Seismic assessment of a cable-stayed arch bridge under three-component orthotropic earthquake excitation

Abstract

The occurred damages during the past significant earthquakes have proved that vertical seismic excitation has tremendous effect on bridges. Three-component earthquake excitations are preferred to resemble the earthquakes. In this article, a cable-stayed arch bridge, a new type of bridge with the hybrid system of half-through arch and stay-cables, was analyzed under a set of different earthquake excitations (more than 21 ground motion records). Both vertical and horizontal components of the ground motions were considered to act simultaneously at the bridge supports. By using different three-component earthquake excitations, the dynamic responses of the bridge, including the displacements and accelerations of the main parts of the bridge, were obtained. The effects of various parameters such as soil type, epicentral distance, spatial variation of the ground motions, and dimensional variation of the structure were investigated. The results of the numerical study indicate that the cable-stayed arch bridge subjected to both horizontal and vertical components of earthquakes are more vulnerable than those subjected to horizontal ground motion only.

Keywords

cable-stayed arch bridge seismic vulnerability seismic analysis three-component earthquake excitation time-history analysis

Introduction

A cable-stayed arch bridge is a newly proposed hybrid system of a bridge in order to overcome the stability problems of long-span arch bridges as well as the height limitations of the arch. These problems are solved by combining an arch bridge system with a cable-stayed bridge which can lead to construct long-span bridges. For this purpose, Klein and Yamout (2003) proposed a deck system which was supported by both arch and towers using hangers and stay-cables, respectively. As a second system, the first real cable-stayed arch bridge, the Liancheng Bridge (also called the Fourth Xiangjiang River Bridge), was opened to traffic in 2007, in China (Luo et al., 2005). Several research studies have been done on cable-arch bridge. The effects of vehicle loading on dynamic behavior of a cable-stayed arch bridge were studied by Wang et al. (2014). Field tests were carried out to investigate the strengthening of the multi-rib arch bridge using stay cables (Xiang, 2020). Farahmand-Tabar and Barghian (2020, Forthcoming) proposed the modified hanger system for cable-stayed arch bridge to control the dynamic responses of the bridge.

The performance of the cable-stayed arch bridge with long arch span under earthquakes and seismic ground motions highlights the need for further discussion. Earthquake causes severe losses and destroys transport facilities in the quake-hit areas and causes great difficulties for emergency relief work. Due to destructive power of earthquake, seismic-resistant property is essential in the progress of bridge designing and construction (Fan et al., 2001). Several researches have been done to evaluate the seismic behavior of a pure concrete-filled steel tube (CFST) arch or cable-stayed bridge. For example, Li and Ge (2005) studied the seismic responses of a five-span half-through CFST arch bridge. The seismic response analysis of a multi-span and long-span cable-stayed bridge was done by He et al. (2009), Jin et al. (2012), and Sun et al. (2016). It was found that the effects of the vertical component on the bridge response were remarkable. The multi-support excitation shaking table test of a base-isolated steel cable-stayed bridge was investigated by Xu et al. (2018) and Kim et al. (2015) by using a system of multiple shaking tables. Most of these investigations were based on the single- or bi-directional horizontal earthquake excitation. For example, the behavior of the Akashi Kaikyo Bridge under multi-support seismic excitation for low-frequency motions was studied by Bahbouh et al. (2009). They amplified the bridge response owing to impact of the resonance phenomena induced by low-frequency seismic excitations. A two-dimensional nonlinear earthquake response analysis of a bridge-foundation-ground system was studied by Zhang et al. (2008) and Zheng et al. (2016). They found that the inelastic distorsions of the supporting soil has considerable influence on the earthquake response of the bridge owing to the lateral spreading caused by soil liquefaction. Another research was also done by Ghosh and Singh (2009) on bidirectional effects on the response of an isolated bridge considering the effect of the orientation of the ground motion’s major component regarding to the bridge axis, and the importance of this consideration on the bridge response was illustrated. Furthermore, with the field evidence from recent earthquakes and remarkable increase in near-fault strong motion recordings, the awareness of the importance of vertical ground motion has been gradually increased. Therefore, the effects of vertical excitations have been investigated by several researchers. The effect of earthquake’s vertical motion was investigated on reinforced concrete (RC) bridge piers by Rahai (2004). In this study, the dynamic analysis of the model were carried out utilizing different accelerograms, under the horizontal motion only or simultaneous horizontal and vertical motions. The increasement of the axial load, shear, and axial strain by considering the vertical motions was indicated. Narayana Murthy and Patil (2015) investigated the effect of vertical ground excitation on RC structures. In their project, the characteristics of vertical ground motion were introduced comprising critical factors which were considered in a seismic assessment. The influences of vertical excitation on the seismic performance of an isolated bridge with sliding friction bearings were discussed by Wang et al. (2016) considering different bearing friction coefficients and different stiffness levels. The effects of direction of the excitation on the analysis results were presented and the analysis results showed that the vertical excitation had a relatively large effect on the seismic performance for a seismically isolated bridge with sliding friction bearings. An innovative shape memory alloy (SMA) system was proposed by Aryan and Ghassemieh (2014) for bridges to simultaneously control and reduce the effects of vertical and horizontal seismic excitations on the bridge.

However, the effects of multi-component earthquake excitations are significant and needed to be considered in an analysis similar to real earthquakes. The nonlinear seismic response analysis of half-through CFST arch bridge under three-dimensional (3D) earthquake was investigated by Ma et al. (2011) with the result of 10% increasement in the responses of the arch crown. Critical response of structures subjected to the multicomponent earthquake excitation was studied by Lopez et al. (2000) using three uncorrelated components that were defined along its principal axes and the results of parametric variations were presented. In multicomponent seismic analysis, the evaluation of combination rules for the maximum response calculation was done by Lopez et al. (2001) and responses obtained by root of sum of squares (SRSS) rule were compared with complete quadratic combination (CQC) and other rules that showed the underestimation of the SRSS rule by 16%. Likewise, the combination rules for peak response calculation in three-component seismic analysis were evaluated by Hernández and López (2003). In their work, the elastic response was calculated for the system and compared with the critical response. It was shown that the value of $r_{e l a s t i c} / r_{c r i t}$ can be reduced significantly by the inclination of a principal component with respect to the vertical axis compared to the case when the component is vertical. The orthogonal effects in nonlinear analysis of bridges under multicomponent earthquake excitation were studied by Bisadi and Head (2010). To compare the procedure with the results of nonlinear time history analyses at various excitation angles, they applied AASHTO procedure on single-span bridges, which resulted in the sensitivity of the nonlinear model to the excitation angle compared to the linear models and the underestimation of the AASHTO procedure. The highway bridges’ response sensitivity to multi-component earthquake excitation with haphazard orientation—the effect of incidence angle—was investigated by Mackie et al. (2011) and the negligible influence of the incident angle on the mean response was indicated. A study on seismic response of a cable-stayed bridge deck under multi-component non-stationary random ground motion was done by Allam and Datta (2004). They found that the longitudinal component of the ground motion influenced the vertical vibration of the bridge significantly. The seismic testing of a long-span CFST arch bridge was carried out by Yan et al. (2011). They discussed the multiple sub-table cordwood system utilized to accomplish an investigation on the seismic testing of a three-span irregular CFST arch bridge with the aim of studying the dynamic performance of the bridge under spatial earthquake motions. Pushover analysis for predicting the seismic response of cable-stayed bridges under multi-directional excitation was done by Camara and Astiz (2012). A new coupled pushover analysis (CNSP) was suggested as a result to estimate the complex inelastic response of structures subjected to multi-axial strong ground motions. The seismic response of long-span cable-stayed bridge under multi-component/multi-support earthquake excitations and the influence of the coherency between different components of same and different supports were investigated by Quan et al. (2008). It was led to a simple calculation method to account for the multi-component and multi-support effects. The seismic behavior of cable-stayed bridges under multi-component random ground motion—considering an incident angle—was studied by Allam and Datta (1999) using a frequency domain spectral analysis. They also investigated the seismic response of suspension bridges under multi-component non-stationary random ground motion using the Markov method of analysis (Allam and Datta, 2003) so that the longitudinal component of the ground motion had significant influences on the vertical vibration, and the deck responses were considerably influenced by incidence angel. An investigation of the seismic response of a bridge subjected to simultaneous vertical and horizontal excitations was carried out by Chern Kun et al. (2013) by using a series of shake table experiments which was resulted in the importance of the vertical excitation on the increasement of the bending of deck, the development of plastic hinges, and axial force in the bridge piers. Effects of the multi-dimensional and multi-supported seismic excitations in long-span structures were investigated by Lin et al. (2016). The influences of vertical excitation and near fault ground motion were also considered by Huang et al. (2016), Yang et al. (2016), and Wang et al. (2019) on seismic assessment of the bridges.

Finally, the investigation of the seismic performance of a cable-stayed arch bridge under multi-component earthquake excitations is the subject of the present study. In this research, the effects of scaled multi-component earthquake excitations on the bridge were studied considering different parameters such as soil type, epicentral distance and the spatial variation of the seismic ground motions, and dimensional variation of the bridge in order to distinguish the overall behavior of the bridge. Hybrid system of cable-stayed arch bridge is a new type of bridge system which tries to utilize the advantages of both arch and cable-stayed bridges. However, its performance under different cases and conditions should be clarified for its practicability and construction in locations with high seismicity. For this purpose, a full-scale cable-stayed arch bridge was modeled and the seismic analysis was carried out using different ground motion records and earthquakes time histories.

The model data

The Liancheng Bridge model—which is a hybrid system as a mixture of arch bridge and cable-stayed bridge with two pylons—is shown in Figure 1(a) and (b). The bridge’s main span is 400 m in length, and the side spans are 120 m. The bridge has 27 m width and two parallel arch ribs. Each arch rib with a rectangle cross-section comprises six steel tubes, as illustrated in Figure 1(c). These steel tubes with an outer diameter of 850 mm have a thickness between 20 and 28 mm that varies depending on the position of the arch rib. Both parallel main arch ribs are stabilized using 11 wind bracings: two connecting beams and two K-shaped wind bracings under the deck; also, six K-shaped wind bracings and a Ж-shaped one, over the deck. The connecting beams are made of the rectangle steel girders and other wind bracings are composed of steel pipes. The floor system of main arch—which is supported by the two rows of 39 steel wire rope hangers with the intervals of 8 m—is composed of the deck, transverse I-shaped girders, and longitudinal stringers. The stay-cables are anchored on the arch ribs and bridge deck with the intervals of 8 and 10 m, respectively. All cables were modeled as cable element (tension-only bar element without the flexural/torsional stiffness) considering their sag and prestressing according to their length. According to model, the whole bridge was established by the finite-element software, CsiBridge. In the model, both ends of the main towers and main and side arch ribs were fixed in all degrees of freedom. For the ends of the two side spans, translational movements were also fixed in all three directions, whereas rotation along the lateral axis was permitted.

Figure 1.

General view of the Liancheng bridge (in m): (a) elevation, (b) plan view, (c) cross-section of main arch rib, (d) FE model, and (e) pile model under the foundation considering soil–structure interaction (SSI).

The fundamental material properties corresponding to the main structural components of the bridge, comprising the module of elasticity, E, cross-sectional area, A, and element types are presented in Table 1. First 10 mode shapes—achieved from the bridge model—as illustrated in Figure 2, were the same as the available data given by Luo et al. (2005) and Wang et al. (2014), which demonstrate the reliability of the developed model. The assumed damping was 5% and the applied analysis was modal time-history as a solution type with the time steps of 0.01.

Table 1.

Properties of structural components of Liancheng bridge (Wang et al., 2014).

Content	E (N/m²)	A (m²)	Element type
Main arch rib (steel tube)	2.10 × 10¹¹	1.430 × 10⁻³(upper)	Beam column
Main arch rib (steel tube)	2.10 × 10¹¹	1.304 × 10⁻³(lower)	Beam column
Bracing	2.10 × 10¹¹	4.128 × 10⁻³	Bar
Hanger	2.05 × 10¹¹	2.117 × 10⁻³	Cable
Cross girder	2.10 × 10¹¹	8.000 × 10⁻¹	Bar
Stay-cable	1.95 × 10¹¹	4.340 × 10⁻³	Cable
Main tower	3.50 × 10¹⁰	1.143 × 10¹ (upper)	Beam column
	3.50 × 10¹⁰	1.074 × 10¹ (middle)
	3.50 × 10¹⁰	1.304 × 10¹ (lower)
Side arch rib	3.50 × 10¹⁰	8.800 × 10⁰	Beam column

Figure 2.

First 10 mode shapes of cable-stayed arch bridge.

Seismic response analysis

The seismic response of structures is affected by earthquake excitations. It is often difficult to find a suitable number of records that can be matched to the desired response spectrum. The selection method of a ground motion record is important. The reason is that some different seismic responses can be observed if different sets of ground motion records are exerted to a structure; especially if the number of ground motion records—within the set of records—is low as it is recommended in the design codes. So, it is difficult to take into account all those parameters which are significant for the selection of ground motion records for the time-history analysis. For instance, scaling to a certain design level, the magnitude and distance from the fault are three fundamental parameters which have to be precisely selected for an earthquake scenario. To determine the structural response through the time-history analysis—regarding the number of ground motions—the typical practice in structural design is the use of 7 or 11 ground motions based on ASCE05-7 and ATC codes, respectively. However, the proper number of motions is still a topic of needed research. Based on the ASCE/SEI-7 code, if the analyzed ground motions are at least seven, the design values of engineering demand parameters (EDPs) are taken as the average of which are ascertained from the analyses. If less than seven ground motions are analyzed, then, the design values of EDPs are taken as the maximum values of the EDPs for the performance assessment (ASCE/SEI 7-16, 2016).

Despite the further recommendation of the codes that the spectral shape of the selected ground motion records should be in a good agreement with the elastic design spectrum, the number of selected ground motion records may not be adequate to anticipate the unbiased and stable structural response because there are many aspects to select the records of ground motion for time-history analysis. Furthermore, there are various possibilities to select the approach of a few number of ground motion records from a large set of records consistent with an earthquake scenario of a site (Dolšek and Azarbakht, 2008).

For far-field sites, the most important factor—in selecting ground motions for scaling to a target spectrum—is the spectral shape over the period range of interest (currently 0.2 $T_{1}$ to 1.5 $T_{1}$ in ASCE/SEI 7-16, where $T_{1}$ is the translational period of the first mode). Selecting pairs of motions with spectral shapes similar to the target spectrum minimizes the necessity for modification and scaling. Furthermore, selecting records based on their spectral shape and design spectral acceleration (SA) increases the efficiency and accuracy of the procedure (Reyes and Kalkan, 2012). For near-field sites, another considerable factor in selecting ground motions for scaling to a target spectrum is the possible presence of velocity pulses. Velocity pulses exist in many near-fault ground motion records, particularly in the forward directivity region. A relationship has been proposed in Appendix C of the NIST/GCR 11-917-15 report to estimate the proper number of pulse motions. Disaggregation of the seismic hazard curve will identify the combinations of earthquake magnitude, site-to-source distance, and è that dominate the hazard around the period of the structure. This can assist the selection of pulse periods and thus seed ground motions for later scaling (NEHRP Consultants Joint Venture, 2011).

In the present paper, different earthquake records were taken as the input to the bridge, in order to analyze the seismic response of the structure. The records were chosen according to the given properties of Table 2. In this case, 21 various ground motion records—according to Table 3—were adopted in three orthogonal directions. The design response spectrum obtained from Chinese code, GB50011-2016, is according to Figure 3 considering different soil types.

Table 2.

Properties of selected records.

Properties	Range	Type
Magnitude	6–7.5	N/A
Shear velocity of soil $({\bar{V}}_{s 30})$	185-325	Soil type D (IV)
Epicentral distance	<15 km >15 km	Near-Fault Far-Fault
NEHRP soil profile type classifications
I	${\bar{V}}_{s 30} > 1500 m / s$	Hard rock
II	$760 < {\bar{V}}_{s 30} < 1500 m / s$	Rock
III	$360 < {\bar{V}}_{s 30} < 760 m / s$	Very dense soil
IV	$180 < {\bar{V}}_{s 30} < 360 m / s$	Stiff soil

Table 3.

List of selected records capable of being matched to the target response spectrum.

No.	Event name	Year	Station	Magnitude	Mechanism(fault type)	Shear velocity(Vs30, m/s)	Epicentraldistance(km)	Ariasintensity(m/s)
01	ImperialValley, US	1979	Niland Fire Sta.	6.53	Strike Slip	212.00	35.640	0.2
02	Darfield, New Zealand	2010	DORC	7.00	Strike Slip	280.26	29.960	0.2
03	Northridge	1994	San Jacinto-CDF F.S.	6.69	Reverse	306.76	147.47	0.1
04	Loma Prieta, Italy	1989	Salinas-John&work	6.93	Rev. Oblique	279.56	28.660	0.2
05	Kobe, Japan	1995	OSAJ	6.90	Strike Slip	256.00	21.350	0.2
06	Chichi, Taiwan	1999	CHY092	6.20	Strike Slip	253.72	33.020	0.1
07	Tabas, Iran	1978	Boshrooyeh	7.35	Reverse	324.57	24.070	0.3
08	Big Bear	1992	SanBernardino-E&H	6.46	Strike slip	296.97	34.980	0.3
09	Coalinga	1983	Park field-Zone 6	6.36	Reverse	266.65	31.640	0.1
10	Morgan Hill	1984	Hollister D. Array #3	6.19	Strike slip	215.54	26.420	0.1
11	Parkfield	2004	Monarch Peak	6.00	Strike slip	308.00	29.310	0.0
12	Iwate, Japan	2008	UgoTown-Nishimo.	6.90	Reverse	317.41	37.080	0.2
13	Landers	1992	Palm Springs Airp.	7.28	Strike slip	312.47	36.150	0.4
14	Friuli, Italy	1976	Codroipo	6.50	Reverse	249.28	33.320	0.1
15^a	Loma Prieta, Italy	1989	Gilroy-Historic Bldg.	6.93	Rev. Oblique	308.55	10.270	0.7
16	Darfield, New Zealand	2010	LRSC	7.00	Strike Slip	295.74	9.3800	0.2
17	Imperial Valley, US	1979	Westmorland Fire Sta.	6.53	Strike Slip	193.67	14.750	0.1
18	Chuetsu-oki, Japan	2004	Mitsuke Kazuiti Arita	6.80	Reverse	274.23	11.350	0.8
19	Parkfield	1966	Cholame-Shan. Arr.#5	6.19	Strike slip	289.56	9.5800	0.9
20	Morgan Hill	1984	Halls Valley	6.19	Strike slip	281.61	3.4500	0.9
21	Victoria, Mexico	1980	Victoria Hospital Sot	6.33	Strike slip	242.05	6.0700	0.0
Selected records considering various soil types
01	Iwate, Japan	2008	UgoTown-Nishimo.	6.90	Reverse	317.41	37.08	0.2
02	Iwate, Japan	2008	YMT002	6.90	Reverse	365.59	36.92	0.1
03	Iwate, Japan	2008	AKTH05	6.90	Reverse	829.46	37.45	0.2
04	San Fernando	1971	LA-Hollywood Stor F	6.61	Reverse	316.46	22.77	0.7
05	San Fernando	1971	Lake Hughes #1	6.61	Reverse	425.34	22.23	0.3
06	San Fernando	1971	Pasadena-Old Seis. Lab	6.61	Reverse	969.07	21.50	0.3
07	Lytle Creek	1970	Colton-So Cal Edison	5.33	Reverse Obl.	301.95	29.18	0.0
08	Lytle Creek	1970	Devil’s Canyon	5.33	Reverse Obl .	667.13	18.39	0.1
09	Lytle Creek	1970	Cedar Springs	5.33	Reverse Obl.	813.48	17.40	0.0

Pulse-like record (the only pulse-like record capable of being matched to the target response spectrum).

Figure 3.

Design response spectrum (GB50011-2016) and matched records.

All the selected records were matched with the response spectrum using the SeismoMatch software with the parameters according to Table 4. SeismoMatch is an application capable of adjusting earthquake accelerograms to be matched with the specific target response spectrum, using the wavelets algorithm proposed by Hancock et al. (2006).

Table 4.

SeismoMatch matching parameters.

Matching parameters				Alpha model		PGA correction		Integration parameter
Parameters	Values	Parameters	Values	Parameters	Values	Parameters	Values	Parameters	Values
Mismatch Tolerence	0.3	Max num. of waves	10	a1	1.25	Adjustment frequency	25	Gamma	0.5
Max Iteration	30	Additional waves	20	a2	0.25	Damping	0.05	Beta	0.25
Scale Factor	1	Off diagonal reduction	0.7	f1	1	Number of cycles	6	Max dt/T	0.02
Min Eigen Value	0.1	Group size	250	f2	4

PGA: peak ground acceleration.

According to Figure 3, the earthquake excitations were matched to the target spectrum and were applied in three directions to represent a logical reflection of the structure under the earthquake.

Numerical results and discussion

In order to investigate the seismic behavior of the cable-stayed arch bridge, initially, the SA of the measurement points of the bridge are illustrated in Figure 4. In these figures, the ground motion records are equal to the records which were presented in Table 3. The measurement points for the responses are the arch crown, towers peak, and the middle of the bridge deck.

Figure 4.

The spectral accelerations of arch, deck, and tower.

It is apparent from Figure 4 that for the several responses, the maximum accelerations are within the first 10 mode such as the transverse and vertical directions of tower and arch, respectively, and deck in both of these directions. In several cases, the maximum accelerations have been happened in the same frequencies. As an instance, in the frequency of 1 cycle/s, both arch and deck experienced the maximum acceleration in the vertical direction. Likewise, both tower and arch experienced the maximum acceleration in the frequency of 4 cycles/s in longitudinal direction. For each direction, some parts of the bridge were influenced more than the others with higher responses. For the longitudinal and vertical directions, the tower and deck were influenced more than other part, respectively. According to Table 5, the displacements and accelerations of different parts of the bridge were obtained from various earthquake excitations that could be compared with each other. The mean value of each parameter was taken as the corresponding response.

Table 5.

Max responses of bridge components under dead load and seismic records.

Event name	Displacement (cm)									Acceleration (m/s²)
	Arch crown			Tower			Center of deck			Arch crown			Tower			Center of deck
	$Ux$	$Uy$	$Uz$	$Ux$	$Uy$	$Uz$	$Ux$	$Uy$	$Uz$	Long.	$Tra$ .	Vert.	Long.	$Tra$ .	Vert.	Long.	$Tra$ .	Vert.
Imp. Valley	0.46	17.24	−15.79	12.76	7.49	−2.43	1.55	11.37	−27.16	1.06	1.35	1.01	1.49	2.65	0.39	1.55	0.87	2.58
Darfield	0.51	20.43	−16.14	12.86	5.93	−2.33	1.51	9.78	−26.83	1.73	1.45	1.17	2.02	2.61	0.47	1.51	1.35	1.82
Northridge	0.47	22.71	−16.54	12.70	4.90	−2.37	1.57	12.12	−27.21	1.19	1.42	0.95	1.62	2.34	0.41	1.41	0.90	1.93
Loma P.	0.45	18.33	−15.65	12.81	5.51	−2.40	1.82	10.33	−26.78	1.48	1.55	1.27	1.85	3.18	0.48	2.15	1.28	2.39
Kobe	0.62	24.01	−15.98	13.38	7.89	−2.51	1.67	11.04	−26.97	1.15	1.22	1.08	1.70	2.75	0.47	1.38	1.04	2.22
Chichi	0.47	22.17	−15.92	13.42	5.03	−2.33	1.39	11.73	−27.92	1.63	1.01	1.22	1.59	2.46	0.32	1.45	1.31	2.92
Tabas	0.53	22.67	−15.79	12.92	4.61	−2.42	1.46	8.82	−27.45	1.56	1.47	1.23	1.76	2.22	0.53	1.66	1.04	2.83
Big Bear	0.53	19.6	−16.25	13.03	5.74	−2.44	1.65	11.70	−26.86	1.22	1.76	1.20	1.53	3.79	0.54	1.73	1.40	1.87
Coalinga	0.57	20.09	−16.90	12.93	6.32	−2.48	1.61	11.76	−28.25	1.34	1.20	1.03	1.54	2.04	0.41	1.45	0.90	2.11
Morgan H.	0.51	18.16	−16.10	13.05	5.23	−2.40	1.59	11.42	−27.78	1.44	1.33	1.05	1.47	2.39	0.56	1.49	0.95	1.99
Park field	0.42	21.72	−16.49	12.66	7.19	−2.41	1.48	12.22	−27.97	1.14	1.09	0.93	1.23	2.41	0.29	1.23	0.89	2.22
Iwate	0.43	22.31	−15.94	13.09	5.80	−2.32	1.52	11.95	−28.42	1.78	1.10	1.42	2.25	2.95	0.49	1.39	1.13	2.97
Landers	0.45	22.38	−15.71	13.30	7.78	−2.52	1.54	9.920	−27.02	1.63	1.14	1.47	1.78	2.9	0.49	1.29	1.47	2.19
Friuli	0.53	19.59	−16.51	13.11	5.41	−2.39	1.67	11.88	−27.21	1.45	1.27	1.05	1.80	2.66	0.39	1.63	1.09	1.93
Loma P.	0.45	23.05	−16.55	12.94	7.51	−2.38	1.65	11.00	−27.55	1.68	1.44	1.30	2.25	2.21	0.50	1.55	1.56	2.07
Darfield.	0.42	21.64	−16.51	12.94	5.59	−2.48	1.60	12.02	−27.86	1.32	1.25	1.13	1.49	2.63	0.47	1.93	1.30	2.00
Imp. Valley	0.52	24.81	−16.35	13.37	6.24	−2.39	1.67	11.48	−26.70	1.52	1.01	1.11	1.60	3.02	0.50	1.07	1.28	1.64
Chuet.–oki	0.55	23.09	−16.44	13.23	6.68	−2.49	1.55	11.98	−27.03	1.53	1.29	1.09	1.91	3.09	0.44	1.84	1.30	1.90
Park field	0.50	14.16	−16.76	13.28	6.13	−2.34	1.62	10.86	−27.71	1.65	1.15	0.93	1.87	2.89	0.49	1.70	1.25	1.55
Morgan H.	0.68	20.01	−15.66	13.42	6.14	−2.48	1.99	12.30	−27.68	1.78	1.31	1.16	1.90	2.69	0.49	1.90	1.33	2.16
Victoria	0.44	21.14	−16.07	12.85	6.52	−2.34	1.63	9.950	−26.67	0.85	1.16	0.85	0.99	2.11	0.25	1.56	1.20	1.62
Mean of max responses of bridge components under far- and near-fault records
Far field	0.50	20.82	−13.32	13.00	6.06	−1.74	1.57	11.15	−20.79	1.41	1.31	1.15	1.69	2.67	0.45	1.53	1.12	2.28
Near field	0.51	21.13	−12.20	13.15	6.40	−1.73	1.67	11.37	−20.26	1.48	1.23	1.08	1.72	2.66	0.45	1.65	1.32	1.85
Mean	0.50	20.92	−12.28	13.05	6.17	−1.74	1.61	11.22	−20.62	1.43	1.28	1.13	1.7	2.67	0.45	1.57	1.18	2.14
Diff. (%)	2.00	1.49	8.41	1.15	5.61	0.57	6.4	2.00	2.60	5.00	6.11	6.10	1.80	0.37	2.20	7.84	15.2	18.9
Stand. Dev.	0.79	0.11	0.24	0.01	0.07	0.16	0.37	0.05	0.06	0.05	0.06	0.05	0.02	0.01	0.01	0.08	0.14	0.3

Capacity assessment of the bridge model

To evaluate the capacity of the bridge under seismic load, the pushover analysis can be carried out considering the nonlinear behavior of the bridge elements. The important parts of the bridge against the seismic loading are bent columns; thus, the pushover analysis should be carried out on isolated bent columns with equivalent loads of the whole bridge. The pushover curve for bent columns in each direction is presented in Figure 5. The effects of different soil types related to seismic loading (Figure 3) are considered in the capacity curves. By considering different performance level, the plastic hinges are generated on bent columns in each direction. If bent columns are pushed with same target displacement ratio of lateral direction, the pushover curve in longitudinal direction remains linear due to the stiffness of the bridge in longitudinal direction. Thus, the process continues with higher target displacement ratio until the collapse level to achieve the capacity in longitudinal direction. The obtained curves represent the capacity of the bridge and they can be a criterion for results to be compared. Therefore, according to Table 6, demand to capacity ratio (D/C) is obtained using the considered pushover analysis indicating that the bridge remains in linear domain and does not reach to its ultimate capacity while subjecting to seismic records which have been matched to design response spectrum.

Figure 5.

Capacity curves of the bent columns in longitudinal and transversal directions.

Table 6.

The displacement demand and capacity of bent columns.

Soil type	Station (m)	Longitudinal			Transversal
Soil type	Station (m)	Demand (cm)	Capacity (cm)	D/C ratio	Demand (cm)	Capacity (cm)	D/C ratio
IV	120	0.94	62.11	0.015	10.32	51.88	0.20
III		0.71	45.81	0.016	7.87	47.20	0.17
II		0.54	33.28	0.016	6.97	41.80	0.17
IV	520	0.95	62.69	0.015	10.39	51.87	0.20
III		0.72	56.98	0.013	7.92	47.53	0.17
II		0.55	44.96	0.012	7.02	42.13	0.17

Effects of the epicentral distance of ground motion records on responses of the bridge model

In this section, the obtained results of far-fault records (mean responses) were compared with the mean near-fault responses. According to Table 5, far- and near-fault displacement and acceleration responses were compared with each other. Considering the forces of the stay cables and hangers in Figure 6, it was found that the influence of the near-fault excitations on responses of the stay cables is more than hangers (with the maximum difference of 27.11%). In contrast, these influences were reverse for hangers which meant that the effects of the far-fault records were dominant (with the maximum difference of 4.16%). The differences are small because the whole records were matched to the target response spectrum that produce records with minor but inherent differences. It is worth noticing that at the stations of 55, 150, and 184 m, the differences are minimum. In contrast, at the locations of 15, 85, and 304 m, the differences are maximum, which show the vulnerability of the bridge in these positions and it is eligible for special considerations. Among near-fault records, maximum responses (Table 5) were obtained by Loma Prieta, as the only applicable pulse-like record for the present study, which shows the nature and influence of the pulse-like records.

Figure 6.

Mean responses (axial force) of cables and hangers under far- and near-fault records.

In order to compare the obtained responses in different parts of the bridge under far- and near-fault excitations, all of the responses were shown together considering the direction of the responses in Figure 7. It was found that the longitudinal responses were not considerable in comparison with the responses of other directions. Also, it is observed that the influence of the excitation type (far- and near-fault) on different parts of the bridge is not the same, and for the responses of the transverse and vertical directions, near-fault records had more influence on the whole bridge.

Figure 7.

Comparison of the evaluated responses (disp.) for bridge segments under far- and near-fault excitation.

Effects of the vertical component of the earthquake on responses of the bridge model

Ignoring the vertical acceleration of ground motions has tremendous effect on the structures especially when considering the near-fault ground motions. In Figure 8 and according to Table 7, it is obvious that the three-component excitation (horizontal and vertical) affects the bridge axial load remarkably comparing with horizontal excitations that indicate the importance of considering the vertical component of the bridge with horizontal excitations as three-component earthquake excitations.

Figure 8.

Comparison of the effect of the three-component earthquake excitation and horizontal excitation on the arch base axial force under the typical far- and near-fault ground motion records.

Table 7.

The effect of 2D and 3D excitations (with/without vertical component) in far- and near fault conditions.

Event	Maximum response (kN)
	Far-fault			Near-fault
	2D Excitation	3D Excitation	Differences (%)	2D Excitation	3D Excitation	Differences (%)
Loma Prieta	−25,434.98	−26,195.23	2.99	−25,590.84	−26,657.20	4.17
Imperial Valley	−25,655.58	−26,242.95	2.29	−25,932.65	−26,855.67	3.56
Darfield	−25,561.76	−26,563.85	3.92	−25,425.17	−26,634.77	4.76
Parkfield	−25,606.88	−27,297.06	6.6	−25,470.08	−26,595.61	4.42
Moran Hill	−25,497.13	−26,596.00	4.31	−25,571.55	−26,789.19	4.76

Effects of the soil type on the responses of the bridge model

In order to investigate the effect of the soil type on the seismic behavior of the cable-stayed arch bridge, the bridge was analyzed considering different soil types. For this purpose, several ground motion records were selected regarding their soil types and corresponding shear wave velocities according to NEHRP soil profile type classifications (Table 2). Then, the selected records were matched to the target design response spectrum of the corresponding soil type based on the specifications of the GB50011-2016 as illustrated in Figure 3. According to Table 3, the records of the Iwate, San Fernando, and Lytle Creek were chosen so that all the parameters except shear wave velocity were kept approximately constant. Due to the inaccessibility of the similar conditions among the other records and the convergence problems while matching, only three records were chosen for comparing the effect of the soil type. However, analyzing with three records (less than seven records) is permitted according to ASCE/SEI-7 in which the maximum of three responses is considered as the response.

Based on the results of Table 8, the responses of the soil type IV (stiff soil) were higher in comparison with the soil types II and III. The responses were decreased by changing the soil type from IV to III and II which meant that by making the soil stiffer and more dense the responses became lower.

Table 8.

Maximum responses of bridge components under records of different soil types.

Soil Type	Event	Displacement (cm)									Acceleration (m/s²)
		Arch crown			Tower			Center of deck			Arch crown			Tower			Center of deck
		$Ux$	$Uy$	$Uz$	$Ux$	$Uy$	$Uz$	$Ux$	$Uy$	$Uz$	Long.	$Tra$	Vert.	Long.	$Tra$	Vert.	Long.	$Tra$	Vert.
IV	Iwate	0.43	22.31	−11.30	13.09	5.80	−1.71	1.52	11.9	−20.11	1.78	1.10	1.42	2.25	2.95	0.49	1.39	1.13	2.97
	San Fern.	0.48	31.36	−12.00	12.64	6.60	−1.72	1.43	8.77	−21.19	2.92	1.27	1.50	3.14	3.16	0.80	2.17	1.93	1.85
	Lytle Creek	0.29	24.88	−12.33	12.51	5.82	−1.88	1.43	15.9	−20.59	1.69	1.08	1.03	1.74	2.84	0.41	1.43	1.19	1.80
	Response	0.48	31.36	−12.33	13.09	6.60	−1.88	1.52	15.9	−21.19	2.92	1.27	1.50	3.14	3.16	0.80	2.17	1.93	2.97
III	Iwate	0.39	21.03	−12.23	12.43	4.88	−1.87	1.54	8.85	−21.45	1.68	1.41	0.72	1.90	1.86	0.36	1.35	0.80	1.90
	San Fern.	0.37	19.34	−12.59	12.23	4.72	−1.82	1.40	8.69	−21.48	2.03	1.21	1.44	2.46	2.76	0.51	1.70	1.14	1.69
	Lytle Creek	0.5	21.03	−13.21	12.79	4.89	−1.90	1.35	8.85	−22.36	1.37	1.44	1.00	1.72	1.88	0.33	1.64	0.80	2.26
	Response	0.5	21.03	−13.21	12.79	4.89	−1.90	1.54	8.85	−21.48	2.03	1.44	1.44	2.46	2.76	0.51	1.70	1.14	2.26
II	Iwate	0.25	18.31	−13.20	12.06	4.62	−1.92	1.52	8.53	−22.32	−1.33	1.31	0.83	1.80	1.85	0.40	1.74	0.83	1.49
	San Fern.	0.41	19.70	−12.59	12.59	4.72	−1.82	1.57	7.67	−22.41	1.96	1.08	1.10	2.03	1.53	0.51	1.36	0.88	1.27
	Lytle Creek	0.37	19.42	−12.80	12.10	3.89	−1.88	1.43	8.82	−22.27	2.05	0.98	1.14	2.17	1.61	0.57	1.69	0.63	1.38
	Response	0.41	19.70	13.20	12.59	4.72	−1.92	1.57	8.82	−22.41	2.05	1.31	1.14	2.17	1.85	0.57	1.74	0.88	1.49

Effects of considering spatial variation of seismic ground motion on the responses of the bridge model

Assuming a uniform earthquake motion along the whole bridge could not be realistic, especially for the bridges with long spans. The reason is due to the variation in the ground motion at the multiple supports through traveling seismic waves that lead to different seismic responses in comparison with those generated by uniform motion at the whole supports (Bi et al., 2013; He et al., 2016; Ma et al., 2019; Shrestha et al., 2016a, 2016b). For this purpose, a model with a piled foundation should be established considering the soil–structure interactions (SSI) in order to illustrate the variation in the responses of supports. For considering the SSI effects, a pile model (Figure 1(e)) with springs was applied at the interval of 0.5 m along piles’ height in both horizontal directions.

Initially, the structure with the pile foundation was analyzed under seismic time histories. In this case, the seismic forces were applied to the structure’s center of mass. Then, the ground motions were applied to each support at the side of the bridge with appropriate time delays (regarding the wave velocity of the ground motion and the distance between two supports) to represent the wave passage effect. According to the illustrations of Figure 9, the influence of applying seismic ground motions to the bridge foundations is remarkable on the transverse direction. The responses in the mentioned direction, considering the spatial variation, were become severe in the figure with the previously obtained responses of the same direction. Furthermore, the responses of each support, while considering spatial variation, were increased from one support to another because of the influence of the traveling seismic waves.

Figure 9.

Response comparison considering the spatial variation of typical ground motion of Loma Prieta.

Effects of the width/rise to span ratio on responses of the bridge model

In order to generalize the investigated results, different bridge width-to-span and arch’s rise-to-span ratios were chosen as the parameters of the bridge. To consider the effects of the bridge’s width variation, different values were chosen as the bridge width. The maximum width value for the bridge was set equal to the Liancheng bridge width (27 m). In this case, the distance of two arch ribs is 34 m. The width variation was investigated with values lower than 27 m and the distance of arc ribs was set proportional to width value. According to Table 9, by decreasing the bridge width, the responses were decreased.

Table 9.

Mean responses of bridge components under width variation and height variation.

Width (height)/span	Displacement (cm)									Acceleration (m/s²)
	Arch crown			Tower			Center of deck			Arch crown			Tower			Center of deck
	$Ux$	$Uy$	$Uz$	$Ux$	$Uy$	$Uz$	$Ux$	$Uy$	$Uz$	Long.	$Tra$	Vert.	Long.	$Tra$	Vert.	Long.	$Tra$	Vert.
Width variation of both deck and arch ribs
9/100	0.50	20.92	−16.19	13.05	6.17	−2.41	1.61	11.22	−27.38	1.43	1.28	1.13	1.70	2.67	0.45	1.57	1.18	2.14
8/100	0.52	20.72	−15.45	11.84	6.03	−2.35	1.44	11.58	25.24	1.44	1.24	1.15	1.71	2.71	0.45	1.57	1.28	2.03
7/100	0.54	20.52	−14.70	10.62	5.89	−2.28	1.26	11.94	−23.08	1.45	1.19	1.16	1.72	2.74	0.44	1.57	1.38	1.91
Width variation of the deck
7/100	0.50	20.92	−16.19	13.05	6.17	−2.41	1.61	11.22	−27.38	1.43	1.28	1.13	1.70	2.67	0.45	1.57	1.18	2.14
6/100	0.52	20.91	−15.50	12.00	6.15	−2.36	1.44	11.60	−25.32	1.44	1.26	1.15	1.73	2.72	0.45	1.57	1.25	2.04
5/100	0.54	20.90	−14.81	10.95	6.13	−2.31	1.27	11.98	−23.25	1.44	1.23	1.17	1.75	2.76	0.45	1.56	1.31	1.94
Height variation of the arch
74/400	0.50	20.92	−16.19	13.05	6.17	−2.41	1.61	11.22	−27.38	1.43	1.28	1.13	1.70	2.67	0.45	1.57	1.18	2.14
72/400	0.48	21.30	−16.93	13.37	6.04	−2.39	1.42	10.09	−27.50	1.38	1.23	1.12	1.65	2.67	0.45	1.50	1.26	2.05
69/400	0.46	21.68	−17.67	13.68	5.90	−2.36	1.22	8.96	−27.61	1.32	1.17	1.11	1.60	2.67	0.45	1.43	1.34	1.95

The cause of reduction in responses is decreasing the weight and mass of the bridge. Therefore, in the case of deck with decreased width and closer arch ribs (while other parameters were kept constant), the least responses were obtained in comparison with the case study bridge and the model with reduced deck only.

To consider the effects of the bridge’s length and height variation, different rise to span values were chosen. Again, the maximum height value for the bridge was set equal to the height of the liancheng bridge because of the stability problems. According to Table 9, by increasing the rise to span ratio in the bridge, the responses were increased and the situation became severe. The reason is that the bridge become more stable by reducing the rise to span ratio.

Conclusion

The effects of three-component earthquake excitations on the cable-stayed CFST arch bridge were investigated through an analytical approach considering the variation of different parameters. Taking into account the investigation and observations from the case study, the following can be concluded:

The cable-stayed arch bridge subjected to both horizontal and vertical components of earthquakes is more vulnerable than those subjected to horizontal ground motion only. The effects of vertical seismic excitation on the cable-arch bridge can be tremendous and ignoring the vertical acceleration of ground motions may cause many damages. Approximately 4% average increasement in maximum responses is seen by including the vertical excitation of the earthquake.

The vertical and horizontal components of the ground motion have mutual effects on each other and on the overall responses of the bridge. For example, the longitudinal components of ground motion have also considerable influences on the vertical vibration of the bridge deck. So, in order to decrease the effects of vertical accelerations of earthquakes besides the effects of horizontal accelerations, it is important to extend practical methods.

Moreover, the vertical ground motion increases the axial force level and variation in columns significantly. Increase in the axial force results in corresponding reduction in shear capacity within the vertical members and increases the potential for shear failure. Thus, waiving the vertical component of the ground motion in the design process of the cable-arch bridge can cause critical underrate in demands and therefore can endanger the overall safety of the structure. Thus, including the vertical ground motion especially in the vicinity of active faults is crucial for the reliable seismic assessment of the structures.

The magnitude and epicentral distance of the earthquakes have direct relation to the intensity of the responses which means that by increasing the magnitude and by being in near-fault zone the responses become increased about 3% in average. Based on the results, in the majority of responses, the effects of near-fault excitations are dominant. However, the soil type is a determinative criterion so that the soil type IV leads to the maximum responses. By considering the spatial variation of the seismic ground motion, the structures were exposed to serve condition regarding the response variation at supports.

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) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Salar Farahmand-Tabar

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