Rapid calculation method for the safety factors of three-dimensional homogeneous slopes

• Slope stability analysis is crucial in geotechnical engineering, and rapid safety factor (FOS) calculation matters for engineering safety and geological disaster prevention. This study proposes a rapid FOS calculation method for 3D homogeneous slopes. First, it simplifies the model, builds a 3D slope numerical model, and systematically explores how soil parameters (cohesion, internal friction angle, unit weight) and geometric parameters (slope height, angle, top width, toe extension length) affect FOS. Then, it derives a 3D slope critical failure state curve (CFSC) from the data and further obtains an explicit FOS expression. This expression enables rapid FOS calculation using the above basic parameters and also has parameter inversion function to solve unknown parameters when FOS and other parameters are known. Finally, typical engineering cases verify that its results match software-calculated FOS, confirming the method’s engineering applicability and computational reliability. Slope stability analysis is a key research area in geotechnical engineering and holds significant theoretical value and practical importance for engineering safety and geological hazard prevention via the rapid calculation of safety factors. In this study, a rapid calculation method for the safety factor of three-dimensional homogeneous slopes is proposed. First, the model is simplified, and a three-dimensional numerical slope model is constructed. A systematic investigation is conducted on the influence of soil parameters and geometric parameters (cohesion, internal friction angle, soil density, slope height, slope angle, crest width, and toe length) on the slope safety factor. On the basis of the obtained data, a three-dimensional critical failure state curve for slopes is derived. An explicit expression for the three-dimensional slope safety factor is subsequently derived from this critical failure curve. This expression enables rapid calculation of the safety factor through basic slope parameters. Notably, the methodology employed in this study also incorporates parameter inversion capabilities, enabling the determination of unknown parameters under known safety factors and other specified conditions. The obtained results were found to be consistent with the safety factors calculated by the software via systematic validation using three typical engineering case studies, confirming the engineering applicability and computational reliability of the method proposed in this paper.