# Study of Load Calculation Models for Anti-Sliding Short Piles Using Finite Difference Method
## 1 Introduction  
Currently, landslides have emerged as among the most prevalent and severe geological disasters globally [1]. In landslide management practices worldwide, the utilization of anti-sliding piles for reinforcement has become the favored option. Anti-sliding piles, serving as slope support structures, find extensive application in landslide control due to their flexible placement and robust anti-sliding capabilities. In engineering practice, the majority of employed anti-sliding piles are cantilevered ones, relying primarily on the anchoring force exerted at the pile base, embedded in stable strata, to counteract the landslide thrust. Nonetheless, traditional cantilevered anti-sliding piles fail to fully realize their slope protection potential, leading to material wastage and elevated costs. Recently, in certain extensive and intricate landslide control projects, buried anti-sliding short piles [2; 3], also referred to as embedded anti-sliding piles, have been employed to reduce pile length and economize on construction expenses. Anti-sliding short piles present several advantages, such as shorter pile lengths, a more logical distribution of internal forces within the pile body, reduced cross-sectional dimensions, and diminished reinforcement needs. These factors, combined with their capacity to mitigate environmental and ecological impacts, especially when slope reduction and load reduction strategies leadto substantial disturbances, render the use of anti-sliding short piles exceedingly promising in the context of sustainable geological disaster control project development. Numerous scholars have performed qualitative analyses of the stress mechanisms and characteristics of short anti-sliding piles through model experiments. [PERSON] [4] conducted indoor model tests on fully buried anti-sliding piles, analyzing the internal forces, deformations, and displacement curves of these piles. They determined the distribution patterns of internal forces within anti-sliding short piles under the influence of landslide thrust and identified their failure modes. [PERSON] [5] explored the question of an appropriate pile length for anti-sliding piles through model tests and numerical analyses. The focus was on efficiently increasing pile length to ensure they effectively contribute to slope stabilization without extending beyond the slope's crest. [PERSON] [6] carried out model tests on anti-sliding short piles and delineated three stages in the loading process: the zero displacement stage, effective deformation stage, and failure stage. They defined the boundaries of these stages as the critical starting load and critical anti-sliding load. With the rapid advancement of computer technology, numerical analysis has gained widespread use in geotechnical engineering analysis and calculations due to its cost-effectiveness and swift results [7; 8; 9; 10; 11; 12]. The study of anti-sliding short piles follows suit. [PERSON], [PERSON] [13] used the distribution of horizontal thrust behind anti-sliding short piles, and the magnitude of the resistance force in front of these piles was examined using ANSYS finite element software ([[https://www.ansys.com/](https://www.ansys.com/)]([https://www.ansys.com/](https://www.ansys.com/)), accessed on 8 November 2023). [PERSON] and [PERSON] [14; 15; 16; 17] investigated the mechanisms, conditions, and optimal pile spacing related to the soil arching effect created by anti-sliding piles through computer numerical simulation. [PERSON] [18], utilizing FLAC3D software ([[https://www.itasca.fr/en/software/flac3d](https://www.itasca.fr/en/software/flac3d)]([https://www.itasca.fr/en/software/flac3d](https://www.itasca.fr/en/software/flac3d)), accessed on 8 November 2023), performed numerical simulations of anti-sliding short piles. The analysis included an examination of the impact of parameters such as pile length, pile diameter, pile wall thickness, and soil properties on the stress performance of the piles.