All over the world, concrete gravity dams have to withstand lots of environmental hazards and time-varying external loading during an earthquake. Therefore, the risk assessment of this structure with time may become an important study for the dam structure, which is related to the chemo-mechanical effect on the aging concrete. The focusing point of this study is to propose an earthquake assessment procedure to determine the failure probability with time of any concrete gravity dam for the future if we consider the material deterioration. This material decay is mainly associated with the modulus of elasticity of the concrete and it is explained briefly in the manuscript.