Response Characteristics of Irregular Continuous Rigid Frame Bridges with Long-Span and High-Rise Piers under Ground Motion Excitations with Different Fault Distances

Abstract

An innovative seismic performance evaluation strategy for irregular rigid frame bridges with a long-span and high-rise piers under the action of ground motions with different fault distances is presented in this paper. A total of 129 mainshock records taken during the Wenchuan earthquake, from national seismic stations with different fault distances, were analyzed using statistical methods, to determine the attenuation characteristics of the intensity index of the Wenchuan earthquake records from the perspective of aseismic engineering, and the attenuation of the acceleration response spectrum is discussed. The Miaoziping Bridge on the Dujiangyan–Wenchuan Expressway, which was damaged in the Wenchuan earthquake, is taken as the analysis background; two sets of samples for long-span continuous rigid frame bridges with different pier heights are constructed, to discuss the seismic response characteristics of continuous long-span rigid frame bridges; and representative values for the natural periods of these two bridge structural groups are subsequently compared and analyzed. After the peak responses for various bridges with various pier heights are determined through a response spectrum analysis under the action of ground motions with different fault distances, and the surfaces for the obtained peak responses are fitted and the response characteristics for different fault distances are discussed. It is shown in the results that the seismic response characteristics of the continuous rigid frame bridges with long-span and high-rise piers were significantly different under the action of the ground motions with different fault distances, and the seismic responses of these two bridge groups were distinctly larger under the action of near-fault ground motions. Furthermore, based on the above research, suggestions for the pier arrangement and bridge site selection for continuous rigid frame bridges with long-span and high-rise piers are also discussed. The results of this paper also provide some theoretical guidance for the sustainable development of bridges with long-span and high-rise piers, from the perspective of bridge seismic response characteristics.

1. Introduction

It is known that there are numerous densely distributed seismic zones in China’s western region. For railway and highway bridges built in this area, the seismic demands are different from bridges in other areas [1]. In addition, the western mountain area features deep valleys and high mountains. Bridges located in this region are generally irregular structures and their seismic responses have obvious near-fault characteristics [1,2]. With the sustainable development of China’s transport system, there are more and more completed and under-construction railways and highways in the western region, such as the Sichuan–Tibet Railway, Sichuan–Qinghai Railway, Chengdu–Lanzhou Railway, Lijiang–Shangri-La railway, as well as the Ya’An-Xichang Expressway, Tibetan region Expressway, etc. Thus, how to evaluate the seismic performance of bridges on these routes has received increased attention [2].

In comparison with general continuous rigid frame bridges, the structural characteristics of the frequently adopted bridge structural type in western China are usually include long-span and high-rise piers. Moreover, there are notable height differences between adjacent piers, sometimes up to thirty or forty meters. In recent years, the earthquake activity in Western China has been frequent, and the impact of earthquake-induced damage to bridges has been reported as high compared with other transportation systems. Despite comprehensive research efforts [3,4,5] since the recognition of the problems of this irregular structural system [6,7], a large percentage of damage and the collapse of bridges during earthquakes is still attributed to the irregular bridge structure; for example, Baihua Bridge in China [8] and Huilan overpass Bridge in China [9]. Detailed analysis of the seismic-induced damage to bridges revealed that approximately 50% of the failures were either directly or indirectly attributable to an irregular structure, stiffness/strength, or mass distributions [7]. Both the 2008 Wenchuan earthquake in China [10] and the 2016 Kumamoto earthquake in Japan [11] showed that the current seismic design methods and seismic performance evaluation standards for irregular structures are insufficient, and there is an urgent need for a set of seismic performance evaluation standards for irregular bridges.

Currently, methods such as the seismic fragility analysis method, dynamic time history analysis method, and response spectrum analysis method are the most common and preferred options for the seismic performance analysis and evaluation of bridge structures. These methods also provide a substantial theoretical basis for the sustainable development of bridge seismic response analysis. Significant scientific efforts and resources have been committed in recent decades to improving the assessment of seismic risk, to reduce the loss of life and property. Fragiadakis M et al. [12] summarized the state of the art of the existing methods, as well as problems with ground motions and structural performance assessment. Kassem M M et al. [13] presented a review of the different methodologies developed for the assessment of the seismic fragility of highway bridges. Moreover, numerous studies [14,15] on the application of the seismic fragility method to bridges have been performed. Simultaneously, extensive research into dynamic time history analysis and response spectrum analysis [16,17,18,19] has been conducted, to achieve an appropriate assessment of the seismic performance analysis of bridge structures.

A large number of ground motion records are required for an incremental dynamic analysis if seismic fragility analysis is adopted to evaluate the seismic performance of a bridge structure [13]. This means it is a time-consuming and complicated job to evaluate the seismic performance of irregular bridges under the actions of ground motions with different fault distances. Meanwhile, several representative ground motion records are generally selected for engaging in dynamic time history analysis [16,17,18,19], and because of the constraints on specified ground movements, the calculation findings do not have general applicability. Moreover, maximum bridge structural responses can also be determined from a response spectrum analysis under a given ground motion; i.e., the relationship between the most unfavorable response of bridge structures and the ground motion parameters is specified using a response spectrum analysis [20].

Statistical processing of the responses of a simple oscillator to a wide variety of ground motions is involved in response spectrum analysis, and the characteristics of ground motion and structural response are specified clearly and simply in this method [21]. Therefore, considerable attention has been devoted to developing ground motion response spectra and their use in the response analysis of bridges. Brinissat M et al. [22] applied the response spectrum method to evaluate the seismic responses of a prestressed reinforced concrete girder. Gupta T et al. [23] used the response spectrum method to calculate a numerical model of a three-span bridge with different inclination and curvature angle combinations, and the seismic behavior of a curved bridge under various combinations was discussed. Chen et al. [24] applied the response spectrum method to a long-span cable-stayed bridge and studied the influence of seawater depth on the seismic characteristics and seismic response of bridges near the sea. Xing et al. [25] studied the response spectrum characteristics of near-fault Taiwan Chi-Chi ground motions and their influence on a long-span concrete-filled steel tubular arch bridge. Haciefendioglu K et al. [26] used the response spectrum method to study the effects of ground motion due to explosive loads on the dynamic response of historical masonry arch bridges. However, few works in the literature have been devoted to the seismic response analysis of irregular rigid frame bridges with long-span and high-rise piers under the action of ground motions with different fault distances using the response spectrum method.

In light of the above discussions, this study intended to provide an innovative and simple seismic performance evaluation strategy for irregular rigid frame bridges with long-span and high-rise piers under the action of ground motions with different faults. Thus, a statistical regression analysis on the attenuation characteristics of the ground motion intensity index was carried out first, which indirectly reflected the change in structural maximum response with different fault distances. Then, the main vibration mode and representative natural periods of the two bridge groups were determined, which corresponded to the horizontal axis of the maximum response spectrum. Finally, the given ground motion attenuation characteristics and structural dynamic characteristics, an innovative study is conducted to evaluate the seismic risk of two long-span irregular bridge groups with different pier heights.

2. Brief Introduction to Response Spectrum Analysis

The seismic response spectrum of a single-degree-of-freedom oscillator is taken as a case study to briefly introduce response spectrum analysis. The motion differential equation of a single-degree-of-freedom oscillator under the action of ground motion is derived from the D’Alembert principle [27].

$$m(\ddot{{\delta }_g}+\ddot{y})+c\dot{y}+ky=0$$

(1)

where $m$, $c,$ and $k$ are the mass, damping, and stiffness of the oscillator, respectively. $\ddot{y}$, $\dot{y},$and $y$ are the acceleration, velocity, and displacement of the oscillator, respectively. $\ddot{{\delta }_g}$ is the ground motion acceleration time history record.

Equation (1) can be expressed as

$$\ddot{y}+2\zeta \omega \dot{y}+{\omega }^{2}y=-\ddot{{\delta }_g}$$

(2)

where $\zeta$ is the damping ratio, and $\zeta =c/c_{cr}$. $c_{cr}$ is the critical damping. $\omega$ is the undamped circular frequency.

The oscillator displacement can be solved using the Duhamel integral [27]

$$\mathrm{y}\left(t\right)=\frac{1}{{\omega }_d}{\int }_0^{\mathrm{t}}{e}^{-\zeta \omega (t-\tau )}\ddot{{\delta }_g}(\tau )sin{\omega }_d(t-\tau )d\tau$$

(3)

where ${\omega }_d$ represents the damped circular frequency, ${\omega }_d=\omega \sqrt{1-{\zeta }^2}$.

The relative velocity and acceleration of the oscillator can be obtained from the first and the second derivatives of Equation (3), respectively.

$$\dot{y}\left(t\right)=-\frac{\omega }{{\omega }_d}{\int }_0^t{e}^{-\zeta \omega \left(t-\tau \right)}\ddot{{\delta }_g}(\tau )cos[{\omega }_d\left(t-\tau \right)+\alpha ]d\tau$$

(4)

$$\ddot{y}\left(t\right)=-\frac{{\omega }^2}{{\omega }_d}{\int }_0^t{e}^{-\zeta \omega \left(t-\tau \right)}\ddot{{\delta }_g}(\tau )sin{[\omega }_d\left(t-\tau \right)+2\alpha ]d\tau$$

(5)

where $\alpha =tan\zeta$. It can be assumed that ${\omega }_d\approx \omega$ when the structural damping ratio is small, and the above two equations can be simplified as

$$\dot{y}\left(t\right)={\int }_0^t{e}^{-\zeta \omega \left(t-\tau \right)}\ddot{{\delta }_g}(\tau )cos[{\omega }_d(t-\tau )]d\tau$$

(6)

$$\ddot{y}\left(t\right)=\omega {\int }_0^t{e}^{-\zeta \omega \left(t-\tau \right)}\ddot{{\delta }_g}(\tau )sin[{\omega }_d(t-\tau )]d\tau$$

(7)

Due to the complexities of ground motions, it is necessary to use irregular functions to express $\ddot{{\delta }_g}$. Therefore, the numerical integration method is an optimal way to obtain the response time history curve of the system. By changing the period and damping ratio of the single-degree-of-freedom system, several seismic response time-history curves can be obtained using the action of a given ground motion. After the maximum is found from the curve, the relative displacement response spectrum, pseudo velocity response spectrum, and pseudo acceleration response spectrum can be calculated [27].

The absolute maximal responses of a set of single-degree-of-freedom systems with different periods and the same damping ratio under the action of a given ground motion is determined using the response spectrum, as shown in Figure 1. The response spectrum shows the relationship between the maximum absolute value of the response and the period. Although the response spectrum is defined using the reaction of a set of single-degree-of-freedom systems, it reflects the nature of the ground motion process. According to response spectrum theory, the actual maximum response of the structure can be determined by taking the spectral values of a particular coordinate. In other words, a response spectrum is determined using just the acceleration time history record, and the shape of the response spectrum does not change with the structure. For structures with different damping ratios and different natural periods, the response value is obtained by taking the spectrum value corresponding to the coordinate that stands for the period of the structure.

3. Statistical Characteristic Analysis

3.1. Selection of Strong Earthquake Records

The ground motion records used in this paper were derived from the Wenchuan earthquake and were provided by the China Strong Motion Networks Center. Records whose intensity index discreteness was relatively large and whose seismic waveforms had serious errors were removed from the 174 national stations, and the ground motion records from the remaining 129 stations with known site conditions and fault distances were collected to analyze the statistical characteristics of Wenchuan Earthquake.

According to the fault distances, the ground motion records of 129 stations were grouped. To avoid the number of stations being too small in a certain group and preventing an accurate result, the number of stations in each group had to be relatively balanced. Finally, the records with different fault distances were divided into seven groups, as shown in Figure 2.

Since the original records had baseline drift, background noise, and errors caused by sensor tilting, the raw records could not be used directly. In this paper, background noise elimination and baseline correction were carried out on the ground motion records, according to works in the literature [28,29]. Uncorrected (solid black line) and corrected (solid blue line) ground motion records are shown in Figure 3.

3.2. Attenuation Characteristic Analysis

3.2.1. Acceleration Response Spectrum Calculation

According to the acceleration records of the Wenchuan earthquake, acceleration response spectrums were obtained and a statistical regression analysis was performed based on the fault distance groups in Figure 2. Then, the ratio of vertical and horizontal acceleration spectral responses, including UD vs. EW and UD vs. NS, was obtained and the attenuation characteristics of the acceleration response spectrum were obtained. Earthquakes propagate inside and on the surface of the Earth in the form of waves that have different directions. In order to comprehensively analyze the attenuation characteristics of ground motions, corresponding acceleration response spectra of the selected ground motions are given in different directions. The acceleration response spectrums for the selected ground motions from the seven groups in different directions were plotted in a logarithmic coordinate system, as shown in Figure 4, Figure 5 and Figure 6. The average response spectrums of the ground motions of the seven groups with different fault distances are also plotted in the figures using thick solid lines, while the last subfigure in Figure 4, Figure 5 and Figure 6 summarizes the seven average acceleration spectrums. In these three figures, “R”, “Sa”, and “Period” denote the fault distance, acceleration spectrum, and natural period, respectively, of a single-degree-of-freedom structure.

The following can be observed from Figure 4, Figure 5 and Figure 6:

• The farther the fault distance, the smaller the value of the acceleration response spectrum in three directions. In a near-fault Earthquake (i.e., fault distances within 50 km in this paper), the attenuation of the acceleration spectrum is very rapid when increasing the fault distance. In a far-fault Earthquake (i.e., fault distances within 300–550 km in this paper), the attenuation of the acceleration spectrum is slow. In a mid-fault Earthquake (i.e., fault distances within 50–300 km in this paper), the attenuation rate of the acceleration response spectrum lies between the two aforementioned rates.
• The maximums of the acceleration spectrum values vary in the range of 0.1–0.5 s, which is related to the predominant periods of site soils. The typical period for the seismic records used in this paper is 0.35 to 0.45 s.

3.2.2. Response Spectral Ratio Calculation

Furthermore, a statistical regression analysis was performed on the response spectral ratios for vertical and horizontal ground motions with various fault distances to determine the attenuation characteristics of the response spectral ratios. The ratio curves of the ground motions of the seven groups with different directions and different fault distances are shown in Figure 7 and Figure 8. The average response spectral ratios for the ground motions of the seven groups with different fault distances are also plotted in these two figures using thick solid lines, and the final subfigure in Figure 7 and Figure 8 summarizes the seven average spectra ratios. Meanwhile, the recommended spectral ratio for vertical and horizontal ground motions in the industry specification Guidelines for Seismic Design of Highway Bridges (2008) [30] is also plotted using brown horizontal solid line in the final subfigures of Figure 7 and Figure 8. UD/EW in Figure 7 are the ratios of the vertical (UD) and EW horizontal ground motions, and UD/NS in Figure 8 are the ratios of the vertical (UD) and NS horizontal ground motions, respectively.

The following conclusions can be drawn from these two figures:

• With increasing fault distances, the spectral ratios of the ground motions indicate a decreasing trend in both UD vs. EW and UD vs. NS directions.
• In the range 0~150 km, the spectral ratio in the UD vs. EW and UD vs. NS directions appears as two wave crests for both the short-period (0.01–0.1 s) and long-period (3–10 s), which have a value larger than 0.65, which is adopted in the Guidelines for Seismic Design of Highway Bridges (2008). This indicates that using 0.65 to estimate the vertical response spectrum is insecure for a near-fault earthquake. The spectral ratio curves in the preceding two directions in the range 150–300 km appear as only one wave crest located in the long period (3~10 s) with a value larger than 0.65; the ratio curves are flat in the range 300–550 km and are all below the commonly used value of 0.65, which indicates that, for far site vibration, it is safer to use a spectral ratio of 0.65 to estimate the vertical seismic action and the actual ground motion for structural analysis.
• The spectral ratio in the short period is larger than that in the long period with a fault distance R < 50 km in both directions, which indicates that the vertical response spectra in the near-fault ground motion records are dominated by high-frequency components, while low-frequency components account for a small proportion. The spectral ratio in the long period is larger than that in the short period with a fault distance R = 50–300 km in both directions, which demonstrates that the proportion of low-frequency components is larger than that of the high-frequency components in the mid-field and far-field ground motion records. This phenomenon is mainly attributable to the fault type of the Wenchuan Earthquake, whose fault type was thrust fault, and the vertical motion components of the thrust fault being large. In addition, the vertical radiations of the seismic wave are relatively large, so the long-period components of the acceleration spectra are relatively rich in the vertical direction.

4. Seismic Response Analysis of Irregular Continuous Rigid Frame Bridges with Long-Span and High-Rise Piers

Taking the main bridge of the Miaoziping Bridge as the research background, two groups of samples of long-span rigid frame bridges with different pier heights were constructed. Then, analysis of the vibration characteristics was carried out. According to the principle that the cumulative coefficient of mode mass participation is greater than 90%, the effective mode order and order frequency (or period) were extracted. The change in the structural acceleration response with different fault distances during the effective period of each order was further studied. The response spectra of the two bridge samples with different pier heights were used to qualitatively evaluate the action characteristics under the effect of the ground motion of the Wenchuan Earthquake. Meanwhile, the research results can provide a reference for the sustainable development of bridges with long-span and high-rise piers.

4.1. Engineering Background

The main bridge of the Miaoziping Bridge is a continuous rigid frame bridge. The whole span is arranged as 125 m + 220 m + 125 m. The main girder is a single-box, single-chamber, prestressed concrete box section. The main piers, namely 2#Pier and 3#Pier, adopt a rectangular hollow concrete section. The junction piers, namely 1#Pier and 4#Pier, have variable double-column thin-walled hollow sections, with a slope of 75:1 in the longitudinal direction. Two bidirectional movable pot bearings are arranged at each junction pier. The configurations of the column cross-section and a full-bridge overview are shown in Figure 9.

The Miaoziping Bridge is about 15 km away in a northwest direction from Dujiangyan City and about 15 km away from the epicenter of the Wenchuan earthquake, and it was seriously damaged in the Wenchuan earthquake [31].

4.2. Bridge Sample Establishments

We set up two types of bridge sample, and the number of bridge samples for each type was 10. The first type of bridge samples were defined as a group of long-span and high-pier bridges with a small difference in pier height, and their structural form is shown in Figure 10a. The second type of bridge samples were defined as a group of long-span and high-pier bridges with large variations in pier height, and their structural form is shown in Figure 10b. The height of the 1# and 4# piers was kept unchanged, and the height difference between the 2# and 3# piers was varied in different ways. Then both types of bridge samples were set up. The pier height data of the 2# and 3# piers of each type of bridge sample are shown in

Table 1. Pier height data of the bridge sample.

Bridge Sample Number	2#Pier (m)		3#Pier (m)		2#Pier/3#Pier
	1st Type	2nd Type	1st Type	2nd Type	1st Type	2nd Type
1	45.20	56.67	44.07	99.57	1.03	0.57
2	56.67	68.15	55.17	99.57	1.03	0.68
3	68.15	79.62	66.27	99.57	1.03	0.8
4	79.62	91.10	77.37	99.57	1.03	0.91
5	91.10	102.57	88.47	99.57	1.03	1.03
6	102.57	114.05	99.57	99.57	1.03	1.15
7	114.05	125.52	110.67	99.57	1.03	1.26
8	125.52	137.00	121.77	99.57	1.03	1.38
9	137.00	148.47	132.87	99.57	1.03	1.49
10	148.47	159.95	143.97	99.57	1.03	1.61

.

4.3. Natural Vibration Period Analysis of the Two Types of Bridge

Based on the calculation results from the modal analysis of the two types of bridge samples, the mass participation percentages of each vibration mode in three directions are shown in Figure 11 and Figure 12. In the figures, the X-direction, Y-direction, and Z-direction stand for the longitudinal direction, transverse direction, and vertical direction of the bridge, respectively. The gradient color in the figures represents the percentage size of the mass participation percentages of each vibration mode, and the specific percentage size can be seen on the right of each subgraph.

The results in Figure 11 and Figure 12 show the following: (1) For both types of bridge sample, the required vibration order in the X-direction and Y-direction was 30 when the mode mass cumulative participation percentage reached 90%, while that in the Z-direction was 70, which indicates that the participation of the higher-mode was more obvious in the vertical deformation of both types of bridge sample, so the vertical motion form was more complex. (2) For the first type of bridge samples, the third-order to fourth-order modes were mainly in the X-direction, the first-order to third-order were the main modes in the Y-direction, and the main modes were sixth-order to eighth-order in the Z-direction. However, for the second type of bridge samples, the third-order to fourth-order modes were mainly in the X-direction, and first-order to second-order were the main modes in the Y-direction. Compared with the first type of bridge samples, the orders of the horizontal main modes were lower. In the Z-direction, the seventh-order mode was dominant, and with the increase in pier height, the vertical main mode stayed constant, while the participation of the high-order modes began to increase and the bridges showed more complex forms of motion. (3) For both types of bridge samples, with the increase in the pier height, the proportion of deformation participation of the main mode in the three directions gradually decreased, and that of the high-order modes gradually increased.

The period variation ranges of the two types of bridge samples in the horizontal and vertical directions are shown in Figure 13 and Figure 14. The two horizontal axes are the logarithmic coordinate system.

The results in Figure 13 and Figure 14 show that (1) as the pier height increased, the mode period of the lower order (1–5th order) varied greatly, while that of the higher order varied gently, which indicated that the low-order mode period was more sensitive to the variation in pier height. (2) The results in Figure 11, Figure 12, Figure 13 and Figure 14 show that the mode period corresponding to the main modes of the first type of bridge samples was 1.0 s to 3.5 s in the X-direction, 1.0–5.0 s in the Y-direction, and 0.5–1.0 s in the Z-direction. From Figure 12, Figure 13 and Figure 14, it is clear that for the second type of bridge samples, the mode period was 1.35–2.57 s in the X-direction, 2.02–5.00 s in the Y-direction, and 0.67–0.76 s in the Z-direction. Compared with the first type of bridge samples, the second type of bridge samples were characterized by a shorter period in the X-direction and Z-direction and a longer period in the Y-direction.

4.4. Peak Seismic Response Analysis

The representative mode period was determined based on the preceding section. Then, the structural peak response surface corresponding to the change in acceleration spectra with different fault distances under the effect of ground motion in the EW, NS, and UD directions was fitted using the bilinear interpolation algorithm, as shown in Figure 15. To highlight the law of the change, the X axes (namely, fault distance) and Y axes (namely, period) both used the logarithmic coordinate system.

With the action of horizontal earthquakes, the following can be concluded from Figure 15: (1) Under the action of a horizontal ground motion whose fault distance was 0–50 km, the peak acceleration of the structure with a representative natural period from 0.1 s to 1.0 s was relatively large, while that of structures with a representative natural period from 1.0 s to 3.0 s was intermediate and that of structures with a representative natural periods from 3.1 s to 5.0 s was relatively small; (2) Under the action of a horizontal ground motion with fault distance within 50–200 km, the peak acceleration of the structures with a representative natural period from 0.1 to 1.0 s decreased faster than that of the structures with representative natural periods from 1.0 to 5.0 s, and the disparity with the peak acceleration of the structures with natural periods of 1.0–3.0 s and 3.1–5.0 s decreased. (3) Under the action of a horizontal ground motion whose fault distance was within 200–540 km, the peak acceleration responses of the structures with different representative natural periods were consistent and their values were relatively small. (4) With the increase in pier height, the main order of the vibration modes of the two types of bridge samples in the horizontal direction gradually tended to become lower order, and the corresponding natural period became longer. This indicated that the higher the pier height, the longer the representative natural period, and the greater the distance from the dangerous range of the natural period (namely, 0.1–1.0 s). Thus, it can be reported that with the increase in pier height, the peak response of the structural acceleration decreased under the action of a near-fault ground motion whose fault distance was within 0–50 km, which indicates that the bridges with a greater pier height had a better ability to resist the near-fault ground motion in the horizontal direction.

For the action of vertical earthquakes, the following can be seen in Figure 15: (1) Under the action of a vertical ground motion whose fault distance was within 0–50 km, the vertical peak acceleration response of a structure with a representative vibration period from 0.3 to 0.4 s appeared to have the maximum value; (2) Under the action of a vertical ground motion with a fault distance within 50–200 km, the peak acceleration response of the structures with a representative natural period from 0.1 to 1.0 s decreased faster than that of the structures with representative natural vibration periods from 1.0 to 5.0 s. (3) Under the action of a vertical ground motion with fault distances within 200–540 km, the peak acceleration responses of the structures with different natural periods were consistent and their values were relatively small. (4) With the increase in pier height, the main order of the vibration modes of the two types of bridge samples changes little, and the corresponding representative natural periods of both types of bridge samples were 0.5–1.0 s and 0.67–0.76 s, respectively. The proportion of higher-mode participation was greater than for the horizontal direction with increasing pier height, which indicates that the peak response of the vertical acceleration of the long-span and high-pier irregular rigid frame bridge was greater than that of the low-pier bridge under the action of near-fault ground motions with a fault distance within 0–50 km. Namely, the higher the pier height, the greater the possibility of failure in the near-fault vertical ground motion.

5. Conclusions

Based on the Wenchuan earthquake, the attenuation law of the intensity index and acceleration spectra of near-fault and far-field ground motion were studied. Taking the main bridge of Miaoziping Bridge as the engineering background, the responses of two types of rigid frame bridge samples with different pier heights were analyzed. The main conclusions of this paper are as follows:

(1)

The greater the fault distance, the smaller the value of the acceleration response spectrum. The near-fault reaction spectrum was attenuated quickly as the fault distance increased, whereas the far-fault response spectrum was attenuated slowly, and the mid-fault response spectrum was attenuated in the middle.

(2)

For near-fault earthquakes with fault distances less than 50 km, the ratios of vertical and horizontal PGA were more than 2/3. Therefore, it is unsafe to estimate the vertical seismic action by adopting a ratio of 2/3 in the area near the fault.

(3)

In this paper, the main period range in the longitudinal and vertical directions for the second type of bridge samples was shorter than that of the first type of bridge samples, while the main period range in the transverse direction became longer. From the perspective of the dynamic characteristics of the structure and the characteristics of the ground motion of the Wenchuan Earthquake, the longitudinal and vertical seismic responses of the second type of bridge samples was more severe than those of the first type of bridge samples, and the potential damage would be greater under the action of earthquakes with a fault distance less than 50 km. For this reason, during selection of the structural form of long-span and high-pier rigid frame bridges, it is better to choose a simple shape as far as possible, which means that the quality and stiffness distribution should not only be symmetrical for the superstructure, the main pier should also be symmetrically arranged to improve the overall seismic performance.

(4)

Limited to the two types of bridge samples discussed in this paper, the peak acceleration response of the short-period bridge structures under the action of near-fault ground motions was very large, and as the fault distances increased, the response was attenuated rapidly. When the fault distances were between 200 km and 540 km, the response tended to be flat.

(5)

It is suggested that the location of a high-pier and long-span continuous rigid frame bridge should avoid faults as much as possible, with an avoidance distance of at least 50 km.

(6)

The results of this paper show that the fault distance has a great influence on the ground motion response of a bridge when a bridge site is being selected, and the selection of a bridge site with a large fault distance can reduce the seismic response of the bridge to a certain extent, which is conducive to improving the long-term performance of the bridge, which is a reflection of the sustainability of the bridge’s performance from the perspective of bridge site selection.

(7)

According to the comparative study of the two bridges in this paper, the results show that long-span and high-pier continuous rigid frame bridges with a symmetrical arrangement of piers have better seismic performance, which is a reflection of the sustainability of the bridge’s performance from the point of view of the selection of the bridge form.