Estimating the collapse limit state of concrete gravity dams within the framework of performance based design is challenging due to the uncertainty in modelling the response of these systems and the strong dependence of the behavior on the ground motion. The purpose of the study is to investigate the seismic expected damage levels by using the overlapping lattice modeling (OLM) approach with incremental dynamic analysis (IDA) for two representative dam monoliths. OLM employs pin connected bar elements extending over a predefined horizon to discretize the continuum similar to the concept used in peridynamics. The constitutive model of concrete was calibrated by using tension tests prior to the dam simulations. The most important advantage of the OLM approach was the ability of the simulations to capture the discrete crack propagation in a much better. Nonlinear finite element analyses by using a smeared rotating crack model for concrete were also conducted to compare the estimations of OLM. The results of IDA showed that initial cracking occurred at the dam base followed by the inclined cracking of the dam body resulting in significant damage. A strong dependence of the damage patterns on the ground motion was noted. OLM estimations of crack lengths tended to be longer and more discrete as opposed to the more diffused and shorter cracks obtained with the nonlinear finite element simulations. Results demonstrate the promising nature OLM to capture dynamic crack propagation in concrete media.