Development of a p-multiplier for laterally loaded single batter piles in sand based on simple upper bound analysis

Batter piles are prevalently found in foundation pits, bridges, transmission towers, and wharf structures, serving to withstand lateral loads. Nevertheless, the investigation and analysis methods related to batter piles remain scarce. Considering the limitations of existing p-multipliers for batter piles, this research develops an enhanced p-multiplier rooted in the soil failure mechanisms and upper bound analysis. The proposed p-multiplier is initially derived from simplified 2D soil failure modes, and then further enhanced based on extended 3D soil failure modes, which effectively reflect the 3D effects of soil-pile interaction. Comparative analyses demonstrate that the proposed p-multiplier well captures the influence of pile inclination and soil internal friction angle on soil resistance, showing superiority over previous studies. Moreover, incorporating the proposed p-multiplier with $p-y$ curves allows rapid and fair assessment on the lateral behavior of single batter piles in sand, and the reliability is validated by two reported cases of batter piles. However, due to the ignorance of shaft friction and lateral component of axial displacement of batter pile, the proposed method is recommended for small batter angles. In the range of $-{15}^{°}{15}^{°}$, the proposed method is adequate as verified by the experimental results.