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.