The seepage of the fractured rock mass in dam foundations involves complex fluid-structure coupling behavior, due to practical hydrogeological conditions. In this work, the seepage characteristics of the fractured rock mass and their correlations with the structural permeable mediums are experimentally explored to reveal the cracking effect on the hydromechanical properties firstly. Subsequently, the tangential and the compression creep damage constitutive models are, respectively, established by introducing a nonlinear viscoplastic body to improve the Nishihara model. Afterwards, an innovative evolution equation of the permeability coefficient considering the creep damage is proposed. It can indicate the time effect of the porosity, the permeability, and damage variables of the fractured rock mass under the long-term infiltration action of the hydraulic pressures. Ultimately, the proposed methods are applied to the seepage simulation on the dam foundation of the Longyangxia hydropower station and the significantly increased leakage is in good agreement with the measured values during the storage period. It was further confirmed that the crack expansion and penetration in the rock masses can be constantly intensified by the seepage pressures. The research results can provide a reference for engineering repair and supervision through controlling the permeability performance for long-term operations.