Research on the bearing mechanism and structural design method of embedded foundations for transmission towers under slope conditions

Introduction Embedded foundations, prized for their high bearing capacity and compact footprint, are a prevalent and innovative solution for transmission tower support. Nevertheless, their bearing mechanism remains insufficiently understood, particularly under complex terrains like slopes, where dedicated design methods are lacking. Methods A comprehensive numerical simulation study was conducted to analyze the mechanical response of embedded foundations under uplift loads. The investigation encompassed various scenarios defined by slope gradient, foundation geometry, and size. The study examined the displacement response of foundations and surrounding rock masses under incremental loading, investigated the interaction mechanism on slopes, and traced the progressive evolution of fracture surfaces. By analyzing maximum shear strain nephograms under ultimate load, the spatial distribution characteristics of the fracture surface in the rock mass were determined, leading to the establishment of a predictive model for fracture surface geometry around foundations on slopes. Results The findings reveal that plastic zones initially form at the foundation-rock interface upon surpassing the foundation's self-weight load. With increasing load, these zones propagate deeper, expanding and interconnecting. The fracture surface trajectory demonstrates a clear relationship with slope gradient: its angle on the downhill side increases, while on the uphill side it decreases, with the change approximately equal to the slope gradient. Near the slope face, fracture surfaces assume a near-circular shape, whose diameter is proportional to foundation size but remains largely invariant with changes in slope gradient or other parameters. Based on limit equilibrium analysis, a set of calculation formulas for ultimate uplift resistance under slope conditions was derived and validated. Discussion The proposed formula successfully reduces to the established flat-ground condition when the slope gradient is zero and has been implemented in practical engineering. This study provides a theoretical foundation and a practical analytical tool for designing embedded foundations in complex slope environments.