## 1 Introduction  
In mountains and valleys frequently prone to earthquakes, many bridge pile foundations are constructed on potential landslide slopes and need to be reinforced through the design of seismic support structures. As one of the common structural forms, anti-slide piles have been extensively used to reinforce the bridge foundations on slopes. Thus far, fruitful research had been conducted on the dynamic response of slopes reinforced with front and back rows of anti-slide piles. [PERSON] et al. [1] performed a shaking table test to study a cut slope of the Yuxi-Mengzi railway which was reinforced by double-row anti-slide piles. It was revealed that the existence of anti-slide piles reduced acceleration response. The earth pressure of the lower-row pile increased higher than the upper one, which increased with the earthquake magnitude. [PERSON] et al. [2] pointed out that the soil acceleration would change suddenly when the slope was cracked or near to failure in a model test, suggesting that the strength and stiffness of the upper part of the anti-slide piles in the back row should be strengthened. [PERSON] [3] and [PERSON] [4], respectively, analyzed the design method of a strengthening slope with the front and back rows of anti-slide piles, and the numerical simulation and elastic foundation beam model analysis provided a beneficial reference for seismic reinforcement design. [PERSON] and [PERSON] [5] carried out theoretical and experimental studies on the characteristics of force and deformation of slope bridge foundation. The results showed that the P-\(\Delta\) effect should be considered in the calculation of bridge pile deflection, otherwise the calculated displacement of the bridge foundation is smaller. [PERSON] et al. [6] established the static differential equations of bridge pile foundation considering the effect of slope, and determined the calculation formulas of force and deformation of the pile foundation according to the finite difference method. [PERSON] et al. [7] designed bearing tests of bridge pile foundation on three different slopes, and analyzed the distribution law of the internal force of the pile foundation as well as the soil pressure distribution under horizontal and vertical loads. On this basis, [PERSON] et al. [8] carried out a shaking table test of a bridge foundation reinforced by the rear anti-slide piles in a small distance. The pattern of the dynamic interaction between the bridge foundation and the rear anti-slide piles was analyzed, the spectral response characteristics subjected to seismic waves was summarized, and the variation pattern of the peak ground acceleration (PGA) amplification factor and the landslide thrust of a silty clay slope was obtained. In high-intensity earthquake areas where the rock strata exhibit a fractured occurrence, there are numerous engineering cases of using the front and back rows of anti-slide piles to reinforce a bridge foundation on a gravel soil slope, yet the related experimental research lags behind engineering practice. For the seismic condition of bridge pier located on a gravel soil slope, the pile foundation is subjected to a non-negligible horizontal thrust. Therefore, the resulting horizontal deformation of the pile shaft should be controlled to ensure the serviceability of bridges. In current engineering practice, the front and back rows of anti-slide piles are mostly designed on the basis of the existing experience or a simple theoretical calculation. The rationality of the design remains open to question and hence calls for experimental verification. The Chengdu-Lanzhou Railway crosses the eastern side of the Qinghai-Tibet Plateau. The seismic fault zone along the railway has a complex structure [9], and earthquakes are prone to occur frequently in this region, as shown in Figure 1. Through preliminary investigations, the pier pile foundation of the site of Jiuzhaigou Bridge was reinforced by front-back row anti-slide piles.