The field-enriched finite element method uses a scalar field defined as a field variable to describe cracks and characterize their impact on the displacement field and stress field of the solution model. It is capable of avoiding remeshing and employing level set functions to describe cracks when simulating the propagation of cracks. In this work, a field-enriched finite element model with gravity effects is proposed to simulate the large-scale failure process of engineering rock masses, and several numerical cases of geotechnical engineering are successfully analyzed. First, by introducing the unified tensile fracture criterion into the numerical model, the large-scale failure process of the intact slope is simulated. Second, the sliding process of rock slopes containing en echelon joints is numerically investigated. Third, the cracking process of the concrete dam is analyzed. Finally, the effects of joint and bedding plane inclination angles on the stability of tunnel chamber in transversely isotropic rock mass are studied. The numerical results indicate that the numerical method proposed in this work can accurately solve the large-scale failure process of rock masses.