform on the sea and bad environment [ 1– 3]. The East Sea Bridge Project in China is a precast box girder bridge extending approximately 20 km, the precast segmental construction technology is adopted in the hollow piers and the large-tonnage monolithic installation method is used in the superstructures [ 4]. These methods make the project complete successfully in schedule. In precast prestressed pier construction, hollow section is usually used instead of solid section to reduce the weight of the segmental pier. With the application of the precast hollow bridge piers in high seismic risk zone, their seismic performance is increasingly concerned by the designers and researchers.

Many researchers have studied on the seismic performance of cast-in-place hollow concrete bridge piers [ 5– 11], while the behavior of precast hollow concrete piers has been less investigated. Arai and Hishiki [ 12] conducted cyclic loading experiment of four rectangle hollow precast pier specimens, in which steel pipes were continuously crossed the joint as the pipe of un-bonded prestressed steel bars. The test result showed that the precast segmental bridge piers had more deformation capacity, less residual plastic displacement and less energy dissipation capacity than reinforced concrete bridge piers. Chang et al. [ 13] tested large-scale rectangular hollow precast bridge piers under cyclic loading, in which the bonded prestressed steel bars were used. The experiment results showed that the bridge pier had good deformation capacity and less residual plastic deformation. Yamashita and Sanders [ 14] carried on the shaking table experiment of post-tensioned un-bonded rectangular hollow bridge piers. The specimen performed very well with essentially no residual plastic displacement and only limited spalling at the base. The joints between the first and the second segments and between the second and the third segments remained closed. All significant behavior occurred at the base of the first segment. To improve the energy dissipation capacity of precast hollow piers, longitudinal mild steel reinforcement crossing the column segment joints were proposed, and could significantly increase the hysteretic energy dissipation of the columns. Large-scale pseudo-static test of un-bounded prestressed rectangular hollow bridge piers were carried out by Ou et al. [ 15– 17], and Wang et al. [ 18]. There were some steel bars crossing the joints for energy dissipation in the test specimens. The result showed that the energy dissipation steel bars could improve the energy dissipation capacity of the bridge pier. With the increase use of the energy dissipation steel bars, the residual plastic deformation increased.

At present in China, the precast segmental bridge piers are one of new applications appealed by bridge engineers. The current codes provide no guidance and specific design details for precast bridge pier system, especially in high seismic zones. Some experimental studies of seismic performance have been carried out on precast solid bridge piers by Wang and Ge [ 19– 20], while very little research has been done on seismic performance of hollow precast segmental bridge piers. The seismic behavior of precast hollow piers is governed by different design details. Therefore, seismic performance of precast hollow piers with different design details needs to be studied through experiments and analysis.

To get an overall understanding about the seismic behavior of precast hollow bridge piers under seismic load, this paper investigated the seismic performance of the hollow cast-in-place reinforced concrete bridge pier, cast-in-place prestressed concrete bridge pier and precast segmental bridge pier through experiments and analysis. The present work is just first step in a broader endeavor to evaluate the seismic performance of precast hollow bridge piers. Their detailed seismic performance in terms of ductility, energy dissipation, self-centering capability and damage mechanisms were compared and analyzed. Then a method modeling the different kinds of bridge piers were presented, the accuracy of the method was calibrated by experiments. Data from the testing and analysis provide valuable insight into the nature of the seismic performance of bridge piers with different connection details.

Experimental procedure

Test scheme

There are some main structural forms of single-column hollow concrete bridge piers in practice. That is monolithic cast-in-place reinforced or prestressed concrete bridge pier, reinforced and prestressed concrete bridge pier with cast-in-place concrete joint at the bottom, segmental prestressed concrete bridge pier with dry joints, etc. To further investigate the seismic performance of the precast hollow concrete bridge piers, five precast hollow pier specimens were tested under constant axial force and cyclically reversed lateral load. A conventional cast-in-place hollow concrete bridge pier was also tested as a reference specimen. The names and types of specimens are shown in Fig. 1.

Specimen design

The hollow pier specimens were designed based on the East Sea Bridge project in China. The scale of the specimens is 1/4. The overall size of column, pile cap and loading end was 360 mm × 500 mm × 1240 mm, 1200 mm× 1200 mm × 500 mm and 600 mm × 600 mm × 360mm respectively, as shown in Fig. 2. The effective height of pier was 1750 mm. To anchor the prestressed strands, there was a 500 × 120 × 1200 mm notch at the bottom of pile cap. The concrete compressive strength was 63.6 MPa. The volume ratio of polymerization fibers in fiber concrete was about 2%. The yield strength of longitudinal reinforcement was 335 MPa. The yield strength of stirrup was 235 MPa. The prestressed strands were high-strength low relaxation strand (7Φ5 steel wires) with diameter of 15.24 mm. The yield strength of prestressed strand was 1670 MPa.

The segmental assembly bridge pier was divided into 3 segments. There was no shear key between the adjacent segments and non-prestressed reinforcement did not continue across the joint. The ratio of axial compression corresponding to dead load and prestress was both 10%. The detailing of reinforcements and prestressed strands is shown in Fig. 2 and Table 1. The parameters of prestressed strands are shown in Table 2.

For the precast bridge pier with cast-in-place concrete joint, the construction of joint is shown in Fig. 3. For the precast segmental pier, the specimen was constructed by match casting and connected by the prestressed strands. The ducts for the bonded prestressed strands in the pier were injected with grout after post-tensioning strands.

Test setup and loading history

The pseudo-static test setup is shown in Figs. 4 and 5, in which the specimen was inverted and mounted to a reaction frame. One actuator at one end was anchored to the reaction frame and provided constant axial load. The pier top was loaded by actuator to apply lateral cyclic loading.

The cyclic loading history is shown in Fig. 6. At the beginning, the lateral displacement level was 2, 3, 5, 7, 10, 15mm respectively. Then the lateral displacement was applied to top of pier with increments of 5mm. Each displacement level was repeated three times to measure the strength degradation behavior of the specimens. All the specimens were tested to failure. Failure of specimens was generally marked by the strength decreases to 85% of specimen maximum value. Each test specimen was instrumented with load cells, displacement transducers, and strain gauges to monitor displacement and corresponding load as well as strains and relative deformations.

Test results

Observed damage of specimens

Figure 7 and Fig. 8 show the visual observation on the damages and mode of failures of the test specimens, it is known that there are two main damage modes for bridge pier. The one is the damage happened at the bottom end of the piers, such as, cast-in-place pier with full-length reinforcements S1 and precast segmental specimen with cast-in-place concrete joint at the bottom of pier S2, S3 and S4, The other is the damage near segmental joint. It was mainly for segmental specimen S5 and S6 with no reinforcements cross the joint. The damages of each type of pier are described as follows.

Cast-in-place pier specimen and precast specimen with cast-in-place concrete joint

For specimen S1, at early stages of loading, several horizontal flexural cracks were found on the surface perpendicular to the loading direction in the region close to the bottom of the piers. As the applied lateral displacement increased, the horizontal cracks gradually became inclined and propagated to the neutral axis of the piers after yielding of longitudinal reinforcement due to the influence of shear. Concrete spalling at the corner and concrete crushing in plastic hinge region became severe at 3.1% drift. After that, cyclical effect led to gradual degradation in the strength, the buckling and fracture of the longitudinal reinforcement and the concrete cover spalling and crushing over a length of 0.5D above the pier bottom were found at the drift of 3.7%.

The specimen S2, S3 and S4 also showed the flexural damage mode in the plastic hinge region, which was similar to that of the specimen S1. The loading drift corresponding to damage phenomenon was shown in Table3. The damage photos of four specimens at the end of the test were shown in Fig. 7.

Precast segmental specimens

For specimen S5 and S6, no flexural cracks were observed on the pier at little displacement. The joint opening between foundation and the first segment was observed as the applied lateral displacement increased, like the rocking structure shown in Fig. 9(a). During the test, opening at the second joint between the pier segments near the cap was also observed. The cover concrete of the end segment cracked vertically and appeared a certain degree of spalling near the footing. The cover concrete spalling did not appear around the joints of other segments. Because no shear keys at the joint, slight sliding was observed between the segments. When the drift reached to 3.1% and 4.3% for specimen S5 and S6 respectively, the flexural strength of specimens were reduced significantly. The spalling and crushing of cover concrete and joint opening of the hollow precast segmental specimens were shown in Fig. 8.

The rocking phenomenon

From the damage process above, the precast segmental specimen will rock in the connection region, as shown in Fig. 9(a). For capturing the opening and closing of the joint, and the top drift of the specimen, an analytical model is put forward as Fig. 9(b). But the formula to calculate the value of parameter c should be raised first from experiment.

The open width δ and the opening depth c of the joint at the bottom of the pier with the lateral displacement increased are shown in Fig. 10. It is known that the open width δ of joint is become bigger and in a linear trend with the displacement increasing, especially that of the specimen S5 (Fig. 10(a)). The open width is found to be nearly proportional to drift of the segment. Equation (1) developed through a linear regression analysis is found to best predict the relation of the open width δ, the drift of the column and the width of section. In the moment-curvature analysis, the contact length c is of concern. And the parameter c/B is defined as the remaining ratio between the contact area and that of the whole rectangular section. Figure 10(b) shows the relationship between the parameter c/B and drift. The contact length c of joint is not change synchronously with the lateral displacement increased. At the beginning of loading, the contact length c of joint increases abruptly, then changes slowly when the local concrete crush observed at the joint. Hence, Eq. (2) can be used to calculate the remaining contact length for rectangular section rocking column. It is also a simplified formula to model the joint of rocking column using the fiber finite element method, as shown in Fig. 9 (b). If the length of the elastic beam element is (B-2c)/2, instead B/2, the calculated opening width δ will be close to the real value.

(1) \delta =\mathrm{0.85}{\displaystyle \frac{{\mathrm{\Delta }}_{\mathrm{t}\mathrm{o}\mathrm{p}}B}{H}},

(2) c=\mathrm{0.2}B.

Load-displacement hysteretic curves

The hysteretic curve of six specimens under the cyclic loading are shown in Fig. 11. The curves showed that there are two types of the load-displacement hysteretic curve corresponding to different design details. The one type is for pier with full-length reinforcement, the other is for precast segmental pier without reinforcements cross the segmental joints.

Cast-in-place pier specimen and precast specimen with cast-in-place concrete joint

The shape of the hysteretic loops for specimen S1 (Fig. 11(a)) and specimen S2 (Fig. 11(b)) were spindle at the beginning, then bow, quadrangle at last. The plump hysteretic loop showed the energy dissipation capacity was stronger. The prestressed specimens S3 and S4 had higher post-yield stiffness, ultimate strength and narrower hysteretic curves. Due to the existing of axial prestress, the recentering characteristic of the precast system was observed from the hysteretic curves, i.e., less residual plastic displacement than that of RC specimens S1 and S2. Comparing to the bonded prestressed concrete specimen S3 (Fig. 11(c)), it was found that the ultimate strength of the hybrid prestressed concrete specimen S4 (Fig. 11(d)) was lower, but the residual displacement was also less. It was confirmed that the unbonded prestressed strands tended to strengthen their origin-oriented behavior of hyesteretic curve during unloading.

Segmental specimen

The clear difference between the hysteresis loops shape of the S3,S4 and S5, S6 underlined the difference between the two mechanisms of deformation. The shape of the hysteretic loops of the segmental pier was flag. Due to the existing of prestessed strands, good re-centering capacity of the precast segmental pier was also observed from the hysteresis loops.

Comparing the hysteretic loop of specimen S5 (Fig. 11(e)) with specimen S6 (Fig. 11(f)), the hysteretic loop of specimen S5 was in spindle shape at the beginning, then developing to bowl shape, at last to narrow flag shape with a little slip. The hysteretic loop was not plump and the residual plastic displacement was very little. The hysteretic loop of specimen S6 was developing quickly from spindle shape at the beginning to narrow flag shape. With the loading, the area of hysteretic loop was increases slowly but it was still not plump. The hysteretic loop gradually revolved clockwise around the origin, which made the residual plastic displacement in an increasing trend.

Discussion of test results

The key parameters of six specimens, such as envelope of cyclic load-displacement curve, ductility factor, energy dissipation capacity, residual plastic displacement are described in the followings.

Envelope of cyclic load-displacement curves characters

For each test specimen, the peak load in each loading direction at every drift ratio level is plotted against the corresponding displacement values to obtain the envelop curves as shown in the Fig. 12. As for the specimens with longitudinal continuous reinforcement in the pier (S1~S4), the envelope curves shows that the strength of specimen vary in the rising at first, then, short steady and degradation stage at last. Due to the detail of cast-in-place concrete joint, the peak strength of specimen S2 is higher than specimen S1. The added prestressed strands make the peak strengths of specimen S3 and S4 higher than that of specimen S2, and moreover, the layout of setting the prestressed strands at the edge of section is more efficiently to improve the ultimate strength.

The envelope curves of the segmental specimens S5 and S6 shows relatively longer strength platform after reaching its ultimate load. Compared with the specimens S1 to S4, the strength of the unbonded prestressed segmental pier is lower, but the displacement capacity is larger. The layout of setting the prestressed strands at the edge of section could delay the degradation of strength after reaching the maximum strength.

The yield force, idealized yield displacement, peak force, ultimate lateral force, ultimate displacement and ductility of envelope curves of specimens are listed in Table 4. The displacement ductility μ_m is defined by the formula below:

(3) {\mu }_m={\displaystyle \frac{U_m}{U_y}}.

By using the load-displacement curve in Fig. 13, the idealized yield displacement U_y is defined as the displacement of the intersection point of the following two lines: the straight line that passes through the origin and B of the envelope curve, and the straight line that passes through P_max on the envelope curve and is parallel to the x-axis. The ultimate displacement U_m is defined as the displacement that occurs when the strength of the descending branch of the load-displacement envelope curve becomes less than 0.85P_max, as shown in the Fig. 13.

The result shows that the ductility of reinforced concrete pier S1 and S2 is better than that of the prestressed reinforced concrete pier S3 and S4. The ductility of the hybrid prestressed reinforced concrete pier S4 is better than that of the bonded prestreesed reinforced concrete pier S3. The unbonded prestressed segment pier has obvious advantage in the displacement ductility.

Energy dissipation capacity

The amount of cumulative dissipation energy E_AD in Table 5 is the sum of the dissipation energy \mathrm{\Delta }{W}_i of each load cycle which could be calculated according to the hysteresis loop in Fig. 11. Figure 14 shows the cumulative energy dissipation capacity of the six specimens. The result shows that, after concrete spalling was observed, the energy dissipation capacity of specimens shows significant increased. Moreover, at the same displacement level, energy dissipation capacity of the monolithtic piers S1 to S4 is larger than the precast segmental piers S5 and S6. The precast segmental prestressed pier S5 and S6 shows the limited energy dissipation capacity due to the damage only focus on joints resulting narrow hysteretic loops. The prestressed reinforced concrete piers S3 and S4 are higher than reinforced concrete piers S1 and S2. Comparing to the specimen S3, the energy dissipation capacity of specimen S4 reduces by 9%. The specimen S6 with the prestressed strands at the edge of section is higher than specimen S5 with the prestressed strands in the center of section.

Figure 15 shows the equivalent viscous damping of six specimens. For the monolithtic specimen and precast specimen with the cast-in-place concrete joint, the equivalent viscous damping coefficient is in a growing trend with the lateral displacement increased. The specimen S1 and S2 shows the higher equivalent viscous damping ratio. The minimum value of the equivalent viscous damping coefficient of specimen S1 is 0.07 and its ratio of the maximum and minimum values is 2.77 as shown in Table 6. The equivalent viscous damping coefficient of specimen S4 with hybrid prestressed strands is only 5% smaller than specimen S3. For the segmental specimen S5 and S6, the equivalent viscous damping coefficient is smaller and its changing trend is plain. The equivalent viscous damping ration of specimen S3 and S4 is close to S1 and S2. Based on the discussion above, the energy dissipation capacity of specimen with boned prestressed strands at the edge of section and the hybrid prestressed layout maybe is better for precast segmental bridge pier.

Residual plastic displacement

Small residual displacement of bridge piers can provide good serviceability after a large earthquake. So the residual displacement index is a more important factor for the seismic performance of bridge piers. The relation between residual plastic displacement and drift of six specimens is shown in Fig. 16. The maxmum top drift of the six specimens up to 3.71%, the maximum residual plastic drift of specimen S1 and S2 are around 2.1%–2.6%; Specimen S3 and S4 have a maximum residual plastic dift of 1.09%–1.2%, slightly less than S1 and S2; Precast segmental piers S5 and S6 have a maximum residual plastic dift of 0.17%–0.57%, which is significantly less than the other specimens. These showed that The residual plastic dift of the conventional reinforced concrete specimen is larger than precast prestressed specimens. The unbonded prestressed strands set in the center of the section can more effectively reduce the residual plastic displacement.

Numerical analysis model

In the study, a numerical analysis model approach of prestressing bridge column systems (CIP or precast segment construction) was developed to capture physical characteristics and seismic performance based on theory of elasto-plastic fiber beam-column element. These characteristics include crushing of extreme concrete fibers, yielding of PT tendons which across the segment joints (unbonded and bonded), physical characteristics of the segment-to-segment joints, and energy dissipation et al. The analytical model consists of segment of column, prestressing tendon and joint between segments. The detailed finite element model of prestressing bridge column has been created using the computer software OpenSees. Segment of column is modeled by fiber beam-column elements with nonlinear constitutive models of the concrete and reinforcement steel. The “concrete02” with tensile capacity was used to model the concrete material. Mander’s model was used to define the properties of the confined concrete. The bi-linear steel material “Steel02” was used to model the einforcements. The initial modulus of elasticity of 2 × 10⁵ MPa was assumed up to the yielding stress. The strain hardening slope was defined as 0.2% of the initial modulus of elasticity. The “uniaxialMaterial ElasticPP” was used to model the post-tensioning rod constitutive relationship. An initial strain corresponding to the initial force in the rod was specified. Unbonded and bonded prestressing tendon is modeled with different ways. Unbonded prestressed tendons was modeled by ‘tension-only’ bilinear truss elements, each node of the truss is laterally constrained to the corresponding segmental column element node. Bonded prestressing tendons are modeled as fibers of beam-column element with uniaxial hysteretic material models. No bond-slip of the bonded tendon is considered. Joint model is used to simulate physical characteristics of the segment-to-segment joints. It consists of a group of zero-length element with “compression-only” nonlinear hysteretic spring element representing concrete damage expected at the segmental joints and gap element modeling opening and closing of segment joint, see Fig. 17(a). Zero-length nonlinear elements are distributed from the edge of section to the distance of c (in Fig. 9) along the crossection, and gap elements are placed in the point from the edge distance of c along the cross section. No sliding is considered at the segment-to-segment joints.

Figure 17(b) shows the analytical models of six specimens based on the proposed model approach. The support footing is modeled as rigid beam element. Nonlinear fiber beam-column element is used to simulate column segment. Bonded tendons are modeled as fibers of section with the prestressing tendon material. Unbonded tendons is modeled by truss elements with an initial strain representing the prestressing force and restrained to the segmental column only at the anchor points on each end of the unit. The column axial force is applied to the top of the columns representing the dead load and service load of superstructure.

To check the accurency of the developed numerical analysis model, the analytical model must be calibrated by experiments. The developed analytical model is employed to simulate six specimens under cyclic loading. The joints, bonded and unbonded prestressing tendons and concrete segment are simulated with method mentioned above. Cyclic lateral load analyses are performed. The analytical force-displacement curves of specimens are compared with experimental results, as shown in Fig. 11.

Figure 11(a) presents a comparison of the analytical lateral force-displacement result with the experimental result of conventional concrete column S1, it shows that the developed analytical model can be used to simulate key characteristics of reinforced concrete bridge piers reasonably. Therefore, it ensures that the analytical model can capture material nonlinear characteristics of the concrete segment.

Figure 11(b), (c) and (d) show the comparison between the analytical results of unbonded, bonded prestressing CIP column and test results, the backbone curve and energy dissipation match the experimental results for both small and large displacements. This illustrates the developed analytical model can effectively present the mechanical property of unbonded and bonded prestressing tendons of CIP column.

For precast segmental bridge columns, behavior of segmental joints is emulated with mentioned joint model above. Eight zero-length nonlinear elements with “compression-only” nonlinear hysteretic springs allowing for concrete crush at the segmental joints are placed symmetrically at the edges of the cross-section and two gap elements are placed in the distance of c from the edge of cross section.

Figure 11(e) and (f) show the analytical force-displacement curves of precast segmental prestressing bridge columns. Comparing the test result of S5 and S6, the backbone curve, yield displacement and energy dissipation match the experimental results reasonably. However, the comparison also indicates that the residual plastic displacements of analytical simulation are smaller than experimental results.

Based on the comparison between analytical and experimental results of specimens, see Fig. 11, the calculated results of developed modeling approach are in good agreement with test results.

Conclusion

Some experimental studies of seismic performance have been carried out on precast solid bridge piers, while few work has been done on seismic performance of hollow precast segmental bridge piers. Six hollow section bridge pier specimens were tested using quasi-static test and the analytical research were done using the fiber beam-column element method. The following conclusions and findings are drawn on the basis of the results of this investigation:

1) Within the limited test specimens presented in this paper, the precast pier with cast-in-place concrete joint between the pier and the foundation with continuous reinforcements and prestressed strands, could emulate the seismic performance of current cast-in-place systems and can be used in seismic high risk areas.

2) It is found that the precast hollow piers show excellent displacement capacities. According to the seismic performance, there are two types of the bridge pier specimens. For monolithtic cast-in-place bridge pier and precast pier with cast-in-place concrete joint between the pier and the foundation with continuous reinforcements, the damage mode is flexural damage in the plastic hinge region. For precast segmental bridge pier with no continuous reinforcements crossing the joint, the damage mode is joint opening and closing.

3) Compared with reinforced concrete bridge pier, the prestressed strands can improve the strength and reduce the residual plastic displacement, because the bonded prestressed strands could increase energy dissipation capacity and the unbonded presressed strands play an important role on reducing the residual plastic displacement. The hybrid prestressed strands make the pier achieve better seismic performance, not only on reducing the residual plastic displacement but also on increasing the energy dissipation capacity.

4) For the precast segmental specimens, the seismic behaviors are mainly dominated by the opening of joints, slightly sliding between segments and cover concrete spalling and confined concrete crushed near footing. The segmental piers have less residual plastic displacement, which is beneficial to structure serviceability after earthquake. For the effect of the prestressed layout, the un-bonded prestressed strand in the center of the section is beneficial to reducing residual plastic displacement and bonded prestressed strands at the edge of section is beneficial to energy dissipation capacity and strength.

5) The numerical models which can be easily carried out in the structural analysis software for seismic response of the prestressing bridge columns is developed. Segmental joints are modeled by a group of parallel zero-length element with ‘compression-only’ nonlinear hysteretic springs representing concrete damage expected at the segmental joints and gap element simulating mechanical characteristics of the segment-to-segment joint.

6) Compared with experimental results of prestressing bridge columns, analytical simulation demonstrates that the developed numerical analysis model provides the reasonable accuracy.

7) Some key parameters of the developed numerical model need further to be calibrated by more experiments of prestressing bridge columns to improve its accuracy and suitability, especially on predicting residual plastic displacement. Moreover, sliding at the segment-to-segment joints and bond slip of the bonded tendons need be considered in the next phrase.

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