Failure evaluation and prediction of a structure are important procedures when inspecting aged dams. This study establishes a failure criterion model on the basis of an efficient method for the risk assessment of an aged dam. The proposed methodology incorporates discontinuous deformation analysis (DDA) with a numerical manifold method (NMM) to process predictable simulation. According to large-scale analyses, the programs of DDA+NMM follow the energy-conservation principle to simulate the interaction of deformable blocks and disconnected joints within a discontinuous system, which consists of many blocks shaped in an arbitrary polygon. However, for small-scale estimation, disjoined layers are assumed along seepage flow lines which are potentially yielded by saturated groundwater levels because of overbalance precipitation. The computation recruits open-source programs to efficiently evaluate an aged earth dam by modeling the groundwater seepage flow lines as possible block joints and creating reasonable risk criteria. An aged dam built in Taiwan more than 70 years ago, serves as the case study. The necessary parameters regarding the geotechnical and geometrical properties are adopted from an official report of dam safety assessment. Four types of potential failure modes attributable to dam topology and critical joint distribution are categorized by several combinations of critical risk factors coupled with extreme loading conditions. Both static and dynamic simulations of various levels of water pressure, uplift force, possible joints, and material coefficients are applied. Furthermore, a risk-assessment criterion table, with three-level risk indexes, provides a reference for failure alerts for the proposed dam structure. As the result, the assessment procedure can help in predicting potential failure modes as well as in determining risk-assessment criteria for proper hazard-prevention strategies for aged dam structures in the future.