## 2 Analytical Model  
In Figure 2, the slip surface is the interface during the sliding process of the sliding body. The front anti-sliding pile represents the pile in the double row that is relatively close to the landslide front. The rear anti-sliding pile represents the pile in the double row of piles relative to the rear edge of the landslide. The potential slip surface refers to the new sliding surface generated when the overtop failure occurs after setting the buried pile. Line OA is the initial horizontal sliding surface, and line segments OB and BD are the potential sliding surface over the top. The angle between OB and the horizontal line is called the initial rupture angle. The extended line segment OB intersects at point Q at the front pile, and the angle formed by the line BD and BQ is called the secondary fracture angle. Line segment AB represents the load-bearing section length of the rear pile, and line segment CD represents the load-bearing section length of the front pile.  
In previous literature [9], a simplified calculation method for load section length of single-row submerged anti-slide piles was derived. On this basis, this paper proposes a simplified calculation model for strengthening the slope with double rows of buried piles, as shown in Figure 2. When overtopping failure occurs, a new potentially dangerous sliding surface is generated in the local sliding body above the sliding surface, which is generally shorter than the original potential sliding surface. If only a single row of buried piles is installed, the topsoil of the piles will slide along the OB fracture surface, and, when the sliding body is thicker, a larger landslide thrust will be generated, and the possibility of overtopping failure is greater. If double rows of buried piles are set and the load sections at the front and back are equal in length, the soil at the top of the pile will still follow the OB sliding surface of the fracture plane when the top failure occurs, and the anti-sliding effect is the same as that of single rows of buried piles, which cannot strengthen the anti-sliding effect. If double rows of buried piles are set and the load section length of the front row is slightly higher than that of the back row, a kick point (point B) will be generated on the fracture surface, forming an OB-BD fracture surface. Compared with the top failure mode of single rows of buried piles, the double rows of buried piles have stronger anti-sliding ability. Therefore, the analysis model of this paper is the double-row buried pile with load section in front slightly longer than that in back.  
When the top failure occurs, only part of the sliding force of the back sliding body OAB is applied to the pile body because the back pile body AB prevents the deformation from the top of the pile to the sliding surface. The soil POBF at the top of the pile slides forward along the fracture plane OB, and the fracture angle is the angle between OB and the horizontal plane. In this case, since the deformation of the soil mass at the top of the back pile is not constrained, the soil pressure at the top of the pile is transmitted along the fracture plane OB to the soil mass at the top of the front pile and the soil mass between the rows. Moreover, the soil pressure at this part of the soil mass continues to be transmitted along the fracture plane BD, at which time a new angle of rupture \(\angle\)DBQ will be generated, and the overtop failure will eventually occur.