Seismic experimental study on a concrete pylon from a typical medium span cable-stayed bridge

Abstract

According to the current seismic design codes of bridges in China, cable-stayed bridges have been usually required to remain elastic even subjected to strong earthquakes. However, the possibilities of pylon plastic behavior were revealed in recent earthquake damages. The lack of due diligence in the nonlinear seismic behavior of the pylon has caused a blurry understanding about the seismic performance of such widely built though less strong earthquake experienced structures. In light of this point, a 1/20 scaled concrete pylon model which from a typical medium span cable-stayed bridge was designed and tested on the shaking table longitudinally. The dynamic response and seismic behavior of the pylon were measured, evaluated and compared to reveal its vulnerable parts and nonlinear seismic performance. The results show that most parts of the concrete pylon remain elastic even under very strong excitations, which means a sufficient safety margin for current pylon longitudinal design. The most vulnerable parts of the pylon appeared first at the pylon bottom region, cracks opening and closing at the pylon bottom were observed during the test, and then extended to the lower column and middle column around the lower strut.

Keywords

cable-stayed bridge / pylon / shaking table test / seismic behavior

Introduction

Cable-stayed bridges have been widely constructed owing to their elegant shapes and economical cost over the past decades. For most engineering practices, bridge pylons are usually required to remain almost elastic even under occasionally occurred earthquakes in accordance with the bridge seismic guidelines [¹]. However, strong earthquakes including some near fault ground motions occurred in the past decades can result in severe damages to many civil engineering structures due to their special features caused by forward rupture directivity and fling step effects [²–⁴].

As a fact, China has many bridges been built or in construction in the regions where strong earthquakes are most likely to occur, such as 1999 Chi-Chi Earthquake in Taiwan and 2008 Wenchuan Earthquake in Sichuan. Therefore, even the bridge has been well designed in accordance with the seismic codes or guidelines, strong earthquakes may still cause unexpected damages.

The type of connection between the bridge deck and tower is one of the most important factors that affect the response of cable-stayed bridges. A strong connection between the tower and the deck will reduce the displacement response. However, such form of connection will increase the magnitude of base shear and bending moment at the bottom of the towers [⁵]. According to current conservative seismic design of pylons, most bridges are theoretically and practically ensured to behave fully elastic under the site-specific ground motions by setting dampers between the deck and tower which can mitigate the seismic induced responses in the longitudinal direction [⁶–⁸].

Chang et al. [²] reported the spalling and splitting of the concrete around the core at the bottom region of the pylon of Chilu cable-stayed bridge which was under construction during the 1999 Chi-Chi Earthquake. As one major type of the important lifelines, particularly in metropolitan areas, nonlinear seismic behavior of the pylon of the cable stayed bridges under strong earthquakes has attracted more and more attention from the bridge engineering and research communities [⁹–¹¹].

Some researchers have studied the seismic response of cable-stayed bridges using experimental method. Several shaking table tests of scaled long span bridge models have been reported in the past few decades. Garevski et al. [¹²] performed damping and seismic response measurement tests of a small scale physical cable stayed bridge model, and Caetano et al. [¹³,¹⁴] focused on the effect of dynamic cable interaction with the deck and towers by shaking table tests performed on a 1/150 physical aluminum alloy model of Jindo Bridge. Wang et al. [¹⁵] performed a shaking table test for a 1/60 Plexiglas model to study the dynamic behavior of a self-anchored suspension bridge. Very recently, Wang et al. [¹⁶,¹⁷] have carried out the transverse seismic behavior studies of a cable-stayed bridge model excited by shaking tables only in transverse direction.

As well known, cable-stayed bridges usually have better seismic performance owing to their longer periods, particularly in longitudinal direction. Therefore, their longitudinal seismic damage analysis when subjected to strong ground motions are less carried out compared to the transverse studies. To the authors’ knowledge, we are lack of real earthquake examinations and meanwhile the nonlinear seismic behavior study of the concrete pylon is insufficient either in longitudinal or in transverse directions. The seismic performance of such bridges under strong earthquakes is still far from well understood.

To advance the research on this topic, a typical medium span cable stayed bridge in China was selected as the prototype for shaking table test study. A 1/20 scaled H-shape pylon model consists of the pylon itself and an mass loading system was specially designed, constructed and then tested on the shaking table subjected to selected ground motions longitudinally to investigate the seismic behavior of medium span cable stayed bridges with twin H-shape concrete pylons under strong ground motion shaking in longitudinal direction.

Design of the test model

Similarity coefficient

According to the laws of similarity of dynamic testing as applied in many shaking table tests [¹⁸], the geometrical similarity coefficient S_l=0.05 was first determined, and then the similarity coefficient of the elastic modulus S_E=0.3 was required to meet the maximum payload of the shaking table’s capacity (25 t). Considering the objective of this test, the similarity coefficient of acceleration S_a was also required as 1 to count in the real gravity effect, thus the last coefficient of mass density S_r=6 was calculated from Eq. (1) [¹⁸], and Table 1 shows all the concerned coefficients of the test model.

(1){(a\rho l/E)}_m={(a\rho l/E)}_p,

where a is acceleration, \rho is mass density, l is representative length, E is the modulus of elasticity of the material, and m and p represent model and prototype, respectively.

Model design

The purpose of this test is to investigate the seismic behavior of the concrete pylon of the typical cable stayed bridge in longitudinal direction. The prototype adopted is a widely applied structure form for cable stayed bridges, i.e., there is no connection between the bridge deck and the lower cross beam in longitudinal direction, resulting in a floating movement of deck under dynamic loading. Therefore, the model was designed as the so called “floating system” in longitudinal direction.

To simplify the construction, both the column and the crossbeam used solid rectangular sections which satisfied similarity laws for axial and bending stiffness of the pylon. The total height of the model is 4.785 m. As aforementioned, the mass density S_r requires to be 6 to satisfy the similarity equation, however, it is not practical even when micro-concrete is used, which means additional artificial mass are required to attach on the model. Xiang et al. [¹⁹] proposed the single-mass simplified model for floating cable-stayed bridges, and they stated that most of girder’s inertia forces were transferred to pylon tip by the outermost pairs of cables under longitudinal earthquake waves. The modal analysis of the real bridge of a floating cable-stayed bridge found that the first-order longitudinal mode plays an absolute advantage in structure response. Therefore, based on the single-mass simplified model and modal analysis method [²⁰], we got the simplified test model of the real bridge, as shown in Fig. 1.

The finite element (FE) analysis showed that the first-order modal mass participation factor of the test model is over 90%, hence only first order effective mass was taken into account in simplifying the test model. Based on the similarity equation, the pylon needs additional artificial mass of 5.42 t. The distribution of the additional mass and first-order mode along the height of the pylon were shown in Table 2.

Equations (2) and (3) define the effective modal mass M_{\mathrm{1}}^{\ast } and effective modal heights h_{\mathrm{1}}^{\ast } [²⁰]. Applying the data in Table 2 into Eqs. (2) and (3), we obtained that M_{\mathrm{1}}^{\ast } is 3.248 t and h_{\mathrm{1}}^{\ast } is 3.084 m. Based on the equivalent bending moment at the pylon base, we lumped the equivalent artificial mass at the top of each pylon column using two 1.26 t concrete blocks, resulting the equivalent height of 3.985 m from the pylon bottom to the center of the mass block, as shown in Fig. 2.

(2)M_n^{*}={\left({\displaystyle \sum _{j=\mathrm{1}}^N{m}_j{\phi }_{jn}}\right)}^{\mathrm{2}}/{\displaystyle \sum _{j=\mathrm{1}}^N{m}_j{\phi }_{jn}^{\mathrm{2}}},

(3)h_n^{*}={\displaystyle \sum _{j=\mathrm{1}}^N{h}_j{m}_j{\phi }_{jn}}/{\displaystyle \sum _{j=\mathrm{1}}^N{m}_j{\phi }_{jn}}\mathrm{.}

In the loading system, the deck was connected to the pylon by 4 pairs of steel cables which transfer all deck’s dead load to pylon, and this only satisfied the mass similarity law considering its dynamic loading mechanics under longitudinal excitation in a floating system [¹⁹]. In addition, 2 vertical steel columns on each side were set up to support the deck and more importantly for safety reasons.

Construction and installation of the test model

A 2.6 m (T)×1.4 m (L)×0.3 m (V) C30 concrete pedestal weighting 3 t was first poured as the pylon base which will be bolted with the table surface in the future. And then the construction of the pylon was started from the positioning of rebars, and then concrete was poured from the pylon bottom to the top in 3 separate times, during the cast of the upper column of pylon, the shaped rolls were embedded to be used as the cable hinges (Fig. 3).

After the model was shaped and the concrete had the targeted strength, it was lifted by in-door crane to the table surface. However, in order to make a more “real” pylon representing the reasonable dead load status, the assembling of the bridge followed the 3 steps below:

1) Locate the pylon, deck and supporting columns, and then put the steel blocks into the box and sealed with motor.

2) Wear the steel wire from the embedded hinge (Fig. 3(b)) to the deck ring together with a cable force sensor for each cable, the cable targeted force was calculated from the FE analysis to ensure that 90% of the steel masses will be transferred to the pylon via cables, which makes the axial-load ratio at the pylon end section reach to 10%, the left 10% weight of the box will be taken by the vertical columns via roller bearings which in order to slide longitudinally while get excited.

3) adjust the cable forces to the targeted values through trial and error. After 10 times of adjustment, the 8-cable gained targeted forces and the model was in a balanced dead load state. The model ready for test is shown in Fig. 3(c).

Input ground motions and testing program

Considering the test purpose and the table capacity, 3 types of ground motion records were selected: The 1940 Imperial Valley Earthquake El Centro wave, 1999 Chi-Chi Tcu076 wave and one site-specific ground motion (artificial wave). The site-specific ground motion corresponds to 2457-year return period which given by the seismic risk assessment of the bridge construction site. All the ground motions were condensed according to the time scale factor in Table 1, and scaled to the same peak ground acceleration (PGA) of 0.1 g, as shown in Fig. 4. The scaled acceleration spectrum of the employed records is shown Fig. 5. It can be expected that the site-specific ground shaking will induce the most severe seismic response on the test model compared to the other two inputs. Therefore, in order to trace the nonlinear behavior most likely trigged by the site-specific input and meanwhile compare the seismic responses with the other 2 real earthquake records, the test loading cases were arranged in Table 3. For the safety reason, the maximum PGA of this test is set to 0.6 g for the site-specific ground motion.

Test results

The response of the bridge model was measured at 256 Hz using 70 sensors in total. The displacements and accelerations for the deck and pylon were measured by 13 displacement transducers and 33 accelerometers, respectively. The strains in the longitudinal reinforcement at critical sections of the pylon were measured by 16 strain gauges. The forces for the cables were measured by 8 force transducers. The critical sections are the bottom section of the pylon column, the sections just above the lower cross beam, and the upper and lower beam of the pylon.

Test observation

Excited by the white noise at PGA of 0.05 g, the deck was observed sliding longitudinally relative to the roller bearings in expectation, the corresponding 0.763 Hz frequency was successfully identified and it is very close to the calculated value of 0.713 Hz, indicating the mass, stiffness and loading system worked properly and correctly. Later on, with the input of increasing intensity of the El Centro waves, the longitudinal vibration was excited. One can easily notice that El Centro wave induced less response compared to the other two waves due to the its spectrum characteristics as shown in Fig. 5.

Actually, after the first 3 cases’ running, the model pylon behaved quite perfect, no cracks or damages were found. However, after the running of Case 4, first horizontal cracks appeared at the pylon bottom area as shown in Fig. 6. And then, Tcu record was used as the input, one can find that even for the same PGA, the model vibrated much more severe in Case 6 than in Case 2 (El Centro wave). Cracks were also found at the middle column and lower column area near the lower strut as shown in Fig. 7. This is mainly because of the self-vibration of the tower pylon that excited by the Tcu076 input, which is one of the near fault ground motions containing more energy in the high-frequency domain.

Further development of cracks was clearly observed after case 9 at the pylon bottom area and in the middle column near lower strut, and then, with the input of the increased PGA of site-specific waves (SS waves), the vibration went severe and more cracks appeared successively and some of them extended to the side surface of the pylon column. When the input PGA reached 0.5 g, the number of cracks was rapidly increased in the middle column of the pylon, as shown in Fig. 7. After the last running of site-specific wave at 0.6 g, the vibration of the pylon tip concrete block was very severe and considered as in the risk of hitting the shaking table surface, therefore the test was called off after running the last white noise sweep. Eventually, more cracks were observed in many other locations as shown in Fig. 8.

As seen from Fig. 8, the cracks were marked on the surface of the model after the test. Assuming the model standing in Fig. 3(c)) represents an east west direction, then there was an obviously damage area along the 30 cm above the pylon bottom (i.e., approximately one section height from the bottom) in west elevation where several horizontal cracks extending to the south side, where through cracks were further developed and extended to the side surface. Meanwhile, damages were also observed at the lower and middle pylon column near the lower strut, while the upper part of the column just slightly damaged and most cracks in this region closed after the shake. Usually, in the longitudinal direction, the tower pylon is controlled by its first-order mode which lead the worst damage occurred at its pylon bottom. However, as shown in Fig. 8, the middle pylon column can also be identified as a vulnerable part when subjected to near fault ground motions, which can attribute to the higher order mode triggered by this type of ground motion.

In conclusion, through the test observation, the pylon columns mainly bended under the longitudinal excitations, and the cracks induced are mainly in horizontal direction. The cracks first appeared in the bottom of the pylon, and then extended to lower and middle column near the lower strut. With the increasing intensity of the input excitations, more and more cracks appeared and some of the cracks became wider and wider, especially in the region of 30 cm above the pylon bottom, which indicates that the current stirrup ratio in this area may still not be sufficient enough. However, on the other hand, most of the cracks closed after the test under the dead load itself.

Seismic responses

Dynamic characteristics

In addition to the 3 different types of earthquake waves, 0.05 g white noise were inserted into the running cases just as in Table 3 to identify the model frequency and its variation after the input of each kind of earthquake waves. Due to the lower amplitudes in higher frequencies, noise disturbance could be critical to test signals, which resulted in failing to identify the higher modes, so that only the first two modes were successfully recognized, while they are in good accordance with the FE results as shown in Fig. 9.

Also, the test results show that the natural frequency of the tested model went down from 0.763 to 0.654 Hz after the running of the site-specific ground input at 0.35 g (Case 17) and thereafter. Remember that the test observation did reveal that the cracks extended to the side surface of the pylon column near the lower column at this level of input, which indicates the damage at this stage increased much faster than in the cases before. As we all known, due to the gravity effect, most tiny cracks will be closed when the excitation ceased, therefore the integrated stiffness of the model won’t change a lot. However, when the input motion is so big that it can induce through type cracks, the stiffness will be surely decreased accordingly.

Seismic induced acceleration

Figure 10 shows the maximum acceleration distribution along the pylon height under the 3 earthquake waves. It can be seen that for different type of earthquakes, the distribution of maximum acceleration seemed almost the same: The acceleration in the middle height of pylon was amplified most, which indicated the contribution of the column distributed mass in addition to the big concentrated concrete mass block at the tip of the pylon.

Seismic induced displacement

Displacement time histories of the test model can be achieved from two ways: 1) is directly from the displacement transducers and 2) is from the time integral of recorded accelerations, and they should be consistent with the other. Due to the limitation of displacement channels, only 7 displacement transducers were placed along the pylon model. As we made the comparison of way 2) with way 1) in Fig. 11 for the pylon tip displacement, one can see the high correspondence as expected.

Figure 12 shows the variation of displacement responses with the increasing PGAs for the mass block and deck according to the results via way 2). It can be seen that for different type of earthquakes, the distribution of maximum displacement seemed almost the same, and under the small value of PGAs, the variation is linear while fluctuate under large PGAs, and the site-specific ground motion can induce higher displacement response.

Seismic induced steel strain

Though several strain gauges were placed along the pylon columns, only those placed around the outmost bars are effective, the other strain gauge data are invalid due to low signal to noise ratio. The strain of the outermost longitudinal bars is plotted in Fig. 13, and the maximum longitudinal strain responses at locations 0.06 and 0.18 m which higher above the pylon base were also plotted in Fig. 14.

It can be seen that for different type of earthquakes, the distribution of maximum strains seems very close, and the site-specific ground motion again induces the largest strain response but in a slightly different location. By comparing with the corresponding original displacement data, it inferred that this difference might be caused by a suspicious collected signal when subjected to severe intensity of input. Strain near the pylon bottom was amplified the most. And under small value of PGAs, the strain variation is linear up while clearly goes down at 0.4 g, which indicates that yielding of the tender bar may occur at this level of PGA. One can find the yielding strain is approximately 1900 me.

Seismic induced base moment-curvature relationship

According to the section moment calculated from the recorded accelerations, the relationship between moment and curvature at pylon base was plotted in Fig. 15. It can be concluded that the behavior of the pylon is still mainly elastic and hence reliable though sever vibration of the pylon was observed.

The hysteretic loops can be seen as diffusing and narrow, though it varies with the input waves and the increase of input PGAs. Even at larger PGAs, one can see the hysteretic loops is not fullness, which indicates that only minor damages occurred to the pylon though cracks were observed everywhere around the columns base. However, on the other hand, starting from case No. 19 in Table 3, the model’s fundamental vibrating frequency decreased from 0.763 to 0.654 Hz, and it can be seen from Fig. 14 that the PGA level where the outmost steel bar firstly yield is 0.4 g, which indicates a certain stiffness degradation of the pylon structure occurred.

Conclusions and suggestions

Though cable stayed bridges have been widely built in the past decades and strong earthquakes occurred recurrently in recent years, seismic damage reports about cable stayed bridges are still insufficient. In order to better understand the seismic performance of this type of bridges, a typical concrete pylon from a medium span cable stayed bridge was designed, fabricated, installed and tested on the shaking table, the test results show that:

1) The horizontal cracks first appeared at the bottom of the pylon and then extended to lower and middle column near the lower strut during the shaking. When subjected to low excitations, the cracks closed after the shaking, and the column still stays elastic.

2) With increased intensity of the input, more cracks appeared and some of the cracks became wider, especially in the region of 30cm above the pylon bottom, eventually cracks were further developed and extended to the side surface after the outer circle longitudinal rebar yielded, which indicated that the current stirrup ratio may still not be sufficient enough, the spalling of the cover concrete and exposure of outer circle rebar may occur.

3) The pylon conserves certain ductile capacity after the first yielding of the longitudinal rebar at the pylon base, and the self-centering capability of the pylon may eliminate the aware of large residual displacement, which verified the possibility of applying limited ductility design of the pylon in the future.

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