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The size effect of a quasi-brittle fracture is associated with the size of fracture process zone relative to the structural characteristic length. In numerical simulations using damage models, the nonlocal enhancement is commonly adopted to regularize the softening response. However, the conventional nonlocal enhancement, both integral and gradient approaches, induces a spurious spreading of damage zone. Since the evolution of fracture process zone cannot be captured well, the conventional nonlocal enhancement cannot predict the size effect phenomenon accurately. In this paper, the localizing gradient enhancement is adopted to avoid the spurious spreading of damage. Considering the three-point bend test of concrete beams, it is demonstrated that the dissipation profiles obtained with the localizing gradient enhancement compare well with those of reference meso-scale lattice models. With the correct damage evolution process, the localizing gradient enhancement is shown to capture the size effect phenomenon accurately for a series of geometrically similar concrete beams, using only a single set of material parameters.