To quantify the stability of slope under earthquake action

the vector sum method was optimized and its dynamic safety factor was calculated. Based on the failure mode of slope under earthquake action

which is the combination of the slope top crack and the slope foot shear crack

the safety factor formula of the vector sum method under pull-shear failure was derived

the slope safety factor and the potential sliding surface curve were obtained by self-programming

and the method was verified by a case study. For a rocky slope with weathered layer

dynamic stability analysis was carried out by using old and new vector sum methods. Results show that the potential sliding surface of the slope would move towards the interior of the slope with the duration of the earthquake. The safety factors obtained by the two methods were consistent

but the decline trend angle of the tension-shear failure mode was larger. In the tension-shear failure mode

the safety factor of the slope decreased

and the comprehensive safety factor of the slope was reduced by 3%

indicating that the original method overestimated the stability of the slope. The optimized vector sum method could reflect the stability of slope more realistically during earthquake and provide more accurate theoretical guidance for seismic design.