Abstract: This study introduces a novel linear programming model to address slope stability issues by converting the safety factor calculation into a linear programming problem to determine the horizontal seismic force influence coefficient. In addition to constraints such as normal stress convexity and the Mohr-Coulomb criterion, the model integrates thrust line position constraints into the linear programming framework. This approach further narrows the upper and lower bounds of the limit equilibrium solution and improves computational accuracy. Reasonable assumptions for inter-slice force distribution are established, effectively constraining the range of thrust action points. This enables rapid determination of thrust line positions and informs slope reinforcement measures. Numerical examples show that the obtained upper and lower bounds of the safety factor are relatively narrow. Although the safety factors are close to those from the improved Morgenstern–Price method, the thrust line positions derived here are more reasonable. This method prevents local failure, eliminates stress discontinuities, and ensures the thrust line positions remain within a reasonable range.

Key words: slope, thrust line position, rigorous limit equilibrium, factor of safety, upper and lower bound solutions