Improvement of the generalized method of slices incorporating multiple force interactions

In response to the limitations of the traditional generalized method of slices when dealing with complex external loads and reinforcement measures, as well as the requirement for complex programming in its solution, a systematic improvement of the generalized method of slices was undertaken. Firstly, an extended mechanical model for the generalized method of slices was constructed. This model can simultaneously consider eight types of forces, including gravity, pore water pressure, bidirectional seismic forces, bidirectional distributed loads, slope surface concentrated forces, and slip surface anchoring forces. A unified framework for various calculation formulas was established, ensuring the convergence of the algorithm. Secondly, based on the Lagrange’s mean value theorem, an approximate solution method for the generalized method of slices was proposed, reducing the application difficulty of the algorithm. Finally, the validity of the aforementioned work was demonstrated through the ACADS examples and a classic example. The results indicate that the established model exhibits good applicability, which is not limited by the type of slip surface, soil layer conditions, or loading conditions. The proposed approximate method demonstrates satisfactory computational accuracy, convergence speed, and reasonableness of initial iteration values. These characteristics are largely unaffected by the number of slices and the choice of inter-slice force function. To achieve satisfactory accuracy and enhance computational efficiency, it is recommended to control the number of slices to be greater than or equal to 32, and to prioritize the assumption of an inter-slice force function where the tangent of the inclination angle is constant. This research enhances the capability of the generalized method of slices to simulate complex working conditions and provides a solution that balances both accuracy and efficiency for its engineering applications.