From the viewpoint of probability theory

combined with the deterministic vector sum method

the stability evaluation methods are studied for the bank sections of gravity dam under random seismic loads. Firstly

deterministic stability evaluation is made through the history curve of safety factors

which is obtained by dynamic vector sum method

under a certain seismic load. Secondly

the probability density function(PDF) of the minimum value of dynamic stability safety factors and the dynamic reliability are got through the Gram-Charlier series fitting method and the weighted maximum entropy method under random seismic loads. Thirdly

comprehensive evaluation is made by both deterministic results and probabilistic ones during the whole design period. The example results show that the deterministic and probabilistic methods can complement each other to make a comprehensive seismic stability evaluation for the bank sections of the gravity dam during the whole design period.