Conventional geotechnical software limits the use of the strength reduction method (SRM) based on the Mohr–Coulomb failure criterion to analyze the slope safety factor (SF). The use of this constitutive model is impractical for predicting the behavior of all soil types. In the present study, an innovative numerical technique based on SRM was developed to determine SF using the finite element method and considering the extended Cam–clay constitutive model for clayey gravel soil as opposed to the Mohr–Coulomb model. In this regard, a novel user subroutine code was employed in ABAQUS to reduce the stabilizing forces to determine the failure surfaces and resist and drive shear stresses on a slope. After validating the proposed technique, it was employed to investigate the performance of terraced slopes in the context of a case study. The impacts of geometric parameters and different water table elevations on the SF were examined. The results indicated that an increase in the upper and lower slope heights led to a decrease in SF, and a slight increase in the horizontal offset led to an increase in the SF. Moreover, when the water table elevation was lower than the toe of the terraced slope, the SF increased because of the increase in the uplift force as a resistant component.