Although the limit equilibrium method for rigid bodies and the nonlinear finite element method are commonly used to analyze the deep anti-sliding stability of gravity dams

the limit equilibrium method does not capture the feature of progressive failure of gravity dam

and the nonlinear finite element method cannot effectively simulate the behavior of discontinuous rock masses. In addition

a unified failure criterion has yet to be developed for the finite element analysis. Using the calculated boundary stresses based on the discrete block method

a formulation is derived for calculating the factor of safety with regard to the deep anti-sliding stability of gravity dams with multiple sliding planes

and the physical meaning of the dam foundation failure criterion based on the energy mutation of the dam-foundation system is clarified. By comparing the calculated results of the finite element method and the limit equilibrium method

the proposed method and criterion are validated. A case study is performed on the 12th section of Xiangjiaba Gravity Dam

and the results indicate that the instability zone of dam foundation is composed of a yield zone of rock mass foundation and a sliding zone of structural planes. This implies that the proposed method and criterion is capable of addressing the deep anti-sliding stability of gravity dams

and yielding a reasonable factor of safety for dam design.