Cracks are always a serious concern in the stability analysis of gravity dams. One of the main reasons for the initiation of cracks is overflow. In most previous crack propagation analyses, the presence of water and different configuration of the materials is not considered. In this study, to adequately evaluate the crack development in gravity dams subjected to overflow, a polygonal grain-based model (P-GBM), enriched in considering the influence of joint roughness through the Barton-Bandis (B-B) model, is employed in a distinct element framework. To take into account the effect of joint softening on the tensile strength of cracks, the B-B model is improved by a polynomial tensile law. Then, the model is verified by Brazilian and Uniaxial tests containing various combinations of rock and mortar. The numerical results demonstrated a good agreement by the experiments in terms of the strength characteristics and fracture phenomenon. Then, failure analysis for two heterogeneous gravity dams with various complexities under the reservoir overflow is investigated. Performing the risk analysis with different flood scenarios revealed that because of considering the joint-water interactions, the P-GBM suitably predicts the crack propagation. The crack path begins nearly horizontal and then turns downwards toward the dam's toe. Once cracks form, they act as conduits for water movement and allow more water to penetrate, which increases the pore water pressure and accelerates the propagation of cracks. Also, the critical dam displacements in terms of cracking (initiation, horizontal, and inclined parts) are investigated with different approaches, such as the tangent intersection method, the external second-order work, and the broken joint index. The results revealed that all three techniques determine suitably the critical heights and horizontal displacements in various flood scenarios. The polygonal grain-based technique simulates the rock and mortar combinations in good agreement with experimental tests.The improved Barton-Bandis joint model for softening can reasonably predict the tension behavior of materials.The impact of water on the dam structure and inside the cracks during an overflow is assessed for two case studies by a distinct element method.For a 6 m overtopping, the cracks develop inside the dam body horizontally parallel to the crest. For a 12 m overtopping, the cracks extend to the downstream direction of the dam, and the dam body is severely damaged.