2. School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China;
3. Key Laboratory of High Speed Railway Engineering, Ministry of Education, PRC, Chengdu 610031, China
As a common geotechnical retaining structure, anti-slide piles are widely used in the retaining engineering of pile foundations on steep slopes (Yang Zhifa et al., 2003; Yang Kaiye, 2016). In particular, after the 2008 Wenchuan earthquake happened, the seismic strengthening of bridges became increasingly prominent in mountainous regions, and similar engineering forms appear in large numbers. According to investigations of both domestic and foreign literature, the seismic study on strengthening bridge foundation with support projects is very rare. The researchers' focus on the seismic damage analysis of bridges in the liquefaction site and the seismic response of bridge pile foundations.
Yuan Zehua used a typical working site of the Chengdu-Lanzhou railway as an example (Yuan Zehua, 2016), and analyzed the failure process of bridge piles on the accumulative landslide by static model tests and numerical simulation. Shirato et al. (2006) innovated the ductile seismic design of abutment piles on liquefied sites (Shirato M. et al., 2006). On the basis of investigating the existing abutment failure modes, several typical forms of abutment failure were extracted, and the load combinations were reconstructed. This method was incorporated into the 2002 Japanese Design Code of Highway Bridges. Falamarz-Sheikhabadi M.R. conducted a numerical simulation analysis of a pier pile group of the Mogollon Ring Bridge (Falamarz-Sheikhabadi M.R. et al., 2016), demonstrating the impact of structural and geotechnical contact on the earthquake damage of the pier foundation. Moreover, the pier burial and the flexibility of pile foundation can significantly affect the general seismic response of the piers. Du Xiuli et al. (2008) summarized the destruction rules and characteristics of mountainous bridges by surveying in the Wenchuan earthquake area (Du Xiuli et al., 2008), and preliminarily discussed the causes and prevention measures of earthquake damage. Some reasonable suggestions were provided for seismic strengthening of bridges in mountainous areas.
This paper takes the working site of the Jiuzhaigou Bridge of the Chengdu-Lanzhou Railway as a prototype and builds a 3-D dynamic analysis model based on the shaking table model test (Lei Da et al., 2017). The rationality of the 3-D model was verified by comparing the bending moment of the bridge piles, the peak soil pressure, and the PGA amplification factor. Meanwhile, the variation rules of bridge piles' bending moment, shearing force and horizontal displacement were analyzed, and the seismic strengthening characteristics of the front and rear row anti-slide piles were discussed.
1 BRIEF INTRODUCTION OF PHYSICAL MODELS AND 3-D MODELING 1.1 Shaking Table Model Test OverviewTaking the landslide near the Jiuzhaigou Bridge of the Chengdu-Lanzhou railway under construction as an example, it was appropriately simplified and the physical model was made according to a 1:70 reduced-scale. The sliding body was a mixture of coarse sand and small gravel, simulating the gravel soil. The bedrock weathered weakly, and was simulated by modified red clay which was included of a certain proportion of cement and river sand. This material could ensure the necessary strength and rigidity by compacting. The pier foundation and anti-slide piles were made of micro concrete according to reinforcement ratio and stirrup ratio, and then they were buried in a reserved position. The three dimensions of anti-slide piles were 4.3cm×2.9cm×38.6cm at the front row and 5cm×3.6cm×65.7cm at the rear row, the bridge pile foundation was arranged in three rows, there were three sizes of the bridge pile length that were 57.1cm, 46.4cm, and 39.3cm, the pile diameter was 2.9cm, and there was a rectangular gravity bridge pier located beyond the piles cap with a height of 40cm. The model panorama is shown in Fig. 1, and the measuring points are shown in Fig. 2 and Fig. 3.
Prototype dimensions were used to carry out the modeling work. Concrete units such as piers, cushion cap, and span load were elastic constitutive models. Soils and bedrocks were modeled by using the Mohr-Coulomb constitutive models (Itasca F., 1997; Manual I.F., 2006). The contact surface grids which were assigned parameters were used to model the sliding surface. The physical and mechanical parameters of solid element materials are shown in Table 1, and the parameter indexes of contact surface grids are shown in Table 2. In order to facilitate the deformation analysis of anti-slide piles and bridge pile foundation, the pile elements were used in the simulation (Jiang Xin et al., 2012; Wu Runze et al., 2013), and the parameter values are shown in Table 3, with the 3-D simulation model as shown in Fig. 4.
In order to facilitate analysis, the sine wave with simple waveform and a certain amplitude were applied. The frequency of sine waves was firmed at 3Hz and the peak acceleration increased in a stepwise process. The acceleration-time curve of seismic waves is shown in Fig. 5. In order to simulate the effect of infinite ground, a series of dampers were set around the 3-D simulation model to perform free field coupling (Lin Yuliang et al., 2016; Isam S. et al., 2012), and the Rayleigh damping was selected to conduct dynamic calculation (Mánica M. et al., 2014), which can closely reproduce the dissipation of seismic wave energy in the soil.
The 0.1g 3Hz sine wave working condition is analyzed as an example; the results of the 3-D simulation and shaking table model test are compared. Other operating conditions are similar and will not be described again.
2.1.1 Bending Moment in Lateral Bridge PilesAs shown in Fig. 6, the 3-D simulation results are consistent with the shaking table model test; they have similar distribution rules of bending moments.As the dynamic performance is affected by the dynamic load of the bridge pier and the bedrock's anchorage effect, larger bending moments occur at the pile top and the interface of bedrock and soil, and the largest bending moment is near the pile top. With the increase of burial depth, the soil resistance of the bridge foundation is strengthened; the negative moment of pile tops gradually become positive bending moments, the maximum positive bending moment is formed closed to the sliding surface, and the following bending moment decreases in bedrock.
Fig. 7 shows that the 3-D simulation results are basically consistent with the shaking table model test. The peak soil pressure can be approximated as a rectangular distribution. Due to the moderate distance between bridge foundation and the rear-row anti-slide piles, the dynamic interaction is weak between them. Meanwhile, the soil acceleration response is restrained in this area. For the gravel soil layer, the horizontal soil pressure changes small in depth.
Fig. 8 shows that the acceleration response is stronger in the slide section and weaker between the bridge pier and rear-row anti-slide piles. It indicates that the anti-slide piles can effectively bear landslide thrust in rear row, and the impact of dynamic soil pressure is weakened on bridge pile deformation. Due to the limited size of the shaking table model, there is no accelerometer placed on the slope surface between the bridge pier and rear-row anti-slide piles, it leads to smaller PGA amplification factor in the corresponding area. Besides that, there are two accelerometers which are arranged at the middle position between the front-row anti-slide piles and bridge pier, few measuring points result in widespread larger PGA amplification factor on steep slope in the anti-slide section. The 3-D simulation shows that the dynamic response is relatively strong in front of the bridge pier. In the later stage of the shaking table model test, a large amount of soil collapsed in front of the bridge pier, and the bridge pile foundation was exposed. The PGA amplification factor result of 3-D simulation model is consistent with the experimental phenomenon, and the front-row anti-slide piles should be closed to the bridge foundation so that the necessary seismic resistance is guaranteed, and the front-row anti-slide piles play an auxiliary supporting role. Since there are only two measuring points in the bedrock in the shaking table model, the data sample is too small, which results in a certain change trend of the PGA amplification factor in the bedrock. The data sample of the 3-D simulation model increase significantly, and the analysis shows that the PGA amplification factor is maintained at a low level inside the bedrock, which could be explained as phenomena of the rigid body.
The soil surface is very steep and less dynamically constrained in front of the bridge pier. Meanwhile, the soil is effectively constrained between the bridge foundation and rear-row anti-slide piles. Due to the different dynamic characteristics of the soil around the bridge pier, the seismic response is mainly investigated in two sides of bridge foundation. The piles are analyzed at central axis, the acceleration peak values of the loaded sine waves are 0.03g, 0.05g, 0.08g and 0.1g respectively, so that the force deformation laws of bridge piles are analyzed with the increase of seismic intensity.
2.2.1 Bending MomentFig. 9 shows that the pile's bending moment increases with the increase of peak acceleration. Due to the influence of the inertial forces of the upper structures such as the bridge pier and span load, there are large negative bending moments at the pile tops of the bridge foundation, and the largest one appears at lateral bridge piles. As the steep slope is free in motion in front of the bridge pier, the soil dynamic response is stronger in this area and there is not sufficient resistance to the bridge pile's force deformation, the maximum positive bending moment appears at the sliding surface in the front side of bridge piles, then it decreases with the buried depth within bedrock. For the lateral bridge piles, the soil is dynamically constrained between bridge foundation and rear-row anti-slide piles, the seismic resistance is provided for the force deformation of bridge piles, it leads the maximum positive moment of the bridge piles which appear beyond the sliding surface and decrease along the burial depth. Compared with the distribution law of bending moment in the two sides of bridge piles, the negative moment value is greater along the pile length; it shows that the inertial force of the superstructure has a great influence on the deformation of the bridge pile foundation. The bending moment of the pile top can be used as the design index on the force deformation of bridge foundation. For the front bridge piles, the maximum positive moment is in the middle of the soil in loading 0.03g 3Hz sine wave, moreover, it appears at sliding surface in other loading conditions. For the rear bridge piles, the maximum positive moment appears at the second point above sliding surface in loading 0.03g 3Hz sine wave and 0.05g 3Hz sine wave, meanwhile, it appears at the first point above sliding surface in loading 0.08g 3Hz sine wave and 0.1g 3Hz sine wave. This phenomenon is summarized as the lack of soil resistance in increasing seismic intensity, and the maximum positive moment of bridge piles moves down in height. Compared with the decay rate of negative bending moment in pile tops of bridge foundation, the line slope of negative moment is relatively large and the decay rate is slower in the front of bridge piles, because the soil resistance is weak around. However, the negative moment of pile top decreases quickly in lateral bridge piles, for the reason that there is larger seismic resistance in soil. All these phenomena are consistent with the shaking table model test results.
Fig. 10 shows that the shearing force of bridge piles increases with the increase of peak acceleration. For the influence of the inertial force of bridge superstructure, there is a certain positive shearing force at the pile top, and it is larger in lateral bridge piles. Since the soil is relatively free in dynamic characteristics in front of the bridge pier, the seismic resistance is small and it results in the positive shearing force appearing above sliding surface. As the anchoring force operates in bedrock, there is a peak shearing force below sliding surface and it decreases along the pile depth. The confinement effect is stronger behind bridge pier, the positive shearing force decreases along pile depth and changes to negative value gradually, the negative shearing force develops with the anchoring force in bedrock. Compared with the peak shearing forces in two sides of bridge foundation, the largest appears on the pile top in lateral bridge foundation.
Fig. 11 shows the horizontal displacement of bridge piles increase in continuous loading of sine waves. The horizontal displacement increase quickly on sliding surface and it can be approximated to zero in bedrock.
(1) The dynamic load of the bridge pier and upper structure has important influence on the force deformation of bridge piles. Lowering the height of bridge pier and reducing the weight of the upper structure is beneficial to the mechanical state of bridge piles.
(2) The bending moment and shearing force are larger in lateral bridge piles, and the maximum values are concentrated near the pile tops. It is suggested that the lateral bridge piles need to be seriously analyzed in seismic design and the mechanical forces of pile tops should be controlled in lateral bridge piles.
(3) The stronger the PGA amplification factor of the soil is in slide section and in front of bridge pier, the higher the possibility of displacement and collapsing happening. The PGA amplification factor maintains at a low level in bedrock and is approximately a rigid body.
(4) When the anti-slide piles are designed to reinforce the bridge foundation in landslides, the rear-row anti-slide piles play a major role in anti-seismic engineering, the front-row anti-slide piles play an auxiliary role to increase the soil resistance of bridge piles.
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2. 西南交大土木工程学院，成都 610031;
3. 中华人民共和国教育部高铁工程实验室，成都 610031