Earthquake Reaearch in China  2017, Vol. 31 Issue (3): 403-413
Shaking Table Test Study on Dynamic Characteristics of Bridge Foundation Reinforcement on Slopes
Lei Da1,2, Qi Zhihui1,2, Jiang Guanlu1,2, Wang Zhimeng3, Li Anhong3     
1. School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China;
2. Key Laboratory of High-Speed Railway Engineering, Ministry of Education, Chengdu 610031, China;
3. China Railway Eryuan Engineering Group Co. Ltd., Chengdu 610031, China
Abstract: With the fast development of bridge construction in mountainous and seismic areas, it is necessary to conduct related research. Based on the design of a shaking table model test, here are the following test results:the filtering effect exists in soil and is affected by the dynamic constraint conditions, the amplitude is strengthened around the natural frequency and weakened in other frequency bands in the Fourier spectrum. Since the acceleration scaling effect occurred on a sloped surface, the acceleration response decreases from the outside to the inside in soil. The dynamic response is relatively strong near the slip surface in bedrock due to the reflection of seismic waves. The failure mode of landslide is decided by the slope angle and slipping mass distribution, and the test shows the front row stabilizing piles should keep a proper distance from bridge foundation so that seismic resistance can be guaranteed for the bridge foundation.
Key words: Shaking table test     Stabilizing pile     Filtering effect     Dynamic response Failure mode    


For the influence of topographic and geological conditions, many railway bridge foundations are constructed on slopes in seismic areas, and it is necessary to design retaining structures to have integral reinforcement (Song Xiaodong et al., 2004). At present, there is little research on the dynamic performance of bridge foundation consolidation with retaining structures, and the existing research mainly concerns dynamic characteristics of individual bridge foundations.

Kobayashi Hiroshi et al. (2002) conduced a hybrid vibration experiment on the seismic behavior of the bridge-soil system. Based on the results, the seismic response of bridge was quantitatively studied. An Tongxiang et al.(2006) researched an isolating foundation of the bridge pier by installing isolation materials between the footing and the pier foundation (An Tongxiang et al., 2006), the governing equations of motion were derived, and dynamic response analyses and model vibration tests on a single pier were carried out. In engineering practice, some reinforcement projects of bridge foundation lack a full dynamic study on slopes and the design is based on the semi empirical theory (Zhao Wen et al., 2004; Zhou Huoming et al., 2009), which probably leads the consolidation design to be conservative or risky in operation, as there have been some bridge foundation failures caused by improper design according to surveys on the Wenchuan earthquake (Zhuang Weilin et al., 2009; Wang Dongsheng et al., 2011). Thus, it is necessary to carry out relevant test research.

Due to the limitation of research funding and test practicability, it is almost impossible to conducta field test. However, the shaking table model test can simulate the failure process well and study the change laws of dynamic characteristics (Lin Meeiling et al., 2006; Hao J. et al., 2014). Supported by the Science and Technology Research Fund of the Railway Ministry, a shaking table model test of bridge foundation reinforcement with the front and back row stabilizing piles is designed; the failure developing process of the landslide model and the acceleration response are observed under seismic sine waves of different frequency and amplitude. According to the contour plot analysis of the PGA amplification factor, the dynamic characteristics of landslide failure are discussed.


A rigid model box was fixed on a unidirectional electro-hydraulic shaking table with an internal size of 3.7m × 1.5m × 2.1m (length × width × height). The reflection of seismic waves can be reduced at most by lining of foam and rubber materials on the inside walls (Liu Jingbo et al., 2008).

2.1 Design of Similarity Relations

According to the dimensional analysis theory (Ma Haichun et al., 2014), based on analyzing physical conditions, geometrical conditions, and dynamic balance conditions, the similarity criterions are listed as follows:

$ \frac{{{C}_{C}}}{{{C}_{l}}{{C}_{\gamma }}}=1\frac{{{C}_{a}}}{{{C}_{l}}C_{\omega }^{2}}\text{=1}\frac{{{C}_{\sigma }}}{{{C}_{\text{l}}}{{C}_{\gamma }}}\text{=1}\frac{{{C}_{g}}}{{{C}_{l}}C_{\omega }^{\text{2}}}\text{=1}{{C}_{\omega }}{{C}_{T}}\text{-1}\ {{C}_{s}}\text{=}{{C}_{l}}{{C}_{\varepsilon }}\text{=1}\ {{C}_{\varphi }}\text{=1}\ {{C}_{\mu }}\text{=1} $

As the physical size, weight and acceleration are the main controlling factors in similarity relationships, according to the Buckingham π theorem, the similar constants of physical quantities are derived in following Table 1.

Table 1 Similar constants of physical quantities
2.2 Model Filling and Sensors Layout

The prototype is a potential landslide in Jiuzhaigou bridge on the Chengdu-Lanzhou railway in Fig. 1. The sliding body is gravel soil and the weak weathered bedrock is relatively complete. The bridge foundation is consolidated with stabilizing piles and there are a few pre-stressed anchorage piles that are behind the main bridge pier, and the upper part of the back row of stabilizing piles is filled with compacted soil. According to the similarity theory, a simplified reduced-scale model of 1:70 is made in Fig. 2 and there are two rows of stabilizing piles near the main bridge pier. The pile spacings are all 8.6cm and the three-dimensional size of the stabilizing piles are 4.3cm × 2.9cm × 38.6cm in the front row and 5cm × 3.6cm × 65.7cm in the back row. The main bridge foundation consists of 15 circular piles which are in three parallel rows, there are three different bridge pile lengths, which are 57.1cm, 46.4cm, 39.3cm and the pile diameter is 2.9cm equally, while a rectangular gravity bridge pier is constructed with a height of 40cm on the pile cap. The retaining structure and bridge foundation are made of micro concrete while their reinforcement ratio is the same as the prototype.

Fig. 1 Longitudinal section of the prototype

Fig. 2 Reduced-scale model

The sliding body is simulated with gravel of density 2100kg/m3, friction of 38.6°, moisture content of 7.6% and grading curve shown in Fig. 3. The bedrock is a mixture of crushed red clay, river sand, cement, and is filled artificially. As the dynamic load of box girders affects the bridge foundation effectively in an earthquake (Sung Yuchi et al., 2015; Ling Xianzhang et al., 2006; Tang Liang et al., 2009), a tin box is fixed at the top of the bridge pier and a sliding track is welded in the central axis of the tin box so that the iron weight can slide freely on rails in Fig. 4. The two iron weights simulate box girders and keep a distance from each other according to the similarity relationship. In order to test the dynamic characteristics of the soil and bridge foundation, there are 11 measuring points of horizontal acceleration which are placed on the central axis in the following Figs. 5 and 6.

Fig. 3 Particle grading curve

Fig. 4 Box girder model

Fig. 5 Cross section of central axis

Fig. 6 Plane graph
2.3 Loading Scheme of Seismic Waves

In consideration of the frequency and strength in an earthquake, the 3Hz sine wave and 10Hz sine wave are adopted in experiment and the peak acceleration gradually increase by 0.1g, the seismic waveforms are shown in Fig. 7. With the aim of detecting the natural soil frequency, the white Gaussian noise is loaded before formal testing, and the particular loading scheme is shown in Table 2.

Fig. 7 Seismic waveforms

Table 2 Loading scheme of seismic waves

The slip mass is affected by continuous shear and a little soil slip along slope surface before the seismic conditions of a 0.4g 3Hz sine wave, the following noticeable tension cracks and collapse firstly appear on the steep slope which is behind the front row stabilizing piles in Fig. 8. As the earthquake energy increases, the model damage develops seriously. The sliding mass totally collapses between two rows of stabilizing piles when the 0.5g 10Hz sine wave is loading on the shaking table in Fig. 9. It is obvious that the overtopping failure appears on the front row stabilizing piles and the sliding body covers them. As the upper section of bridge foundation lacks soil support, the earthquake resistance of bridge foundation decreases. As the lower part of the landslide develops quickly, the upper part of landslide is displaced along the sliding surface, there is a great amount of sliding mass that accumulates behind the back row stabilizing piles in loading the 0.6g 10Hz sine wave in Fig. 10, and the back row stabilizing piles can resist landslide thrust effectively. According to the above, the failure mode is different in the lower and upper parts of the landslide due to the difference of slope angle and sliding mass distribution.

Fig. 8 Partial collapse

Fig. 9 Collapse at lower part of slope

Fig. 10 Landslide failure

There are five representative accelerometers which are analyzed by FFT (fast Fourier transform) in Fig. 11. The natural frequency of sliding body is 17.1Hz according to the FFT analysis of No.2 and 4 accelerometers, they are embedded around the slope surface in the slipping area and have stronger dynamic response compared with other measuring points. Although the No.9 accelerometer is located on the slope surface, the Fourier spectrum amplitude is small as it is in the anti-slide zone. The No.4 accelerometer is buried higher than No.3 in soil, so its spectral amplitude is larger since the acceleration amplification effect appears on the slope surface. It is obvious that the natural vibration response increase with height and filtering effect work in soil in the earthquake. As the No.5 accelerometer is between bridge foundation and the back row stabilizing piles, the dynamic response is restricted and there is no clear phenomenon of resonant response. Since the accidental errors occur between the target acceleration and actual output, signal power is higher in the frequency range of (0-3.7) Hz.

Fig. 11 FFT analysis of white Gaussian noise
4.2 PGA Amplification Factor Analysis

As shown in Fig. 12, the PGA amplification factor decreases from the outside to the inside in the landslide since the acceleration amplification effect appears on the slope. A complex seismic wave field is formed due to the reflection of seismic waves on the interface of bedrock and soil, while the PGA amplification factor increases nearby in bedrock. The PGA amplification factor is relatively larger behind the back row stabilizing piles, and for the wedge soil in the lower part of landslide. On the other hand, the PGA amplification factor is small in the bridges pile cap and the soil which is between the bridge foundation and the back row stabilizing piles. This phenomenon show that the back row stabilizing piles can effectively resist the landslide thrust so that the peak acceleration of bridge foundation is not enlarged. Since the PGA amplification factor is great in front of the bridge foundation, it means the soil resistance of bridge foundation decreases certainly. In the work conditions of 0.1g-0.3g sine waves, the response acceleration maximum arises in the lower part of the sliding region. With the displacement of sliding mass increasing, the dynamic response gradually strengthens in the upper part of the landslide, with the maximum close to the slope top in loading 0.4g 3Hz-0.6g 3Hz sine waves.As the earthquake intensity increases, the failure phenomenon is gradually obvious. As a large amount of sliding body accumulates behind the back row stabilizing piles in loading the 0.6g 10Hz sine wave, the soil is compacted well, the dynamic response weakens accordingly and the PGA amplification factor changes to be smaller. As the soil failure develops on the slope surface in front of the bridge foundation and there are no clear displacement constraints, the soil dynamic response is always strong and it leads to a larger PGA amplification factor, the front row stabilizing piles cannot reinforce soil effectively.

Fig. 12 Contour plot ofthe PGA amplification factor

(1) There is a filtering effect in soil, the amplitude is strengthened around natural frequency and weakened on other frequency bands in the Fourier spectrum. The more the dynamic constraint conditions appear in soil, the weaker the filtering effect is in an earthquake.

(2) The failure process shows that the overtopping failure happens on the front row stabilizing piles and there is a lot of sliding mass that accumulates behind the back row stabilizing piles. The failure mode is different in the lower and upper parts of the landslide due to the difference of slope angle and sliding mass distribution.

(3) Due to the reflection of seismic waves, the complex seismic wave field is formed near the slip surface in bedrock and leads to stronger dynamic response. As the scaling effect of peak acceleration occurs on a slope, the PGA amplification factor decreases from the outside to the inside in a landslide.

(4) With the development of landslide failure, the maximum PGA amplification factor moves to the slope top in the slipping zone. The test shows that the front row stabilizing piles should keep a proper distance from the bridge foundation so that seismic resistance can be guaranteed for the bridge foundation.

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