Research on seismic performance of high-speed railway segmental assembled round-end hollow pier with energy dissipation bar

2.1. Experimental results

Based on a standard precast assembled pier from the Yinchuan-Lanzhou High-speed Railway as a structural reference, a 1:5 large-scale test model was devised and finalized. The test specimen consisted of a segmentally assembled prestressed concrete (PSC) round-end hollow pier, as shown in Fig. 1. The test model stood at an effective height of 2800 mm, with a wall thickness of 140 mm, and an outer wall dimension of 1240 mm × 600 mm. The concrete was de-signed with a strength grade of C40. Longitudinal reinforcement consisted of HRB400 bars with a diameter of 12 mm, with 18 bars arranged in both the inner and outer rings. HPB400 bars with diameters of 8 mm and 6 mm were utilized as stirrups and lacing bars, correspondingly. The key design specifications of the model are detailed in Table 1.

Fig. 1Segmental assembled round-end hollow pier (unit: mm)

Fig. 2Test model and results. Note: Photograph of the quasi-static test of a precast segmental column, taken by Hao Li in August 2020 at the Structural Testing Laboratory of Yantai University

The test specimen underwent loading under displacement control. To identify the initial yield point of the pier, a minor change in displacement was applied during the early loading stage. Once the strain of the longitudinal reinforcement at the base of the pier reached 2000, the current loading displacement marked the initial yield point of the pier. Concurrently, the horizontal resistance at the pier's peak denoted the initial yield force. Subsequent to the pier yielding, the displacement changes during loading intensified. At a specific displacement amplitude, when the pier’s horizontal resistance reduced to below 80 % of its maximum, the corresponding displacement was deemed the ultimate dis-placement of the pier. Simultaneously, the horizontal resistance at the top of the pier at this juncture represented the ultimate bearing force. The findings of the pseudo-static test are depicted in Fig. 2.

2.2. Finite element model development

Based on the experimental model, a fiber-based finite element model of the PSC specimen was established in OpenSees, as shown in Fig. 3. Both the cover and core concretes were modeled with the Concrete01 material, while the reinforcing bars and prestressing tendons were represented using the Steel02 material. Prestressing tendons were simulated with truss elements, with their top nodes rigidly connected to the pier model and the bottom nodes fixed. Bonded energy dissipation bars were discretized at the corresponding locations within the fiber section, whereas unbonded energy dissipation bars were modeled using truss elements with fixed bottom constraints.

Fig. 3Finite element modeling method for the segmental assembled round-end hollow pier

To accurately capture the contact behavior between segments, the bottom joint was simulated using compression-only springs with the ENT (Elastic-No Tension) material. The remaining hollow joints were modeled with zero-length section elements using the same ENT material, with fiber layouts consistent with those of the adjacent sections.

Nonlinear analysis was performed using the Krylov-Newton algorithm, and the displacement increment norm (NormDispIncr) was adopted as the convergence criterion to ensure computational accuracy and stability.

For fiber section discretization, 544 fibers were assigned to the solid segment and 356 fibers to the hollow segment. Previous studies indicate that numerical accuracy is sufficient when the number of fibers exceeds 200; therefore, the adopted discretization meets the requirements for reliable numerical analysis.

2.3. Model validation

The finite element software OpenSees was utilized to analyze the hysteresis behavior of the pier model, and the numerical simulation results were subsequently compared with the experimental findings.

Fig. 4Hysteresis curve

Fig. 5Skeleton curve

The comparison between the numerical simulation and experimental results is presented in Figs. 4-6. The maximum horizontal resistance at the pier top obtained from the numerical simulation is 143.4 kN, while the experimental value is 137.8 kN, corresponding to an error of 4.1 %. The cumulative energy dissipation is 82725.9 kN⋅mm in the simulation and 84086.7 kN⋅mm in the experiment, resulting in an error of 1.6 %.

Overall, the numerical and experimental results show good agreement in terms of the hysteretic response, skeleton curve, and energy dissipation capacity. Small differences exist due to modeling assumptions, material idealization, and experimental uncertainties; however, these discrepancies remain within an acceptable range and satisfy the requirements for engineering reference. The results indicate that the nonlinear finite element model can reliably capture the mechanical behavior of the segmentally assembled round-end hollow pier.

Fig. 6Energy dissipation

3.1. Effect of energy dissipation bar diameter

The diameter of the energy dissipation bar is a crucial design parameter that impacts the seismic performance of segmental assembled piers. It directly influences the energy dissipation capacity of each bar. This section explores the effect of the energy dissipation bar diameter on the seismic performance indicators of segmental assembled piers. The diameter range studied was set at 10-35 mm with a 5 mm increment. Table 2 illustrates the changes in the diameter of the energy dissipation bar, while the quantity and layout of the energy dissipation bar are depicted in Fig. 7.

Fig. 7Energy dissipation bar arrangement (unit: mm)

The numerical models for the piers were developed using the corrected numerical modeling method mentioned earlier. Subsequently, a hysteretic analysis was conducted, with the displacement loading system matching that of the test. The findings of the calculations are illustrated in Fig. 7.

Based on the examination of Fig. 8(a) and (b), as the diameter of the energy dissipation bar increases, the bearing capacity of each energy dissipation bar and the horizontal resistance of the segmental assembled pier show a continuous increase. The maximum horizontal resistance of PSCE1 is 96.2 kN, while for PSCE6, it reaches 196.8 kN, resulting in a horizontal resistance that is 2.05 times higher than the original value.

Fig. 8Impact of energy dissipation bar diameter on hysteretic behavior of bridge piers

a) Hysteresis curve

b) Skeleton curve

c) Residual displacement

d) Loading stiffness

e) Unloading stiffness

f) Hysteretic energy dissipation

The analysis of Fig. 8(c) reveals that as the segmental assembled pier oscillates, the energy dissipation bar undergoes collaborative deformation. As the diameter of the energy dissipation bar increases, the plastic deformation of each energy dissipation bar also increases, leading to a rise in the residual deformation of the segmental assembled pier following the reciprocating motion. This effect is more pronounced with larger loading displacements, as the greater the displacement amplitude, the deeper the energy dissipation bar enters the plastic state, resulting in a larger residual deformation post reciprocating motion. Consequently, during the later stages of the loading process, the variation in residual deformation becomes more apparent among segmental assembled piers with energy dissipation bars of different diameters. The maximum residual displacement is 1.38 mm for PSCE1, 46.83 mm for PSCE6, with the latter experiencing a residual displacement 33.93 times that of the original displacement. Notably, for PSCE5, a loading displacement amplitude of 140 mm causes the residual displacement angle to exceed 1 %; while for PSCE6, at 126 mm loading displacement amplitude, the residual displacement angle also surpasses 1 %, further escalating to over 1.75 % at a loading displacement amplitude of 140 mm.

Based on the analysis of Fig. 8(d) and (e), it is observed that as the diameter of the energy dissipation bar increases, the force required for unit deformation of each energy dissipation bar also increases. This, in turn, leads to a rise in the loading stiffness and un-loading stiffness of the segmental assembled pier. Specifically, the maximum loading stiffness of PSCE1 is 4.8 kN/mm, while that of PSCE6 is 14.26 kN/mm, representing 2.97 times increase from the original value. Similarly, the maximum unloading stiffness of PSCE1 is 5.02 kN/mm, and for PSCE6, it is 14.27 kN/mm, indicating 2.84 times increase from the original stiffness.

The analysis of Fig. 8(f) indicates that as the diameter of the energy dissipation bar increases, the energy dissipation capacity of each bar also rises, consequently enhancing the overall energy dissipation capability of segmental assembled piers. Moreover, as the loading displacement amplitude increases, the penetration of each energy dissipation bar into the plastic state deepens, leading to a more effective energy dissipation performance. The maximum energy dissipation for a single cycle of PSCE1 is 4689.36 kN⋅mm, while for PSCE6, it reaches 31351.15 kN⋅mm. This represents a significant increase, with the maximum energy dissipation for a single cycle being 6.69 times greater than the original value.

3.2. Effect of energy dissipation bar quantity

When determining the diameter of the energy dissipation bar, the energy dissipation capacity level of each bar is established. The total energy dissipation capacity level of the bars is influenced by the quantity of energy dissipation bars utilized. As a result, the quantity of energy dissipation bars plays a crucial role in determining the seismic performance of the segmental assembled pier. Designers must carefully choose the quantity of energy dissipation bars to ensure that the segmental assembled pier can meet the desired seismic performance standards. This study aims to investigate how the quantity of energy dissipation bars impacts the seismic performance indicators of segmental assembled piers. The range of variation for the quantity of energy dissipation bars was set between 2 and 12, with an increment of 2, as outlined in Table 3. The diameter of the energy dissipation bar was established at 25 mm, with the detailed arrangement shown in Fig. 9.

Fig. 9Arrangement of energy dissipation bars of varying quantities (unit: mm)

The hysteresis analysis of the numerical models using OpenSees was performed, and the findings are illustrated in Fig. 10.

Based on the examination of Fig. 10(a) and (b), incorporating additional energy dissipation bars resulted in an increase in the overall bearing capacity of these bars. Consequently, this enhancement indirectly elevated the horizontal bearing capacity of the segmental assembled piers. The PSCE7 exhibited a maximum horizontal resistance of 101.27 kN, while the PSCE12 displayed 171.74 kN. Notably, the horizontal reaction was amplified to 1.70 times its original value.

Fig. 10Influence of the quantity of energy dissipation bar on the hysteretic behavior of the pier

a) Hysteresis curve

b) Skeleton curve

c) Residual displacement

d) Loading stiffness

e) Unloading stiffness

f) Hysteretic energy dissipation

The analysis of Fig. 10(c) reveals that as the number of energy dissipation bars increases, the total residual displacement of the energy dissipation bar post-reciprocation also increases. This subsequently elevates the residual displacement of the segmental assembled pier after an earthquake. Additionally, with a higher loading displacement amplitude, the difference in residual displacement among models with varying numbers of energy dissipation bars becomes more pronounced. This is primarily due to the increased loading displacement amplitude intensifying the plastic state penetration of each energy dissipation bar. Specifically, the maximum residual displacement is 1.55 mm for PSCE7 and significantly higher at 33.21 mm for PSCE12, representing a 21.43-fold increase from the original displacement. Notably, when the loading displacement amplitude reaches 140 mm for PSCE12, the residual displacement angle surpasses 1 %.

Moreover, the analysis depicted in Fig. 10(d) and (e) illustrates that as the number of energy dissipation bars rises, the total thrust stiffness of these bars increases, consequently enhancing the loading and unloading stiffness of segmental assembled piers. The highest loading stiffness is recorded at 5.17 kN/mm for PSCE7 and notably higher at 12.14 kN/mm for PSCE12, representing a 2.35-fold increase from the original stiffness. Similarly, the maximum unloading stiffness reaches 5.57 kN/mm for PSCE7 and 12.13 kN/mm for PSCE12, indicating a 2.18-fold increase from the initial stiffness value.

Based on the analysis presented in Fig. 10(f), the overall energy dissipation capacity of the energy dissipation bar increases as the quantity of energy dissipation bars rises. This enhancement indirectly boosts the seismic energy dissipation capability of segmental assembled piers. As the loading displacement amplitude increases, each energy dissipation bar's tendency to reach a plastic state intensifies. Furthermore, the variation in the number of energy dissipation bars significantly influences the total seismic energy dissipation level of segmental assembled piers. Specifically, the maximum dissipation energy for a single cycle of PSCE7 is recorded at 6294.88 kN⋅mm, while for PSCE12, it reaches 24411.12 kN⋅mm. Consequently, the maximum dissipation energy for a single cycle increases to 3.88 times the original value.

3.3. Effect of energy dissipation bar arrangement

Once the diameter of the energy dissipation bar is established, its energy dissipation capacity becomes fixed. Likewise, determining the quantity of energy dissipation bars sets the number available for providing energy dissipation. The arrangement of these bars plays a crucial role in the overall energy dissipation and vibration absorption capabilities, consequently influencing the seismic performance of the segmented assembled pier.

In this section, the energy dissipation bars are evenly distributed along the longitudinal direction of the bridge, with 4 bars on each side. The spacing between the energy dissipation bars on either side ranges from 80 mm to 280 mm, with a variation of 40 mm, as illustrated in Fig. 11. The diameter of the energy dissipation bars is set at 25 mm, with a total of 8 bars determined for installation.

Pier modeling and calculation analysis were conducted using OpenSees, with the outcomes shown in Fig. 12.

Analyzing Fig. 12(a) and (b) reveals that altering the arrangement of the energy dissipation bar impacts both the duration and extent of the energy dissipation bar’s deformation, consequently influencing the lateral resistance of segmental assembled piers. The maximum lateral resistance of PSCE13 is 143.09 kN, while that of PSCE18 is 146.54 kN, resulting in 1.02 times increase from the original value. It is evident that a greater spacing between the energy dissipation bars on each side leads to a higher lateral resistance of the segmental assembled pier. Despite some enhancement, the magnitude of the increase is relatively modest.

Based on the analysis of Fig. 12(c), as the segmental assembled pier undergoes reciprocal movement, the energy dissipation bar deforms accordingly. The reconfiguration of the energy dissipation bar impacts both the timing and extent of its plastic deformation, subsequently influencing the residual displacement of the segmental assembled piers post motion. Notably, the maximum residual displacement is 5.60 mm for PSCE13 and 10.79 mm for PSCE18, showing an increase by a factor of 1.93. However, it is important to highlight that the residual displacement angles of all six numerical models remain within acceptable limits.

Fig. 11Change of arrangement of energy dissipation bar (unit: mm)

Fig. 12Impact of energy dissipation bar arrangement on hysteretic performance of pier

a) Hysteresis curve

b) Skeleton curve

c) Residual displacement

d) Loading stiffness

e) Unloading stiffness

f) Hysteretic energy dissipation

Based on the analysis of Fig. 12(d) and (e), it was found that the maximum loading stiffness of PSCE13 is 4.25 kN/mm, while that of PSCE18 is 10.89 kN/mm. The loading stiffness increased by 2.56 times compared to the original values. In terms of the maximum unloading stiffness, PSCE13 measures at 4.23 kN/mm, and PSCE18 at 11.91 kN/mm. The unloading stiffness increased to 2.82 times of the original values. Nevertheless, as the loading displacement progresses, the loading and unloading stiffness of each numerical model converge due to the consistent lateral stiffness of each energy dissipation bar and the constant total number of energy dissipation bars.

Based on the findings presented in Fig. 12(f), it is evident that the maximum dissipation energy for a single-cycle of PSCE13 is 11600.32 kN·mm, whereas for PSCE18, it amounts to 20138.74 kN·mm. The separation between the energy dissipation bars on either side ranges from 80-280mm, resulting in the maximum dissipation energy for a single-cycle increasing to 1.74 times its original value.

4.1. Selection of earthquake ground motions

Ten far-field earthquake motions, ten near-field earthquake motions without a pulse, and ten near-field earthquake motions with a pulse were chosen from the PEER database, as outlined in Table 4. Subsequently, the corresponding earthquake motion response spectrum was generated and illustrated in Fig. 13. The far-field earthquake motions originate from fault distances exceeding 30 km, while near-field earthquake motions without a pulse stem from fault distances less than 20 km. On the other hand, near-field earthquake motions with a pulse also come from fault distances less than 20 km, exhibiting a distinct velocity pulse lasting more than 1 second. To analyze the seismic response of the pier to various earthquake intensities, all motions were initially normalized. Following this, the peak acceleration of each earthquake motion was adjusted to 0.2 g, 0.4 g, 0.6 g, 0.8 g, and 1.0 g before being applied to the pier model for computation.

Fig. 13Acceleration response spectrum

4.2. Comparative analysis of vibration absorption performance

For example, consider the calculation results of a pier subjected to RSN269 (PGA is 0.4 g) and RSN180 earthquake motion (PGA is 1.0 g) as shown in Fig. 14.

Analysis of Fig. 14(a) shows that during the RSN269 earthquake motion, the pier top of PSCE4 exhibits a vibration absorption rate of 68 % for maximum displacement response, with residual displacement only at 1/7 of PSC. These findings suggest that the energy dissipation bar effectively mitigates the pier top’s displacement response. There is no significant plastic deformation or damage to the energy dissipation bar under earthquake conditions. It also indicates a certain level of elastic resilience, resulting in a smaller residual displacement for PSCE4 compared to PSC post-earthquake.

In Fig. 14(b) analysis, under the RSN180 earthquake motion, the maximum displacement response vibration absorption rate of the pier top of PSCE4 is 67 %, yet the residual displacement is notably greater than that of PSC. This indicates that while the energy dissipation bar notably reduces the pier top’s displacement response, it undergoes substantial plastic deformation or failure during the earthquake motion. Consequently, this leads to a significantly larger residual displacement for PSCE4 compared to PSC post-earthquake.

Fig. 14Comparative analysis of seismic response of bridge piers

a) RSN269

b) RSN180

Furthermore, to investigate how various types of earthquake motion affect the vibration absorption capability of energy dissipation bars, the discrepancies in the average maximum displacement response and residual displacement of the pier's top after an earthquake were compared across three different types of earthquake motions, as illustrated in Fig. 15.

Fig. 15Comparison of the average seismic response values of piers subjected to various types of earthquake motions

a) Mean value of maximum displacement at the top of the pier

b) Mean value of residual displacement at the top of the pier

According to the analysis presented in Fig. 15(a), when subjected to seismic activity, the maximum displacement at the top of the pier for PSCE4 is notably lower than PSC. The efficiency of vibration absorption becomes more pronounced as the Peak Ground Acceleration (PGA) increases. For instance, during a 1.0 g near-field pulse earthquake, the energy dissipation bar exhibits a 68 % absorption rate due to the significant swing of the pier under intense seismic conditions. The plastic deformation of the energy dissipation bar aids in dissipating the seismic energy input to the pier. Moreover, the proximity of the earthquake's epicenter amplifies the maximum displacement at the pier top, with the near-field pulse earthquake causing the greatest displacement compared to other types of seismic motions. The disparity in displacement becomes more significant with higher PGAs. For instance, in the case of PSC, at 0.2 g, there is a 0.68 mm variation in maximum displacement, while at 1.0 g, this difference increases to 3.56 mm.

Based on the analysis presented in Fig. 15(b), as the peak ground acceleration (PGA) continues to rise, the average residual displacement of PSCE4 surpasses that of PSC. This trend is observed across various seismic scenarios, including near-field seismic events with pulse (0.4 g-1.0 g) and without pulse (1.0 g), as well as far-field seismic events (0.6 g-1.0 g). This observation can be attributed to the behavior of the energy dissipation bar. In the presence of minor seismic activities, the energy dissipation bar predominantly maintains its elasticity, thereby mitigating displacement responses at the pier's apex and offering elastic resilience to the structure. Conversely, during intense seismic events, substantial plastic deformation of the energy dissipation bar indirectly contributes to increased residual deformation in the pier post-earthquake. Furthermore, it is noted that the average residual displacement of piers subjected to near-field seismic motions exceeds that of those under far-field motions, with a more pronounced effect as PGA values escalate.