# Study of Load Calculation Models for Anti-Sliding Short Piles Using Finite Difference Method
## 1 Introduction
These experiments and finite element analyses primarily concentrate on the stress characteristics, interactions between the piles and the soil, optimal pile spacing, and the determination of pile length for anti-sliding short piles. Nonetheless, the design and calculation theory for anti-sliding short piles remain insufficiently developed. Current calculation theories do not comprehensively capture the genuine stress characteristics of anti-sliding short piles. Furthermore, unified regulations or guidelines for their design calculations are lacking. Engineers frequently depend on their individual calculation methodologies and engineering expertise for analysis. To gain an accurate understanding of the stress characteristics and stress distribution patterns of anti-sliding short piles, it is imperative to establish a scientifically effective structural calculation method for these piles from a theoretical perspective. Extensive engineering practice has demonstrated the safety and reliability of the finite difference method for structural calculations [19; 20; 21; 22; 23; 24]. The finite difference method's principle entails approximating the differential equations of the elastic foundation beam using finite difference equations. This is achieved by substituting the function values at finite nodes in the difference equations for the derivatives of various orders in the original differential equations. This approach converts the differential solving process into algebraic solving, rendering it an approximate numerical solution method. Compared to differential equations, the finite difference method offers advantages in terms of its intuitive mathematical concepts, ease of expression, and its status as a relatively mature numerical solution method with a lengthy history of development. Nonetheless, existing research is typically focused on cantilever anti-sliding piles, and there is limited research on finite difference calculation methods for anti-sliding short piles. [PERSON] et al. [25] employed the m-k method to derive finite difference equations for the displacement and internal forces of deeply buried anti-slide piles, enabling the calculation of the entire pile's internal forces and displacements through a programmed approach. Their research confirmed the suitability of the finite difference method for calculating the internal forces of anti-sliding short piles. However, this study segregated the load-bearing section and the embedded section, resulting in a relatively intricate internal force calculation process using the continuity condition at the sliding surface. Additionally, the m-k method is primarily tailored for landslide control scenarios where the upper sliding surface consists of soil and the lower part is rock [26], a relatively specific circumstance. In practical engineering, the embedded section of anti-sliding piles often traverses multiple geological layers. Conventional \"m methods\" and \"K methods\" are designed for single-layer soil or rock foundations. Consequently, industry regulations recommend employing weighted averaging techniques to convert layered foundations into equivalent single-layer homogeneous foundations. For instance, the railway industry standard [27] employs the area-equivalent method for foundation coefficient calculation, while the highway industry standard [28] utilizes the flexural curve weighting method. Therefore, [PERSON] [29] utilized a weighted conversion based on the pile's deflection curve to compute the proportionate average coefficient of multi-layer foundations, providing precise results for internal forces in anti-slide piles. This paper builds upon previous research on anti-sliding short piles and finite difference methods for cantilever anti-sliding piles. It analyzes the landslide thrust acting on anti-sliding short piles and the distribution of soil resistance on the pile body [30]. The paper commences with a stress analysis of anti-sliding short piles for reinforcing cohesive soil landslides.