A Simplified Method for Calculating the Lateral Bearing Capacity of Rectangular Piles in Sloping Ground

Evaluating the lateral bearing behavior of rectangular piles in sloping ground is computationally demanding due to the complex three-dimensional spatial pile-soil interaction. To circumvent the inefficiency of full-scale numerical modeling and the limitations of conventional p-y methods, this study proposes a simplified analytical framework for rapid preliminary design. By systematically isolating the topographical slope effect and the cross-sectional shape effect, a series of mathematical modification factors, namely the ultimate lateral capacity factor KH, the maximum bending moment factor KM, and the maximum reverse shear force factor KQ, were established utilizing a standard level-ground square pile as the computational baseline. The results indicate that increasing the slope angle from 0° to 30° reduces the lateral capacity by approximately 14–20%, whereas increasing the aspect ratio from 1 to 4 effectively compensates for this reduction, improving the capacity by approximately 75%. However, the correspondingly enhanced flexural stiffness simultaneously triggers a substantial non-linear amplification in both the maximum bending moment and the deep reverse shear force. Benchmark comparisons show a maximum deviation of 4.58% for lateral capacity, while the maximum deviations in bending moment and reverse shear force are 10.43% and 9.78%, respectively. By integrating these modification factors with conventional equivalent calculation methods, this study provides an efficient analytical tool for rectangular pile foundation design in sloping ground.