Seismic Performance of Tall-Pier Girder Bridge with Novel Transverse Steel Dampers Under Near-Fault Ground Motions

Abstract

This study develops a novel transverse steel damper (TSD) to enhance the seismic performance of tall-pier girder bridges, featuring superior lateral strength and energy dissipation capacity. The TSD’s design and arrangement are presented, with its hysteretic behavior simulated in ABAQUS. Key parameters (yield strength: 3000 kN; initial gap: 100 mm; post-yield stiffness ratio: 15%) are optimized through seismic analysis under near-fault ground motions, incorporating pulse characteristic investigations. The optimized TSD effectively reduces bearing displacements and results in smaller pier top displacements and internal forces compared to the bridge with fixed bearings. Due to the higher-order mode effects, there is no direct correlation between top displacements and bottom internal forces. As pier height decreases, the S-shaped shear force and bending moment envelopes gradually become linear, reflecting the reduced influence of these modes. Medium- to long-period pulse-like motions amplify seismic responses due to resonance (pulse period ≈ fundamental period) or susceptibility to large low-frequency spectral values. Higher-order mode effects on bending moments and shear forces intensify under prominent high-frequency components. However, the main velocity pulse typically masks the influence of high-order modes by the overwhelming seismic responses due to large spectral values at medium to long periods.

1. Introduction

In recent years, numerous highway bridges have been constructed across Western China, with many piers exceeding 40 m and some even surpassing 100 m [1]. Due to their ability to span wide canyons and steep terrain, tall-pier girder bridges have been widely used in mountainous regions [2]. However, these bridges are often near active faults and face severe challenges from near-fault pulse-like ground motions [3]. Earthquakes such as the 2008 Wenchuan M8.0 [4], 2010 Yushu M7.1 [5], 2013 Lushan M7.0 [6], and 2017 Jiuzhaigou [7] events have revealed serious threats to the seismic safety of tall-pier bridges.

To improve seismic performance of bridges under earthquakes, many strategies have been employed. For instance, isolation bearings, such as high-damping rubber bearing (HDRB) [8,9], lead–rubber bearing (LRB) [10,11,12], and friction pendulum bearing (FPB) [13,14,15] have been widely used to reduce seismic responses of bridges. The isolation principle of these bearings is to elongate the fundamental period of the structure while absorbing earthquake energy [16]. Earthquake-induced inertial forces transmitted to the substructure from the superstructure can be reduced, while displacement responses are often enlarged. Fluid viscous damper (FVD) is an alternative device popularly used in long-span bridges [17,18,19], which upgrades seismic performance by dissipating earthquake energy and limiting bearing displacement. Usually, these isolation bearings and FVDs are effective for improving longitudinal seismic performance of bridges, but their suitability for reducing transverse seismic responses is insufficient. Specifically, elongating the transverse fundamental period of tall pier bridges is problematic due to the risk of falling girders. In addition, there is often little space to arrange FVDs in the transverse direction and allow them to function fully in tall pier bridges.

Currently, the combination of isolation bearings and shear keys is the main solution for the transverse seismic design of bridges. Reinforced concrete shear keys (RCSKs) are widely used in abutments and pier caps, which can serve as structural fuses to limit the inertial force transmitted to the substructure [20,21]. However, the strength of RCSKs degrades quickly after concrete cracking and rebar yielding, and they are not easy to repair once damaged. To address this issue, various steel shear keys have been developed. Zhou et al. [22] investigated the low cycle fatigue performance of a metallic hysteretic damper. Yue et al. [23] proposed a novel shear key and developed an analytical model based on experimental mechanical behavior. Huang et al. [24] introduced an arc-shaped shear key capable of effectively limiting girder displacement and enhancing energy dissipation.

These shear keys have been applied in various bridges. Bi et al. [25] compared the seismic responses of simply supported beam bridges with and without shear keys through numerical simulations. Xiang et al. [26] suggested setting the shear key strength at 50% to 60% of the pier yield strength for optimal control. Özşahin et al. [27] studied the appropriate gap between shear keys and superstructures in simply supported beam bridges, finding that reasonable gap control helps suppress excessive deck rotation and damage. Abbasi et al. [28] explored the effects of shear keys on seismic responses in different frame bridges, which can control overall bridge behavior under moderate earthquakes. Wu [29] analyzed shear key force distribution in skewed bridges, recommending increased gaps to reduce stress and proposing a simplified design method for low seismic zones. Shen et al. [30] validated the effectiveness of transverse steel dampers in controlling transverse seismic responses in suspension bridges under near-fault motions.

The aforementioned studies provide a useful reference for transverse seismic design of bridges. However, though existing steel dampers exhibit strength enhancement after yielding, they may not provide sufficient yield strength, plastic dissipated energy, and anti-torsion ability, since they are often composed of several parallel steel plates [22,23,24]. Moreover, existing publications concerning transverse shear keys mainly focus on cable-stayed bridges [22] and suspension bridges [30], as well as girder bridges with mid and short piers [26,27,28,29]. To date, little research has been conducted on seismic improvement using shear keys for tall-pier girder bridges. Compared to mid and short piers, inertial forces generated by mass distributed along tall piers are considerable and can exceed those induced by the superstructure [31]. Tall-pier girder bridges possess longer fundamental structural periods, potentially augmenting dynamic responses under pulse-like motions containing long-period velocity pulses [32,33,34]. Their seismic performance is notably influenced by higher-order modes [35], often resulting in mid-height plastic hinges within piers [36]. Therefore, it is important to investigate the seismic performance of tall-pier girder bridges equipped with shear keys under near-fault pulse-like ground motions.

In this study, a novel transverse steel damper (TSD) is proposed to improve the seismic performance of tall-pier girder bridges. First, the detailed design and implementation scheme of the TSD within the bridge system are described. The hysteretic behavior of the TSD is simulated using ABAQUS 2024, and a simplified analytical model is established. Second, key TSD parameters are optimized based on the seismic responses of the bridge under near-fault ground motions. Third, the influence of pulse periods and velocity pulses on bridge seismic responses is explored. Finally, significant conclusions are summarized.

2. Analytical Model and Seismic Input

2.1. Overview of the Bridge

A multi-span tall-pier composite girder bridge is selected for this investigation, as shown in Figure 1a. The substructure consists of tall piers with variable hollow cross-sections, while the superstructure is a double-box prestressed steel-concrete composite girder. In this bridge, pier No. 2 (87.4 m) is classified as the tall pier, pier No. 4 (61.0 m) as the mid pier, and pier No. 1 (46.3 m) as the short pier. C30 concrete is used for the piles and pile caps, whereas C40 concrete is specified for the piers and pier caps.

High damping rubber bearings (HDRBs) are installed between the concrete bearing pads and the bottom of the steel box girder. The detailed design parameters are presented in

Table 1. Design parameters of the HDRB.

Bearing	Vertical Load Capacity (kN)	Compressive Stiffness (kN/mm)	Equivalent Damping Ratio (%)	Dimension (mm)
				Transverse	Longitudinal	Height
HDRB	13,864	2713	15	1070	1070	414

, according to the vertical load and the HDRB standard [37]. To restrict superstructure displacement responses under strong near-fault earthquakes and enhance the bridge’s seismic performance, a novel transverse steel damper (TSD) is proposed. As illustrated in Figure 1b, the TSDs are positioned on both sides of each pier cap.

2.2. Hysteretic Behavior of the TSD

The TSD is designed to meet the following objectives: (1) provide good displacement adaptability without compromising energy dissipation capacity, thereby accommodating the bridge’s daily deformation requirements; (2) establish a clear and reliable horizontal load transfer path to ensure energy dissipation efficiency and safety under seismic loading; (3) facilitate straightforward modeling in finite element platforms for numerical analysis. Additionally, traditional X-shaped steel plate dampers are prone to torsional failure under in-plane torsional responses potentially induced by non-uniform motions.

To satisfy these requirements, a novel TSD is developed in this study (Figure 2). The device incorporates a hollow steel plate at its top to enhance overall yield strength and resistance. The core energy-dissipating component consists of three rectangular steel plates and six additional 8 mm slotted steel plates to enhance energy dissipation capacity. Based on this configuration, a detailed finite element model of the TSD is established using the ABAQUS platform and analyzed under cyclic loading. As shown in Figure 3a, the equivalent stress cloud indicates stress concentration primarily within the slotted steel plates, verifying the mechanical reliability of the TSD. The force–displacement hysteretic curve of the TSD is shown in Figure 3b, exhibiting full and symmetric loops that indicate excellent energy dissipation capacity. Consistent with the existing literature, the hysteretic behavior of the TSD can be characterized by a widely adopted bilinear model.

To determine the optimal TSD parameters, a sensitivity analysis of seismic responses in the tall-pier girder bridge will be conducted in the next section. The specific parameters investigated are detailed in

Table 2. Parameters for the optimization of the TSD.

Case	Parameter	Yield Strength	Initial Gap	Post-Yield Stiffness Ratio
		(kN)	(mm)	(%)
1	Different yield strength	1000	80	5
2		2000	80	5
3		3000	80	5
4		4000	80	5
5		5000	80	5
6		6000	80	5
7		1000	100	5
8		2000	100	5
9		3000	100	5
10		4000	100	5
11		5000	100	5
12		6000	100	5
13		1000	120	5
14		2000	120	5
15		3000	120	5
16		4000	120	5
17		5000	120	5
18		6000	120	5
19	Different initial gap	2000	40	5
20		2000	60	5
21		2000	80	5
22		2000	100	5
23		2000	120	5
24		2000	140	5
25		3000	40	5
26		3000	60	5
27		3000	80	5
28		3000	100	5
29		3000	120	5
30		3000	140	5
31		4000	40	5
32		4000	60	5
33		4000	80	5
34		4000	100	5
35		4000	120	5
36		4000	140	5
37	Different post-yield stiffness ratio	3000	80	5
38		3000	80	10
39		3000	80	15
40		3000	80	20
41		3000	80	25
42		3000	100	5
43		3000	100	10
44		3000	100	15
45		3000	100	20
46		3000	100	25

. Cases 1–18 examine the effect of yield strengths from 1000 kN to 6000 kN, with the initial gaps at 80 mm, 100 mm, and 120 mm and the post-yield stiffness ratio at 5%. Cases 19–36 evaluate the effect of initial gaps from 40 mm to 140 mm, with the yield strengths at 2000 kN, 3000 kN, and 4000 kN and the post-yield stiffness ratio at 5%. Cases 37–46 evaluate the effect of post-yield stiffness ratios from 5% to 25%, with the yield strengths at 3000 kN and the initial gaps at 80 mm and 120 mm. Furthermore, bridge models without TSD (the no-TSD model) and with fixed bearings (the fixed HDRB model) are also provided to check the effectiveness of the TSD.

2.3. Finite Element Analytical Model

A three-dimensional (3D) finite element model of the tall-pier girder bridge is established in SAP2000, as shown in Figure 4a. The superstructure and substructure are modeled using 3D elastic frame elements. The girder’s secondary dead load is applied as equivalent distribution mass. HDRBs and TSDs are modeled using a bilinear hysteretic rule (Figure 3b and Figure 4b). The mechanical parameters of HDRBs are listed in Table 1. Pile–soil interaction is accounted for via the m-method (Figure 4c) [38], with equivalent spring stiffness calculated and calibrated using the distributed spring model. The values of m for tall piers are based on the bridge’s geotechnical report and Specifications for Design of Foundation of Highway Bridges and Culverts [39].

2.4. Selection of Ground Motions

To investigate the influence of pulse characteristics on the transverse seismic performance of tall-pier girder bridges under near-fault earthquakes, a series of ground motions are selected from the NGA-West2 database. The primary information on the selected ground motions is shown in

Table 3. The selected ground motions.

RSN	Earthquake	Mw	Rp (km)	PGA (m/s2)	PGV (m/s)	Tg (s)	Tp (s)	Note
181	Imperial Valley-06	6.53	1.35	4.341	1.216	0.822	3.773	For the TSD optimization
2466	Chi-Chi Taiwan-03	6.2	3.52	2.005	0.3	0.822	1.057	Short-period (Tpm = 1.12 s)
2495	Chi-Chi Taiwan-03	6.2	22.37	4.565	0.698	1.072	1.379
2627	Chi-Chi Taiwan-03	6.2	14.66	5.168	0.614	0.654	0.924
2457	Chi-Chi Taiwan-03	6.2	19.65	1.838	0.327	0.919	3.185	Medium-period (Tpm = 2.959 s)
2734	Chi-Chi Taiwan-04	6.2	6.2	1.838	0.327	0.435	2.436
3317	Chi-Chi Taiwan-06	6.3	35.97	1.264	0.342	1.426	3.255
1244	Chi-Chi Taiwan	7.62	9.94	3.783	1.088	1.033	5.341	Long-period (Tpm = 5.208 s)
1475	Chi-Chi_ Taiwan	7.62	56.12	1.062	0.457	0.876	5.285
1510	Chi-Chi_ Taiwan	7.62	0.89	3.045	1.048	1.033	4.998
1513	Chi-Chi_ Taiwan	7.62	10.97	5.8067	0.7054	0.5422	-	Non-pulse
2370	Chi-Chi_ Taiwan-02	5.9	45.89	0.2989	0.0284	0.7067	-
2381	Chi-Chi Taiwan-02	5.9	42.77	0.4352	0.0574	0.8263	-

. The pulse-like record RSN 181 from the Imperial Valley-06 station is used for TSD parameter optimization.

To specifically examine pulse period effects on seismic responses, four groups of near-fault records from the Chi-Chi Taiwan station are collected. Note that the bridge’s fundamental transverse period is 3.06 s, and records RSN 2457, 2734, and 3317 (mean pulse period T_pm = 2.959 s) are chosen to represent medium-period motions. Using this group as a baseline, short-period motions (T_pm = 1.12 s) and long-period motions (T_pm = 5.208 s) are determined. In addition, three non-pulse records (RSN 1513, 2370, and 2381) are included for comparison. The acceleration response spectra of these records, scaled to a peak ground acceleration (PGA) of 1.0 g, along with their mean spectra, are shown in Figure 5. Reflecting the seismic intensity at the bridge site, a PGA of 0.3 g is used for both TSD optimization and pulse characteristic investigations.

3. Optimization of the TSD

3.1. Different Yield Strength Variations

Under strong earthquakes, excessive displacements may exceed bearing capacity limits, increasing girder unseating and structural failure risks. The TSD effectively controls maximum transverse bearing displacements, though its efficiency depends critically on the yield strength. Insufficient yield strength provides inadequate displacement resistance, while excessively high values amplify pier seismic responses. Parametric analyses are performed to determine the optimal TSD yield strength. Displacement responses of the tall pier with different yield strengths are shown in Figure 6. The force–displacement hysteretic curves of the TSD are shown in Figure 7. The corresponding bending moment and shear force at the pier bottom are shown in Figure 8.

As Figure 6a indicates, TSD displacement decreases with increasing yield strength, implying that a higher yield strength enhances the TSD’s lateral resistance. Figure 6b shows that HDRB transverse displacement gradually decreases with increasing yield strength, with significant reductions compared to the no-TSD model. Figure 6c reveals that pier top displacement increases as yield strength increases and is larger than in the no-TSD model but smaller than in the fixed HDRB model. The opposite trend between Figure 6b,c indicates that enhancement of yield strength can effectively limit horizontal girder displacement but augment pier top displacement since more inertial forces are transmitted to the substructure. Moreover, HDRB displacement with an 80 mm initial gap is smallest when the yield strength ranges from 2000 kN to 6000 kN, yet produces the largest top displacement. Though a 120 mm initial gap results in the smallest pier top displacement, it yields the largest HDRB displacement when the yield strength exceeds 3000 kN. This is mainly because the strength enhancement of the TSD occurs earlier at a smaller initial gap and dissipates less earthquake energy, as shown in Figure 6c. Figure 7 indicates that higher yield strength reduces TSD energy dissipation capability. Nearly linear hysteretic behaviors are observed when the yield strengths are 4000 kN and 6000 kN.

Figure 8a demonstrates a significantly increasing bending moment at the pier bottom with higher yield strength. While TSD-equipped bridges exhibit a larger moment than the no-TSD model, the bending moment with initial gaps of 80 mm and 100 mm will be larger than that in the fixed HDRB model when yield strength is over 4000 kN. Figure 8b shows increasing shear forces at the pier bottom with a higher yield strength. It is noteworthy that the shear force exceeds that of the fixed HDRB model when yield strength reaches certain thresholds. Compared to the fixed HDRB model, the TSD with large yield strength may produce larger bottom internal forces, even though pier top displacements are smaller.

3.2. Different Initial Gap Variations

Under strong seismic excitations, bearing responses are significantly influenced by the TSD’s initial gap. The bearing–TSD interaction alters internal force transmission paths and displacement responses during seismic events. The maximum displacement responses of the tall pier with different initial gaps are shown in Figure 9. The force–displacement hysteretic curves of the TSD are shown in Figure 10. The corresponding bending moment and shear force at the pier bottom are shown in Figure 11.

Figure 9a shows a complex trend of TSD displacements with varying initial gaps under different yield strengths. Figure 9b indicates that bearing displacements all increase with larger initial gaps up to 100 mm and are substantially smaller than in the no-TSD model. Overall, displacements of the TSD and HDRB decrease as yield strength increases from 2000 kN to 4000 kN. Figure 9c shows that pier top displacement gradually decreases as the initial gap increases, achieving a stable trend earlier with smaller yield strength. These displacements are larger than those in the no-TSD model due to the greater inertial force transmitted to the pier cap. Overall, pier top displacements fall below those in the fixed HDRB model when the initial gap exceeds 80 mm for yield strengths of 3000 kN and 4000 kN. For a yield strength of 2000 kN, the pier top displacement stabilizes after 80 mm, with all displacements below those in the fixed HDRB model. Figure 10 shows fuller hysteretic loops at a smaller yield strength, indicating better energy dissipation capacity.

Figure 11a shows that for TSD models with yield strengths of 2000 kN and 3000 kN, bending moment gradually decreases with increasing initial gap, and greater yield strength leads to a larger bending moment. Figure 11b shows that with increasing initial gap, bottom shear force fluctuates, which may be due to higher-order mode effects. In addition, a higher yield strength leads to larger shear forces, which are larger than those in the no-TSD model. However, when yield strength is 4000 kN, both bending moment and shear forces are nearly always larger than in the fixed HDRB model for initial gaps below 100 mm, which is different from the variation observed for pier top displacement (Figure 9c). Both pier top displacement and bottom internal forces approach the levels in the no-TSD model when the initial gap increases. However, HDRB displacements do not approach the levels in the no-TSD model as the initial gap increases. This is mainly because the seismic responses of piers (especially shear force) are mainly contributed by their own mass instead of the steel girder mass. As the initial gap increases, inertial forces of the steel girder transmitted to the substructure are reduced, bringing responses close to those of the no-TSD model. Nonetheless, the existence of the TSD will limit girder displacement and dissipate earthquake energy, leading to an obvious reduction in HDRB displacement compared to the no-TSD model.

3.3. Different Post-Yield Stiffness Ratio Variations

The maximum displacement responses of a tall pier with different post-yield stiffness ratios are shown in Figure 12. The force–displacement hysteretic curves of the TSD are shown in Figure 13. The corresponding bending moment and shear force at the pier bottom are shown in Figure 14.

Figure 12a shows that TSD displacements under a 100 mm initial gap generally decrease when post-yield stiffness ratios are over 10%, as increased stiffness provides greater post-yield strength that limits further deformation. A pronounced drop in TSD displacement occurs at a 15% post-yield stiffness ratio. Figure 12b indicates slightly decreasing HDRB transverse displacements with higher stiffness ratios, remaining substantially smaller than in the no-TSD model. In addition, models with larger initial gaps exhibit greater HDRB transverse displacement responses. Compared to yield strength and initial gap, the post-yield stiffness ratio exerts a weaker influence on bearing displacement control, as it primarily affects restoring force rather than energy dissipation capacity. While higher stiffness ratios usually enhance post-earthquake re-centering and reduce residual displacement, their contribution to energy dissipation is often limited, as shown in Figure 13. Figure 12c shows pier top displacements in models with TSD consistently exceeding those in the no-TSD model, but remaining below levels in the fixed HDRB model. Furthermore, a slight increase in pier top displacement occurs with higher post-yield stiffness ratios, attributable to enhanced impact forces and reduced energy dissipation.

Figure 14 shows that the no-TSD model has the smallest bottom bending moments and shear forces. Bridges with TSDs exhibit smaller bending moments than the fixed HDRB model. However, for an initial gap of 80 mm, shear forces exceed those in the fixed HDRB model, which contradicts the trend observed for pier top displacements (Figure 12c). This occurs because shear forces are more susceptible to higher-order mode effects.

3.4. Seismic Performance Comparisons

Considering bearing displacement, top displacement, and bottom bending moment responses, the optimal parameters for the TSD are defined as a yield strength of 3000 kN, an initial gap of 100 mm, and a post-yield stiffness ratio of 15%. This combination provides a balanced energy dissipation capacity and effective control of internal forces. Note that there is no direct corresponding relationship between pier top displacements and bottom internal forces (especially shear force), which is quite different from the behaviors in mid- and short-piers [25,26,27]. To further illustrate the seismic performance of the tall-pier girder bridge, displacement and internal force envelopes for the optimized TSD model, no-TSD model, and fixed HDRB model are shown in Figure 15. In addition, simulations using reinforced concrete shear keys (RCSKs) are also presented, where the four-line skeleton and hysteretic rules of RCSKs can be found in [40].

Figure 15a shows that the displacement envelope of the optimized TSD model is smaller than that of the fixed HDRB model and RCSK model but larger than that of the no-TSD model. The RCSK model exhibits a larger displacement envelope than the TSD model and slightly smaller than that of the fixed HDRB model. Figure 15b shows that the bending moment envelope of the TSD model exhibits an S-shape, with the bending moment within the lower 50 m of pier height reduced compared to the fixed HDRB model. The bending moment envelope of the TSD model is lower than that of the RCSK model within the lower 35 m. The significant bending moment in the pier’s mid-height region may also induce a secondary plastic hinge away from the bottom [41,42]. Figure 15c demonstrates more complex shear force envelope shapes. Although the bottom shear forces are nearly identical for all models except the no-TSD model, shear forces along the pier body are obviously reduced when using the optimized TSD. This indicates that higher-order modes disrupt the linear correlation between top displacement and bottom internal forces in tall piers.

The time history curves of the top displacement, HDRB displacement, and bottom bending moment are shown in Figure 16. As seen, the pier top displacement and pier bottom bending moment are greatly reduced with the optimized TSD. The RCSK model can reduce pier top displacement and bottom bending moment, but it produces larger HDRB displacement than the optimized TSD model, since its strength degrades after the peak point. The axial force-bending moment (PM) curves for the key bottom section under different conditions are shown in Figure 17. The optimized TSD model remains entirely within the equivalent yield envelope throughout, ensuring elastic behavior at the pier bottom. However, obvious damage occurs at the pier bottom for the fixed HDRB model, since its PM curves break through the sectional equivalent yield envelope. Therefore, the proposed TSD parameters (yield strength: 3000 kN, initial gap: 100 mm, post-yield stiffness ratio: 15%) are validated as suitable for this bridge.

4. Influence of Pulse Characteristics

For tall-pier girder bridges, the influence of higher-order modes is significant and cannot be neglected. Furthermore, the effect of near-fault pulse-like motion characteristics on the seismic responses of tall piers remains to be explored. Therefore, this section employs 12 near-fault pulse-like motions listed in Table 3 to investigate the effects of the pulse period and velocity pulse characteristics on bridge seismic responses.

4.1. Effect of Pulse Period

The displacement envelopes of piers are shown in Figure 18. Displacement magnitude generally increases with pier height. As shown in Figure 18b, the maximum displacement responses occur under medium-period pulse-like motions, primarily due to resonance arising from the close match between the bridge’s fundamental structural period (3.06 s) and the pulse period (Figure 5c). Significant displacements also arise under long-period pulse-like motions, reflecting the slender tall-pier bridge’s sensitivity to high spectral accelerations in the low-frequency range of motions (Figure 5d). Notably, displacement responses under short-period and non-pulse motions are similar, which is primarily explained by the nearly overlapping mean spectra beyond 1.8 s (Figure 5f). The spectral amplification for short-period pulse-like motions occurs between 1.2 s and 1.8 s, which is far away from the fundamental structural period of the tall-pier girder bridge (3.06 s).

The bending moment envelopes of piers are shown in Figure 19. Figure 19a,d reveal that the tall pier exhibits an S-shaped moment distribution under short-period and non-pulse excitations, indicating significant higher-order mode influence. Additionally, the large moment at the mid-height suggests a potential second plastic hinge region that is distinct from the conventional plastic hinge at the pier bottom. As pier height decreases, the mid pier shows only a slight S-shaped moment distribution. The contribution of higher-order modes diminishes substantially with reduced pier height. For the short pier, bending moment envelopes become nearly linear, demonstrating a significant reduction in higher-mode effects.

The fundamental structural period plays a crucial role in bending moment responses. Tall-pier girder bridges typically exhibit longer structural periods, shifting resonance away from motions with dominant high-frequency components. Consequently, bending moment responses under short-period motions and non-pulse motions are reduced. Conversely, significant bending moment amplification occurs in tall piers subjected to medium- to long-period excitations. This amplification stems primarily from tall piers’ lower stiffness and complex higher-order mode shapes, where the fundamental structural period aligns more closely with pulse periods, inducing pronounced resonant responses. Further analyses reveal that medium-period motions induce higher bending moments than long-period motions due to closer matching between the fundamental structural period and pulse period, intensifying moments at the pier bottom. Therefore, resonance effects from period matching critically determine the magnitude and distribution of seismic responses in tall-pier girder bridges under near-fault motions.

The shear force envelopes of piers are shown in Figure 20. Unlike displacement and bending moment responses, tall piers exhibit distinct S-shaped distributions under all four input motion types, indicating significant higher-order mode effects. This occurs because shear force is primarily induced by inertial forces from the partial mass, while bending moment is also influenced by the distance to the supports. For tall piers, shear forces decrease from the base to approximately 50 m height due to accumulated inertial forces from the middle to lower regions. Above 50 m, shear force distributions become less consistent, likely affected by complex pier–superstructure interaction. Medium piers show weakened S-shaped distributions, reflecting diminished higher-mode influence. For piers below 50 m, shear force envelopes progressively become linear along the pier, indicating that the dynamic responses are predominantly governed by the fundamental structural mode.

To clarify the interaction mechanism between TSD and higher-order mode effects, the seismic response envelopes without the TSD under short-period motions are shown in Figure 21. Comparing Figure 19a and Figure 21b, it can be drawn that the TSD will exacerbate higher-order mode effects, as evidenced by the S-shaped envelopes. This can be attributed to the fact that the TSD will indirectly increase the horizontal stiffness of the tall pier by limiting the pier top displacement when collision occurs. Meanwhile, the energy dissipation capacity of the TSD may reduce the seismic responses from higher-order modes, resulting in smaller pier top displacement and bottom bending moment. Given that shear forces mainly depend on local mass, the influence of the TSD and higher-order modes on shear force is more complex, which will be investigated further through additional simulations in future work.

4.2. Effect of Velocity Pulse

The wavelet analysis framework [43] and the method proposed by Baker et al. [44] are used to separate the main velocity pulse from the original pulse-like motions, as shown in Table 3. Each motion is decomposed into two components: the main velocity pulse and the residual velocity component. The time history curves of the original waves and the separated components are shown in Figure 22. The spectral decomposition of the medium-period motions is shown in Figure 23, indicating that the main velocity pulse mainly affects the spectral values around the pulse periods. Similarly, the main velocity pulse of short-period motions and long-period motions primarily affects spectral values in the high-frequency range and low-frequency range, respectively. This decomposition assesses the dominant influence of the main velocity pulse on seismic responses of the tall-pier girder bridge.

Displacement, bending moment, and shear force envelopes of the tall pier under original and residual motions are compared in Figure 24. Removal of the main velocity pulse significantly reduces displacement and bending moment responses, with reductions exceeding 50% in some cases. This confirms the critical role of the main velocity pulse in triggering resonant responses in tall-pier bridges, highlighting the strong coupling between the fundamental structural period and pulse period. Comparisons in Figure 24e,f show evident shear force reductions under medium- and long-period motions after pulse removal. For short-period motions, however, shear distributions display a marked increase at the pier bottom in some cases, despite moderate reductions at the pier top. Furthermore, bending moment and shear force envelopes exhibit a more obvious S-shape, indicating that residual high-frequency components excite higher-order modes more obviously after removal of the main velocity pulse. However, higher-order mode effects induced by high-frequency components are masked by dominant seismic responses from large spectral values in medium to long periods.

Furthermore, TSD’s sensitivity to the residual component is analyzed using record RSN2734, and the seismic responses for different TSD parameters are shown in Figure 25 and Figure 26. The variation trends of pier top displacement and bottom bending moment under the residual component are similar to those from the original wave, though their values are much smaller due to the removal of the pulse component. Both pier top displacement and bottom bending moment under the residual component increase with increasing yield strength, while decreasing with increasing initial gap. In addition, the influence of the post-yield stiffness ratio on pier top displacement and bottom bending moment under the residual component is also not obvious.

5. Conclusions

This study proposes a novel transverse steel damper (TSD) with enhanced lateral strength and energy dissipation capacity. Based on a six-span tall-pier girder bridge, seismic responses under varying TSD parameters are systematically analyzed, while the influence of pulse characteristics is investigated. The key findings are summarized below:

(1) The novel TSD is modeled and validated under cyclic loading using ABAQUS, demonstrating excellent hysteretic behavior and mechanical stability. It provides a viable solution for lateral restraint and energy dissipation in tall-pier girder bridges.

(2) The use of TSDs effectively reduces bearing displacements while increasing pier-top displacements and pier-bottom internal forces as additional inertial forces are transmitted to the pier cap. However, displacements and internal forces in the bridge with TSDs are smaller than those in the bridge with fixed bearings.

(3) As yield strength increases, bearing displacements decrease, while pier-top displacements and pier-bottom internal forces increase. Conversely, larger initial gaps increase bearing displacements but reduce pier-top displacements and pier-bottom internal forces. However, the post-yield stiffness ratio exhibits a negligible influence on the seismic responses of tall-pier bridges. The optimized parameters are a yield strength of 3000 kN, an initial gap of 100 mm, and a post-yield stiffness ratio of 15%. The displacements and internal forces of the pier are greatly reduced using these parameters.

(4) Tall piers develop S-shaped bending moment distributions under short-period and non-pulse motions, while S-shaped shear force distributions manifest under all motions owing to higher-order mode effects. As pier heights decrease, the influence of these modes progressively diminishes, evidenced by bending moment and shear force distributions transitioning toward linear profiles along the pier height.

(5) Medium-period pulse-like motions maximize seismic responses due to resonance (pulse period ≈ fundamental structural period). Long-period pulse-like motions also generate large seismic responses owing to the susceptibility of tall-pier girder bridges to high spectral accelerations in the low-frequency range. Under short-period and non-pulse motions, however, seismic responses remain minimal since pulse periods and site characteristic periods are far from the fundamental structural period.

(6) Removing the main velocity pulse significantly reduces pier displacements and internal forces. However, more pronounced S-shaped envelope distributions are found in bending moments and shear forces under residual motions, implying significant higher-order mode effects. This indicates that higher-order modes exhibit greater sensitivity to the residual high-frequency components of pulse-like motions. Furthermore, these effects are masked by dominant responses from large spectral values in medium to long periods.

Despite its promising numerical performance, the TSD faces practical challenges that require attention before its implementation in real bridges. First, TSD installation requires sufficient space and is easy to replace, particularly in retrofits. Second, long-term durability concerns arise due to steel’s susceptibility to corrosion. Third, low-cycle fatigue performance requires experimental validation, and hysteretic behavior should be calibrated using measured cyclic responses.