This study investigated the fracture characteristics of plain concrete and polypropylene fiber-reinforced concrete (PFRC) using pre-notched three-point bending beam tests with the digital speckle correlation method (DSCM). Then, the fracture instability behavior of the two types of beams was simulated in finite elements based on the plastic damage model and the cohesion model, for which the applicability was assessed. Furthermore, the stability of the Big Gang Mountain Dam made from plain concrete or PFRC subjected to the earth-quake loading was simulated with the plastic damage model. The results show that the limiting length of the non-local deformation zone can be used as an indicator of instability damage in a concrete structure. The simulation results of the plastic damage model agreed well with the local deformation in the pre-notched three-point bending beam test obtained from the DSCM. The plastic damage model was found to be capable of describing the residual strength phenomenon, which the cohesive model was not capable of. The damage evolution regions of the PFRC dam are strictly constrained in some regions without the occurrence of the local deformation band across the dam, and PFRC can dramatically reduce the failure risk under earthquake loading. The numerical solution proves that PFRC is an advisable material for avoiding failure in concrete dams.